# REACTION DYNAMICS INVOLVING IONS, RADICALS, NEUTRAL AND EXCITED SPECIES

EDITED BY : Stefano Falcinelli, Antonio Aguilar, Paolo Tosi and Marzio Rosi PUBLISHED IN : Frontiers in Chemistry

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ISSN 1664-8714 ISBN 978-2-88963-430-9 DOI 10.3389/978-2-88963-430-9

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# REACTION DYNAMICS INVOLVING IONS, RADICALS, NEUTRAL AND EXCITED SPECIES

Topic Editors: Stefano Falcinelli, University of Perugia, Italy Antonio Aguilar, University of Barcelona, Spain Paolo Tosi, University of Trento, Italy Marzio Rosi, University of Perugia, Italy

Citation: Falcinelli, S., Aguilar, A., Tosi, P., Rosi, M., eds. (2020). Reaction Dynamics Involving Ions, Radicals, Neutral and Excited Species. Lausanne: Frontiers Media SA. doi: 10.3389/978-2-88963-430-9

# Table of Contents

*06 Editorial: Reaction Dynamics Involving Ions, Radicals, Neutral and Excited Species*

Stefano Falcinelli, Antonio Aguilar, Paolo Tosi and Marzio Rosi

*10 Theoretical Investigation on H2O2-Ng (He, Ne, Ar, Kr, Xe, and Rn) Complexes Suitable for Stereodynamics: Interactions and Thermal Chiral Rate Consequences*

Yuri Alves de Oliveira Só, Pedro Henrique de Oliveira Neto, Luiz Guilherme Machado de Macedo and Ricardo Gargano


Juan Ramón Avilés–Moreno, Giel Berden, Jos Oomens and Bruno Martínez–Haya


Astrid Bergeat, Sébastien B. Morales, Christian Naulin, Jacek Kłos and François Lique


Eva Canaval, Noora Hyttinen, Benjamin Schmidbauer, Lukas Fischer and Armin Hansel

*121 Global Isomeric Survey of Elusive Cyclopropanetrione: Unknown but Viable Isomers*

Jing-fan Xin, Xiao-ru Han, Fei-fei He and Yi-hong Ding


Dario De Fazio, Alfredo Aguado and Carlo Petrongolo

*157 Ion-Pair Formation in Neutral Potassium-Neutral Pyrimidine Collisions: Electron Transfer Experiments*

Mónica Mendes, Beatriz Pamplona, Sarvesh Kumar, Filipe Ferreira da Silva, Antonio Aguilar, Gustavo García, Marie-Christine Bacchus-Montabonel and Paulo Limao-Vieira

*167 Photoelectron-Photofragment Coincidence Spectroscopy With Ions Prepared in a Cryogenic Octopole Accumulation Trap: Collisional Excitation and Buffer Gas Cooling*

Ben B. Shen, Katharine G. Lunny, Yanice Benitez and Robert E. Continetti

*177 Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures*

Dario De Fazio, Vincenzo Aquilanti and Simonetta Cavalli

*187 Radiation Damage Mechanisms of Chemotherapeutically Active Nitroimidazole Derived Compounds* Jacopo Chiarinelli, Anna Rita Casavola, Mattea Carmen Castrovilli,

Paola Bolognesi, Antonella Cartoni, Feng Wang, R. Richter, Daniele Catone, Sanja Tosic, Bratislav P. Marinkovic and Lorenzo Avaldi


Silvia Grande, Francesco Tampieri, Anton Nikiforov, Agata Giardina, Antonio Barbon, Pieter Cools, Rino Morent, Cristina Paradisi, Ester Marotta and Nathalie De Geyter

*226 Molecular Beam Scattering Experiments as a Sensitive Probe of the Interaction in Bromine–Noble Gas Complexes*

David Cappelletti, Antonio Cinti, Andrea Nicoziani, Stefano Falcinelli and Fernando Pirani


Andrea Lombardi, Fernando Pirani, Massimiliano Bartolomei, Cecilia Coletti and Antonio Laganà

*264 Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity*

Valter H. Carvalho-Silva, Nayara D. Coutinho and Vincenzo Aquilanti


Jelle Vekeman, Noelia Faginas-Lago, Andrea Lombardi, Alfredo Sánchez de Merás, Inmaculada García Cuesta and Marzio Rosi

*296 Compendium of the Reactions of H3O+ With Selected Ketones of Relevance to Breath Analysis Using Proton Transfer Reaction Mass Spectrometry*

Michaela Malásková, David Olivenza-León, Felix Piel, Paweł Mochalski, Philipp Sulzer, Simone Jürschik, Chris A. Mayhew and Tilmann D. Märk


Stefano Falcinelli, Marzio Rosi, Fernando Pirani, Davide Bassi, Michele Alagia, Luca Schio, Robert Richter, Stefano Stranges, Nadia Balucani, Vincent Lorent and Franco Vecchiocattivi

# Editorial: Reaction Dynamics Involving Ions, Radicals, Neutral and Excited Species

Stefano Falcinelli <sup>1</sup> \*, Antonio Aguilar <sup>2</sup> , Paolo Tosi <sup>3</sup> and Marzio Rosi <sup>1</sup>

<sup>1</sup> Department of Civil and Environmental Engineering, University of Perugia, Perugia, Italy, <sup>2</sup> Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Barcelona, Spain, <sup>3</sup> Department of Physics, University of Trento, Trento, Italy

Keywords: ions, radicals, metastable atoms, plasma chemistry, synchrotron radiation, astrochemistry

#### **Editorial on the Research Topic**

#### **Reaction Dynamics Involving Ions, Radicals, Neutral and Excited Species**

The aim of this Research Topic is to provide relevant contributions relating to the study of the reactivity of ionic and excited species with atoms, molecules, and radicals of interest in atomic and molecular physics as well as in chemical reaction dynamics. It is well-known that single and multiple ionized species (H+, He+, H<sup>+</sup> 3 , HCO+, H3O+, He2<sup>+</sup> 2 , CO2<sup>+</sup> 2 , etc.), excited atoms and molecules [e.g., O(1D), N(2D), H<sup>∗</sup> (2s<sup>2</sup> S1/2), He<sup>∗</sup> (21,3S0,1), N<sup>∗</sup> 2 (A36<sup>+</sup> u ), etc.], and radicals (OH, SH, NH, NH2, CH2, CH3, etc.) play an important role in many chemical systems such as flames, natural plasmas (planetary ionospheres, comet tails, interstellar clouds), and biological environments (e.g., biological tissues damaged when high-energy radiation interacts with a living cell). Such processes have long attracted the attention of the scientific community, as shown by the large number of papers and review articles on this topic, and some specific features make them very interesting from a fundamental point of view in Physical Chemistry and Chemical Physics. However, many applications to important fields like radiation chemistry, plasma physics and chemistry, combustion processes, and the development of laser sources are also possible. In particular, the chemistry of ionic species (both singly and doubly charged ions) is of particular relevance to the conversion of CO<sup>2</sup> by non-thermal plasma technology. This topic has gained increasing interest in the last few years due to a number of potential advantages, such as working at room temperature with no switch-on inertia or the possibility of obtaining value-added products, like gaseous or liquid fuels, from carbon dioxide with the addition of a hydrogen source (e.g., H2O, H2, CH4, and other hydrocarbons). Such characteristics make this a promising candidate as a technology for the storage of energy from renewable and intermittent sources into chemical energy (see, for instance, Falcinelli et al., 2017; Falcinelli, 2019; Heijkers et al., 2019; and references therein).

This high-quality article collection serves as an opportunity to pay tribute to Davide Bassi, James M. Farrar, and Franco Vecchiocattivi for their relevant contributions over the last 40 years in the fields of atomic and molecular collisions and of reaction dynamics involving ions, radicals, neutral, and excited species. Their biographical notes follow the general description of the articles in this Research Topic.

The articles provide a fairly broad picture of the research conducted nowadays on this scientific topic, both from an experimental and a theoretical point of view. Among the published articles, 20 report experimental data that is then discussed and interpreted with the help of appropriate theoretical models, while nine are purely theoretical studies.

Edited and reviewed by: Bretislav Friedrich, Fritz-Haber-Institut, Germany

> \*Correspondence: Stefano Falcinelli stefano.falcinelli@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 25 October 2019 Accepted: 26 November 2019 Published: 17 December 2019

#### Citation:

Falcinelli S, Aguilar A, Tosi P and Rosi M (2019) Editorial: Reaction Dynamics Involving Ions, Radicals, Neutral and Excited Species. Front. Chem. 7:859. doi: 10.3389/fchem.2019.00859

**6**

From the experimental point of view, it has to be noted that the molecular beam technique applied to the study of chemical reaction dynamics, coupled with mass spectrometry and spectroscopic techniques (Deckers and Fenn, 1963; Herschbach, 1966; Lee et al., 1969; Scoles et al., 1988; Zare, 2012), constitutes the fundamental scientific background linking all the works presented here.

Almost all of the experimental studies have been carried out using the molecular beam technique. In particular, the two review articles in the collection give an overview of two important applications of this technique: Falcinelli et al. present recent results on the stereo-dynamics of Penning ionization, and Ascenzi et al. report on the possibility of aligning or orienting molecules by collisions in gaseous streams. Furthermore, molecular beams are employed in three different investigations: (i) by Cappelletti et al. in scattering experiments, as a sensitive probe of the intermolecular potentials; (ii) by Rosi et al. in a combined experimental and theoretical work, where the flash pyrolysis of 1-butanol, a bioalcohol belonging to a promising family of biofuels, together with RRKM calculations allowed the characterization of its thermal decomposition; (iii) by Bergeat et al., who in their cross-sectional measurements of C+D<sup>2</sup> inelastic collisions were able to achieve new insights into the dynamics of collision-induced spin-orbit excitation/relaxation of atomic carbon.

In the study of the characterization and reactive behavior of ionic species, a pair of interesting papers point out the important role of the charge transfer (see Pei and Farrar) and proton transfer (see Canaval et al.) in ion-molecule reactions involving simple cations, as O++CH<sup>4</sup> and NH<sup>+</sup> 4 reacting with various organic molecules [acetone, methyl vinyl ketone, methyl ethyl ketone, and eight monoterpene isomers (C10H16)], respectively. Moreover, three articles report on the production, characterization, and reactivity of anions (see Shen et al.; Mendes et al.; Avilés-Moreno et al.).

The largest number of experimental works (seven papers) concern the use of synchrotron radiation in studies of the microscopic dynamics of processes involving cationic (Ascenzi et al.; Hrodmarsson et al.; Catone et al.) and dicationic species (Falcinelli et al.). A group of interesting papers concerns the spectroscopic characterization of important molecules: Ferrari et al. focused their work on femtosecond transient absorption spectroscopy of Cobalt tris(acetylacetonate) [Co(AcAc)3] in solution; Bolognesi et al. were able to perform core-shell investigation of 2-nitroimidazole. Finally, using synchrotron radiation, Chiarinelli et al. combined photoionization mass spectrometry, the photoelectron-photoion coincidence spectroscopic technique, and computational methods to investigate the fragmentation of metronidazole and misonidazole. In this way, these authors were able to clarify the radiation damage mechanisms of chemotherapeutically active nitroimidazole-derived compounds.

Among the experimental works in this Research Topic, we highlight the paper by Malásková et al., who have compiled a compendium of the reactions of H3O<sup>+</sup> with selected ketones of relevance to breath analysis using the PTR-MS technique (Proton Transfer Reaction Mass Spectrometry). This analytical technique, which is particularly powerful for real-time measurements, is able to provide a valuable database of use to other researchers in the field of breath analysis to aid in the analysis and quantification of trace amounts of ketones in human breath.

Moreover, one paper in the collection is related to the formation of radical and ionic species by plasma-treated organic solvents (see Grande et al.). Another article reports on the characterization of the fluorophores of acridone family compounds by spectrofluorimetric measurements (see Gonzalez-Garcia et al.).

From a theoretical point of view, this Research Topic collects together nine high-quality articles on reaction dynamics. González-Sánchez et al. present a detailed theoretical and computational analysis of the quantum inelastic dynamics involving the lower rotational levels of the MgH<sup>−</sup> (X16+) molecular anion in collision with He atoms. De Fazio et al. report on the non-adiabatic, conical-intersection quantum dynamics of the He<sup>+</sup> + H<sup>2</sup> → He + H + H<sup>+</sup> reaction, whereas the quantum dynamics and kinetics of the F + H<sup>2</sup> and F + D<sup>2</sup> reactions at low and ultra-low temperatures have been investigated by De Fazio et al.. Furthermore, the chiral rate as a function of temperature between enantiomeric conformations of H2O<sup>2</sup> and Ng (Ng = He, Ne, Ar, Kr, Xe, and Rn) has been studied by de Oliveira Sò et al. at the MP2(full)/aug-cc-pVTZ level of theory through a fully basis set superposition error (BSSE)-corrected potential energy surface.

Molecular dynamics calculations have been performed by Vekeman et al. in investigating graphene layers and proposing them as membranes of subnanometer size suitable for CH4/N<sup>2</sup> separation and gas uptake. Moreover, a procedure adopting an analytic formulation of the potential energy surface (PES), accounting for the dependence of the electrostatic and nonelectrostatic components of the intermolecular interaction on the deformation of the monomers, has been used by Lombardi et al. in the generation of a full dimensional PES for the CO + N<sup>2</sup> system. Furthermore, Xin et al. constructed the first global PES of singlet cyclopropanetrione (C3O3) at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level, from which the kinetic stability of a wide range of C3O<sup>3</sup> isomers can be determined by investigating their isomerization and fragmentation pathways.

A deep understanding of the dependence of reaction rates on temperature has been provided by Carvalho-Silva et al., with particular attention to the derivation of the temperature dependence of viscosity. On the other hand, Pietanza et al. investigated the role of the process of dissociative electron attachment from vibrationally excited CO molecules in affecting the whole kinetics of reacting CO under conditions where appreciable concentrations of vibrationally excited states are present.

At the end of this editorial, before the biographical notes of our three colleagues and friends to whom this Research Topic Issue is dedicated, we would like to point out the way we worked together and with all the scientists and colleagues who were glad to share this editorial initiative with us. It is the same attitude, the same lifestyle and behavior that binds Davide, Jim, and Franco: Research and Science carried out within the context of strong human relationships in which ethical, respectful, and friendly behavior is much more important than competition. This is something very special, belonging to Plato's hyperuranion, the realm of ideas that human beings should try to emulate: a beautiful and healthy challenge in our lives.

## DAVIDE BASSI

Davide Bassi (DB) was born in Genoa (Italy) on September 30, 1948. In 1971, he graduated with honors in Physics from the University of Genoa, defending a thesis (under the supervision of Fernando Tommasini and Giacinto Scoles) in which the first evidence of orbiting collisions between atoms was shown. In 1975, he joined the University of Trento, where he established a new Molecular Beam Laboratory. In 1987, he was named full professor of Experimental Physics.

The research activity of DB includes the following topics:

(a) elementary interactions of hydrogen in the gas phase; (b) spectroscopy of atoms, molecules, and clusters; (c) reaction dynamics of ion/neutral systems; (d) ion and neutral beams.

Part of this work has been carried out in cooperation with external laboratories [Department of Chemistry, University of Waterloo (CND), Institut für Ionenphysik, Leopold Franzens Universität, Innsbruck (A), Laboratoire de Physique des Lasers, Universitè Paris Nord, Villetaneuse (F), LURE, Centre Universitaire Paris-Sud, Orsay (F), Dipartimento di Chimica, Università di Perugia (I), Elettra, Gas Phase Beam Line, Trieste (I), Departament de Química Física, and Universitat de Barcelona (E)].

DB has been involved in many research projects supported by the European Commission. In particular, he has been the coordinator of the MCInet European network on the "Generation, stability, and reaction dynamics of Multiply-Charged Ions" (2000–2004). In 2006, he received the SASP Award—in the form of the Erwin Schrödinger Gold Medal—for his contributions to ion-neutral collision studies.

As a spin-off of his "blue sky" research activity, DB developed many industrial applications in the fields of high-vacuum and gas detection technologies. He has been a consultant to private enterprises and participated in the development of longterm joint initiatives between the University of Trento and industrial companies.

From 2004 to 2013, he served as rector of the University of Trento. DB retired from the University of Trento in 2013, at the age of 65, but is still active in the academic arena. Presently, he is a member of the Board of Directors of the Università della Svizzera Italiana (USI) in Lugano (CH) and president of the Ethics Committee of the Italian Institute of Technology (IIT).

## JAMES MARTIN FARRAR

James Martin Farrar was born in Pittsburgh (Pennsylvania, USA) on June 15, 1948. He received his B.A. degree in Chemistry from Washington University in St. Louis in 1970. His first research experience in chemical kinetics was in the laboratory of Professor Joseph Kurz, a classical physical organic chemist. Although Jim was only an undergraduate, Kurz treated him like a colleague, and he found the question "how do chemical reactions actually occur?" to be fascinating. Jim entered the graduate program at the University of Chicago in the Fall of 1970 as a National Science Foundation Graduate Fellow and joined the newly established molecular beam research group of Professor Yuan-Tseh Lee. The group's research was devoted to understanding "where the energy goes in a chemical reaction." It was during this time in Chicago that Jim met Franco Vecchiocattivi and began to appreciate the importance of ionic interactions and the chemical reactions of ions. The nature of energy redistribution in chemically activated species was also central to the research in Chicago, overlapping with the important work of Davide Bassi on intramolecular vibrational relaxation in optically excited molecules. Following the completion of his degree in June of 1974, Jim spent 2 years in the group of Professor Bruce Mahan learning about the spectroscopy and dynamics of gas-phase ions, topics also of central importance to the research interests of Bassi and Vecchiocattivi. Jim joined the faculty at Rochester in July of 1976, setting up a research laboratory dedicated to applying mass spectrometry and molecular beam methods to the study of gasphase ion chemistry. He was named an Alfred P. Sloan Fellow in 1981 and was promoted to Associate Professor in 1982. Following his promotion to Professor in 1986, he began a program of research to study the photochemistry of mass-selected solvated metal ions. That work provided evidence of the existence of Rydberg states that serve as precursors for ion-pair production and solvated electron formation. Jim was named a Fellow of the American Physical Society in 1987 and was a Visiting Fellow at JILA at the University of Colorado in 1988. In the early 1990s, Jim and Franco and their colleagues from the University of Perugia initiated a collaboration on collisional ionization that has led to many scientific and personnel exchanges between Rochester and Perugia. Jim served as Chair of the Chemistry Department at Rochester from 1997 to 2000. His most recent research work has applied velocity map imaging methods to the study of ionradical reactions. The group's research was supported by the U.S. Department of Energy and the National Science Foundation from 1978 to 2017.

## FRANCO VECCHIOCATTIVI

Franco Vecchiocattivi (FV) was born in Rome (Italy) on July 27, 1945. In 1968, he graduated in Chemistry from the University "La Sapienza" (Rome, Italy), defending a thesis on "Ion-molecule reactions of ethylenimine in the gaseous phase." After his graduation, he moved to the University of Perugia (Italy), where he joined the first group in Italy that, under the guidance of G. G. Volpi, dealt with the experimental study of the dynamics of chemical reactions with the use of the molecular beam technique.

With the exception of some periods of scientific activity at foreign universities, FV carried out his main teaching and scientific activities at the University of Perugia, where he mainly taught basic courses in general Chemistry for freshmen and more specialized courses for advanced students. At the end of 2015, FV retired from his teaching appointment (full Professor of Chemistry) at the University of Perugia.

In 1973, FV spent half a year at the University of Chicago (USA) in the laboratory of Y. T. Lee, exploiting crossed molecular beam experiments for the study of reactive cross-sections. During that period at the University of Chicago, he collaborated with J. M. Farrar, who was a graduate student at that time.

Upon returning to Perugia from the United States, he started, in collaboration with F. Pirani, a systematic study of the interactions between atoms and simple molecules, integrating high-resolution scattering cross-section measurements with gaseous property data (multiproperty analysis) and producing results of interest for gaseous chemistry.

In 1979 and again in 1981, FV visited the laboratory of V. Kempter at the University of Freiburg (Germany), working on experiments on chemi-ionization reactions at hyperthermal energies.

Returning to Perugia from his visits to Germany, in collaboration with B. G. Brunetti, he designed and built an apparatus to measure total and partial cross-sections of collisional autoionization processes with metastable noble gas atoms in the thermal collision energy range.

#### REFERENCES


In 1990, FV started a fruitful collaboration with J. M. Farrar of the University of Rochester (NY, USA), which continues today. Among his many other scientific collaborations have been those with J. Baudon (University Paris-Nord, France), T. Kasai (University of Osaka, Japan), and A. Aguilar-Navarro (University of Barcelona, Spain).

In recent years, in collaboration with S. Falcinelli, FV started to conduct research at the Gasphase beamline of the ELETTRA Synchrotron of Trieste (Italy), dealing mainly with double photoionization processes of molecules at the threshold.

## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, participated in writing the manuscript, and approved it for publication.

#### ACKNOWLEDGMENTS

This work was dedicated to our colleagues and friends Davide Bassi, James M. Farrar, and Franco Vecchiocattivi. We thank all the authors who participated in this collection of articles, giving honor to them for their relevant contributions to the Research Topic of ion chemistry.

bombardment detector. Rev. Sci. Instr. 40:1402. doi: 10.1063/1.16 83809


**Conflict of Interest:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Falcinelli, Aguilar, Tosi and Rosi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Theoretical Investigation on H2O2-Ng (He, Ne, Ar, Kr, Xe, and Rn) Complexes Suitable for Stereodynamics: Interactions and Thermal Chiral Rate Consequences

Yuri Alves de Oliveira Só<sup>1</sup> , Pedro Henrique de Oliveira Neto<sup>1</sup> , Luiz Guilherme Machado de Macedo<sup>2</sup> and Ricardo Gargano<sup>1</sup> \*

1 Institute of Physics, University of Brasília, Brasília, Brazil, <sup>2</sup> Institute of Biological Sciences, Faculty of Biotechnology, Federal University of Pará, Belém, Brazil

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Vincenzo Aquilanti, University of Perugia, Italy Luca Evangelisti, University of Bologna, Italy

> \*Correspondence: Ricardo Gargano gargano@unb.br

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 08 November 2018 Accepted: 24 December 2018 Published: 18 January 2019

#### Citation:

Só YAdO, Neto PHdO, de Macedo LGM and Gargano R (2019) Theoretical Investigation on H2O2-Ng (He, Ne, Ar, Kr, Xe, and Rn) Complexes Suitable for Stereodynamics: Interactions and Thermal Chiral Rate Consequences. Front. Chem. 6:671. doi: 10.3389/fchem.2018.00671 Although molecular collisions of noble gases (Ng) can be theoretically used to distinguish between the enantiomers of hydrogen peroxide - H2O<sup>2</sup> (HP), little is known about the effects of HP-Ng interactions on the chiral rate. In this work, the chiral rate as a function of temperature (CRT) between enantiomeric conformations of HP and Ng (Ng=He, Ne, Ar, Kr, Xe, and Rn) are presented at MP2(full)/aug-cc-pVTZ level of theory through a fully basis set superposition error (BSSE) corrected potential energy surface. The results show that: (a) the CRT is highly affected even at a small decrease in the height of trans-barrier; (b) its smallest values occur with Ne for all temperatures between 100 and 4,000 K; (c) that the decrease of CRT shows an inverse correlation with respect to the average valence electron energy of the Ng and (d) Ne and He may be the noble gases more suitable for study the oriented collision dynamics of HP. In addition to binding energies, the electron density ρ and its Laplacian ∇ <sup>2</sup>ρ topological analyses were also performed within the atoms in molecules (AIM) theory in order to determine the nature of the HP-Ng interactions. The results of this work provide a more complete foundation on experiments to study HP's chirality using Ng in crossed molecular beams without a light source.

Keywords: hydrogen peroxide, noble gases, stereodynamics, chirality, thermal chiral rate, enantiomers, TST method, AIM theory

## 1. INTRODUCTION

Hydrogen peroxide - H2O<sup>2</sup> (HP) is a molecule of interest in a large and diverse number of fields in addition to its industrial uses. For example, it has emerged as a major metabolite in redox signaling and regulation (Antunes and Brito, 2017; Sies, 2017), and its presence was observed in Martian atmosphere (Encrenaz et al., 2004) and also on the surface of Jupiter's moon Europa (Carlson et al., 1999). The HP is interesting since it is simplest molecule that exhibits internal (torsional) rotation and chirality. Furthermore, this molecule can form dimers (Dobado and Molina, 1993; González et al., 1997), clusters (Yu and Yang, 2011), complexes with water (Mo et al., 1994; González et al., 1997) and with biologically important molecules such as adenine (Dobado and Molina, 1999), DNA (Piatnytskyi et al., 2016), glycine (Shi and Zhou, 2004) or nitrosamines (Roohi et al., 2010). These features indicate that HP should be a better proton donor for hydrogen bonding than water. Thus, the understanding of how the relative orientation of the O-H can lead to a weakly complex or a chemical reaction has also been paid considerable attention due to its implication in atmospheric chemistry and oxidation reactions (Lundell et al., 1998, 2001; Daza et al., 2000; Goebel et al., 2000, 2001a,b, 2002; Molina et al., 2002; Pehkonen et al., 2004; Mucha and Mielke, 2009; Grzechnik et al., 2013). Moreover, HP's properties have been investigated, such as its isolated chirality (Roncaratti and Aquilanti, 2010), stereomutation (Fehrensen et al., 2007; Bitencourt et al., 2008), size-dimensional wave packets (Wang et al., 2012), spectroscopy (Hunt et al., 1965; Małyszek and Koput, 2013; Al-Refaie et al., 2015) and rotation barriers (Song et al., 2005).

On the other hand, the hydrogen peroxide seems to be a prototypical model to be used into experiments to observe chirality in crossed molecular beam without a light source (Palazzetti et al., 2013), a frontier in research of stereodynamics which is still at early stages (Su et al., 2013; Lombardi and Palazzetti, 2018). In these kind of experiments, the molecular orientation control on the intense continuous beam is mandatory to the phenomena of chiral selectivity to be demonstrated (Aquilanti et al., 2005). For this reason, the interaction between HP and atoms, molecules and ions is so relevant to sterodynamics studies (Barreto et al., 2007, 2010; Lombardi et al., 2011; Roncaratti et al., 2014; Leal et al., 2016).

In the present paper we investigated the dynamics of the chiral molecule HP interacting by van der Waals forces with noble gases Ng (Ng=He, Ne, Ar, Kr, Xe and Rn) in order to obtain the chiral rate as a function of temperature (CRT) for these complexes, as well as its consequences for the chiral kinetic interconversion when tunneling effect is included. The aim of this work was to understand how the kinetic interconversion of the two HP's isomers is affected along collisional events through a basis set superposition error (Boys and Bernardi, 1970) (BSSE) corrected potential energy surface (PES). In addition, the electron density ρ(r) and its Laplacian ∇ <sup>2</sup>ρ(r) topological analyses were also performed within the atoms in molecules (AIM) theory in order to determine the nature of the intermolecular interactions.

## 2. METHODOLOGY

#### 2.1. Computational Details

All calculations were performed using the Gaussian09 package (Frisch et al., 2009). The structures were optimized without constraints at MP2(full) method in conjunction with aug-ccpVTZ-PP for Xe and Rn (Peterson et al., 2003) and aug-ccpVTZ for the remaining atoms (Dunning, 1989; Woon and Dunning Jr, 1993; Wilson et al., 1999). Vibrational frequencies at the same level of theory were also performed in order to ensure that each minimum has only positive frequencies and that each transition state has only a single imaginary frequency, as well as to obtain the zero point vibrational energy (ZPE). The counterpoise method of Boys and Bernardi (1970) was used to correct the BSSE for binding energy.

AIM analysis (Matta and Boyd, 2007) and graphic representations were performed with the AIMALL program (Keith, 2017) using the MP2(full) density (wavefunction) as input as described in the AIM theory (Dobado et al., 1998; Cortés-Guzmán and Bader, 2005).

#### 2.2. Overview of the Transition State Theory

The transition state theory (TST)(Truhlar et al., 1996) was developed primarily by Henry Eyring (Eyring, 1935) and Michael Polanyi (Polanyi and Wigner, 1928) between 1928 and 1935. The TST is an improvement over the so-called theory of collisions (Lewis, 1967), and it is widely used to calculate the rate constants of chemical reactions.

The start point of TST is the existence of a transition state (TS) between the reagents and products. Located at the top of the potential energy barrier and it assumes a quasi-equilibrium between reactants and activated transition state complexes. For a bimolecular reaction given by

$$R\_1 + R\_2 \leftrightharpoons \text{TS} \to P\_1 + P\_2.\tag{1}$$

The TS is characterized by a single imaginary frequency along the reaction coordinate of the molecular system which is represented here by ν¯1. In its turn, the reaction coordinate can be represented by angular changes in bond distances during the chemical reaction (Henkelman et al., 2002).

The equation that determines the reaction rate is known as the Eyring equation, given by

$$k\_{\rm rate}(T) = \kappa(T)\frac{k\_B T}{h}\frac{\overline{q}\_{m,\rm TS}^{\circ}}{q\_{m,\rm R\_1}^{\circ}q\_{m,\rm R\_2}^{\circ}}N\_A e^{-E\_b^0/RT},\tag{2}$$

where 0 < κ(T) ≤ 1 is the so-called transmission coefficient, k<sup>B</sup> is the Boltzmann constant, h is the Planck constant, q ◦ <sup>m</sup> is the standard molar partition function, N<sup>A</sup> is the Avogadro constant, R is the gas constant and E 0 b is the barrier energy with zero-point energy correction. In addition, the TS, R<sup>1</sup> and R<sup>2</sup> subscripts stand for the transition state and reagents, respectively. Thus, the rate constant is determined by the parameters that characterize both reagents and the TS.

The general partition function is formed by the product of translational q trans., rotational q rot., vibrational q vib. and electronic q ele. partition functions. The translational partition function for a free particle with mass m moving along the length dimension l<sup>x</sup> can be evaluated by considering that the separation of energy levels is small and that a large number of states are accessible at room temperatures. Therefore, the energy levels should be continuous and the sum contribution of the translational partition function becomes an integral. Which the solution for the three-dimensional case is (Atkins et al., 2013)

$$q^{\text{trans.}} = \frac{(2\pi mk\_B T)^{3/2}}{h^3} l\_{\text{x}} l\_{\text{y}} l\_{\text{z}} \tag{3}$$

Although the system can be excited at normal modes, the energy levels are discrete for the rotational mode. The three degrees of freedom of spatial rotation and the three moments of inertia IA, I<sup>B</sup> and I<sup>C</sup> must be taken into account for a non-linear molecule (Atkins et al., 2013), thus

$$q^{\rm rot.} = \frac{(\pi)^{1/2}}{\sigma} \left(\frac{8\pi^2 I\_A I\_B I\_C k\_B T}{h^2}\right)^{3/2},\tag{4}$$

where σ is the so-called number of symmetry. The vibrational mode has reasonably spaced energy which must be taken into account since they are partially occupied. As a consequence, the vibrational partition function is strictly calculated as a sum over the occupied states. In the case of n vibrational degrees of freedom, the vibrational partition function is given by the product of n partition functions,

$$q^{\rm vib.} = \prod\_{i}^{n} \frac{1}{1 - e^{-h\upsilon\_{i}/k\_{B}T}},\tag{5}$$

where ν<sup>i</sup> is each of the fundamental vibrational frequencies. In most cases, only the lowest energy state is occupied and the electronic energies should not contribute considerably to the total partition function (Atkins et al., 2013). A good approximation is to disregard the contributions of the nuclear and electronic spins and to vanish the fundamental energy level for the electronic partition function. Under these considerations the electronic partition function should be equal to unity (Atkins et al., 2013)

$$q^{\text{ele.}} = 1.\tag{6}$$

On the other hand, the coefficient κ(T) represents the tunneling effect of the reaction coordinate of the chemical system and it is usually important for light atoms or molecules at low temperatures. Thus, tunneling estimates were made using both Wigner (Polanyi and Wigner, 1928) and Eckart (Eckart, 1930) methods.

The Wigner tunneling correction proposes a parabolic potential,

$$V\_{\text{Wigner}}(\mathbf{s}) = E\_b - \frac{1}{2}m(2\pi\bar{\nu}\_1)^2\mathbf{s}^2,\tag{7}$$

where E<sup>b</sup> corresponds the energy potential barrier of MEP, ν¯<sup>1</sup> is the imaginary frequency of transition state and s is the coordinate

reaction. This implies in a transmission coefficient given by Bell (1959)

$$\kappa\_{\text{Wigner}}(T) = 1 - \frac{1}{24} \left(\frac{h\bar{\nu}\_1}{k\_B T}\right)^2,\tag{8}$$

For very low temperatures, the Wigner tunneling effect is not very effective, and for this reason, it was also employed Eckart tunneling correction (Truhlar et al., 1985).

The Eckart tunneling correction uses a potential of the type

$$V(\mathbf{x}) = \frac{A\mathcal{e}^{\alpha \mathbf{x}}}{1 + \mathcal{e}^{\alpha \mathbf{x}}} + \frac{B\mathcal{e}^{\alpha \mathbf{x}}}{(1 + \mathcal{e}^{\alpha \mathbf{x}})^2},\tag{9}$$

where α is a parameter described by

$$\alpha^2 = -\frac{\mu \langle \bar{\upsilon}\_1 \rangle^2 B}{2E\_b^0 (E\_b^0 - A)}\tag{10}$$

and µ is the reduced mass of the system. These parameters determine the barrier width. Here it is important to note that the A and B can be positive, negative or zero. The A parameter corresponds to the energy difference V(x → −∞) and V(x → +∞), and B is a parameter that measures the height of the barrier given by

$$B = 2E\_b^0 - A + 2\sqrt{E\_b^0(E\_b^0 - A)}.\tag{11}$$

So the most usual form for the Eckart's potential in the study of reaction rates is (Truhlar et al., 1985)

$$V\_{\text{Eckart}}(s) = \frac{A e^{\alpha(s-s\_0)}}{1 + e^{\alpha(s-s\_0)}} + \frac{B e^{\alpha(s-s\_0)}}{[1 + e^{\alpha(s-s\_0)}]^2},\tag{12}$$

where s is the coordinate of the reaction and s<sup>0</sup> is the reaction coordinate corresponding to the maximum of the barrier, which is given by

$$s\_0 = -\frac{1}{\alpha} \ln \left( \frac{A+B}{A-B} \right). \tag{13}$$

Finally, the transmission probability (Bell, 1980), obtained through the solution of the Schrödinger equation with Eckart's potential, is expressed by the following equation

$$P\_{\text{Eckart}}(E) = 1 - \frac{\cosh[2\pi(k-\beta)] + \cosh(2\pi\delta)}{\cosh[2\pi(k+\beta)] + \cosh(2\pi\delta)},\tag{14}$$

where k, β and δ depend on ν¯1, A, B and energy (E).

The quantum tunneling correction κ(T) can thus be calculated from the ratio between the quantum rate kquan.(T) and the classical rate kclass.(T) in which the particles cross the barrier. Thus, the Eckart tunneling correction with transmission coefficient is given by

$$\kappa(T) = \frac{k\_{\text{quant.}}(T)}{k\_{\text{class.}}(T)} = \frac{e^{E\_b/k\_B T}}{k\_B T} \int\_0^\infty dE \, P\_{\text{Eckart}}(E) e^{-E/k\_B T}, \quad \text{(15)}$$

where integration is performed over all possible energies.

#### 3. RESULTS AND DISCUSSION

#### 3.0.1. Geometric Parameters, Interactions and AIM Analysis

The details about the generation of the potential energy surface are described in another work of our group (Roncaratti et al., 2014), so it will be commented briefly here. First, all HP geometry

TABLE 1 | Geometrical parameters (in Å and degree) obtained at MP2(full)/aug-cc-pVTZ level for isolated HP and HP-Ng (Ng=He, Ne, Ar, and Kr) complexes and MP2(full)/aug-cc-pVTZ-PP level for HP-Ng (Ng=Xe and Rn) complexes.


(a)Values obtained by Molina et al. (2002) at MP2/6-311+G(3df,2p) level with BSSE corrections.

parameters were kept frozen at their equilibrium values of DOO = 1.45Å, DOH = 0.966Å and the angle HOO = 100.8◦ . The Ng's position is expressed in terms of the polar coordinates as represented in **Figure 1**, where R is the distance of Ng relative to the middle of O-O bond and α is the polar angle with respect to an axis perpendicular to the O-O bond (z axis). The two planes defined by O-O-H atoms are then rotated around the O-O axis, with steps of 1◦ . In addition, α was equal to 0◦ , 45◦ , 90◦ and R distance was varied from 2 to 5Å with steps 0.1Å.

Topological studies performed on this adjusted potential energy surface (PES) showed that the HP and HP-Ng complexes have two overall minimum configurations, termed cis (labeled as θ−) and trans (labeled as θ+), separated by two potential barriers,

TABLE 2 | Binding energies (in kcal/mol) of HP−Ng complexes obtained at MP2(full)/aug−cc−pVTZ level for HP−Ng (Ng=He, Ne, Ar, and Kr) and MP2(full)/aug−cc−pVTZ−PP level for HP−Ng (Ng=Xe and Rn)<sup>a</sup> .


denoted here as cis-barrier and trans-barrier. The potential energy curves (PEC) obtained from the PES are then presented in **Figure 2**.

The PECs obtained for HP-Ng complexes are similar in shape and depth. The cis-barriers for the HP-Ng complexes are all smaller than the respective value for the free HP. The free HP has a cis-barrier of 7.5594 kcal/mol whereas the values for the complexes increase monotonically from 6.9828 kcal/mol for HP-Rn up to 7.5107 kcal/mol for HP-He. In addition the trans-barrier values are also lower than the respective value for the free HP, which is 1.0427 kcal/mol, and their values are 1.0928 kcal/mol for HP-He, 1.0817 kcal/mol for HP-Ne, 1.0651 kcal/mol for HP-Ar, 1.0676 kcal/mol for HP-Kr, 1.0736 kcal/mol for HP-Rn and 1.0749 kcal/mol for HP-Xe complexes. For the free HP, the cis-barrier and trans-barrier experimental energies (Hunt et al., 1965) are 7.0334 ± 0.0715 kcal/mol and 1.1036 ± 0.0114 kcal/mol, respectively. These values are in a good agreement with our results. However, for

TABLE 3 | Bond critical point (BCP) data for charge density ρ (in ×10−3e/a 3 0 ), Laplacian of the charge density ∇ <sup>2</sup>ρ (in ×10−2e/a 5 0 ), electronic energy density H(r) and ellipticity ε for configurations 1(cis), 2(cis-barrier), 3(trans) and 4(trans-barrier) of the HP-Ng complexes.


<sup>a</sup>Where D<sup>e</sup> is the electronic binding energy, D0=De+ZPE is the electronic binding energy with the zero point energy ZPE, DBSSE <sup>e</sup> =De+BSSE and DBSSE 0 =D0+BSSE are the electronic binding energies with BSSE correction.

(b)Values obtained by Molina et al. (2002) at MP2/6−311+G(3df,2p) level, for some complexes, with BSSE corrections.

the HP-Ng complexes we did not find experimental data for comparison.

The results concerning geometric parameters, interactions and their characterization are summarized in **Tables 1**–**3**. The geometrical parameters obtained at MP2(full)/aug-cc-pVTZ, optimized without any constraints for two minimum structures and transition states (presented ascis and trans barriers) are given in **Table 1** together with the graphical representation in **Figure 3**. **Table 2** lists the binding energies corrected and uncorrected for the BSSE. **Table 3** shows the numerical results for AIM analysis and **Figure 4** depicts the ∇ <sup>2</sup>ρ(r) contour plots for cis and trans barrier configurations.

The PESs yield θ− and θ+ as true minima, i.e. without any imaginary frequencies in accordance with results from literature (Maciel et al., 2006; Roncaratti et al., 2014). In addition, all transition state structures displayed a well characterized imaginary frequency around 600 cm−<sup>1</sup> for cis and 400 cm−<sup>1</sup> for trans barriers (see **Supplementary Information** for further details). **Figure 5** describes a schematic representation of vibrational modes of the isolated HP in the transition state with the actual frequencies and an imaginary frequency, which represents the frequency along the reaction coordinate.

For the HP-Ng complexes, the geometrical parameters are almost the same when compared with isolated HP in agreement with the weak interaction of these systems. The HP-Ng distances increase from He up Rn. On average, they are close to 2.55Å(He), 2.65Å(Ne), 2.75Å(Ar), 2.85Å(Kr), 3.00Å(Xe), and 3.06Å(Rn).

Regarding the binding energies, HP-He and HP-Ne are all repulsive, being less repulsive for the cis barrier configuration. This can be understood as a consequence of the fact that the noble gases turn out to be the hardest elements (Furtado et al., 2015) and this hardness decreases when the Ng atomic number is increased (the hardness in this context is a resistance to changes in its electronic population Furtado et al., 2015 coupled to Ng's high electronegativity Allen and Huheey, 1980). Although the BSSE increases monotonically from He to Rn, the binding

point, and also represent the zero flux surface.

energies also become more attractive as the atomic number increases.

For the four structures of each HP-Ng, the higher binding values are always observed for the cis-barrier configuration. As it will pointed latter, the decrease of the rate through the two barriers are not correlated with the binding energy, suggesting the hyperconjugation effects on HP may be important for the decrease of the interaction rate.

Regarding the AIM analysis, the existence of (3,−1) bond critical point (BCP) and its associated atomic interaction line indicates that electronic charge density is accumulated between the linked nuclei (Bader, 1991). In its turn, the values of the charge density ρ(r) in BCP are small while their corresponding ∇ <sup>2</sup>ρ(r) are positive in accordance with a closed shell type of interaction. As a consequence, all configurations of all complexes show an interaction of a van der Waals type. Since higher ellipticity suggests conjugation and hyperconjugation effects of electron delocalization, these effects seem more pronounced in the HP-He and HP-Ne complexes. Another interesting feature is that all cis-barrier configurations of all complexes show a (3,+1) BCP indicating a cyclic nature.

#### 3.0.2. Thermal Chiral Rate Analysis

The temperature dependence of the rate constant for cis to trans (i.e., through trans-barrier) and trans to cis (i.e., through cis-barrier) conformations for HP and HP-Ng complexes are presented in **Figure 6**. These results, in addition to conventional rate, are also exhibited with Eckart's or Wigner's tunneling corrections.

It was found that for the entire 100 K up to 4,000 K range the HP-Ne has the lowest rates for both barriers among all noble gas complexes, followed by HP-He. This result suggests that Ne and He are the noble gases more suitable for study the oriented

FIGURE 5 | Schematic representation of vibrational modes of the H2O2 isolated in the transition state. There are 6 vibrational modes, 5 of them correspond to the actual frequencies (ν2, ν3, ν4, ν5, and ν6) and one of them corresponds to the imaginary frequency ν¯1, which represents the frequency along the reaction coordinate.

collision dynamics with HP. In fact, the decrease of CRT shows an inverse correlation with respect the average valence electron energy (Allen, 1989), which follows the sequence (from higher to lower values): Ne, He, Ar, Kr; with Xe and Rn having very close values.

Nevertheless, there is a trend of rate increase as are move from Ar up to Rn. It is interesting to note that although this behavior is very similar regarding the cis-barrier for all rates (conventional, Wigner e Eckart), it seems that the tunneling is more important to describe the trans barrier's rate, where there is a significant difference for Eckart's values specially in the 100–200 K range when compared to respective Wigner and conventional results.

The final thermal rate constant can be expressed in the two familiar Arrhenius forms. In this work, the first is the Arrhenius modified form given by

$$k\left(T\right) = AT^{\eta}e^{-E\_d/RT},\tag{16}$$

where A is the pre-exponential factor, T a temperature, n is a real number, R is the universal gas constant and E<sup>a</sup> is the activation energy. The second is the d-Arrhenius form (Aquilanti et al., 2010; Silva et al., 2013; Carvalho-Silva et al., 2017) expressed by

$$k(T) = A\left(1 - d\frac{E\_a}{RT}\right)^{1/d} \tag{17}$$

where d is a parameter that yield the degree of deformation of the exponential function.

The curve obtained by the reaction rate constant vs. the temperature can be fitted (Ramalho et al., 2011) to obtain the parameters A, n and E<sup>a</sup> for the Arrhenius modified form, as presented in **Table 4**, and the parameters A, d, and E<sup>a</sup> for d-Arrhenius form, as presented in **Table 5**. This feature confirms the trend of lower k(T) observed for HP-Ng complexes for both barriers when compared to isolated HP.

It can be also observed in **Figure 6** that the trans to cis conformation rate of HP is lower (in the range 100–200 K) than the corresponding ones for HP-Ar, HP-Kr, HP-Xe, and HP-Rn. In the case of the chiral transition from cis to trans, the rates of all HP-Ng complexes are lower than that of the isolated HP. These results showed that the transition rate from cis to trans is greater than the corresponding trans to cis for both the isolated HP molecule and for all HP-Ng complexes. This suggests that the most important barrier that separates the chiral configurations of the isolated HP and the HP-Ng complexes is the trans-barrier, since it is the smallest. The energy of the HP's trans-barrier is relatively small (1.0427 kcal/mol) compared to its cis-barrier (7.5595 kcal/mol) as already seen in **Figure 2**.

An interesting result is presented in the **Table 6**. Although the increase in the trans-barrier of the HP-Ng complexes relative to HP is considerably small (see **Figure 7**), the change in the transition rate from cis to trans is relatively high. This is verified for high (4,000 K), room (298.15 K) and also for low temperatures (100 K). The most pronounced decrease in the rate corresponds to the HP-Ne complex, in which the decrease of the trans-barrier of just 0.0389 kcal/mol (see **Figure 6**) corresponds to a decrease

FIGURE 6 | Temperature dependence (from 100 K up to 4,000 K) of the rate constant for conventional (C), Wigner (W), and Eckart (E) tunneling corrections, for cis to trans (left column) and trans to cis (right column) chiral conformations of H2O2 and H2O2-Ng complexes.


TABLE 4 | Adjusted parameters for the modified Arrhenius equation for conventional (C), Wigner (W) and Eckart (E) models with Ea in kcal/mol.


TABLE 5 | Adjusted parameters for the d-Arrhenius equation for conventional (C), Wigner (W) and Eckart (E) models with Ea in kcal/mol.

TABLE 6 | Difference between heights of trans-barrier of HP and HP-Ng complexes and relative decrease of the transition rate of cis to trans configuration for representative temperatures (4, 000, 298.15, and 100 K).


(a)∆ = Eb-trans(HP) − Eb-trans(HP-Ng).

of over 60% for the cis-trans transition rate, followed by HP-He. It is also interesting to note that this small change in energy barrier but with a substantial change in rate was also observed for other HP-Ng complexes. For example, HP-Ar complex showed a decrease of just 0.0224 kcal/mol but a 28.68% decrease of rate at 100 K.

Finally, at a temperature close to 300K, the Boltzmann distribution shows that about 16% of HP's population has higher energy than the trans-barrier with thermal fluctuations of approximately 1.7686 kcal/mol (Ball and Brindley, 2016). It has also been found that at low temperatures the chiral interconversion quantum encapsulation time of HP is very small. At a temperature of 100 K this time is <1 pico-second (Bitencourt et al., 2008), and at temperatures close to 0 K which can reach 3 pico-seconds.

## 4. CONCLUSIONS

The obtained results indicate that the chiral transition rate of trans to cis configuration of hydrogen peroxide

in the presence of the noble gases He and Ne were the lowest over the entire temperature range of 4,000–100 K.

The AIM analysis shows that the interaction between H2O<sup>2</sup> and the noble gases should be a van der Waals type. Although the H2O<sup>2</sup> acts as an acid in the context of this investigation, the high hardness and high electronegativity of the nobles gases hold their electrons very tight to permit a covalence bond between H2O<sup>2</sup> and Ng. On the other hand, it seems that both He and Ne are better able to affect the hyperconjugation effect and destabilizing repulsion among the lone pairs that are responsible for rotational barriers (Song et al., 2005). This may explain why the chiral transition rate decreases more for the complexes composed by Ne and He atoms, the hardest and more electronegative noble gases (Furtado et al., 2015).

Finally, the trans-barrier plays an important role because it is much smaller than the cis-barrier. The results showed that a small increase in the trans-barrier height in the complexes is responsible for a significant decrease in the rate of transition from cis to trans. Thus, these effects may contribute to the feasibility of separating one or the other enantiomer of the H2O<sup>2</sup> molecule.

### AUTHOR CONTRIBUTIONS

RG conceived and supervised the study. RG also helped write the paper. YS performed the H2O2-Ng electronic and thermal chiral rate calculations. PN determined the H2O2-Ng minimum and transition state configurations and LdM used the AIM theory

#### REFERENCES


to perform the H2O2-Ng topological analyses and wrote the manuscript, which was reviewed by all authors.

#### ACKNOWLEDGMENTS

We gratefully acknowledge the financial support from the Brazilian Research Councils CNPq and FAPDF.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2018.00671/full#supplementary-material


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Só, Neto, de Macedo and Gargano. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

## Collisional Quantum Dynamics for MgH<sup>−</sup> ( <sup>1</sup>6+) With He as a Buffer Gas: Ionic State-Changing Reactions in Cold Traps

Lola González-Sánchez <sup>1</sup> , Susana Gómez-Carrasco<sup>1</sup> , Alberto M. Santadaría<sup>2</sup> , Roland Wester <sup>3</sup> and Francesco A. Gianturco<sup>3</sup> \*

<sup>1</sup> Departamento de Química Física, University of Salamanca, Salamanca, Spain, <sup>2</sup> Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary, <sup>3</sup> Department of Physics, Institut für Ionenphysik und Angewandte Physik, Universitaet Innsbruck, Innsbruck, Austria

#### Edited by:

Stefano Falcinelli, University of Perugia, Italy

#### Reviewed by:

Franco Vecchiocattivi, University of Perugia, Italy James M. Farrar, University of Rochester, United States

> \*Correspondence: Francesco A. Gianturco francesco.gianturco@uibk.ac.at

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 03 January 2019 Accepted: 23 January 2019 Published: 12 February 2019

#### Citation:

González-Sánchez L, Gómez-Carrasco S, Santadaría AM, Wester R and Gianturco FA (2019) Collisional Quantum Dynamics for MgH<sup>−</sup> ( <sup>1</sup>6+) With He as a Buffer Gas: Ionic State-Changing Reactions in Cold Traps. Front. Chem. 7:64. doi: 10.3389/fchem.2019.00064 We present in this paper a detailed theoretical and computational analysis of the quantum inelastic dynamics involving the lower rotational levels of the MgH<sup>−</sup> (X16+) molecular anion in collision with He atoms which provide the buffer gas in a cold trap. The interaction potential between the molecular partner and the He (1S) gaseous atoms is obtained from accurate quantum chemical calculations at the post-Hartree-Fock level as described in this paper. The spatial features and the interaction strength of the present potential energy surface (PES) are analyzed in detail and in comparison with similar, earlier results involving the MgH<sup>+</sup> ( <sup>1</sup>6) cation interacting with He atoms. The quantum, multichannel dynamics is then carried out using the newly obtained PES and the final inelastic rats constants, over the range of temperatures which are expected to be present in a cold ion trap experiment, are obtained to generate the multichannel kinetics of population changes observed for the molecular ion during the collisional cooling process. The rotational populations finally achieved at specific temperatures are linked to state-selective laser photo-detachment experiments to be carried out in our laboratory.All intermediate steps of the quantum modeling are also compared with the behavior of the corresponding MgH<sup>+</sup> cation in the trap and the marked differences which exist between the collisional dynamics of the two systems are dicussed and explained. The feasibility of the present anion to be involved in state-selective photo-detachment experiments is fully analyzed and suggestions are made for the best performing conditions to be selected during trap experiments.

Keywords: molecular collisions, atom molecule interactions, rotational state changing dynamics, collisional cooling/heating in ion traps, kinetic states evolution

## 1. INTRODUCTION

The investigation of chemical processes at very low temperature, and the analyses of the physics involved to understand their mechanism at the molecular level, has gone through a marked development in the last decade or so. The new scientific vistas offered by their findings and the many possibilities for various applications which have become associated with cold and ultracold molecules have been reported in detail in several recent reviews (Bell and Softley, 2009; Carr et al., 2009; Dulieu and Gabbanini, 2009; Gianturco and Tacconi, 2009; Herschbach, 2009; Krems et al., 2009; Bai et al., 2011; Quéméner and Julienne, 2012; Willitsch, 2017). We shall therefore not repeat here all the current motivations and all the types of opportunities discussed there, but simply note that such wealth of new information points at very pursuing effects in the domain of precision measurements, high-resolution spectroscopy for a surprising variety of molecular systems, quantum simulation and quantum computing by interrogation of cold, trapped molecular ions.

As an example, several experimental groups have combined the use of radio-frequency ion traps with the additional presence of optical dipole traps and also magneto-optical traps (Grier et al., 2009; Schmid et al., 2010; Hall et al., 2011; Rellergert et al., 2011; Hall and Willitsch, 2012; Ratschbacher et al., 2012) in order to obtain confinement of both cold molecular ions and cold atoms. Such successful achievements point at the real possibility of studying ionic chemical reactions in a new temperature domain down to a few millikelvin. Furthermore, the combination of crossed-beam experiments with threedimensional velocity map imaging has allowed to elucidate, albeit at higher collision energies than that of the millikelvin, the dependence of charge-transfer processes on angular distributions and on the chosen vibrational state of the molecular partner in the reaction (Williams et al., 2018).

With the same token, the confinement down to temperatures of a few K of simple molecular anions in cold ion traps with the presence of He as a buffer gas has been another achievement for unraveling quantum effects, at the low temperature regimes, for specific molecular processes involving laser-assisted selective photo-detachment (Hauser et al., 2015; Hernández Vera et al., 2018; Lakhmanskaya et al., 2018). In that work, in fact, both the experiments and the calculations of OH<sup>−</sup> and NH<sup>−</sup> 2 anionic systems (trapped down to 10–20 K temperature regimes) have shown clearly that it is possible for such trapped molecules to be kept in specific rotational states of their ground electronic state and |v >= 0 vibrational state. Such selected initial conditions can then be used to study photo-detachment processes where only one or two rotational states are depleted from the trap by laser detachment of their access electron (Gianturco et al., 2018).

If therefore becomes of direct interest from the above findings to further investigate polar molecular anions which could be employed for direct selective photo-detachment experiments and also modeled from quantum simulations of their structural and dynamical aspects. We have recently studied in detail the electronic properties of the MgH<sup>−</sup> (X26+) anion and of its corresponding neutral (González-Sánchez et al., 2017), MgH (X26+) with the aim of accurately assessing the adiabatic electron affinity (AEA) value of the anion, as well as which electronic states of both systems would become relevant during a photo-detachment experiment.

Since such experiments involve the preparation of the partner molecular anion in specific rotovibrational states of its ground electronic state (Lakhmanskaya et al., 2018), one further needs to realistically assess the corresponding efficiency of collisionally "cooling" the internal states of the molecular anion in a trap that employs He as a buffer gas. Hence, the present work intends to present in detail the interaction forces acting between an MgH<sup>−</sup> molecular target in its |v >= 0 state and the He gas in the buffer role, populating by collisions a few of the lower rotational states of the anion within the trap.

We have recently carried out, in fact, a detailed calculation comparing the electronic properties and structural features of the isolated MgH<sup>−</sup> anion and of its neutral counterpart, MgH (X26+), as the two main partners of a selective photodetachment experiment (González-Sánchez et al., 2017). In order to further investigate the experimental preparation of MgH<sup>−</sup> molecules in specific rotational states, we now need to examine the dynamics of state-changing kinetics of MgH<sup>−</sup> in a cold ion trap and under the presence of He gas as a buffer gas uploaded in the cold trap (Hauser et al., 2015; Hernández Vera et al., 2018).

To achieve such end, we therefore discuss in the following section 2 the structural features of the potential energy surface (PES) involving the MgH<sup>−</sup> anionic molecule and the He atom . In particular, we shall describe the spatial anisotropy of such interaction and its effect on driving specific rotational statechanging inelastic collisions in the trap. The next section 3 will briefly outline our quantum treatment of the time-independent description of the scattering events within the multichannel formulation of the Schrödinger Equation (TISE) and present our results for a broad range of inelastic cross sections, computed at the relative collision energies which map those present in the cold trap regime. We shall further analyse those data in order to extract specific propensity rules on the relative sizes of the transition probabilities during collisions.

The ensuing section 4 will report the computed state-to-state inelastic rates over the relevant range of temperatures . Our final considerations and conclusions will be given by the last section 5.

## 2. INTERACTION POTENTIAL AND SPATIAL ANISOTROPY OF THE PES

All calculations have been performed using a C<sup>s</sup> point group of symmetry. The aug-cc-pV5Z basis set has been used for both H and He. The core-valence aug-cc-pwCV5Z basis set has been used for the Mg atom. A standard Hartree Fock calculation is initially done, followed next by a complete active space calculation (CASSCF) in which 6 active electrons are distributed among 11 active orbitals (8a' and 3a"). The latter correspond to the 3s, 3p, and 3d orbitals for the Mg atom plus the 1s orbitals for H and He. In all calculations, the core orbitals (4a' and 1a") are kept doubly occupied. After that, a multi-reference configuration interaction (MRCI) calculation is done including single and double excitations and a perturbative estimation for higher order excitation (Davidson correction).

The calculations are done in bond coordinates, Mg-H, H-He, and the angle Mg-H-He.The grid includes 13 angular points, 20 radial points for the Mg-H distance and 37 radial points for the H-He distance.

The above points where in turn transformed into (r, R, θ) Jacobi coordinates in order to carry out the quantum scattering calculations (see below). As a first instance, we have treated the

dynamics using a Rigid-Rotor (RR) description of the target molecular ion. Hence, the RR grid involved the (req, R, θ) set of points, for which we generated 37 points in R and 15 points for θ. The req=1.7368 Å as discussed in González-Sánchez et al. (2017) and all calculations were carried out using the MOLPRO computational package Werner et al. (2015).

The data shown by **Figure 1** report the spatial features of the potential energy surface (PES) that describes the RR MgH<sup>−</sup> anion interacting with the He atom.

The Mg<sup>−</sup> end of the molecule is placed on the negative region of the projection plane, while the H atom is next to the offaxes location of the attractive well region of the PES. The excess electron is clearly largely located on the Mg-side of the molecular ion and therefore the strongest interaction with the He atom is, as expected, around the H-region of the molecular anion.

Since we have previously analyzed a similar PES involving the MgH<sup>+</sup> cation in its X16<sup>+</sup> electronic state (Tacconi et al., 2011; Caruso et al., 2012), it is interesting to compare the two types of interaction potentials to extract further structural information on the present system.

The panels shown by **Figure 2** report the on-plane projections of the PES associated to the MgH<sup>+</sup> (X16+) with He (upper panel) and the one describing the MgH<sup>−</sup> (X16+) with He in the lower panels. Both Mg-ends of the molecules are on the negative region of the x/r cos(θ) axis in the panels. Distances in Å and energy levels in cm−<sup>1</sup> .

One clearly see by comparison that the cationic partner present a stronger interaction with the He atom: the latter is markedly attracted on the Mg-end of the molecular cation while it shows its weaker attractive well for the anion on the H-end of the MgH<sup>−</sup> molecule. Furthermore, we see that the present anion exhibits a large region round the molecule where the interaction remains repulsive, while He gets much closer to the Mg region in the case of the cation, as shown the upper panel. Such differences are clearly linked with the extra negative charge bound to the MgH<sup>−</sup> partner with respect to the cation, as we shall further analyse below.

As we shall discuss in the next section, the spatial anisotropy of the interaction, i.e., its strength over radial range and its dependence on the orientational Jacobi angle θ, are important markers for the dynamical torque which is being applied to the rotating molecule as it collides with the He atom (Tacconi et al., 2011; Caruso et al., 2012). To better locate the differences in coupling angular strength of this PES we then expand the RR PES in terms of Legendre Polynomials:

$$V^{RR}(\mathbb{R}, \theta) = \sum\_{\lambda}^{\lambda\_{\max}} V^{RR}\_{\lambda}(\mathbb{R}) P\_{\lambda}(\cos(\theta)) \tag{1}$$

where the radial multipolar coefficients are obtained by a wellknown numerical quadrature:

$$V\_{\lambda}^{RR}(\boldsymbol{R}) = \int\_{-1}^{1} V^{RR}(\boldsymbol{R}, \theta) P\_{\lambda}(\cos(\theta)) d\cos(\theta) \tag{2}$$

Because of the strong orientational anisotropy of the present system, the index of the sum of equation 1 was required to extend up to λmax=20 to generate converged coefficients. A pictorial view of the radial features of those coefficients, from λ=0 to λ=6, are reported in **Figure 3**.

In the main figure one sees that the λ=1 coefficient is the strongest one in the region closer to the molecular anion and it keeps its attractive features down to the shortest distance from the center of mass (c.o.m.) of the molecular anion. The smaller panel shows an enlargement in the region of the larger distances where most of the higher multipoles are repulsive or only weakly attractive. One sees from it that the spherical term, the λ=0 coefficient, is only very weekly attractive, and even more weakly so is the λ=2 coefficient. All other terms are essentially repulsive and show the outset of their repulsive walls at fairly large distances. Thus, we could say that the λ=1 coefficient dominates the short-range interaction while all other coefficients are strongly repulsive and exhibit the starting of their repulsive features at larger distances.

An interesting comparison with the behavior of the same multipolar coefficients but for the case of the closed-shell cation, the MgH<sup>+</sup> (X16+) partner to the He atom, is shown by the data of **Figure 4**: the anion's multipolar coefficients are given by solid lines, while those for the cation are shown by dashed curves. The following considerations could be had by looking at the data reported in this figure:

1. In the short-range region of relative distances we see that the dominant coefficient for the MgH<sup>−</sup> target is the one controlled by the P1(cos(θ)) polynomial, while for MgH<sup>+</sup> the spherical term for λ=0 is the strongest coefficient;


the interaction region of the cation. The excess negative charge on the anionic molecular partner causes the He atom to experience a larger region of the interaction where repulsive around the molecular target dominate.

A qualitative justification for these differences in the behavior of the two PESs which we are comparing here could be had by looking at the spatial shape of the electron densities of the highest occupied molecular orbitals (HOMOs) pertaining to the two different molecular ions. These are shown as 3D pictures in the two panels of **Figure 5**.

It is interesting to note that the extra electron in the doublyoccupied MO of MgH<sup>−</sup> is essentially located along the bond of the molecule and as a σ orbital, for which the P1(cos(θ)) symmetry is dominant. On the other hand, the most diffused (also doubly occupied) MO for the cation partner is clearly of σ-symmetry and presents a reduced orientational anisotroy of this external charge region to the incoming He atom. Thus, we could surmise that the V1(R) coefficient for the MgH−/He interaction is more important than its V0(R) contribution, while the opposite occurs for the MgH+/He interaction, as shown by **Figures 3**, **4**.

Another interesting piece of information could be gathered from the behavior of the interaction forces in the long-range (LR) region as given by the perturbative expansions of the expression for the intermolecular forces (Stone, 2013):

$$V(R,\theta|r\_{eq}) \stackrel{R \to \infty}{=} V\_{LR}(R,\theta) \sim -\frac{\alpha\_{He}}{2R^4} - 2\alpha\_{He}\frac{\mu P\_1(\cos\theta)}{R^5} \tag{3}$$

$$-\frac{\alpha\_{He}\mu^2}{R^6} \tag{4}$$

$$\alpha\_{\text{max}} \qquad \qquad P\_2(\cos\theta)$$

$$- \left( \alpha\_{He} \mu^2 + Q \alpha\_{He} \right) \frac{P\_2(\cos \theta)}{R^7} \tag{5}$$
  $\dots$ 

Where αHe is the dipole polarizability for the neutral He atom (1.3837 a 3 0 ; Masili and Starace, 2003) and µ the electric dipole moment of MgH<sup>−</sup> (X16+) (0.733 a.u.; González-Sánchez et al., 2017). In the present instance, the positive value of the dipole moment dominates the interaction in the outer radial region where the PES can become attractive. This feature is adding to the attractive features of the V<sup>0</sup> term which is important in the same radial region where the V1(R) becomes repulsive.

On the other hand, the MgH<sup>+</sup> partner has a larger dipole moment (1.44 a.u.; Sadlej and Urban, 1991) but, directed from the positive centroid of charges to the negative one, hence along the positive direction of the z-axis (Sadlej and Urban, 1991). This implies a negative sign in equation 3, i.e., opposite to the case of MgH−. The result, together with the smaller spatial region

where the coefficients in equation 1 become repulsive, is that the spherical term dominates the multipolar expansion as shown by **Figure 4**.

In conclusion, given the differences shown by the present anionic PES with respect to that of its cation, we expect that the collisional dynamics in cold traps involving state-changing processes will be different for the present system. Such differences will be presented and discussed in the following sections.

#### 3. THE QUANTUM DYNAMICS OF STATE-CHANGING COLLISIONS

The inelastic quantum dynamics we wish to study now involves solely the rotational levels of the anionic target, while it is considered to be in its ground vibrational level after the preparation in the cold traps (Hauser et al., 2015). The rotational constant of the MgH<sup>−</sup> rigid rotor (RR) is 5.6988 cm−<sup>1</sup> (González-Sánchez et al., 2017), which is slightly smaller than the one for the corresponding cation MgH+: 6.3870 cm−<sup>1</sup> (Sadlej and Urban, 1991).

In **Figure 6**, we report a pictorial view of the involved energy levels for the X16<sup>+</sup> electronic states of the two molecular ions.

It is interesting to note that the present anion shows smaller energy gaps between its lower levels, those which we expect to be involved in possible experiments of selective photo-detachment (Hauser et al., 2015).

This property is likely to play a role when the relative rates for state-changing dynamics will be discussed below in comparison with the MgH+/He system which we have recently analyzed (González-Sánchez et al., 2018a).

The next computational step involves solving the quantum inelastic dynamics of MgH<sup>−</sup> collisions with He atoms using the time-independent formulation of the multichannel coupled scattering eq.s. This method involves the well-known coupledchannel approach subject to the standard boundary conditions, the one leading to the calculation of the matrix elements of the full scattering S-matrix (Taylor, 2012). For this purpose, we have employed our in-house numerical code ASPIN and details of its implementation have been given before (López-Durán et al., 2008; González-Sánchez et al., 2015). We therefore do not discuss it again in the present work. Suffice it to say that the physical observables which we obtain from the ASPIN scattering code are in this case the state-to-state partial cross sections for each of the contributing total angular momentum J: σ J (j ′ ← j|Ei), with E<sup>i</sup> giving the initial relative energy between partners. The further summation over the contributing angular momenta (which, in the present case, was take up to Jmax = 50) will therefore yield the corresponding state-to-state partial integral cross sections:

$$\sigma(j' \leftarrow j|E\_i) = \sum\_{j}^{f\_{\text{max}}} \sigma^f(j' \leftarrow j|E\_i) \tag{6}$$

From them we can further obtain the partial rotational quenching and heating rate constants, Kjj′(T) at the temperature of interest:

$$K\_{\vec{\jmath}\vec{\jmath}'}(T) = \int \sigma(\mathbf{j}' \leftarrow j|E) \sqrt{\frac{4E}{\pi \text{(k\_BT)}^3}} \exp\left(-E/k\_BT\right) \text{E dE} \tag{7}$$

We have integrated the computed cross sections over an extended range of collision energies for the corresponding cross sections, ensuring that the threshold behavior is well-described by a dense grid of values. We have further used and extended the range of energies well beyond that necessary to map the required interval of temperatures. Numerical convergence has been checked to have reached more than 0.01 stability of the final rates.

The results from the above calculations will be presented and discussed in the following section.

#### 4. ROTATIONALLY INELASTIC PROCESSES AND KINETIC EVOLUTION IN THE TRAP

#### 4.1. Behavior of State-Changing Cross Sections

The radial integration for the cross sections of Equation (6) was extended out to Rmax = 1000 Å, while the angular anisotropy of the interaction potential of Equation (1) was extended out to λmax

= 19 in order to guarantee numerical convergence of the stateto-state inelastic probabilities included in the present treatment. We actually computed a broad range of elastic and inelastic cross sections which were employed to generate the corresponding rates from Equation (7). However, we present in **Figures 7**, **8** a small sampling of them to show briefly their general sizes and energy dependence for excitation and de-excitation processes.

The data reported in the **Figure 7** show clearly the strong dominance of the 1j=1 cross sections with respect to all the other rotational excitation processes. The λ=1 coupling term of the PES shown by **Figure 3** is the strongest coupling term between target levels, a feature which directly reflects on the (0→1) excitation cross section being the largest at nearly all energies considered in that **Figure 7**. In the region of interest, i.e., around 100–200 cm−<sup>1</sup> , we see that the increasing of the energy gaps between levels involved in 1j = 1 transitions causes the corresponding cross sections to become uniformly smaller: all the direct coupling

terms with λ >1 are seen in **Figure 3** to be of similar strength and all chiefly acting in the outer radial region, so that the changes in the energy gap chiefly control the relative sizes of the corresponding inelastic cross sections.

The data reported by **Figure 8** involve both the excitation cross sections (upper panel) and de-excitation cross sections (lower panel) for the case of the molecular target being initially in its j = 3 rotational state. The dominance of the 1j = ±1 propensity rule for the size of the cross sections is clearly visible in both panels, while the increasing of the energy gaps between levels is again causing the size of the cross section to decrease as the 1j values increase.

At least for the case of the three lowest rotational levels of the target molecule, it is also interesting to make a comparison

between the cross sections behavior in the case of MgH<sup>−</sup> in the trap (present results) and those obtained for the case where the cation is instead in the trap (discussed by us in more detail in González-Sánchez et al., 2018b). The comparison is reported by the three panels of **Figure 9** below.

The top panel in that figure shows both the excitation and deexcitation cross sections involving the lowest two rotational levels of MgH<sup>+</sup> (solid lines) and MgH<sup>−</sup> (dashed lines). We have seen before (see **Figure 6**) that the energy gap is smaller for the anion in comparison with the cation. On the other hand, the direct coupling potential, the V1(R) multipolar coefficient in **Figure 3**, is stronger for the anion than for the cation case. The present results however indicate that the excitation process produces fairly similar cross sections for the two systems, although the cation's cross sections are larger at threshold energies. Since we are dealing with low collision energies, the range of action of the PES also plays a significant role. From the data in **Figures 2**, **3**, we see that the He atom gets much closer to the MgH<sup>+</sup> target than it does for the MgH<sup>−</sup> case, thereby reducing the radial extension of its torque effects in the latter case with respect to the former. Furthermore, the LR forces of Equations (3–5) have opposite signs of their dipolar coefficients in Equation (3), with the MgH<sup>+</sup> being overall positive with respect to MgH<sup>−</sup> which remains negative. This would imply slightly weaker LR contributions for the cation in relation to the anion. Such different features contribute to the threshold differences in size and behavior of the cross sections between these two molecular ions.

The data in the middle panel report now the excitations and de-excitation cross sections involving the 1j=±1 transitions between |j >= 1 and |j >= 2 levels. The relative behavior remains substantially the same, and for the same reasons listed above, with the cation exhibiting markedly larger cross sections for de-excitation processes near threshold.

Finally, the data in the bottom pane involve the 1j=±2 transitions between the lowest possible levels: |j >= 0 and |j >= 2. Here again the cross sections are fairly similar in size, with the exception of the near-threshold de-excitation cross sections which are again larger for the MgH<sup>+</sup> target in comparison with the MgH<sup>−</sup> case.

In conclusion, we found that both ions behave fairly similarly, in spite of their structural differences, when looking at statechanging cross sections. The main difference being the larger de-excitation cross sections for the cation at energies very near the energy threshold. Such differences, however, can play a definite role when comparing state-changing rates at the low temperatures of an ion trap. These effects will be further discussed in the following subsection.

#### 4.2. Computed Inelastic Collisional Rates

By a numerical quadrature of the computed cross sections of equation 6, as indicate by equation 7, we can obtain the corresponding rates as a function of trap's temperature (González-Sánchez et al., 2015, 2018b; Schiller et al., 2017).

The data shown by **Figure 10** report the computed rates for excitation processes between the lowest five rotational states, of MgH<sup>−</sup> (X16+) that we expect to be involved in the cold ion traps of the planned experiments (Hauser et al., 2015; Gianturco et al., 2018). Those given by **Figure 11** describe the corresponding de-excitation transition rates between the set of

rotational states of the rotationally cooling anion in the trap. The following considerations can be made by a perusal of the figures data:


temperatures. On the other hand, one also sees there that all rates are in the range of 10−<sup>10</sup> cm<sup>3</sup> s −1 , i.e., similar in size to those found earlier for the MgH<sup>+</sup> cation in cold traps under similar conditions (González-Sánchez et al., 2018b).

To further investigate the comparative behavior of the two systems, we present in **Figure 12** a direct comparison between excitation and de-excitation rates involving transitions between the two lowest rotational states of MgH<sup>−</sup> and MgH<sup>+</sup> molecular ions.

By looking at the two excitation rates shown in the figure, we see that the differences in structural features between the two PESs have little influence of the final rates: the (0→1) excitation rates are of the same order of magnitude, with that pertaining to the MgH<sup>−</sup> partner remaining invariably somewhat smaller in the lowest range of temperatures. As discussed earlier, this system shows a reduced radial range within which the 1j=1 torque can act in comparison with that acting for MgH+. As a consequence, we see the smaller values for the corresponding rates.

This difference is even more marked when we look at the rotation-cooling (de-excitation) rates between the lowest two rotational states. The rates for the MgH<sup>−</sup> partner are around 50% smaller than those shown by the MgH<sup>+</sup> cation, especially over the lowest range of temperatures up to about 15 K.

### 4.3. Collisional Evolution of Rotational Population

In order to gain more insight into the kinetic effects of population-changes in the trapped anions after the uploading of the He atoms, and as it was recently demonstrated by work in our group (Hauser et al., 2015; Hernández Vera et al., 2018), it is possible to manipulate experimentally the relative populations of the rotational quantum states of a rigid rotor confined in a cold ion trap. The method, which can also be applied to the present problem, consists in depleting by an intense photo-detachment laser one or more of the lower excited rotational states of the anion while however leaving the population of its ground state intact. During the corresponding computational modeling of the physics involved one usually neglects any induced or spontaneous radiative dipole transition in the molecular anion. This is justified by noting that, given the low temperature of the black-body radiation distribution in the trap, and the usual smallness of the Einstein coefficients found for the radiative emissions between the lower rotational levels in earlier work (Schiller et al., 2017), we do not expect that such radiative processes would play here a significant role in competition with the collisional depletion paths.

The initial step is therefore that of writing down the master equations which follow the rotational state population changes by collisional energy transfers:

$$\frac{d\,n\_i(t)}{dt} = \sum\_{j \neq i} n\_j(t)C\_{ji} - n\_i(t)\sum\_{j \neq i} P\_{ij} \tag{8}$$

where Pij is the destruction rate coefficient for level i, with its formation rate given by the Cji coefficient. They are given by:

$$P\_{ij} = n\_{He} K\_{i \to j}(T) + K\_{PD} \tag{9}$$

$$\mathcal{C}\_{\vec{\mathbb{M}}} = \mathfrak{n}\_{He} \mathcal{K}\_{\vec{\mathbb{S}} \stackrel{\rightarrow}{\rightarrow} \vec{\mathbb{I}}}(T) \tag{10}$$

Equation (9) contains both the collisional state-changing rate Ki→j(T) and the KPD(s −1 ) photo-detachment rate for the situation where the molecular ion population is further altered by switching on a photo-detaching laser source after reaching an equilibrium distribution by pure collisional evolution of the rotational state populations. In the present modeling we will focus on the collisional evolution of the system and initially take the KPD rate to be equal to zero (no laser has been switched on). The steady-state solution of the kinetic eq.s is reached when the populations ni(t) get to their values when t ∼ ∞. They are found by solving equation 8 upon setting d**n**(t)/dt = 0 and therefore solving the resulting algebraic equations. We also verified that the steady-state population fractions, for each anionic rotational level, correspond to a Boltzmann distribution with Trot = T (Schiller et al., 2017).

The data reported by **Figure 13** show the steady-state populations for the lowest seven rotational levels of MgH<sup>−</sup> (X16+) over a range of temperature up to 100 K.

In that same figure we also show the steady-state population which has been achieved in our calculations for the corresponding MgH<sup>+</sup> (X16+) cation under the same dynamical conditions (González-Sánchez et al., 2018a). We see clearly that, for temperatures up to about 15 K, the fractional population of the |j >=0 state in MgH<sup>−</sup> is about 40%, while that of the |j >=1 state is about 45% and the |j >=2 state is around 15%. It is around T = 2–4 K that all anions are occupying the |j >=0 level by more than 98%. The cationic molecule, on the other hand, has reached at 15 K a fractional population for the |j >=0 level around 50% and around 43% for its |j >=1 level. On the whole, in fact, we see that the collisional state-changing of rotational level fractional populations, after He atom uploading in the trap, is more efficiently occurring with MgH<sup>+</sup> than for MgH−, although both systems show similar steady-state behavior of their fractional populations.

Another way of further comparing the collisional evolution of rotational level populations in the cold trap (the purely collisiondriven evolution) is to compute the changes of population fractions at fixed T values and as a function of time after the buffer gas upload. The results are shown by the six panels reported by **Figure 14**.

The data of **Figure 14** examine six different values of T, following those considered by the earlier experiments on the MgH+/He system (Hansen et al., 2014). The following comments can be made by considering the data in the six panels, where only the lowest five rotational state fractional populations are shown:

1. At the lowest temperatures considered in this study (lowest two panels in figure) we see that the MgH<sup>+</sup> cation reached steady-state conditions after about 2 s, while the MgH<sup>−</sup> species

appear to take much larger for the |j >=0, 1, and 2 states to reach stationarity;

populations for the same set of levels for the MgH<sup>+</sup> (thin lines). See main text for further details.


On the whole, therefore, we can say from the above numerical experiments that the MgH<sup>−</sup> anion would be less efficient than it cationic counterpart in achieving steady-state conditions in the trap and that lower temperatures would be needed to attain 80% fractional population for its rotational ground state.

## 5. SUMMARY AND CONCLUSIONS

In the present work we have analyzed in some detail the quantum dynamical modeling of the fractional rotational population of a molecular anion, the MgH−(X16+) which can evolve within a cold ion trap environment after the collisional interaction that follows the uploading of He atoms as a buffer gas. The population density of the uploaded gas has been taken to be of 10<sup>10</sup> cm−<sup>3</sup> as discussed by the experiments involving its corresponding cation MgH+(X16+) (Hansen et al., 2014). Our calculations involved the evaluation from first principles of the PES of the electronic energy for the molecular anion and the He atom in the trap. Thus, we were able to analyze in detail the orientational anisotropy of that potential and could then compare it with the features of the same type of interaction between the He atom and the molecular cation MgH<sup>+</sup> which we had computed and analyzed in our earlier work (González-Sánchez et al., 2018a). The major differences between the two PES indicate more repulsive effects coming from the extra electron of the molecular anion, which then cause the presence of a sort of "excluded volume" around the molecule for the approaching He atom which is larger for the anionic partner than it is for the cationic one. The different directional features of the permanent dipoles are also found to affect the relative strength of the orientational forces which dynamically drive the collisional state-changing processes.

The quantum, time-independent multi-channel approach is employed to treat the coupled-channel (CC) scattering problem and up to six different rotational states of the target are coupled during the dynamical study of the partial, state-to-state inelastic cross sections at the relevant collision energies.

The comparison with the same set of data for the MgH+/He set up in the cold trap indicates that, although their inelastic cross sections are fairly similar in relative sizes and in energy dependence, the MgH<sup>+</sup> turns out to be more efficiently cooled by collisions to its lowest rotational state than the anionic counterpart. As a result of these differences, we found that the dominating state-changing rates are in both case those for the 1 = ±1 processes and that down to T values < 30 K the anionic molecules show smaller inelastic rates than those found for the cation.

We have further studied the time evolution of the fractional populations of the lower rotational states in order to model the collisional preparation of the anionic molecule in the trap to further perform state-selected photo-detachment experiments as already done in our group for OH−/He (Hauser et al., 2015) and for NH<sup>−</sup> 2 /He (Gianturco et al., 2018; Hernández Vera et al., 2018; Lakhmanskaya et al., 2018). The time evolution of the fractional populations at different temperatures for the trap is shown by our present calculations to be less efficient than in the case of MgH+/He and that lower temperatures would be needed to reach a steady-state population dominated by the lowest two rotational states. However, the fact that the collisional statechanging rates for the MgH−/He system are still found to be fairly large indicates that such system can indeed be efficiently prepared for state-selective photo-detachment experiments in cold traps. Our next task will therefore be that of modeling the optimal conditions under which laser photo-detachment experiments should be carried out for the present anionic molecule.

#### AUTHOR CONTRIBUTIONS

SG-C and AS were involved in producing the ab initio PES used for the quantum dynamics. LG-S carried out the quantum CC calculations. FG suggested the problem and wrote up the

#### REFERENCES


initial draft of the presentation of the results. RW with all other authors discussed the physical meaning of the computational findings and contributed to the production of the final version of this paper.

#### ACKNOWLEDGMENTS

LG-S acknowledges financial support from MINECO (Spain), Grant CTQ2015-65033-P. The computational results were obtained using in-house computer codes running on the HPC infrastructure LEO of the University of Innsbruck. This work was supported by various STSM travelling Grants from COST Action CM1401, held by LG-S. FG and RW thank the support by the Austrian Science Fund (FWF), Project No. 29558-N36.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 González-Sánchez, Gómez-Carrasco, Santadaría, Wester and Gianturco. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Coupled Excited-State Dynamics in N-Substituted 2-Methoxy-9-Acridones

M. Carmen Gonzalez-Garcia<sup>1</sup> , Pilar Herrero-Foncubierta1,2, Silvia Castro<sup>2</sup> , Sandra Resa<sup>2</sup> , Jose M. Alvarez-Pez <sup>1</sup> , Delia Miguel <sup>1</sup> , Juan M. Cuerva<sup>2</sup> , Emilio Garcia-Fernandez <sup>1</sup> and Angel Orte<sup>1</sup> \*

*<sup>1</sup> Departamento de Fisicoquimica, Facultad de Farmacia, Unidad de Excelencia en Quimica Aplicada a Biomedicina y Medioambiente (UEQ), Universidad de Granada, Granada, Spain, <sup>2</sup> Departamento de Quimica Organica, Facultad de Ciencias, Unidad de Excelencia en Quimica Aplicada a Biomedicina y Medioambiente (UEQ), Universidad de Granada, Granada, Spain*

#### Edited by:

*Antonio Aguilar, University of Barcelona, Spain*

#### Reviewed by:

*Jose Andres Fernandez, University of the Basque Country, Spain Sugata Chowdhury, National Institute of Standards and Technology (NIST), United States*

\*Correspondence: *Angel Orte*

*angelort@ugr.es*

#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

Received: *25 December 2018* Accepted: *18 February 2019* Published: *12 March 2019*

#### Citation:

*Gonzalez-Garcia MC, Herrero-Foncubierta P, Castro S, Resa S, Alvarez-Pez JM, Miguel D, Cuerva JM, Garcia-Fernandez E and Orte A (2019) Coupled Excited-State Dynamics in N-Substituted 2-Methoxy-9-Acridones. Front. Chem. 7:129. doi: 10.3389/fchem.2019.00129* Fluorophores of the acridone family have been widely employed in many applications, such as DNA sequencing, the detection of biomolecules, and the monitoring of enzymatic systems, as well as being the bases of intracellular sensors and even antitumoral agents. They have been widely used in fluorescence imaging due to their excellent photophysical properties, in terms of quantum yield and stability. However, frequently, the fluorescence emission data from acridones are not easily interpretable due to complex excited-state dynamics. The formation of π-stacking aggregates and excimers and excited-state proton transfer (ESPT) reactions usually result in emission features that are dependent on the experimental conditions. Therefore, an in-depth understanding of the dynamics involved in the excited-state transients of these dyes is mandatory for their appropriate application. Herein, we synthesized and fully characterized different 2-methoxy-9-acridone dyes. Their transient fluorescence emission spectra exhibited a complex dynamic behavior that can be linked to several excited-state reactions. We performed a thorough study of the excited-state dynamics of these dyes by means of time-resolved fluorimetry supported by computational calculations. All this allowed us to establish a multistate kinetic scheme, involving an ESPT reaction coupled to an excimer formation process. We have unraveled the rich dynamics behind this complex behavior, which provides a better understanding of the excited states of these dyes.

Keywords: excited-state dynamics, fluorophores, excited-state proton transfer, excimers, kinetics, computational photophysics

## INTRODUCTION

Fluorescence imaging can be a valuable tool for studying biomolecules in complex biological environments because of characteristics such as its great sensitivity, high spatial resolution, and ease to use (Nalbant et al., 2004). Nevertheless, the application of fluorescence intensity as a key parameter has some drawbacks since its use may require knowledge of the relative concentration of the fluorophore, and this is usually unknown in biological structures. Unlike other fluorescence parameters, the fluorescence lifetime is an intrinsic property of a fluorophore and therefore does not depend on the fluorophore concentration, as well as being independent of the excitation wavelength (Berezin and Achilefu, 2010). However, the fluorescence lifetime is highly sensitive to environmental factors, such as solvent polarity (Orte et al., 2016; Ripoll et al., 2018), conformational changes (Tomin, 2010), and excited-state reactions (Alvarez-Pez et al., 2001), among others. These characteristics together with the independence from the concentration of the fluorophore make fluorescence lifetime imaging (FLIM) an advantageous method over fluorescence intensity measurements. In addition, another advantage of using FLIM is that the fluorescence lifetime allows for discrimination between the fluorescence from different fluorophores, despite the overlap in their wavelengths of emission (Berezin and Achilefu, 2010). This property allows for differentiating between the autofluorescence of cells and tissues and that of the fluorescent labels that are used as probes. This discrimination is even more specific when the employed fluorescent probes have a long lifetime since the fluorophores that generate the biological background usually possess short lifetimes (Stevens et al., 2008; Berezin and Achilefu, 2010). Therefore, fluorophores with large lifetimes are of choice in biological sensing using FLIM (Ruedas-Rama et al., 2015). Indeed, by applying the FLIM methodology and the single molecule approach, we have been able to evaluate the transport of extracellular phosphate into preosteoblast cells during osteoblast differentiation (Paredes et al., 2013) and to monitor pH changes within the cellular cytoplasm using pH-sensitive nanoparticles (Orte et al., 2013).

Among the various groups of small fluorescent molecules with large lifetimes, those based on the acridone moiety show fluorescence emission in the 400–500 nm region with lifetimes >10 ns, as well as pH independence in the physiological range (Smith et al., 2004). Approximately 270 alkaloids of the acridone family have been described (Michael, 2017), and due to their multiple uses, a large number of acridone derivatives have also been synthesized. Among their most noteworthy properties are the effects of acridones and synthetic analogs as antineoplastic agents (Kuete et al., 2015; Fomani et al., 2016; Schelz et al., 2016). Antibacterial and antiviral activities have also been described (Wansi et al., 2006). Likewise, acridone derivatives have found diverse usage as detection reagents for biomolecules (Kitagawa et al., 1995) and metal ions (Fukuzumi and Ohkubo, 2002), as well as tunable photosensitizers for photoredox catalysis (Chen et al., 2018).

The acridone moiety presents a ketone in a tricyclic chromophoric system with planar geometry that favors πstacking interactions between neighboring molecules, which may lead to the formation of excimers. An excimer is defined as a dimer between two identical monomers, one of them in the ground state and the other in the excited state (Lakowicz, 2006). The formation of an excimer is induced by the orientation of two chromophores, especially in the aggregated assemblies, upon absorption of a photon, which is associated with the π-stacking interactions. Excimers normally show redshifted absorption and emission spectra with respect to those of the monomer.

Aromatic molecules with unoccupied π <sup>∗</sup> molecular orbitals can also undergo excited-state intermolecular proton transfer, as mediated by solvent molecules. In some cases, proton transfer may occur in hydrogen-bonded dimers. The great majority of acridone derivatives present these π-stacking interactions as well as intermolecular hydrogen bond formation (Liu et al., 2000). Precisely, the formation/cleavage of the π-stacking interactions provide some crystals of acridone derivatives with molecular-packing-dependent emission properties, which are useful in photonic devices and biological sensing (Chen et al., 2016; Takeda and Akutagawa, 2016; Bricks et al., 2018). A complex, hydrogen bonded with the solvent, is formed in the ground state so that its absorption and emission spectra are also redshifted relative to those of the non-hydrogen-bonded solutes (Lakowicz, 2006). Conversely, electron acceptors with unoccupied π <sup>∗</sup> orbitals can accept electrons when the excited state is reached. In this case, the increased electronic density results in a decrease in the excited-state dissociation constant. The number of photobases that have been investigated is substantially lower than that of photoacids, limiting knowledge about the possible usefulness of photobases (Sheng et al., 2018).

Although a few reports on the fluorescence spectra and fluorescence lifetimes of some acridone derivatives in solution have been published (Smith et al., 2004), as well as their behavior as very weak acids in their excited states (Schulman and Sturgeon, 1977), a detailed investigation of their photophysics in solution has not yet been described. Therefore, it is essential to elucidate the dynamics of the excited-state in the molecular and supramolecular forms that are present at the different pHvalues to thoroughly understand the photophysics of acridones in solution.

The dynamics of the excited-state processes of fluorescent molecules can be made accessible by time-resolved fluorescence measurements. Usually, the fluorescence decay trace of an excited-state system is described by a sum of exponential functions in terms of the decay times and their preexponential factors. However, the most important parameters, when an excited-state dynamic process is present, are the rate constants defining the excited states along with the excitation and emission spectra associated with the species involved in the kinetic system (Boens et al., 2004). To determine these parameters, a multidimensional fluorescence decay data surface should be measured under a variety of experimental conditions, and from the resulting set of fluorescence decays, the rate constants and the spectra associated with excitation and emission can be linked and determined. Such a global analysis, in which the rate constants of the excited-state processes and the associated spectral parameters are the linked variables to be calculated, is called global compartmental analysis (GCA) (Boens and Ameloot, 2006).

Herein, we prepared two different N-substituted 2-methoxy-9-acridone derivatives and studied their photophysical dynamics by formulating an appropriate kinetic scheme, involving all the detected excited-state reactions, and analyzed these species using global analysis. Intricate excited-state dynamics were found to involve coupled excited-state reactions, including proton transfer and excimer formation. To the best of our knowledge, this report is the first to resolve such coupled excited-state dynamics.

#### MATERIALS AND METHODS

#### Syntheses of N-modified 2-Methoxy-9-Acridones

We focused our attention on the central moiety of 2-methoxy-9(10H)-acridone. To link this fluorescent moiety to other chemical groups and biomolecules, we added a 3-hydroxypropyl radical to the nitrogen atom of the chromophore. We obtained the N-(3-hydroxypropyl)-2-methoxy-9-acridone, **1**, in high yield as a suitable candidate for our studies (see **Supplementary Materials** for the synthesis reaction and characterization, and **Supplementary Figures S1**–**S4**). To investigate the effect of the hydroxy group of **1** on the proton transfer reactions, we prepared the N-(3-methoxypropyl)-2 methoxy-9-acridone, **2**, lacking the terminal hydroxy group, as described in the **Supplementary Materials** (and characterization in **Supplementary Figures S5**, **S6**). As a control, we also measured the precursor 2-methoxy-9(10H)-acridone (see **Supplementary Materials**). **Figure 1** shows the chemical structures of the two acridone derivatives prepared in this study.

#### Reagents

Reagents were purchased from Sigma-Aldrich at the maximum purity available (molecular biology quality). Solvents were spectroscopic grade. Aqueous solutions were prepared with MilliQ water and their pH were set with appropriate amount of acetic acid, sodium acetate, HNO3, and NaOH.

#### Instrumentation

To absorption spectra of the 2-methoxy-9-acridone derivatives, we used a UV-Visible double-beam absorption spectrophotometer (Lambda 650; PerkinElmer, U.S.A.). Steady-state fluorescence spectra were collected on a FP-8300 spectrofluorometer (Jasco, Japan). All measurements were recorded using 10 × 10 mm cuvettes. The pH of each sample was measured immediately after recording each spectrum.

Fluorescence decay traces were recorded on a FluoTime 200 time-resolved fluorimeter (PicoQuant, Germany), with a TimeHarp 200 event tagging card working in single-photon timing mode. The excitation source was a 375-nm pulsed diode laser (LDH-375, PicoQuant) controlled by a PDL-800 driver (PicoQuant) and working at a repetition rate of 10 MHz. The fluorescence decay traces were collected at 440, 470, 500, and 530 nm, as the emission wavelengths, until 2 × 10<sup>4</sup> counts were reached in the peak channel. For TRES acquisition, the fluorescence decay traces were obtained from 425 to 572 nm, every 3 nm. A constant period of time was employed to collect all the traces. For the cases when the laser power had to be changed for collecting a larger number of counts, the appropriate correction factors were applied to normalize the collection time.

#### Data Analysis

The absorbance vs. pH curves were globally fitted to Equation (1), where A λ is the absorbance at wavelength λ, C<sup>T</sup> is the total concentration of the dye; b is the optical path; pK<sup>a</sup> is the acidity constant, a globally adjustable parameter; and ε λ HA and ε λ A are the wavelength-dependent molar absorptivity coefficients of the protonated and deprotonated forms, respectively. Six different traces, obtained at the wavelengths of 405, 410, 415, 420, 425, and 450 nm, were employed in the fittings.

$$A^{\dot{\lambda}} = C\_T b \left( \varepsilon\_{HA}^{\dot{\lambda}} \frac{10^{-\rho H}}{10^{-\rho H} + 10^{-\rho K\_d}} + \varepsilon\_A^{\dot{\lambda}} \frac{10^{-\rho K\_d}}{10^{-\rho H} + 10^{-\rho K\_d}} \right) \tag{1}$$

The fluorescence intensity vs. pH curves were globally fitted to Equation (2), where I/A is the fluorescence intensity at a certain emission wavelength, λem, after excitation at λex and normalized by the absorbance at the excitation wavelength in each point; pK ∗ a is the globally shared excited-state acidity constant; and fHA and f<sup>A</sup> are proportionality factors directly related to the quantum yield of the protonated (HA) and deprotonated (A) forms, respectively.

$$\frac{I}{A} = f\_{HA} \cdot \frac{10^{-\rho H}}{10^{-\rho H} + 10^{-\rho K\_a^\*}} + f\_A \cdot \frac{10^{-\rho K\_a^\*}}{10^{-\rho H} + 10^{-\rho K\_a^\*}} \tag{2}$$

All non-linear least squares fitting procedures were implemented in Origin Pro 9.0 (OriginLab Corp., U.S.A.).

The fluorescence decay traces were analyzed with the FluoFit software (PicoQuant) by using iterative deconvolution methods. The instrument response function (IRF) was obtained at the excitation wavelength from a scattering LUDOX solution. The fluorescence decay traces were fitted to a sum of two or three exponential decay components.

Time-resolved emission spectra (TRES) and speciesassociated emission spectra (SAEMS) were obtained though fluorescence decay traces collected over the 425–572 nm spectral range, with 1λ = 3 nm, and corrected for the same instrumental conditions and the same total acquisition time. TRES spectra were calculated using Equation (3) for total decay times of 0, 0.5, 0.8, 1, 1.2, 1.5, 3, 5, 8, 10, and 15 ns.

$$I\_{\lambda}\left(t\right) = \sum\_{i=1}^{n} p\_i \cdot e^{\frac{-t}{t\_i}}\tag{3}$$

In Equation (3), Iλ(t) is the time-dependent emission intensity at emission wavelength λ, fitted to an exponential model with n species; p<sup>i</sup> is the amplitude of species i at λ; and τ<sup>i</sup> is the corresponding decay time for species i.

The SAEMS represent the spectral contribution of each one of the species, i, estimated at each emission wavelength per Equation (4), in which the spectra need to be corrected by the corresponding total spectrum obtained at steady-state (Iss,λ).

$$I\_{i, \lambda} = \frac{p\_i \cdot \mathbf{r}\_i}{\sum\_{i=1}^n p\_i \cdot \mathbf{r}\_i} I\_{ss, \lambda} \tag{4}$$

#### Theoretical Calculations for the Absorption and Emission Spectra

To corroborate the empirical observations of compound **1**, theoretical simulations of the absorption and emission spectra of the protonated and deprotonated species of this molecule were performed. The calculation of every spectrum started with the optimization of the corresponding species by looking for the most stable geometry, followed by the determination of the

vertical excitation energies and finally the emission wavelengths from the relaxation of the first excited state (S1) geometry and from the vertical emission to the ground state (GS). All the calculations were performed using the Gaussian 09 suite. The geometry optimizations of the different conformers and species of compound **1** were computed at the DFT CAM-B3LYP/6- 31G∗∗ level of theory. To verify that the found stationary points were true minima, the harmonic frequencies were computed. Time-dependent density functional theory was employed to describe the electronic transitions. Solvent effects were included by means of the integral equation formalism of the polarizable continuum method (IEF-PCM). All calculations were performed using the long-range corrected hybrid functional CAM-B3LYP and the 6-31G (d,p) basis set.

## RESULTS

#### Photophysical Properties and Acid-Base Equilibria

We first investigated the UV-visible absorption and fluorescence emission properties of **1** in aqueous solution, exploring its acidbase equilibria. In the pH range between 2 and 12, the absorption and emission spectra of the dye were practically invariable. Just when the pH was lowered below 0, spectral changes arose (**Figure 2A**). At a pH of approximately −1.0, the S0 → S1 absorption band displayed a maximum at 418 nm and several shoulders due to vibrational structures. Upon a pH increase, a broad band with two maxima at 407 and 426 nm appeared. The spectral changes at acidic pH-values are related to the protonation of the chromophore group of **1**. The hydroxyl radical in the 3-hydroxypropyl side group may also exhibit acid-base properties. However, since the group is not conjugated and far from the chromophoric moiety, its protonation-deprotonation equilibrium would not affect the spectral properties of the dye in the visible region. The equilibrium constant and pK<sup>a</sup> of the detected protonation transition was obtained by globally fitting the absorbance vs. pH curves, collected at several wavelengths, to the general equations of Beer's Law and chemical equilibrium (**Figure 2B**). Six different A vs. pH traces were globally fitted, with the pK<sup>a</sup> as a global adjustable parameter, using a non-linear least squares fitting procedure. We recovered a pK<sup>a</sup> value of −0.94 ± 0.15, confirming the very weak basic character of acridone **1**, hence, the very strong acidic character of its protonated form.

The investigation of the steady-state emission spectra of **1** at different pH-values also showed a similar behavior (**Figure 3A**).

An almost invariable emission spectrum was found at pHvalues higher than 2.0, with an emission maximum centered at 465 nm. As the pH of the environment was decreased, a new spectral shape arose, exhibiting an emission maximum at 490 nm and a notable secondary band centered at 530 nm. This shift to lower energies in the transitions upon protonation was also evident by the change in the color of the solution to a greener shade (**Figure 3B**). However, by inspecting the curves of

intensity emission vs. pH, the protonation transition seemed to occur at higher pH-values than that obtained in the absorbance measurements. This result suggests that the basic form of species **1** at this acid-base equilibrium was stronger in the excited state, thus, leaving a weaker conjugate acid. This behavior opens up the possibility of excited-state dynamics; expressly, excited-state proton transfer (ESPT) reactions can take place when the acidbase properties of the molecule notably change upon excitation.

After being promoted to the excited state, fast protonation, or deprotonation reactions may occur during the lifetime of this excited state when a suitable proton donor-acceptor is present. In this case, hydronium ions and water molecules may act as the proton donor and acceptor, respectively. Provided the ESPT reaction is fast enough so that the apparent equilibrium is rapidly reached, the steady-state intensity emission is capable of describing the excited-state equilibrium constant, which is pK<sup>a</sup> ∗ (Alvarez-Pez et al., 2001). Therefore, the I vs. pH curves of **1**, collected at different emission wavelengths, were globally fitted, as described in section Data Analysis, and the pK<sup>a</sup> ∗ was estimated to be 0.91 ± 0.08 (**Figure 3C**). The increase in the pK<sup>a</sup> value in the excited state confirms the enhanced basicity of the deprotonated form of **1**. This compound is one of the few examples of photobases, which have recently been suggested as potential candidates for light-driven pH-jump experiments (Sheng et al., 2018).

## Excited-State Dynamics: Coupled ESPT and Excimer Formation

Time-resolved fluorimetry represents the most suitable technique to investigate and characterize the excited-state dynamics of fluorescent probes. The fluorescence decay traces implicitly hold kinetic information about radiative and non-radiative deactivation processes, as well as reactions that alter the excited-state population of fluorescent molecules. Therefore, we employed this technique to explore the ESPT reaction of dye **1**. First, we focused on the pH range in which the ESPT reaction occurred, by collecting fluorescence decay traces at several λem to obtain more accurate estimations of the decay times from global fits. A simple ESPT reaction involving two prototropic species would show fluorescence decay traces with two different decay times as the solution of the corresponding excited-state kinetic equations (Boens and Ameloot, 2006). However, in the pH range between −1 and 2.5, we obtained fluorescence decay traces that required three different exponential terms (**Figure 4**). The shortest decay time, varying from 0.27 to 0.68 ns, was a rise time at long emission wavelengths, as it was characterized by a negative pre-exponential factor (**Supplementary Figure S7**). The presence of negative pre-exponentials is a unique feature of excited-state dynamics, indicating that the excited-state reaction results in a product with a higher emissive yield at the studied wavelength. The intermediate decay time decreased from 1.75 to 0.83 ns in the pH range between −1 and 2.5. Finally, the longest decay time varied from 22.36 to 17.41 ns, with a transition near the pH-value of approximately pK<sup>a</sup> ∗ , as expected for an ESPT reaction. The TRES showed the transformation of the initially excited, emissive species into a species exhibiting a redshifted shoulder (**Figure 5A**). The analysis of the SAEMS when excited-state dynamics are present can provide information on which kinetic processes occur first, as well as the spectra of the deactivating and forming species. The three SAEMS of these fluorescence decay traces presented a complex dynamic situation (**Figure 5B**). The initially excited form, emitting in the blue edge (**Figure 5B**, red line), showed a transformation into a second form with a redshifted emission (the negative section of the fast decaying species). The species associated with the intermediate decay time (**Figure 5B**, blue line) still exhibited a negative region in the red-edge, indicating the formation of a different emissive species. This negative, redshifted shoulder correlated well with the emission shoulder found in the cation emission of **1** in very acidic media. Finally, the spectrum associated with the long decay time (**Figure 5B**, black line) represented the coupled decay of all the interrelated species. These results suggest two main points: (1) the coexistence of two different excited-state reactions, with different dynamics, and (2) the formation of the cationic species upon excitation, hence, a photobase behavior of the dye.

To investigate the coexistence of the two excited-state reactions, we moved to near-neutral pH-values. When the pH is far from the range at which the ESPT reaction is feasible, one would expect mono-exponential decay traces from a single emitting species. In contrast, for the pH range from 2.5 to 13.5, we found a biexponential decay behavior. Importantly, the shortest decay time was a rise time in the emission wavelengths

beyond 500 nm, where a secondary emission band was detected in the steady-state emission spectra. This result indicates that the secondary band formed upon excitation, with fast kinetics. This was also confirmed by studying the TRES and SAEMS under the same conditions (**Figures 5C,D**, and **Supplementary Figure S8**). The presence of an isoemissive point in the TRES (**Figure 5C**) clearly indicated the transformation of the initially excited species into a redshifted emitting form (the negative region in the SAMES associated with the fast decay time, **Figure 5D**). The appearance of a redshifted, broad band is a typical feature of an excimer-like arrangement, whereby dimers are formed during the excited state (Lakowicz, 2006). Hence, our hypothesis is that the excited-state dynamics found for compound **1** are due to excimer formation. To test this hypothesis, we collected fluorescence decay traces at different total concentrations of **1**, as the dynamics of excimer formation must be concentrationdependent. Indeed, the short rise time decreased from 0.94 ns at 7.5 × 10−<sup>8</sup> M to 0.77 ns at 2.5 × 10−<sup>5</sup> M (**Figure 6A**),

values from the global fits of the fluorescence decay traces, whereas lines represent the simulated decay times according to the kinetic scheme including

an acid-base excited-state reaction and excimer formation.

indicating that the excimer formation became faster with the concentration increments. Likewise, the negative pre-exponential also gained statistical weight with increasing concentrations of **1** (**Figure 6B**), confirming that the excimer formation reaction occurred to a greater extent. The excimer formation hypothesis was further supported by theoretical calculations, in which the most likely geometry of the excimer was obtained (see section Theoretical Calculations). The appearance of a rise time in the fluorescence decay traces is an unequivocal feature that the emitting species at the redshifted band is in fact formed mainly in the excited-state, and hence it is an excimer. Nevertheless, the πrich structure of the acridone moiety may promote aggregation by π-stacking also in the ground state. In order to test this, we focused on the ground-state, absorption spectrum of **1**, at different concentrations. The absorption spectra remained invariable in shape, and the absorbance strictly followed the Beer's Law (see **Supplementary Figure S9**). The concentrationindependence of the absorption spectrum does not support the formation of dimers or aggregates in the ground state. Hence, we can conclude that the interaction occurs mainly involving an excited monomer.

Finally, at high pH-values, a decrease in the long decay time was detected (**Figure 4B**). This decrease was accompanied by a decrease in the total emission intensity. These features could be interpreted as an additional acid-base reaction occurring under highly basic conditions (Schulman and Sturgeon, 1977); however, the absence of acidic hydrogen atoms or electron acceptor positions make this hypothesis unlikely. Likewise, the absorption spectrum of **1** did not change at these pH-values. Therefore, we concluded that this effect was mainly caused by an OH−-mediated quenching of the excited state.

Hence, this situation represents a challenging kinetic system, with coupled excited-state dynamics, involving both an ESPT reaction and an excimer formation reaction, together with an additional quenching reaction at high pH. Since the excitedstate dynamics were more complex than expected, further investigations were required to gain insight into the system. Our approach to fully analyze and solve the excited-state dynamics of this system consisted of a GCA methodology, which included all the emissive species found (see section Compartmental Analysis of the Coupled Excited-State Dynamics).

To rule out the possibility of the hydroxy group in the Npropyl chain being involved in an intramolecular proton transfer, we synthesized N-(3-methoxypropyl)-2-methoxy-9-acridone, **2**, as a control. In **2**, the terminal hydroxyl radical has been converted into a methoxy radical, so that proton transfer reactions are hindered at this position. The spectroscopic features (absorbance and steady-state emission spectra) and the acidbase behavior of **2** were very similar to those of **1** (see **Supplementary Figure S10**). The obtained ground state pK<sup>a</sup> was −0.80 ± 0.13 for the cation → neutral transition, whereas the recovered excited-state pK ∗ a value was 1.04 ± 0.04. Likewise, compound **2** also displayed a biexponential behavior in the fluorescence decay traces at pH-values between 2.5 and 13.5, with a short rise time of 0.8 ns (**Supplementary Figure S10C**), supporting the efficient formation of an excited-state excimer. The emission of **2** also exhibited a quenching caused by

hydroxyl groups at high pH-values. All these results illustrate the similarities between both dyes. Indeed, this was expected, as the hydroxyl in **1** and the methoxy in **2** and the chromophore moiety are not conjugated while being sufficiently separated to not cause a measurable effect on the dynamics of the first excited state.

#### Theoretical Calculations

To support the conclusions drawn about the photophysical properties of **1**, we performed theoretical calculations, minimizing the energy and estimating the most likely absorption and emission transitions in the gas phase of the forms depicted in **Figure 7** (see **Tables S1**, **S2**). The first point to be investigated was elucidating the actual protonation position. We considered two possibilities for protonation: at the acridone nitrogen (AP) or at the carbonyl oxygen (APC). The theoretical calculations demonstrated that a larger negative charge was concentrated at the carbonyl oxygen, making this position more likely to be protonated. Likewise, when comparing the calculated absorption and emission spectra (**Figure 8**), the APC form was the one that effectively showed a redshifted HOMO → LUMO transition, as we found experimentally at low pH-values. Hence, we concluded that protonation is most likely at the carbonyl group.

We also explored the potential structure of a dimer (Dim in **Figure 7**) to simulate the excimer formation. After optimizing the geometry (**Figure 8C**), the calculated absorption spectrum of Dim exhibited a redshift compared to that of the neutral AN, but not to energies as low as that of the cationic form (**Figure 8A**). This result is in agreement with the experimental data, especially the TRES and SAEMS spectra (**Figure 5**). Nonetheless, we could not obtain a simulated emission transition for Dim in the gas phase. However, we obtained the emission transition for Dim in water, which exhibited a redshift compared to that of the AN and was in agreement with the experimental results. Further work to include general and specific solvent effects on these simulations is in progress.

## Compartmental Analysis of the Coupled Excited-State Dynamics

The qualitative analysis of the spectroscopic and kinetic results, supported by the theoretical calculations, suggested the presence of coupled ESPT and excimer formation reactions, and a quenching process mediated by OH<sup>−</sup> ions. To solve such challenging dynamics, we employed the GCA approach. This approach shows superior performance in the analysis of the complex excited-state dynamics of fluorescent dyes,

in terms of reliability and identifiability of the obtained results (Boens and Ameloot, 2006).

**Figure 9** shows the overall kinetic scheme that we considered herein to analyze the excited-state dynamics of the Nmodified 2-methoxy-9 acridones, specifically compound **1**. The kinetic scheme involves the excited-state protonation (kCN) and deprotonation (kNC) of the neutral (N) and acidic (C) forms, respectively; as well as the formation (kDN) and dissociation (kND) of a neutral excimer (D). The excimer formation rate, kDN, would be concentration-dependent; however, as a single concentration was studied globally, it can be considered a pseudofirst-order constant.

When the system in solution is excited by an infinitesimal δpulse of light at time t = 0, the time evolution of the different excited species gathered in the vector **x**(t), in which each element represents the concentration of one of the excited species (D, N, or C), follows the differential equation

$$
\dot{\mathbf{x}}(t) = \mathbf{A} \cdot \mathbf{x}(t) \tag{5}
$$

where **x**˙ (t) is the time derivative of vector **x**(t) and **A** is the 3 × 3 compartmental matrix, which contains all the kinetic processes of each species (Orte et al., 2005b; Boens and De Schryver, 2006). In this particular case, the matrix **A** has the form

$$\mathbf{A} = \begin{pmatrix} -(k\_{\rm{0D}} + k\_{\rm{ND}}) & k\_{\rm{DN}} & 0 \\ k\_{\rm{ND}} & -(k\_{\rm{0N}} + k\_{\rm{DN}} + k\_{\rm{CN}} \cdot \left[ H^{+} \right] + k\_{\rm{q}} \left[ OH^{-} \right] & k\_{\rm{NC}} \\ 0 & k\_{\rm{CN}} \cdot \left[ H^{+} \right] & -(k\_{\rm{NC}} + k\_{\rm{0C}}) \end{pmatrix} \tag{6}$$

In a coupled, compartmental system such as this, the fluorescence decay traces collected at different emission wavelengths would be described by three different decay times τ<sup>i</sup> (unless non-emissive species are present). The τ<sup>i</sup> values are related to the eigenvalues of matrix **A**, γ<sup>i</sup> , through Equation (7).

$$\gamma\_i = -\frac{1}{\mathfrak{r}\_i} \tag{7}$$

If an analytical expression for the eigenvalues γ<sup>i</sup> could be obtained, the dynamic system could be resolved by a nonlinear least squares fitting to the experimental data. However, the intricacy of the compartmental matrix prevents obtaining an explicit expression for the eigenvalues. Hence, we designed an iterative process to assess the value of each kinetic rate constant in the model.

The first step involved analyzing the limiting values of the eigenvalues at very low pH. In this limit, the long decay time is given by k0<sup>C</sup> −1 , and the intermediate decay time is given by <sup>k</sup>0<sup>D</sup> <sup>+</sup> <sup>k</sup>ND−<sup>1</sup> . Therefore, by using the experimental values of the decay times at very low pH, we obtained k0C = 0.044 ns−<sup>1</sup> and S<sup>1</sup> = k0D + kND = 0.570 ns−<sup>1</sup> . Then, we focused on the pH region between 3 and 11, in which only two invariable decay times were experimentally obtained (**Figure 4B**). In this region, the pH is sufficiently high so that the acidic form does not intervene, and low enough so that the hydroxyl-mediated quenching is negligible. Under these experimental conditions, the compartmental matrix can be reduced as follows.

$$\mathbf{A} = \begin{pmatrix} -\left(k\_{\rm 0D} + k\_{\rm ND}\right) & k\_{\rm DN} \\ k\_{\rm ND} & -\left(k\_{\rm 0N} + k\_{\rm DN}\right) \end{pmatrix} \tag{8}$$

This bicompartmental model indeed predicts fluorescence decay traces with two pH-independent decay times, as we experimentally observed. However, as there are four different rate constants and only two eigenvalues, the system cannot be unequivocally determined. We then set an initial guess for k0D (so that kND was immediately defined through S1) and employed the experimental decay times to determine k0N and kDN, as there were only two remaining unknowns. With these guesses for the rate constants in the near-neutral pH region, we moved to the acidic region and employed the experimental values of the three decay times to estimate kNC and kCN, taking into account the relation between the sum of the eigenvalues and the rate constants (Equation 9) (Boens and De Schryver, 2006) and the

FIGURE 7 | Different structures of 1 studied by theoretical calculations.

FIGURE 9 | Scheme of the tricompartmental excited-state system of the N-substituted 2-methoxy-9-acridones employed in this work. The different species present are: D, the excimer; N, the neutral prototropic form; and C, the acid form. The kinetic scheme considers the formation and dissociation of the excimer (*k*DN and *k*ND, respectively), the ESPT reaction between N and C (*k*CN for the protonation, and *k*NC for the deprotonation), the radiative deactivation processes (*k*0D, *k*0N, and *k*0C), and the nonradiative quenching of N mediated by OH<sup>−</sup> ions (*kq*). We did not find experimental evidence of the formation of dimers in the ground state, therefore, this reaction is represented by a dashed line. The vertical distance between the ground and the excited states for each species is proportional to the experimental bandgap based on the emission spectra.

experimental value of pK<sup>a</sup> ∗ (Equation 10).

$$\sum\_{i} \chi\_{i} = -\mathbb{S}\_{1} - k\_{0N} - k\_{\mathrm{DN}} - k\_{0\mathrm{C}} - k\_{\mathrm{NC}} - k\_{\mathrm{CN}} \cdot \left[ H^{+} \right] \tag{9}$$

$$K\_a^\* = \frac{k\_{\rm NC}}{k\_{\rm CN}}\tag{10}$$

With the new values for k0N, kDN, kNC, and kCN, we obtained a new guess for k0D (and hence, the linearly dependent kND) by performing a non-linear curve fitting of the experimental values of the long decay time. Then, we repeated the process iteratively until consistent solutions for all the rate constants were achieved, as depicted in **Supplementary Figure S11**.

Finally, we moved to the high pH region to assess the value for the quenching constant k<sup>q</sup> over the neutral form. For this pH region, the bicompartmental matrix has the form

$$\mathbf{A} = \begin{pmatrix} -\left(k\_{0D} + k\_{\text{ND}}\right) & k\_{\text{DN}}\\ k\_{\text{ND}} & -\left(k\_{0N} + k\_{\text{DN}} + k\_q \left[OH^-\right]\right) \end{pmatrix} \tag{11}$$



(*a*)*The associated error for k*0*<sup>D</sup> is very large, so that it cannot be well defined. However, what it is well defined is the sum S<sup>1</sup>* = *k*0*<sup>D</sup>* + *kND* = *0.57* ± *0.03.*

(*b*)*The kDN rate constant is a pseudofirst-order rate for the excimer formation at a constant concentration.*

Analytical expressions for the two eigenvalues can be obtained, with each one assuming the positive or negative root of the following equation (where S<sup>1</sup> = k0D + kND and S<sup>2</sup> = k0N + kDN). excited-state dynamics, of two N-substituted 2-methoxy-9 acridone derivatives.

The acid-base ground-state equilibria of compounds **1** and **2** are in agreement with previous data on 2-methoxy-9(10H) acridone (Schulman and Sturgeon, 1977), i.e., a negative groundstate pK<sup>a</sup> and a notable decrease in the acidity constant upon excitation. In our case, an increase of 1.85 units of pK<sup>a</sup> was found upon excitation of **1**, and 1.84 for compound **2**. These effects are clear examples of photobase behavior, a significantly less studied effect compared to that of photoacids (Sheng et al., 2018). The protonation position was established to occur at the O-atom of the carbonyl group, which acts as an electron acceptor group, whereas the N-atom has an electron donating behavior. This feature as well as the potential steric hindrance of the substituted N-atom make the O-atom the most likely position for protonation (Nikolov et al., 1998). We found additional support for this conjecture from the theoretical calculations (**Figure 8**), which evidenced that protonation at the N-atom would result in a blueshifted absorption with respect to that of the neutral. In contrast, the simulated results for protonation at the carbonyl were in agreement with the experimental the redshifted absorption and emission spectra of the cationic species.

Interestingly, when compounds **1** and **2** were dissolved at near-neutral pH, far from acidic media in which the cation

$$\gamma\_{1,2} = \frac{-\mathcal{S}\_1 - \mathcal{S}\_2 - k\_q \left[ OH^- \right] \pm \sqrt{k\_q \left[ OH^- \right] \left[ k\_q \left[ OH^- \right] - 2 \left( \mathcal{S}\_1 + \mathcal{S}\_2 \right) \right] + (\mathcal{S}\_1 + \mathcal{S}\_2)^2 - 4 \left( k\_{\rm DN} \mathcal{S}\_1 + k\_{\rm D0} \mathcal{S}\_2 - k\_{\rm D0} k\_{\rm N} \right)}}{2} \tag{12}$$

We globally fitted the two experimental decay times, obtained between pH 6.3 and 13.5, to Equation (12), leaving as fixed parameters the already known rate constants, and as a globally adjustable parameter, the value of kq. We obtained a value of 0.035 M−<sup>1</sup> ns−<sup>1</sup> for this constant.

**Table 1** gathers the recovered values of all the rate constants for the excited-state reaction depicted in **Figure 9**. With all these rate constants well-defined, we could predict and simulate all three decay times through the eigenvalues of the complete tricompartmental matrix **A** (Equation 6). These simulations can be seen as the lines in **Figure 4B**, in which one can observe the perfect agreement between the predicted and the experimental values.

#### DISCUSSION

Modified acridone derivatives are among the most widely used compounds with biological activity, due to their small size and easy incorporation into cellular compartments and to their interaction with nucleic acids. With these interesting applications, an in-depth knowledge of their underlying photophysical behavior is mandatory for their usage as antitumoral agents (Cholewinski et al., 2011), in photodynamic therapy or as laser and OLED active media (Sharma et al., 2016; Pander et al., 2018). Herein, we analyzed in-depth the acid-base and spectroscopic properties, as well as the may be involved, striking excited-state dynamics were found (**Figures 4**–**6**). We assigned this result to the formation of an emissive excimer. In a previous report, intermolecular hydrogen bonding was found as the mechanism behind the stabilization of dimers in 4-acridinecarboxamide imines, as suggested by AM1 calculations (Fröhlichová et al., 2009). However, this action was driven by the proton at the acridone N-atom, and in our case, substitution at this position prevented such hydrogen bonding. We also ruled out the possibility of an intramolecular proton transfer involving the hydroxyl radical at the N-hydroxypropyl substituent in **1** with two arguments: (1) theoretical calculations for intramolecular hydrogen bonding could not be optimized, and (2) the results from **2**, lacking the terminal OH group, were practically identical to those from **1**. We also explored the dependency of the formation of the excimer on concentration, and found that the short-lived decay rate became faster and gained statistical weight as the concentration was increased (**Figure 6**), supporting the idea of an intermolecular process. Likewise, we ruled out the possibility of groundstate dimerization or aggregation (**Supplementary Figure S9**). Therefore, we confirmed an excited-state dimerization, which must be driven by π-stacking interactions. Furthermore, we demonstrated, with data from compound **2**, that such behavior is common and may be general for the N-substituted-9 acridone moiety.

At high pH-values, we found a decrease in the long fluorescence decay time (**Figure 4**). This result could be interpreted in terms of an additional pKa, following further deprotonation, as happens in 9-(10H)-acridone and 2-methoxy-9(10H)-acridone (Schulman and Sturgeon, 1977). To test this conjecture, we also obtained the absorption and emission spectra of 2-methoxy-9(10H)-acridone, in which the N position of the chromophoric moiety is not substituted. An additional deprotonation event was evident since both the absorption and emission spectra exhibited clear changes, with the appearance of a blueshifted shoulder, and a clearer vibronic structure at high hydroxyl concentrations (**Supplementary Figure S12**). This confirmed the potential deprotonation of the N-position, and the formation of an anionic species, as previously postulated (Schulman and Sturgeon, 1977). However, this position is hindered in compounds **1** and **2**. Therefore, the decreases in fluorescence intensity and fluorescence lifetime cannot be caused by deprotonation and must be caused by a hydroxylmediated quenching, such as that proposed to affect lanthanide luminescence emissions (Yan et al., 1995; Orlovskii et al., 2016).

With all these data, we established intricate excited-state dynamics (**Figure 9**) in which coupled ESPT reactions and excimer formation-dissociation coexisted with a hydroxylmediated quenching process. This coupled kinetic system was approached with a tricompartmental approach and a thorough iterative fitting protocol. The application of GCA to the study of the complex excited-state dynamics of fluorescent dyes yielded a remarkable improvement in terms of the capabilities and reliability of the obtained results. From simple two-state excitedstate reactions (Boens and Ameloot, 2006) to buffer-mediated ESPT reactions (Boens et al., 2004; Crovetto et al., 2004; Orte et al., 2005a) and complex three-state systems (Orte et al., 2005b), the GCA provided invaluable tools to gain in-depth information on those photophysical systems. Such studies have also helped in the experimental design of experiments suitable enough to obtain unique values for all the rate constants involved in the dynamic systems (Boens et al., 2004; Boens and Ameloot, 2006). To fully solve the system, at very high acidic concentrations, the reduction of available water molecules had to be considered, as previously done in the study of the superphotoacid 2′ ,7′ -difluorofluorescein (Orte et al., 2005b). The complex excited-state dynamics found at acidic pH were successfully modeled, and all the rate constants were defined. The excited-state deprotonation rate of the cationic form was lower than those of the superphotoacids (Tolbert and Solntsev, 2002), indicating that the contribution of the cationic form was weaker in the excited-state. Therefore, the 2-methoxy radical induces a greater electron density to the acridone moiety, which usually results in a stronger base character than that of the unsubstituted acridones (Schulman and Sturgeon, 1977). This notion is supported by the quantum mechanics calculations. In the excited state, the cationic form exhibits an increased electron density on the central oxygen of the acridone moiety, as evidenced in the molecular orbital representations. This position is where the cation is protonated, hence, this shift of the electron density toward the protonable group in the excited-state makes it a weaker acid. For the rest of the pH range, the kinetic rate constants found (**Table 1**) fully describe the excited-state dynamics of the system. Interestingly, we tried other kinetic schemes different to **Figure 9** and found that none were suited to fully explain the system. For instance, we tried a simpler scheme in which the dissociation of the excimer was not considered (kND → 0). In such a case, the model predicted a pH-independent intermediate decay time at low pH-values. This was not in agreement with our observations; therefore, the presence of a dissociation pathway of the excimer was justified, and the validity of **Figure 9** over the entire pH range was confirmed.

In conclusion, N-substituted 2-methoxy-9-acridone derivatives exhibit a rich, dynamic photophysical behavior. Hence, not only are they interesting as potential long-lifetime sensors for FLIM applications, but their strong photobase behavior opens up possibilities for their use in light-driven pH-jump experiments.

## DATA AVAILABILITY

Datasets are available on request. The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

## AUTHOR CONTRIBUTIONS

PH-F, SR, and DM: syntheses and characterization of new compounds. SC: theoretical calculations. DM and JC: design and supervision of the syntheses of new compounds. MG-G and EG-F: spectroscopy experiments. MG-G and AO: Excited-state dynamics and GCA analyses. JA-P, MG-G, and AO: writing of the original draft with input from all authors, who read and approved the submitted version.

## FUNDING

This work has been funded with Grant CTQ2017- 85658-R (Spanish Ministry of Economy and Competitiveness; Agencia Estatal de Investigacion, AEI; and European Regional Development Fund, ERDF) and P12-FQM-790 (Junta de Andalucia).

## ACKNOWLEDGMENTS

We acknowledge support from the Unidad de Excelencia de Química aplicada a Biomedicina y Medioambiente (UEQ), Universidad de Granada. SR is grateful for a FPU fellowship (Spanish Ministry of Education, Culture, and Sports).

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00129/full#supplementary-material

## REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Gonzalez-Garcia, Herrero-Foncubierta, Castro, Resa, Alvarez-Pez, Miguel, Cuerva, Garcia-Fernandez and Orte. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A Cl<sup>−</sup> Hinge for Cyclen Macrocycles: Ionic Interactions and Tweezer–Like Complexes

Juan Ramón Avilés–Moreno<sup>1</sup> , Giel Berden<sup>2</sup> , Jos Oomens <sup>2</sup> and Bruno Martínez–Haya<sup>1</sup> \*

<sup>1</sup> Department of Physical, Chemical and Natural Systems, Universidad Pablo de Olavide, Seville, Spain, <sup>2</sup> FELIX Laboratory, Institute for Molecules and Materials, Radboud University, Nijmegen, Netherlands

The supramolecular networks derived from the complexation of polyazamacrocycles with halide anions constitute fundamental building blocks of a broad range of modern materials. This study provides insights into the conformational framework that supports the binding of protonated cyclen macrocyles (1,4,7,10-Tetraazacyclododecane) by chloride anions through NHδ<sup>+</sup> · · · Cl<sup>−</sup> interactions. The isolated complex comprised of two cyclen hosts linked by one Cl<sup>−</sup> anion is characterized by means of infrared action spectroscopy and ion mobility mass spectrometry, in combination with quantum chemical computations. The Cl<sup>−</sup> anion is found to act as a hinge that bridges the protonated NH<sup>+</sup> <sup>2</sup> moieties of the two macrocycles leading to a molecular tweezer configuration. Different types of conformations emerge, depending on whether the trimer adopts an open arrangement, with significant freedom for internal rotation of the cyclen moieties, or it locks in a folded conformation with intermolecular H-bonds between the two cyclen backbones. The ion mobility collision cross section supports that folded configurations of the complex are dominant under isolated conditions in the gas phase. The IRMPD spectroscopy experiments suggest that two qualitatively different families of folded conformations coexist at room temperature, featuring either peripheral or inner positions of the anion with respect to the macrocycle cavities, These findings should have implications in the growth of extended networks in the nanoscale and in sensing applications.

#### Edited by:

Stefano Falcinelli, University of Perugia, Italy

#### Reviewed by:

John Dyke, University of Southampton, United Kingdom Fernando Pirani, University of Perugia, Italy

> \*Correspondence: Bruno Martínez–Haya bmarhay@upo.es

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 06 February 2019 Accepted: 27 February 2019 Published: 22 March 2019

#### Citation:

Avilés–Moreno JR, Berden G, Oomens J and Martínez–Haya B (2019) A Cl<sup>−</sup> Hinge for Cyclen Macrocycles: Ionic Interactions and Tweezer–Like Complexes. Front. Chem. 7:143. doi: 10.3389/fchem.2019.00143 Keywords: molecular recognition, macrocycles, cyclen, chloride, infrared spectroscopy

## 1. INTRODUCTION

The supramolecular complexes of polyazamacrocycles with halide anions conform intermediate arrangements in the synthesis of a broad range of modern nanostructured materials, with typically catalytic or ion-exchange activity (Alper et al., 1991; Ilioudis and Steed, 2001; Warden et al., 2004a; Mateus et al., 2010; Park et al., 2012; Wenzel et al., 2012; Lee et al., 2013, 2015; Evans and Beer, 2014; Busschaert et al., 2015). The rationalization of the mechanisms of growth of specific molecular networks is challenging and benefits from the fundamental insights and the validation of computational methods gained from the study of precursor macrocycle–anion clusters. The conformational landscape of these clusters can actually become quite complex, depending on the size of the macrocycle and on the degree of protonation of its amine groups Avilés–Moreno et al. Cl<sup>−</sup> Hinge for Cyclen Macrocycles

(Boudon et al., 1991; Ilioudis and Steed, 2001; Warden et al., 2004a,b; Wichmann et al., 2006; Mateus et al., 2010; Wang et al., 2016). The aim of this work is to contribute to the understanding of the anionic supramolecular chemistry of azamacrocycles through the characterization of benchmark aggregates involving the binding of Cl<sup>−</sup> to protonated cyclen (tetraazacyclododecane).

Previous works have investigated the recognition and binding of anions by azamacrocyles and related receptors employing condensed-phase methods, typically UV-vis absorption and fluorescence, NMR spectroscopy, or crystallography techniques (Ilioudis and Steed, 2001; Wichmann et al., 2006; Wenzel et al., 2012; Evans and Beer, 2014; Busschaert et al., 2015). Our investigation is rather based on a systematic investigation of complexes of well-defined stoichiometry under isolated conditions (Rijs and Oomens, 2015). On the one hand, ion mobility mass spectrometry (Jurado-Campos et al., 2018) is employed to obtain a measure of the conformational shape of the complexes. On the other hand, action infrared action spectroscopy (Polfer and Oomens, 2009) serves to elucidate the vibrational modes of the complex after mass selection and storage in an ion trap. The two experimental approaches provide complementary information: where ion mobility probes global structure (overall shape), infrared action spectroscopy is sensitive to the effect that conformations have on the local structure of the complex (atomic interactions and bond strengths). The experiments are analyzed in the light of quantum chemical modeling of the conformational and vibrational features of the isolated molecular systems. In a recent investigation, we employed this methodology to characterize protonated cyclen and provide insights into the structure and intramolecular interactions in the isolated macrocycle (Avilés-Moreno et al., 2018). The present study focuses on supramolecular features that should be relevant to the modeling of azamacrocycle networks, such as the preferred coordination arrangement sustained by the Cl<sup>−</sup> anions and the relative stability of packed sandwich-like configurations vs. open chain-like arrangements. Intermolecular and intramolecular proton bonding networks are analyzed and their implication in the structure of the complex is discussed. Despite the challenges imposed by proton interactions to the accurate description of the system, it is shown that the interrelation between experimental spectroscopy and computations provides insights into fundamental supramolecular features of azamacrocycle/halide frameworks.

## 2. METHODS

#### 2.1. IRMPD Spectroscopy

The infrared multiple photon dissociation (IRMPD) spectroscopy experiments were carried out at the Fourier Transform Ion Cyclotron Resonance mass spectrometry (FT– ICR) beamline of the free electron laser FELIX.<sup>1</sup> IRMPD is a type of action spectroscopy, based on the detection of photofragments produced by the sequential absorption of infrared photons at resonant wavelengths (Polfer and Oomens, 2009).

The ionic complexes were produced by means of electrospray ionization of a 1 mM solution of cyclen (97% purity) and KCl salt (99.9 % purity) in 1:1 water/methanol, acidified with diluted HCl. The resulting product ions were pulse injected into the ICR cell for storage at room temperature. The mass spectrum displayed strong signals at the nominal masses m/z = 381/383, which were assigned to the (cyclen·H+)2·Cl<sup>−</sup> ions (i.e., two protonated cyclen macrocycles bound to a chloride anion). This identification was based on the relative intensities of the isotopic peaks (35Cl/37Cl ∼ 3:1, indicating the presence of one chloride anion) and on the corresponding exact masses (m/z = 381.321/383.318) as determined in separate experiments in which the sample solution was electrosprayed into a high resolution orbitrap mass spectrometer (model Q-Exactive Focus, Thermo Scientific, mass resolution M/1M= 70000).

For the IRMPD spectroscopy experiments, the mass isolated ions were irradiated with 8 free-electron laser infrared macro– pulses. Each macro–pulse is approximately 5 microsecond long, has an energy of about 35 mJ, and consists of a train of micro– pulses with a repetition frequency of 1 GHz. The nominal spectral bandwidth of the radiation amounts to 0.5% of the central wavelength. The dominant IRMPD cationic fragment detected in the present experiment was protonated cyclen (m/z = 173). The IRMPD spectrum was constructed by monitoring the total fragment yield as a function of the wavenumber of the radiation, with linear corrections of the ion yield to account for changes in laser pulse power during scans.

#### 2.2. Ion Mobility Spectrometry

Ion mobility of the isolated (cyclen·H+)2·Cl<sup>−</sup> complexes with m/z = 381 was performed in two separate commercial equipments, namely a Bruker TIMS-TOF mass spectrometer and a Waters Vion IMS QTOF mass spectrometer, with N<sup>2</sup> as buffer collision gas. Several replicates were run leading to a data dispersion of less than 0.1% for the average cross section in each equipment. The resulting room temperature N<sup>2</sup> collision cross sections of the ions were 196.4 and 200.3 Å<sup>2</sup> , respectively. Such difference can be attributed to the technical specificities of the two ion mobility spectrometers, resulting in slightly different calibrations of the cross sections. The value 198 ± 2 Å<sup>2</sup> will be assumed in the present work.

#### 2.3. Quantum Chemistry Calculations

Ab initio MP2 quantum chemical computations were employed to characterize the low energy conformations of the (cyclen·H+)2·Cl<sup>−</sup> ions. An initial ensemble of candidate molecular structures was produced by means of simulated annealing with the universal force field. Additional initial conformations were inspired by the NMR and crystallography data available for related azamacrocyle polychloride complexes (Boudon et al., 1991; Ilioudis and Steed, 2001; Warden et al., 2004b). Independent computations were run for the (cyclen·H+)·Cl<sup>−</sup> subunit to include its most stable coordination arrangements as building blocks in potential seeding structures of the full trimeric complex.

About one hundred non-redundant structures of the complexes were produced, which were initially optimized

<sup>1</sup>http://www.ru.nl/felix/

with density functional theory at the B3LYP-D3 level (B3LYP functional with Grimme's D3 dispersion correction) with the 6-311++G(d,p) basis set. The around fifty most stable conformers were subsequently reoptimized at the MP2/6-311++G(d,p) level. Relative vibrational zero-point corrected electronic energies (1Ezp) were considered to rank the conformations. Natural bond orbital (NBO) analysis (Foster and Weinhold, 1980) was employed for a detailed characterization of the ionic interactions that contribute to the conformational stabilization of the chloride-cyclen complexes.

For comparison with the ion mobility measurements, room temperature collision cross sections with N<sup>2</sup> were computed for the low energy MP2 conformers of the (cyclen·H+)2·Cl<sup>−</sup> complex. For this purpose, we employed a classical trajectory method adapted from previous studies (Mesleh et al., 1996; Campuzano et al., 2012), in which the atoms in the molecular system are treated as individual scattering centers. Within this approach, each atom interacts with N<sup>2</sup> through short-range van der Waals forces and longer-range charge-induced dipole forces. The effective charges for the atoms were adopted from the natural charges derived from the MP2 computation. This methodology was successfully applied in recent ion mobility investigations in our group, involving protonated monomers, dimers, and trimers of alcohols, cetones, and aldehydes of different size (Jurado-Campos et al., 2018).

The theoretical IR spectrum of each conformer was produced by convoluting the normal modes of vibration obtained in the MP2 computation with a line broadening of 25 cm−<sup>1</sup> (full width at half maximum) and a scaling of the MP2 harmonic vibrational frequencies by a factor 0.97. It will be shown that the agreement of the computational IR spectra with the IRMPD measurements demands consideration of anharmonic behavior. Anharmonic corrections of the fundamental vibrational modes of the two most stable conformers of the complex were computed at the B3LYP-D3/6-311++G(d,p) level, with the generalized secondorder vibrational perturbation method (GVPT2) (Barone et al., 2012; Bloino et al., 2012), as implemented in Gaussian 09 (Frisch et al., 2009). A full anharmonic computation was not possible with our computational resources. Therefore, restricted mode computations (Barone et al., 2012) were performed in which the anharmonic treatment was applied exclusively to selected ensembles of fundamental modes involving motions of the protonated -NH<sup>+</sup> <sup>2</sup> moiety, following a similar strategy as the one applied in a previous study for protonated cylen (Avilés-Moreno et al., 2018). The harmonic B3LYP-D3 vibrational frequencies were scaled by a factor 0.985. No scaling factor was applied to the computed anharmonic frequencies.

#### 3. RESULTS

## 3.1. Binary Complex (Cyclen·H+)·Cl<sup>−</sup>

A previous study in our group served to characterize the most salient structural features of isolated protonated cyclen (Avilés-Moreno et al., 2018). It was found that a strong proton bond is formed between two nitrogen atoms across the cyclen cavity. As a result, the vibrational modes of the macrocycle are severely perturbed, posing a serious challenge to the accurate description

indicated (in kJ·mol−<sup>1</sup> ).

of the system. The initial issue that we try to elucidate in this work is to what extent the binding of the chloride anion alters the structure of protonated cyclen. The charge redistribution that accompanies NHδ+· · · Cl<sup>−</sup> bonding can be expected to induce changes in the structure of the cyclen substrate and the strength of the intracavity proton bond.

Our MP2/6-311++G(d,p) computations for the binary cyclenH+·Cl<sup>−</sup> ion pair complex led to the two most stable configurations **B<sup>1</sup>** and **B2**, depicted in **Figure 1**. In the conformation of lowest energy, **B1**, chloride binding induces a reorientation of the NH<sup>+</sup> 2 group in cyclen, leading to a NHδ+· · · N bond angle of 132<sup>o</sup> and a proton bond distance of 2.4 Å across the cavity, in comparison to 161<sup>o</sup> and 1.7 Å in isolated protonated cyclen. Consequently, the intramolecular proton bond is disrupted and the associated stabilization energy, as determined from NBO analysis, decreases by one order of magnitude (15 vs. 220 kJ·mol−<sup>1</sup> ), whereas the protonchloride bond is stabilized by as much as 447 kJ·mol−<sup>1</sup> . In the conformation next in energy for the binary complex, **B2**, the chloride anion occupies a more centered position above the cyclen cavity where it benefits from additional H-bonding with two inward-oriented neutral NH groups in addition to the proton-chloride bond. The distortion of the internal proton bonding in the macrocycle is in this case less appreciable than in conformer **B1**; the NHδ+· · · N bond angle and the proton bond distance are kept at values similar to isolated protonated cyclen, namely 170<sup>o</sup> and 1.8 Å, respectively. The NBO stabilization energy of the intracavity proton bond in **B<sup>2</sup>** stays at a value of 209 kJ·mol−<sup>1</sup> , similar to that of the isolated macrocycle. The corresponding energy of the NHδ+· · · Cl<sup>−</sup> bond is large

(286 kJ·mol−<sup>1</sup> ), but it diminishes appreciably with respect to **B1**. Finally, the contribution of the lateral NH· · · Cl<sup>−</sup> bonds is significant but comparably more moderate, as it amounts to 36 kJ·mol−<sup>1</sup> per bond.

In summary, the MP2 computation predicts two conformations relatively close in energy for the binary complex (cyclen·H+)·Cl−. The internal structure of the two conformations differ in qualitative aspects, such as the relative position of the Cl<sup>−</sup> anion, the orientation of the neutral NH bonds of the macrocycle and the strength of the intracavity proton bond. Both conformers constitute plausible building blocks of the (cyclen·H+)2·Cl<sup>−</sup> complex object of the present study. In fact, it is shown below that binary subunits resembling **B<sup>1</sup>** and **B<sup>2</sup>** are present in most of the low energy arrangements obtained independently for the ternary complex.

## 3.2. Ternary Complex (Cyclen·H+)2·Cl<sup>−</sup>

An ensemble of prototypical low energy folded and open configurations of the (cyclenH+)2·Cl<sup>−</sup> complex predicted by the MP2 computation is depicted in **Figures 2**, **3**. The six conformations of lowest energy, **T1**–**T6**, correspond to folded arrangements stabilized by H-bonding interactions between the cyclen backbones in addition to the NHδ+· · · Cl<sup>−</sup> bonds. Open chain-like conformations, with negligible interactions between the two cyclen hosts were also found in our survey. The most stable of these conformations, **T<sup>7</sup>** and **T<sup>8</sup>** (**Figure 3**), lie ca. 30 kJ·mol−<sup>1</sup> higher in energy than the lowest energy folded conformer **T1**. Despite such high relative energy, the stretched configurations may be entropically favored by the rotational freedom of the two cyclen macrocycles around the chloride bonds. It is therefore not necessarily straightforward to draw predictions about the balance of the net populations of the folded vs. stretched conformational subsets.

We performed ion mobility measurements to assess the overall configuration of the (cyclen·H+)2·Cl<sup>−</sup> complex, seeking to elucidate whether open or folded arrangements are dominant under isolated conditions. Ion mobility mass spectrometry allows to discern between conformations with a significant difference in effective size. Clearly, the compact folded arrangement in conformers **T1**–**T<sup>6</sup>** must have a smaller "collisional" size in comparison to the stretched conformers **T<sup>8</sup>** and **T9**. The experiments yielded a room temperature N<sup>2</sup> collision cross section of 198 ± 2 Å<sup>2</sup> , where the 1% uncertainty is associated with the dispersion of the results obtained in two separate equipments, as mentioned in section 2. The ion mobility spectra displayed a single drift peak with no trace of additional peaks that could be interpreted in terms of the simultaneous presence of complexes in conformational subsets with substantial differences in collision cross section (the full-width at half maximum of the drift peak accounts to less than 3 Å<sup>2</sup> in cross section).

The N<sup>2</sup> collision cross sections obtained in the classical trajectory calculation are indicated next to the corresponding conformers in **Figures 2**, **3**. The simulation predicts cross sections within 193–198 Å<sup>2</sup> for the folded conformers **T1**–**T6**, and consistently larger values of 212 and 218 Å<sup>2</sup> for **T<sup>7</sup>** and **T8**, respectively. The statistical error of the simulations is of less than ±1 Å<sup>2</sup> . A greater source of uncertainty in these simulations arises from the choice of partial charges assumed for the atoms of the system. The NBO natural charge model employed in this study is recognized as a sensible framework with little sensitivity to the choice of basis set (Mao, 2014). Nevertheless, other choices are possible, which may have a sizeable impact on the estimated cross section. Test simulations with Mulliken partial charges for the present system led to cross sections within 2% of the values obtained with NBO charges (i.e., deviations were in all cases smaller than 4 Å<sup>2</sup> ). Differences of similar magnitude have been reported in previous ion mobility studies of other ions (Lee et al., 2018). In the light of these results, it can be concluded that the ion mobility measurements support the greater stability of the folded conformations of the (cyclenH+)2·Cl<sup>−</sup> complex (represented by **T1**–**T6**), under the present isolated conditions.

**Figure 2** shows that in the folded arrangements, the two macrocyles are linked through NHδ+· · · Cl−· · · <sup>δ</sup>+HN bonds, in which the anion virtually acts as a flexible hinge that allows different types of relative orientations and H-bonding interactions between the cyclen backbones. Note that the **B<sup>1</sup>** and **B<sup>2</sup>** conformers of the (cyclen·H+)·Cl<sup>−</sup> ion pair complex can be recognized with slight variations as building blocks of the ternary complexes. **B<sup>1</sup>** can be identified in conformers **T1**–**T4**, although with an inward reorientation of one of the NH bonds in some cases. The higher lying conformers, **T<sup>5</sup>** and **T6**, can be visualized as combinations of **B<sup>1</sup>** and **B<sup>2</sup>** subunits. Interestingly, the stabilization energies associated with the intermolecular proton-halide and the intramolecular protonnitrogen bonds characteristic of the binary conformations **B<sup>1</sup>** and **B<sup>2</sup>** are qualitatively conserved in the ternary conformers. This finding is illustrated in **Figure 3** for selected configurations. It can be appreciated that in **T<sup>1</sup>** strong NHδ+· · · Cl<sup>−</sup> bonds are formed, at the cost of a significant weakening of the intracavity proton bond of the cyclen macrocycles, in the same way as found for the **B<sup>1</sup>** conformer. Incidentally, it is also shown that these same features are present in the open conformations **T<sup>7</sup>** and **T8**, which can actually be considered stretched counterparts of conformer **T1**. Finally, inspection of the stabilization energies in conformer **T<sup>5</sup>** reveals that its subunit analogous to **B<sup>2</sup>** maintains a strong intramolecular proton bond and a somewhat weaker proton bond with Cl<sup>−</sup> than its other **B1**–like subunit.

The proton-bonding and H-bonding arrangements predicted by the MP2 computations can be expected to lead to differentiated spectral signatures amenable of being discerned experimentally. The IRMPD spectrum measured for the (cyclen·H+)2·Cl<sup>−</sup> complex is displayed in **Figure 4**, where it is compared to the computational IR spectra associated with the low energy conformers **T1**–**T6**. The IRMPD spectrum displays a complex progression of partially overlapping bands of varying intensity within the spectral window covered by the present experiments. The MP2 computation reproduces correctly most of the features of the observed IRMPD bands, which facilitates the interpretation of the spectrum. **Table 1** provides a qualitative assignment of the main bands, based on the dominant vibrational motions predicted by the computation in each spectral region. Importantly, the fundamental modes more closely associated to bending motions of the charged NH<sup>+</sup> <sup>2</sup> moieties are located on the high frequency region (scissoring, wagging, band A) and on the low frequency region (rocking, bands G and I) of the recorded spectrum. The central part of the spectral range (1,000– 1,500 cm−<sup>1</sup> ) displays vibrational motions of the remaining groups of the cyclen backbone (C-C and C-N stretching, NH and CH<sup>2</sup> bending vibrations).

The MP2 infrared spectrum for the lowest energy conformer **T<sup>1</sup>** resembles nicely the structure of the IRMPD measurement over most part of the spectral range. The most remarkable difference is related to the apparent absence of band A in the MP2 spectrum. Bands B through F are reproduced fairly well by the computation, despite some differences in their relative intensities. A partial matching is found for bands G, H, and I, associated with rocking vibrations of the NH<sup>+</sup> 2 and NH groups, although in these cases significant discrepancies in shape and relative intensities are found between computation and experiment. In particular, the MP2 computation predicts strong band components in the IR spectrum of **T<sup>1</sup>** within 680–800 cm−<sup>1</sup> , which overestimate the relative yield measured for band H and may contain contributions actually related to band I, for which no clear trace is found in the MP2 spectrum. The MP2 spectra of the higher lying conformers, **T2**–**T6**, display similar discrepancies with experiment for bands H and I, although the agreement improves in the case of **T3**.

The MP2 spectrum of conformers **T4**, **T5**, and **T<sup>6</sup>** do show qualitative differences with respect to **T1**–**T<sup>3</sup>** in the high frequency range. The main novel feature is the presence of intense vibrational transitions for the scissoring bending modes of the NH<sup>+</sup> 2 protonated group at frequencies above 1,500 cm−<sup>1</sup> . This result is remarkable, as it serves to rationalize the presence of band A in the IRMPD spectrum. Double peak structures are found with different positions and relative spacings for each of the conformers. The best agreement is found for **T<sup>5</sup>** which displays transitions in the range 1,560–1,620 cm−<sup>1</sup> , which is coincident with the envelope of the experimental band A. The analogous scissoring transitions predicted for the **T<sup>1</sup>** conformer appear at lower frequencies, ∼ 1,450–1,520 cm−<sup>1</sup> , overlapping in

TABLE 1 | Assignment for the main bands observed in the IRMPD spectrum of the (cyclen·H <sup>+</sup>)2·Cl<sup>−</sup> complex, based on the dominant type of vibrational motions predicted by the MP2/6-311++G\*\* computation (see labels in Figure 4).


frequency with the CH<sup>2</sup> scissoring and NH wagging transitions that conform band B in the MP2 spectrum. This aspect is appreciated in **Figure 5** (red histograms), as discussed below in detail. It becomes apparent from the result of the MP2 computations, that the fundamental modes of the -NH<sup>+</sup> <sup>2</sup> moiety are particularly sensitive to the conformational subtleties of the halide coordination arrangements.

Despite the discrepancies described above, the fairly good overall agreement found between the IRMPD measurement and the computational IR spectra, validates the low energy landscape of the complex described by the conformations depicted in **Figure 2**. Conformational arrangements of the types represented by **T1**–**T<sup>6</sup>** plausibly coexist at room temperature under the present experimental conditions. The joint contribution of various types of folded conformers seems to be required for an appropriate reproduction of the most salient features of the IRMPD spectrum. Whereas, the MP2 spectra of the six conformers reproduce most of the observed bands, **T<sup>5</sup>** and similar conformations improve the agreement and are definitely required to account for band A. In addition, band B of the IRMPD spectrum displays a broadened structure, with a hint of a non-resolved shoulder on its blue flank, that is well-accounted for by the joint contributions of the several conformers.

Our previous IRMPD study of protonated cyclen suggested that anharmonic behavior must be taken into account for the accurate description of the vibrational spectrum (Avilés-Moreno et al., 2018). Therefore, it seemed timely to incorporate anharmonicity to the modeling of the (cyclen·H+)2·Cl<sup>−</sup> complex, seeking to improve the comparison of the computational and experimental spectra. The focus was in the regions below 800 cm−<sup>1</sup> and above 1,400 cm−<sup>1</sup> where the most appreciable differences are found. These spectral regions contain fundamental modes involving vibrational motions of the NH<sup>+</sup> 2 group (see **Table 1**). The most intense of those modes at a harmonic level were selected for the anharmonic treatment, while the rest of modes were kept within the harmonic approximation.

**Figure 5** illustrates the resulting harmonic and partial anharmonic spectra obtained at the B3LYP-D3/6-311++G\*\* level for conformers **T<sup>1</sup>** and **T5**. A histogram representation of

the fundamental frequencies is included, in which the modes chosen for the anharmonic treatment are highlighted in red color for a better visualization of the changes induced by anharmonicity. A total of 12 and 9 fundamental modes were included in the anharmonic computations for **T<sup>1</sup>** and **T5**, respectively. It is interesting to find that the incorporation of the anharmonic corrections brings the computational spectra to a significant better agreement with the IRMPD measurement. For the **T<sup>1</sup>** conformer, the anharmonic computation reproduces quite accurately the position and relative intensities of bands H and I. The effect in the high frequency range of the spectral window is less noticeable, as the anharmonic modes shift slightly with respect to their harmonic counterparts but stay within the envelopes of bands B and C. For the **T<sup>5</sup>** conformer, the agreement for bands H and I also improves appreciably. In this case, the most remarkable finding is related to band A, for which the

protonated moiety of cyclen (modes represented in red color in the bar

diagrams).

anharmonic computation predicts a single dominant vibrational transition at ∼1,600 cm−<sup>1</sup> (as opposed to the bimodal peak structure of the harmonic computation), in excellent agreement with the IRMPD measurement.

The present incursion into the anharmonic behavior of the isolated (cyclen·H+)2·Cl<sup>−</sup> complex provides a more solid qualitative and quantitative support to the conclusion, anticipated from the harmonic computations, that a joint contribution of folded conformations of the **T<sup>1</sup>** and **T<sup>5</sup>** types is required to reproduce the main signatures of the IRMPD spectrum. Hence, the room temperature conformational landscape of the complex can be considered to be wellrepresented by the ensemble of low energy structures compiled in **Figure 2**.

#### 4. SUMMARY AND CONCLUDING REMARKS

A combination of action IRMPD spectroscopy and ion mobility mass spectrometry with quantum chemical computations has served to elucidate the preferential conformations and coordination arrangements in the isolated supramolecular system comprised by two protonated cyclen macrocycles linked by a chloride anion.

The Cl<sup>−</sup> anion bridges the protonated NH<sup>+</sup> <sup>2</sup> moieties of the two macrocycles, leading to a molecular tweezer configuration. The IRMPD experiments suggests that various types of folded conformations coexist at room temperature, featuring either peripheral or inner positions of the anion with respect to the macrocycle cavities and H-bonds between the cyclen backbones (**Figure 2**). Open chain–like configurations (**Figure 3**) lay appreciably higher in energy according to the MP2 computations, and their significant population at room temperature is also ruled out by the ion mobility measurements.

The NH<sup>+</sup> 2 -halide bond shows robustness and flexibility as to provide for a varied landscape of coordination structures with azamacrocycles. The opening and folding of the (cyclen·H+)2·Cl<sup>−</sup> complex in condensed phase can be expected to be modulated by the interactions with neighboring species and solvent molecules, plausibly leading to sensing or caging properties, as well as serving as seeding substrates for the growth of extended networks through additional protonation and incorporation of anions.

The modeling of these materials presents however important challenges, due to the multiple intermolecular and intramolecular proton bonding potentially involved. This study has shown that the proton interactions characteristic of isolated protonated cyclen and of the binary (cyclen·H+)·Cl<sup>−</sup> complex, are to a large extent retained in the (cyclen·H+)2·Cl<sup>−</sup> complex, although with significant differences among the low-energy conformations. In particular, the strength of the intramolecular NH+· · · N proton bond in the cyclen macrocycle and of the intermolecular NH<sup>+</sup> 2 · · · Cl<sup>−</sup> bonds are sensitive to fine details of the coordination geometry and the orientation of the charged moiety with respect to the macrocycle cavity. A complex, plausibly dynamic, picture of halide bonding in azamacrocycles emerges, taking into account that a variety of conformers are likely to be populated at room temperature. Whereas, the overall conformations of the complexes may be captured at a moderate level of theory, the assessment of electronic structure, bond strengths, and the related spectroscopic features is demanding. This study has served to illustrate that the accurate description of the vibrational features of polyazamacrocycles requires an anharmonic treatment of the protonated -NH<sup>+</sup> <sup>2</sup> moieties. Importantly, the application of partial schemes to treat anharmonicity, restricted to specific ensembles of fundamental modes, has been shown to provide a fair approximation to the vibrational spectrum over a broad frequency region. This should be relevant in particular if spectroscopic signatures are to be employed for the elucidation of the coordination structures achieved between the azamacrocycle and the halide anions. We expect that the fundamental insights laid out in this study constitute a valuable benchmark to guide the modeling and characterization of this class of materials.

## DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

## REFERENCES


## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

## FUNDING

I hereby declare that all sources of funding received for the research have been submitted.

#### ACKNOWLEDGMENTS

The research leading to this result has been supported by the project CALIPSOplus under the Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. This study is part of project P12-FQM-4938 of the research programme of Junta de Andalucia and FEDER. We thank C3UPO for the HPC support and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) for the support of the FELIX Laboratory. We are in debt with the pioneering works of professors D. Bassi (Trento), J.M. Farrar (Rochester), and F. Vecchiocattivi (Perugia), who have been inspiring in our own quest for understanding structure and interactions in gas-phase molecular systems of progressively increasing complexity.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Avilés–Moreno, Berden, Oomens and Martínez–Haya. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Gas Phase Oxidation of Carbon Monoxide by Sulfur Dioxide Radical Cation: Reaction Dynamics and Kinetic Trend With the Temperature

Daniele Catone<sup>1</sup> , Mauro Satta<sup>2</sup> \*, Antonella Cartoni 3,4 \*, Mattea C. Castrovilli <sup>4</sup> , Paola Bolognesi <sup>4</sup> , Stefano Turchini <sup>1</sup> and Lorenzo Avaldi <sup>4</sup>

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Nicola Tasinato, Scuola Normale Superiore di Pisa, Italy Xingzhong Cao, Institute of High Energy Physics (CAS), China

#### \*Correspondence:

Antonella Cartoni antonella.cartoni@uniroma1.it Mauro Satta mauro.satta@cnr.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 09 January 2019 Accepted: 25 February 2019 Published: 26 March 2019

#### Citation:

Catone D, Satta M, Cartoni A, Castrovilli MC, Bolognesi P, Turchini S and Avaldi L (2019) Gas Phase Oxidation of Carbon Monoxide by Sulfur Dioxide Radical Cation: Reaction Dynamics and Kinetic Trend With the Temperature. Front. Chem. 7:140. doi: 10.3389/fchem.2019.00140 1 Istituto di Struttura della Materia, Consiglio Nazionale Delle Ricerche (CNR-ISM), Area della Ricerca di Roma Tor Vergata, Rome, Italy, <sup>2</sup> Istituto per lo Studio dei Materiali Nanostrutturati (CNR-ISMN), Dipartimento di Chimica, Sapienza Università di Roma, Rome, Italy, <sup>3</sup> Dipartimento di Chimica, Sapienza Università di Roma, Rome, Italy, <sup>4</sup> Istituto di Struttura della Materia, Consiglio Nazionale Delle Ricerche (CNR-ISM), Area della Ricerca di Roma 1, Rome, Italy

Gas phase ion chemistry has fundamental and applicative purposes since it allows the study of the chemical processes in a solvent free environment and represents models for reactions occurring in the space at low and high temperatures. In this work the ion-molecule reaction of sulfur dioxide ion SO.<sup>+</sup> <sup>2</sup> with carbon monoxide CO is investigated in a joint experimental and theoretical study. The reaction is a fast and exothermic chemical oxidation of CO into more stable CO<sup>2</sup> by a metal free species, as SO.<sup>+</sup> 2 , excited into ro-vibrational levels of the electronic ground state by synchrotron radiation. The results show that the reaction is hampered by the enhancement of internal energy of sulfur dioxide ion and the only ionic product is SO.+. The theoretical approach of variational transition state theory (VTST) based on density functional electronic structure calculations, shows an interesting and peculiar reaction dynamics of the interacting system along the reaction path. Two energy minima corresponding to [SO2–CO].<sup>+</sup> and [OS–OCO].<sup>+</sup> complexes are identified. These minima are separated by an intersystem crossing barrier which couples the bent <sup>3</sup>B<sup>2</sup> state of CO<sup>2</sup> with C2v symmetry and the <sup>1</sup>A<sup>1</sup> state with linear D∞<sup>h</sup> symmetry. The spin and charge reorganization along the minimum energy path (MEP) are analyzed and eventually the charge and spin remain allocated to the SO.<sup>+</sup> moiety and the stable CO<sup>2</sup> molecule is easily produced. There is no bottleneck that slows down the reaction and the values of the rate coefficient k at different temperatures are calculated with capture theory. A value of 2.95 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> is obtained at 300 K in agreement with the literature experimental measurement of 3.00 × 10−<sup>10</sup> ± 20% cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> , and a negative trend with temperature is predicted consistently with the experimental observations.

Keywords: rate constants, temperature, VTST, synchrotron radiation, oxidation, reaction dynamics

## INTRODUCTION

The oxidation of carbon monoxide into carbon dioxide is a challenging topic in chemistry as well as the oxidation of other simple molecules as methane and alcohols (Ten Brink et al., 2000; Guo et al., 2014; Schwarz et al., 2017). CO has a little dipole moment µ<sup>D</sup> of 0.112 D with a partial negative charge on C, the bond length and the polarizability are, respectively 1.13 Å and 1.953 Å<sup>3</sup> (Linstrom and Mallard, 2005). Carbon monoxide is one of the most common environmental pollutants, mainly produced by human activities. It is not a green-friendly molecule due to its high toxicity and many efforts have been devoted to efficiently transform it into CO<sup>2</sup> with molecular oxygen O2. The oxidation is thermodynamically favored but kinetically demanding and relative high temperature and metal catalysts are used. Different metal catalysts have been studied both in solution and at the interface of a solid phase: a growing activity is directed toward the achievement of reactions at room temperature, which represents a more economic solution (Wu et al., 2014; Zhu et al., 2015). Recently, the role of cations in the catalytic converters has been demonstrated to be fundamental for the oxidation at low temperatures (Peterson et al., 2014). At the microscopic level the oxidation corresponds to an "O" atom transfer to CO molecule and in principle neutral or ionic species with high tendency to promote O-transfer should be able to oxidize CO (1H ◦ <sup>f</sup> = −26.42 kcal mol−<sup>1</sup> ) into more stable CO<sup>2</sup> (1H ◦ <sup>f</sup> = −94.05 kcal mol−<sup>1</sup> ) (Linstrom and Mallard, 2005). Although O<sup>2</sup> is the most important oxidant due to its abundance in the Earth's atmosphere, other species, like ions or radical cations, can oxidize CO, also at room temperature and without catalysts (Anicich, 1993a,b; Bacskay and Mackie, 2005). The investigation of the dynamics of these processes is of fundamental interest and may be helpful to develop models for a more efficient, green-friendly and metal-free oxidation of CO (Crabtree, 2009). Moreover, these reactions could also play a role in the chemistry of Interstellar medium and extraterrestrial atmospheres as well as in Earth's atmosphere, mainly troposphere, where H2O, CO, CO2, NOx, O3, SO<sup>2</sup> (present in fraction of ppm, depending on environmental conditions and geographical position, Speidel et al., 2007), and other reactive molecules are in their neutral and ionized forms due to corona discharge phenomena (Cacace and de Petris, 2000; Petrie and Bohme, 2007; Larsson et al., 2012). Recently, we have studied the dynamics of the reaction of hydrogen atom transfer (HAT) of SO.<sup>+</sup> 2 radical cation with methane and water: the HSO<sup>+</sup> 2 ions are formed with high reaction efficiencies in both reactions, but with different kinetic trends vs. temperature (Cartoni et al., 2017). In this work we focus our attention on sulfur dioxide, as the oxidant agent, i.e., source of oxygen atoms. Indeed, SO.<sup>+</sup> 2 can be also a source of "O" in the reactions with neutrals which are more stable in their oxidized form, as in the CO case, since the 1H ◦ f of SO.<sup>+</sup> 2 and SO.<sup>+</sup> is similar, being 213.0 and 239.2 kcal mol−<sup>1</sup> , respectively (Lias et al., 1988). This work reports the investigation of the oxidation of CO molecule in the gas-phase by the metal free radical cation sulfur dioxide:

$$\rm{SO\_2^+} + \rm{CO} \rightarrow \rm{SO^+} + \rm{CO\_2} \tag{1}$$

The rate constant of this reaction, 3.00 × 10−<sup>10</sup> ± 20% cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> , is known from literature at 300 K (Fehsenfeld and Ferguson, 1973), but to the best of our knowledge no experimental details or other data are reported. From the heats of formation (1H ◦ f ) the reaction results exothermic by 41.4 kcal mol−<sup>1</sup> (Lias et al., 1988). Here the reaction dynamics has been explored theoretically by a combination of Density Functional Theory (DFT), Variational Transition State Theory (VTST) (Truhlar and Garrett, 1984; Bao and Truhlar, 2017) and capture theory, which allows to explore the minimum energy path (MEP) of the reaction and to obtain the rate constant as a function of temperature. The effects of spin and charge of the [SO2–CO].<sup>+</sup> complex along the reaction path have been evaluated and discussed to obtain mechanistic details of the process. Estimation of the reaction efficiency (φ = k/kcoll), where k is the experimental rate constant and kcoll the collision rate (Bowers, 1979), has been obtained. The experimental study has been performed at the Elettra synchrotron (Trieste) using tunable VUV radiation to generate "hot" SO.<sup>+</sup> 2 ions in vibrationally excited ionic ground state. The trend of the reaction as a function of photon energy has been measured and compared with the theoretical calculations. This study provides important mechanistic details of the reaction that, in perspective, can be proposed as a possible alternative to be explored for the oxidation of carbon monoxide and for the removal of CO, produced both by human and natural activities, from the lower atmosphere. This is a hot topic in environmental science, since the reaction with oxygen is quite slow and the oxidation with the hydroxyl radical OH, despite seeming to be the main route for the tropospheric CO elimination, is not the only operative mechanism (Jaffe, 1968; Badr and Probert, 1995; Carpenter and Nightingale, 2015). All along the paper the radical symbol '. ' has been omitted for the sake of simplicity.

#### MATERIALS AND METHODS

#### Materials

All the samples were used at room temperature. Sulfur dioxide was purchased from Sigma-Aldrich with a purity >99.98%, whereas CO is from SIAD with purity >99.99%. The security of CO gas line has been continuously checked with the Carbon Monoxide Alarm Ei204EN model from Ei Electronics (Ireland).

#### Experimental Section

The ion-molecule reaction of SO<sup>+</sup> <sup>2</sup> with CO has been investigated at the "Circular Polarization" beamline (CiPo) of ELETTRA synchrotron (Trieste, Italy). The characteristics and the experimental performance of the CiPo beamline at ELETTRA as well of the experimental set-up are reported in previous works (Derossi et al., 1995; Cartoni et al., 2014, 2017, 2018; Castrovilli et al., 2014; Satta et al., 2015a). Briefly, the beamline is provided with an electromagnetic elliptical undulator/wiggler and a Normal Incidence Monochromator to cover the 8–40 eV energy range. The aluminum grating, with a resolving power of about 1,000, was used for the experiment in the energy range 8–17 eV. The SO<sup>+</sup> 2 ions are produced from SO<sup>2</sup> in the ion source (pressure of about 5.0 × 10−<sup>6</sup> mbar) and transported into an octupole, where they react with the neutral reagent CO at a pressure in the range of 10−6–10−<sup>5</sup> mbar. The experiment has been done by recording the ion yields of ionic reagent and products as a function of the photon energy, hν, between 12 and 15 eV (energy step = 100 meV and dwell time = 5 s/point) at the fixed pressure of the neutral reagent (about 10−6–10−<sup>5</sup> mbar) and nominal collision energy (CE) zero. The CE = 0 eV is determined by measuring the SO<sup>+</sup> 2 yield as a function of the retarding field at the entrance of the octupole. An average energy spread of 100 meV was evaluated. The mass spectrum resulting from this ion-molecule reaction has been acquired in the mass over charge range 10<m/z<70 (dwell time of 2s/point) at the photon energy hν = 14.0 eV and CE = 0 eV. No impurities were detected. The production of a very little amount of SO<sup>+</sup> in the ion source, due to the second order radiation, has been observed and considered in data analysis. SO<sup>+</sup> ions do not react with CO as also reported in the literature (Anicich, 1993a,b). The reaction efficiencies were evaluated by calculating the experimental ratio of product/reagent ion intensity (SO+/SO<sup>+</sup> 2 ), and using statistical propagation error formula to estimate the error bars. Data analysis has been performed using OriginPro8 program.

#### Theoretical Section

The optimal choice of the computational level for the energetic and dynamic description of the title reaction has been a subtle task due to the difficulty to concurrently reproduce the correct magnitude and direction of the electric dipole moment of CO, and the enthalpies of the oxygen-breaking reactions CO<sup>2</sup> → CO + O(3P) and SO<sup>+</sup> <sup>2</sup> <sup>→</sup> SO<sup>+</sup> <sup>+</sup> O(3P). The energetic of these dissociation reactions has to be correctly described in order to obtain a reasonable MEP along which the oxygen transfer takes place. Several levels of ab-initio methods, including Second-Order Møller-Plesset Perturbation Theory MP2 (Head-Gordon et al., 1988), Becke 3-Parameter (Exchange), Lee, Yang and Parr B3LYP (Lee et al., 1988) and Minnesota Functionals M06L (Zhao and Truhlar, 2006) with different basis sets, have been tested. The τ (kinetic energy density) dependent functional Voorhis and Scuseria's kinetic-energy-dependent exchange–correlation, VSXC (van Voorhis and Scuseria, 1998), produces reasonable energetic data when applied to open shell molecules (Johansson, 2006; Gao et al., 2013; Gao and Li, 2014). The VSXC has demonstrated the ability to reproduce both the CO electric dipole moment and reaction enthalpies with the basis set Augmented Triple-zeta correlation-consistent polarized, aug-ccpvtz (Dunning, 1989) on sulfur and carbon atoms, and cc-pvtz on the three oxygen atoms. The electric dipole moment of CO has been calculated as 0.189 D which is in agreement with the experimental value of 0.112 D (Linstrom and Mallard, 2005), with the electric negative pole correctly located on the carbon atom. The enthalpies of the oxygen dissociation from CO<sup>2</sup> and SO<sup>+</sup> 2 have been calculated, 131.9 and 86.2 kcal mol−<sup>1</sup> respectively, while the corresponding experimental values are 127.3 and 84.4 kcal mol−<sup>1</sup> (Linstrom and Mallard, 2005), with computational errors below 5%. The calculation of the reaction enthalpy of the title reaction gives 45.7 kcal mol−<sup>1</sup> , which is in agreement with the experimental value of 41.4 kcal mol−<sup>1</sup> (Lias et al., 1988). All these calculations have been corrected by the zero point energies (ZPE), with the underlying harmonic vibrational frequencies scaled by the coefficient 0.986 (Alecu et al., 2010).

The MEP of the reaction has been studied by partial geometrical optimization of all the nuclear degrees of freedom except the molecular coordinates over which the scan has been performed. The symmetry of the system and the barrierless nature of this reaction do not allow for the use of a single coordinate to describe the whole MEP over which the exothermic reactive process occurs. The reaction has been divided in three sections: the first one considers the initial evolution with the reactants coming together and forming the initial complex (the scanning coordinate is S-C distance); the second section involves the transformation of the initial complex into a second, more stable one (here the scan has been performed over C-O distance); the third part of the MEP follows the reaction from this more stable complex to the products region (the scanning coordinate is the S-O distance). For a better understanding of the construction of the MEP see also the section Results and Discussion. The charge and spin population are based on the Mulliken analysis of the electron density (Mulliken, 1955). All the quantum chemical calculations were performed with the Gaussian09 package (Frisch et al., 2016)

The MEP has been used to compute the total molecular partition functions [Q(T)] of the reactive complex [SO2– CO]<sup>+</sup> in the range of temperatures 300–6,000 K. Within the Variation Transition State Theory (VTST) (Bao and Truhlar, 2017) these partition functions are used to localize the kinetic bottleneck of the reactive flux of trajectories moving along the MEP. The relative structure will be discussed in the following sections together with the temperature dependent Langevin rate coefficient modified and parametrized for the ion-polar molecules reactions (Su, 1994). This rate coefficient depends on the polarizability and dipole moment of the neutral reagent molecule, which we have calculated at the same level of theory described above, and whose values in atomic units are, respectively 12.86 and 0.0744. The electron charge and spin densities have been described by surfaces with isovalue of 0.2 au and 0.02 au, respectively.

#### RESULTS AND DISCUSSION

The photoelectron spectrum of SO<sup>2</sup> reported in the literatures (Wang et al., 1987; Holland et al., 1994; Li et al., 2004) shows two bands in the energy range 12-15 eV, the ground X <sup>2</sup>A<sup>1</sup> state (12.349 eV) and two excited electronic states: <sup>2</sup>B<sup>2</sup> (12.988 eV) and <sup>2</sup>A<sup>2</sup> (13.338 eV) very close in energy. As already widely discussed in our previous work (Cartoni et al., 2017) the SO<sup>+</sup> 2 ions produced in these excited states decay to excited ro-vibrational levels of the electronic ground state of the ion in a time scale of about 10 ns (Dujardin and Leach, 1981; Lévêque et al., 2014), i.e., shorter than the few ms needed to reach the reaction zone, where the interaction with the CO molecule occurs. Moreover, as checked in our measurements and demonstrated by a photoelectron-photoion coincidence (PEPICO) study (Brehm et al., 1973) the SO<sup>+</sup> 2 ions do not dissociate in the energy range explored in this work. Following these experimental evidences the reagent SO<sup>+</sup> 2 is considered a hot ion in its electronic ground state with an increasing internal energy as photon energy increases from the ionization threshold of SO<sup>2</sup> at 12.349 eV (Linstrom and Mallard, 2005). The mass spectrum obtained by the ion-molecule reaction between SO<sup>+</sup> 2 and CO is shown in **Figure 1A**, while the mass spectrum of SO<sup>2</sup> alone, before the reaction, is shown in the supplementary material (**Figure 1S**).

The only ionic product observed is the ion SO<sup>+</sup> at m/z 48 produced by the "oxygen-transfer" from SO<sup>+</sup> 2 to CO. Accordingly, the CO<sup>2</sup> molecule is the neutral counterpart generated in this reaction. In **Figure 1B** the SO<sup>+</sup> ion intensity as function of CO pressure at the photon energy 14.0 eV is reported. The trend shows that SO<sup>+</sup> is produced by reaction (1). The yields of the reagent SO<sup>+</sup> 2 and product SO<sup>+</sup> ions have also been recorded as function of photon energy and different fixed pressures of reagent gas, CO. The SO+/SO<sup>+</sup> 2 ratios vs. photon energy are reported in **Figure 2**.

The results show clearly that, at all pressures, the reaction is not favored by the increased internal energy of SO<sup>+</sup> 2 , suggesting the formation of a possible weakly bound complex between SO<sup>+</sup> 2 and CO and a very fast process. To the purpose the reaction efficiency, φ, relative to the collision rate (kcoll) (Su and Chesnavich, 1982; Su, 1994) of the reaction was estimated considering the experimental kinetic constant k = 3.00 × 10−<sup>10</sup> ± 20% cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> at 300 K (Fehsenfeld and Ferguson, 1973). The calculated φ values were around 1 considering both the kcoll = 2.81 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> (Su and Chesnavich, 1982) and 2.95 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> (Su, 1994) at 300 K, the latter model being more accurate. The high reaction efficiency demonstrates the effectiveness of this reaction.

To explore the reaction dynamic of this interesting and apparently simple system, a challenging and complete theoretical study has been performed.

The MEP is characterized by a barrier connecting two minima corresponding to a first reagent complex [SO2–CO]<sup>+</sup> **1**, and a second more stable product complex [OS–OCO]<sup>+</sup> **2** (**Figure 3**). This energy barrier is well-below the energy of the reagents, and hence the entire reaction results to be barrierless. The labels of the oxygen atoms used trough this discussion are those presented in **Figure 3** where the O<sup>a</sup> is the inactive spectator oxygen bound to the S atom, O<sup>b</sup> is the atom transferred from the S to the C atom, and the O<sup>c</sup> is the inactive atom bound to the carbon atom.

The MEP connecting the asymptotic energy levels of the SO<sup>+</sup> 2 and CO reagents with those of the products has been divided in three parts (see **Figure 3**): (i) from the reagents to the first complex **1** [SO2–CO]+, where the scanning coordinate is the S-C distance; (ii) the second part of the MEP connects the first complex **1** to the second one [OS–OCO]<sup>+</sup> **2**, and the scanning coordinate is the Ob-C distance; (iii) the last section of the MEP describes the system from the second complex **2** to the final products SO<sup>+</sup> and CO2, with the Ob-S distance as scanning coordinate. The first complex, [SO2–CO]<sup>+</sup> **1**, has a C2v symmetry and an energy of −0.974 eV (−22.5 kcal mol−<sup>1</sup> ) with respect to

TABLE 1 | Main geometrical parameters of the adduct ions of the [SO2/CO].<sup>+</sup> system showed in Figure 3 along the minimum energy path, calculated at the DFT level of theory (see main text for further details).


R is in Å and θ in deg.

the energy of the reagents (which is the energy reference for all the energies given therein). The S-C distance is 3.1 Å, the O<sup>b</sup> and C atoms are 2.7 Å apart and the OSO angle of 123.8 deg (see also **Table 1**).

In the central panel of **Figure 3** it is represented the region of the MEP with the barrier, at an energy of −0.626 eV (−14.4 kcal mol−<sup>1</sup> ), which leads the system to the region of the products, by passing through an intersystem crossing point which connects the <sup>1</sup>A<sup>1</sup> and <sup>3</sup>B<sup>2</sup> lower electronic energy levels of CO<sup>2</sup> (Zhou et al., 2013 see **Figures 2S**, **3S** in the supplementary material for the discussion of the angle dependence OCO over the triplet and singlet ground states for CO<sup>2</sup> alone and OCO inside the reacting system). The minimum energy geometry of the <sup>3</sup>B<sup>2</sup> state of CO<sup>2</sup> has a C2v symmetry, whereas its <sup>1</sup>A<sup>1</sup> has a linear D∞<sup>h</sup> symmetry. This crossing can be analyzed also through the spin and charge Mulliken population shown in **Figures 4**, **5**. The triplet-singlet change has been obtained in the spin population (**Figure 4**) of OCO in the complex, which switches from the structure **BC**, in which the OCO has a bent geometry with high spin resembling the <sup>3</sup>B<sup>2</sup> state of CO2, into the **AC** complex in which the OCO is linear and has a low spin electronic distribution.

This crossing is associated with a sudden change in the electronic density: before the crossing the complex **BC** has a planar node in the wavefunction along the C-O<sup>b</sup> bond, while after the crossing the planar node is transferred to the S-O<sup>b</sup> bond in structure **AC** (see **Figure 5**). The second complex **2** has the minimum [OS–OCO]<sup>+</sup> energy along the MEP with a value of −2.888 eV (−66.6 kcal mol−<sup>1</sup> ), and a S-O<sup>b</sup> distance of 2.3 Å. In this complex **2** the OCO has almost D∞<sup>h</sup> symmetry, with the two C-O distances, C-O<sup>b</sup> and C-Oc, of 1.2 Å. After the crossing the high spin density is entirely located on the SO subsystem, with the S atom increasing its spin population up to that of the free SO<sup>+</sup> +0.641 h, whereas the spin population of the O ¯ <sup>a</sup> reaches the value of +0.359 h. Another interesting feature appearing ¯ both in **Figures 4**, **5** is the discontinuity in the spin and partial charge atomic population at the S-C distance of about 3.75 Å. Here there is a symmetry modification of the system, which changes from the C<sup>s</sup> symmetry of the initial complex (see leftmost structure in **Figure 3**), to the C2v symmetry of the [SO2–CO]<sup>+</sup> complex **1**. Indeed, at greater S-C distances the CO and SO<sup>2</sup> are bound only via the S-Ob-C atoms, whereas the interaction for shorter S-C distances is characterized by double Oa-C and Ob-C intermolecular forces. The C2v symmetry of this part of the

FIGURE 4 | The atomic spin Mulliken population is presented for the nuclei of the molecular adducts along the coordinates that describe the MEP. The structures represent the most relevant molecular complexes during the reaction: the first minimum complex (1), the structures before (BC) and after (AC) intersystem crossing, and second complex (2) are presented. The green isosurfaces represent the spin density surface around the atoms participating in the reaction. The gray arrows indicate the values of the different coordinates corresponding to the four relevant molecular structures. For further details see the main text.

products. The structures and the electronic isodensity surfaces of the first minimum complex (1), structures before (BC) and after (AC) intersystem crossing, and second complex (2) are presented. The gray arrows indicate the values of the different coordinates corresponding to the four relevant molecular structures. For further details see the main text.

reaction is confirmed by the fact that the O<sup>a</sup> and O<sup>b</sup> atomic partial charges are almost equal in the region of the MEP that foregoes the first complex **1**, and also in the region that follows the same complex almost up to the point of intersystem crossing at ROb−<sup>C</sup> of 1.55 Å.

Because of the barrierless nature of the MEP associated with the O transfer from SO<sup>+</sup> 2 to CO, the VTST (Carelli et al., 2011; Satta et al., 2015b; Bao and Truhlar, 2017 ) is the computational model used to study the dynamics of this reaction. We have considered a molecular partition function Qirc defined as the total molecular partition function with the vibrational part built over all the frequencies except the one relative to the internal reaction coordinate (IRC). The Qirc, including the zero point contribution is reported as a function of the three distances used to calculate the MEP of the reaction (**Figure 6**). However, the reaction coordinate ranges over which the Qirc has been built

FIGURE 6 | Molecular partition function of the adduct [SO2–CO]<sup>+</sup> during the reaction at T <sup>=</sup> 300 K. The three panels correspond to the three reactive regions of the approaching reactants, intersystem crossing, and products formation. Complex (1), (2) and intersystem crossing are indicated with gray arrows. The green star indicates the location of the variational transition state (VTS).

is different from that of the MEP because otherwise it was not possible to define correctly the IRC frequency needed by VTST.

In the first approaching region (**Figure 6** left panel), Qirc increases and then rapidly decreases up to a minimum value corresponding to the formation of the first complex [SO2–CO]<sup>+</sup> **1**; in the second region (**Figure 6** central panel) there is a first small barrier in the molecular partition function and then there is a decrease up to a double minimum at ROb−<sup>C</sup> of 1.7 Å. This is followed by a second barrier that brings very rapidly the system to the absolute minimum of the molecular partition function at ROb−<sup>S</sup> of 2.4 Å, corresponding to a geometry that resembles very strongly the [OS–OCO]<sup>+</sup> complex **2** (**Figure 6** right panel). The overall behavior of the molecular partition function at T = 300 K, with its absolute minimum in the region of the MEP that brings the system, after the intersystem crossing, from the more stable complex to the products, is such that the reaction has not a bottleneck up to the formation of the complex **2**. Indeed this minimum corresponds to a dynamic state that resembles the products, and that cannot re-escape to the region of the reactants due to the energy barrier associated with the <sup>3</sup>B2/ <sup>1</sup>A<sup>1</sup> crossing involving the C2v/D∞<sup>h</sup> symmetry change of the forming CO2. The same qualitative behavior is observed for higher temperatures up to 6,000 K. The barrierless reaction has the VTST dynamic slowdown essentially in the region where the products are formed, hence the rate of the reaction can be determined by the capture theory. The simple Langevin formula for ion-molecule reaction predicts a constant rate coefficient with temperature, and since we aim to study the experimental decrease of the reaction probability with temperature, a capture collision rate constant based on trajectory calculations has been computed. In particular, we followed the parametrization of kinetic energy dependences of ion-polar molecule collision rate constants developed by Su (1994). This approach, which uses the dipole moment of the neutral reactant together with its polarizability, gives a temperature dependent rate coefficient k. In **Figure 7** it is reported the k for a temperature range from 300 up to 6,000 K. Its value at 300 K is 2.95 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> , in very good agreement with the experimental value of 3.00 × 10−<sup>10</sup> ± 20% cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> (Fehsenfeld and Ferguson, 1973). The increase of temperature determines a slow decrease in the rate coefficient, and at 6,000 K the rate of the reaction is only about 2% less than that at 300 K. This slow thermal trend is due to the quasi apolar nature of the CO molecule, which has a very low electric dipole moment (0.112 D). The model predicts that, at increasing temperature, the effect of the dipole moment of the neutral reactant on the effective interaction potential will be of weak decreasing strength: the thermal rotation average of the dipole moment will overcame the orientation effects induced by the charge of the ion. At variance, in the case of water, which has an electric dipole moment about 16 times greater than that of CO, the calculated rate coefficient decreases by a factor of 2.4 from 300 to 5,000 K (Cartoni et al., 2017). Even if we cannot directly compare the experimental SO+/SO<sup>+</sup> 2 ratio with the calculated rate coefficients, both the experimental and computational data show the same behavior: the reaction efficiency decreases with increasing energy content. The experimental trend is the same at the three pressures investigated, where almost the same decrease of about a factor of three is observed as a function of photon energy. A direct quantitative comparison between theory and experiments is not achievable because in the experiments the thermal condition could not be fulfilled.

The spin and charge trend calculated along the MEP, where effectively the spin and charge remain on SO<sup>+</sup> moiety, thanks to the crossing point, could contribute to the high efficiency observed in this reaction.

## CONCLUSIONS

In this work a joint experimental and theoretical study of the ion-molecule reaction of the metal free sulfur dioxide ion SO<sup>+</sup> 2 with carbon monoxide CO is reported. The "O" atom transfer reaction from SO<sup>+</sup> 2 to CO is fast and efficient (<sup>φ</sup> <sup>=</sup> k/kcoll ∼=1) and highly exothermic by about 45 kcal/mol, with an interesting reaction dynamics along the reaction path. Two energy minima are identified, [SO2–CO]<sup>+</sup> and [OS–OCO]<sup>+</sup> separated by an intersystem crossing barrier, with energy below that of the reagents, which couples the bent <sup>3</sup>B<sup>2</sup> state of CO<sup>2</sup> with C2v symmetry with <sup>1</sup>A<sup>1</sup> state with linear D∞<sup>h</sup> symmetry. The spin and charge reorganization along the MEP are analyzed and eventually the charge and spin remain allocated to the SO<sup>+</sup> moiety while CO<sup>2</sup> molecule is rapidly formed. The values of the rate coefficient k at different temperatures are calculated with the capture theory. The value of 2.95 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> is obtained at 300 K in very good agreement with the literature experimental value 3.00 × 10−<sup>10</sup> cm<sup>3</sup> s <sup>−</sup>1molecule−<sup>1</sup> ± 20%. The k values have a predicted negative trend with temperature, as also observed in the experiments. In the experimental conditions the formation of the weakly bound interacting collision complex is not favored at high internal energy of SO<sup>+</sup> 2 , probably due to an increase of the elastic scattering processes between nonthermalized reagents, namely a room temperature CO and a hyperthermal SO<sup>+</sup> 2 .

## DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

## AUTHOR CONTRIBUTIONS

AC planned the experiments. DC, AC, MC, PB, and ST contributed to the experiments. DC performed data analysis. MS performed the theoretical calculations. AC and MS wrote the manuscript. LA reviewed the manuscript. All authors gave their contribution to the discussion of the results and the preparation of the manuscripts.

#### FUNDING

This work was supported by the Ministry of Education, University and Research (MIUR RBFR10SQZI), Fund for Basic Research Investments.

## ACKNOWLEDGMENTS

The authors thank S. Rinaldi, F. Zuccaro, and M. Brolatti for technical assistance.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00140/full#supplementary-material

## REFERENCES


Mulliken, R. S. (1955). Electronic population analysis on LCAO–MO molecular wave functions. I. J. Chem. Phys. 23, 1833–1840. doi: 10.1063/1.1740588


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Catone, Satta, Cartoni, Castrovilli, Bolognesi, Turchini and Avaldi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Quantum Behavior of Spin-Orbit Inelastic Scattering of C-Atoms by D<sup>2</sup> at Low Energy

Astrid Bergeat <sup>1</sup> \*, Sébastien B. Morales <sup>1</sup> , Christian Naulin<sup>1</sup> , Jacek Kłos <sup>2</sup> and François Lique<sup>3</sup>

<sup>1</sup> Univ. Bordeaux, CNRS, ISM, UMR 5255, Talence, France, <sup>2</sup> Department of Chemistry and Biochemistry, University of Maryland, College Park, MD, United States, <sup>3</sup> LOMC - UMR 6294, CNRS-Université du Havre, Le Havre, France

Fine-structure populations and collision–induced energy transfer in atoms are of interest for many fields, from combustion to astrophysics. In particular, neutral carbon atoms are known to play a role in interstellar media, either as probes of physical conditions (ground state <sup>3</sup>P<sup>j</sup> spin-orbit populations), or as cooling agent (collisional excitation followed by radiative decay). This work aims at investigating the spin-orbit excitation of atomic carbon in its ground electronic state due to collisions with molecular deuterium, an isotopic variant of H2, the most abundant molecule in the interstellar medium. Spin-orbit excitations of C(3P<sup>j</sup> ) by H<sup>2</sup> or D<sup>2</sup> are governed by non-adiabatic and spin-orbit couplings, which make the theoretical treatment challenging, since the Born-Oppenheimer approximation no longer holds. Inelastic collisional cross-sections were determined for the C(3P0) + D<sup>2</sup> → C(3P<sup>j</sup> ) + D<sup>2</sup> (with j = 1 and 2) excitation process. Experimental data were acquired in a crossed beam experiment at low collision energies, down to the excitation thresholds (at 16.42 and 43.41 cm−<sup>1</sup> , respectively). C-atoms were produced mainly in their ground spin-orbit state, <sup>3</sup>P0, by dissociation of CO in a dielectric discharge through an Even-Lavie pulsed valve. The C-atom beam was crossed with a D<sup>2</sup> beam from a second valve. The state-to-state cross-sections were derived from the C(3P<sup>j</sup> ) (j = 1 or 2) signal measured as a function of the beam crossing angle, i.e., as a function of the collision energy. The results show different quantum behaviors for excitation to C(3P1) or C(3P2) when C(3P0) collides with ortho-D<sup>2</sup> or normal-D2. These experimental results are analyzed and discussed in the light of highly accurate quantum calculations. A good agreement between experimental and theoretical results is found. The present data are compared with those obtained for the C-He and C-H<sup>2</sup> collisional systems to get new insights into the dynamics of collision induced spin-orbit excitation/relaxation of atomic carbon.

Keywords: chemical physics, dynamics of molecular collisions, inelastic collisions, astrochemistry, crossedmolecular beam, theoretical calculations, spin-orbit excitation

## INTRODUCTION

Processes controlling internal state population distributions of atomic or molecular species are of interest in many fields. This is especially the case for astrophysics. In particular, information concerning the physical conditions prevailing in interstellar media can only be retrieved from spectra yielding the internal states relative populations of the observed species, which result from

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Robert Forrey, Penn State Berks, United States Stefan Willitsch, Universität Basel, Switzerland

\*Correspondence: Astrid Bergeat astrid.bergeat@u-bordeaux.fr

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 02 January 2019 Accepted: 04 March 2019 Published: 28 March 2019

#### Citation:

Bergeat A, Morales SB, Naulin C, Kłos J and Lique F (2019) Quantum Behavior of Spin-Orbit Inelastic Scattering of C-Atoms by D2 at Low Energy. Front. Chem. 7:164. doi: 10.3389/fchem.2019.00164

**69**

the equilibrium between collisional and radiative processes. For that purpose, neutral carbon atoms are of particular interest, since they are known to play a role in interstellar media, either as probes of physical conditions (ground state <sup>3</sup>P<sup>j</sup> spinorbit populations), or as a cooling agent (collisional excitation followed by a radiative decay). Indeed, C atoms are very abundant in many interstellar regions ranging from dense molecular clouds to planetary nebulae (Zmuidzinas et al., 1988; Bensby and Feltzing, 2006; Herbst and Yates, 2013). Hence, modeling the fine-structure population of C atoms is of major interest for astrochemical models. Such models rely on both collisional and radiative data. Collisional cross-sections and rate coefficients implying the C atoms and the dominant collisional partners in the interstellar medium (H2, He, H) have then to be determined at low temperatures. However, when molecular collisions (reactive or inelastic) occur at low energy/temperature, in the near cold regime (1–50 K), resonances are predicted by theory for many systems. Such resonances have been clearly observed in the collision energy dependent integral crosssections (ICS) for spin-orbit excitation of C(3P0) by collisions with He (Bergeat et al., 2018) and H<sup>2</sup> (Kłos et al., 2018). These processes are governed by non-adiabatic and spin-orbit couplings, which makes the theoretical treatment challenging since the Born-Oppenheimer (Born and Oppenheimer, 1927) approximation no longer holds. The challenge was successfully overcome for the C(3P)+He two-atomic system (Bergeat et al., 2018): the excellent agreement between experimental results and theory allowed a detailed description of resonance features by theory to be obtained. The situation was quite more complex for the C(3P)+H<sup>2</sup> three-atomic system (Kłos et al., 2018), where multiple diabatic potential energy surfaces (PESs) along with spin-orbit and non-adiabatic couplings are necessary to describe its dynamics. A good agreement was also found, not sufficient however to allow for a clear assignment of resonances involving too great of a number of partial waves. Moreover, at higher collision energies, an intersystem crossing may occur with the PESs emerging from the C(1D)+H<sup>2</sup> insertion reaction. In the energy regions close to the intersystem crossing, one can expect, that the use of only triplet PESs will be too approximate to describe the collisional excitation of the C atom, which was not investigated in the study of C+H<sup>2</sup> collisions (Kłos et al., 2018). Moreover, most recently, Shen et al. (2017) elucidated importance of the stationary points, in particular the so-called van der Waals saddles in the entrance channel region of the C(1D)-H<sup>2</sup> reaction. Therefore, it is also of interest to confirm the characterization of the entrance channel in the C(3P)-H<sup>2</sup> system. Our experiments will allow to test the C(3P)-H<sup>2</sup> PESs in the lower region of collision energies.

In order to get a clearer insight into the latter system, new experiments and calculations have been performed on the isotopolog system so that the C(3P0) + D<sup>2</sup> → C(3Pj) + D<sup>2</sup> (with j = 1 and 2) collisional process have been studied. Measurements of state-to-state cross-sections as a function of the collision energy for C(3P)-D<sup>2</sup> scattering have been achieved, using the same apparatus as the one described in our previous studies on C(3P)-He (H2) inelastic collisions. Quantum dynamical calculations were performed with the same TABLE 1 | Characteristics of the molecular beams used in the determination of the integral cross-sections.


<sup>a</sup>Temperature set point of the cold head. The effective temperature of the pulsed valve is limited by losses due to thermal radiation. The effective nozzle temperatures deduced from the He beam velocity are given in parentheses.

<sup>b</sup>Beam velocity peak values and spreads were deduced from temporal profiles recorded at the crossing point by REMPI detection, and at d = 393.3 mm downstream, with a fast-ionization gauge (FIG) inserted perpendicular to the molecular beam.

<sup>c</sup>Pulse duration at the crossing point (hwe) deduced from the REMPI signals.

<sup>d</sup>Angular divergence (HWE).

PESs as for C(3P)-H<sup>2</sup> system and differing by the reactant reduced mass and rotational constant of D2: it thus provides a further test of these potential energy surfaces that are mandatory to accurately describe and understand the dynamics of the title system.

#### METHODS

#### Experiment

Integral cross-sections were measured using a crossed beam apparatus, with variable crossing angle. The C and D<sup>2</sup> beams with low velocities and high velocity resolution (see **Table 1**) were obtained using two cryogenically cooled Even-Lavie pulsed valves (Pentlehner et al., 2009) and collided at a beam intersection angle which could be continuously varied from 90◦ to 12.5◦ (Chefdeville et al., 2012). C-atoms were produced by dissociation of CO diluted in neon in a dielectric barrier discharge incorporated in the faceplate of the valve (Even, 2015). ortho-D<sup>2</sup> (hereafter o-D2) was produced after spin-conversion in a cryogenic cell by liquefaction of normal-D<sup>2</sup> (hereafter n-D2) on NiSO<sup>4</sup> catalyst at low temperature (<20 K), every 45 min. The n-D<sup>2</sup> and o-D<sup>2</sup> beam velocities were changed by adjusting the temperature of the valve cold head (see **Table 1** for the different experimental conditions).

The collision energy, ET, in our crossed beam machine was varied by changing the angle between the two supersonic beams from χ = 90◦ to 20 or 13◦ : E<sup>T</sup> = 1 2 µ n v 2 <sup>C</sup> + v 2 D2 <sup>−</sup> <sup>2</sup>vCvD<sup>2</sup> cosχ o .

The carbon atoms were probed in their various spin-orbit states via (2+1) resonance-enhanced multiphoton ionization (REMPI) technique, using 2-photon 2p2 3P<sup>j</sup> → 2p3p <sup>3</sup>P<sup>j</sup> transitions (excitation laser tuned at 280.3 nm) at 140.149 nm, 140.157 nm and 140.170 nm for the C(3P0), C(3P1) and C(3P2), respectively (Geppert et al., 2003). A third photon ionized the carbon atoms and C<sup>+</sup> is detected by a time-of-flight (TOF) mass spectrometer. Populations of ca 90–96% for C(3P0), 4– 10% for C(3P1), and < 1% for C(3P2) were deduced from the intensities of these transitions, consistently with previous Bergeat et al. C(3P<sup>j</sup>

experimental conditions #2, #3, and #4 given in Table 1.

studies (Bergeat et al., 2018; Kłos et al., 2018). The laser beam was perpendicular to the crossing beams plane, hence avoiding any Doppler shift while scanning the crossing angle, χ, for the ICS measurements. Spectra obtained by 3+1 REMPI on the transitions C <sup>1</sup>5<sup>u</sup> v ′ = 3, j ′ ←− X <sup>1</sup>6<sup>+</sup> g (v ′′ = 0, j ′′) were employed to detect individual D<sup>2</sup> rotational levels (see **Figure 1**). Only the lowest rotational level of each nuclear spin modification, i.e., jD<sup>2</sup> = 0 and 1 for o-D<sup>2</sup> and p-D2, respectively, was found to be populated in the supersonic beams. The only exception was for o-D2, 100 K: a small signal can be seen for the R(2) transition. The ortho converted-D<sup>2</sup> was found to contain <6% para-D2. These values were found to change inappreciably over the D<sup>2</sup> velocities (or the temperature of the valve) and over 1.5 h.

The beam velocities and spreads (**Table 1**) were deduced from temporal profiles recorded at the crossing point by REMPI detection or with a fast ionization gauge (FIG) inserted perpendicular to the molecular beam, and at d = 393.3 mm downstream, with a second FIG. D<sup>2</sup> can be detected with the

FIGURE 2 | REMPI or FIG profiles at crossing point, of n-D2 (for a cold head at 45 K). D<sup>2</sup> molecules in the rotational levels j = 0 and 1, were detected using the R(0) and R(1) transitions (blue circles and red diamonds); C(3P2) atoms, produced by collisions with the D<sup>2</sup> beam at 70◦ of the C beam were also detected (orange stars). Vertical error bars correspond to statistical uncertainties of 50 laser shots at 95% of the confidence interval. FIG signal of the D2 beam was also recorded at the crossing point using a small skimmer of 1.26 mm aperture in front of the FIG (magenta solid line) and is the average of 128 measurements done by the scope.

FIG, and by REMPI at the crossing point but not during the ICS measurements: it was then detected indirectly via the excited carbon C(3P1 or 2) produced by collisions of C atoms with D2. In the latter case, the trigger delay of the D<sup>2</sup> beam for the ICS measurements was adjusted to obtain a maximum REMPI signal of carbon atoms in the (3P1) or (3P2) states. Typical REMPI profiles obtained for D<sup>2</sup> produced in the experimental condition #3 where the cold head temperature was set at 45 K (**Table 1**) are given in **Figure 2**. To confirm the beam profiles obtained indirectly during the ICS measurements, two other experiments were also performed independently with the REMPI technique directly on D<sup>2</sup> molecules (see **Figure 1**) or with a FIG inserted perpendicular to the molecular beam. Typical results of time-offlight (TOF) profiles are given **Figure 2** for n-D<sup>2</sup> beam in the experimental conditions #3. All the profiles of D<sup>2</sup> (jD<sup>2</sup> = 0 and 1) may be superimposed: only the intensities differ due to the population distribution, which means that all the rotational states are generated during the expansion and uniformly spread into the beam of n-D2. Once the profile at the crossing point achieved, the D<sup>2</sup> beam arrival time, measured with the FIG at d = 393.3 mm downstream, yielded the D<sup>2</sup> velocity. All profiles were fitted to Gaussian functions, with peak positions t<sup>0</sup> and t<sup>1</sup> and halfwidth at 1/e (HWE), yielding the peak velocities v = d / (t<sup>1</sup> – t0), and the velocity spreads δvHWE from the pulse broadening (Naulin and Bergeat, 2018). The response time of the FIG was previously determined to be ∼3 µs [see Supplementary Materials of Chefdeville et al. (2013)], and t<sup>1</sup> values are thus accordingly corrected. With this method, the velocities of the D<sup>2</sup> beam were checked, before, during and after the ICS measurements

of each day to ensure the absence of any drift. Typical results for o-D<sup>2</sup> generated under the conditions #2 and #4 are given in **Figure 3**. To determine the angular spread of the beam, the FIG at the crossing point, mounted on a translation stage, was moved perpendicularly to the beam axis to enable measurements at various positions. A depth gauge allows the exact re-positioning of the FIG. It should be noted that the TOF profiles don't change with the position of the FIG, which means that the transverse velocity is negligible compared to the beam velocity. The area of the TOF profiles or the maximum intensity varies with the position of the FIG: the angular spreads given in **Table 1** were determined by fitting the curves with Gaussian functions (see **Figure 4**).

Carbon atoms can only be detected by REMPI at the crossing point, but not with the FIG, contrarily to metastable Ne<sup>∗</sup> atoms also generated within the discharge. They give a signal due to surface ionization with the FIG operated with a null filament current. Since C(3P) and Ne<sup>∗</sup> profiles obtained by REMPI at the crossing point are very similar, it was assumed that their velocities were likely to be identical.

FIGURE 4 | Evolution of the maximum intensities at crossing point measured with the FIG. Black squares: n-D2 beam under experimental condition #2 with a distance from the valve to the crossing point of 138.7 mm. Blue open circles: Ne beam with a distance from the valve to the crossing point of 350.94 mm. Red stars, metastable Ne\* probed with a null current of the FIG.

Again, beam profiles could also be measured at the crossing point when replacing the mass spectrometer by a FIG. The two profiles obtained for metastable Ne<sup>∗</sup> are identical (see **Figure 5**). As for D2, Ne<sup>∗</sup> velocity values and spreads could

the FIG. Each profile is the average of 128 measurements done by the scope. Upper TOF scale: Ne\* far-FIG signal recorded at 393.3 mm downstream using a screen with a hole of 6mm-diameter in front of the far FIG (black solid line).

be determined from profiles at the crossing point and at d = 393.3 mm downstream.

ICSs were obtained from the averaged REMPI signal intensities IREMPI and the relative velocity v<sup>r</sup> of the C and D<sup>2</sup> beams as IREMPI/(v<sup>r</sup> h1ti), where h1ti is the mean interaction time between the two beam pulses which takes full account of the density-to-flux transformation under our working conditions (Naulin and Costes, 2014), and assuming a forward angular distribution of scattered C-atoms as for the C-H<sup>2</sup> system (Kłos et al., 2018). To monitor the efficiency of the discharge, the Ne<sup>∗</sup> signal from the FIG 393.3 mm downstream the crossing point was used. Moreover, the UV laser was detected by a photodiode at the entrance of the main chamber. Data points acquired with poor discharge conditions and laser power lower than 80% of the average over the whole scan were discarded. Since the densities of the two beams were not quantitatively determined, we could not extract absolute cross-sections. Relative experimental cross-sections for C(3P0) + o-, n-D<sup>2</sup> → C(3Pj=1, 2) + o-, n-D<sup>2</sup> inelastic collisions were obtained by accumulating at each angle signals from several thousand beam pulses. They were normalized by the sum of the experimental cross-sections in the energy ranges 22 −114 cm−<sup>1</sup> for C(3P0) → C(3P1) transition, and 26 – 165 cm−<sup>1</sup> for C(3P0) → C(3P2) transition. All the plotted vertical error bars represent statistical fluctuations at a 95% confidence interval.

#### Theory

The full set of electronic PESs is identical for C-H<sup>2</sup> and C-D<sup>2</sup> systems and depends only on the mutual distances of the three atoms involved. Hence, in our scattering calculations of C(3Pj) with o- and p-D<sup>2</sup> we employed the most recent highly-correlated C(3Pj)-H<sup>2</sup> PESs of Kłos et al. (2018) that were computed with the explicitly correlated multireference configuration interaction method (ic-MRCI-F12) (Shiozaki and Werner, 2011, 2013; Shiozaki et al., 2011) with large atomic basis set. Briefly, the interaction of the open-shell C(3Pj) atom with the H<sup>2</sup> molecule gives rise to two adiabatic potentials of the A′′ symmetry (wave function anti-symmetric with respect to the reflection in three-atomic plane) and one of A′ symmetry (symmetric with respect to the in-plane reflection). The two adiabatic potentials were diabatized before the dynamical calculations and the diabatization procedure provided additional off-diagonal coupling. We refer the readers to Kłos et al. (2018) for more details about ab initio calculations of the PESs. The geometry of the H<sup>2</sup> molecule in the C-H<sup>2</sup> PESs is fixed at the r<sup>0</sup> = 0.767 Å distance corresponding to an average over the lowest vibrational state v = 0 and considered as a rigid rotor. As we substitute both H atoms with D isotopologs, we do not need to modify center of mass of the diatomic as the molecule is still homonuclear. In a case of a single isotope substitution to form an HD molecule, one would need to shift the center of mass accordingly. The rigid rotor approach for C-H<sup>2</sup> and C-D<sup>2</sup> can use the same set of rigid rotor 2-dimensional PESs assuming that we neglect any mass effects in description of H<sup>2</sup> and D<sup>2</sup> that can change slightly the equilibrium distance. The difference between vibrationally averaged distance r<sup>0</sup> for the D<sup>2</sup> molecule and H<sup>2</sup> molecule

is only about 0.008 Å. Therefore, within these assumptions and approximations we can use our C-H<sup>2</sup> PESs for the C-D<sup>2</sup> system.

To obtain integral cross-sections we solved Close-Coupling equations of Arthurs and Dalgarno (1960) using the HIBRIDON package<sup>1</sup> . For the C(3Pj)-D<sup>2</sup> scattering we use the reduced mass of 3.0158368 a.m.u. The rotational constant of the D<sup>2</sup> molecule (Huber and Herzberg, 1979) is B<sup>0</sup> = 29.9037 cm−<sup>1</sup> and the spinorbit energy levels of C(3Pj) atom (Cooksy et al., 1986; Yamamoto and Saito, 1991), listed in NIST basic atomic spectroscopic data are 0, 16.42 and 43.41cm−<sup>1</sup> for C(3P0), C(3P1), and C(3P2), respectively. The Close-Coupling equations are propagated using hybrid Alexander-Manolopoulos propagator from the initial distance of R = 1.0 to 80 a0. The cross-sections were checked for

<sup>1</sup>Hibridon is a Package of Programs for the Time-Independent Quantum Treatment of Inelastic Collisions and Photodissociation written by M. H. Alexander, D. E. Manolopoulos, H.-J. Werner, and B. Follmeg, with contributions by P. F. Vohralik, D. Lemoine, G. Corey, R. Gordon, B. Johnson, T. Orlikowski, A. Berning, A. Degli-Esposti, C. Rist, P. J. Dagdigian, B. Pouilly, G. van der Sanden, M. Yang, F. de Weerd, S. Gregurick, J. Kłos and F. Lique. Available online at: {http://www2.chem.umd.edu/groups/alexander/hibridon/hib43/}

FIGURE 7 | Experimental and theoretical cross-sections for C(3P0) <sup>+</sup> <sup>o</sup>-D<sup>2</sup> <sup>→</sup> C(3P1) <sup>+</sup> <sup>o</sup>-D<sup>2</sup> inelastic collisions. (A) theory convoluted to experimental resolution for individual transitions of C(3P<sup>j</sup> ) with o-D2(jD<sup>2</sup> <sup>=</sup> 0): C(3P0) <sup>→</sup> C(3P1) (blue solid line), C(3P1) <sup>→</sup> C(3P2) (green solid line), and C(3P1) <sup>→</sup> C(3P0) (red solid line); (B) experiment (red open circles in the conditions #1 and #4 and black stars in the conditions #1 and #3 described in Table 1); theoretical contributions of transitions C(3P0) <sup>→</sup> C(3P1) (blue dotted line), C(3P1) <sup>→</sup> C(3P2) (green dotted line), C(3P1) <sup>→</sup> C(3P0) (red dotted line), and total (orange solid line), assuming a 7% initial population of C(3P1): C(3P2) is populated by C(3P0) <sup>→</sup> C(3P1) (main contribution) and depopulated by C(3P1) <sup>→</sup> C(3P2) and C(3P1) <sup>→</sup> C(3P0) transitions, resulting in a total ICStot = 0.93 σ0−<sup>1</sup> – 0.07 (σ1−<sup>2</sup> + σ1−0). To allow for easier comparison, experimental ICS scale is adjusted such that the area in the [22 – 116] cm−<sup>1</sup> range is the same as for the theoretical ICS calculated. Vertical error bars represent the statistical uncertainties at the 95% confidence interval; each point corresponds to 2020 (experimental conditions #1 and #4) and 1680 (experimental conditions #1 and #3) laser shots per angle, scanning the beam intersection angle between 90◦ and 13◦ , with −1 ◦ decrement. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties.

convergence with respect to the inclusion of a sufficient number of partial waves and energetically closed channels. The o-D<sup>2</sup> basis included all levels with a rotational quantum number jD<sup>2</sup> ≤ 6. State-to-state excitation cross-sections were obtained between all the fine-structure levels of C(3P) over the collision energy range relevant to the experiments (0 – 800 cm−<sup>1</sup> ) on the grid of energies with a step of 0.1 cm−<sup>1</sup> (see **Figure 6**). C-H<sup>2</sup> and C-D<sup>2</sup> calculations differ by the different energy structure of the partners and by a different reduced mass.

#### RESULTS AND DISCUSSION

As expected, the excitation functions, i.e., the variation of the ICSs as a function of relative translation energy, for C(3P0) + D<sup>2</sup> → C(3P1) + D<sup>2</sup> and C(3P0) + D<sup>2</sup> →

FIGURE 8 | Experimental and theoretical cross-sections for C(3P0) <sup>+</sup> <sup>n</sup>-D<sup>2</sup> <sup>→</sup> C(3P1) <sup>+</sup> <sup>n</sup>-D<sup>2</sup> inelastic collisions. (A) theory convoluted to experimental resolution for individual transitions of C(3P<sup>j</sup> ) with D2(jD<sup>2</sup> <sup>=</sup> 0) and D2(jD<sup>2</sup> = 1): C(3P0) <sup>→</sup> C(3P1) (blue solid line and cyan dashed line), C(3P1) <sup>→</sup> C(3P2) (green solid line and dashed line), C(3P1) <sup>→</sup> C(3P0) (red solid line and pink dashed line); (B) experiment (black stars in the conditions #1 and #3 described in Table 1); theoretical contributions of transitions C(3P0) <sup>→</sup> C(3P1) (blue dotted line), C(3P1) <sup>→</sup> C(3P2) (green dotted line), C(3P1) <sup>→</sup> C(3P0) (red dotted line), and total (orange solid line), assuming that n-D2 is composed of 33% of jD<sup>2</sup> <sup>=</sup> 1 and 66% of <sup>j</sup>D<sup>2</sup> <sup>=</sup> 0 and a 7% initial population of C(3P1): C(3P1) is populated by C(3P0) <sup>→</sup> C(3P1) (main contribution) and depopulated by the C(3P1) <sup>→</sup> C(3P2) and C(3P1) <sup>→</sup> C(3P0) transitions by collision with D2(jD<sup>2</sup> <sup>=</sup> 0) and D2(jD<sup>2</sup> = 1), resulting in a total ICStot = 0.93 (0.33σ0−1,j(D2)=<sup>1</sup> <sup>+</sup> 0.66 <sup>σ</sup>0−1,j(D2)=<sup>0</sup> ) – 0.07 {0.33(σ1−2,j(D2)=<sup>1</sup> <sup>+</sup> <sup>σ</sup>1−0,j(D2)=<sup>1</sup> ) <sup>+</sup> 0.66(σ1−2,j(D2)=<sup>0</sup> <sup>+</sup> <sup>σ</sup>1−0,j(D2)=<sup>0</sup> )}. To allow for easier comparison, experimental ICS scale is adjusted such that the area in the [22 – 114] cm−<sup>1</sup> range is the same as for the theoretical ICS calculated. Vertical error bars represent the statistical uncertainties at the 95% confidence interval; each point corresponds to 2060 laser shots per angle, scanning the beam intersection angle between 90◦ and 14◦ , with −1 ◦ decrement. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties.

C(3P2) + D<sup>2</sup> (**Figures 7**–**11**) all exhibit a threshold behavior corresponding to the spin-orbit energy differences: E( <sup>3</sup>P1) – E( <sup>3</sup>P0) = 16.42 cm−<sup>1</sup> and E( <sup>3</sup>P2) – E( <sup>3</sup>P0) = 43.41 cm−<sup>1</sup> . In **Figure 6** are displayed the calculated ICSs for all transitions which may contribute to the observed signals. It is worth noting that the ICSs for relaxation transitions rapidly decrease at high energies. To allow for comparison with experimental data, these ICSs were convoluted with the experimental energy resolution (**Figure 12**).

## C(3P0) + o(n)-D<sup>2</sup> → C(3P1) + o(n)-D<sup>2</sup> Transitions

Results for the C(3P0) excitation by collision with o- and n-D<sup>2</sup> are displayed in **Figures 7**, **8**, respectively. The convoluted theoretical angular momentum value, Jt

.

FIGURE 10 | Experimental and theoretical cross-sections for C(3P0 or1) <sup>+</sup> <sup>o</sup>-D<sup>2</sup> <sup>→</sup> C(3P2) <sup>+</sup> <sup>o</sup>-D<sup>2</sup> inelastic collisions. (A) theory convoluted to experimental resolution for individual transitions: C(3P0) <sup>→</sup> C(3P2) (violet solid line), C(3P1) <sup>→</sup> C(3P2) (green solid line); (B) experiment (blue open triangles in the conditions #1 and #2 and black stars in the conditions #1 and #3 described in Table 1); theoretical contributions of transitions C(3P0) <sup>→</sup> C(3P2) (violet dotted line), C(3P1) <sup>→</sup> C(3P2) (green dotted line) and total (orange solid line), assuming a 7% initial population of C(3P1): C(3P2) is populated by C(3P0) <sup>→</sup> C(3P2) (main contribution), and C(3P1) <sup>→</sup> C(3P2) excitation transitions, resulting in a total ICStot = 0.93σ0−<sup>2</sup> + 0.07σ1−2. To allow for easier comparison, experimental ICS scale is adjusted such that the area in the [26 – 167] cm−<sup>1</sup> range is the same as for the theoretical ICS calculated. Vertical error bars represent the statistical uncertainties at the 95% confidence interval; each point corresponds to 630 (experimental conditions #1 and #2) and 1500 (experimental conditions #1 and #3) laser shots per angle, scanning the beam intersection angle between 90◦ and 13◦ (experimental conditions #1 and #2) or 20◦ (experimental conditions #1 and #3), with −1 ◦ decrement. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties.

ICSs for involved transitions, given in the upper panels, are also displayed in the lower panels weighted by their estimated contributions to the total process: due to the presence of a small amount of C(3P1), transitions C(3P1) → C(3P0) and C(3P1) → C(3P2) need to be taken into account. The resulting total ICS can then be compared to experimental results.

For collisions with o-D<sup>2</sup> (**Figure 7**), two sets of experiments were achieved, under different D2-beam conditions, with different velocities: consequently, data for a given energy have been acquired at different crossing angles. The excellent agreement between both experimental sets ensures the absence of any bias in the method used to recover the ICS from the REMPI signal, which involves estimating the mean interaction time h1ti, which depends on the crossing angle (**Figure 12**). Only transitions involving D<sup>2</sup> (jD<sup>2</sup> = 0) are taken into account in the overall convoluted theoretical ICS, which indeed is not the case for collisions with n-D<sup>2</sup> (**Figure 8**), where transitions involving D<sup>2</sup> (jD<sup>2</sup> = 1) also need to be taken into account with relative weights of 2/3 and 1/3, respectively.

Resonance structures observed experimentally are very similar to the theoretical ones, however slightly shifted in energy. The agreement is better for o-D<sup>2</sup> than for n-D2, since more contributions are involved in the latter case. In particular, the first two peaks at ca. 26.5 and 41.3 cm−<sup>1</sup> for jD<sup>2</sup> = 0 are well resolved in both theory and experiment for o-D<sup>2</sup> (**Figure 7A**), but are blurred out by the peak at ca. 31 cm−<sup>1</sup> for jD<sup>2</sup> = 1 for n-D<sup>2</sup> (**Figure 8B**). In **Figure 9** are displayed partial cross sections for C(3P0) → C(3P1) corresponding to partial waves with total angular momenta J<sup>t</sup> from 1 to 20 that contribute within the 16–100 cm−<sup>1</sup> total energy range. The peaks around 20 and 40 already appear at J<sup>t</sup> = 1 (thick black solid line) and are associated with opening of carbon spin orbit channels. The first lowest partial waves form sharp peaks around 20 cm−<sup>1</sup> , whereas a broader peak around 30–40 cm−<sup>1</sup> is due to the build-up of partial waves with J<sup>t</sup> = 8–12. The peak around 60 cm−<sup>1</sup> comes from a shape resonance for J<sup>t</sup> = 14. A sharp shape resonance also appears for J<sup>t</sup> = 17 near 90 cm−<sup>1</sup> .

FIGURE 11 | Experimental and theoretical cross-sections for C(3P0 or 1) <sup>+</sup> <sup>n</sup>-D<sup>2</sup> <sup>→</sup> C(3P2) <sup>+</sup> <sup>n</sup>-D<sup>2</sup> inelastic collisions. (A) theory convoluted to experimental resolution for individual transitions of C(3P<sup>j</sup> ) with D2(jD<sup>2</sup> = 0) and D2(jD<sup>2</sup> <sup>=</sup> 1): C(3P0) <sup>→</sup> C(3P2) (violet solid line and magenta dashed line), C(3P1) <sup>→</sup> C(3P2) (green solid line and dashed line); (B) experiment (blue open triangles in the conditions #1 and #2 and black stars in the conditions #1 and #3 described in Table 1); theoretical contributions of transitions C(3P0) <sup>→</sup> C(3P2) (violet dotted line), C(3P1) <sup>→</sup> C(3P2) (green dotted line), and total (orange solid line), assuming that n-D<sup>2</sup> is composed of 33% of jD<sup>2</sup> = 1 and 66% of jD<sup>2</sup> <sup>=</sup> 0 and a 7% initial population of C(3P1): C(3P2) is populated by C(3P0) <sup>→</sup> C(3P2) (main contribution) and C(3P1) <sup>→</sup> C(3P2) excitation transitions by collision with D2(jD<sup>2</sup> <sup>=</sup> 0) and D2(jD<sup>2</sup> = 1), resulting in a total ICStot <sup>=</sup> 0.93 (0.33σ0−2,j(D2)=<sup>1</sup> <sup>+</sup> 0.66 <sup>σ</sup>0−2,j(D2)=<sup>0</sup> ) + 0.07 (0.33σ1−2,j(D2)=1<sup>+</sup> 0.66σ1−2,j(D2)=<sup>0</sup> ). To allow for easier comparison, experimental ICS scale is adjusted such that the area in the [26 – 165] cm−<sup>1</sup> range is the same as for the theoretical ICS calculated. Vertical error bars represent the statistical uncertainties at the 95% confidence interval; each point corresponds to 980 (experimental conditions #1 and #2) and 1150 (experimental conditions #1 and #3) laser shots per angle, scanning the beam intersection angle between 90◦ and 13◦ (experimental conditions #1 and #2) or 20◦ (experimental conditions #1 and #3), with −1 ◦ decrement. The plotted error bars on energy are estimated from velocity and crossing angle uncertainties.

## C(3P0) + o(n)-D<sup>2</sup> → C(3P2) + o(n)-D<sup>2</sup> Transitions

Results for the C(3P0) excitation by collision with o- and n-D<sup>2</sup> are displayed in **Figures 10**, **11**. The convoluted theoretical ICSs for involved transitions, given in the upper panels, are also displayed in the lower panels weighted by their estimated contributions to the total process: again, due to the presence of a small amount of C(3P1), transition C(3P1) → C(3P2) need to be taken into account. Note that the collisional de-excitation of C(3P2) is not taken into account here since its initial population is negligible: furthermore, it would result in a negative offset below threshold

FIGURE 12 | Interaction time (A,B), and collision energy spread (C), calculated for the experimental conditions of previous Figures of the C + o-D<sup>2</sup> collision energy transfers: in blue dashed lines for the experimental conditions #1(C) and #3(D2, 45 K), in olive solid lines for #1(C) and #2(D2, 100 K) and in black dot lines for #1(C) and #4(D2, 10 K). Note that the angular spread is the main source of collision energy spread. All data are plotted as a function of the collision energy, ET . For the interaction time, a forward distribution is considered: (A) for the C(3P0) <sup>→</sup> C(3P1) transition and (B) for the C(3P0) <sup>→</sup> C(3P2) transition, same labels as for the collision energy spread.

(Kłos et al., 2018), and o-D2(blue solid line).

not observed. The resulting total ICS can then be compared to experimental results.

In both cases, two sets of experiments were achieved, under different D2-beam conditions, with different velocities. Whereas both experimental sets are in good agreement for o-D<sup>2</sup> (**Figure 10B**) up to 160 cm−<sup>1</sup> , it is not the case for n-D<sup>2</sup> experiments. However, the beam velocity mismatch is larger for C(3P0) → C(3P2) experiments (v<sup>c</sup> = 815; vD2 = 845 and 1180 ms−<sup>1</sup> , resulting in E<sup>T</sup> = 179 and 262 cm−<sup>1</sup> at χ = 90◦ ) than for C(3P0) → C(3P1) experiments (v<sup>c</sup> = 815; vD2 = 694 and 855 ms−<sup>1</sup> , resulting in E<sup>T</sup> = 146 and 179 cm−<sup>1</sup> at χ = 90◦ ): at 90◦ , the interaction time is much shorter than at lower angles: a variation (even small) in its estimated value can result in a larger variation of the ICS value (= IREMPI/(v<sup>r</sup> h1ti)). It is however worth noting that the increase of the cross-section at high energies is too high to be due to a h1ti possible underestimate. It could be due to an energy transfer involving relaxation of D<sup>2</sup> (jD<sup>2</sup> = 2 → 0): however, ICSs involving such a relaxation are monotonously decreasing (**Figure 6**), which would imply that their contribution should be much more intense at low energies resulting in a significant positive offset not observed. Furthermore, ICSs corresponding to rotational (de-)excitation of D<sup>2</sup> are weak (**Figure 6**). This is due to a weak anisotropy of the PES with respect to D<sup>2</sup> rotation that leads to a weak coupling between the D<sup>2</sup> rotational states. It also explains that the magnitudes of the ICSs are similar for all D<sup>2</sup> rotational state. In addition, the energy splitting between jD<sup>2</sup> = 0 and jD<sup>2</sup> = 2 state of D<sup>2</sup> is so large that the excitation probability is very small.

Another possibility to be considered is the coupling with the C(1D2) state: its crossing with triplet PESs is estimated around 300 cm−<sup>1</sup> by theory. Excitation to the <sup>1</sup>D<sup>2</sup> state is closed but the increase of the ICS may be due to indirect coupling that will favor the <sup>3</sup>P<sup>2</sup> state over the <sup>3</sup>P1. This would result in a decrease of the ICS for the <sup>3</sup>P<sup>1</sup> in the same energy domain (not probed in the present experiments).

The cross-sections observed are different in shape, but almost similar in average. Resonances are less visible for the C(3P0) → C(3P2) than for C(3P0) → C(3P1) ICS: actually, there are many more resonances for the 0–2 transition than for 0–1, especially for jD<sup>2</sup> = 1, resulting in a smoother shape. On average, their amplitudes differ by a factor of ∼2. Similar differences were found for the O–H system (Lique et al., 2018). The fact that the C(3P0) – C(3P2), C(3P1) – C(3P2), and C(3P0) – C(3P1) transitions have more of less the same magnitude may be partly explained by the huge well depth that would lead to a significant redistribution of the flux over all open C-atom spin-orbit states.

## Comparison of C–D<sup>2</sup> With C–H<sup>2</sup> and C–He Systems

As shown in **Figure 13**, there is a great difference between C– He and C–H<sup>2</sup> (D2) systems, due to quite different excitation processes. For C–He, the interaction is a weak van der Waals forces and the excitation is thus essentially governed by spin-orbit coupling (Bergeat et al., 2018). For C–H<sup>2</sup> (D2), the interaction consists in a deep potential well and the system can then be chemically bound and collisional energy transfers therefore are much more efficient, as clearly shown in **Figure 13**. However, there is a decrease in the C(3P0) – C(3P1) ICSs around 50 cm−<sup>1</sup>

#### REFERENCES

Arthurs, A. M., and Dalgarno, A. (1960). The theory of scattering by a rigid rotator. Proc. R. Soc. Lond. Ser. A 256:540. doi: 10.1098/rspa.1960.0125

for all systems, essentially due to the opening of the C(3P0) – C(3P2) excitation. Concerning C–D<sup>2</sup> and C–H<sup>2</sup> systems, apart the resonances, ICSs are expected to be similar when no rotational (de-)excitation of H<sup>2</sup> (D2) is involved as can be seen in **Figure 13**.

#### CONCLUSION

In this work, we have presented a joint theoretical and experimental study of the spin-orbit transitions of C(3Pj) by collisions with D2. Integral cross-sections have been experimentally observed in a crossed beam apparatus down to collision energies below ca. 5.5 cm−<sup>1</sup> (66 J mol−<sup>1</sup> ) and compared to state-of-the-art non-Born-Oppenheimer quantum dynamical calculations for C(3P0) → C(3P1) and C(3P0) →

C(3P2) transitions. Results have been compared to similar systems previously studied (C(3Pj) + H2, and He) (Bergeat et al., 2018; Kłos et al., 2018). The overall agreement obtained, in particular for C(3Pj) + H<sup>2</sup> and C(3Pj) + D<sup>2</sup> for which calculations are performed using the same potential energy surfaces, confirms the validity of these potentials which can be confidently used to compute (de-)excitation rates of Catoms in the low energy domain relevant to astrophysical modeling of cold molecular clouds. However, the present results validate the low energy data generated from theses PESs but the calculations at higher energy would require to revise the theoretical approach and probably to add the excited state of C-atom.

### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and are available on request.

#### AUTHOR CONTRIBUTIONS

AB, SM, and CN carried out the experimental measurements and data analysis. FL and JK performed the theoretical calculations. The manuscript was written through contributions of all authors.

## FUNDING

This work was supported by the Programme National Physique et Chimie du Milieu Interstellaire (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. AB, FL, SM, and CN acknowledge also financial support from the Agence Nationale de la Recherche, contract Hydrides (ANR-12-B505- 0011-02). JK acknowledges financial support from the U. S. National Science Foundation, under the grant No. CHE-1565872 to M. H. Alexander.

Bensby, T., and Feltzing, S. (2006). The origin and chemical evolution of carbon in the Galactic thin and thick discs. Mon. Not. R. Astron. Soc. 367, 1181–1193. doi: 10.1111/j.1365-2966.2006. 10037.x


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Bergeat, Morales, Naulin, Kłos and Lique. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Dissociative Electron Attachment From Vibrationally Excited Molecules in Nanosecond Repetitively Pulsed CO Discharges and Afterglows

Lucia Daniela Pietanza\*, Gianpiero Colonna and Mario Capitelli

P.Las.M.I. Lab, CNR-Nanotec, Bari, Italy

Non-equilibrium vibrational distributions and electron energy distributions of CO in nanosecond repetitively pulsed (NRP) discharges and afterglows have been determined from a coupled solution of the time dependent Boltzmann equation for the electron energy distribution function (eedf) of free electrons and the master equations for the vibrational distribution function (vdf) of CO and the electronic excited states of CO and O and C atoms. Emphasis is given to the role of dissociative electron attachment (DEA) from vibrationally excited states in affecting the eedf and vdf under extreme conditions, i.e., an optically thick plasma with quenching processes involving the electronic excited states, populated by a sequence of discharge pulses and corresponding afterglows. In particular, the quenching process of the a35 electronic state of CO determines a pumping of vibrational quanta in the ground state, which in turn largely modifies the CO vdf promoting the activation of DEA process. DEA rate coefficients have been obtained by using a complete set of vibrational (v) dependent cross sections through the CO<sup>−</sup> X <sup>2</sup>5 channel and by using the experimental v = 0 cross section of Rapp and Briglia, which should include the contribution of other CO<sup>−</sup> resonant states. The importance of the last contribution has been also estimated by using a scaling law to extend the v = 0 cross section over all the vibrational ladder of CO. In particular, this mechanism becomes competitive with the other reactive channels for very short inter-pulse delay times, i.e., the tid = 1 µs, being less important for longer inter-pulse delay times, i.e., the tid = 25 µs.

Keywords: nanosecond pulsed discharges, afterglows, CO vibrational distribution, electron energy distribution function, dissociative electron attachment, global rates

## INTRODUCTION

Non-equilibrium plasma kinetics is a topic of large interest for many applications in different fields such as plasma chemistry, plasma and laser physics, hypersonic and shock wave flows (Capitelli et al., 2016). Particular attention is paid to the development of kinetic models which couple the Boltzmann equation for the electron energy distribution function (eedf) with the state-to-state vibrational kinetics for the calculation of the vibrational distribution function (vdf) of molecules and the collisional-radiative models for the electronic excited state densities. This approach become essential when the chemistry at the basis of the relevant application is dependent on the high lying vibrational levels of the considered molecules (Capitelli et al., 2016).

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Dilip H. Dagade, Shivaji University, India Barbara Michela Giuliano, Centro de Astrobiología (CSIC-INTA), Spain

> \*Correspondence: Lucia Daniela Pietanza luciadaniela.pietanza@cnr.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 02 January 2019 Accepted: 04 March 2019 Published: 29 March 2019

#### Citation:

Pietanza LD, Colonna G and Capitelli M (2019) Dissociative Electron Attachment From Vibrationally Excited Molecules in Nanosecond Repetitively Pulsed CO Discharges and Afterglows. Front. Chem. 7:163. doi: 10.3389/fchem.2019.00163

An example in this direction is represented by the formation of negative H<sup>−</sup> ions in magnetic multi-cusp H<sup>2</sup> plasmas (Bretagne et al., 1985; Hassouni et al., 1998; Capitelli et al., 2006) and more in general in RF discharges to be used as negative ion beam source for neutral heating in tokamak devices. In this case, the dissociative attachment from highly excited vibrational levels rather than from the ground state vibrational level is responsible of negative ion production.

A second example is represented by expanding hypersonic and shock wave flows where the correct description of the dissociation process depends on the whole vibrational distributions of considered molecules (Capitelli et al., 2016).

A third example, largely investigated in the present days, is the activation of CO<sup>2</sup> in cold plasmas, where the dissociation process involves either the electron impact dissociation process of asymmetric mode of CO<sup>2</sup> or the heavy particle dissociation processes assisted by vibrational excitation (Capitelli et al., 2017). In addition, the reacting CO<sup>2</sup> plasma forms CO and O<sup>2</sup> molecules that in turn undergo a complicated non-equilibrium vibrational kinetics coupled to the Boltzmann equation for eedf. The description of CO2, CO, O<sup>2</sup> vdf's needs of accurate sets of state-to-state cross sections which requires the intensive use of quantum chemistry and molecular dynamics methodologies (Capitelli et al., 2016; Barreto et al., 2017). This last aspect has been in particular developed by Laporta et al. (2012, 2014, 2016) which have calculated complete sets of electron molecule cross sections including dissociative attachment from the whole vibrational ladder of CO and O2. The set of O<sup>2</sup> cross sections have been recently used by Annusova et al. (2018) for O<sup>2</sup> discharges operating at low pressure.

In this contest, nano-repetitively pulsed (NRP) CO discharges, fed by a sequence of modulated ns pulses followed by the corresponding afterglow of different durations, have been recently investigated (Pietanza et al., 2018a,b). To this end, a self-consistent model based on the coupling of the Boltzmann equation for the electron energy distribution function (eedf), the vibrational kinetics and the plasma chemistry of reacting mixture has been used (Capitelli et al., 2016; Pietanza et al., 2017a,b, 2018a,b).

Four models were considered in Pietanza et al. (2018b) depending on the hypotheses on the processes involving the electronic states of CO and of oxygen and carbon atoms. In particular, we have considered: (1) an optically thick CO plasma, with and without quenching processes and (2) an optically thin CO plasma, with and without quenching processes. The thick case assumes that all the spontaneous lines emitted by the CO, O and C electronic excited states are completely re-absorbed, while in the thin case such radiation totally escapes from the plasma.

Among the quenching processes included in the model, particular emphasis was given to the quenching process involving the metastable a <sup>3</sup>5 state of CO, which was also supposed to pump the vibrational v = 27 level of the ground electronic state of CO (Pietanza et al., 2017a,b, 2018a,b).

The previous different models predict different time dependent behavior of the electronic excited state population with a direct consequence on the eedf and on the electron impact rate coefficients and an indirect one on the vdf.

In the previous papers (Pietanza et al., 2018a,b), we neglected the role of dissociative electron attachment (DEA) of CO in the kinetics. This assumption is justified for conditions where the reacting mixture does not contain appreciable concentrations of high lying vibrational levels. The DEA process through the X <sup>2</sup>5 resonant channel of CO−, labeled as DEA(X <sup>2</sup>5), i.e., the process

$$e + CO\left(X^1 \Sigma^+, \,\nu\right) \to CO^-\left(X^2 \Pi\right) \to C\left(^3P\right) + O^-\left(^2P\right) \quad \text{(1)}$$

presents a small v = 0 cross section, which, however, exponentially increases with the increase of vibrational quantum number v, as recently shown by Laporta et al. (2016).

The results of Laporta et al. (2016) do not include the DEA process through the other resonant states of CO−, in particular the A <sup>2</sup>6 state. The experimental v = 0 cross section measured by Rapp and Briglia (1965) and reported by Itikawa (2015), which should include such contributions, is much higher than the v = 0 cross section involving the state X <sup>2</sup>5 considered by Laporta et al. (2016). No data are at the moment available for the dependence of the experimental cross section on v, which however should be weaker than the corresponding behavior of the X <sup>2</sup>5 state as discussed in the paper of Laporta et al. (2016). An analysis of this aspect will be carried out in section Scaling Laws for Rapp and Briglia DEA Cross Section.

The aim of the present paper is to investigate the role of DEA process from vibrationally excited CO molecules in affecting the whole kinetics of reacting CO under conditions where appreciable concentrations of vibrationally excited states are present. These conditions can be found in the NRP atmospheric CO discharges with inter-pulse delay times tid = 1 µs, where memory effects along the different pulses (Pietanza et al., 2018a,b) can result in very excited vdf and eedf. Calculations for tid = 25 µs are also reported to be compared to the tid = 1 µs case.

For the present study, we select, between the different models, reported in Pietanza et al. (2018b), that one corresponding to optically thick plasmas with quenching processes, i.e., with the presence of the deactivation of the metastable a <sup>3</sup>5 state and consequent vibrational excitation of the vibrational manifold of CO.

The paper is divided into 6 sections. After the introduction, section The Model describes the model emphasizing the main differences with that one developed in Pietanza et al. (2018a,b), i.e., the inclusion of the DEA process for CO. Section Short Inter-Pulse Delay Time discusses the results for the short interpulse delay time case (tid = 1 µs), emphasizing the role of DEA in affecting macroscopic quantities, such as the molar fractions of the different species, including electrons, the electron and vibrational temperatures and the reactive channel rate coefficients, and microscopic quantities, such as vdf and eedf.

Section DEA Rate Coefficients reports the DEA rate coefficients under selected pulses, discussing the role of DEA from the complete set of cross sections involving the state X <sup>2</sup>5 (DEA(X <sup>2</sup>5)), as compared with the v = 0 experimental contribution, DEARB. Section Long Inter-pulse Delay Time reports results for a longer inter-pulse delay time case, i.e., tid = 25 µs. Section Scaling Laws for Rapp and Briglia DEA Cross Section considers a scaling law for the cross sections of DEA measured by Rapp and Briglia (1965) and their role in affecting the global results. Finally, section Conclusions reports conclusions and perspectives.

#### THE MODEL

The model is based on the solution of a time dependent Boltzmann equation for the calculation of the eedf, coupled to the non-equilibrium vibrational kinetics of CO molecules for the calculation of the vdf in the ground electronic state of CO and the electronic excited state kinetics of CO, C, and O species, as well as, with a simple dissociation-recombination and ionizationrecombination kinetics describing the plasma mixture (Capitelli et al., 2016; Pietanza et al., 2017a,b, 2018a,b).

All the kinetics are self consistently and time dependent solved. Equations and details can be found in Pietanza et al. (2017a, 2018a,b).

The plasma mixture considered is composed by the following species: CO(X <sup>1</sup>6+, <sup>v</sup> <sup>=</sup> 1–80), CO2, C, O, CO+, CO<sup>+</sup> 2 , C+, O+, and e−. The energy level diagrams of CO, C and O are schematically represented in Figure 1 of Pietanza et al. (2018a).

Besides the ground state vibrational ladder, we consider several CO electronic excited states: three triplet states, a <sup>3</sup>5 (6.006 eV), a ′3Σ+(6.863), b <sup>3</sup>Σ+(10.40 eV) and four singlet states, A <sup>1</sup>5 (8.03 eV), B <sup>1</sup>Σ+(10.78 eV), C <sup>1</sup>Σ+(11.40 eV), and E <sup>1</sup>Σ+(11.52 eV).

For C and O atoms, only four and five electronic levels, including the ground one, are accounted, namely C(3P), C(1D), C(<sup>1</sup> S), C(<sup>5</sup> S 0 ) and O(3P), O(1D), O(<sup>1</sup> S), O(<sup>3</sup> S 0 ) and O(<sup>5</sup> S 0 ), while CO2, C<sup>+</sup> and O<sup>+</sup> are considered only in their ground states (see Figure 1b of Pietanza et al., 2018a).

The plasma chemistry model is the same presented in Pietanza et al. (2018a,b), but with the inclusion of the DEA process for CO. All the processes included into the model are listed in **Table 1**. In particular, CO dissociation can occur by direct electron impact mechanism (DEM), see process C1, and by pure vibrational excitation mechanism (PVM), see processes C<sup>2</sup> (PVM1) and C<sup>3</sup> (PVM2), involving all the vibrational ladder. Beside DEM process, also resonant electron impact dissociation (RES) process is included in the model, see process C4, in which dissociation is induced indirectly through the activation of the intermediate negative ion vibrational state CO−( <sup>2</sup>5). The corresponding cross sections are generally lower than the direct ones (process C1), but dramatically increase with the vibrational quantum number, as in the case of DEA, being thus comparable to the DEM ones for higher vibrational levels.

The PVM<sup>2</sup> process (C3) is called Boudouard or disproportioning reaction and the corresponding rate coefficient has been obtained by the equations used in Gorse et al. (1984), with an activation energy of 8.3 eV, recently calculated by Barreto et al. (2017). C and O recombination process forming CO molecules (C5) together with CO, C and O ionization (C6-C8) and CO+, C+, and O<sup>+</sup> recombination processes (C9-C11) are also included into the model.

The explicit rate coefficient expressions of processes C1-C<sup>11</sup> in **Table 1** can be found in Pietanza et al. (2017a, 2018a,b).

In addition, in the present work, we include also DEA process for CO through the X <sup>2</sup>5 channel (DEA(X <sup>2</sup>5)) from all the vibrational levels, see processes C<sup>12</sup> in **Table 1**. The relevant vibrational state-resolved cross sections are provided by Laporta et al. (2016).

We insert also the experimental DEA process from v = 0, see process C<sup>13</sup> in **Table 1**, whose cross section was reported by Rapp and Briglia (1965) and Itikawa (2015). This cross section should include the contribution of other resonant channels, as for example the CO−(A <sup>2</sup>6) state. Unfortunately, higher vibrational state cross sections of process C<sup>13</sup> are not available up to now, however, due to the importance of the process, section Scaling Laws for Rapp and Briglia DEA Cross Section will discuss possible scaling laws, useful to extend the v = 0 cross section


also to higher vibrational levels and the effect of inclusion of such cross sections in the kinetics.

As inverse process of C<sup>12</sup> and C13, we include process C14, with a global rate coefficient of 5 10−<sup>10</sup> cm<sup>3</sup> /s taken from Fehsenfeld et al. (1966).

The CO vdf is obtained from the corresponding vibrational master equations including the following e-V, V-V, V-T, SE and reactive contribution (see Pietanza et al., 2018a,b).

$$\frac{dN\_\nu}{dt} = \left(\frac{dN\_\nu}{dt}\right)\_{\varepsilon-V} + \left(\frac{dN\_\nu}{dt}\right)\_{V-V} + \left(\frac{dN\_\nu}{dt}\right)\_{V-T} $$

$$ + \left(\frac{dN\_\nu}{dt}\right)\_{SE} + \left(\frac{dN\_\nu}{dt}\right)\_{React} \tag{2} $$

The e-V (electron-vibration) term describes the energy exchange between electrons and the CO vibrational ladder. A complete set of resonant e-V cross sections involving all the CO vibrational ladder has been provided by Laporta et al. (2012). The V-V, V-T, SE terms correspond to vibrational energy exchange processes due to vibration-vibration (V-V), vibration-translation (V-T), and spontaneous emission (SE). Finally, the last term describes the reactive channel contribution due to the dissociationrecombination (C1-C5) and ionization-recombination processes, involving the CO vibrational ladder (C6) reported in **Table 1**. This last term includes also the contribution of the quenching of the metastable a <sup>3</sup>5 state of CO, which is assumed to pump energy into the level v = 27

$$\text{CO} \left( a^3 \Pi, \,\,\nu = 0 \right) + \text{CO} \rightarrow \text{CO} \left( X^1 \Sigma^+, \,\,\nu = 27 \right) + \text{CO} \quad \text{(3)}$$

This process, which has an essential role in modifying the vdf, is included with an upper limit rate coefficient of 1.21 10−<sup>10</sup> cm<sup>3</sup> /s.

The electronic excited state kinetics of CO, O, and C atoms, instead, is described by the following differential equation in which the terms due to electron impact excitation and deexcitation, spontaneous emission and quenching processes are

FIGURE 2 | Time evolution of electron and O<sup>−</sup> molar fractions (t id = 1 µs).

calculated with and without DEA processes (t

accounted, i.e.,

$$\frac{dn\_i}{dt} = K\_{\text{exc}}^i n\_e n\_0 - K\_{de-\text{exc}}^i n\_e n\_i - \sum\_{j$$

where n<sup>i</sup> is the population density of the i th electronic state, K i exc and K i de−exc the electron impact excitation (from ground) and de-excitation rate coefficients, n<sup>e</sup> and n<sup>0</sup> the electron and ground state densities, λij the escape factor and Aij the Einstein coefficient of spontaneous emission toward lower electronic states j. K i exc and K i de−exc rate coefficients are calculated by integrating the instantaneous eedf over the corresponding electron impact cross sections, taken from the Itikawa database for CO (Itikawa, 2015), from Laher and Gilmor for O (Laher and Gilmor, 1990) and Wang et al. for C (Wang et al., 2013). In the present paper, we consider an optically thick plasma so that λij =0 for all considered optical transitions involving the electronic excited states. The Q term includes all the quenching processes, the most important for CO is that one in equation (3). Also some other quenching processes for C and O electronic states are included in the model as reported in Pietanza et al. (2018a,b).

#### RESULTS: GENERAL CONSIDERATIONS

In this section, we report results for a NRP discharge sustained by a sequence of modulated electric field pulses with a pulse duration t<sup>p</sup> = 20 ns and an inter-pulse delay time tid = 1 µs (sections Short Inter-pulse Delay Time and DEA Rate Coefficients), while the results with tid = 25 µs are presented in section Long Inter-Pulse Delay Time.

pure vibrational mechanism (PVM1, PVM2) as a function of time when DEA processes are included into the model (t id = 1 µs).

Pietanza et al. Dissociative Electron Attachment for CO

The electric field is characterized by a time-dependent profile (Pietanza et al., 2018a,b) described by the following analytical expression

$$E(t) = \begin{cases} E\_M \left( 1 - e^{-\frac{f}{t\_r}} \right) & t \in [0, t\_r) \\ E\_M & t \in \left[ t\_r, t\_p - t\_f \right) \\ E\_M e^{-\frac{f}{t\_f}} & t \in \left[ t\_p - t\_f, t\_p \right) \\ 0 & t \in \left[ t\_p, t\_{pd} \right] \end{cases} \tag{5}$$

where E<sup>M</sup> is the peak intensity, t<sup>r</sup> and t<sup>f</sup> the rise and fall times and their characteristic times τ<sup>r</sup> and τ<sup>f</sup> , t<sup>p</sup> the pulse and tpd the postdischarge duration. Successive pulses are separated by an interpulse delay time tid = t<sup>p</sup> + tpd. In particular, in the simulations EM/N = 160 Td, t<sup>r</sup> = t<sup>f</sup> = 7.5 ns, τ<sup>r</sup> = τ<sup>f</sup> = 1.35 ns, where N is the total number density (cm−<sup>3</sup> ). **Figure 1** reports the time behavior of the applied reduced electric field E/N (E/N = 0 in the afterglow) in one pulse (20 ns), showing that it presents a maximum value of 160 Td in the time interval [7.5 ns, 12.5 ns].

In the short inter-pulse delay time case (tid = 1 µs), we limit our discussion to the first 4 pulses and corresponding afterglows, while in the long inter-pulse delay time case (tid = 25 µs), we consider 20 pulses and corresponding afterglows.

In both cases, we consider an atmospheric (P = 1 atm) CO plasma at constant gas temperature (T<sup>g</sup> = 1,000 K) and, as initial condition, we fix a Boltzmann distribution of the vibrational levels at T<sup>v</sup> (t = 0) = T<sup>g</sup> and a Maxwell eedf at Te(t = 0) = Tg. The initial molar fractions of the considered species are about 1 for CO, 10−<sup>6</sup> for electrons and negligible values for the other considered species.

#### Short Inter-Pulse Delay Time

In this section, we analyze the effect of introducing DEA process in a short inter-pulse delay time case study, i.e., tid = 1 µs. In general, the results with the insertion of DEA from all vibrational levels qualitatively follow those described in Pietanza et al. (2018a,b), presenting, however, for the considered case study, no-negligible differences with the progression of the considered pulses. This point will appear clear in the following.

First, we report, in **Figure 2**, the electron and O<sup>−</sup> molar fractions as a function of the time when the DEA processes are included and the corresponding electron molar fraction when the DEA processes are neglected.

The differences in the electron molar fraction in the two cases increase with the pulses: at the last pulse, the electron molar fraction, at the maximum of the discharge, is 5.05 10−<sup>4</sup> with DEA and 9.0 10−<sup>5</sup> without DEA, while, at the end of the post-discharge, 4.45 10−<sup>6</sup> with DEA and 1.6 10−<sup>6</sup> without DEA. The increase of electron density when DEA is inserted in the kinetics is due to the effect of the global associative attachment (reaction C<sup>14</sup> in **Table 1**).

**Figures 3A,B** compares the time evolution of electron temperature (from the average electron energy) and the 0–1 vibrational temperature calculated with and without the DEA processes. In both quantities, we observe larger

values when taking into account the DEA processes due to the corresponding behavior of electron molar fraction as reported in **Figure 2**.

**Figure 4** reports the time evolution of the dissociation rate coefficients by electron impact (DEM) and by pure vibrational mechanism (PVM<sup>1</sup> and PVM2) in the case in which DEA processes are included. We can note that the DEM rate coefficient slightly prevails on the Boudouard one (i.e., the PVM<sup>2</sup> one) under discharge conditions becoming less important in the corresponding afterglows. Actually, during the discharge, the electron density reaches its maximum peak value strongly increasing all electron impact processes. During the afterglow, the decrease of electron density and the presence of excited vdf makes the dissociation process induced by vibrational excitation, in particular the PVM<sup>2</sup> mechanism, prevail over the others.

Let us now examine the trend of the eedf calculated with and without DEA. **Figures 5A–D** reports the eedf for selected pulses (1st and 4th) at different times during the discharge (t = 12.5 and t = 20 ns) and at the end of corresponding afterglows (t = 1 µs).

In particular, during the first pulse discharge and afterglow, the eedf plots with and without DEA are coincident, i.e., no role is exercised by DEA in affecting eedf. For both discharge and post discharge conditions of the first pulse, a well-structured eedf appears due to superelastic electronic collisions considered in the kinetics, as discusses in Pietanza et al. (2018a,b).

In the fourth pulse, the differences between DEA and no-DEA eedf is negligible at 12.5 ns while it becomes important at the end of pulse (t = 20 ns) and at the end of the post-discharge (t = 1µs). This behavior follows the dependence of eedf on the time evolution of either E/N and the vibrational temperature.

**Figures 6A–D** report the trend of vdf for the same conditions reported in **Figure 5**. The differences between the DEA and the no-DEA results are absent in the first pulse (**Figures 6A,B**), becoming important in the fourth pulse and corresponding afterglow (**Figures 6C,D**), following the eedf's behavior. It is evident the effect of the quenching process of the CO(a <sup>3</sup>5) state [see equation (3)], which pumps vibrational energy in the ground state at v = 27 affecting the corresponding vdf either in discharge and post discharge conditions. In the last considered pulse, a redistribution of vibrational quanta over the whole vibrational ladder in both discharge and post discharge conditions is observed. This redistribution is due to e-V processes under discharge conditions (large ionization degree), and to V-V up pumping mechanism under post-discharge conditions. The excited vibrational distributions shown in **Figure 6** are responsible of the increase of DEA rate coefficients as it will be discussed in the following sections.

modulated with the actual molar fractions of vibrational levels (f(v)DEA(X25)(v)) and f(0)DEARB(0) at different pulses (1st and 4th) and different times (t = 12.5 ns, t = 20 ns and t = 1 µs).

#### DEA Rate Coefficients

In this section, we want to emphasize the role of vibrational excitation in enhancing the total DEA rate coefficients.

This point can be better understood by looking to the dependence of DEA(v) rate coefficients as a function of vibrational quantum number reported in **Figures 7A,B** as well as their partial contributions, i.e. f(v)DEA(v), reported in **Figures 8A,B** for the selected two pulses, where f(v) represents the molar fraction of the vth vibrational state. **Figures 7A,B**, in particular, shows the calculated DEA(X25)(v) rate coefficients as a function of vibrational quantum number v as well as the DEARB(0) rate coefficients calculated from the v = 0 experimental Rapp and Briglia cross section. In general, the DEA(X25)(v) rate coefficients overcome the DEARB(0) one in a vast range (5 < v <80) of the vibrational quantum number, independently of the considered pulse. The situation changes when multiplying the DEA rates for f(v) (**Figures 8A,B**). Inspection of the figure shows the increasing importance with the sequence of the pulses of the f(v)DEA(X25)(v) contribution as compared with the f(0)DEARB(0) one, following the form of the reported vdf in **Figures 6A–D**.

In the first pulse, f(0)DEARB(0) is larger than f(v)DEA(X25) in the whole v range at the maximum of E/N value (t = 12.5 ns) and also at t = 20 ns and in the post-discharge (t = 1 µs). In the last pulse, instead, f(v)DEA(X25)(v) overcome f(0)DEARB(0) in a vast range of v especially at the end of the pulse, i.e., 20 ns.

The competition between the different DEA channels are evidenced in **Figures 9A–D** which shows the behavior of the DEA rate coefficients as a function of the time for the first and fourth pulses and afterglows. The contribution labeled as DEA(X25) is calculated by

$$DEA\left(\mathbf{X}^2 \Pi\right) = \sum\_{\nu} f(\nu) DEA\left(\mathbf{X}^2 \Pi\right)(\nu) \tag{6}$$

In the first pulse, during the discharge regime, f(0)DEARB(0) is larger than DEA(X25) until 12.5 ns, becoming very similar from 12.5 to 20 ns. The two main contributions are competitive in the post discharge regime (**Figure 9B**). In both situations, f(0)DEA(X25)(0) is orders of magnitude lower.

The situation reported for the fourth pulse (discharge regime) reduces the differences between f(0)DEARB(0) and DEA(X25) until 12.5 ns inverting the situation from 12.5 to 20 ns. In the

post discharge regime DEA(X25) > f(0)DEARB(0) until 400 ns, the two terms appearing similar for t > 500 ns.

#### LONG INTER-PULSE DELAY TIME

This case study differs from the previous one only by the inter-pulse delay time which is longer, i.e., tid = 25 µs. A more stable behavior is observed in this case as discussed in Pietanza et al. (2018a,b) resulting in a quasi-stable sequence of pulses and afterglows with a small dependence of the results on the DEA processes. **Figure 10** reports the electron molar fraction calculated with and without DEA up to the 20th pulse. In the same figure, we report the molar fraction O−. The differences, even though not negligible, are much smaller than the previous tid = 1 µs case. Moreover, as it can be seen from **Figure 10**, the electron molar fraction is of the order of 10−<sup>5</sup> not able to promote the role of vibrational excited states in the whole kinetics.

**Figures 11**, **12** report the vdf and the eedf at the three selected pulses, at the end of the discharge (t = 20 ns) and of the post-discharge (t = 25 µs). Their time evolution in each pulse repeat themselves without the memory effects observed in the tid = 1 µs case. Moreover, the insertion of DEA processes has a smaller influence as compared with the corresponding results in the tid = 1 µs, especially for the eedf.

**Figure 13** reports the different DEA rate coefficients, i.e., f(0)DEARB(0), DEA(X25), and f(0)DEA(X25)(0), as a function of time in discharge and post discharge conditions for the first and the 20th pulse, in the tid = 25 µs case. Qualitatively, the results follow those reported in **Figure 9** even though the DEA(X25) contribution decreases its importance due to the presence of less pumped vibrational distributions. It is worth noting the no-time dependence of f(0)DEARB(0) contribution in the post discharge for both pulses compared with the strong decay of DEA(X25). The behavior of f(0)DEARB(0) is controlled by the form of the eedf strongly influenced by the superelastic electronic collisions, while the decay of DEA(X25) is controlled by the corresponding decay of vdf.

## SCALING LAWS FOR RAPP AND BRIGLIA DEA CROSS SECTION

As already underlined, vibrational-state resolved DEA cross sections are available only for the X25 channel (Laporta et al., 2016) and no data do exist for the dependence on v of the experimental v = 0 cross section of Rapp and Briglia (1965).

Due to the importance of the latter cross section, the insertion of the corresponding vibrational state dependence could have an impact on the kinetics results. In this section, we discuss such impact by making reasonable scaling law assumptions on the v-dependence of the experimental DEARB cross section.

As a first hypothesis, we can use the same v-dependence of the X <sup>2</sup>5 channel cross section, i.e., by applying

$$
\sigma\_{\nu>0}^{RB} = \sigma\_{\nu>0}^{L} \left( \frac{\sigma\_0^{RB}}{\sigma\_0^L} \right)^{MAX} \tag{7}
$$

where σ RB v>0 and σ L v>0 are, respectively, the DEARB(v) and the DEA(X25)(v) cross section of the vth vibrational level and σ RB <sup>0</sup> MAX and σ L <sup>0</sup> MAX the corresponding maximum value of the v = 0 cross section.

However, such scaling law predicts too high cross section values which go beyond the reasonable limit of the rigid sphere model, i.e., by supposing a maximum radius of 3 Å at v = 80, πa 2 <sup>0</sup> ≈ 30 Å<sup>2</sup> . For this reason, the following reduced scaling law can be used to limit the increase of the cross section for high v levels, with n a parameter which can assume positive integer or fractional values

$$
\sigma\_{\nu > 0}^{RB} = \frac{\sigma\_\nu^L}{\nu^n} \left( \frac{\sigma\_0^{RB}}{\sigma\_0^L} \right)^{MAX} \tag{8}
$$

Let us now examine the effect on the kinetics of the DEARB scaled cross sections obtained according equation (8) with n = 3. **Figure 14** compares the f(0)DEARB(0), the DEA(X25) and the DEARB(n = 3) rate coefficient contributions obtained by including the scaled cross sections in the tid = 1 µs test case. The DEARB(n = 3) contribution is calculated by

$$DEA\_{RB}(n=3) = \sum\_{\nu} f(\nu) DEA\_{RB}^{scaled\_{-\nu}=3}(\nu) \tag{9}$$

where DEAscaled\_n=<sup>3</sup> RB (v) are the corresponding DEARB rate coefficients calculated from the scaled cross sections of equation (8) with n = 3.

The insertion of such cross sections shows results very similar to those obtained by including only the v = 0 contribution, i.e., the f(0)DEARB(0) and DEARB(n = 3) contributions are essentially equal in the first pulse. Differences occur in the last considered pulse (4th) for t > 12 ns as well as in the post discharge regime.

## CONCLUSIONS

The introduction of DEA from vibrationally excited states of CO plays an important role in NRP CO discharges with an interpulse delay times tid = 1 µs having a minor role with tid = 25 µs. The bulk of results have been obtained by inserting in the

global kinetic model, described in Pietanza et al. (2018a,b), the DEA process through the resonant state X <sup>2</sup>5 characterized by v-state resolved cross sections

and the experimental DEA cross section, which should include the effect of all the other resonant state, i.e., A <sup>2</sup>6, . . . .

$$\varkappa + \text{CO}\left(\text{X}^1 \Sigma^+, \nu\right) \to \text{CO}^-\left(\text{X}^2 \Pi\right) \to \text{C}\left(^3P\right) + \text{O}^-\left(^2P\right) \text{ (10)}$$

$$\begin{aligned} \iota + \text{CO}\left(\text{X}^1 \Sigma^+, \,\, \nu = 0\right) &\to \text{CO}^-\left(\text{A}^2 \Sigma, \,\, ...\right) \to \text{C}\left(^3P\right) \\ + \text{O}^-\left(^2P\right) &\text{ } \end{aligned} \tag{11}$$

for which we do not have the dependence on the vibrational quantum number.

A scaling law has been considered obtaining a complete set of cross sections for the transition described by equation (11). Insertion of this new set of cross sections on the kinetics shows results qualitatively in line with the bulk of results obtained by inserting only the v = 0 contribution, showing however some differences especially in the last considered pulses, when important vibrationally excited vdf are achieved. However, future work in this direction is necessary to better characterize the dissociative cross sections for all resonant states beyond the contribution of CO<sup>−</sup> X <sup>2</sup>5 .

Another important point to be better investigated is the characterization of the process

$$\left(\text{C} + \text{O}^{-} \rightarrow \text{e}^{-} + \text{CO}\left(\text{X}^{1}\Sigma^{+}, \text{v} = 0\right)\right) \tag{12}$$

which produces a source of extra-electrons, becoming important to form extended vibrational distributions able to increase the DEA process. This point should be better quantified by considering the inverse reaction as populating the different vibrational levels, i.e.,

$$\left(\text{C} + \text{O}^{-} \rightarrow \text{e}^{-} + \text{CO}\left(\text{X}^{1}\Sigma^{+}, \text{v} > \text{0}\right) \tag{13}$$

A perspective of this work will be the insertion of the CO reacting kinetics developed in the present work, as well as in Pietanza et al. (2018a,b) and Pietanza et al. (2017a,b), in a complex model for the activation of CO<sup>2</sup> under non-equilibrium plasmas (Kozak and Bogaerts, 2014, 2015; Pietanza et al., 2016a,b, 2017c; Belov et al., 2017; Bogaerts et al., 2017a,b; Capitelli et al., 2017; Klarenaar et al., 2017; Silva et al., 2018). At the moment, the existing data of the dissociative electron attachment of CO<sup>2</sup> include only the global process in the cold gas approximation (i.e., the different vibrational ladders are in the ground state). No theoretical data with the present accuracy for CO do exist and probably one could use the present CO dissociative attachment cross sections to find a scaling law for CO2.

The insertion of the complicated kinetics of CO in the corresponding kinetics of CO<sup>2</sup> will elucidate the role of CO processes in affecting eedf and vdf of the reacting CO<sup>2</sup> mixture

when the dissociation of CO<sup>2</sup> is larger than 10%. In doing so one should also try to develop simplified models able to reduce the number of components as well as to insert analytical forms of vdf for describing the actual vibrational distributions of the different components (Colonna et al., 1999, 2006; Grofulovic et al., 2018; Macdonald et al., 2018).

## DATA AVAILABILITY

Publicly available datasets were analyzed in this study. This data can be found here: https://fr.lxcat.net/data/set\_type.php.

## REFERENCES


## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

## ACKNOWLEDGMENTS

We thank Roberto Celiberto, Vincenzo Laporta, and Annarita Laricchiuta for useful discussions.

and singlet triplet CO vibrationally excited states: implications for the nonequilibrium vibrational kinetics of CO/CO<sup>2</sup> plasmas. Eur. Phys. J. D 71:259. doi: 10.1140/epjd/e2017-80103-1


plasma chemistry and plasma reactor. Plasma Sour. Sci. Technol. 26:063001. doi: 10.1088/1361-6595/aa6ada


coefficients for carbon monoxide. Plasma Sour. Sci. Technol. 21:045005. doi: 10.1088/0963-0252/21/4/045005


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Pietanza, Colonna and Capitelli. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Core Shell Investigation of 2-nitroimidazole

Paola Bolognesi <sup>1</sup> \*, Vincenzo Carravetta<sup>2</sup> , Luca Sementa<sup>2</sup> , Giovanni Barcaro<sup>2</sup> , Susanna Monti <sup>3</sup> , Preeti Manjari Mishra<sup>4</sup> , Antonella Cartoni 1,5, Mattea C. Castrovilli <sup>1</sup> , Jacopo Chiarinelli 1,6, Sanja Tosic<sup>7</sup> , Bratislav P. Marinkovic<sup>7</sup> , Robert Richter <sup>8</sup> and Lorenzo Avaldi <sup>1</sup>

<sup>1</sup> CNR-Istituto di Struttura della Materia, Area della Ricerca di Roma 1, Montelibretti, Italy, <sup>2</sup> CNR-Istituto per i Processi Chimico Fisici, Pisa, Italy, <sup>3</sup> CNR-Istituto di Chimica dei Composti Organo Metallici, Pisa, Italy, <sup>4</sup> Stored and Cooled Ions Division, Max Planck Institute for Nuclear Physics, Heidelberg, Germany, <sup>5</sup> Dipartimento di Chimica, Sapienza Università di Roma, Rome, Italy, <sup>6</sup> Dipartimento di Scienze, Università degli Studi di Roma 3, Rome, Italy, <sup>7</sup> Institute of Physics, University of Belgrade, Belgrade, Serbia, <sup>8</sup> Elettra Sincrotrone Trieste, Area Science Park, Trieste, Italy

Tunability and selectivity of synchrotron radiation have been used to study the excitation and ionization of 2-nitroimidazole at the C, N, and O K-edges. The combination of a set of different measurements (X-ray photoelectron spectroscopy, near-edge photoabsorption spectroscopy, Resonant Auger electron spectroscopy, and mass spectrometry) and computational modeling have successfully disclosed local effects due to the chemical environment on both excitation/ionization and fragmentation of the molecule.

Edited by:

Paolo Tosi, University of Trento, Italy

#### Reviewed by:

Nikolai V. Kryzhevoi, Universitt Heidelberg, Germany Luca Evangelisti, University of Bologna, Italy

> \*Correspondence: Paola Bolognesi paola.bolognesi@cnr.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 04 January 2019 Accepted: 28 February 2019 Published: 02 April 2019

#### Citation:

Bolognesi P, Carravetta V, Sementa L, Barcaro G, Monti S, Manjari Mishra P, Cartoni A, Castrovilli MC, Chiarinelli J, Tosic S, Marinkovic BP, Richter R and Avaldi L (2019) Core Shell Investigation of 2-nitroimidazole. Front. Chem. 7:151. doi: 10.3389/fchem.2019.00151 Keywords: XPS, NEXAFS, mass spectrometry, 2-nitroimidazole, DFT, MCFCS calculations

## 1. INTRODUCTION

Inner shell electrons are localized on specific molecular sites, due to their "atomic-like" nature, and, because they are affected by the chemical environment, can provide details on specific molecular bonds. By means of the tunable and monochromatic X-ray synchrotron radiation, it is possible to deposit well-defined quanta of energy in selected molecular sites and to probe specific electronic configurations through core shell excitation and ionization. The question that arises then, is whether the molecular fragmentation induced by inner shell processes is also site-selective, i.e., affected by the "localization" of the core hole, as well as, in the case of photoabsorption, by the localization and character of the excited orbital. For more than three decades (Eberhardt et al., 1983; Hanson, 1990), this question has been addressed by using different experimental techniques, which combined ion, electron, and electron-ion coincidence spectroscopies to study both core ionization (Rühl et al., 1993; Nagaoka et al., 2011) and excitation (Rühl et al., 1993; Okada et al., 2003; Tanaka et al., 2006; Céolin et al., 2008; Bernini et al., 2012; Lin et al., 2014, 2015; Salén et al., 2014). The features in the absorption spectra are used to "localize" the electron vacancy, through a suitable choice of the photon energy, without detecting the photoelectron as in the case of core ionization. It has been argued that a localized core excitation could be used as a sort of "molecular knife"(Tanaka et al., 2001) to induce controlled bond breakings near the atom of the primary excitation. It is usually observed that the molecular fragmentation following core excitation is strongly influenced by both the molecular site of the initial excitation and the character of the excited molecular orbital. In fact, significant variations in the fragment branching ratios have been observed across different excitation thresholds. In some cases, (Ueda et al., 1999; Liu et al., 2005), an ultrafast molecular fragmentation takes place on a time scale comparable to the electronic decay time of the core hole. In such cases, the process being driven by the elongation of specific bonds adjacent to the core excited atom will be dominated by the formation of specific fragments "cut" around the atomic site of excitation. However, in most cases the "molecular knife" interpretation of the site-selective bond scission is questionable, due to the existence of many fast electronic relaxation channels ending with the removal of one or more electrons from the valence shell and subsequent delocalization of the excess energy. Therefore, the "degree of localization" of the primary excitation is rapidly lost. Indeed, some authors suggested that the sitespecific fragmentation patterns could be explained as a "memory effect"(Larkins, 1990; Habenicht et al., 1991), where the electronic relaxation is driven by the overlap between the core-hole and the valence orbitals in the final state and depends on the electron density of the valence orbitals near the excitation site. This was confirmed by electron-ion coincidence experiments on 2Br-pyrimidine (Bolognesi et al., 2015), where the preferential formation of certain fragments observed at selected resonant core excitation energies was found to depend on the overlap between inner shell excited and the valence ion states, while a direct correlation between a site-selected excitation and a bond breakage could not be established. Within this scenario, site-selective fragmentation patterns are mainly due to selective electronic relaxation mechanisms, which lead to the population of dissociative single and doubly ionized valence states, that are fragmented following their own peculiar pattern. The goal of the present study is to explore the electronic structure of 2-nitroimidazole (2NIM) in the core excitation and ionization regions at the C, N, and O K edges by experiments and quantum mechanics calculations and to investigate the possible correlations between these core excited electronic states and the following molecular fragmentation.

The nitroimidazole molecule (C3H3N3O2) is made of an imidazole ring, (C3H4N2), where a hydrogen atom is replaced by the nitrogen dioxide (NO2) group bound to a carbon atom. For the X-ray photoelectron spectra (XPS) a qualitative approach, based on the known properties of the building blocks of nitroimidazoles, provides an excellent guideline for the interpretation of the spectrum, confirmed by the differential Density Functional Theory (1DFT) calculations. The 2NIM core levels can be related to those of the two building blocks by a predictable chemical shift due to the higher electronegativity of the nitro group. The near-edge X-ray absorption fine spectra (NEXAFS) accurately assigned by quantum mechanics calculations, provide a description of the electronic structure of the main core excited states. Finally, the mass spectrometry experiments allow to follow the fate of the dissociative core excited/ionised states by evolution of the partial ion yields across the different thresholds.

The photoionization and photofragmentation properties of nitroimidazole isomers, including 2NIM, have already been investigated in the valence region for the neutral (Bolognesi et al., 2016; Cartoni et al., 2018) and protonated (Feketeová et al., 2015b) molecule. The 4(5)NIM isomers have also been studied by XPS and NEXAFS (Feketeová et al., 2015a) as well as by ion-ion coincidence experiments (PIPICO) (Itälä et al., 2017). Sections 2 and 3 describe the experimental and theoretical methods, while section 4 is devoted to the description and discussion of the XPS, NEXAFS, and mass spectrometry measurements. Section 5 contains summary and conclusions.

## 2. EXPERIMENTAL

The experiments were performed at the Gas Phase photoemission beamline (Blyth et al., 1999) of the Elettra synchrotron (Trieste, Italy) using the end station, already described in previous studies, for photoemission and mass spectrometry measurements (Bolognesi et al., 2015). Briefly, the radiation source of the Gas Phase beamline is an undulator (Diviacco et al., 1992) that provides fully linearly polarized radiation in the energy range from 13.5 to about 900 eV. Monochromatization of the radiation is provided by five interchangeable gratings and the energy selected photon beam reaches the interaction region in a spot size of a diameter of about 300 µm. The experimental apparatus is a high vacuum chamber hosting a hemispherical analyzer (VG 220i) and a custom made Wiley McLaren (Wiley and McLaren, 1955) time-of-flight (TOF) spectrometer mounted opposite to each other at the magic angle with respect to the polarization axis of the photon beam. The hemispherical analyzer, which mounts six channeltron detectors for parallel acquisition, was used to measure the XPS spectra of the C, N, and O (1s) orbitals of 2NIM at about 90 eV above their respective ionization thresholds, with an overall energy resolution of 0.3 eV. Each XPS spectrum required an acquisition time of about 10 h, with a typical counting rate of the order of 10 counts/s. The chosen photon energies are sufficiently far from the ionization thresholds so that post-collision interaction effects can be neglected. The TOF spectrometer was operated with an extraction field of 700 Vcm−<sup>1</sup> and antisymmetric polarization of the repeller/extractor electrodes (Directed Energy Inc. model PVM4210). The operation mode can be either a continuous extraction, for the measurement of the total ion yield in the NEXAFS spectra, or a pulsed extraction for mass spectrometry, using a pulse generator (Stanford Research DG535) at 1 kHz frequency. In the NEXAFS spectra the photon energy resolution was 20 and 50 meV at the C, N, and O K-edges, respectively. The measured yields were normalized to the photon beam intensity variation read by a photodiode placed at the end of the beamline. The mass spectra were measured at several photon energies in the C, N, and O K near-edge regions, with a step size of 0.25 eV and a typical acquisition time of 800 s per point. In the data analysis, the background was subtracted to each raw mass spectrum and then the intensity of each m/z fragment was evaluated as the sum of yields within the time-of-flight range of interest (corresponding to about m/z ± 0.5). Then, the branching ratio of each fragment was obtained by normalization to the total ion yield.

Both the XPS and NEXAFS spectra were calibrated according to the well-known references of CO<sup>2</sup> (Wight and Brion, 1974; Tronc et al., 1979, 1980; Hatamoto et al., 2007) (C(1s)−<sup>1</sup> at 297.6 eV, O(1s)−<sup>1</sup> at 541.3 eV, C(1s)→ π ∗ at 290.77 eV and O(1s)→ π ∗ at 535.4 eV) and N<sup>2</sup> (Thomas and Shaw Jr, 1974; Sodhi and Brion, 1984) (N(1s)−<sup>1</sup> at 409.9 eV and N(1s)→ π ∗ at 400.87 eV), inserted as diffuse gases in the vacuum chamber. The 2NIM sample (molar mass 113 Da and 98% purity) was purchased from Sigma Aldrich. The powder was introduced into the vacuum chamber in a crucible and heated to about 80◦C to be sublimated for gas phase analysis. The background pressure was 2 x 10−<sup>8</sup>

mbar and a cold finger was used to reduce contamination from background residual water.

## 3. THEORY

Calculations were carried out for both ionization (XPS) and excitation (NEXAFS) of the core shells of the three C, three N, and two O atoms of 2NIM. The photoemission spectra were modeled by all-electron differential methods fully including electronic relaxation (1HF) and partially including electronic correlation (1DFT) by using the DALTON code (Angeli et al., 2013). With the same code, we carried out accurate multiconfigurational self-consistent field (MCSCF) calculations to assign a peculiar feature appearing in the oxygen K-edge XPS spectrum due to a shake-up process. The Restricted Active Shell (RAS) approximation, describing the electron correlation in the highest 12 valence levels, and the medium size Ahlrichs-VTZ basis set (Schäfer et al., 1992) were adopted. A valence electron method introduced recently (Iannuzzi and Hutter, 2007), with the use of a potential to describe the relaxation of the core hole, was employed for the simulation of the NEXAFS spectra. These calculations were performed with cp2k (Lippert et al., 1999) within the all-electron implementation of the Gaussian Augmented Plane Wave (GAPW) (Krack and Parrinello, 2000) method. The Kohn-Sham (KS) wave-functions were projected on a set of Gaussian contracted functions. We employed two different atomic basis sets: aug-cc-pVTZ (Dunning Jr, 1989) for the molecular structure optimization and aug-cc-pVQZ to improve the accuracy of the higher excited states of NEXAFS spectra.

The computational efficiency of the GAPW method relies on an auxiliary electronic density that is partitioned in an electronic part, smoothly varying between atoms and in an electronic part, rapidly varying close to the nuclei. For a fast evaluation of the Coulomb and Exchange potentials, a planewave expansion is adopted to project the former, whereas combinations of localized atomic functions describe the latter. Thus, beyond Gaussian basis sets, we used plane waves with an energy cut-off of 300Ry to expand the smooth part of the auxiliary electronic density. The BLYP (Becke, 1988; Lee et al., 1988) density functional was chosen for the exchange and correlation part of the KS hamiltonian. We calculated the NEXAFS spectra by following the protocol described by Iannuzzi and Hutter (2007) which is based on the direct calculation of both the excitation energy and the dipole transition element between the selected core orbitals and a certain number of virtual orbitals obtained through a full-core-hole transition potential (Jayawardane et al., 2001; Hetényi et al., 2004) on the adsorbing atoms. This method predicts accurate relative positions of the main NEXAFS features. In order to get the absolute energy scale for the full set of excitations at a given K-edge, we performed DFT calculations to estimate the energy difference between the ground state and the first core-excited state. The Stieltjes Imaging method (Langhoff, 1980; Cacelli et al., 1991) was applied to the discretized excitation spectrum, followed by a convolution with a Gaussian (FWMH = 0.2 eV) to mimic both the finite lifetime of the excited states and the limited experimental resolution.

## 4. RESULTS AND DISCUSSION

The presentation of the results is organized in three subsections, devoted to the XPS, NEXAFS, and mass spectrometric experiments, respectively. For the XPS and NEXAFS experiments, a qualitative approach, based on the spectroscopy of imidazole and nitrogen dioxide molecules, guided a first assignment of the different features of the spectra. This was then fully validated by the 1HF, 1DFT, 1MCSCF, and TDDFT calculations: the discussion of the observed chemical shifts unravels the role played by the nitro group in the stabilization of the imidazole ring atoms. The theoretical prediction of the NEXAFS spectra allows to disentangle the contribution of the different non-equivalent atoms in each absorption spectrum and to analyze the charge distribution in the lowest unoccupied molecular orbitals, LUMO, and LUMO+1. The last subsection reports the results of the time of flight mass spectra measured at several photon energies in the C, N, and O near K-edge regions and the discussion of the site-selective molecular fragmentation.

## 4.1. The XPS Spectra

The XPS spectra of 2NIM at the C, N, and O K edges are shown in **Figure 1**. The main C and N spectral features were tentatively fitted with three Gaussian functions with the same area, corresponding to the number of non-equivalent atoms of the same species. The results are indicated as peaks A to C for carbon, and D to F for nitrogen. In the O case, the two non-equivalent atoms O7 and O8 are expected to be nondegenerate. However, the calculated splitting of about 100 meV (see **Table 1**) combined with the vibrational broadening makes the two peaks unresolvable in the XPS measurement within the present experimental resolution. Therefore, only the average position of the two contributions is reported in the experimental data and the O (1s) peak is labeled G.

A first qualitative assignment of these XPS spectra is suggested by the energy positions of the main XPS bands for imidazole (Apen et al., 1993; Thomason et al., 2015) and nitrogen dioxide (Davis et al., 1973; Jolly et al., 1984), i.e., the building blocks of the nitroimidazole molecule. The core binding energies (BE) of these building blocks are represented by the vertical bars in **Figure 1**, and the corresponding values are reported in **Table 1**, together with the binding energies of 4- and 5-NIM isomers from Feketeová et al. (2015a). An overview of the 2NIM, imidazole and nitrogen dioxide XPS binding energies is also displayed in the diagram of **Figure 2**. Based on the qualitative analogies among the nitroimidazole isomers and their building block molecules, we assign the 2NIM XPS peaks A to G for increasing binding energies to the C4, C5, C2, N3, N1, N6, O7/8 atoms, respectively. This qualitative assignment is fully validated by our 1DFT calculations, also reported in **Table 1**. Apart from an average shift of about 1.1 eV for the C and N spectra and –0.42 eV for O, there is good agreement between the theoretical predictions and both

energy about 90 eV above their respective ionization thresholds: experimental points (black circles) and best fitting with Gaussian functions (red and green lines). The energy position of the XPS lines of imidazole and nitrogen dioxide are also shown as blue bars in the C, N, and O cases, respectively (see also Figure 2 and references in the caption for source data). In the bottom panel, the inset shows the structure of the 2NIM molecule and its atoms numbering.

the experimental observations, and the qualitative assignment provided by the "building block approach."

The three C(1s) XPS peaks in all nitroimidazoles show a clear influence of the presence and specific location of the NO<sup>2</sup> group on the imidazole ring. In fact, all C(1s) binding energies (black levels in **Figure 2**) are chemically shifted toward higher values with respect to those of the corresponding atoms in the imidazole molecule. These positive shifts are due to the electron withdrawing of the NO<sup>2</sup> group, producing a charge transfer from the imidazole ring to the nitro group, which reduces the electronic relaxation around a core hole on the ring atoms, increasing their binding energies. In 2NIM, this effect is more pronounced on the C2 atom, which is directly involved in the C2-NO<sup>2</sup> bonding. The experimental data provided 1.82 eV for the C2 chemical shift, to be compared with an average shift of 1.1 eV for C4 and C5 with respect to imidazole. It should be noted that according to the Koopmans theorem (KT), ground state HF calculations predict chemical shifts of 2.5, 1.3, and 1.6 eV for the C2, C4, and C5 atoms, respectively, going from imidazole to 2NIM. 1SCF calculations, fully including electron relaxation around a specific core hole, predict instead 2.2, 1.7, and 0.7 eV respectively, to be compared to experimental values of 1.8, 1.2, and 1.0 eV (see **Figure 1**). It is clear, from this comparison, that an interpretation of the chemical shift as due to an "initial state effect" (KT) is only a rough approximation and can be erroneous in the prediction of the relative size of the chemical shift for nonequivalent atoms in the molecule. The inclusion of electronic relaxation around the core hole (final state effect) can instead provide a reliable estimation of the chemical shift.

For the N(1s) XPS spectrum, the comparison between 2NIM and its building blocks is more complex; in fact, it is necessary to distinguish the case of the ring atoms N1 and N3 of the imidazole and the N6 atom of the NO<sup>2</sup> molecule. The building block values are significantly separated in energy (around 7 eV), clearly manifesting the influence of the chemical environment on the core binding energy, with the nitrogen atoms surrounded by the two strongly electronegative oxygen atoms in NO2, or by carbon atoms, when embedded in the imidazole ring. In 2NIM, the N3 and N1(1s) electron binding energies, similar to the C case, present a positive shift with respect to imidazole, while N6 presents a negative shift with respect to nitrogen dioxide, i.e., shifting toward smaller binding energies. This can be explained by considering the same effect already discussed in the C case where, in the C2-NO<sup>2</sup> bond, the nitro group withdraws electron charge mostly from the C2 atom, but also, by inductive effect, from the entire imidazole ring. Therefore, the reduced screening on the N3 and N1 ring atoms increases their (1s) electron binding energies while on the N6 atom of the nitro group this has the opposite effect, increasing the shielding and therefore decreasing the N6(1s) binding energy with respect to the NO<sup>2</sup> isolated molecule.

In the binding energy of the O(1s) electrons, similarly to the N6 case, there is a significant negative shift of about –2.5 eV in 2NIM with respect to NO2. The break of symmetry with respect to the isolated NO<sup>2</sup> molecule is likely to introduce a chemical shift between the O7/O8 atoms. Theoretically, this has been estimated to be of 0.1 eV. In the experimental XPS spectrum at the O K-edge a small band at about 540.2 eV is clearly visible. To assign this particular feature, accurate MCSCF calculations were performed to include in the theoretical model both the electron relaxation described by the HF method and electron correlation. This was explicitly done for all the outer 12 valence electrons and the energy of the 2NIM ground state, the O(1s) core hole state and the lowest energy shake-up state are reported in the second column of **Table 2**. The MCSCF calculations predict an energy for the lowest shake-up state (HOMO-LUMO excitation) that is 1.6 eV above that of the core hole state, in excellent


TABLE 1 | Comparison of present experimental and theoretical core ionization potentials of 2NIM with equivalent experimental and theoretical data for the 4- and 5NIM isomers (Feketeová et al., 2015a), imidazole (Becke, 1988), and nitric dioxide (Jayawardane et al., 2001).

The latter two molecules can be considered as building blocks of the nitroimidazole family of molecules (see text). Numbers in parenthesis represent the uncertainty of the present fitting procedure. \*NO<sup>2</sup> being an open shell molecule, the core ionization leads to two (3A<sup>1</sup> and <sup>1</sup>A1) states due to spin coupling.

agreement with the energy position of the peculiar band observed around 540.2 eV that therefore can be ascribed to a shake-up process. This is a clear example that the HOMO-LUMO energy difference predicted by a calculation for the initial ground state (estimated as large as about 10 eV at the HF level) should be considered only as a very rough approximation for the prediction of the energy level of the lowest shake-up state. In the present case the unusually low energy of the shake-up state derives from the electron distribution of the LUMO orbital in the final state which is mostly located close to the core hole (see next section). Similarly to the 4(5)NIM and related compounds, the O(1s) XPS spectrum shows a broad maximum at about 542 eV. This feature could not be ascribed to the presence of any possible residual gas or fragment from the decomposition of the 2NIM molecule. In the present work we do not have definite assignment for this feature, but in the work of (Feketeová et al., 2015a) it was assigned as a π − π ∗ shake-up.

## 4.2. The NEXAFS Spectra

The comparison between the experimental and theoretical NEXAFS spectra of 2NIM at the C, N, and O K-edges is reported in **Figures 3A–C**. All the computed spectra were convoluted with a Gaussian function (width = 0.2 eV) to mimic both the experimental response function and the vibrational broadening, and shifted by arbitrary amounts, reported in their respective figures, to obtain a good matching with the low energy bands of the experimental spectra. The calculated spectra neglect the vibrational distribution of the electronic states. This may change the position of the centroid, the shape and the relative intensity of the bands. Nevertheless, there is a very good agreement between theoretical predictions and experimental data in the low energy part of the spectra, i.e., in the region of the excitations involving the LUMO and LUMO+1. Some discrepancies are observed in the region approaching the continuum, due to the poor reproduction of the region of the Rydberg excitation by the adopted theoretical methods. The different colors in **Figures 3A–C** represent the individual contributions from the non-equivalent atoms and allow identifying the role played by each one in the different energy regions of the spectra, in particular on the discrete features at the low energy side corresponding to excitations to the lowest virtual orbitals. The charge distribution of the LUMO and LUMO+1 orbitals are reported in **Figures 3D–F**, showing that these orbitals are all of π and antibonding nature. Above the ionization thresholds, broad features usually assigned to transitions to σ ∗ shape resonances are also observed. This kind of excited state involves antibonding σ orbitals quite localized in the core hole region and, as a consequence, the transition dipole moment can be large. However, their usually strong dissociative character, leads to a spreading of such intensity on a large band by a coupling, which depends on the atomic site and the bond environment. In all cases, the excitation energies of the nonequivalent atoms follow the same ordering as in the XPS spectra (see **Table 1**), even though the charge distribution of the different excited orbitals may produce a different core hole screening for each site and therefore modify the values of the chemical shift with respect to the ones measured in XPS. Concerning the comparison of 2NIM to imidazole, an opposite behavior can be observed in the binding energy shifts of the XPS and NEXAFS spectra. Indeed, while ionization energies of 2NIM shift to larger values with respect to imidazole, the excitation energies shift to a lower one, indicating a stabilization of the LUMO orbitals. This is clearly illustrated in **Figure 2**, where the binding energies of the LUMO (red bars, assigned according to the theoretical calculation) and of the ionization (black bars) at the C, N, and O K edges are reported for nitrogen dioxide, 2NIM and imidazole. Although in the core excitation the molecule is neutral, the LUMO is embedded in the field of an ion with a localized charge. This leads to a lowering of the LUMO energy with respect to the ground state of the molecule. This stabilization strongly depends on the charge of the core hole and its screening. In the case of 2NIM, the NO<sup>2</sup> group removes the charge to screen the core hole and the binding energy as well as the attractive force of the partially screened core hole on the LUMO electron increases, thus the LUMO in 2NIM is stabilized with respect to imidazole. This shows that the effect of the substituent group is opposite on the binding energy of the core orbitals and on the excitation energy of the LUMO. Another contribution to the lowering of the LUMO energy in the 2NIM is likely due to the hyperconjugation of the

FIGURE 2 | Diagram of the binding energies (black) and of the lowest (LUMO) excitation energies (red) at the O, N, and C K edges and at the valence shell (Kimura, 1981; Schwell et al., 2008; Cartoni et al., 2018), for nitrogen dioxide (Davis et al., 1973; Au and Brion, 1997; Jayawardane et al., 2001) (left), 2NIM (center) and imidazole (right) (Apen et al., 1993; Thomason et al., 2015) molecules.

TABLE 2 | Results of MCSCF calculations for: ground state, O core hole state and lowest energy O shake-up state of 2NIM; total energy in second column and relative energy (binding energy) in third column.


NO<sup>2</sup> π orbitals with the aromatic orbitals of the imidazole ring. It is not straightforward to evaluate the amount of these two contributions in the observed lowering of the LUMO, but it is realistic to consider that both of them are present.

In the C NEXAFS spectrum (**Figure 3A**) we observed several structures, labeled a to g, organized in four main groups. The first group contains the partially resolved features a to c at 286, 286.6, and 287 eV, respectively. Previously published NEXAFS measurements of 4(5)NIM have empirically assigned this group of peaks (energy region 285.3–287.0 eV), to a series of C(1s)→ π ∗ transitions (Feketeová et al., 2015a). In the present work, supported by the theoretical predictions, we assigned the feature a mainly to a C5(1s)-LUMO transition with a minor contribution from the C4-LUMO, feature b to the C4(1s)-LUMO+1 transition with a minor contribution from the C2(1s)-LUMO and then feature c to C5(1s)-LUMO+1 transition. The tiny feature d at 288.6 eV is dominated by the C4 contribution while e and f, at 289.4 and 290.3 eV, respectively, are dominated by core excitations from C2, approaching the C4 and C5(1s) ionization continua. The broad feature g at 292–295 eV can be attributed, by present calculations, to σ ∗ resonances, with the strongest contributions due to excitations from the C2 core orbital to antibonding orbitals along C2-N6 and C2-N1 and, to a minor extent, from the C5 core orbital to antibonding orbitals along C5- N1. In the C NEXAFS like in the XPS there was a positive shift, i.e., toward higher excitation energies, of the C2(1s) excitation spectrum with respect to the C4 and C5 contributions, which are very close in energy. The gas phase electron energy loss (EEL) measurement of imidazole (Apen et al., 1993) assigned the overlapping contribution of the LUMO excitations from the three C atoms to a large, unresolved feature at 286.7 eV.

In the N NEXAFS spectrum, three distinct features labeled h, i, and l at 398.9, 401.1, and 403.9 eV were observed experimentally and were very well reproduced in both position and relative intensities by the theoretical predictions. According to the present calculations, their assignment follows the same ordering as in the XPS spectrum. The first feature, h, is attributed entirely to the N3(1s) excitation to the LUMO orbital, the second one, i, to the overlapping of the (1s) excitation from N1 to LUMO and from N3 to LUMO+1, while the third and strongest feature, l, has a mixed contribution from all three N sites, but is dominated by the N6(1s) to LUMO. The position and assignment of these three features are very close to the ones reported for the 4(5)NIM, i.e., about 400.55, 401.7, and 403.9 eV, respectively (Feketeová et al., 2015a), indicating that the N core excitation is not a sensitive fingerprint to distinguish the nitroimidazole isomers. Similar to the C case, an opposite trend was observed in the core ionization and excitation at the N K-edge. Indeed, the N3 and N1(1s) excitations of imidazole are located at 399.9 and 402.3 eV, respectively (Apen et al., 1993) (i.e., at higher excitation energy with respect to 2NIM) and the N(1s) excitation in NO<sup>2</sup> is located at an average value of 402.34 eV (Zang et al., 1990; Gejo et al., 2003) (i.e., at lower energy compared to 2NIM). This is the opposite behavior with respect to the XPS, where N3 and N1 (1s) BE were shifted at higher binding energies compared to imidazole, while N6 was shifted toward lower binding energies compared to nitric dioxide. The increased electronic density with respect to NO<sup>2</sup> results in a decreased binding energy of N6 while, as discussed above, the attraction of the screened hole on the electron of the LUMO destabilizes the LUMO itself. Considering that the hyperconjugation should always have a stabilizing effect on the LUMO, this result indicates that the most relevant effect in determining the stabilization/destabilization of the LUMO is the variation of the hole screening. The m and n features at around 407 and 409 eV, respectively, can be attributed,using present calculations, to a partial contribution of π ∗ transitions to LUMO+1 and LUMO+2 orbitals from the N6 core orbital as well as to σ ∗ transitions from N1 core orbital to antibonding

orbitals along N1-H and N1-C2. Similar broad features were also observed in both imidazole (at 411.4 and 415 eV), where they are attributed to C-N<sup>∗</sup> transitions, and in NO2, at 416.16 eV.

At the O K-edge, the NEXAFS spectrum below the ionization continuum is dominated by the intense peak o at 530.85 eV, containing the overlapping contribution of the core excitations to the LUMO at atoms O7 and O8. Similarly to the XPS spectrum, the chemical shift between O7 and O8 does not give rise to a measurable shift in the observed peaks, as confirmed by the theoretical prediction of a chemical shift of 0.1 eV (see **Table 1**). The position of the O(1s) LUMO+1, peak p at about 534 eV, is also quite well predicted by the theoretical model. Considering the shift of the O(1s) edge in the theoretical NEXAFS spectra, features r and s, at around 538 and 541 eV, respectively, can be attributed, by the present calculations, to transitions to σ ∗ orbitals along N6-O.

Concerning the charge distributions reported in **Figures 3D–F**, the most evident difference between the LUMO and LUMO+1 orbitals can be observed along the C2-N6 bond, which has a bonding/antibonding character in case of excitation to the LUMO/LUMO+1 states, respectively. More subtle differences are present among the different sites of excitation but, since the charge is quite delocalized, no evident correlation between the localization of the core hole and the charge distribution could be made.

#### 4.3. Mass Spectra and Partial Ion Yield

The molecular fragmentation of 2NIM following the C, N, and O core excitation/ionization has been investigated by measuring time-of-flight (TOF) mass spectra at several photon energies across their respective near-edge regions. The mass spectra measured in the energy regions of the transitions from the C, N and O(1s) to the LUMO orbital are reported in **Figures 4A–C**, respectively, and compared with the ones obtained in the region just below their respective resonance regions. The assignment of the main fragments of interest in the present work is reported in **Figure 4** and the list of all fragments is collected in **Table S1**. In general, the enhanced photoabsorption cross section at the core excitation energies affects the intensity of all fragments, thus the partial ion yields vs. photon energy, mimics the overall shape of the NEXAFS spectrum. However, the fragmentation pattern itself, and therefore the molecular branching ratio, depend on the location of the inner hole (Okada et al., 2003; Tanaka et al., 2006; Céolin et al., 2008; Bernini et al., 2012; Lin et al., 2014, 2015; Salén et al., 2014). To prove this, **Figure 4** shows the superposition of the fragmentation mass spectra measured "on" and "off " resonance and the quantity (Yieldon -Yieldoff ) / Yieldoff for the major fragments as vertical bars at the bottom of each panel. This quantity allows the variation of the yield "on" resonance, with respect to the "off " resonance one, to be evaluated for each fragment. A value of 1, for example, means that the yield on resonance has doubled, i.e., suffered 100% variation.

Beginning with the 2NIM parent ion (m/z 113) one sees that its contribution to the mass spectra at the three edges is negligible, showing only a minor resonant enhancement in the case of C(1s)−→ π ∗ excitation (**Figure 4A**). The fragments at m/z 97 (2NIM-O)+, 83 (2NIM-NO)+, and 67 (2NIM-NO2) + involve the nitro group and share the property of leaving the imidazole moiety unfragmented, even though we cannot infer about its structure as a ring or an open/rearranged feature. Their contribution to the mass spectra is small, however these fragments show significant resonant behavior. At the C(1s)−→ π ∗ resonance the (2NIM–NO2) <sup>+</sup> displays a noticeable decrease, while the 66<sup>+</sup> fragment, which corresponds to a further loss of a H atom from (2NIM-NO2) <sup>+</sup>, shows a smaller decrease (**Figure 4A**). The variation of fragment 83<sup>+</sup> is significant. According to a mass spectrometric and PEPICO study in the

valence region (Bolognesi et al., 2016), fragment 83<sup>+</sup> originates from a (slow) molecular rearrangement of the nitro group, with a swap in position between the O and N atoms, losing the NO group. The reduction of the intensity of this fragment suggests that C(1s) core excitation triggers "faster" fragmentation or decay processes with respect to this "slow" molecular rearrangement, which is therefore hampered. At the N(1s) −→ π ∗ resonance (**Figure 4B**), the NO<sup>2</sup> loss channel does resonate, doubling the intensity of the fragments at m/z 66 and 67, while at the O(1s) −→ π ∗ resonance (see **Figure 4C**) both fragments display a very large increase, more than doubling their intensity. At this resonant excitation energy, an even larger increase is observed in fragment m/z 97 due to the O loss. This fragment is barely present in the "off " resonance as well as in the mass spectra at the C and N continua and π ∗ resonances. The complementary fragments NO<sup>+</sup> 2 (m/z 46), NO<sup>+</sup> (m/z 30), and O<sup>+</sup> (m/z 16) do not display appreciable relative variations in the "on" resonance, a part of the NO<sup>+</sup> 2 fragment which suffers a small decrease at the N and O(1s)−→ π ∗ resonances. This may indicate that (i) the observed NO<sup>+</sup> and NO<sup>+</sup> 2 ions are mostly produced by direct photoionization and/or (ii) the complementary NO and NO<sup>2</sup> molecules or their fragments are lost as neutral species. These interpretations may be confirmed by a quantitative comparison of the absolute variation of the intensity of the complementary fragments. However, such an estimate based on the present data is unreliable, because it would be affected by the kinetic energy distribution of the involved fragments, which in turn affects the detection efficiency. photoioni-photoion coincidence (PEPIPICO) experiments (Itälä et al., 2017) reported that the dominant contribution in the fragmentation of doubly/multiply charged 4(5)NIM ions just above the C K-edge corresponds to the release of NO+, while NO<sup>+</sup> 2 is either hardly produced or has a large probability to fragment, consistent with our observations.

The m/z 56, assigned to the HNCHCO<sup>+</sup> fragment, is a peculiar fingerprint of 2NIM, not present in 4(5)NIM at least up to 60 eV photon energy (Bolognesi et al., 2016). Similar to 30<sup>+</sup> and 28+, its formation in the VUV energy range is related to the loss of NO and the subsequent fragmentation of the residual 83<sup>+</sup> fragment. It provides a minor contribution to the mass spectra, with a decrease of intensity at the core excitation, in particular in the C case, **Figure 4A**. Its branching ratio does not display peculiar resonance effects (see **Figures 5A,B**). Passing through core excitations and ionizations the fragmentation mechanisms could be different from the ones identified in the valence region, mainly due to the possibility for multiply-charged ion formations. However, the PEPIPICO experiments of (Itälä et al., 2017) in 4(5)NIM at 317 eV photon energy (i.e., still well below the N K edge) do not display any significant signal for ion pairs including m/z fragments heavier than 46. Therefore, we deduced that double ionization events are not the major channels for the production of heavier fragments in 2NIM too.

The largest contribution to the 2NIM mass spectrum was provided by fragments in the m/z regions 38–42 and 24–30. The first region was dominated by the m/z 40 fragment due to C2H2N<sup>+</sup> and its correlated species C2HN<sup>+</sup> and C2N+, while the other region was populated by light species like NO<sup>+</sup> (m/z 30), CO<sup>+</sup> /HCNH<sup>+</sup> (m/z 28) and its correlated species HCN<sup>+</sup> and CN<sup>+</sup> due to fragmentation of both the imidazole or the nitro group. All the fragments in the m/z region 38–42 displayed a resonance effect with an increase of their intensity at the three π ∗ excitations, while in the region m/z 24–30 the HCN<sup>+</sup> and CN<sup>+</sup> fragments displayed an opposite behavior and decreased their relative intensity at the N and O(1s) → π ∗ resonances, showing how the "localization" of the core hole produces large effects on these fragmentation patterns.

A more complete view of the effect of the excitation of the inner-shell resonances is provided by the branching ratios variation of selected fragments reported vs. photon energy in **Figures 5A–C** for the C, N, and O K edge regions, respectively, while their values at selected photon energies spanning from 60 (Bolognesi et al., 2016) to 538 eV are reported in **Table S1** and displayed in **Figure S1**.

As already mentioned in the discussion of **Figure 4**, the 2NIM parent ion (m/z 113) branching ratio decreased significantly with increased photon energy up to the oxygen K edge where its branching ratio vanishes (**Figure S1**). This trend is very common in molecular species, due to the large amount of energy delivered by inner shell excitation/ionization and to the many active fragmentation channels. Indeed, PEPICO experiments on

FIGURE 5 | The branching ratios of some selected fragments of 2NIM reported vs. photon energy at the C, N, and O K edge regions. The fragments with a positive or negative variation vs. photon energy are shown in the top and middle panels, respectively. The bottom panels show the corresponding NEXAFS spectra to help identification of the main resonances.

2NIM in the VUV energy range, clearly demonstrated that the molecular fragmentation is state-selective; just after the opening of the first fragmentation channel (the NO loss, at around 10.6 eV), the branching ratio of the parent ion drops to zero (Bolognesi et al., 2015, 2016; Cartoni et al., 2018) indicating that the lowest lying molecular orbital is the only one that allows preservation of the parent ion as an intact unit in the photoionization event, at least within a microsecond time scale. Therefore, with increased photon energy the cross section and, as a consequence, the contribution of the electronic ground state to the fragmentation mass spectrum, becomes less and less relevant and eventually negligible. Furthermore, the parent ion does not show any resonant behavior, as discussed above, indicating that the coupling of these core excited states to the cation electronic ground state is very poor. This was confirmed by the photoelectron spectra taken at the three main resonances at the N edge, which showed that the Resonant Auger process does not lead to an appreciable population of the cation HOMO state. Among the three regions shown in **Figure 5**, the carbon region (**Figure 5A**) is the one that displays the smallest variations. Weak resonance effects are observed in the region of the a-c resonances (see **Figure 3A** for the labeling), while some effects on m/z 30, 28, and 40 are observed in correspondence of the d-f resonances, with an enhancement of the m/z 30 branching ratio and a depletion on the other two.

In this region, according to the calculations, the main process is due to the population of the LUMO involved in the excitation of the C2 atom, the one directly bound to NO2. In the region of the nitrogen inner shell resonances (**Figure 5B**), the branching ratios of most of the fragments display resonance effects, attenuated in the case of m/z 53, 66, and 67. It is interesting to observe that at the h resonance, attributed to the population of the LUMO by the promotion of an electron from the N3(1s) orbital, the effects are opposite for the m/z 28, 39, and 40 and the m/z 12, 16, 26, 27, and 56. This opposite behavior is also observed in the region of the i resonance, but seems to disappear at the l resonance, where mainly the excitation of the LUMO with the core hole in the N6 site occurs. The observations in the oxygen region (**Figure 5C**) are similar, with large effects effects in the region of the o resonance. The branching ratios of fragments m/z 40 and 28 display a clear decrease for increasing photon energy (**Figure S1**) with an interesting enhancement on-resonance (**Figure 5**). These observations may suggest the important role of valence/inner valence fragmentation processes in the production of these fragments. The cross section of valence/inner valence states decreases at larger photon energies and in the core ionization continua, but shows significant enhancements at the core resonant excitations, where the valence shell states can be efficiently populated via Resonant Auger emission as shown in the N case, for example (**Figure 6**).

The resonant photoemission leads to a preferential population of the inner valence states (via spectator Resonant Auger decay) as compared to the direct photoemission measured just below the first resonance. In the binding energy region 13–18 eV, the PEPICO experiments (Bolognesi et al., 2016; Cartoni et al., 2018) have shown that the fragmentation is dominated by the release of fragments 28+, 40+. In the valence single ion states, fragment 40<sup>+</sup> originates by a chain of events where, following

the NO<sup>2</sup> loss, the subsequent fragmentation of fragment 67<sup>+</sup> by HCN loss, leads to the HNCCH<sup>+</sup> fragment, that can exist both in its linear or ring structure (Bolognesi et al., 2016; Cartoni et al., 2018). Formation of fragment 28+, instead, is triggered by the NO loss, leading to fragment 83<sup>+</sup> that, after several molecular rearrangements and the release of HCN and CO neutral species, ends up in the HCNH<sup>+</sup> fragment at m/z 28. Moreover, at these core excitation energies, additional mechanisms of formation involving the fragmentation double and multiply charged ions, may also become active. A general trend is that for increasing photon energy the branching ratios of "small" fragments (m/z ≤ 30, with the exception of m/z 28) increases in comparison to the larger ones (see m/z 12 and 30 in **Figure S1**). Their branching ratios increase as new core ionization thresholds are crossed, while they decrease at resonant excitation energies. Considering the many pathways that could produce these fragments, their detailed discussion would be uncertain. However, they likely result from a stepwise fragmentation process, involving highly excited singly or multiply-charge ions. Thus, the observed difference can be

explained by the formation of excited dications via Auger decay when the excitation occurs above the K-edge, while on resonance, the Resonant Auger Electron processes populate cation states, hampering fragmentation patterns that require larger amount of energy.

## 5. CONCLUSIONS

The core excitation and ionization of 2NIM has been investigated by a set of complementary experimental techniques, which span from electron spectroscopies to mass spectrometry and by accurate computational methods for the prediction of photoemission and photoabsorption spectra. The XPS spectra can be interpreted at a qualitative level, by a building block approach with imidazole and nitrogen dioxide as constituents of nitroimidazoles; this assignment has been confirmed by theoretical simulations of the spectra. The electronegativity of the NO<sup>2</sup> ligand withdraws charge from the imidazole ring affecting its stability. We observed, in fact, that an initial state picture, corresponding to the KT approximation, may provide a rough, sometimes misleading, prediction of the chemical shifts in NIM. A reasonable prediction can only be obtained considering final state effects (polarization and screening due to the increased/decreased number of electrons around the ionization site). Moreover, the building block approach must be considered with caution when one of the constituents of the larger molecule, such as the NO<sup>2</sup> ligand in 2NIM, may change geometry (NO<sup>+</sup> 2 is straight in gas phase and bent in 2NIM) and electronic structure (NO<sup>2</sup> is a radical, while 2NIM is not). While the core levels can be qualitatively related to the two different components, chemically shifted from the imidazole and NO<sup>2</sup> value by the predictable effect of the nitro group electronegativity, only 1DFT calculations could confirm the qualitative assignment and the relative values of the chemical shifts. This can be related to the recent observation in the photofragmentation spectra of 2NIM where, at least in the VUV energy region, the NO-loss was the most favorable fragmentation channel, from which all others followed. An intense "shoulder" observed on the high energy side of the main peak in the O(1s) photoemission spectrum, was assigned, by accurate MCSCF calculations, to the lowest shake-up state (HOMO-LUMO excitation) that is predicted to be located at an energy 1.6 eV above that of the core hole state. The unusually low energy of the shake-up state derives from the electron distribution of the LUMO orbital in the final state, which is mostly located close to the core hole.

In the NEXAFS spectra, the combined experimental and theoretical study provided the observation and assignment of the major features due to core electron excitation from the different, and well identifiable, atomic sites in the molecule as well as a description of the corresponding charge distribution in the LUMO and LUMO +1 orbitals. A stabilization of the LUMO

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has been observed in 2NIM with respect to imidazole. In the mass spectrometry experiments, the tunability of the photon energy has been used to follow the evolution of the partial ion yields across the different core excited/ionized states of the molecule. Significant effects, especially for channels involving the release of the nitro group, were observed in terms of a variation of the branching ratios in the investigated regions. The cases of the NO2, NO, and O losses provide clear evidence of a correlation between the localization of the vacancy and the fragmentation mechanism. This may be considered as possible evidence of a "molecular knife" picture. On the other hand, for the smaller fragments, the observed effects could be rationalized considering that the preferential decay of core excited states is the Resonant Auger decay, which populates the cation states in the valence/inner valence region. The leading mechanism is therefore more of a "memory effect," ruled by the coupling of the inner shell electronically excited state to the valence/inner valence states, and their following fragmentation.

#### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and/or the **Supplementary Files**.

#### AUTHOR CONTRIBUTIONS

PB, PM, ST, BM, RR, and LA performed the experiment. VC, LS, GB, and SM performed the theoretical calculations. AC, MC, and JC participated in the data analysis and interpretation. PB and LA planned the experiment and prepared the manuscript. All authors contributed to the interpretation of the results and the revision of the manuscript.

## FUNDING

We gratefully acknowledge support from the Progetto di Grande Rilevanza of the Italian Ministero degli Affari Esteri e della Cooperazione Internazionale (MAECI) Italia-Serbia A nanoview of radiation-biomatter interaction. ST and BM acknowledge the support from MESTD project #OI 171020.

## ACKNOWLEDGMENTS

The authors thank K.C. Prince for useful discussions.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00151/full#supplementary-material

Apen, E., Hitchcock, A. P., and Gland, J. L. (1993). Experimental studies of the core excitation of imidazole, 4, 5-dicyanoimidazole, and s-triazine. J. Phys. Chem. 97, 6859–6866. doi: 10.1021/j100128a019

Au, J. W., and Brion, C. (1997). Absolute oscillator strenghts for the valenceshell photoabsorption (2-200 eV) and the molecular and dissociative photoionization (11-80 eV) of nitrogen dioxide. Chem. Phys. 218, 109–126. doi: 10.1016/S0301-0104(97)00065-7


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer LE declared a past co-authorship with one of the authors VC to the handling editor.

Copyright © 2019 Bolognesi, Carravetta, Sementa, Barcaro, Monti, Manjari Mishra, Cartoni, Castrovilli, Chiarinelli, Tosic, Marinkovic, Richter and Avaldi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

## NH<sup>+</sup> 4 Association and Proton Transfer Reactions With a Series of Organic Molecules

Eva Canaval <sup>1</sup> , Noora Hyttinen2†, Benjamin Schmidbauer <sup>1</sup> , Lukas Fischer <sup>1</sup> and Armin Hansel <sup>1</sup> \*

#### Edited by:

*Paolo Tosi, University of Trento, Italy*

#### Reviewed by:

*Oh-Hoon Kwon, Ulsan National Institute of Science and Technology, South Korea Fuminori Misaizu, Tohoku University, Japan Pawel K. Misztal, University of California, Berkeley, United States*

#### \*Correspondence:

*Armin Hansel armin.hansel@uibk.ac.at*

#### †Present Address:

*Noora Hyttinen, Nano and Molecular Systems Research Unit, University of Oulu, Oulu, Finland*

#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *07 January 2019* Accepted: *13 March 2019* Published: *03 April 2019*

#### Citation:

*Canaval E, Hyttinen N, Schmidbauer B, Fischer L and Hansel A (2019) NH*<sup>+</sup> *4 Association and Proton Transfer Reactions With a Series of Organic Molecules. Front. Chem. 7:191. doi: 10.3389/fchem.2019.00191* *1 Institute of Ion Physics and Applied Physics, University of Innsbruck, Innsbruck, Austria, <sup>2</sup> Department of Chemistry and Institute for Atmospheric and Earth System Research (INAR), University of Helsinki, Helsinki, Finland*

In this study, we present reactions of NH<sup>+</sup> <sup>4</sup> with a series of analytes (A): acetone (C3H6O), methyl vinyl ketone (C4H6O), methyl ethyl ketone (C4H8O), and eight monoterpene isomers (C10H16) using a Selective Reagent Ionization Time-of-Flight Mass Spectrometer (SRI-ToF-MS). We studied the ion-molecule reactions at collision energies of 55 and 80 meV. The ketones, having a substantially lower proton affinity than NH3, produce only cluster ions NH<sup>+</sup> 4 (A) in detectable amounts at 55 meV. At 80 meV, no cluster ions were detected meaning that these adduct ions are formed by strongly temperature dependent association reactions. Bond energies of cluster ions and proton affinities for most monoterpenes are not known and were estimated by high level quantum chemical calculations. The calculations reveal monoterpene proton affinities, which range from slightly smaller to substantially higher than the proton affinity of NH3. Proton affinities and cluster bond energies allow to group the monoterpenes as a function of the enthalpy for the dissociation reaction *NH*<sup>+</sup> 4 *A* → *AH*<sup>+</sup> + *NH*3. We find that this enthalpy can be used to predict the NH<sup>+</sup> 4 (A) cluster ion yield. The present study explains product ion formation involving NH<sup>+</sup> 4 ion chemistry. This is of importance for chemical ionization mass spectrometry (CIMS) utilizing NH<sup>+</sup> 4 as well as NH<sup>+</sup> 4 (H2O) as reagent ions to quantitatively detect atmospherically important organic compounds in real-time.

Keywords: NH<sup>+</sup> 4 , chemical ionization, PTR-ToF-MS, association reactions, monoterpenes, acetone, methyl vinyl ketone (MVK), methyl ethyl ketone (MEK)

## INTRODUCTION

In the 1990's proton transfer reaction mass spectrometry (Hansel et al., 1995; Lindinger et al., 1998b) using H3O<sup>+</sup> reagent ions became a widely used analytical instrument with applications in environmental science, medical applications, and food technology due to the large amount of volatile organic molecules, which can be quantitatively ionized. H3O<sup>+</sup> undergoes proton transfer reactions with every analyte having a higher proton affinity (PA) than water [PA(H2O) = 165.0 kcal/mol (Hunter and Lias, 1998)]. In contrast, NH<sup>+</sup> 4 ionization is more specific. Due to the higher proton affinity of ammonia PA(NH3) = 204.0 kcal/mol (Hunter and Lias, 1998), exothermic, thus

**106**

fast, proton transfer reactions between NH<sup>+</sup> 4 and analyte are limited to a much smaller number of molecules. If the analyte (A) possesses a proton affinity sufficiently larger than NH3, then reaction (1):

$$NH\_4^+ + A \rightarrow AH^+ + NH\_3 \tag{1}$$

is exothermic and will occur on every collisions, which means that the reaction rate is close to the collisional limit value (Lindinger et al., 1998b). Lindinger et al. (1998a) used proton transfer reactions of NH<sup>+</sup> 4 to separate the isomeric molecules α-pinene [PA = 204–209 kcal/mol (Lindinger et al., 1998a; Solouki and Szulejko, 2007)] and 2-ethyl-3,5-dimethylpyrazine [PA > 204 kcal/mol (Lindinger et al., 1998a)], both having a molecular mass of 136 Th, and found that α-pinene was not ionized by NH<sup>+</sup> 4 . Keough and Destefano (1981) discussed several factors affecting reactivity in ammonia chemical ionization (CI) mass spectrometry. At that time analyte molecules were introduced directly into the ion source where ammonia is present in large excess. The presence of large amounts of NH<sup>3</sup> and analyte at a typical ion source pressure of one Torr complicates the interpretation of product ion formation due to secondary reactions. Since the introduction of PTR-MS in the early 1990's, a strict separation of the ion source from the reaction region (drift tube) was achieved. This is one key factor why chemical ionization using the PTR-MS design became a quantitative analytical instrument. Keough and Destefano (1981) investigated a series of organic compounds with NH<sup>+</sup> 4 - chemical ionization. They concluded that analytes having a PA < 188 kcal/mol do not yield useful intensities of NH<sup>+</sup> 4 (A) adduct ions. Very recently, ammonia chemical ionization was found to be an extremely sensitive method detecting quantitatively first generation oxidized molecules as well as highly oxidized organic molecules with NH<sup>+</sup> 4 adduct ion chemistry (Berndt et al., 2018a,b; Hansel et al., 2018). Zhou et al. (2018) applied NH<sup>+</sup> 4 chemical ionization in an atmospheric pressure chemical ionization tandem mass spectrometer and investigated the ionization mechanism of molecules with a hydroperoxide moiety.

Here we present detailed results on the mechanism of chemical ionization of eight monoterpenes (C10H16) by NH<sup>+</sup> 4 chemical ionization. Additionally, we investigated the reaction of acetone (C3H6O), methyl vinyl ketone (MVK, C4H6O) and methyl ethyl ketone (MEK, C4H8O) in reactions with NH<sup>+</sup> 4 . We have chosen the following atmospherically most relevant monoterpenes according to Sindelarova et al. (2014) and Smolander et al. (2014): α-pinene, β-pinene, limonene, ocimene, myrcene, sabinene, 3-carene, and camphene. Ion chemistry was performed at twice the thermal energy (KEcm = 55 meV) and at a somewhat elevated collision energy (KEcm = 80 meV). Additionally, we investigated the effect of absolute humidity on the outcome of the individual reactions. To confirm the experimental results, quantum mechanical calculations on the proton affinities, adduct ion geometries, cluster-bond energies, and reaction enthalpies were performed.

## MATERIALS AND METHODS

#### Experimental Setup and Measurement Procedure

The experimental setup is illustrated in **Figure 1**. For the investigations of the monoterpenes, a temperature stabilized diffusion source was built. Humidified synthetic air was used to dilute the calibration compound diffusing from the diffusion tube. Humidification of the synthetic air was achieved with a Liquid Calibration Unit (LCU, Ionicon Analytik), which also controlled the carrier gas flow set to 3 slm and the variable liquid water flow. For each calibration compound we measured seven different absolute humidities ranging from 4 ± 3 to 25 ± 3 ppth (parts per thousand).

#### Liquid Calibration Unit (LCU)

The Liquid Calibration Unit (LCU, Ionicon Analytik, Austria) was used to quantitatively evaporate certain amounts of water into the synthetic air stream resulting in absolute humidities in the range of 3–30 ppth. The calibration of the ketones was performed by dynamic dilution of calibration gas standards (Apel Riemer Environmental Inc., Broomfield (CO), USA) in a humidified carrier gas generated by the LCU. Highly watersoluble compounds can be calibrated precisely with the LCU. As monoterpenes are non-polar compounds they are not quite soluble in water. Therefore, we decided to build a temperaturecontrolled diffusion device, which was combined with the humidified synthetic air stream from the LCU to generate known amounts of monoterpenes in the parts per billion range.

#### Temperature Stabilized Diffusion Tube

Each diffusion tube containing several milliliters of the respective liquid calibration compound consisted of a 1/8 inch PFA tubing plug (Parker-Hannifin Corporation, Tucson, USA) connected to

FIGURE 1 | Illustration of the experimental setup. Calibration compounds were either taken from the calibration gas standards or from the diffusion source, which was flushed with a constant synthetic air flow controlled by a mass flow controller (MFC). Different humidity steps were adjusted with the Liquid Calibration Unit (LCU) and monitored by an infrared gas analyzer (IRGA). The humidified synthetic air containing the respective calibration compound(s) was introduced to a selective reagent ion time of flight mass spectrometer (SRI-ToF-MS).

a PEEK capillary (Vici Valco, Switzerland) of defined length and inner diameter. The capillary was connected through a gas tight 1/8–1/4 inch tee reducer with the carrier gas stream from the LCU. As described in Fuller et al. (1966), the diffusion rate of a diffusion source is strongly temperature dependent. For this purpose, the diffusion tube was placed in a water bath filled with 50 ml water and wrapped with a heating wire and isolation foam. The water temperature was kept constant at 303 ± 3 K and controlled by a temperature controller (Cal3300, CAL Controls Ltd., Libertyville, USA) connected to a type K thermocouple. The heat capacity of the thermally isolated water bath helped to achieve constant volume mixing ratios (VMR) of individual calibration compounds in the air stream. VMR calculations of the individual analyte in the carrier gas have been performed according to McKelvey and Hoelscher (1957). Assuming that saturation of the head space in the diffusion source has occurred, the diffusion rate r [g s−<sup>1</sup> ] of the analyte can be calculated according to Equation (2):

$$r = \frac{D \cdot P \cdot M \cdot A}{R \cdot T \cdot L} \cdot \ln\left(\frac{P}{P - P\_s}\right),\tag{2}$$

where D [cm<sup>2</sup> s −1 ] is the diffusion coefficient, M [g mol−<sup>1</sup> ] the molecular weight of the analyte, P [Pa] the total pressure, A [cm<sup>2</sup> ] the cross-sectional area of the capillary, L [cm] the length of the capillary, R = 8.314 · 10<sup>6</sup> cm<sup>3</sup> Pa mol−<sup>1</sup> K −1 the gas constant, and P<sup>s</sup> [Pa] the saturation vapor pressure of the liquid analyte. Saturation vapor pressures P<sup>s</sup> were calculated with MPBWIN v1.43 (© 2000 U.S. Environmental Protection Agency) for the temperature of the diffusion source. Gaussian error analysis estimates an accuracy of the diffusion rate r of ±1% and an accuracy of the obtained volume mixing ratios of ±10– 15%. An overview of all values and estimated errors is given in **Supplementary Table 2**.

#### Instrumentation SRI-ToF-MS

The Selective Reagent Ion Time-of-Flight Mass Spectrometer (SRI-ToF-MS) used in this study is based on the PTR-ToF-MS described by Graus et al. (2010) and is adapted for the use with different reagent ions. In principle, it inhibits several advantageous features. The ion source is flushed with ∼100 sccm helium, producing only He<sup>+</sup> and metastable He<sup>∗</sup> . The chemical ionization gas NH<sup>3</sup> (Linde AG, Pullach, Germany) is added later to the source where reactions with He<sup>+</sup> and He<sup>∗</sup> lead to the formation of NH<sup>+</sup> 4 reagent ions. Compared to a standard PTR-ToF-MS, the SRI-ToF-MS is equipped with an ion-funnel located between the ion source and the drift tube having a length of 9 cm. To prevent photochemical reactions in the drift tube, the shape of the ion funnel is constructed in such a way that photons created in the glow discharge ion source don't reach the drift tube. Moreover, the direction of the gas flow through the drift tube and through the ion funnel is opposite to the ion drift direction. This pumping architecture prevents He and CI gases, as well as radicals created in the discharge, from entering the drift region. The metal drift rings used in common PTR-MS instruments are replaced by conductive PEEK rings with a thickness of 6 mm and an inner diameter of 12 mm allowing the measurement of compounds, which catalytically react on metal surfaces. The drift rings are separated by Teflon© spacers of 6 mm thickness. In the present study, the SRI-ToF-MS was operated at 2.3 mbar drift pressure and 35◦C drift temperature. The drift voltage was varied between 250 V (E = 27.8 V cm−<sup>1</sup> ) and 400 V (E = 44.4 V cm−<sup>1</sup> ) resulting in an E/N value of 51 and 81 Td, respectively. E is the electric field strength and N the gas number density (1 Td equals 10−<sup>17</sup> V cm<sup>2</sup> ). Data processing was performed with an adapted version of the data processing routine described in Breitenlechner et al. (2017) and further data analysis was done with Matlab2018a©. Subsequently, to compensate variations in the reagent ion signal and the mass-depended ion transmission in TOF mass spectrometers, product ion signals (e.g., compound i being detected at mass mi) measured in counts per second (cps) were duty-cycle corrected (dcps; dcps(i) = cps(i)· √ 100/mi) and normalized to 10<sup>6</sup> cps of NH<sup>+</sup> 4 (normalized counts per second, ncps). To study collision induced dissociation (CID) of adduct ions, we ramped the extraction voltage applied to the lenses in the ion transfer region located between the drift tube and the mass spectrometer. For an E/N of 51 Td in the drift tube, we ramped the extraction voltage in 5 V steps between 15 and 25 V. For an E/N of 81 Td the extraction voltages were changed between 20 and 30 V. The errors of the averaged ion signals in each voltage and humidity step are the standard deviations.

#### Calculation of Reaction Thermodynamics

In the drift tube, the ions travel as a result of the applied electric field strength E with an increased drift velocity v<sup>d</sup> through the buffer gas (Lindinger et al., 1998a):

$$\nu\_d = \mu \cdot E = \mu\_0 \cdot N\_0 \cdot \frac{E}{N} \tag{3}$$

We used ion mobility values <sup>µ</sup><sup>0</sup> of NH<sup>+</sup> 4 in N<sup>2</sup> from Abedi et al. (2014) and adapted them to the gas number density N in our instrument. N<sup>0</sup> is the gas number density at standard temperature and pressure. Thus, the drift time t of the ions traveling through the drift tube of length l can be calculated by:

$$t = \frac{l}{\nu\_d} = \frac{l}{\mu\_0 N\_0} \cdot \frac{N}{E} \tag{4}$$

The reduction of reagent ions [NH<sup>+</sup> 4 ] in reactions with the analyte in the drift region is small, thus the reaction can be treated as a pseudo-first order reaction. The density of protonated analytes [AH+] is then given according to Lindinger et al. (1998a) by:

$$\left[AH^{+}\right] \approx \left[NH\_{4}^{+}\right]\left[A\right] \cdot kt \tag{5}$$

Where [A] is the density of analyte A, k the reaction rate coefficient and t the drift time. The ratio - AH<sup>+</sup> /[NH<sup>+</sup> 4 ] is proportional to the detected ion signal ratio i(AH+)/i(NH<sup>+</sup> 4 ). Commonly the sensitivity (ε) is defined as the detected analyte signal at a volume mixing ratio of 1 ppbv (parts per billion per volume, 1 ppbv = 10−<sup>9</sup> ) normalized to a reagent ion signal i(NH<sup>+</sup> 4 ) of 10<sup>6</sup> cps (Lindinger et al., 1998b). Combining Equations (4) and (5) and using that the volume mixing ratio (VMR) of A is related to [A] by VMR (A) · N = [A], the theoretically maximum sensitivity εcalc can be calculated as:

$$
\varepsilon\_{\rm calc} = 10^{-3} \cdot k \cdot t \cdot N = 10^{-3} \cdot k \cdot \frac{l}{\mu\_0 N\_0} \cdot \frac{N^2}{E} \tag{6}
$$

We compare the calculated sensitivity with the experimentally observed sensitivity εmeas. By dynamically diluting either the calibration gas standard or the diffused analyte from the diffusion source, we obtain a known volume mixing ratio VMR(A) of the analyte A. To determine the sensitivity of an analyte A, the contributions of all product ions of the reaction with NH<sup>+</sup> <sup>4</sup> must be considered (Cappellin et al., 2012). The measured sensitivity (εmeas) of a substance A is then given by the slope of a linear fit through the scatter plot of the normalized and duty cycle corrected ion signals of all product ions vs. the volume mixing ratio. The efficiency (eff) of a reaction is then given by

$$
\varepsilon eff = \frac{\varepsilon\_{meas}}{\varepsilon\_{calc}} \cdot 100 \tag{7}
$$

The center-of-mass kinetic energy KEcm is calculated according to Lindinger et al. (1998a):

$$KE\_{cm} = \frac{m\_b}{m\_b + M\_{ion}} \left( KE\_{ion} - \frac{3}{2} k\_b T \right) + \frac{3}{2} k\_b T \tag{8}$$

With KEion being the mean kinetic energy of ion drifting in the buffer gas:

$$KE\_{ion} = \frac{3}{2}k\_b T + \frac{m\_b \nu\_d^2}{2} + \frac{M\_{ion} \nu\_d^2}{2},\tag{9}$$

where m<sup>b</sup> is the mass of the buffer gas, Mion the mass of the ions and k<sup>b</sup> the Boltzmann constant.

Collisional limiting rate coefficients (kc) of ion molecule reactions are calculated according to Su and Chesnavich (1982) and Su (1994) using dipole moments and polarizabilities of the respective analyte (see **Supplementary Table 1**). **Table 1** gives an overview of all reactions. It is worth to mention that we don't have to consider the back reaction of reaction (1) even if the proton affinity of A is only a few kcal/mol higher than the one of NH<sup>3</sup> in analogy to the H3O+–formaldehyde reaction system (Hansel et al., 1997). In our case the efficiency of the back reaction is negligible, as in the SRI-ToF the CI gas NH<sup>3</sup> does not enter the drift region.

#### Quantum Chemical Calculations

Proton affinities are not available for most monoterpenes, thus quantum chemical calculations were performed. Known proton affinities for ammonia, acetone, methyl vinyl ketone and methyl ethyl ketone were compared with our calculations. Additionally, the change of standard enthalpies for the ionmolecule reactions, possible protonation sites and probable NH<sup>+</sup> 4 adduct ion structures were calculated. The conformers were sampled using the systematic conformer search algorithm and the MMFF94 force field on Spartan'16 (Wavefunction, 2016).


All conformers were optimized at the B3LYP/6-31+G ∗ level of theory using the Gaussian 09 program (Frisch et al., 2009). The geometries of all conformers within 2 kcal/mol of the lowest-energy conformer were optimized and the harmonic frequencies were calculated at the ωB97X-D/aug-cc-pVTZ level of theory using the ultrafine integration grid. The B3LYP/6- 31+G ∗ geometry optimization was omitted for some of the protonation products to avoid the breaking and forming of C-C bonds in the cation product. We found the lowest enthalpy protonation products of the monoterpenes by placing the proton to each of the double bond carbons of the compounds at a time. Generally, the most stable protonation product is found when the positively charged carbon of the protonated structure is tertiary. For 3-carene, we found an energetically more favorable structure where the proton was not added to a double bond carbon. Final single-point energies were calculated at the CCSD(T)-F12/VDZ-F12 level of theory for the lowest enthalpy conformers using the MOLPRO program version 2015.1 (Werner et al., 2012, 2015).

#### Chemicals

(R)-(-)-limonene (analytical standard), ocimene (mixture of isomers, >90%), camphene (>95%), sabinene (75%), (+) α-pinene (>99%), and myrcene (analytical standard) were obtained from Sigma Aldrich (Vienna, Austria). (+)-3-carene (>98.5%) and (-)-β-pinene (>99.0%) were purchased from Fluka. Pressured synthetic air grade 5.8 was obtained from Messer (Gumpoldskirchen, Austria), the calibration standard gases were fabricated by Apel Riemer Environmental Inc. (Broomfield, United States). Bottled NH<sup>3</sup> grade 3.8 was purchased from Linde AG (Pullach, Germany).

## RESULTS AND DISCUSSION

#### Characteristics of the Diffusion Source

The monoterpenes β-pinene and limonene are also present in our calibration gas standards from Apel Riemer Environmental Inc., Broomfield (CO), USA. They certify an accuracy of typically ±10%. We compared the gas calibration results with our home build diffusion source. The agreement between the estimated sensitivities of the diffusion source and the gas standard differed not more than 25% for these two compounds. As many physical and chemical properties of the investigated monoterpenes are not experimentally determined, we had to rely on calculated values for saturation vapor pressures P<sup>s</sup> and diffusion coefficients D. Thus, the error of the diffusion source seems very reasonable. To understand the principles of the investigated ion-molecule reactions it is of greater importance that the diffusion rate of the analyte remains constant over the entire measurement period. In our experiment we detected volume mixing ratio drifts of the diffusion source in the range of ± 3% only. Overall we estimate a calibration error of less than ± 30% taking into account also dilution errors from calibrated flow controllers.

#### Reagent Ion Distribution

Typical reagent ion distributions are shown in **Figure 2** as a function of humidity and CID voltage settings. The reagent ion distribution is dominated by NH<sup>+</sup> 4 . At all voltage settings and humidity steps the NH<sup>+</sup> 4 signal dominates with typically 10<sup>6</sup> dcps. The next prominent reagent ion is the hydrated ammonium ion NH<sup>+</sup> 4 (H2O) (m/z = 36.04 Th), which is typically two orders of magnitude lower in intensity even at humid conditions and low E/N settings. The most abundant other "impurity" ions are NH<sup>+</sup> 4 (NH3) (m/z = 35.04 Th), H3O<sup>+</sup> (m/z = 19.02 Th), NO<sup>+</sup> (m/z = 29.99 Th) and O<sup>+</sup> 2 (m/z = 31.99 Th). Negligible amounts of H3O+(H2O)<sup>2</sup> cluster ions are also present. The Gibb's free energies 1G to dissociate the respective cluster ions at 310 K drift tube temperature are: NH<sup>+</sup> 4 (H2O) 1G = 13.0 kcal/mol (Meot-Ner and Speller, 1986), H3O+H2O(H2O) 1G = 13.2 kcal/mol (Kebarle et al., 1967), NH<sup>+</sup> 4 (NH3) 1G = 17.9 kcal/mol (Payzant et al., 1973). In the drift tube we increased the ion energy above thermal applying E/N values of 51 and 81 Td, respectively. Thus, 1G dissociation energies of the cluster ions become even smaller for higher E/N settings. This is one reason why cluster ion intensities at 81 Td are substantially lower than at 51 Td. The other reason is that the formation of cluster ions is suppressed as a function of ion collision energy in the drift tube (Hansel et al., 1997; Lindinger et al., 1998a). With increasing extraction voltages, the amount of weakly bound cluster ions decrease due to collision induced dissociation (CID) in the ion transfer region. Overall we can conclude that the prevailing reagent ion reacting with the analytes in the drift tube is NH<sup>+</sup> 4 .

#### Reactions of NH<sup>+</sup> <sup>4</sup> With Small Ketones

First, we investigated the reaction of NH<sup>+</sup> <sup>4</sup> with acetone, methyl vinyl ketone (MVK) and methyl ethyl ketone (MEK). In **Figure 3**, measured sensitivities of acetone, MVK and MEK at dry and humid conditions and at two E/N values, 51 and 81 Td, are shown. As illustrated in **Figure 3**, all ketones are detected as NH<sup>+</sup> 4 (A) cluster ions: acetone: m/z = 76.08 Th, MVK: m/z = 88.08 Th, MEK: m/z = 90.09 Th. At an elevated E/N value of 81 Td, no cluster ions were observed. This is in agreement with first studies of ammonia chemical ionization of ketones with mass analyzed ion kinetic energy (MIKE) spectrometry (Maquestiaut et al., 1980). No protonated ketones have been observed. For all three ketones, proton transfer reactions with NH<sup>+</sup> 4 are energetically unfavorable due to their lower proton affinities compared to ammonia of PA(NH3) = 204 kcal/mol [PA(acetone) = 194 kcal/mol, PA(MVK) = 199.5 kcal/mol, PA(MEK) = 197.7 kcal/mol (Hunter and Lias, 1998)]. In SRI-ToF-MS, NH<sup>+</sup> 4 (A) cluster formation proceeds prevailingly as ternary association reactions under dry conditions. The standard reaction mechanism for ternary (three body or collisionally stabilized) ion-neutral reactions proceeds as follows:

$$A^{+} + B \stackrel{k+}{\leftrightharpoons}\_{k-}^{k+} AB^{+} \stackrel{\ast}{\rightarrow} \begin{array}{c} AB^{+} + M \stackrel{\ast}{\ \cdot}, \end{array} \tag{10}$$

where M is a third body, and k<sup>+</sup> and k<sup>−</sup> the reactions rates in the respective direction (Ikezoe et al., 1987). Fast ligand switching reactions of type (11), where the water ligand is exchanged by a more strongly bound ketone, could in principle also produce NH<sup>+</sup> 4 (A) cluster ions but don't contribute much at 2.3 mbar and at elevated collision energies under dry conditions.

$$\text{NH}\_4^+ \text{ (} H\_2O \text{)} + A \rightarrow \text{NH}\_4^+ \\ A + H\_2O \text{ } \tag{11}$$

18.04) signal.

**Figure 2** shows that NH<sup>+</sup> 4 (H2O) reagent ions are less abundant < 1% even at humid conditions and at low E/N values.

4

4

**Table 1** gives an overview of the calculated collisional rate coefficient (kc) at the respective collision energy (KEcm), the calculated sensitivity (εcalc) using kc, the measured sensitivity (εmeas) and the reaction efficiency (eff) for all compounds studied under dry and humid conditions, and at 51 and 81 Td, respectively. The ketones show reaction efficiencies ranging from 4.2% (acetone), and 5.9% (MVK) to 9.4% (MEK) at dry conditions and a KEcm of 0.055 eV. These efficiencies indicate a rather high effective binary rate coefficient, which is most likely due to the long lifetime of the intermediate (NH4A)+<sup>∗</sup> against unimolecular decomposition (i.e., k<sup>−</sup> is small relative to the stabilization rate in collisions with M) for these polyatomic intermediates, which vary with complexity (Johnston, 1966). It is also indicative that the NH<sup>+</sup> 4 -ketone cluster is strongly bound, as confirmed by quantum chemical calculations, see **Table 2** and (Frege et al., 2018). In the lowest energy geometry of the NH<sup>+</sup> 4 ketone cluster, one of the hydrogen atoms of NH<sup>+</sup> 4 is hydrogen bonded to the oxygen of the carbonyl group (see **Figure 4**) resulting in typical bond energies of ∼ 26 kcal/mol. Adams et al. (2003) studied the association reactions of NH<sup>+</sup> <sup>4</sup> with a series of organic molecules using a Selected Ion Flow Tube (SIFT). In this study, Adams et al. (2003) reported that the reaction efficiency for acetone is 22% at 300 K and at 0.5 Torr He pressure. When the efficiency is high as for acetone, this indicates that the ternary reaction is close to pressure saturation, i.e., independent of the He pressure, and in this case only a lower limit to the ternary rate coefficient can be obtained. Earlier studies have shown that the ternary rate coefficient k decreases dramatically as a function of temperature (collision energy) with k α T −n , where n ranges from 2 to 3 (Adams and Smith, 1981). An E/N of 51 Td corresponds to 0.055 eV (≈ 600 K). According to Breitenlechner (2011) the fluctuation of the electric field strength along the central axis of the drift tube of the SRI-ToF-MS is within ±10%. Using k α T <sup>−</sup><sup>n</sup> with n = 2–3 reduces the reaction efficiency for the NH<sup>+</sup> 4 -acetone cluster ion formation at 51 Td to 22% × 2 −(2to3) = 5.5–2.8% in excellent agreement with our measured reaction

4

efficiency of 4.2%. At an E/N of 81 Td we could not observe any NH<sup>+</sup> 4 -ketone cluster ions reliably. This is most likely due to the short lifetime of the more excited (NH4A)+<sup>∗</sup> intermediates at this enhanced collision energy. Under humid conditions the reaction efficiencies of all ketones are increased by about 5% at 51 Td. This increase is somewhat unexpected and might be due to a larger amount of NH<sup>+</sup> 4 (H2O) cluster ions in the drift tube than measured even at the lowest extraction voltage setting of 15 V. **Figure 2** shows that about 1% of all reagent ions comprise the hydrated ammonium cluster ions. We would need about 5% of hydrated ammonium cluster ions, which undergo exothermic thus fast ligand switching reactions according reaction (11). Reaction (11) is exothermic for all three ketones. The bond energy of NH<sup>+</sup> 4 (H2O) is 20.6 kcal/mol (Meot-Ner and Speller, 1986) (see **Table 1**), which is smaller compared to the NH<sup>+</sup> 4 ketone bond energies ranging from 25.9 kcal/mol (MEK), 26.4 kcal/mol (acetone) to 27.3 kcal/mol (MVK) (see **Table 2**). Increasing the extraction voltage from 15 to 25 V decreases the NH<sup>+</sup> 4 -ketone adduct ions due to CID in the extraction region by 60–70% (**Figure 3**). In comparison, the NH<sup>+</sup> 4 (H2O) reagent ions show an even more pronounced decrease as a function of extraction voltage (**Figure 2**). At 25 V, more than 95% of hydrated ammonium cluster ions are lost compared to 15 V extraction voltage. This demonstrates again that cluster ions with a lower bond energy are lost more efficiently in the ion transfer region, supporting our assumption that NH<sup>+</sup> 4 (H2O) cluster ions could be lost even at an extraction voltage of 15 V. In any case our measured amount of NH<sup>+</sup> 4 (H2O) cluster ions (1% compared to NH<sup>+</sup> 4 ) is a lower limit and the enhanced ketone reactivity at humid conditions indicate a higher amount of 5%.

#### Reactions of NH<sup>+</sup> <sup>4</sup> With Monoterpenes Product Ion Formation

We investigated the reaction of NH<sup>+</sup> <sup>4</sup> with eight atmospherically most common monoterpenes at dry and humid conditions, and at two E/N values 51 and 81 Td. In contrast to the measured ketones, for which proton transfer reactions are energetically unfavorable, the proton affinities of the monoterpenes range from 201.2 kcal/mol (limonene) to 215.9 kcal/mol (sabinene), according to our quantum chemical calculations (**Table 2**). Experimental proton affinities of monoterpenes are rare and exist only for limonene (PA = 209.1 ± 1.2 kcal/mol; Tereza Fernandez et al., 1998), camphene (PA = 205.7 ± 3.2 kcal/mol; Solouki and Szulejko, 2007). For α-pinene (Lindinger et al., 1998a) suggested an upper limit PA < 204 kcal/mol whereas (Solouki and Szulejko, 2007) estimate ∼209 kcal/mol. The few experimentally measured proton affinities are in reasonable agreement with our calculations. A list of calculated proton affinities is given in **Table 2**. Our calculated proton affinity of NH<sup>3</sup> is 203.8 kcal/mol, which is in excellent agreement with experimental values of 204 kcal/mol (Hunter and Lias, 1998). All investigated monoterpenes, except limonene, have higher proton affinities than ammonia making the proton transfer reaction (1) exothermic. Our results show significant differences in the TABLE 2 | Overview of the bond energies (BE), reaction enthalpies (1Hr ), proton affinities (PA), and protonated structures, calculated at the CCSD(T)-F12/VDZ-F12//ωB97X-D/aug-cc-pVTZ level of theory at 298 K.


*(Continued)*

TABLE 2 | Continued


*BE describes the NH*<sup>+</sup> *4 -A bond energy,* 1*H<sup>r</sup> is the reaction enthalpy of the reaction NH*<sup>+</sup> *4 A* → *AH*<sup>+</sup> + *NH3. We expect errors in computed proton affinities and binding enthalpies to be smaller than 1 kcal/mol. PA literature values are also given if available. a* (*Hunter and Lias, 1998).*

*b* (*Lindinger et al., 1998b).*

*c* (*Solouki and Szulejko, 2007).*

product ion distribution of the eight studied monoterpenes. As expected we identified the protonated terpene ion C10H16- H<sup>+</sup> (m/z = 137.13 Th), but also fragment ion C6H + 9 (m/z = 81.07 Th) and for some monoterpenes additionally small amounts of fragments C7H + <sup>11</sup> (m/z = 95.08 Th) and C7H + 9 (m/z = 93.07 Th). Here we record only ion signals, which are detected with relative intensities >1%. Other fragments reported in the literature for H3O<sup>+</sup> chemical ionization using PTR-MS instruments (Wang et al., 2003; Schoon et al., 2004; Tani et al., 2004; Materic et al., 2017 ´ ) have not been observed. This could be explained by the smaller amount of transferred internal energy using NH<sup>+</sup> 4 instead of H3O<sup>+</sup> as reagent ion. The difference in proton affinities between the precursor ion and the respective monoterpene is transferred to the product ion causing fragmentation. Besides proton transfer product ions and corresponding fragment ions, we observe also cluster ions NH<sup>+</sup> 4 attached to monoterpenes for all eight monoterpenes. Product ion distributions for the eight monoterpenes are shown in **Figures 5**–**9** and **Supplementary Figures 1–3** at dry and humid conditions, at two E/N values 51 and 81 Td and as a function of extraction voltages.

First, we will discuss the results for dry conditions at an E/N of 51 Td and an extraction voltage of 20 V only. Camphene (**Figure 5**) and sabinene (**Supplementary Figure 1**) are the monoterpenes producing only 5% cluster ions NH<sup>+</sup> 4 -C10H<sup>16</sup> (m/z 154.16). The main product ions are protonated monoterpenes C10H16-H<sup>+</sup> (m/z = 137.13 Th) and the corresponding fragment ion C6H + 9 (m/z = 81.07 Th). In the case of sabinene (PA = 215.9 kcal/mol) 85% of product ions are protonated sabinene and 10% are found as C6H + 9 (m/z = 81.07 Th) fragment, while camphene (PA = 207.2 kcal/mol) produces 93% protonated camphene and only 2% C6H + 9 fragment ions. Sabinene, having a higher proton affinity compared to camphene, shows a higher amount of fragment ions. Hence more internal energy is generated in the proton transfer channel of sabinene explaining the higher amount of fragmentation. Ocimene (PA = 210.7 kcal/mol) (**Supplementary Figure 2**) and the two bicyclic monoterpenes βpinene (PA = 208.7 kcal/mol) (**Supplementary Figure 3**) and αpinene (PA = 206.3 kcal/mol) (**Figure 6**) produce 30–40% cluster ions NH<sup>+</sup> 4 -C10H16. The remaining fraction is found prevailingly as protonated monoterpene C10H16-H<sup>+</sup> and to a lesser amount at the C6H + 9 fragment ion. For the acyclic monoterpene myrcene (PA = 204.2 kcal/mol) (**Figure 7**) and bicyclic 3-carene (PA = 205.4 kcal/mol) (**Figure 8**) we detect approximately 50% of the product ion signal at the protonated mass. 3-carene exhibited a slightly dominant cluster ion yield (∼54%). Limonene (PA = 201.2 kcal/mol) (**Figure 9**) shows the highest yield of cluster ions NH<sup>+</sup> 4 -C10H16, namely ∼85% and the rest is the unfragmented C10H16-H<sup>+</sup> ion.

We performed detailed quantum chemical calculations to better understand the NH<sup>+</sup> 4 reaction mechanism with monoterpenes. **Table 2** gives an overview of calculated proton affinities compared to literature values, the bond energies (BE, in enthalpy) of cluster ions NH<sup>+</sup> 4 -A, and reaction enthalpies 1H<sup>r</sup> of reaction (12).

$$NH\_4^+A \rightarrow AH^+ + NH\_3 \tag{12}$$

The structures of protonated compounds are also shown in **Table 2**. In the cases of 3-carene and limonene we calculated two structures with similar proton affinities, respectively. The lowest enthalpy geometries of all NH<sup>+</sup> 4 (A) cluster ions are shown in **Figure 4**. The calculations of the lowest enthalpy conformers of NH<sup>+</sup> 4 -monoterpene cluster ions reveal that at least one hydrogen of the NH<sup>+</sup> 4 forms a hydrogen bond to the C=C double bond with a typical bond energy of ∼19 kcal/mol. Some monoterpenes have more than one C=C double bond offering the possibility to form a second hydrogen bond. This is the case for myrcene (BE = 20.9 kcal/mol), limonene (BE = 22.3 kcal/mol), and ocimene (BE = 26 kcal/mol). Bond energies of these monoterpenes are only slightly higher (3–7 kcal/mol) than singly bonding monoterpenes. This is in contrast to calculated NH<sup>+</sup> 4 bond energies of compounds containing several carbonyl groups. Introducing a second C=O group increases the stability of the cluster ion considerably (almost 2-fold). Additionally, the position of the second functional group to form an optimal hydrogen bond (with a 180◦ angle of N-H-O) strongly influences the stability of NH<sup>+</sup> 4 -carbonyl adduct ions (Frege et al., 2018). To predict the yield of the cluster ion formation channel for the NH<sup>+</sup> 4 monoterpene reactions we correlated the fraction of measured cluster ions as a function of monoterpene proton affinities resulting in a correlation coefficient of R<sup>2</sup> = 0.5 (not shown). The assumption is that monoterpenes with highest proton affinities could perform a quite exothermic direct proton transfer or form an energetically excited (NH4-A)+∗ intermediate that quickly dissociates forming AH<sup>+</sup> + NH3. We therefore expected to find no cluster ion signal for sabinene (PA = 215.9 kcal/mol). As already discussed and shown in **Supplementary Figure 1** the cluster ion yield for sabinene is solely 5% under dry conditions.

Limonene (PA = 201.2 kcal/mol) has the smallest PA, which is even smaller than NH3, and should form exclusively adduct ions only. We observe a cluster ion yield of 85%, which is the highest one of all monoterpenes investigated. But still, there exists a 15% channel at 0.057 eV collision energy producing protonated limonene. At 0.084 eV and dry conditions the yield of the proton transfer channel (including fragment ions) increases to 30% at the lowest extraction voltage (20 V). Increasing the extraction voltage from 20 to 30 V increases this channel even further reaching 50% (**Figure 9**). This means that the collision energy in the drift tube also leads to additional excitation of the (NH4-A)+∗- intermediate, which is needed for the AH<sup>+</sup> + NH<sup>3</sup> channel to become thermodynamically accessible. Increasing the extraction voltage at 0.084 eV collision energy shows a further decrease of the NH<sup>+</sup> 4 (A) cluster ions, and a gain of AH<sup>+</sup> and corresponding fragment ions. This is seen not only for sabinene but also for all investigated monoterpenes (**Figures 5**–**9** and **Supplementary Figures 1–3**). This means that even stabilized NH<sup>+</sup> 4 (A) cluster ions (and AH<sup>+</sup> ions) keep more internal energy at higher collision energies in the drift tube and it is then easier to form additional AH<sup>+</sup> (and corresponding fragment ions) in the ion transfer region through collision induced dissociation (CID). We found the best correlation coefficient (R<sup>2</sup> = 0.79) to predict the yield of the cluster ion formation channel for monoterpenes (see **Figure 10**) when the fraction of measured adduct ions was correlated as a function of the reaction enthalpy 1H<sup>r</sup> of reaction (12), which is the difference in proton affinities plus the bond energy BE: 1H<sup>r</sup> = PA(NH3) – PA(A) + BE(NH<sup>+</sup> 4 -A). This is shown in **Figure 10**, meaning that highest adduct ion yields are formed when compound A is strongly bond to NH<sup>+</sup> 4 and the difference in proton affinity is small resulting in smallest internal energy of the (NH4A)+∗ intermediate.

**Table 1** gives an overview of the calculated collisional rate coefficient (kc) at the respective collision energy (KEcm), the calculated sensitivity (εcalc) using kc, the measured sensitivity (εmeas) and the reaction efficiency (eff) for all compounds studied under dry and humid conditions and at 51 and 81 Td. The monoterpenes show reaction efficiencies ranging from 18.4% (ocimene) to 34.6% (camphene) at dry conditions and a KEcm of 0.057 eV (51 Td). These efficiencies take into account the proton transfer channel, as well as the adduct ion formation channel. Limonene (adduct channel 85%) has a reaction efficiency (eff.) of 20.2%, which indicates a very high effective binary rate coefficient of the cluster channel, which is most likely due to the long lifetime of the intermediate (NH4A)+<sup>∗</sup> against unimolecular decomposition. Also 3-carene (eff. 32.6%) and myrcene (eff. 21.3%) both having an adduct channel yield of 50% have very high effective binary rate coefficients. Compared to the three ketones (acetone, MVK and MEK), the monoterpenes in general have larger effective binary rate coefficients (cluster ion channel) at 0.057 eV. While in the case of the ketones, no reaction products at all are observed at elevated collision energies (KEcm = 0.084 eV; 81 Td), the adduct ion channel for the monoterpenes is somewhat smaller at this energy compared to 0.057 eV (51 Td) but still quite prominent. The intrinsic difference between the ketone and the monoterpene reaction system is that in the case of the ketones, no rearrangement (exothermic proton transfer) is thermodynamically accessible

in the (NH4A)+<sup>∗</sup> intermediate. The proton in the (NH4A)+<sup>∗</sup> intermediate, when A is a monoterpene, is not strictly localized at the NH3. This can be anticipated comparing the calculated structures of the protonated monoterpenes (**Table 2**) and the geometries of NH<sup>+</sup> 4 (A) cluster ions. The delocalization of the charge in the intermediate could enhance the lifetime of the intermediate. Another explanation for the enhanced lifetime of the (NH4A)+<sup>∗</sup> intermediate is the higher molecular complexity in the case of A being a monoterpene compared to small ketones.

#### Effect of Humidity

The product ion distribution was slightly shifted when changed from dry to humid conditions. More cluster ions (∼ 3%) were found under humid conditions (**Figures 5**–**9**, **Supplementary Figures 1–3**). As mentioned before, more water molecules in the sample air lead to an increased formation of NH<sup>+</sup> 4 (H2O) reagent ions. The hydrated ammonium might be able to undergo ligand switching with the monoterpenes, which could explain the slight increase of cluster ions.

#### Selective Detection of Monoterpene Isomers

Since more than a decade different methods have been tested to differentiate the monoterpene isomers using H3O+-CIMS technology. Müller et al. (2009) coupled a PTR front part to a Triple Quadrupole Tandem MS and a Linear Ion Trap and performed MS/MS studies. The CID spectra of mass selected protonated monoterpene isomers were too similar to specify individual monoterpenes in complex mixtures. Misztal et al. (2012) operated a PTR-MS in an alternating drift voltage mode using 9 ascending and 9 descending voltage steps. The different "time points" of fragmentation of the resulting monoterpene ion signals were used to differentiate between the isomers. Their conclusion was that this method extends the selectivity of the PTR-MS method but cannot compete with the gold standard of GC-MS identification. Here we presented another possibility to separate monoterpene isomers due to their different cluster ion formation in reactions with NH<sup>+</sup> 4 reagent ions. We used eight different monoterpenes and found that limonene produces with 85% yield NH<sup>+</sup> 4 (A) cluster ions while sabinene and camphene have a corresponding cluster ion yield of <5%. In order to predict the yield of the cluster ion formation channel of monoterpenes we propose using the reaction enthalpy of the reaction NH<sup>+</sup> <sup>4</sup> A →

FIGURE 6 | α-pinene product ion distributions are shown at dry (7 ± 1 ppth; left) and humid (26 ± 1 ppth; right) conditions as a function of extraction voltage settings at an E/N value of 51 Td (top) and 81 Td (bottom), respectively.

at an E/N value of 51 Td (top) and 81 Td (bottom), respectively.

AH<sup>+</sup> + NH<sup>3</sup> as shown in **Figure 10**. SRI-TOF-MS allows to switch between different reagent ions such as H3O<sup>+</sup> and NH<sup>+</sup> 4 which could be used to extend the selectivity of this CIMS method. But the challenge in separating all monoterpene isomers remains. The fundamental problem arises from the large number of possible isomers that are present at the same time in the real atmosphere.

## CONCLUSION

In this laboratory study, we investigated the reactions of NH<sup>+</sup> 4 with a series of organic analytes (A): acetone (C3H6O), methyl vinyl ketone (C4H6O), methyl ethyl ketone (C4H8O) and eight monoterpene isomers (C10H16). The reactivity and product ion distribution were studied at two different collision energies and as a function of absolute humidity. Compounds having a lower proton affinity than NH<sup>3</sup> produced only cluster ions NH<sup>+</sup> 4 (A). This is the case for the ketones acetone, MVK and MEK, which were observed only at a low collision energy of 0.055 eV. At an elevated collision energy of 0.080 eV no cluster ions of the carbonyls could be detected, meaning that these product ions are formed by association reactions, which are strongly temperature dependent in agreement with earlier observations of Adams et al. (2003). Collision induced dissociation of cluster ions has been studied by varying the extraction voltage applied between the drift tube and the TOF mass analyzer giving a first indication of cluster ion bond energies. Bond energies of cluster ions and proton affinities for most of the compounds used here are not known and have been estimated in the present study by high level quantum chemical calculations. In addition to cluster ion formation, also proton transfer reactions were

observed for compounds having a higher proton affinity than that of NH3. The monoterpenes have proton affinities ranging from slightly lower to substantially higher than NH3. Calculated proton affinities and cluster bond energies allow to group these compounds as a function of the enthalpy for the dissociation reaction NH<sup>+</sup> <sup>4</sup> <sup>A</sup> <sup>→</sup> AH<sup>+</sup> <sup>+</sup> NH3. We find that this enthalpy can be used for the monoterpenes to predict the NH<sup>+</sup> 4 (A) clusters ion yield. The present study explains product ion formation involving NH<sup>+</sup> 4 ion chemistry. This is of importance for chemical ionization mass spectrometry (CIMS) utilizing NH<sup>+</sup> 4 as well as NH<sup>+</sup> 4 (H2O) as reagent ions to detect pure hydrocarbon precursor having at least one C=C double bond as well as oxygenated organic compounds in real-time (Berndt et al., 2018a). Here we demonstrated that not only carbonyl compounds, but also hydrocarbons having a higher proton affinity than NH3, such as the monoterpenes, can be quantitatively detected with NH<sup>+</sup> 4 reagent ions.

#### DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

#### REFERENCES


#### AUTHOR CONTRIBUTIONS

BS and EC ran the experiments and analyzed the data. NH performed the quantum chemical calculations. EC, NH, BS, LF, and AH took part in the data discussion. LF implemented the raw data analysis software. AH and EC wrote the manuscript. All authors contributed to improvements of the manuscript.

#### FUNDING

This study has received financial funding from the Austrian Ministry for Science and Research (BMBWF Austria) within the program Sparkling Science (SPA 06/222 – CHAMPIONS). NH thanks the European Research Council (Grant No. 692891- DAMOCLES) for funding and CSC-IT Center for Science, Finland, for computational resources.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00191/full#supplementary-material


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Canaval, Hyttinen, Schmidbauer, Fischer and Hansel. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Global Isomeric Survey of Elusive Cyclopropanetrione: Unknown but Viable Isomers

#### Jing-fan Xin1,2, Xiao-ru Han<sup>1</sup> , Fei-fei He<sup>1</sup> \* and Yi-hong Ding<sup>1</sup> \*

<sup>1</sup> Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, China, <sup>2</sup> Inner Mongolia Key Laboratory of Photoelectric Functional Materials, College of Chemistry and Chemical Engineering, Chifeng University, Chifeng, China

Despite the great interest in energy storage application, stable neutral CnO<sup>n</sup> (n > 1) structures either in thermodynamics or kinetics have yet been largely limited due to the rather high tendency to release the very stable CO molecule. The neutral cyclopropanetrione (C3O3) cluster has long remained elusive since no isomer with sufficient kinetic stability has been found either experimentally or theoretically. In this work, we constructed the first global potential energy surface of singlet C3O<sup>3</sup> at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level, from which the kinetic stability of a wide range of C3O<sup>3</sup> isomers can be determined by investigating their isomerization and fragmentation pathways. Amongst, a three-membered ring structure 01 is the global C3O<sup>3</sup> isomer with a barrier of 10.6 kcal/mol at the sophisticated W1BD level. In particular, two carbene-type isomers 02 and 04 possess appreciable destruction barriers of 20.3 and 24.7 kcal/mol at W1BD, respectively. Thus, 02 and 04 can be useful building blocks for constructing larger high-energy density carbon-oxygen clusters. Moreover, with the carbene center, both might effectively functionalize various nano-materials while retaining the electrochemical active carbonyl and epoxyl moieties that are very desirable in alkali metal-ion batteries.

Keywords: neutral cyclopropanetrione, C3O3 , global isomeric survey, kinetic stability, computational study, high-energy density materials, alkali metal-ion battery

## INTRODUCTION

Carbon (C) and oxygen (O) are key elements on earth and in space. Clusters constituted simply by them form a special class of oxides of carbon, namely oxocarbons (Rubin and Gleiter, 2000; Horiuchi et al., 2010; Kikuchi et al., 2014; Davis and Sajeev, 2017; Wang et al., 2018a). The huge energy release from CnO<sup>n</sup> to nCO provides great promise that a kinetically stabilized CnO<sup>n</sup> might find applications in the so-called high-energy density materials (HEDMs) (Schmidt et al., 2000; Gambi et al., 2001; Corkran and Ball, 2004; Xia et al., 2017). In fact, the polymeric CO networks as potential HEDMs have been computationally predicted to exist under the high-pressure environments (Lipp et al., 2005; Ryu et al., 2016, 2017). Yet finitesized CnO<sup>n</sup> clusters with both high-energy and appreciable kinetic stability against destruction (i.e., isomerization/fragmentation) still remain unknown. Moreover, there have been growing evidences that the rich oxygen density in form of carbonyl and epoxyl groups are key in development of alkali metal-ion electrodes for sustainable ion batteries (Chen et al., 2009; Seo et al., 2011; Kim et al., 2014; Zhao et al., 2016; Larm et al., 2018; Wang et al., 2018b). Kinetically stable CnO<sup>n</sup> that natively bear rich oxygens would surely find interest in such applications.

#### Edited by:

Marzio Rosi, University of Perugia, Italy

#### Reviewed by:

Cecilia Coletti, Università degli Studi G. d'Annunzio Chieti e Pescara, Italy Fanny Vazart, Université Grenoble Alpes, France

#### \*Correspondence:

Fei-fei He hff16@tsinghua.org.cn Yi-hong Ding yhdd@jlu.edu.cn

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 09 January 2019 Accepted: 14 March 2019 Published: 03 April 2019

#### Citation:

Xin J, Han X, He F and Ding Y (2019) Global Isomeric Survey of Elusive Cyclopropanetrione: Unknown but Viable Isomers. Front. Chem. 7:193. doi: 10.3389/fchem.2019.00193 Xin et al. Cyclopropanetrione: Unknown but Viable Isomers

The structure, bonding and stability of chemically bound CnO<sup>n</sup> have been explored in a large number of publications (Frenking, 1990; Schröder et al., 1998, 1999; Talbi and Chandler, 2000; Sabzyan and Noorbala, 2003; Zhou et al., 2010; Bao et al., 2012; Guo et al., 2012; Hu et al., 2012; Dixon et al., 2015; Liu et al., 2015; Hansen et al., 2016). To our surprise, larger CO oligomers in poly-cyclic form with n = 8, 9, 10, 12 were reported early (in 1967 and 1984; Verter and Dominic, 1967; Nallaiah, 1984). Their easy accessibility is in accordance with their good thermodynamic stability with respect to nCO (Schröder et al., 1999), and these low-lying clusters surely cannot be used for HEDMs. However, the detection and characterization of CnO<sup>n</sup> with intermediate size has been found quite difficult, partly due to their worse thermodynamic stability (Schleyer et al., 2000). The possible existence of C2O<sup>2</sup> was suggested more than 200 years ago (Staudinger and Anthes, 1913). Yet the combined spectroscopic and theoretical study has shown that the most feasible isomer, triplet linear OCCO, could only be transient or fleeting due to the low intersystem crossing barrier 3.0 kcal/mol (Schröder et al., 1998). Up to now, a conclusive spectroscopic characterization of OCCO still remains missing (Dixon et al., 2015; Lunny et al., 2018). For the monocyclic structures (n = 3–6), their generation and characterization were reported recently in the negative ion photoelectron (NIPE) mass spectroscopic studies (Hsu and Lin, 1978; Guo et al., 2012; Bao et al., 2013; Chen et al., 2014). We must note that the observed monocyclic C3O<sup>3</sup> was just a hilltop structure with two imaginary frequencies (Chen et al., 2014). In spite of the available structural and thermodynamic information (Sabzyan and Noorbala, 2003; Sahu and Lee, 2005; Zhou et al., 2010; Bao et al., 2012; Liu et al., 2015; Hansen et al., 2016), to our best knowledge, very little study has been made to address the kinetic stability of CnO<sup>n</sup> (n > 2) isomers, i.e., their lowest barriers against isomerization/fragmentation.

In this work, we focus on the cyclopropanetrione cluster (C3O3) that could present the smallest mono C3-ring. Three distinct types of singlet C3O<sup>3</sup> isomers (**A**–**C** in **Scheme 1**) have been reported in literatures (Hsu and Lin, 1978; Hu et al., 2012; Chen et al., 2014). The long expected and hotly studied monocyclic singlet isomer **A** is actually a second-order saddle point, and its observation can only be realized under very extreme experimental conditions (e.g., NIPE; Chen et al., 2014). The isomers **B** and **C** of C3O<sup>3</sup> were computationally reported in 2012 (Hu et al., 2012), yet their kinetic stability is still uncertain. We can say that at present, no C3O<sup>3</sup> with reasonable kinetic stability has been shown either experimentally or computationally. Thus, C3O<sup>3</sup> represents a quite "elusive" oxocarbon system.

Surely, the key to resolve this problem is to build a global potential energy surface (PES) picture of C3O3, which involves both the C3O<sup>3</sup> isomers and the isomerization/fragmentation transition states as many possible. With the PES, the kinetic stability of each C3O<sup>3</sup> isomer can then be determined. Unfortunately, building the global PES for such a high-energy and hexatomic molecule should be time-consuming, tedious and even exhaustive. In the present work, applying an effective global PES search strategy, we computationally constructed the first global potential energy surface (PES) of singlet C3O3, which helped us determine the kinetic stability of a wide range of isomers. Amongst them we for the first time identified the global isomer of C3O3, i.e., **01**. In particular, two carbene-like isomers **02** and **04** have the potential use in energy storage applications (e.g., HEDM and ion batteries). Such a thorough PES would provide a good base for future theoretical and laboratory studies of these C3O<sup>3</sup> isomers.

#### COMPUTATIONAL DETAILS

The search of isomers and transition states of singlet C3O<sup>3</sup> was carried out on a locally developed platform "global potential energy surface survey (GPESS)" (Shao and Ding, 2010; Ding, 2015; Bo and Ding, 2018). The flow chart of our strategies for constructing C3O<sup>3</sup> PES is shown in the Supporting Information (**SI\_1**). The isomeric search was based on the grid search program "grid-based isomeric search strategy" at the B3LYP/6-31G(d) level (Parr and Yang, 1989; Becke, 1992; Perdew et al., 1992) for both geometries and frequencies. The transition state (TS) search was divided into two types, i.e., the isomeric conversion and the isomeric decomposition. For the interconversion TS search, the "QST2" algorithm (Foresman and Frisch, 1996; Hrarchian and Schlegel, 2005), was applied, which yet has a difficulty in placing atoms in the same atomic order between reactant and product (especially for molecules with many homo-atomic elements). This was treated in GPESS by automatic enumeration of all possible combinations. Besides, the decomposition TS search was considered directing to some relatively stable molecular fragments like CO and CO2. The connection of each transition state was determined by the intrinsic reaction coordinate (IRC) (Fukui, 1981) calculations. The effectiveness of such isomeric and TS search strategies has been confirmed in study of various small to medium-sized systems (Cui et al., 2011; Gao and Ding, 2012; Tang et al., 2012; Guo et al., 2013a,b, 2014; Zhang and Ding, 2014, 2015; He and Ding, 2016; Xu et al., 2017; Bo et al., 2019).

Further, the geometry and frequencies of each isomeric and transition state structure were refined at the B3LYP/augcc-pVTZ optimization level followed by the CCSD(T)/aug-ccpVTZ single-point energy calculations. The eventual energy includes the Gibbs free energy corrections (GFEC). The overall were included in CCSD(T)/aug-cc-pVTZ single-point energy calculation. For all the obtained isomers, we carried out the "stability" analysis of the wave-function at the B3LYP/augcc-pVTZ level, applying the broken-symmetry strategy of Noodleman (Noodleman, 1981; Noodleman and Davidson, 1986). For key species, the composite CBS-QB3 (Montgomery et al., 1999, 2000) and W1BD (Barnes et al., 2009) methods were applied to get more reliable energy. All the calculations were carried out with the GAUSSIAN03 and GAUSSIAN09 program packages (Frisch et al., 2004, 2013).

## RESULTS AND DISCUSSIONS

## Potential Energy Surface of Singlet C3O<sup>3</sup>

By means of the extensive "grid" isomeric search and the transition state search strategies, we eventually located a total of 22 singlet chemically bound isomers and 46 transition states (Supporting Information, **SI\_2, SI\_3**). Note that our study found many other transition states whose imaginary frequency is only associated with the evolution of one separate part, isomer.

TABLE 1 | RE values for singlet C3O<sup>3</sup> isomers with respect to 3CO as well as the destruction barriers for each isomer at the CCSD(T)//B3LYP+GFEC level.


<sup>a</sup>The Gibbs free energy values at CBS-QB3.

<sup>b</sup>The Gibbs free energy values at W1BD.

while the other part is just a spectator. These transition states are not related to the evaluation of the kinetic stability of C3O<sup>3</sup> isomers and thus not discussed. The relative energies (RE) with respect to **P1** 3CO (0.0) and the corresponding destruction barriers of each singlet isomer are listed in **Table 1**. For simplicity, "CCSD(T)//B3LYP+GFEC" represents the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ values with GFEC. The structures of singlet isomers are listed in **Figure 1**. The schematic potential energy surface of singlet C3O<sup>3</sup> isomers is given in **Figure 2**. Energies for singlet C3O<sup>3</sup> isomers, transition states and products are shown in **SI**\_**4**, **SI**\_**5**, **SI**\_**6**. The natural molecular orbitals for **01**, **02**, **04** are shown in **SI**\_**8**.

#### Global Isomer

The global C3O<sup>3</sup> isomer is **01**, which lies 86.0 kcal/mol higher than the fragments 3CO (0.0). This indicates that C3O<sup>3</sup> is truly an energized system. As shown in **Figure 1**, the exocyclic C(4)- C(5) bond distance of **01** is 1.30 Å, indicative of the ketene-like >C=C=O bonding. To our surprise, C(4) is somewhat pyramidal in contrast to the usual sp<sup>2</sup> -C, for which three connected bonds are in a plane. So, **01** should have contribution from two resonant structures (A) >C=C=O and (B) >C(:)← CO (see **Scheme 2**).

To test the bonding picture **B** in isomer **01**, we computed the three-membered ring (3MR) C2O<sup>2</sup> when the exocyclic CO is formally removed from **01**. The 3MR C2O<sup>2</sup> is truly a singlet local minimum structure and is electronically stable during the

"stability" analysis. Its triplet structure does not exist, which upon optimization would collapse to the ground structure, i.e., triplet OCCO. The electronic stability of the unsaturated carbon in 3MR C2O<sup>2</sup> must originate from the lone-pair electronic stabilization of the neighboring O-atom. So, C(4) in **01** has the significant closedshell divalent carbene character with one electron lone pair (:) and one vacant orbital that is occupied by the Lewis base CO. This bonding picture is supported by two facts. First, the leaving barrier of CO (22.5 kcal/mol) is roughly quarter of the typical C-C single bond energy (85.4 kcal/mol; Sanderson, 1983) and the reverse association barrier between CO and 3MR-C is negligibly tiny. Note that the barrier becomes negative as −1.3 kcal/mol at the CCSD(T)//B3LYP+GFEC level, which is just a result of the single-point energy calculation at a lower-level geometry. This phenomenon usually occurs for low-barrier processes. This is well-indicative of the donor-acceptor interaction as shown in B). Second, there is an appreciable binding energy between the 3MR-C atom and the Lewis acid AlCl<sup>3</sup> (12.6 kcal/mol at the B3LYP/aug-cc-pVTZ+ZPVE level), suggestive of the existence of an electron lone pair on C(4).

## Viable and Fleeting Isomers

According to Hoffmann et al. (2008), a viable molecule should be resistant to fragmentation, isomerization, and dimerization or higher chemical aggregation. For a gas-phase molecule like C3O3, the aggregation can usually be omitted (the chance of bimolecular association is very little). So, the kinetic stability against both fragmentation and isomerization is the key to determine the lifetime of a C3O<sup>3</sup> structure. Species with several kcal/mol should better be viewed as fleeting or transient. For safety, in this work, the value 10 kcal/mol is artificially taken as the bar of "fleeting" or "transient."

Among the 22 located singlet C3O<sup>3</sup> isomers, a total of seven isomers (**01**, **02**, **04**, **08**, **09**, **11**, **20**) were identified to have the destruction barriers of ≥10 kcal/mol. The easiest conversion pathway for the global isomer **01** is to decompose into **P1** 3CO with a marginal barrier of 10.3 kcal/mol. Two four-membered ring (4MR) isomers **02** and **04** (lie at 123.7 and 133.7 kcal/mol, respectively) both contain a C(µ-O)2C=C core (µ for "bridge"). In particular, both **02** and **04** feature the unsaturated carbenes. Their most feasible primary pathways are different, i.e., **P5** CO + c-OCCO for **02** and **P2** (u)CCO + CO<sup>2</sup> for **04** with the corresponding barriers of 17.8 and 24.3 kcal/mol. Isomers **08** and **11** (at 156.6 and 227.0 kcal/mol, respectively) are bicyclic and spiral. Their most feasible product is **P5** CO+c-OCCO via the direct and indirect pathways with the corresponding barriers 13.7 and 12.2 kcal/mol. For isomer **09** with bridge-OO, the most favorable product is **P2** (u)CCO + CO<sup>2</sup> with the barriers 13.2 kcal/mol. The very high-energy **cis**/**trans** chainlike isomers **20** (285.5 kcal/mol) and **21** (288.9 kcal/mol) both have

a terminal-OO and can be interconverted to each other. As shown in **SI\_9**, **21** might undergo the intersystem crossing during fragmentation to CCO (triplet)+COO, which greatly decrease its kinetic stability (<10 kcal/mol). By contrast, the interconversion governs the kinetic stability of **20** and its the destruction barrier is 10.3 kcal/mol.

The remaining 15 singlet C3O<sup>3</sup> isomers have smaller destructions barriers of ≤10 kcal/mol, i.e., **01b** (-1.3), **03** (6.1), **05** (1.5), **06** (4.7), **07** (0.7), **10** (4.9), **12** (0.5), **13** (2.6), **14** (0.5), **15** (0.9), **16** (0.9), **17** (5.4), **18** (2.9), **19** (3.0), **20** (6.9). The values in () are the respective destruction barriers in kcal/mol. Amongst them isomer **20** has the largest destruction barrier 6.9 kcal/mol. Clearly, the 15 isomers should be considered as "fleeting" or "transient." Note that isomer **01b** has a physically troublesome negative barrier height value −1.3 kcal/mol according to the transition state theory, although the barrier height is a reasonable one (0.2 kcal/mol) at B3LYP/aug-cc-pVTZ+GFEC level. This is an indication that **01b** is either not a minimum or faces a negligibly small barrier at the CCSD(T) level.

To determine whether a single-reference-based electron correlation procedure (here is CCSD(T)/aug-cc-pVTZ) is appropriate or not, the T1 diagnostic values (T1Diag) were computed. A large T1 (i.e., >0.02) probably indicates that a multireference electron correlation procedure is needed (Lee and Taylor, 1989). In our work, the T1Diag values lie below the threshold 0.02 for key isomers and transition states (see **SI\_7**). Understandably, for the –OO isomers **20** and **21**, the T1Diag values are greater, i.e., around 0.04 for isomers and around 0.03 for transition states. Other species have acceptable T1Diag values of around 0.02 except **ts04/07**, **ts08/P1**, **uts09/P2,** and **ts11/P2**, whose T1Diag values are close to 0.03.

In the present study on the C3O<sup>3</sup> PES construction as well as the composite CBS and W1BD calculations were all based on the B3LYP method. We thus further performed the comparative study of B3LYP with B3LYP-D3BJ (Grimme et al., 2011) and B2PLYP-D3(Grimme, 2006; Grimme et al., 2010) using the same aug-cc-pVTZ basis set followed by the CCSD(T)/augcc-pVTZ single-point energy calculations for both the isomeric and destruction transition state strucutures for key structures, i.e., **01**, **02**, **04**, **01-TS**, **02-TS,** and **04-TS** (see **SI\_10**, **SI\_11**). For the geometries (bond length, bond angle, dihedral angle), B3LYP agrees excellently with B3LYP-D3BJ and B2PLYP-D3 for **02**, **04**, **02-TS,** and **04-TS**. The deviation is relatively larger for **01** and **01-TS** with largest differences value of bond length, bond angle and dihedral angle are 0.11 Å, 4.2◦ , and 10.5◦ , respectively. This must be due to the unique electronic structure of **01** as bearing two resonant structures >C=C=O and >C(:)← CO (as discussed above). Yet the relative energies and destruction barriers at CCSD(T)//B3LYP agree quite well with those at CCSD(T)//B3LYP-D3BJ and CCSD(T)//B2PLYP-D3 within 1.0 kcal/mol for all the three isomers.

#### Implications

Let us compare our extensive potential energy surface study with literatures. Only three singlet C3O<sup>3</sup> structures (**A**, **B**, **C**) have been proposed (see **Scheme 1**). The second-order saddle point nature of **A** was reproduced in our work. The structures **B** and **C** predicted as local minima in 2012 at B3LYP/6-31G(d) level correspond to **01** and **05**, respectively in our work. To our great surprise, **01** (**B**) was reported to lie by 34.9 kcal/mol higher in energy than **05** (**C**) in the 2012 work, in sharp contrast to the present study that **01** (**B**) is the global minimum and 47.6 kcal/mol more stable than **05** (**C**). After careful repetition and analysis, the reason for such dramatic discrepancy was found to be that the 2012 study actually used the results at two different levels for comparison, i.e., B3LYP/6-31G (with no d function) for **01** (**B**) and B3LYP/6-31G(d) **05** (**C**). Thus, the present work for the first time predicted **01** as the global minimum of C3O3.

The two carbene-like isomers **02** and **04** with good kinetic stability deserve special attention. First, they provide much promise to design larger oxocarbon clusters with similar structural backbones. Second, the intrinsic carbene-reactivity allows them to be used in functionalizing various nano-materials such as graphenes (Bruce, 1991; Rit et al., 2016; Meyer, 2018). In particular, both isomers have one carbonyl (C=O) and two epoxyl (O<) groups, which could make them promising in the alkali metal-ion batteries (Wang et al., 2013; Zan, 2014; Deng et al., 2017; Zhao et al., 2017).

In particular, the destruction barrier 24.3 kcal/mol of the isomer **04** is quite close to those of the already synthesized species, e.g., N2CO (25.8 kcal/mol; Korkin et al., 1996) and pentazole anion N − 5 (25.2 kcal/mol; Rahm and Brinck, 2010). With very huge energy release to 3CO (133.7 kcal/mol), **04** deserves to be taken as a HEDM candidate.

In short, we constructed the first global potential energy surface of singlet C3O<sup>3</sup> through the thorough isomeric and transition state search strategies. The detailed isomerization/fragmentation and stability data presented in this work should provide an important base for future laboratory study of C3O<sup>3</sup> isomers.

## CONCLUSIONS

The key contribution of our work can be summarized as follow:


## DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and/or the **Supplementary Files**.

## AUTHOR CONTRIBUTIONS

JX formulated the problem, did ab initio calculations, searched for literatures, wrote, and finalized the manuscript. XH did composite CBS-QB3 and W1BD calculations, participated in data collection, and analysis. FH formulated the problem, did ab initio calculations, and wrote the first manuscript draft. YD formulated the problem, generated key concepts, guided the whole research, and finalized the manuscript.

## FUNDING

This work was funded by the National Natural Science Foundation of China (No. 21773082, 21473069).

## ACKNOWLEDGMENTS

The reviewers' helpful comments and suggestions are greatly acknowledged.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00193/full#supplementary-material

## REFERENCES


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Xin, Han, He and Ding. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Isotope Effects in the Predissociation of Excited States of N<sup>2</sup> <sup>+</sup> Produced by Photoionization of <sup>14</sup>N<sup>2</sup> and <sup>15</sup>N<sup>2</sup> at Energies Between 24.2 and 25.6 eV

Helgi R. Hrodmarsson<sup>1</sup> , Roland Thissen<sup>2</sup> , Danielle Dowek <sup>3</sup> , Gustavo A. Garcia<sup>1</sup> , Laurent Nahon<sup>1</sup> and Thomas R. Govers <sup>4</sup> \*

<sup>1</sup> Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin BP 48, Gif-sur-Yvette, France, <sup>2</sup> Laboratoire de Chimie Physique, Université Paris-Sud, Orsay, France, <sup>3</sup> Institut des Sciences Moléculaires, Université Paris-Sud, Orsay, France, <sup>4</sup> Soleil Synchrotron, Paris, France

#### Edited by:

Paolo Tosi, University of Trento, Italy

#### Reviewed by:

Lorenzo Avaldi, Institute of the Structure of Matter, Italian National Research Council, Italy Ingo Fischer, University of Wuerzburg, Germany

#### \*Correspondence:

Thomas R. Govers thomas.govers@orange.fr

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 08 February 2019 Accepted: 21 March 2019 Published: 12 April 2019

#### Citation:

Hrodmarsson HR, Thissen R, Dowek D, Garcia GA, Nahon L and Govers TR (2019) Isotope Effects in the Predissociation of Excited States of N2 <sup>+</sup> Produced by Photoionization of <sup>14</sup>N<sup>2</sup> and <sup>15</sup>N<sup>2</sup> at Energies Between 24.2 and 25.6 eV. Front. Chem. 7:222. doi: 10.3389/fchem.2019.00222 Photoelectron/photoion imaging spectrometry employing dispersed VUV radiation from the SOLEIL synchrotron has been used to study the predissociation of N<sup>2</sup> <sup>+</sup> states located up to 1.3 eV above the ion's first dissociation limit. Branching ratios for unimolecular decay into either N<sup>2</sup> <sup>+</sup> or N<sup>+</sup> were obtained by measuring coincidences between threshold electrons and mass-selected product ions, using a supersonic beam of either <sup>14</sup>N<sup>2</sup> or <sup>15</sup>N<sup>2</sup> as photoionization target. The results confirm that predissociation of the C26 + <sup>u</sup> state of <sup>14</sup>N<sup>2</sup> <sup>+</sup> is faster than emission to the electronic ground-state by a factor 10 or more for all vibrational levels v′ ≥ 3, while for <sup>15</sup>N<sup>2</sup> <sup>+</sup> the two decay modes have comparable probabilities for the levels v′ = 3, 4, and 5. In contrast, no significant isotope effect could be observed for the other states of N<sup>2</sup> <sup>+</sup> identified in the photoelectron spectrum. For both <sup>14</sup>N<sup>2</sup> <sup>+</sup> and <sup>15</sup>N<sup>2</sup> <sup>+</sup> isotopologues all vibrational levels of these other states decay to an extent of at least 95% by predissociation.

Keywords: photoionization, nitrogen, predissociation, charge exchange, helium, TPEPICO

## INTRODUCTION

The properties of the excited states of N<sup>2</sup> <sup>+</sup> in the neighborhood of its first dissociation limit are of relevance to thermal charge exchange between He<sup>+</sup> and N<sup>2</sup> and its possible role in the escape of helium from the earth's atmosphere. For such a reaction to contribute to the loss of helium, its exothermicity should be high enough to impart to the He product a kinetic energy of about 2.5 eV. The identity and relative importance of the primary charge-transfer channels need to be known to evaluate that possibility (see Lie-Svendsen et al., 1992).

Among the doublet states, illustrated in **Figure 1**, the C26<sup>+</sup> u state in particular has been the subject of many experimental and theoretical investigations (van de Runstraat et al., 1974; Paulus et al., 2016, and references therein). Its lower vibrational levels, v ′ ≤ 2, lie below the ground-state N+( <sup>3</sup>P) + N(<sup>4</sup> S) asymptote and fluorescence to the electronic ground-state, N<sup>2</sup> <sup>+</sup> (C26<sup>+</sup> u , v′ ) → X (26<sup>+</sup> g , v′′), is their only known unimolecular decay path. This emission occurs at wavelengths between 127 and 223 nm, and is known as the second negative system of N<sup>2</sup> <sup>+</sup> (Lofthus and Krupenie, 1977). The levels v′ ≥ 3, on the other hand, can also decay by unimolecular predissociation into ground-state atomic fragments. Spectroscopically, the onset of predissociation is characterized by a weakening in the C→X fluorescence, and a decreasing N<sup>2</sup> + (C26<sup>+</sup> u , v′ ) lifetime. In mass spectrometry the predissociation will manifest itself by the production of N<sup>+</sup> ions in competition with that of N<sup>2</sup> +.

The competition between C-state predissociation and fluorescence has first been experimentally quantified by the analysis of the vibrationally resolved C→X emission spectrum. In the work by van de Runstraat et al. (1974) and Govers et al. (1975), the C (v′ ) levels were populated under conditions where their relative populations should reflect a "vertical" ionization process, so that the vibrational fluorescence intensities could be predicted in the absence of predissociation. Comparison with the relative intensities that were actually observed made it possible to determine the ratio between the predissociationand fluorescence probabilities, Apred (v′ )/Aem (v′ ), for each of the C-state vibrational levels v′ = 3–8. Electron- and ion-impact experiments using a room-temperature nitrogen target were conducted for the three isotopologues: <sup>14</sup>N2, <sup>14</sup>N15N, and <sup>15</sup>N2. It was found that the predissociation probability generally increases with increasing vibration, and that it is subject to a strong isotope effect. The quantitative uncertainty in this approach stems largely from the difficulty to predict the initial population of C-state vibrational levels, as will be discussed further below. Two alternate methods can be used to avoid this difficulty. The first one is to measure the individual lifetimes τ (v′ ), since:

$$1/\tau(\mathbf{v}') = \mathbf{A}\_{\rm em}(\mathbf{v}') [1 + \mathbf{A}\_{\rm pred}(\mathbf{v}') / \mathbf{A}\_{\rm em}(\mathbf{v}')] \tag{1}$$

where the emission rate Aem (v′ ) varies little with vibrational number and can be measured for the non-predissociated levels. Such measurements have been reported by Erman (1976) for <sup>14</sup>N<sup>2</sup> <sup>+</sup> (C, v′ ), with v′ = 0–5. They demonstrated a 20-fold decrease in lifetime between v′ = 2 and v′ = 3, but did not confirm the further decrease with increasing vibration. The experiment is difficult because of the low intensities of fluorescence from v′ ≥ 3, and would be easier to carry out with <sup>14</sup>N15N or <sup>15</sup>N2.

The other method, used in the present work, is to concurrently measure mass-selected ion yields, I(N<sup>2</sup> <sup>+</sup>) and I(N+), upon selective ionization of a specific (C, v′ ) level, to directly obtain the respective branching ratios:

$$\begin{aligned} \text{BR(v',N\_2^+)} &= \text{I(v',N\_2^+)/[I(v',N\_2^+) + I(v',N^+)]}; \quad \text{(2)}\\ \text{BR(v',N^+)} &= 1 - \text{BR(v',N\_2^+)} \end{aligned}$$

from which:

$$\mathbf{A}\_{\rm pred}(\mathbf{v}')/\mathbf{A}\_{\rm em}(\mathbf{v}') = [1 - \mathbf{B} \mathbf{R}(\mathbf{v}', \mathbf{N}\_2^+)]/\mathbf{B} \mathbf{R}(\mathbf{v}', \mathbf{N}\_2^+) \tag{3}$$

The TPEPICO (threshold photoelectron/photoion coincidence) technique using a photoelectron/photoion imaging spectrometer is well-suited for this purpose.

#### METHODS

The experiments were performed on the DESIRS VUV beamline (Nahon et al., 2012) of the French synchrotron facility SOLEIL. Horizontally polarized VUV light emitted from an undulator was dispersed by a 6.65 m normal incidence monochromator equipped with a 4,300 grooves/mm grating. Its exit slit was set at 400µm, providing a photon energy bandpass at 24.57 eV of 2.5 meV full width at half maximum ("fwhm"). The photon beam crossed a supersonic molecular beam of nitrogen in the SAPHIRS end station (Tang et al., 2015), which houses the DELICIOUS III double imaging spectrometer (Garcia et al., 2013). It is composed of a velocity map imaging analyzer of photoelectrons and a modified Wiley-McLaren time-of-flight ion imaging device, operated in coincidence. Electrons and ions are extracted and accelerated vertically in opposite directions by a constant electric field, perpendicular to the plane defined by the molecular beam and the photon beam, and they are detected in coincidence by means of delay-line based position sensitive channel plate detectors. The extraction field in the source region was set at 18 V/cm, ensuring full collection of photoelectrons and photoions with kinetic energies up to about 0.8 eV. The electron energy resolution under these conditions is about 3 to 4% and the ion mass resolution 1m/m ≈ 1/350. Unsubstituted nitrogen was N60 grade from Air Liquide, while the <sup>15</sup>N<sup>2</sup> isotopolog was supplied by Aldrich, with a <sup>14</sup>N<sup>2</sup> content of <2%.

In the present experiments, the stagnation pressure of the 30µm diameter nozzle was 0.7 Bar, and the supersonic beam was defined by two consecutive skimmers, the first of which, with a diameter of 1 mm, was located 10 mm downstream from the nozzle, and the second, with a diameter of 2 mm, at a distance of 25 mm. The crossing point with the photon beam was located at 5 cm from the nozzle, far downstream from the onset of freezing of the rotational distribution of the expanding nitrogen. An estimate of the rotational population can thus be obtained from the data obtained by Mori et al. (2005) who report results for a pressure x nozzle diameter product of 15 Torr.mm, close to our value of 16 Torr.mm. Under these conditions, the rotational distribution has its maximum at N = 3, and 90% of the N<sup>2</sup> molecules have a rotational quantum number of N = 7 or less. In comparison, the average N for room-temperature nitrogen is 9. Downstream from rotational freezing, Mori et al. (2005) found the limiting population of the lower rotational levels to be characterized by a rotational "temperature" between 30 and 40 K. In comparison, the present N<sup>2</sup> <sup>+</sup> velocity distribution extracted from the ion position and TOF (see Tang et al., 2015) was consistent with a beam translational temperature close to 50 K.

The absence of significant mass dependence of the ion detection efficiency was verified by measuring the ratio of the threshold photoelectron/photoion coincidences to the corresponding number of electron starts, which yields the absolute ion detection efficiency as outlined by Brehm et al. (1995). At the threshold for He ionization, the amu = 4 detection efficiency was found to be 28 ± 1%, while at the thresholds for ionization to <sup>14</sup>N<sup>2</sup> <sup>+</sup> and <sup>15</sup>N<sup>2</sup> <sup>+</sup>, the mass 28 and mass 30 detection efficiencies were found to be 31 ± 1% and 29 ± 1%, respectively. As the response of the micro channel plates depends primarily on the ion's impact velocity, the close similarity between the data obtained for mass 4 and for masses 28 and 30 indicates that mass discrimination between N<sup>2</sup> <sup>+</sup> and N<sup>+</sup> can be neglected. As indicated above, discrimination resulting from the

kinetic energy of the N<sup>+</sup> fragments is negligible up to values of about 0.8 eV, while the highest value reached in this work is only 0.66 eV. Branching ratios for N<sup>2</sup> <sup>+</sup> and N<sup>+</sup> production can thus directly be extracted from their relative coincidence rates in the TPEPICO spectra.

## RESULTS

The photon energy calibration and bandwidth were verified with a He beam as target by measuring the onset for coincidences between He<sup>+</sup> ions and photoelectrons observed upon scanning the photon energy between 24.56 and 24.62 eV in 1 meV steps. The threshold was found at a nominal value of 24.5865 eV, which agrees within 1 meV with the published value of 24.5874 eV (Kandula et al., 2010). The spectra shown in this paper have been corrected for this offset. The photon energy width was measured as 2.5 meV, fwhm. Throughout this paper we used the conversion factor 1 eV = 8065.544005 cm−<sup>1</sup> (Mohr et al., 2016).

**Figure 2** shows our <sup>14</sup>N<sup>2</sup> TPEPICO spectrum obtained by selecting coincidences with electrons having energies between 0 and 5 meV. The black trace shows the N<sup>+</sup> coincidence rate, and the red trace, drawn upside down, corresponds to N<sup>2</sup> <sup>+</sup> coincidences.

One readily identifies the vibrational levels v′ = 3, 4, 5, and 6 of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> C-state, as indicated. The marks and labels in the top of **Figure 3** correspond to the vibrational progressions called S1, S2, and S3 in the TPES (threshold photoelectron spectrum) measured by Yoshii et al. (1997). The vibrational quantum numbers are positioned at the photon energies obtained from their tabulated wavelengths. The S1 progression corresponds to the D′ <sup>2</sup>5<sup>g</sup> state of **Figure 1**, as will be discussed further below. The S2 and S3 progressions have been assigned to the <sup>2</sup>6<sup>−</sup> u and <sup>2</sup>1<sup>u</sup> states shown in **Figure 1**, respectively (Yoshii et al., 1997).

The C, v ′ = 5 level has a fwhm of 10 meV, somewhat larger than the compounded instrumental width of 6 meV. Yoshii et al. (1997), with a slightly better resolution and a supersonic molecular beam target, measured a threshold photoelectron width of 7.5 meV. Yencha et al. (2014), who used a static target cooled to 77 K and an instrumental resolution of 18 meV, obtained a halfwidth of about 32 meV. From the data reported by Merkt and Guyon (1993), one can evaluate the width of the rotational band structure for a 300 K gas target to be of the order of 20–30 meV. The narrowness of the C, v′ = 5 peak observed by Yoshii et al. (1997) and in the present experiments indicates that the supersonic beams used in these two investigations ensure a target rotational distribution significantly narrower than that of a static gas at 77 K, in agreement with the findings of Mori et al. (2005) mentioned above.

**Table 1** compares the energy positions of the spectral features of **Figure 1** with those obtained from the analysis of the <sup>14</sup>N<sup>2</sup> + (C26<sup>+</sup> u , v′ ) → X (26<sup>+</sup> g , v′′) emission spectrum by Joshi (1996b), the ZEKE measurements of Merkt and Guyon (1993) and the TPES spectrum of Yoshii et al. (1997). The assignments are listed in the right-hand column, with the vibrational number indicated in parenthesis. Our energy peaks for the C-state agree within 1 meV with those obtained from the C→X emission bandheads measured by Joshi (1996b) and the <sup>14</sup>N<sup>2</sup> ionization threshold of Huber and Jungen (1990). The feature observed at 24.677 eV is

FIGURE 2 | TPEPICO spectrum for <sup>14</sup>N<sup>2</sup> between 24.0 and 25.24 eV showing the vibrational levels v′ <sup>=</sup> 3–6 of the C <sup>2</sup><sup>6</sup> + u state of <sup>14</sup>N<sup>2</sup> <sup>+</sup>. The photon energy was scanned in 1 meV increments, and the electron-ion coincidences were integrated during 40 s after each step. Coincidences with <sup>14</sup>N <sup>+</sup> ions are indicated in black, those with <sup>14</sup>N<sup>2</sup> <sup>+</sup> are shown upside down, in red.

also seen in the TPES spectrum of Yoshii et al. (1997), but is as yet unassigned. The S1(13) peak, which Yoshii et al. (1997)situate at 24.793 eV is reported at 24.788 eV by Baltzer et al. (1992) and at 24.780 eV by Yencha et al. (2014), which substantiates the assignment of the peak we observed at 24.779 eV.

All of the features listed in **Table 1** are observed in **Figure 2** as coincidences between threshold electrons and <sup>14</sup>N<sup>+</sup> ions, while the <sup>14</sup>N<sup>2</sup> <sup>+</sup> signals, if any, cannot be distinguished from the noise level, with the exception of faint <sup>14</sup>N<sup>2</sup> <sup>+</sup> contributions at the location of the C, v′ = 3 and v′ = 4 levels. In other words, above



The energy values are indicated in eV. The last column lists the proposed <sup>14</sup>N<sup>2</sup> <sup>+</sup> state assignments. The S1, S2, and S3 labels refer to the vibrational progressions as identified by Yoshii et al. and "C" refers to the C26 + <sup>u</sup> state of <sup>14</sup>N<sup>2</sup> <sup>+</sup>. The numbers in brackets are the vibrational quantum numbers.

the dissociation threshold at 24.2878 eV, less than about 5% of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> produced at the peak positions in the spectrum will survive as molecular ions during the time of about 3 µs that the parent ion spends in the ion acceleration region.

The TPEPICO spectrum obtained when <sup>15</sup>N<sup>2</sup> is used as a target is illustrated by **Figure 3**. Contrary to the absence of significant <sup>14</sup>N<sup>2</sup> <sup>+</sup> signals in **Figure 2**, the data obtained with <sup>15</sup>N<sup>2</sup> show several clear molecular ion peaks above the <sup>15</sup>N<sup>+</sup> + <sup>15</sup>N threshold at 24.2927 eV. Because of the neutral's lower zero-point energy, this limit lies 4.9 meV higher than the 24.2878 eV value for <sup>14</sup>N<sup>+</sup> + <sup>14</sup>N.

The peak energies indicated for the vibrational levels v′ = 3–8 of the <sup>15</sup>N<sup>2</sup> <sup>+</sup> C-state agree within 3 meV with the ionization energies in brackets, obtained from the C→X emission bandheads for <sup>15</sup>N<sup>2</sup> <sup>+</sup> published by Joshi (1966a), and our evaluation of the rotationless <sup>15</sup>N<sup>2</sup> <sup>+</sup> (X, v′ = 0)←15N<sup>2</sup> (X, v = 0) ionization energy as 15.5810 eV. Contrary to the <sup>14</sup>N<sup>2</sup> <sup>+</sup> Cstate, the heavier isotopolog gives rise to clearly distinguished production of <sup>15</sup>N<sup>2</sup> <sup>+</sup> for the vibrational levels v′ = 3, 4, and 5, and to a lesser extent also for v′ = 6 and 7. The corresponding branching ratios will be discussed in section Discussion. Between 25.25 and 25.35 eV the enhanced "noise" in the <sup>15</sup>N<sup>2</sup> <sup>+</sup> coincidence count hints at the possibility of weak decay into molecular ions. Within the limited time of access to the DESIRS beamline, the reproducibility of this observation could not be verified.

The assignment of the spectral features other than the Cstate peaks is based on applying isotope shifts to the progressions labeled S1, S2, and S3 in the 5 meV resolution TPES reported by Yoshii et al. (1997). Vibrational parameters w<sup>e</sup> and wex<sup>e</sup> for <sup>14</sup>N<sup>2</sup> <sup>+</sup> were obtained from Birge-Sponer plots of the vibrational spacings in the energy range of interest, and these were used to calculate the vibrational isotope shifts according to:

$$\begin{aligned} \text{G(v)}\_{15} - \text{G(v)}\_{14} &= \{ \text{v} + 1/2 \}^\* \text{w}\_{\text{e}}^\* [\sqrt{(7/7.5)} - 1] \\ &- \text{ (v} + 1/2\text{)}^2 \text{w}\_{\text{e}} \text{x}\_{\text{e}}^\* (7/7.5 - 1), \end{aligned} \tag{4}$$

where G(v) stands for the vibrational energy of level v with respect to the minimum of the potential well. These shifts were applied to the experimental <sup>14</sup>N<sup>2</sup> <sup>+</sup> energy levels of Yoshii et al. (1997), and the <sup>15</sup>N<sup>2</sup> ionization energies were obtained by allowing for the lowering of the neutral N<sup>2</sup> zero-point energy. The energies for the S1, S2, and S3 vibrational levels obtained in this manner are indicated in the upper part of **Figure 3**. All of the structures observed could thus be attributed to either the C-state or to one of the S1 or S2 or S3 progressions, with the exception of the peaks at 24.650, 25.026, and 25.300 eV which are as of yet unassigned.

#### DISCUSSION

In what follows we shall first discuss the branching ratios for decay of the N<sup>2</sup> <sup>+</sup> C-state levels, and subsequently address the spectroscopic information pertaining to the S1 progression.

#### Branching Ratios for Decay of the N<sup>2</sup> + (C26 + <sup>u</sup> , v′ ) Levels

The vibrational levels v′ ≤ 2 of the C-state decay only by fluorescence to the electronic ground state: N<sup>2</sup> <sup>+</sup> (C26<sup>+</sup> u , v′ ) → (X26<sup>+</sup> g , v′′). Their lifetime is about 79 ns (Erman, 1976), and the higher, predissociated levels necessarily have a shorter lifetime. The timescale for ion detection in the present experiments being of the order of microseconds, the competition between predissociation and fluorescence can therefore be evaluated directly from the relative yields for N<sup>+</sup> and N<sup>2</sup> <sup>+</sup> resulting from photoionization into a specific N<sup>2</sup> <sup>+</sup>(C, v′ ) level.

The corresponding branching ratios were determined by integrating the areas I(N+) and I(N<sup>2</sup> <sup>+</sup>) under the C-state N<sup>+</sup> and N<sup>2</sup> <sup>+</sup> peaks in the TPEPICO scans. The results are shown in **Table 2** for <sup>14</sup>N<sup>2</sup> <sup>+</sup> and in **Table 3** for <sup>15</sup>N<sup>2</sup> <sup>+</sup>. They are expressed as branching ratios for N<sup>2</sup> <sup>+</sup> production, as defined by equation 2, for each of the vibrational levels examined. The competition between C-state predissociation and C→X fluorescence has previously been quantified by comparing measured C→X fluorescence cross sections with those expected in the absence of predissociation. For this purpose, vibrationally resolved fluorescence intensities were measured upon impact of electrons (van de Runstraat et al., 1974) or ions (Govers et al., 1975) on a static room-temperature target of N2, at impact speeds high enough for the excitation to the various C-state vibrational levels to be considered as a "vertical" Franck-Condon process. Summing fluorescence from a particular (C, v′ ) level to all vibrational levels v′′ of the N<sup>2</sup> <sup>+</sup> ground-state, one obtains the vibrational fluorescence cross sections, σem (v′ ), and one can write:

$$
\sigma\_{\rm em}(\mathbf{v}') = \sigma\_{\rm exc}(\mathbf{v}')^\* \mathbf{BR}(\mathbf{v}', \mathbf{N}\_2^+), \tag{5}
$$

where σexc (v′ ) is the excitation cross-section for populating the vibrational level under consideration. Using cross-sections relative to those for v′ = 2, for which the BR(v′ = 2, N<sup>2</sup> <sup>+</sup>) is unity, since predissociation is energetically forbidden, one readily obtains the v′ ≥ 3 branching ratios from the relative emission intensities, provided the excitation ratios are known:

$$\text{BR(v',N}\_2^+) = [\sigma\_{\text{em}}(\text{v'})/\sigma\_{\text{em}}(\text{v'}=2)]/[\sigma\_{\text{exc}}(\text{v'})/\sigma\_{\text{exc}}(\text{v'}=2)]. \tag{6}$$

The excitation ratios were obtained from the N<sup>2</sup> <sup>+</sup> (C, v′ )←N<sup>2</sup> (v = 0) Franck-Condon factors, ("FCF") including configuration interaction ("CI") (see van de Runstraat et al., 1974; Govers et al., 1975 for details).

The data for <sup>14</sup>N<sup>2</sup> <sup>+</sup> are summarized in **Table 2** with the results of the present experiments in the first line. Weak parent ion signals could be distinguished from the background noise only for the levels v′ = 3 and v′ = 4. As a result, only upper limits to the <sup>14</sup>N<sup>2</sup> <sup>+</sup> branching ratios are listed for v′ = 5– 8. The branching ratios in line 4 are those obtained from the fluorescence spectra observed in the ion-impact experiments (Govers et al., 1975); they are somewhat more precise than the closely similar electron-impact results (van de Runstraat et al., 1974). They are obtained by dividing the measured fluorescence intensities, relative to that of the un-predissociated v′ = 2 level (line 3), by the theoretical excitation ratios obtained by assuming a Franck-Condon excitation with configuration interaction (line 2). Line 5 reproduces the <sup>14</sup>N<sup>2</sup> <sup>+</sup> branching ratios obtained by Ehresmann et al. (2006), who analyzed the dispersed C→X fluorescence observed when populating the C-state by photon excitation of the 1s−<sup>1</sup> π ∗ resonance at energies between 400 and 403 eV, using room-temperature <sup>14</sup>N<sup>2</sup> as a target. Lines 6–8 list the ratios between the probability for predissociation to that for C→X fluorescence deduced from the three experiments. The close agreement between the results of Ehresmann et al. (2006) and those summarized in lines 4 and 7 is gratifying, especially considering the difference in the C-state excitation mechanism pertaining to the two types of experiment. It suggests that the excitation ratios in line 2 of **Table 2** can be used with reasonable confidence, at least up to v′ = 6.

The fact that that the present measurements yield <sup>14</sup>N<sup>2</sup> + branching ratios substantially lower than those obtained from the analysis of fluorescence intensities is therefore surprising. We shall see below that in the case of <sup>15</sup>N<sup>2</sup> <sup>+</sup> the difference between the two sets of results is less pronounced, so that an experimental artifact can apparently be excluded. The only explanation that we can propose to account for the lower <sup>14</sup>N<sup>2</sup> <sup>+</sup> branching ratios concerns the rotational temperature of the target nitrogen, as will be further discussed below. In all predissociation experiments conducted so far, the target gas was static nitrogen at room temperature. In the present experiment it was a supersonic beam in which the rotational distribution is much narrower, as discussed in section Method and witnessed by the small widths of the C-state peaks in **Figures 2**, **3**.

In the case of <sup>15</sup>N<sup>2</sup> <sup>+</sup>, distinct parent ion peaks were found for the C-state levels v′ = 3, 4, and 5, weak peaks for v′ = 6 and 7, while only an upper limit could be estimated for v′ = 8. The present branching ratios are summarized in line 1 of **Table 3**. The present <sup>15</sup>N<sup>2</sup> <sup>+</sup> branching ratios shown in line 1 decrease with increasing vibration in a manner quite similar to the fluorescence data, listed in line 4. They show a systematic trend toward lower <sup>15</sup>N<sup>2</sup> <sup>+</sup> production, that is, higher predissociation rates. The corresponding ratios of the rate of predissociation to that of fluorescence are listed in lines 5 and 6.

The fluorescence rate of an electronically excited state is not expected to vary strongly with vibrational quantum number or isotopic substitution, as these parameters to a first approximation affect only the nuclear motion. The strong variation of the Apred (v′ )/Aem (v′ ) ratios in **Tables 2**, **3** is therefore essentially due to changes in the rate of predissociation (van de Runstraat et al., 1974 and references therein).

Two different models have been considered to account for the vibrational dependence of the C-state predissociation rate, and its variation upon isotopic substitution. The first is the accidental predissociation model proposed by Lorquet and Desouter (1972) and further discussed by Lorquet and Lorquet (1974). It incorporates a critical dependence on the energy match between the two interacting bound states. These authors focused on accounting for the observed vibrational and isotopic dependences and did not explicitly consider rotational effects. But as the zero-order energy match will vary with rotation if the two interacting bound states have different rotational constants, rotational effects are quite conceivable within the frame of their accidental predissociation model.

The second model is that of the direct predissociation by the continuum of the B state (see **Figure 1**) proposed by Tellinghuisen and Albritton (1975) and further detailed by Roche and Tellinghuisen (1979). They correctly reproduced the observed vibrational and isotopic dependencies and also explicitly examined the effect of rotation. It was shown that for <sup>15</sup>N<sup>2</sup> <sup>+</sup> the predissociation rate at low N quantum number increases markedly with decreasing rotation. Rotationally cold ( <sup>15</sup>N<sup>2</sup> <sup>+</sup>, C) ions produced by photoionization of a supersonic nitrogen beam, as is the case in the present work, will, according to that analysis, predissociate faster than those produced by ionization of a static room-temperature target, in agreement with the tendency summarized in **Table 3**. However, Roche and Tellinghuisen (1979) also showed that for <sup>14</sup>N<sup>2</sup> <sup>+</sup> the rotational dependence of the predissociation rate is weak, which should lead to only a small difference between the fluorescence- and coincidence results, contrary to what is seen in **Table 2**.

Subsequent theoretical investigations have not yet elucidated the preponderance of accidental predissociation or of direct predissociation in the C-state decay. Langhoff and Bauschlicher (1988) carried out very accurate calculations of the N<sup>2</sup> <sup>+</sup> doublet states and also of the potential energy crossings between the C <sup>2</sup>6<sup>+</sup> u state and close-lying <sup>2</sup>6<sup>−</sup> u and <sup>4</sup>5<sup>u</sup> states. They proposed



The first line lists the values obtained from the TPEPICO spectrum of Figure 2 by dividing the areas of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> coincidence peaks by the sum of those for <sup>14</sup>N <sup>+</sup> and <sup>14</sup>N<sup>2</sup> + coincidences. The uncertainty limits are obtained after propagation of the original Poisson distribution of the photoelectron image pixel counts. Lines 2 to 4 summarize the data of Govers et al. (1975). Line 5 lists the branching ratios obtained by Ehresmann et al. (2006). The respective ratios between the probability for predissociation to that for C→X fluorescence are indicated in lines 6–8.


The first line lists the values obtained from the TPEPICO spectrum of Figure 3 by dividing the areas of the <sup>15</sup>N<sup>2</sup> <sup>+</sup> coincidence peaks by the sum of those for <sup>15</sup>N <sup>+</sup> and <sup>15</sup>N<sup>2</sup> + coincidences. The uncertainty limits are obtained after propagation of the original Poisson distribution of the photoelectron image pixel counts. Lines 2 to 4 summarize the data of Govers et al. (1975). Lines 5 and 6 list the respective ratios between the probability for predissociation to that for C→X fluorescence.

predissociation of the C-state to occur by spin-orbit coupling to the <sup>2</sup>6<sup>−</sup> u state followed by transition to the continuum of the <sup>4</sup>5<sup>u</sup> state, in accordance with the model of Lorquet and Desouter (1972). Hochlaf et al. (1997) showed that another quartet state, e <sup>4</sup>6u, crosses the C-state near the v′ = 3 vibrational level. It correlates with ground-state atomic fragments and offers a pathway for direct predissociation by spin-orbit coupling. More recently, Paulus et al. (2016) published a time-dependent description of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> C-state predissociation through nonadiabatic coupling with the B-state continuum, and they reported predissociation rates that agree quite well with those deduced from the analysis of the C→X fluorescence spectra.

We note that the characteristics of the competition between fluorescence and predissociation, and in particular its dependence on isotopic substitution, are rather unique to the N<sup>2</sup> <sup>+</sup> C-state, as other states in the vicinity of the He<sup>+</sup> recombination energy are fully predissociated for both isotopologues investigated here. This supports the analysis of the isotope effects observed in near-thermal charge transfer between He<sup>+</sup> and N2, whereby it was assumed that it results from the sole decay characteristics of the C-state (Govers et al., 1974, 1977). This assumption, and the high D′ <sup>2</sup>5<sup>g</sup> → A <sup>2</sup>5<sup>u</sup> emission intensities observed in low-pressure charge-transfer experiments, indicate that about 90% of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> product ions result from initial charge transfer into the D′ <sup>2</sup>5<sup>g</sup> state discussed below (Sekiya et al., 1987; Govers, 2016). This reaction is exothermic by <0.9 eV and does not impart to the neutral He the 2.5 eV kinetic energy necessary to escape from the earth's attraction. The only sufficiently exothermic channel identified so far, i.e., charge transfer into the N<sup>2</sup> <sup>+</sup> (B26<sup>+</sup> u , v′ ≤ 5) levels, has a rate constant of the order of 1 to 2.10−<sup>11</sup> cm<sup>3</sup> /s (Govers et al., 1977). This is too small a rate to contribute significantly to the loss of He from the earth's atmosphere (see Lie-Svendsen et al., 1992).

#### Spectroscopy of the S1 Progression

The long vibrational progression labeled S1 by Yoshii et al. (1997) has been identified as resulting from photoionization to the second N<sup>2</sup> <sup>+</sup> state of <sup>2</sup>5<sup>g</sup> symmetry by Baltzer et al. (1992). It was noted that the energy spacings between its lower vibrational levels is smaller than that of the higher ones, as can be understood from the unusual shape of the potential well illustrated in **Figure 1**, which results from avoiding crossings with two other <sup>2</sup>5<sup>g</sup> states. The intensities of the 2 <sup>2</sup>5g(v′ ≤ 2) peaks are low, and extracting the adiabatic ionization potential from the (T)PES spectra is rather uncertain.

In the above analyses of the photoelectron spectra, no use was made of the results obtained by Cossart et al. (1985), who analyzed the previously unidentified emission between 229 and 245 nm resulting from low-energy collisions between He<sup>+</sup> and N<sup>2</sup> (Holland and Maier, 1971; Govers et al., 1977). Using a novel discharge source and photographic recording, they carried out a rotational analysis complemented by SCF ab-initio calculations,

and assigned the most prominent of these emissions to the transition D′ <sup>2</sup>5g(v′ ) → A <sup>2</sup>5<sup>u</sup> (v′′ = 7, 8, and 9). The emitting D′ <sup>2</sup>5g(v′ ) vibrational levels were tentatively labeled as v′ = 0, 1, 2. They are located at 23.698, 23.786, and 23.870 eV above the ground state of <sup>14</sup>N2. There should be only two states of <sup>2</sup>5<sup>g</sup> symmetry in this energy region (Thulstrup and Andersen, 1975), so that the 2 <sup>2</sup>5<sup>g</sup> state identified in the photoelectron spectra and the D′ <sup>2</sup>5<sup>g</sup> state identified by Cossart et al. (1985) must be one and the same state of N<sup>2</sup> +.

Accordingly, we have re-examined the published (T)PES data for the D′ <sup>2</sup>5<sup>g</sup> state while locating the first three vibrational levels at the energy values deduced from the analysis by Cossart et al. (1985). For the energies of the levels v′ = 3 to 10 we used the averages of those determined by (T)PES: Baltzer et al. (1992), Yoshii et al. (1997), Yencha et al. (2014) and this work. From the vibrational energy spacings thus obtained, the vibrational parameters w<sup>e</sup> and wex<sup>e</sup> were deduced from the intercept and slope of the Birge-Sponer plot:

$$\mathbf{G(v'+1) - G(v') = w\_{\mathbf{e}} - 2w\_{\mathbf{e}}x\_{\mathbf{e}}} \\ \text{\*} \\ \text{(v'+1)} \tag{7}$$

The energy of the <sup>14</sup>N<sup>2</sup> <sup>+</sup> D′ <sup>2</sup>5g(v′ = 9) level was fixed at 24.4582 eV, the average value obtained by (T)PES, with an agreement within 1 meV between the four sets of experimental data. The resulting least-squares fit yielded w<sup>e</sup> = 85.53 meV and wex<sup>e</sup> = 0.085 meV, and T<sup>e</sup> = 23.6533 eV (potential minimum above the neutral's ground state).

The vibrational levels for v′ ≥ 10 are not well reproduced by the vibrational parameters quoted above. Using equation 7, a least-squares fit to the averaged <sup>14</sup>N<sup>2</sup> <sup>+</sup> data obtained by Baltzer et al. (1992), Yoshii et al. (1997), Yencha et al. (2014) and ourselves, yielded w<sup>e</sup> = 94.20 meV and wex<sup>e</sup> = 0.085 meV, and T<sup>e</sup> = 23.6533 eV.

For the <sup>15</sup>N<sup>2</sup> <sup>+</sup> D′ <sup>2</sup>5<sup>g</sup> (v′ = 0–10) levels, the vibrational parameters estimated by correcting for the reduced mass were w<sup>e</sup> = 82.63 meV and wex<sup>e</sup> = 0.079 meV, respectively. Allowing for the lowering of the neutral ground state by 0.59 meV, the ionization energies for the first eleven vibrational levels were predicted as indicated in **Table 4**, which shows a satisfactory agreement with the v′ = 7–10 energies observed in in the present experiments.

A separate fit to the present peak positions in **Figure 3** was carried out for the levels v′ ≥ 10. The results are listed in **Table 5**.

Comparing the observed peak values and vibrational ionization energies calculated for the <sup>15</sup>N<sup>2</sup> <sup>+</sup> D′ <sup>2</sup>5<sup>g</sup> state, we note several cases where the difference somewhat erratically exceeds 10 meV. Yet, the accuracy of the experimental energy scale is of the order of 1 meV, and the narrowest peaks in **Figure 3** have a halfwidth of about 10 meV. The differences just mentioned may result in part from overlap with neighboring S2 or S3 states, as seen from the labeling in **Figure 3**. But they also arise from the shape and/or widths of the peaks observed in the TPEPICO spectra. The peaks at 25.134 eV and at 25.194 eV in **Figure 3**, for instance, have narrow halfwidths, of the order of 10 to 15 meV, even though they may comprise contributions from two or three different vibrational states. In contrast, the peaks at 24.430 and at 24.932 eV, where no superposition is expected, have halfwidths of the order of 30–40 meV.

Even with a bandpass for threshold electrons as narrow as 0–5 meV, one cannot exclude contributions from electrons resulting from autoionization of nearby Rydberg states. The variation of relative peak intensities depending on the electron energy bandpass can in fact be used to distinguish structures that localize autoionizing neutral states from those that result

TABLE 4 | Predicted and exptl. ionization energies <sup>15</sup>N<sup>2</sup> <sup>+</sup> D ′ <sup>2</sup>5<sup>g</sup> (v′ <sup>=</sup> 0–10) in eV we = 82.63 meV, wexe = 0.079 meV; Te = 23.6583 eV.


Vibrational parameters and ionization energies predicted from these parameters for the vibrational levels v′ = 0–10 of the D′ <sup>2</sup>5<sup>g</sup> of <sup>15</sup>N<sup>2</sup> <sup>+</sup>. The vibrational parameters were obtained by applying the reduced-mass correction to those obtained for <sup>14</sup>N<sup>2</sup> <sup>+</sup> by a Birge-Sponer fit to the available experimental data. T<sup>e</sup> situates the bottom of the potential well with respect to the ground-state of neutral <sup>15</sup>N2.

TABLE 5 | Fit to <sup>15</sup>N<sup>2</sup> <sup>+</sup> D ′ <sup>2</sup>5<sup>g</sup> (v′ <sup>=</sup> 10–24) in eV w<sup>e</sup> <sup>=</sup> 94.20 meV, wex<sup>e</sup> <sup>=</sup> 0.545 meV; Te = 23.6583 eV.


Ionization energies and vibrational parameters for the vibrational levels v′ = 10–24 of the D ′ <sup>2</sup>5<sup>g</sup> state of <sup>15</sup>N<sup>2</sup> <sup>+</sup>. The vibrational parameters were obtained by a least-squares Birge-Sponer fit to the present S1 peak energies of Figure 3.

from resonant ionization to a specific cation state (Bréchignac et al., 2014). That possibility has not yet been exploited in the present investigation. Baltzer et al. (1992), whose HeII PES is not subject to near-resonant autoionization, noted that the PES peaks corresponding to the D′ <sup>2</sup>5<sup>g</sup> state were 30% broader than those of the C-state.

We consider that the N<sup>2</sup> <sup>+</sup> D′ <sup>2</sup>5<sup>g</sup> (v′ ) energies exhibit irregularities that at least in part reflect the varying strengths of the interactions that cause these levels to predissociate. The D′ <sup>2</sup>5<sup>g</sup> (v′ ≤ 2) levels, which energetically cannot predissociate and only decay by fluorescence to the A <sup>2</sup>5<sup>u</sup> state, have rather long lifetimes, 6.10−<sup>7</sup> s or more, and possibly as large as 10−<sup>5</sup> s (Govers et al., 1977). For the D′ <sup>2</sup>5<sup>g</sup> (v′ ≥ 8) levels situated above the first dissociation limit, even a very weak interaction with a dissociation continuum will therefore cause predissociation to compete effectively with fluorescence. On the other hand, considering the proximity of the repulsive parts of the D′ <sup>2</sup>5<sup>g</sup> and D <sup>2</sup>5<sup>g</sup> potentials, it may well be that their mutual interaction, already invoked by Baltzer et al. (1992), is at certain energies strong enough to locally enhance direct transition to the D-state continuum, while simultaneously attributing a strong dissociative character to the first-order bound D′ level. Narrow peaks in the N<sup>+</sup> coincidence spectrum would in this picture result from rather weak predissociation, and the wider peaks from rapid predissociation, concomitant with locally enhanced transitions to the dissociation continuum. But in either case, because the D′ fluorescence rate is so low, predissociation will dominate radiative decay to stable N<sup>2</sup> <sup>+</sup> so that only N<sup>+</sup> ions are detected in the TPEPICO spectrum.

Information about the lifetime of predissociated molecular ions can be obtained from the asymmetry of the fragment ion time-of-flight peaks (Baer and Tuckett, 2017), provided that the parent ion fragments within the 3 µs it takes to exit the acceleration regions. A preliminary analysis suggests lifetimes of the order of a few microsecond for several of the features

#### REFERENCES


(other than those of the C-state vibrational levels) present in the TPEPICO spectra of **Figures 2**, **3**. A more systematic investigation of such "metastable ions" decay will be discussed in a forthcoming publication.

#### CONCLUSIONS

The direct measurement of the branching ratios between molecular ions and atomic fragments shows that predissociation of N<sup>2</sup> <sup>+</sup> dominates its unimolecular decay as soon as the photoionization energy surpasses the first dissociation limit. The sizable decay by fluorescence of the N<sup>2</sup> <sup>+</sup> (C26<sup>+</sup> u , v′ ≥ 3) levels appear to be a rather unique exception, and the present TPEPICO measurements support the conclusions of earlier fluorescence measurements as to the effect of vibrational excitation and isotopic substitution on the rate of predissociation. The differences noted between the results of the two experiments suggest that rotational excitation may significantly modify the rate of predissociation also. This could be verified by repeating the TPEPICO experiments using an effusive beam, rather than a supersonic beam as photoionization target. It is hoped that such additional data on rotational effects, including those for the mixed <sup>14</sup>N15N<sup>+</sup> isotopolog, will stimulate further theoretical work detailing the mechanism of accidental- and/or direct predissociation of the C26<sup>+</sup> u state.

#### AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

#### ACKNOWLEDGMENTS

We are grateful to the whole SOLEIL staff for providing smooth operation of the ring under project no 20170126.


exchange between He<sup>+</sup> and N2. Chem. Phys. Lett. 26, 134–137. doi: 10.1016/0009-2614(74)89103-7


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer IF declared a past co-authorship with one of the authors GG to the handling editor.

Copyright © 2019 Hrodmarsson, Thissen, Dowek, Garcia, Nahon and Govers. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

## A Velocity Map Imaging Study of the Reactions of O<sup>+</sup> ( <sup>4</sup>S) With CH<sup>4</sup>

Linsen Pei and James M. Farrar\*

*Department of Chemistry, University of Rochester, Rochester, NY, United States*

We present a velocity map imaging study of the key ion-molecule reactions occurring in the O+( <sup>4</sup>S3/2) + CH<sup>4</sup> (X <sup>1</sup>A1) system at collision energies of 1.84 and 2.14 eV. In addition to charge transfer to form CH<sup>+</sup> 4 (X <sup>2</sup>B2), we also present data on formation of CH<sup>+</sup> 3 (X <sup>1</sup>A1'), for which the experimentally determined images provide clear confirmation that the products arise from dissociative charge transfer rather than hydride transfer. Experimental data are also presented on the formation of HCO<sup>+</sup> through a transient [OCH4] <sup>+</sup> complex living many rotational periods. Plausible reaction pathways and intermediate structures are presented to give insight into the routes for formation of these reaction products.

#### Edited by:

*Antonio Aguilar, University of Barcelona, Spain*

#### Reviewed by:

*Daniela Ascenzi, University of Trento, Italy Peter B. Armentrout, The University of Utah, United States*

> \*Correspondence: *James M. Farrar james.farrar@rochester.edu*

#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *16 February 2019* Accepted: *22 March 2019* Published: *12 April 2019*

#### Citation:

*Pei L and Farrar JM (2019) A Velocity Map Imaging Study of the Reactions of O*<sup>+</sup> *( <sup>4</sup>S) With CH4*. *Front. Chem. 7:227. doi: 10.3389/fchem.2019.00227* Keywords: ion-molecule, potential energy surface, atmospheric chemistry, methane, oxygen ion

## INTRODUCTION

The reactions of the oxygen cation with methane and other small hydrocarbons at hyperthermal energies have received significant experimental and theoretical attention in the past 10 to 15 years. That interest has been motivated in large part by understanding the chemistry taking place in many environments, chief among them planetary atmospheres and interstellar clouds (Wakelam et al., 2012). The role that ions play in eroding the surfaces of spacecraft in low-earth orbit has also been a question addressed by these studies (Levandier et al., 2004). The relative simplicity of such reactions has stimulated theoretical studies that have led to fruitful comparisons with experiment, especially for the methane system, as exemplified by the pioneering experimental and theoretical study of the reactions in the O+( 4 S) + CH<sup>4</sup> system by Levandier et al. (2004). Experimentally, this study employed the guided ion beam method to yield absolute cross sections as a function of collision energy for charge transfer, dissociative charge transfer and/or hydride abstraction, and carbonoxygen bond formation. The overwhelmingly favored product for ground state O<sup>+</sup> reactants was charge transfer to produce CH<sup>+</sup> 4 . Theoretically, the study employed ab initio electronic structure calculations of quartet and doublet potential energy surfaces for the (O • CH4) <sup>+</sup> species that provided qualitative interpretations for the dominant reactive pathways.

More recent experiments by Cunha de Miranda et al. (2015) have focused on reactivity in the ground quartet (<sup>4</sup> S) and first two excited doublet (2D and <sup>2</sup>P) states. Electronically state-selected reactant O<sup>+</sup> ions were prepared by dissociative ionization of O<sup>2</sup> using VUV photons from the DESIRS beamline. Like the experiments of Levandier et al., this study has employed guided beam methodology to determine absolute cross sections and branching ratios over an extended collision energy range from thermal to several eV. These experiments confirm that the dominant products Pei and Farrar O<sup>+</sup> Plus Methane

for ground and excited state O<sup>+</sup> reactants are CH<sup>+</sup> 4 and CH<sup>+</sup> 3 , but with branching ratios that have a strong electronic state dependence. For ground state O<sup>+</sup> reactants, the experimental data confirm the results of Levandier et al. that the CH<sup>+</sup> 4 charge transfer product is overwhelmingly favored. However, electronic excitation to the <sup>2</sup>D and <sup>2</sup> S states of O<sup>+</sup> results in a strong preference for CH<sup>+</sup> 3 production. The authors did not report data for the products from C-O bond formation.

Both the experiments of Cunha de Miranda et al. and Levandier et al. make inferences about product energy and angular distributions from guided ion beam data taken at fixed collision energies. Under normal guided beam operation, the amplitude of the radiofrequency (rf) trapping voltage is sufficiently large to transmit all ions irrespective of the relative magnitudes of the longitudinal or transverse components of product velocities. In this mode of operation, measurements of the time-of-flight distributions for individual products yield projections of their speed distributions along the relative velocity vector. Additional experiments in which the rf amplitude is reduced significantly decrease the trapping well depth, allowing products with significant transverse velocities to escape detection. Such experiments yield more sensitive determinations of the forward and backward scattered product intensities, for which the latter are especially diagnostic of resonant charge transfer.

These experiments, along with computations that provide details of the potential energy surfaces, reactive intermediates and their structures, and related trajectory studies (Sun and Schatz, 2005) have answered a number of questions about the formation of the primary CH<sup>+</sup> 4 and CH<sup>+</sup> 3 products, as well as C-O bond formation, especially for ground state O+( 4 S). However, experimental limitations of the guided ion beam method have left open questions about whether CH<sup>+</sup> 3 is formed simply by dissociative charge transfer on the ground quartet state surface, or whether intersystem crossing to the doublet manifold facilitates hydride transfer to provide an additional route for CH<sup>+</sup> 3 production. In contrast to the ground quartet state of O+, each of the excited doublet states of O<sup>+</sup> has a vacant 2p orbital that can accept an electron pair from the hydride ion H−. Furthermore, existing evidence showing that formation of the H2CO<sup>+</sup> and HCO<sup>+</sup> products occurs through a long-lived complex is suggestive, but not robust. In the present study, complete velocity space flux distributions obtained by the velocity map imaging (VMI) method provide the robust evidence necessary to clarify the mechanisms of these important reaction channels.

The objective of the experiments reported here is to clarify the mechanism by which CH<sup>+</sup> 3 is formed, and to provide deeper insight into the production of HCO<sup>+</sup> by C-O bond formation. Velocity space images of these products, along with data for the charge transfer process, are offered in support of the claim that the methyl cation, CH<sup>+</sup> 3 , is produced by dissociative charge transfer on the ground quartet surface via reaction (2) shown below, rather than hydride abstraction via reaction (7), and that the products H2CO<sup>+</sup> and HCO<sup>+</sup> appear to be formed by a spin-allowed condensation mechanism in the quartet manifold of potential surfaces. The observed reactions and their energetics are listed below:

$$\text{CO}^+(\text{^4S}\_{3/2}) + \text{CH}\_4(\text{X}^1\text{A}\_1) \rightarrow \text{CH}\_4^+(\text{X}^2\text{B}\_2) + \text{O}(^3\text{P}\_2)\\\Delta\text{H}=-1.01 \text{eV} \quad \text{(1)}$$

$$\rightarrow \text{CH}\_3^+ (\text{X}^1 \text{A}\_1') + \text{H} (^2 \text{S}\_{1/2}) + \text{O} (^3 \text{P}\_2) \Delta \text{H} = +0.75 \tag{2}$$

$$\rightarrow \text{H}\_2\text{CO}^+(\text{X}^2\text{B}\_2) + 2\text{H}(^2\text{S}\_{1/2})\Delta\text{H} = -1.23 \tag{3}$$

$$\rightarrow \text{H}\_2\text{CO}^+(\text{X}^2\text{B}\_2) + \text{H}\_2(\text{X}^1\text{E}\_{\text{g}}^+) \Delta H = -5.68 \tag{4}$$

$$\rightarrow \text{HCO}^{+}(\text{X}^{1}\Sigma) + 3\text{H}(^{2}\text{S}\_{1/2})\Delta\text{H} = -0.08 \qquad \text{(5)}$$

$$\rightarrow \text{HCO}^{+}(\text{X}^{1}\Sigma) + \text{H}\_{2}(\text{X}^{1}\Sigma\_{\text{g}}^{+}) + \text{H}(^{2}\text{S}\_{1/2})\Delta H = -4.53 \tag{6}$$

$$\rightarrow \mathbf{CH}\_3^+ (\mathbf{X}^1 \mathbf{A}\_1') + \mathbf{OH} (\mathbf{X}^2 \Pi\_{\bar{\mathbf{i}}}) \Delta \mathbf{H} = -\mathbf{3.69} \tag{7}$$

Reaction energetics are taken from Table 1 of Sun and Schatz and Table 3 of Levandier et al.

#### EXPERIMENTAL

As described previously (Pei and Farrar, 2012), the experiment is conducted with a crossed beam instrument employing velocity map product imaging (VMI) detection (Eppink and Parker, 1997). The imaging system determines all product velocities for a given mass in a single detection time window, yielding significant enhancement of detection efficiency through the intrinsic multiplex advantage of the method. Our implementation of VMI is based upon important developments from other laboratories (Reichert et al., 2000, 2002; Reichert and Weisshaar, 2002; Mikosch et al., 2006, 2008; Zhang et al., 2010).

The primary ion beam is formed by electron impact (Udseth et al., 1973) on a mixture of 10% CO in He. The primary product of electron impact on this mixture is He+, which then undergoes charge transfer with CO to form both parent and fragment C<sup>+</sup> and O<sup>+</sup> cations. The electronic state distribution of O<sup>+</sup> produced in this manner can be assessed by using observations by Smith et al. (1992) which showed that charge transfer between O<sup>+</sup> and CO is endoergic for ground state cations, but is exoergic for the 2 S and <sup>2</sup>D excited states. In a crossed beam geometry in which the O<sup>+</sup> ion beam intersected a CO beam, we were unable to detect CO<sup>+</sup> cations. This observation places a limit on excited state O+( <sup>2</sup>D, <sup>2</sup>P) production of less than 1%.

In our experiment, the O+( 4 S) ions produced by electron impact are extracted, mass selected, and decelerated and focused by a series of ion optics, and the continuous beam of ions is delivered to the volume defined by the repeller and extraction electrodes of a VMI detector. The ion beam has a roughly triangular kinetic energy distribution with a FWHM of approximately 0.20 eV in the laboratory frame of reference.

The neutral beam is a supersonic expansion produced by a pulsed solenoid valve located 10 mm upstream from a 1 mm skimmer. The stagnation pressure of the CH<sup>4</sup> gas behind the 0.1 mm diameter nozzle is 3 atm, and the resulting velocity distribution has a FWHM of ∼6–8%. The pressure in the collision chamber is ∼3 × 10−<sup>7</sup> torr with the beams running.

Under the experimental conditions, the relative velocity of the reactants at a collision energy of 1.84 eV is 6,620 m/s. At Ecol = 2.14 eV, the relative velocity of approaching reactants is 7,140 m/s.

The reactant beams intersect at the center of a collision volume defined by two circular electrodes of radius 38 mm spaced by 20 mm. The lower, repeller electrode and the upper, extractor electrode are held at ground potential as the ion and neutral beams intersect. Product detection is achieved by velocity map imaging (Eppink and Parker, 1997) with the two-electrode geometry described by the Suits research group (Townsend et al., 2003). Product detection is initiated by pulsed electric fields applied to the collision volume after reaction has taken place. The detection pulses, applied with separate high voltage pulse generators (DEI PVX-4140, 4150), are synchronized to the arrival of the central portion of the pulsed molecular beam and have a rise time and duration of 25 ns and 1 to 2 µs, respectively to allow all products to escape the volume between the repeller and extractor within the pulse duration.

Delayed pulsed extraction is achieved by pulsing the voltage on the repeller plate, V1, to +2300 V, the precise value dependent on transverse velocity and the filling factor for the MCP detector. The voltage V<sup>2</sup> on the 13 mm aperture extraction electrode is pulsed to a value V<sup>2</sup> = 0.65 V1. A grounded electrode with a 20 mm aperture placed 13 mm above the extraction electrode provides velocity mapping for the product ions at the imaging plane, located 0.6 m downstream from the grounded lens.

Prior to striking the imaging plane of the detector, defined by the front face of a pair of chevron-mounted microchannel plates, the ions pass through a grounded grid. The MCPs are gated by a pulse of base width 80 ns, which results in an effective "on" time of ∼40 ns, during which the product ion cloud is recorded by the phosphor screen following the MCP anode. Under these operating conditions, the three-dimensional ion cloud is effectively "crushed" as it reaches the MCP detection plane.

The light image from the phosphor screen is recorded by a CCD camera (uEye 2230), which transfers the image via a USB interface to a lab computer controlled by LabView software. A typical image represents the accumulation of 5,000 to 20,000 repetitions of the pulsed valve.

#### RESULTS AND DISCUSSION

Velocity space images were collected for the CH<sup>+</sup> 4 , CH<sup>+</sup> 3 , and HCO<sup>+</sup> products at collision energies 1.84 and 2.14 eV. Images for CH<sup>+</sup> 2 and H2CO<sup>+</sup> formation were also detected. Because of the very strong similarities of these images to those for CH<sup>+</sup> 3 and HCO+, respectively, we have not shown them in this paper. Branching fractions for all five observed products are reported in **Table 1** and are compared with the results of Cunha de Miranda et al.

**Figure 1** shows product images for charge transfer to form CH<sup>+</sup> 4 , dissociative charge transfer and/or hydride transfer forming CH<sup>+</sup> 3 , and C-O bond formation to form HCO+. The left column shows products formed at 1.84 eV and the right column shows the corresponding images at 2.14 eV. The dominant products correspond to CH<sup>+</sup> 4 and CH<sup>+</sup> 3 formation, with comparable intensities at both collision energies, as **Table 1** shows. These results are consistent with those of Cunha de Marino et al., although the relative yield of CH<sup>+</sup> 3 is higher in our experiments. Secondary collisions occurring in the experiments with state-selected ions may be responsible for the differences


*<sup>a</sup>This work.*

*<sup>b</sup>Cunha de Miranda et al. (2015).*

in branching fractions. Images for H2CO<sup>+</sup> production are very similar to those for HCO<sup>+</sup> formation, and are not reported here.

The planar MCP detection system recovers images as product ion flux in Cartesian coordinates, either in the laboratory (vx, vy) or in the center of mass frame (ux, uy). Transformation of lab velocity (vx, vy) to center of mass velocity (ux, uy) is accomplished by a simple velocity shift **C** describing the motion of the center of mass of the collision system:

$$\mathbf{u} = \mathbf{v} - \mathbf{C} \tag{8}$$

Because the volume elements in both representations are equal, i.e., dv<sup>x</sup> dv<sup>y</sup> = du<sup>x</sup> duy, (Wolfgang and Cross, 1969; Friedrich and Herman, 1984), center of mass flux P(ux, uy) may be visualized directly from the measured image. The full three-dimensional image and thus kinetic energy and angular distributions may be extracted from the experimental images by application of the BASEX algorithm (Dribinski et al., 2002). We do not report those distributions in this paper.

#### CH<sup>+</sup> 4 Formation

At both collision energies, the CH<sup>+</sup> 4 charge transfer products, shown in the top panel of **Figure 1**, appear near the velocity of the incident CH<sup>4</sup> reactant, consistent with energy resonance, with minimal conversion of reactant kinetic energy into product internal excitation. The circles shown on the images define the maximum kinetic energies accessible to the products, assuming that the total energy of the products, given as the sum of incident kinetic energy and reaction exoergicity, appears as product translation.

This strong peaking of product velocity is consistent with minimal deflection of the CH<sup>4</sup> framework during electron transfer, and is consistent with large impact parameter collisions in which the electron is transferred to the ion at long range. The images show that the CH<sup>+</sup> 4 speed distributions are very narrow, indicative of a very small number of populated CH<sup>+</sup> 4 vibrational states. The energy widths of the CH<sup>+</sup> 4 product distributions are ∼0.13 – 0.15 eV, or 1,000 to 1,200 cm−<sup>1</sup> .

From the perspective that charge transfer is driven not only by energy resonance, but also by the existence of favorable Franck-Condon (FC) factors between the reactant neutral and its corresponding ion, the narrow width suggests that the ionic potential energy surface is very steep in the FC region. However, the nature of the ionization process in CH<sup>4</sup> requires more detailed consideration. Because the geometries of CH<sup>4</sup> and CH<sup>+</sup> 4

a collision energy of 1.84 eV is 6,620 m/s. At Ecol = 2.14 eV the relative velocity of approaching reactants is 7,140 m/s. The top row of images shows the formation of CH<sup>+</sup> 4 by charge transfer, and the circle corresponds to the barycentric speed associated with the thermochemical limit for reaction (1). The middle row of images shows CH<sup>+</sup> 3 produced by dissociative charge transfer, with the circle corresponding to the thermochemical limit for CH<sup>+</sup> 3 + O + H, the atomic products formed with zero relative kinetic energy, reaction (2). The bottom row of images shows HCO<sup>+</sup> formation. The larger circle corresponds to maximum product speed allowed by energy conservation for the formation of HCO<sup>+</sup> <sup>+</sup> <sup>H</sup><sup>2</sup> <sup>+</sup> H, reaction (6). The smaller circle corresponds to the maximum product speed allowed by energy conservation for the formation of HCO<sup>+</sup> + H + H + H, reaction (5).

are significantly different (Coulson and Strauss, 1962; Frost et al., 1967; Dixon, 1971), one expects that electron transfer, like photoabsorption, is constrained by the geometry change accompanying the process. Important early studies of charge transfer at thermal energies (Laudenslager et al., 1974) underscore the criticalrole of energy resonance andfavorable Franck-Condon factors in determining reaction rates, but do not establish criteria that predict which effect is most important. In the present system, the charge transfer process requires crossings between potential surfaces that correspond asymptotically to (O<sup>+</sup> + CH4) and (O + CH<sup>+</sup> 4 ), and the collision dynamics in the vicinity of these crossings modulate the effect of favorable Franck-Condon factors. The high dimensionality of the surfaces makes a detailed quantum analysis of those crossings difficult, if not intractable.

#### CH<sup>+</sup> 3 Formation

The images for CH<sup>+</sup> 3 formation in the middle panels of **Figure 1** clearly resemble those for direct charge transfer, centered on the tip of the CH<sup>4</sup> neutral velocity vector. The images clearly lie outside the circles that define the locus of speeds consistent with three body collision-induced dissociation (CID). Those circles are defined by the maximum speed that a CH<sup>+</sup> 3 product would have when accompanied by an (O,H) pair bound with zero energy. The appearance of CH<sup>+</sup> 3 products outside those circles indicates that three-body CID is not the production mechanism for CH<sup>+</sup> 3 . Rather, that product appears to originate from nascent CH<sup>+</sup> 4 .

The energy resonance condition that governs the formation of CH<sup>+</sup> 4 imparts approximately 1.0 eV of internal energy to the ion. The kinetic energy contribution to the total energy available to the nascent CH<sup>+</sup> 4 arises from the initial kinetic energy less the kinetic energy removed by the oxygen atom also produced in the charge transfer process. Momentum conservation requires that the oxygen atom removes exactly half of the available kinetic energy, or ∼0.9 to 1.1 eV. Thus, the total energy available to the nascent CH<sup>+</sup> 4 products of charge transfer ranges from 1.9 to a∼2.1 eV. Reaction exoergicities show that the appearance potential for CH<sup>+</sup> 3 from CH<sup>+</sup> 4 is 1.84 eV. Considering the incident collision energy spread and the narrow but non-zero energy spread in the internal energy imparted to the nascent CH<sup>+</sup> 4 products, it is clear that a significant fraction of those products have sufficient energy to decay to CH<sup>+</sup> 3 .

The methyl cation may also be formed by hydride transfer from CH<sup>4</sup> to O+, a process exoergic by 3.69 eV. Previous studies have shown that hydride transfer from a methyl carbon atom to O<sup>+</sup> (Curtis and Farrar, 1986) and to CH<sup>+</sup> 3 ions (Zabka et al., 1995) results in kinetic energy release distributions that are significantly broader and peaked to higher energies than electron transfer to the same approaching ion. Moreover, the ground quartet electronic state of O<sup>+</sup> does not contain an empty 2p orbital to accommodate an electron pair from the hydride group H−. Therefore, hydride transfer to O<sup>+</sup> should be strongly suppressed relative to electron transfer owing to its spin-forbidden character, and its dynamics should be very distinct from those of charge transfer. Thus, strong evidence supports the claim that CH<sup>+</sup> 3 is formed by spin-allowed dissociative charge transfer, reaction (2), rather than spin-forbidden hydride transfer, reaction (7). This claim has also been advanced by Cunha de Miranda et al.

The images for CH<sup>+</sup> 3 formation are broadened relative to their CH<sup>+</sup> 4 precursor images. The kinetic energy widths for the parent ions correspond to ∼0.13 to 0.15 eV, and the widths of the CH<sup>+</sup> 3 daughter ions are ∼0.06 eV larger. This broadening corresponds to roughly 20 to 30% of the total energy in excess of the dissociation threshold for CH<sup>+</sup> 4 decay to CH<sup>+</sup> 3 , a result consistent with statistical unimolecular decay theories (Marcus, 1952).

## HCO<sup>+</sup> Formation

The velocity space images for HCO<sup>+</sup> formation are shown in the bottom row of images in **Figure 1**. Despite the kinematic constraint that the HCO<sup>+</sup> products must appear close to the system center of mass in velocity space, the data are clear and precise, and allow the claim that HCO<sup>+</sup> is distributed symmetrically in the center of mass frame and arises from decay of a long-lived precursor. The larger diameter circles shown in the images in the lowest row in **Figure 1** correspond to the maximum speeds the HCO<sup>+</sup> + H<sup>2</sup> + H products could have if all available energy appears in translation. Similarly, the smaller circles correspond to the maximum speeds of HCO<sup>+</sup> products formed along with three hydrogen atoms. At the lower collision energy, most of the flux falls within the smaller circle, suggesting that the spin-allowed pathway is the dominant one, and only a small fraction of the products are accompanied by molecular hydrogen formation. At the higher collision energy, all of the flux falls cleanly within the smaller circle.

The computations reported by Levandier et al. (2004) that consider reaction on both quartet and doublet potential surfaces, and by Sun and Schatz (2005), who focus only on quartet surfaces, provide a computational basis for understanding the reaction dynamics. The reaction coordinate schematic shown in **Figure 2** contains information extracted from those references. This pathway has been explored experimentally by Anderson et al. (Liu et al., 2005) and theoretically by Lorquet et al. (Pires et al., 1978), as well as in the work of Levandier et al. and Sun and Schatz.

As indicated in **Figure 2**, resonance charge transfer occurs on a quartet potential surface, and the nascent products O + CH<sup>+</sup> 4 lead to the important intermediate quartet complex denoted QCP1, as well as a doublet state complex labeled DCP1 in Levandier et al. and Sun and Schatz. In the complex QCP1, which lies 1.7 eV in energy below the O<sup>+</sup> + CH<sup>4</sup> reactants, a hydrogen atom from the methyl cation serves as a bridge between the carbon and oxygen atoms. The transition state QTS1 leading to the H2CO<sup>+</sup> product has charge localized on the methane moiety, with significant spin density on the oxygen atom, and product cation is formed by ejection of two hydrogen atoms. This mechanism allows a doublet state ion to be formed in concert with two doublet state hydrogen atoms on a quartet state surface. The quartet surface shown in **Figure 2** has fairly shallow wells (1.0 eV for the charge transfer products and 1.7. eV for QCP1), has a barrier at QTS1 that lies 0.07 eV above the approaching reactants, and products at 1.23 eV below the reactants. Given the relatively sparse densities of vibrational states in QCP1 and QTS1, it is unlikely that QCP1 will have a lifetime long enough to exhibit the signature of a long-lived complex.

The doublet state complex DCP1 is not directly accessible from the quartet state charge transfer products, and the dotted line connecting them, discussed by Levandier et al. (2004), suggests that an internal conversion process accesses motion on surfaces in the doublet manifold. The complex DCP1 is formed by insertion of O into a C-H bond, leading to the incipient C-O bond in H2CO+. Migration of a hydrogen atom from O to C leads to a three-center transition state, DTS1, lying ∼3 eV above DCP1, that ejects molecular hydrogen in concert with the ground state formaldehyde cation, H2CO+. Formation of HCO<sup>+</sup> over a barrier of ∼0.6 eV is observed computationally, and **Table 1** indicates that H2CO<sup>+</sup> and HCO<sup>+</sup> have comparable intensities.

The formation of H2CO<sup>+</sup> via QCP1 on the quartet surface is accompanied by two hydrogen atoms. In contrast, H2CO<sup>+</sup> production via DCP1 on the doublet surface is accompanied by molecular H<sup>2</sup> formation. Thus, the total energies available to the quartet state products, the sum of collision energy and exoergicity for HCO<sup>+</sup> + 3 H, are ∼1.9 and 2.2 eV for the two collision energies respectively, while ∼6.4 and 6.7 eV are accessible to the HCO<sup>+</sup> + H<sup>2</sup> + H products formed on the doublet surface. At the lower (higher) collision energy, products formed with more than 1.9 (2.2) eV of translation must be assigned to formation on the doublet surface, while products formed with 1.9 (2.2) eV or less may be formed on either surface. Qualitative bounds on the kinetic energy release can be gleaned from the images in **Figure 1**, particularly at the higher collision energy. The data show clearly that kinetic energy release is fairly small, with most of the flux confined within the smaller of the two circles shown in each of the images in the bottom panel of **Figure 1**. Those smaller circles correspond to the maximum speeds accessible to HCO<sup>+</sup> + 3H products. The images support the claim that a very small fraction of the products are formed following internal conversion to the doublet surface.

#### CONCLUSIONS

The experimental data reported here for CH<sup>+</sup> 4 , CH<sup>+</sup> 3 , and HCO<sup>+</sup> formed in the reactions of O+( 4 S) with CH4, in conjunction with reaction pathways proposed by Levandier et al. and Sun and Schatz, provide clear evidence that the primary CH<sup>+</sup> 4 product is formed in a very narrow range of vibrational states by resonant charge transfer. The experimental data for CH<sup>+</sup> 3 formation provide strong evidence that this product, formed with comparable cross section, arises from dissociation of nascent CH<sup>+</sup> 4 on the quartet potential surface, rather than by the spinforbidden process of hydride transfer.

Although HCO<sup>+</sup> production is a minor channel, formed at less than 1% of the total product yield, the pathways for its formation are quite interesting. The spin-allowed quartet surface pathway leads to formation of H2CO<sup>+</sup> in conjunction with ejection of two hydrogen atoms. Unimolecular decay of the nascent H2CO<sup>+</sup> product by C-H bond cleavage yields HCO<sup>+</sup> + H with ∼60 to 65% yield. Computations also suggest a viable pathway for H2CO<sup>+</sup> production (with subsequent decay to HCO+) in concert with an H<sup>2</sup> molecule via internal conversion from the lowest quartet state to the doublet manifold.

The experimental data show that the kinetic energy release for H2CO<sup>+</sup> formation and subsequent decay to HCO<sup>+</sup> is quite low, ∼2 eV or smaller. No products are formed with kinetic energies in the range between 2.2 and 6.7 eV, where energy conservation constrains products to be formed on the doublet surface. There is no experimental evidence to claim that any of the observed reaction products must be formed by spinforbidden processes. Although one might expect that the tight transition state DTS1 preceding H<sup>2</sup> ejection would produce translationally excited products, the data provide no evidence for that expectation.

The experimental data presented here have demonstrated that ion imaging has yielded additional insights into the benchmark O<sup>+</sup> + CH<sup>4</sup> system, complementing important contributions, both experimental and theoretical, already in the literature. We hope that imaging methods will continue to play an important role in elucidating the dynamics of prototypical systems in atmospheric chemistry and astrochemistry.

#### DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

#### REFERENCES


#### AUTHOR CONTRIBUTIONS

LP conducted the experiment reported here, analyzed the data, and produced the figures. JF. suggested the problem and wrote up the initial draft of the presentation of the results. LP and JF discussed the analysis and interpretation of the experimental results together.

### ACKNOWLEDGMENTS

The authors acknowledge support for this work under National Science Foundation grants CHE-1012303 and CHE-1265406.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be interpreted as a potential conflict of interest.

Copyright © 2019 Pei and Farrar. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Non-adiabatic Quantum Dynamics of the Dissociative Charge Transfer He++H2→He+H+H<sup>+</sup>

Dario De Fazio<sup>1</sup> \*, Alfredo Aguado<sup>2</sup> and Carlo Petrongolo<sup>3</sup>

<sup>1</sup> Consiglio Nazionale delle Ricerche, Istituto di Struttura della Materia, Rome, Italy, <sup>2</sup> Departamento de Química Física Aplicada, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid, Spain, <sup>3</sup> Consiglio Nazionale delle Ricerche, Istituto per i Processi Chimico Fisici, Pisa, Italy

We present the non-adiabatic, conical-intersection quantum dynamics of the title collision where reactants and products are in the ground electronic states. Initial-state-resolved reaction probabilities, total integral cross sections, and rate constants of two H<sup>2</sup> vibrational states, v<sup>0</sup> = 0 and 1, in the ground rotational state (j<sup>0</sup> = 0) are obtained at collision energies Ecoll ≤ 3 eV. We employ the lowest two excited diabatic electronic states of HeH<sup>+</sup> 2 and their electronic coupling, a coupled-channel time-dependent real wavepacket method, and a flux analysis. Both probabilities and cross sections present a few groups of resonances at low Ecoll, whose amplitudes decrease with the energy, due to an ion-induced dipole interaction in the entrance channel. At higher Ecoll, reaction probabilities and cross sections increase monotonically up to 3 eV, remaining however quite small. When H<sup>2</sup> is in the v<sup>0</sup> = 1 state, the reactivity increases by ∼2 orders of magnitude at the lowest energies and by ∼1 order at the highest ones. Initial-state resolved rate constants at room temperature are equal to 1.74 × 10−<sup>14</sup> and to 1.98 × 10−<sup>12</sup> cm<sup>3</sup> s <sup>−</sup><sup>1</sup> at v<sup>0</sup> = 0 and 1, respectively. Test calculations for H<sup>2</sup> at j<sup>0</sup> = 1 show that the probabilities can be enhanced by a factor of ∼1/3, that is ortho-H<sup>2</sup> seems ∼4 times more reactive than para-H2.

Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Tomás González-Lezana, Spanish National Research Council (CSIC), Spain Ricardo Gargano, Universidade de Brasília, Brazil

> \*Correspondence: Dario De Fazio defazio.dario@yahoo.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 08 February 2019 Accepted: 27 March 2019 Published: 16 April 2019

#### Citation:

De Fazio D, Aguado A and Petrongolo C (2019) Non-adiabatic Quantum Dynamics of the Dissociative Charge Transfer He++H2→He+H+<sup>H</sup> +. Front. Chem. 7:249. doi: 10.3389/fchem.2019.00249 Keywords: He++H<sup>2</sup> , wavepacket, conical intersection, non-adiabatic, quantum, dynamics

## INTRODUCTION

Atomic Hydrogen and Helium are the dominant chemical species of the early Universe (Galli and Palla, 2013) and of the interstellar medium, and are easily ionized by cosmic rays. Therefore, these atoms and their ions are the astrochemical fundamental reactants (Lepp et al., 2002), together with ubiquitous photons, giving first simple diatoms as H2, H<sup>+</sup> 2 (Stancil et al., 1993), and HeH<sup>+</sup> (Zygelman et al., 1998) and then atom+diatom bimolecular collisions as He+H + 2 (De Fazio et al., 2012), H+HeH<sup>+</sup> (De Fazio, 2014; Gamallo et al., 2015), and He++H2.

When all chemical species are in the ground electronic states, the He+H + 2 reaction is endothermic and rather slow, but the other two are exothermic by about ∼0.7 and 6.2 eV, respectively, as many ion+neutral astrochemical reactions (Herbst and Klemperer, 1973). H+HeH<sup>+</sup> is barrierless and gives quickly the He+H + 2 products, but the collision-induced dissociative charge transfer (DCT) He+( 2 S)+H2(X <sup>1</sup>6<sup>+</sup> g )→He(<sup>1</sup> S)+H(<sup>2</sup> S)+H<sup>+</sup> is very slow at low collision energy Ecoll and at room temperature, if H<sup>2</sup> is in the ground vibro-rotational state. In fact, <sup>H</sup>+HeH+↔He++H<sup>2</sup> occurs on the ground potential energy surface (PES) <sup>X</sup>˜ <sup>2</sup>A' of HeH<sup>+</sup> 2 , which is well-separated from the excited electronic species, but the low-Ecoll DCT involves the first two excited adiabatic electronic states A˜ <sup>2</sup>A' and B˜ <sup>2</sup>A' of HeH<sup>+</sup> 2 , which differ by a two-electron excitation and are coupled by a C2<sup>v</sup> conical intersection (CI) (Preston et al., 1978; McLaughlin and Thompson, 1979). In the latter case the non-adiabatic coupling is weak and the lower, dissociative cone of the intersection seam gives rise to an adiabatic barrier with diabatic character, that is the DCT tends to follow the diabatic PESs without changing the electronic configuration. This strongly inhibits the reactivity that is associated with the tunneling through the barrier (Preston et al., 1978).

This is schematically shown in the correlation diagram of **Figure 1** for the A˜ <sup>2</sup>A' and B˜ <sup>2</sup>A' adiabatic and (1)2A<sup>1</sup> and (2)2B<sup>2</sup> diabatic PESs <sup>V</sup> of HeH<sup>+</sup> 2 , where all chemical species are in the ground electronic states, save H<sup>+</sup> 2 (A <sup>2</sup>6<sup>+</sup> u ) that is unbound, and the energy is referred to the reactant minimum. This diagram is obtained from the ab initio Multi-Reference Configuration-Interaction results of McLaughlin and Thompson (1979), changing the label of the reactant diabatic state <sup>2</sup>A<sup>1</sup> from (5) to (1), and from the analytical fits of the associated diabatic PESs V<sup>11</sup> and V<sup>22</sup> by Aguado et al. (1993). In the scheme of **Figure 1** we omit the ground adiabatic PES, well below the excited PESs and with too small non-adiabatic couplings. However, all three adiabatic PESs are strongly coupled by intense laser pulses (Szidarovszky and Yamanouchi, 2016) when the ground PES becomes populated (Schauer et al., 1989). A more complete description of the reaction dynamics in presence of electric and magnetic fields is out of the scope of the present article. Note in the figure the small ion-induced dipole minimum in the C2v entrance channel at R(He-H2) = 4.45 a0, r(H-H) = 1.42 a0, and V = −0.08 eV and the CI C2<sup>v</sup> minimum at R = 4.89 a0, r = 2.18 a0, and V = 1.34 eV, owing to the intersection (Preston et al., 1978) between the H2(X <sup>1</sup>6<sup>+</sup> g ) and H<sup>+</sup> 2 (A <sup>2</sup>6<sup>+</sup> u ) curves at r = 2.19 a<sup>0</sup> and V = 1.28 eV.

Experimental studies on the He++H2→ He+H+H<sup>+</sup> DCT dynamics date back to 1955 (Stedeford and Hasted, 1955) and 1961 (Giese and Maier, 1961), when the integral cross sections (ICSs) were measured at Ecoll = 4 eV and found <0.05 Å<sup>2</sup> . ICSs as functions of Ecoll were then measured in many works up to 1996 (Dhuicq et al., 1996), finding values from 0.01 up to ∼2 Å<sup>2</sup> , for Ecoll between 3 and 100 eV, by considering H<sup>2</sup> in the ground vibro-rotational state and all ground and excited open states of H. Below 3 eV, the H product is in the ground 1s state and the ICSs are so small and so difficult to measure that experimental values present large discrepancies (Reinig et al., 1992). However, the ICSs increase by one/two orders of magnitude if H<sup>2</sup> is excited by one vibrational quantum (Preston et al., 1978) or Ecoll grows up to ∼100 eV. Differential cross sections were also measured (Dhuicq et al., 1998) at Ecoll > 9 eV, that is for the formation of the H<sup>∗</sup> excited product. Accordingly, small rate constants were observed (Johnsen et al., 1980), with values of (1.5 ± 0.15) × 10−<sup>13</sup> and (1.1 ± 0.1) × 10−13cm<sup>3</sup> s −1 at 78 and 330 K, respectively, that is nearly four order of magnitude lower than the Langevin (Gioumousis and Stevenson, 1958) estimates for ion+neutral barrierless and exothermic reactions.

A few works have also theoretically investigated the dynamics of the DCT collision since 1994, when Aguillon (1994) employed a semiclassical coupled wavepacket (WP) method and the analytical diabatic PESs of Aguado et al. (1993) for computing ICSs for ground and excited vibrational states v<sup>0</sup> of H2, up to v<sup>0</sup> = 4 and in the Ecoll range from 2 to 10 eV. He found total-ICS values from ∼0.001 Å<sup>2</sup> (v<sup>0</sup> = 0, Ecoll = 2 eV) to ∼1 Å<sup>2</sup> (v<sup>0</sup> = 3, Ecoll = 10 eV), in agreement with the most recent measurements (Dhuicq et al., 1996). In a subsequent work (Aguillon, 1998), an improved version of this semiclassical method was used for obtaining new ICS values and differential cross sections. Approximated theoretical models were also employed (Dhuicq et al., 1996) for explaining observed cross sections above 9 eV, when excited H<sup>∗</sup> (n = 2) was produced. Finally, quantum infiniteorder-sudden cross sections were calculated (Martínez et al., 2000) for He++H2→He+H<sup>∗</sup> (n ≥ 2)+H<sup>+</sup> at Ecoll ≥ 10 eV, using the accurate diabatic representation of Aguado et al. (1993) and six more approximated diabatic electronic states (Sidis, 1996).

As far as we know, no further studies of the title reaction have been published and its collision dynamics below ∼2 eV is unknown. In particular, only semiclassical or approximated quantum theoretical studies were carried out, although both conical intersection and barrier tunneling are purely quantum effects. We thus here report a rigorous time-dependent quantum study of the DCT He++H2(v<sup>0</sup> = 0,1)→ He+H+H<sup>+</sup> with all species in the ground electronic state, at thermal and hyperthermal collision energy up to 3 eV, using the diabatic PESs of Aguado et al. (1993) and WP and flux formalisms. In section Theory and Calculations we present the theoretical method and its numerical details. Section Collision Results reports initial-state-resolved total reaction probabilities, ICSs, and thermal rate constants. Finally, we present our conclusions in section Conclusions.

## THEORY AND CALCULATIONS

## Potential Energy Surfaces and Non-adiabatic Coupling

As we said in the Introduction, the HeH<sup>+</sup> 2 adiabatic and diabatic electronic states relevant in the present work were obtained ab initio in McLaughlin and Thompson (1979), fitted analytically in Aguado et al. (1993), and they are schematically plotted in **Figure 1**. We label the adiabatic species and PESs by A˜ <sup>2</sup>A' and B˜ <sup>2</sup>A' and by V<sup>A</sup> and VB, respectively. As already discussed (Aguado et al., 1993), these states belong to the fully symmetric irreducible representation for linear (C∞v) and non-symmetric (CS) geometries, while **Figure 1** shows that they transform as A1/B<sup>2</sup> and B2/A<sup>1</sup> for perpendicular geometries (C2v), before/after the CI, respectively, which rules the title reaction. On the other hand, we label the associated diabatic electronic states and PESs by (1)A<sup>1</sup> and (2)B<sup>2</sup> and by V11, V22, and V12, respectively, where the third surface describes the CI non-adiabatic coupling in the diabatic representation.

In order to simultaneously describe these electronic species and take into account the CI, a fit of the diabatic PESs and coupling V11, V22, and V<sup>12</sup> was made in Aguado et al. (1993). The description of the adiabatic states is obtained as the eigenvalues <sup>V</sup><sup>A</sup> and <sup>V</sup><sup>B</sup> of a 2<sup>×</sup> 2 matrix V<sup>11</sup> V<sup>12</sup> <sup>V</sup><sup>12</sup> <sup>V</sup>22 , in which the interaction term V<sup>12</sup> must have the correct symmetry, being anti-symmetric with respect to the permutation of the H atoms and thus vanishing identically for equal He–H distances. This coupling term V<sup>12</sup> was fitted in Aguado et al. (1993) to reproduce the CI between the A˜ <sup>2</sup>A' and B˜ <sup>2</sup>A' adiabatic states.

The diabatic surfaces where fitted in Aguado et al. (1993) using the Aguado-Paniagua functional form (Aguado and Paniagua, 1992; Aguado et al., 1998) that expands the energy as a multidimensional permutationally invariant polynomial (Aguado et al., 1994, 2001) in Rydberg type variables (Rydberg, 1931) of the form ρAB = RAB exp (−βABRAB), where A and B are two nuclei and RAB is their distance. For the interaction term, a simple expansion in Rydberg functions,

$$\left(V\_{12}\left(R\_{\text{HeH}}, R\_{\text{HeH}'}, R\_{\text{HH}'}\right) = C\_{12}\rho\_{\text{HH}'}\left(\rho\_{\text{HeH}} - \rho\_{\text{HeH}'}\right)\right), \quad \text{(1)}$$

fulfills the anti-symmetric requirement.

The DCT is produced through the CI, as shown in **Figure 2** using nuclear Jacobi coordinates R, r = RHH′ , and γ , at R = 4 a<sup>0</sup> and γ = 0. The top panel shows the adiabatic A˜ <sup>2</sup>A' and B˜ <sup>2</sup>A' PESs of HeH<sup>+</sup> 2 in the reactant channel, obtained from the diabatic Vij surfaces, where A˜ <sup>2</sup>A' correlates with He+( 2 S)+H2(X <sup>1</sup>6<sup>+</sup> g ) for r < 2 a<sup>0</sup> and with He(<sup>1</sup> S)+H + 2 (A <sup>2</sup>6<sup>+</sup> u , unbound) for r > 2 a0. To analyze the accuracy of the fit, we compare the analytical nonadiabatic coupling matrix elements (NACMEs) in the adiabatic representation, obtained from the fitted diabatic energies and coupling, with the ab initio results calculated using the MOLPRO program package (Werner et al., 2018). As done previously for H<sup>+</sup> 4 and H + 5 in Sanz-Sanz et al. (2015), the analytical NACMEs can be calculated from the generalized Hellmann-Feynman theorem,

$$\left<\tilde{A}^2 A'\right| \frac{\partial}{\partial R\_{\rm AB}} \left|\tilde{B}^2 A'\right> = \frac{1}{V\_B - V\_A} \left<\tilde{A}^2 A'\right| \frac{\partial \hat{H}^{el}}{\partial R\_{\rm AB}} \left|\tilde{B}^2 A'\right>,\tag{2}$$

where Hˆ el is the electronic Hamiltonian and the rhsm is obtained from the derivatives of the diabatic energies Vij (Sanz-Sanz et al., 2015). Ab initio calculations have been performed using the Multi-Reference Configuration-Interaction method, with the aug-cc-pVTZ basis set of Dunning (1989) and Woon and Dunning (1994). The ab initio NACMEs are obtained using a first order difference method with an interval of 0.01 a0, and that for RAB = r is compared with the fitted one in the bottom panel of **Figure 2**. The agreement, in form and in position, between both is excellent, indicating that the equation used for the interaction term V<sup>12</sup> is also appropriate to reproduce the NACMEs. The probability density of the first two vibrational states of H2(X <sup>1</sup>6<sup>+</sup> g ) has been included in the top panel of **Figure 2**, in order to analyze the reason why the reaction is faster when H<sup>2</sup> is vibrationally excited (Aguillon, 1994, 1998). While the maximum of the probability density of the vibrational state v<sup>0</sup> = 0 is found at 1.4 a0, those in the first excited vibrational state v<sup>0</sup> = 1 are at 1.25 and 1.73 a0. The latter is close to the region in which the NACME has is maximum, that explains the enhancement of the reactivity as we shall see in section Reaction Probabilities.

In **Figure 3** the ratio between the interaction term and the energy difference of the diabatic states, V12/(V22-V11), is plotted as a function of the RHeH and RHH′ distances, for several values of the angle θ ≤ 180◦ between these distances. This ratio is important for the calculation of the adiabatic PESs from the fitted diabatic ones, according to:

$$V\_{A/B} = \frac{1}{2} \left\{ V\_{11} + V\_{22} - / + \left[ (V\_{11} - V\_{22})^2 + 4V\_{12}^2 \right]^{1/2} \right\}. \tag{3}$$

As expected, V12/(V22-V11) changes sign and its absolute value is maximum in the region of the diabatic crossing line shown in Figures 2, 3 of Aguado et al. (1993).

In conclusion, these results show that the collisional dynamics of DCT He+( 2 S)+H2(X <sup>1</sup>6<sup>+</sup> g )→ He(<sup>1</sup> S)+H(<sup>2</sup> S)+H<sup>+</sup> can be investigated with high accuracy in the present diabatic electronic representation, using the V11, V22, and V<sup>12</sup> PESs.

## Collision Dynamics

Since many years we are presenting our quantum theory (Petrongolo, 1988) and results of non-adiabatic effects in spectroscopy of triatomics and dynamics of atom+diatom collisions and we here report a brief summary, following our work on the CI dynamics of the OH(A <sup>2</sup>6+)+H(<sup>2</sup> S) reaction (Gamallo et al., 2013).

The He++H<sup>2</sup> collision is described by reactant Jacobi coordinates R, r, and γ , by a body-fixed reference frame with the z axis along **R**, and by a HeH<sup>+</sup> 2 spinless rovibronic Hamiltonian Hˆ , which contains the electronic Hˆ el and the total angular

momentum ˆ**J** operators. Hˆ is represented in an orthonormal basis of diabatic electronic states (1)2A<sup>1</sup> and (2)2B2, radial grid |Rr>, associated Legendre |jK>, and symmetry Wigner states |K+p>. Here (1)2A<sup>1</sup> and (2)2B<sup>2</sup> are coupled by Hˆ el owing to the CI, h K¯ is the ˆJ<sup>z</sup> eigenvalue, and we omit J and its space-fixed Z component in |K+p>, where the total parity is p = (−) <sup>J</sup>+Kmin with Kmin = 0 or 1. The 2J+1 values of K are thus factorized in two noninteracting groups, with Kmin≤ K≤ J, of dimensions J+1 or J according to Kmin = 0 or 1, respectively.

Initial-state-resolved reaction probabilities are computed through the quantum, real WP formalism of Gray and Balint-Kurti (1998) and Meijer et al. (1998), essentially equal to the Chebyshev approach of Guo (2012). Shortly, an arccos mapping of the HeH<sup>+</sup> 2 time-dependent Schrödinger equation is solved recursively, using a scaled and shifted Hamiltonian Hˆ <sup>s</sup> and starting from an initial and complex WP |ψ<sup>0</sup> >= |a<sup>0</sup> > +i|b<sup>0</sup> > (Gray and Balint-Kurti, 1998). This initial WP describes

FIGURE 3 | Diabatic PESs: V12/(V22-V11) as function of the nuclear distances RHeH and RHH' = r, and of the included angle θ . Solid/dashed curves correspond to positive/negative values.

the entrance channel He+( 2 S)+H2(X <sup>1</sup>6<sup>+</sup> g ), with the diabatic electronic state (1)2A<sup>1</sup> and the R-dependent term

$$g\_0(\mathbb{R}) = \pi^{-1/4} \alpha^{-1/2} \exp[- (\mathbb{R} - R\_0)^2 / 2\alpha^2]$$

$$\begin{aligned} \exp[-i(2\mu\_\mathbb{R} E\_0)^{1/2} \\ (\mathbb{R} - R\_0)], \quad \text{in atomic units}, \end{aligned} \tag{4}$$

where µ<sup>R</sup> is the He++H<sup>2</sup> reduced mass. The r and angular terms of |ψ<sup>0</sup> > are the vibrational |v<sup>0</sup> > and rotational |j0K<sup>0</sup> > states of H2(X <sup>1</sup>6<sup>+</sup> g ), and finally |K0+p> is the initial overall rotational species. The recursions are

$$\begin{aligned} \left| a\_1 \right\rangle &= \hat{H}\_{\text{s}} \left| a\_0 \right\rangle - \left( 1 - \hat{H}\_{\text{s}}^2 \right)^{1/2} \left| b\_0 \right\rangle, \\ &\quad \text{first complex propagation,} \\ \left| a\_{\text{n+2}} \right\rangle &= 2\hat{H}\_{\text{s}} \left| a\_{\text{n+1}} \right\rangle - \left| a\_{\text{n}} \right\rangle, \end{aligned} \tag{5}$$

$$\text{other real propositions,}\tag{6}$$

where the square root in Equation (5) is evaluated with a Chebyshev expansion, and Equation (6) is a standard Chebyshev propagation of just a real WP, which is also absorbed at R > Rabs and r > rabs by the Gaussians exp[–C R abs(R–Rabs) 2 ] and exp[– C r abs(r–rabs) 2 ], respectively. At the end of the propagation, we

Configuration-Interaction (MRCI) NACME.

obtain the probability via a time-to-energy Fourier transform and a flux analysis (Meijer et al., 1998) on the (2)2B<sup>2</sup> PES.

We compute non-adiabatic initial-state-resolved reaction probabilities P J v0 (Ecoll), with the initial WP on the HeH<sup>+</sup> 2 (1)2A<sup>1</sup> diabatic PES and H2(X <sup>1</sup>6<sup>+</sup> g ) in the ground and first excited vibrational state, v<sup>0</sup> = 0 and 1, and in the ground rotational state j<sup>0</sup> = 0. Then the initial K<sup>0</sup> is equal to Kmin = 0 and the total parity p is (–)<sup>J</sup> . Here we have

$$P\_{\nu\_0}^{J}(E\_{\text{coll}}) = \sum\_{\nu'j'K'} \left| \mathbf{S}\_{2\nu'j'K' \leftarrow 1\nu\_0 \mathbf{0} \mathbf{0}}^{J}(E\_{\text{coll}}) \right|^2,\tag{7}$$

where (1) and (2) are the diabatic electronic states, v ′ , j ′ , and K ′ label open vibrational, rotational, and helicity states of the products, respectively, and **S** J is the state-to-state parity adapted S-matrix at J. The total ICS is then defined by

$$\sigma\_{\nu\_0}(E\_{\text{coll}}) = \frac{\pi}{2\mu\_R E\_{\text{coll}}} \sum\_{J} \left( 2J + 1 \right) P\_{\nu\_0}^{J} \left( E\_{\text{coll}} \right), \tag{8}$$

and the initial-state-resolved rate constant is

$$k\_{\nu\_0}(T) = \left(\frac{8}{\pi \mu\_R k\_B^3 T^3}\right)^{1/2} \int\_0^\infty E\_{\text{coll}} \sigma\_{\nu\_0} \exp\left(-E\_{\text{coll}}/k\_B T\right) dE\_{\text{coll}} \langle \mathfrak{H} \rangle$$

where T is the temperature and k<sup>B</sup> is the Boltzmann constant.

The calculations are done up to J = 150, using the coupledchannel formalism with Coriolis couplings among the K values, up to Kmax, that are necessary for converging the probabilities. Considering the H–H permutation symmetry, the numerical parameters of the WP propagations are listed in **Table 1**: they correspond to 7,053,300 basis states at K = 0, including two coupled electronic states. These parameters span the whole range of Ecoll from 0.0002 to 3 eV, with 1Ecoll = 0.0001 or 0.001 eV below or above 0.2 eV, respectively. The most important parameters that affect the convergence of the calculations are the number of the propagation kilo-steps, kstep, the maximum K value, Kmax, and the dimension of the R grid, nR. We shall see in the next sections some convergence results with respect to kstep and Kmax. The probabilities obtained with nR = 461 of **Table 1** are practically indistinguishable by those corresponding to nR = 559. All calculations are done with our J-K-parallelized Open MPI codes.

## COLLISION RESULTS

#### Reaction Probabilities

We plot in **Figure 4** the opacities functions (2J+1)P J v0 (Ecoll) at J = 20 and 40, v<sup>0</sup> = 0 and 1, Ecoll≤ 3 eV, and Kmax = 0, 1, and 2, with kstep = 5, which converges the probabilities within 0.1% above ∼0.5 eV. The curves at v<sup>0</sup> = 0 and 1 present a similar behavior, namely narrow resonance features at J = 20 and Ecoll≤ 0.5 eV and a smooth, fast increase above. From the comparison among lower and upper panels we see that v<sup>0</sup> = 1 is more reactive

TABLE 1 | Parameters of the quantum dynamics calculations.


Values in atomic units, unless otherwise specified.

than v<sup>0</sup> = 0 by ∼one order of magnitude. Of course, this finding reflects the HeH<sup>+</sup> 2 (A˜ <sup>2</sup>A ′ ) early potential barrier of 1.34 eV and the v<sup>0</sup> = 1 density maximum at 1.73 a<sup>0</sup> (**Figure 2**), close to the NACME maximum. Comparing the curves inside each panel, we observe a very fast convergence in Kmax, so that the Coupled-State approximation (McGuire and Kouri, 1974; Pack, 1974) at Kmax = 0 gives already reasonable results. Just two Ks converge the plots within the graphical accuracy, implying that the Coriolis couplings between K and K ± 1 vanish quickly when the initial K<sup>0</sup> is equal to zero. To reach the high accuracy claimed above at all the partial waves required to give convergent ICSs in all the collision energy range considered, we employ Kmax = 2 and 3 for v<sup>0</sup> = 0 and 1, respectively. In the J = 20 left panels, the dashed lines show the convergent results below 0.5 eV and the weight of the resonances with respect to the background. The resonance features are probably due to rotational metastable states of the C2v ion-induced dipole minimum in the entrance channel. These states, embedded in the collisional continuum, are particular Feshbach resonances induced by the CI (Cederbaum and Friedman, 2003), with lifetimes of the order of the nanosecond. The v<sup>0</sup> = 0 opacities then increase in a monotonic way above 0.6 eV up to a maximum value of ∼0.06 at 3 eV, that is onetwo orders of magnitude larger than the strongest resonance. The v<sup>0</sup> = 1 opacities show the same behavior, but the value at 3 eV is just two times larger than the resonance maximum. However, to converge the resonance energy pattern very different values of the convergent parameters Kmax and kstep are required.

We show in **Figure 5** the opacities at J = 10 and 20, for v<sup>0</sup> = 0, Ecoll ≤ 0.3 V, Kmax = 0, 3, and 4, and kstep = 120. In the upper panels a blow up of 0.05 eV also shows the details of the resonance features. From this figure we can observe that the convergence in Kmax is slower than for high energies. The curves at Kmax = 0 exhibit less peaks and the resonances shift in energy by increasing this parameter. Three main groups of resonances could be identified, decreasing and then disappearing at high Ecoll. This result suggests that the different peaks inside each group correspond to different bending energies of the collision complex (Aquilanti et al., 2005) while different groups correspond to different energies of the symmetric stretching motion. The v<sup>0</sup> = 1 curves have a similar behavior, with the Kmax convergence slightly faster and the resonances at lower energies.

In **Figure 6** the resonance energy patterns at J = 5, 10, 15, and 20, v<sup>0</sup> = 1, and Kmax = 3 are plotted for Ecoll ≤ 0.11 eV at different kstep values. The Kmax value gives a graphical convergence to

the curves and the logarithmic scale of the energy points out the resonance details. Here kstep is much greater than for the background and changes markedly with J and Ecoll. In fact, kstep = 350 is still not enough to converge all the J = 5 and 10 features, especially below 0.01 eV, but kstep = 160 perfectly converges the resonances at J = 15 and 20. As expected, the slowest convergent resonances are the narrowest ones, with largest lifetimes (Aquilanti et al., 2004). Moreover, the lifetimes of the collision complexes decrease at high J and Ecoll, because the centrifugal barrier increases and the resonances are less trapped inside the shallower well. Above J = 25 the well is so shallow that it does not support any resonance and the features disappear. Of course, increasing kstep means increase the collision time that must be of the same order of magnitude of the lifetime of the resonance intermediate to give convergent results.

## Integral Cross Sections and Rate Constants

We plot in **Figure 7** the total ICS at v<sup>0</sup> = 0 and 1, with J ≤ 150 to obtain convergent results up to 3 eV, noting that the convergent requirements change markedly with Ecoll and J. To minimize the computational effort, the total number of partial waves was therefore shared in different groups, and different values of Kmax and kstep were employed in each group, as shown in **Table 2**.

Notwithstanding the large kstep used for the lowest partial waves, test calculations show that some narrow ICS peak slightly increases with more steps. With these input data, a convergence within 0.1% is reached only by the resonance peaks above

0.05 eV. The results in **Figure 7** confirm the general scenario of the opacities: sharp resonances below 0.3 eV and a monotonic increase at larger Ecoll. The J sum now merges the resonances

#### TABLE 2 | Parameters of ICS calculations.


TABLE 3 | Present quantum ICSs/Å<sup>2</sup> vs. those semiclassical (Aguillon, 1998).


in two main groups, the first and stronger below 0.1 eV, and the latter and weaker from 0.1 to 0.3 eV. At v<sup>0</sup> = 0, the strongest resonance is equal to 0.003 Å<sup>2</sup> at 0.0116 eV and the maximum at 3 eV has nearly the same value. At v<sup>0</sup> = 1, the strongest resonance is larger than the value at 3 eV by ∼one order of magnitude, and is equal to 0.455 Å<sup>2</sup> at 0.0096 eV. In conclusion, the one-quantum vibrational excitation of H2(X16<sup>+</sup> g ) increases the cross section by more than two orders of magnitude at ∼0.01–0.02 eV and by ∼20 times at 3 eV.

As said in the Introduction, only the semiclassical theoretical works by Aguillon (1994, 1998) have obtained ICSs at or below 3 eV. We present in **Table 3** a comparison between our quantum ICSs and those estimated from **Figure 4** of Aguillon (1998), showing the good agreement between the results that differ at the most by ∼24% at v<sup>0</sup> = 0 and Ecoll = 2 eV. Taking into account the different theoretical treatment and the small reactivity at these conditions, this implies that the Aguillon semiclassical treatment of the DCT reaction works remarkably well at this collision energies, where the ICSs do not present any quantum resonance.

Finally, we report in **Table 4** and **Figure 8** the initial-stateresolved rate constants kv<sup>0</sup> (T), at v<sup>0</sup> = 0 and 1, as functions of the temperature T up to 2,000 K. Their accuracy is ∼2%, considering the slow convergence of the resonances, and the rates are stable with respect to changes of the parameters in **Tables 1**, **2**. Both rates increase quickly by a factor of ∼30 from 20 to 200 K, with a maximum at ∼250 K equal to 1.75 10−<sup>14</sup> and 1.97 10−<sup>12</sup> cm<sup>3</sup> sec−<sup>1</sup> for v<sup>0</sup> = 0 and 1, respectively. This behavior is associated with the sharp ICS resonances above ∼0.006 eV and is similar to that of H+HeH<sup>+</sup> (De Fazio, 2014). Note that a rateconstant maximum was also found in the adiabatic ground PES dynamics of H+HeH<sup>+</sup> (Esposito et al., 2015) using the PES of

TABLE 4 | Rate constants <sup>k</sup><sup>0</sup> and <sup>k</sup>1/cm<sup>3</sup> s −1


.

Ramachandran et al. (2009), but it was at ∼10,000 K and due to a complete different mechanism. Then the rates slowly decrease with T and become nearly constant above 1,500 K, where they differ by two orders of magnitude. On the overall, this behavior is due to the ICS resonances shown in **Figure 7** overlapped to a nearly Langevin decrease of the associated cross sections up to ∼0.5 eV.

Because we have considered just the ground rotational state of H2(X <sup>1</sup>6<sup>+</sup> g ), j<sup>0</sup> = 0, the present rate constant at v<sup>0</sup> = 0 and 300 K underestimates by a factor of ∼6 the thermal experimental k(330) = (1.1 ± 0.1) × 10−13cm<sup>3</sup> s −1 (Johnsen et al., 1980), which is however 39 years old. The agreement increases if we consider H<sup>2</sup> in the excited rotational states that are open at 300 K, because test calculations suggest that the reactivity can be enhanced by ∼33% when j<sup>0</sup> = 1. Taking into account the H2(X <sup>1</sup>6<sup>+</sup> g ) Fermi-Dirac nuclear spin statistics, the room-temperature populations of j<sup>0</sup> = 0 and 1 are ∼0.13 and 0.66, respectively, and this implies a rotational enhancement of the rate constant by a factor of ∼7. Owing to the room-temperature branching ratio of paraand ortho-H<sup>2</sup> and the rotational effects on the reactivity, we can roughly estimate than ortho-H<sup>2</sup> is ∼4 times more reactive than the para species.

In closing this section, we have also done some test calculations of the reaction probabilities in the adiabatic approximation, on the A˜ <sup>2</sup>A' PES of HeH<sup>+</sup> 2 (see **Figure 1**). Without reaching the accuracy and the stability of the results in section Reaction Probabilities, we present an example at v<sup>0</sup> = 0, J = 0, and kstep = 120, contrasting in **Figure 9** adiabatic A˜ <sup>2</sup>A' and non-adiabatic CI (1)2A1/(2)2B<sup>2</sup> results. Although both probabilities present a resonance structure at low Ecoll and increase above ∼1 eV, the reactivity is dramatically different, with the A˜ <sup>2</sup>A ′ probability hugely larger than the CI one, from 6 orders of magnitude at 0.001 eV to 2 orders at 3 eV. This finding shows that the A˜ <sup>2</sup>A ′ adiabatic PES drives the WP into the exothermic product channel, following a C<sup>s</sup> pathway that avoids the C2<sup>v</sup> barrier of the CI. On the contrary, the non-adiabatic CI WP remains essentially on the initial and repulsive (1)2A<sup>1</sup> diabatic PES V11, owing to the weak non-adiabatic interaction. As expected, only at energies larger than 3 eV the two probabilities seem to merge and the adiabatic approximation is probably less worse. We roughly estimate that the adiabatic A˜ <sup>2</sup>A ′ rate constants at 330 K is ∼1,000 times larger than the experimental value (Johnsen et al., 1980).

## CONCLUSIONS

In this article we have presented quantum non-adiabatic DCT results of the He++H<sup>2</sup> collision, employing an electronic diabatic representation, previously computed by Aguado et al. (1993), a WP time dependent formalism, and a flux analysis. Specifically, we have taken into account the non-adiabatic CI coupling between the first two excited diabatic PESs of HeH<sup>+</sup> 2 . Dynamical calculations are performed for the ground and first excited vibrational states of H2, for investigating vibrational effects on the DCT dynamics, and collision energies up to 3 eV are considered. Reaction probabilities and ICSs present strong and narrow resonance features up to 0.5 eV, due to quasi-bound molecular states embedded in the continuum and trapped in the ion-induced dipole minimum of the reactant channel, near the CI. These features are very hard to converge and affect all the DCT dynamics. These intense resonance features have a determinant role in the radiative chargetransfer formation (Mrugala et al., 2013) of stable HeH<sup>+</sup> 2 , probably present in the interstellar medium (Tennyson and Miller, 1987). At higher collision energies the computational load reduces drastically owing to a near conservation of the helicity quantum number. Our results are in reasonable agreement with previous experimental and theoretical studies of this reaction, confirming the strong vibrational enhancement previously founded. In fact, rate constants increase of about two orders of magnitude just adding one vibrational quantum to the H<sup>2</sup> reactants.

At the best of our knowledge, these are the first rigorous quantum DCT calculations presented for a chemical system, made possible by the joint implementation of time-dependent WP, time-to-energy Fourier transform, and flux methods. On the other hand, a more rigorous approach, as time independent close coupling calculations, cannot be attempted at the present state-of-the-art of the reaction dynamics theories, because of the difficulty of these methods to treat the three-bodies breakup (see e.g., (Pack et al., 1998), and references therein). The results achieved could have relevant consequences in astrophysics and in particular in the early Universe evolution models (Bovino et al., 2011). Although the reaction is probably negligible when the molecular hydrogen is relaxed in its ground vibrational state, the strong increase with the vibrational energy suggests that it could have a role during the early stages of the adiabatic expansion at high redshift, destroying the molecular hydrogen formed and slowing down further cooling of the primordial gas. Of course, to determinate its role, evolution Universe models with at least a vibrational resolution of the chemical network (Coppola et al., 2011, 2012) are required. Moreover, this reaction could be also relevant in other different astrophysical environments, as for example in the study of the Sun atmosphere where the temperature is very high and hydrogen and helium are very abundant species.

## AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

## ACKNOWLEDGMENTS

We are very grateful to P. Gamallo and to the Dipartimento di Biotecnologie, Chimica, e Farmacia, Universita' di Siena, Italy, for the availability of essential computer resources. We want also to thank O. Roncero for fruitful discussions. The research leading to these result has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement n. 610256 (NANOCOSMOS), the HPC Europa3 Project (INFRAIA-2013- 1-730897) with the support of the EC Research Innovation Action under H2020 Programme and the COST Action CM1401 (Our Astrochemical History). Also, we acknowledge support by the Ministerio de Economía y Competitividad under grants No.

REFERENCES


FIS2014-52172-C2-2-P and FIS2017-83473-C2-2-P. CINECA is also acknowledged for computer time awarded via the ISCRA programme.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 De Fazio, Aguado and Petrongolo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Ion-Pair Formation in Neutral Potassium-Neutral Pyrimidine Collisions: Electron Transfer Experiments

Mónica Mendes 1,2, Beatriz Pamplona<sup>1</sup> , Sarvesh Kumar <sup>1</sup> , Filipe Ferreira da Silva<sup>1</sup> , Antonio Aguilar <sup>3</sup> , Gustavo García<sup>2</sup> , Marie-Christine Bacchus-Montabonel <sup>4</sup> \* and Paulo Limao-Vieira<sup>1</sup> \*

<sup>1</sup> Atomic and Molecular Collisions Laboratory, Centre of Physics and Technological Research (CEFITEC), Department of Physics, Universidade NOVA de Lisboa, Costa de Caparica, Portugal, <sup>2</sup> Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas (CSIC), Madrid, Spain, <sup>3</sup> Departament de Ciència de Materials i Química Física, Universitat de Barcelona, Barcelona, Spain, <sup>4</sup> CNRS, Institut Lumière Matière, University of Lyon, Université Claude Bernard Lyon 1, Villeurbanne, France

#### Edited by:

Doo Soo Chung, Seoul National University, South Korea

#### Reviewed by:

Stanislav A. Pshenichnyuk, Ufa Research Centre (RAS), Russia Alexei S. Komolov, Saint Petersburg State University, Russia

#### \*Correspondence:

Marie-Christine Bacchus-Montabonel bacchus@univ-lyon1.fr Paulo Limao-Vieira plimaovieira@fct.unl.pt

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 24 January 2019 Accepted: 01 April 2019 Published: 18 April 2019

#### Citation:

Mendes M, Pamplona B, Kumar S, da Silva FF, Aguilar A, García G, Bacchus-Montabonel M-C and Limao-Vieira P (2019) Ion-Pair Formation in Neutral Potassium-Neutral Pyrimidine Collisions: Electron Transfer Experiments. Front. Chem. 7:264. doi: 10.3389/fchem.2019.00264 We report novel data on ion-pair formation in hyperthermal (30–800 eV) neutral potassium collisions with neutral pyrimidine (Pyr, C4H4N2) molecules. In this collision regime, negative ions formed by electron transfer from the alkali atom to the target molecule were time-of-flight mass analyzed and the fragmentation patterns and branching ratios have been obtained. The most abundant product anions have been assigned to CN<sup>−</sup> and C2H <sup>−</sup> and the electron transfer mechanisms are comprehensively discussed. Particular importance is also given to the efficient loss of integrity of the pyrimidine ring in the presence of an extra electron, which is in contrast to dissociative electron attachment experiments yielding the dehydrogenated parent anion. Theoretical calculations were performed for pyrimidine in the presence of a potassium atom and provided a strong basis for the assignment of the lowest unoccupied molecular orbitals accessed in the collision process. In order to further our knowledge about the collision dynamics, potassium cation (K+) energy loss spectrum has been obtained and within this context, we also discuss the role of the accessible electronic states. A vertical electron affinity of (−5.69 ± 0.20) eV was obtained and may be assigned to a π ∗ 3 (b1) state that leads to CN<sup>−</sup> formation.

Keywords: pyrimidine, negative ions, energy loss, time-of-flight, calculations

## INTRODUCTION

Radiation induced damage by low-energy electrons (<15 eV) has proven to be an efficient mechanism to promote local chemical changes when attaching to DNA/RNA molecular constituents (Boudaïffa et al., 2000). In such electron attachment process as a function of the phase and stage of aggregation, formed transient negative ion (TNI) can subsequently dissociate into stable fragment anions and neutral radical species (Sanche, 2009), where the latter may also trigger complex chemical damage within the biological environment. Another interesting aspect of such electron induced bond breaking pertains to the role of electron transfer processes which may be more prevalent under physiological conditions rather than free electron attachment processes (Wang et al., 2009). As far as electron induced processes are concerned, pyrimidine (Pyr) has been extensively studied as a prototype molecule of DNA and RNA building blocks (thymine, cytosine, and uracil) both in the gas (Baccarelli et al., 2011) and condensed phases (Sanche, 2005; Zheng and Sanche, 2018). Electron interactions with pyrimidine nucleobases are well-represented in the literature, where we note relevant experimental studies on electron transmission spectroscopy (Aflatooni et al., 1998), dissociative electron attachment (DEA) experiments (Huels et al., 1998; Ferreira da Silva et al., 2013), and electron impact ionization studies (Linert et al., 2012). More recently, site-selective bond excision of selected pyrimidines yielding the dehydrogenated parent anion upon electron transfer in collisions with neutral potassium atoms (Almeida et al., 2013a) and with low-energy electrons (Ptasinska et al., 2005) have been reported. N-site de-methylation in pyrimidine bases as studied by low-energy electron attachment and ab initio calculations gave a comprehensive description into the dynamics of the decaying transient anion and more precisely into the competition between dissociation and autodetachment (Almeida et al., 2013b). Potassium-uracil/thymine ring cleavage enhancement was reported in electron transfer experiments and theoretical calculations (Almeida et al., 2014a). Studies on threshold behavior in metastable dissociation of multiphoton ionized thymine and uracil (Pandey et al., 2017) have been also investigated.

The topic of this contribution deals with electron transfer experiments with Pyr (C4H4N2) and within this context, a literature survey reveals that Nenner and Schulz experimental electron transmission spectroscopy data report the three resonances at 0.25 (X˜ <sup>2</sup>A2), 0.77 (A˜ <sup>2</sup>B1), and 4.24 (B˜ <sup>2</sup>B1) eV (Nenner and Schulz, 1975) while Modelli and Burrow (1983), and more recently Modelli et al. (2011), placed the three lowest electron affinities of π ∗ character at −0.39 [π ∗ 1 (a2)], −0.82 [π ∗ 2 (b1)], and −4.26 [π ∗ 1 (b1)] eV and a core-excited resonance at −5.5 eV. An unprecedented investigation on the effect of solvation on electron attachment to pure and hydrated Pyr clusters, has shown that hydration quenches all fragmentation channels in the pyrimidine molecule (Neustetter et al., 2015). Regarding theoretical calculations, we note a detailed study of the effect of the third π ∗ resonance on the angular distributions for electron-pyrimidine scattering (Mašín and Gorfinkiel, 2016) and electron affinities and ionization potentials of DNA radical ions (Sevilla et al., 1995). Total electron-scattering cross sections have been thoroughly investigated in several occasions (Baek et al., 2013; Fuss et al., 2013) together with differential cross sections for low-energy electron-impact excitation (Maljkovic´ et al., 2009; Jones et al., 2012a,b). Theoretical elastic and electronic excitation cross-sections and experimental electronic excitation cross-sections for electron collisions with pyrimidine have been reported by Mašín et al. (2012). Additionally, fragmentation of pyrimidine induced by core ionization by photoelectron-photoion-photoion coincidence (PEPIPICO) spectroscopy (Itälä et al., 2018) and absolute total and partial dissociative cross sections of pyrimidine by electron and proton intermediate impact velocities (Wolff et al., 2014), have been probed. The electronic state spectroscopy of pyrimidine has been comprehensively investigated by different methods, with threshold-electron excitation reported up to 12.5 eV (Pisanias et al., 1973), absolute cross-sections for electronic excitation have been obtained by electron impact up to 18 eV (Regeta et al., 2016) and absolute cross-sections by high-resolution VUV photoabsorption up to 11 eV (Ferreira da Silva et al., 2010). Lowenergy (2–12 eV) electron vibrational and electronic electronenergy-loss (Levesque et al., 2005) and electron stimulated desorption from condensed pyrimidine (Ellis-Gibbings et al., 2017; Zheng and Sanche, 2018) have also been reported. Finally, a comparative study on the role of pyrimidine and water as underlying molecular constituents for describing radiation damage in living tissue, in terms of energy deposition (absorbed dose and stopping power) but also in terms of the number of induced molecular processes (Fuss et al., 2015) has been reported. Thus we consider that the present data on collisional electron-transfer induced dissociation of pyrimidine may serve for future applications in nanoscale models of radiation damage in DNA/RNA as we have recently proposed for the purines (Cunha et al., 2018a,b) and other biological relevant molecules as uridine (Almeida et al., 2014b) and small amino acids (Ferreira da Silva et al., 2016) just to mention a few.

Electron transfer experiments in atom-molecule collisions yielding ion-pair formation (reaction 1), an electron donor (K≡potassium) with low ionization energy (4.34 eV) delivers to the target molecule (Pyr) the extra charge, leaving it in a metastable state (Pyr−# ):

$$\begin{aligned} \text{(K + Pyr \to (K^+Pyr^-) '' \to K^+ + (Pyr)^{\bullet - \#} \to K^+ \\ + \text{ (Pyr - X)^- + X} \end{aligned} $$

which then dissociates into a stable fragment anion and a neutral (X) species. This process is dictated by non-adiabatic transitions between the neutral (K Pyr) and ionic (K<sup>+</sup> Pyr−# ) potential energy curves (and/or surfaces) involved in the collision (Kleyn et al., 1982), where the relative kinetic energy of the collision partners is greater than 1E, the potassium atom ionization energy (IE) minus the electron affinity (EA) of the target molecule. For pyrimidine, a 1E value <5 eV is obtained, meaning that the TNI can be formed with an excess of internal energy. Assessing the internal energy of the TNI requires detailed information of the angular distributions of products anions formed, viz. the products' velocity distribution. Pyrimidine has an electron affinity close to 0 eV (Nenner and Schulz, 1975) meaning that formation of a stable TNI may not be attainable within the µs detection window of the time-of-flight mass spectrometer. In the present experiments the lowest collision energy is 30 eV, the efficiency of such electron transfer process allows to explore complex reactions associated with concerted cleavage of several bonds.

In this manuscript we therefore report for the first time negative ion formation in neutral potassium-neutral pyrimidine collisions, together with K<sup>+</sup> energy loss data and novel ab initio calculations to support the experimental findings. In the next sections, we describe our experimental methods and theoretical methodology. Afterwards, our results are presented and discussed and conclusions from this work are finally summarized.

### EXPERIMENTAL METHODS

The crossed molecular beam setup used to study collisions of neutral potassium (K) atoms with neutral pyrimidine (Pyr), has been described in detail elsewhere (Ferreira da Silva et al., 2011; Almeida et al., 2013a), with recent modifications on the detection systems. Briefly, an effusive target molecular beam crosses a primary beam of fast neutral K atoms and the product anions are analyzed using a reflectron time-of-flight (TOF) mass spectrometer (KORE R-500-6). The K beam is produced in a resonant charge exchange chamber from the interaction of K <sup>+</sup> ions from a potassium ion source (30–800 eV in the lab frame) with gas-phase neutral potassium atoms from an oven source. Residual ions were removed from the primary beam by electrostatic deflecting plates outside the oven. The neutral potassium beam's intensity was monitored using a Langmuir– Taylor ionization detector before and after the collection of each TOF mass spectrum and the beam energy resolution in the collision energy range was ∼0.5 eV (FWHM) as measured with a hemispherical electrostatic energy loss analyser which characterized the K<sup>+</sup> ion signal at a fixed energy, following K collisions with nitromethane (CH3NO2). The effusive beam of pyrimidine from an oven source was admitted into vacuum through a 1 mm diameter capillary where it was crossed with the neutral fast potassium beam. Negative ions formed in the collision region were extracted by a ∼380 V cm−<sup>1</sup> pulsed electrostatic field. The typical base pressure in the collision chamber was 6 × 10−<sup>5</sup> Pa and the working pressure was 4 × 10−<sup>4</sup> Pa. Mass spectra (resolution m/1m ≈ 800) were obtained by subtracting background measurements (without the sample) from the sample measurements. Mass calibration was carried out on the basis of the well-known anionic species formed after potassium collisions with nitromethane (Antunes et al., 2010). Pyrimidine (Pyr) was supplied by Sigma Aldrich with a stated purity of ≥98%. Repeated freeze-pump-thaw cycles were performed before each spectrum collection. The extraction region and the TOF system were heated during the measurements in order to prevent any sample condensation and thus charge accumulation on the electrodes.

The entrance slit of the hemispherical energy analyser used in the K<sup>+</sup> energy loss measurements is aligned in the forward direction with the neutral K beam's optical path. The analyser was operated in constant transmission mode, hence keeping the resolution constant throughout the entire scan where the energy resolution for the present measurements was ∼0.6 eV in the lab frame. The energy loss scale was calibrated using the experimental threshold energy of formation (4.5 eV) from CN−, given that this is the most intense fragment anion formed in K-Pyr collisions.

#### THEORETICAL METHOD

The theoretical description of the charge transfer process in the interaction of a neutral potassium atom with a selected nucleobase, is based on the evolution of the quasi-molecular system formed by the potassium projectile and the molecular target along the reaction coordinate within the framework of the

molecular representation. We have implemented with success the one-dimension coordinate approximation in previous ion/neutral-biomolecule collision systems (Bene et al., 2008; Bacchus-Montabonel and Tergiman, 2012; Almeida et al., 2014a), where the atom-nucleobase collision system is thus treated as a pseudo-diatomic molecule evolving along the coordinate associated with the distance between the impinging atom and the nucleobase (Salem, 1982; Bacchus-Montabonel and Tergiman, 2011b). Within the frame of such approximation, we do not consider the internal degrees of freedom of the biomolecular target, which is reasonable since in very fast collision processes where nuclear vibrational and rotational motions are much slower than the collision time, these can be considered frozen during the collision. The geometry of pyrimidine has been optimized at the MP2 level of theory from the work of Bacchus-Montabonel and Calvo (2015). A perpendicular approach of the potassium atom, pointing at the center of the pyrimidine ring (see **Figure 1**) has been considered, as the charge transfer process has been clearly shown to be favored in such orientation for the case of pyrimidine targets (Bacchus-Montabonel and Tergiman, 2006, 2011a). The potential energy curves along the z reaction coordinate corresponding to the approach of the potassium atom perpendicularly to the pyrimidine ring have been calculated by means of ab-initio methods with the MOLPRO code (Werner et al., 2015). The pyrimidine target is kept frozen in its ground state geometry during the collision process. The calculation has been performed in Cartesian coordinates, with no symmetries. All electrons have been considered for C, N, and H atoms with the VTZ basis set, although the 18 core electrons of potassium have been treated through the ECP18sdf core-electron pseudopotential (Nicklass et al., 1995), with the corresponding basis set. The natural molecular orbitals for K–Pyr have been determined by CAS(3,11) state-averaged CASSCF calculations for the reaction coordinate R = 10 Å corresponding to the

asymptotic region taking account the static electron correlation. The 1s orbitals of carbon, nitrogen and oxygen are treated as frozen cores. The resultant lowest unoccupied molecular orbitals (LUMOs) for pyrimidine are shown in **Figure 2** together with the corresponding orbitals without the presence of potassium. The polarization by the potassium atom induces a global shift in energy of ∼1.5–2.0 eV for the π <sup>∗</sup> orbitals and 2.0 eV for the σ <sup>∗</sup> orbital.

## RESULTS AND DISCUSSION

This is the first investigation on negative ion formation in electron transfer from neutral K atoms with Pyr combining experimental and theoretical methods to comprehensively analyse the full fragmentation pattern. Dissociative electron transfer TOF mass spectra were recorded at lab-frame collision energies of 30–800 eV (∼14–480 eV in the center–of–mass frame and from now on referred as available energy). **Table 1** is a compilation of all fragment anions detected and their proposed assignments in the wide energy range of collisions investigated. **Figure 3** shows the Pyr negative ions TOF mass spectra recorded at 30, 100, and 700 eV lab frame energy (13.8, 56.2, and 419.3 eV available energy), while in **Figure 4** we present the K<sup>+</sup> energy loss spectrum measured in the forward direction in collisions of potassium atoms with pyrimidine at 111 eV lab frame energy (67.2 eV available energy). Branching ratios (BRs) for the major fragments of Pyr as a function of the collision energy are presented in **Figure 5**.

A careful inspection of the TOF mass spectra reveals that they are dominated by the cyanide anion (CN−) and show no evidence of parent anion formation (Pyr−), which is expected since the vertical electron affinity of pyrimidine is −0.39 eV

TABLE 1 | Negative ions formed in potassium collisions with pyrimidine (Pyr).


(Modelli et al., 2011). Another interesting aspect of the collision induced fragmentation pertains to the loss of different HCN units from the dehydrogenated parent anion of Pyr, (Pyr– H)−, yielding C3H2N<sup>−</sup> (and/or the isobaric species C2N − 2 ), and C2H<sup>−</sup> (**Table 1**), with such mechanism also reported in the case of potassium-adenine electron transfer experiments (Cunha et al., 2018a,b). The presence of the K<sup>+</sup> ion in the vicinity of the TNI formed upon K + Pyr → (K+Pyr−) plays a significant role in the decomposition mechanism yielding particular fragmentation channels, which are different from those observed in DEA experiments (Neustetter et al., 2015). Such strong coulomb interaction in the collision complex (K+Pyr−) may delay autodetachment allowing time enough, in particular in the low-collision regime, for the excess energy in the TNI to be redistributed through the different available degrees of freedom enhancing a favorable fragmentation channel. In Pyr the fragmentation predominantly results in CN<sup>−</sup> formation given the high electron affinity of the CN radical (3.8620 ± 0.0050) eV (NIST Chemistry WebBook, 2018). The ab initio calculations in **Figure 2** show that the lowest-lying π ∗ states are considerably shifted to higher energies in the presence of a potassium atom in comparison to respective calculated MOs without the presence of K. During the electron transfer process, an electronic transition accessing a π ∗ state does not lead to direct cleavage of a bond unless a repulsive σ ∗ state is crossed diabatically. In the present experiments the available energy is larger than the threshold for electron transfer (1E = IE(K)−EA(Pyr) = 4.34 + 0.39 = 4.73 eV, with IE(K) being the ionization energy of the potassium atom and EA(Pyr) the Pyr electron affinity), and if the lifetime of the metastable ion is long enough, intramolecular energy redistribution may occur competing with direct dissociation. Such is possible if the nuclear wavepacket survives long enough along the reaction coordinate to allow diabatic coupling between the two states, i.e., π ∗ and σ ∗ . This is discussed in the next sections within the scope of the different π ∗ and σ <sup>∗</sup> MOs involved in the formation of specific fragment anions.

#### K <sup>+</sup> Energy Loss Spectrum

The energy loss spectrum of K<sup>+</sup> ions formed in the forward direction from the collision of potassium atoms with pyrimidine at 111 eV lab frame energy, is shown in **Figure 4**. Note that the lowest energy loss scale appears above ∼ 4 eV to account for the potassium ionization energy, 4.34 eV. Two features are visible at 10.03 and 11.91 eV, the former more intense than the latter and with a full width at half-maximum (FWHM) of ∼1.2 eV. The position of the maxima do not shift with the collision energy within ±0.2 eV. The main anionic yield from the TOF mass spectra at all collision energies is due to CN<sup>−</sup> (**Figures 3**, **5**). The energy loss 1E at the maximum of the features is given by 1E = IE(K) − EAmax, which results on an electron affinity of (−5.69 ± 0.20) eV and (−7.57 ± 0.20) eV, assigned to π ∗ 3 (b1) and a π ∗ CH core-excited resonance, respectively. This is in good agreement with the theoretical calculations presented in **Figure 2**.

## (Pyr–H)<sup>−</sup>

The dehydrogenated closed shell anion (Pyr–H)<sup>−</sup> is formed through the ion-pair reaction:

$$\begin{aligned} \text{(K + Pyr \to (K^+Pyr^-) \to K^+ + (Pyr)^{\theta -} \to K^+ + \text{)} \\ + \text{ (Pyr - H)} ^- + \text{H} \end{aligned} \tag{2}$$

which represents a direct cleavage of the (C–H) bonds and (Pyr)#<sup>−</sup> stems for a TNI formed with an excess of internal energy. Formation of the parent anion with H abstraction has been reported in DEA experiments on pyrimidine through a core-excited resonance at 5.5 eV (Neustetter et al., 2015), where the three lowest π ∗ resonances do not contribute to such anion formation due to their short-lived character. Moreover, recent R-matrix calculations (Mašín et al., 2012) predict higher excited states which may contribute to (Pyr–H)<sup>−</sup> formation. Pyrimidine BR as a function of the available energy (**Figure 5**), shows that (Pyr–H)<sup>−</sup> yield only accounts for 10–20% of the total anions in the 50–480 eV energy region, and vanishes below the threshold of formation at ∼26 eV. Such low anion yield in respect to the other fragment anions is in sharp contrast to the experimental observations in the low-energy collision regime of potassium atoms with DNA/RNA pyrimidines, thymine, and uracil (Almeida et al., 2013a; Ferreira da Silva et al., 2013). Such is certainly due to the different sort of molecular bonding where the presence of N–H bonds (in contrast to the C–H bond) lowers the threshold of the de-hydrogenated parent anion formation, which does not prevail in the case of pyrimidine.

In **Figure 2** we show the three lowest calculated π <sup>∗</sup> MOs at 5.0 eV (π ∗ ring ), 6.6 eV (π ∗ ring ), and 8.0 eV (π ∗ CH) and at higher energy a σ ∗ resonance at 9.4 eV (σ ∗ CH) along the C5–H bond. Pyrimidine BRs in **Figure 5** shows that (Pyr–H)<sup>−</sup> cannot be produced <25 eV which can be related to an electron promotion to the π ∗ ring orbitals yielding instead CN−. Accessing a <sup>π</sup> ∗ CH state may be only possible by increasing the collision energy, and so (Pyr–H)<sup>−</sup> formation certainly occurs through access of the σ ∗ CH state via curve crossing. The present energy loss data provides evidence that the feature at 11.91 eV (see **Figure 4**), 7.57 eV for the electron affinity, is indicative of the vertical transition energy to the π ∗ CH state, and the closeness with the σ ∗ CH state allows us to specify the dominant pathway to dissociation. Alternatively, a direct initial transfer to the σ ∗ state and subsequent dissociation may be considered, playing

(67.2 eV in the center-of-mass system). See text for details.

available energy in the center-of-mass, respectively). See text for details.

a relevant role in the higher-energy collision region where the (Pyr–H)<sup>−</sup> yield predominates in respect to the fragment anions produced through the π ∗ ring /π ∗ CH resonances. Interesting to note the resonances that are prominent in the excitation functions for vibrational excitation, and peaking at ∼10 eV, have been assigned to σ <sup>∗</sup> with pronounced C–H stretching character although ring breathing modes may be present (Regeta et al., 2016).

#### C3H2N <sup>−</sup>/C2N − 2 , C2H −

Hydrogen cyanide abstraction is operative from the dehydrogenated parent anion leading to pyrimidine ring opening, with assignment of the fragment anions indicated in **Table 1**. Formation of C3H2N<sup>−</sup> (and/or the isobaric C2N − 2 ) from potassium collisions with pyrimidine occurs at threshold >38 eV while for C2H<sup>−</sup> above 14 eV in the center-of-mass frame (see **Figure 5**), the latter the second most intense fragment anion up to 250 eV. However, owing to C2H electron affinity, (2.969 ± 0.006) eV (Rienstra-Kiracofe et al., 2002) in contrast with −0.27 eV for C3H2N adiabatic electron affinity (from our present VTZ basis/CASSCF calculation), the former anion may prevail in the electron transfer induced decomposition of the pyrimidine molecule. We also observe a strong competition between C2H<sup>−</sup> and (Pyr–H)<sup>−</sup> formation which is enhanced above 250 eV. The LUMOs of Pyr in **Figure 2** show relevant π ∗ antibonding character with nodes along the C–N bonds. Such electron spin densities are indicative of favorable bond breaking in particular where curve crossing in the diabatically frame description may be relevant (i.e., π ∗ CH/σ ∗ CH). However, at low collision energies (≤ 26 eV), the de-hydrogenated parent anion channel is not operative but is C2H<sup>−</sup> although with modest intensity. The dominant K<sup>+</sup> energy loss features peaks at 10.03 eV (**Figure 4**), 5.69 eV for the electron affinity and lends support to the electron spin densities suggesting that the electron may be initially transferred to the π ∗ ring states. This (Pyr–H)<sup>−</sup> suppression can be rationalized in terms of a slow collision process (>46 fs) enhancing a coulombic stabilization of the TNI by the proximate K <sup>+</sup> ion, increasing the probability of intramolecular electron transfer that may favor dissociation or may favor autodetachment (supressing dissociation), certainly explaining the low yields observed in this energy region. As far as authors are aware, no DEA experiments to pyrimidine have reported these fragment anions. Within the collision energy range studied for pyrimidine, i.e., for the available energy (14–480 eV), such loss of HCN units is operative since the estimated threshold of the decomposition reaction requires −0.89 eV given that 1fH<sup>g</sup> ◦ (C4H4N2) = 196.65 kJ/mol (2.04 eV) (Lavorato et al., 2001), 1fH<sup>g</sup> ◦ (C3H2N) = −242 kJ/mol (−2.51 eV) (Huang et al., 2000), EA (C3H2N) = −26.05 kJ/mol (−0.27eV, from our present VTZ basis/CASSCF calculation), 1fH<sup>g</sup> ◦ (HCN) = 135.14 kJ/mol (1.4 eV), and 1fH<sup>g</sup> ◦ (H) = 218 kJ/mol (2.26 eV) (NIST Chemistry WebBook, 2018).

## CN<sup>−</sup>

The TOF mass spectra in **Figure 3** and the BRs in **Figure 5** are dominated by the cyanide anion in all collision energy range investigated. In sharp contrast to uracil and thymine collisional electron transfer experiments where the unimolecular decomposition process proceeds through the dehydrogenated parent anion as a precursor in the formation of fragments that require bond cleavages in the ring, namely CN<sup>−</sup> (Ferreira da Silva et al., 2013), that is not the case in pyrimidine. In order to aid our understanding of the underlying molecular mechanisms and the accessed states that are responsible for CN<sup>−</sup> formation in K-Pyr collisions, **Figure 2** shows the three low-lying calculated π <sup>∗</sup> orbitals at 5.0, 6.6, and 8.0 eV. At higher energy a σ ∗ resonances at 9.4 eV is present with antibonding character along the C5–H bond. We now turn again our attention to the energy loss data in **Figure 4** where the features have been assigned to transitions to electronic states through π ∗ ring (π ∗ 3 (b1)) and a π ∗ CH core-excited resonances at 5.69 and 7.57 eV, respectively. In the collision energy range investigated, CN<sup>−</sup> is the major fragment anion and is mainly formed through an electron promotion to the π ∗ ring orbitals. Such finding lends support to the theoretical prediction of the π ∗ ring orbitals at 5.0 and 6.6 eV. Accessing the different π <sup>∗</sup> orbitals is achieved by increasing the collision energy and efficient bond breaking should proceed through access of σ ∗ states. However, the present calculations for K-Pyr do not predict any σ ∗ CN states close in energy to the π ∗ ring orbitals since these were performed without the presence of the K <sup>+</sup> ion post-collision. From **Figure 2**, and in the case of the MOs for pyrimidine (left column), the σ ∗ CN state shows strong antibonding character between C6–N1 and C4–N3 bonds. Owing to the similarity in the calculated electron spin densities between Pyr and K+Pyr in **Figure 2**, and apart from the differences in energies, we can anticipate a similar character for the C–N bonds. Notwithstanding, the proposed mechanism as suggested before in the case of the pyrimidines thymine and uracil (Almeida et al., 2011, 2014a), accounts for the initial access to one of the π ∗ states and subsequent intramolecular electron transfer into one of the highly antibonding σ ∗ states enhancing an effective ringbreaking pathway. Such is achieved in electron transfer studies since the presence of the K<sup>+</sup> ion in the vicinity of the TNI may suppress autodetachment long enough for the fragmentation pathway successful competition (Almeida et al., 2011, 2014a).

#### CONCLUSIONS

The present work provides the first comprehensive investigation of the decomposition mechanisms of neutral Pyr in collisions

#### REFERENCES


with neutral potassium atoms yielding ion-pair formation. The major negative ions formed have been investigated as a function of the available energy in the center-of-mass frame, and assigned to the cyanide anion, the de-hydrogenated parent anion, and fragment anions related to the pyrimidine ring opening due to abstraction of HCN units from (Pyr–H)−. The theoretical calculations reveal detailed information about the electronic structure of K+Pyr and hence provide insight into the electronic states that are most likely participate in the major fragment anion channels. We have also shown that ion-pair formation in collisions of potassium atoms with pyrimidine molecules, yields two different electronic states of the metastable parent anion. These states have vertical electron affinities of (−5.69 ± 0.20) and (−7.57 ± 0.20) eV, assigned to π ∗ 3 (b1) and a π ∗ CH states, the latter accessible through a core-excited resonance.

#### AUTHOR CONTRIBUTIONS

MM, BP, and SK have run the experimental set up and collected the TOF mass spectra, energy loss data, and branching ratios. FdS was in charge of the data assessment and preliminary interpretation. M-CB-M was in charge of the theoretical calculations. AA, GG, and PL-V have been in charge of analyzing the data and paper writing together with M-CB-M.

## FUNDING

MM, SK, and FdS acknowledge the Portuguese National Funding Agency FCT-MCTES through PD/BD/106038/2015, PD/BD/142831/2018, and researcher position IF-FCT IF/00380/2014, respectively, and together with PL-V the Research Grants UID/FIS/00068/2019 (CEFITEC), PTDC/FIS-AQM/31215/2017, and PTDC/FIS-AQM/31281/2017. This work was also supported by Radiation Biology and Biophysics Doctoral Training Programme (RaBBiT, PD/00193/2012); UID/Multi/04378/2013 (UCIBIO). GG and AA acknowledge partial financial support from the Spanish Ministerio de Economia, Industria y Competitividad, Project No. FIS2016- 80440 and Project CTQ2013-41307-P. M-CB-M acknowledges support from the computational resources from the CCIN2P3 in Villeurbanne and CCRT/CINES/IDRIS by GENCI (Grand Equipement National de Calcul Intensif) under the allocation A0030807662.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Mendes, Pamplona, Kumar, da Silva, Aguilar, García, Bacchus-Montabonel and Limao-Vieira. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Photoelectron-Photofragment Coincidence Spectroscopy With Ions Prepared in a Cryogenic Octopole Accumulation Trap: Collisional Excitation and Buffer Gas Cooling

#### Ben B. Shen, Katharine G. Lunny, Yanice Benitez and Robert E. Continetti\*

*Department of Chemistry and Biochemistry, University of California, San Diego, San Diego, CA, United States*

#### Edited by:

*Antonio Aguilar, University of Barcelona, Spain*

#### Reviewed by:

*Franco Vecchiocattivi, University of Perugia, Italy Bruno Martinez-Haya, Universidad Pablo de Olavide, Spain*

> \*Correspondence: *Robert E. Continetti rcontinetti@ucsd.edu*

#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *16 February 2019* Accepted: *10 April 2019* Published: *30 April 2019*

#### Citation:

*Shen BB, Lunny KG, Benitez Y and Continetti RE (2019) Photoelectron-Photofragment Coincidence Spectroscopy With Ions Prepared in a Cryogenic Octopole Accumulation Trap: Collisional Excitation and Buffer Gas Cooling. Front. Chem. 7:295. doi: 10.3389/fchem.2019.00295* A cryogenic octopole accumulation trap (COAT) has been coupled to a photoelectron-photofragment coincidence (PPC) spectrometer allowing for improved control over anion vibrational excitation. The anions are heated and cooled via collisions with buffer gas <17 K. Shorter trapping times (500 µs) prevent thermalization and result in anions with high internal excitation while longer trapping times (80 ms) at cryogenic temperatures thermalize the ions to the temperature of the buffer gas. The capabilities of the COAT are demonstrated using PPC spectroscopy of O<sup>−</sup> 3 at 388 nm (Eh<sup>ν</sup> = 3.20 eV). Cooling the precursor anions with COAT resulted in the elimination of the autodetachment of vibrationally excited O<sup>−</sup> 2 produced by the photodissociation O − <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup> <sup>+</sup> <sup>O</sup> − 2 (v ≥ 4). Under heating conditions, a lower limit temperature for the anions was determined to be 1,500 K through Franck-Condon simulations of the photodetachment spectrum of O<sup>−</sup> 3 , considering a significant fraction of the ions undergo photodissociation in competition with photodetachment. The ability to cool or heat ions by varying ion injection and trapping duration in COAT provides a new flexibility for studying the spectroscopy of cold ions as well as thermally activated processes.

Keywords: ion trap, ozonide, photoelectron, photofragment, coincidence spectroscopy, collisional excitation, buffer gas cooling, ozone

## INTRODUCTION

Measurements of energy partitioning for neutral dissociation processes provide significant insights into the chemistry of transient species, providing benchmarks for understanding reaction dynamics (Johnson et al., 2014; Otto et al., 2014a). Experimentally, such measurements are challenging due to the complexity of potential energy surfaces and require spectroscopic probes for all resulting products of a photo-induced process. Anion photodetachment coupled with photoelectron-photofragment coincidence (PPC) spectroscopy provides a broad overview of the reaction dynamics at a fixed photon energy. The photoelectron kinetic energy (eKE) spectrum encodes the distribution of potential energies on the nascent neutral surface, and the corresponding eKE-resolved kinetic energy release (KER) spectra for the neutral products provides a measure of the subsequent dissociation mechanism. In addition, the ability to distinguish photodetachment processes that yield stable neutral products as opposed to dissociative photodetachment (DPD) provides valuable information. However, internal excitation in the precursor anions yields congested PPC spectra (Corderman and Lineberger, 1979; Hock et al., 2012; Boyarkin and Kopysov, 2014; Johnson et al., 2014) leaving ambiguity in the energy available to the neutral fragments in DPD processes. Preparation of precursor anions with known internal energies greatly enhances the ability to determine the energy partitioning for the dissociative pathways. In an effort to better control the internal excitation of precursor anions, a cryogenic octopole accumulation trap (COAT) has been coupled to an existing photoelectron-photofragment coincidence (PPC) spectrometer enabling the preparation of both hot and cold precursor anions as demonstrated through PPC spectroscopy of O<sup>−</sup> 3 .

Spectroscopic studies of ions with high internal excitation yields complex and congested spectra, often obscuring features that yield information about reaction dynamics. Supersonic expansions have been broadly applied in gas-phase experiments for producing molecules with vibrational temperatures below 100 K and rotational temperatures below 20 K (Smalley et al., 1977). Unfortunately, the ionization process itself can induce significant amounts of internal energy, resulting in systemdependent cooling efficacy (Sanz et al., 2005; Johnson et al., 2014; Shen et al., 2014). Previously in PPC experiments, progress was made in the preparation of colder ions by implementing an electrostatic ion beam trap (EIBT). This decoupled the kHz PPC measurements in the EIBT from the pulsed ion source, allowing for a low-repetition rate (10 Hz) for more effective cooling in stronger supersonic expansions. This was demonstrated on small molecules such as HOCO−, giving a detailed characterization of deep tunneling involved in the dissociation of cis-HOCO to H + CO<sup>2</sup> (Johnson et al., 2011). Unfortunately, larger ions such as tert-butoxide ((CH3)3CO−) are not efficiently cooled in a supersonic expansion. This results in observed dissociation dynamics only accessible through non-Boltzmann population of highly vibrationally excited anions (Shen et al., 2014). Results like these have motivated the search for improved methods for producing cold anions in kHz repetition-rate PPC experiments.

Various methods of preparing cold anions were considered for the PPC spectrometer including buffer-gas-cooled radiofrequency (RF) ion traps. Due to the low-duty cycle, a RF ion trap alone is not an ideal approach to performing PPC measurements. PPC measurements provide kinematically complete information on events that lead to a free electron and momentum-matched neutral products detected in coincidence, so a high duty cycle and low event rate are required to minimize contamination from false coincidences (Continetti, 1998, 2001; Stert et al., 1999). Addition of the EIBT to the PPC spectrometer decoupled the source duty cycle from the photodetachment laser interaction duty cycle through the recycling of ions within the EIBT. This allowed the source repetition rate to be reduced to 10 Hz, while maintaining the high PPC data acquisition duty cycle (1 kHz) required to carry out successful multi-particle coincidence experiments. The decoupling of the ion source and EIBT duty cycles paved the way for application of a low-repetition-rate cryogenic radiofrequency (RF) trap as a method for cooling ions prior to PPC measurements.

RF ion traps have been proven to be a robust method of storing and cooling ions via collisions with cold buffer gas and have been extensively used in cooling clusters and larger biomolecules (Gerlich, 1995; Jasik et al., 2013; Redwine et al., 2013; Boyarkin and Kopysov, 2014). The cooling ability of the RF trap is limited not only by the temperature of the ion trap, but also by ion heating induced by the RF electric field (Gerlich, 1995). Within a RF trap, ion oscillation at the frequency of the RF field causes heating through collisions with the buffer gas. The oscillation is highly dependent on the effective potential (Veff) within the trap. Quadrupole traps have a parabolic effective potential, and the large field-induced gradient is expected to lead to a propensity for significant RF heating. Increasing the order (number of electrodes) for a linear RF trap creates an effective potential with a smaller radial field gradient through the flattening of the minima. Gerlich et al. demonstrated with a 22-pole trap that this creates a steep rise in potential near the RF rods (Gerlich, 1995). This allows for a larger area in the center of the trap relatively free of RF heating within which the ions are confined. In the present application, RF ion traps provide flexibility in the preparation of ions for PPC spectroscopy by allowing for cooling as well as heating of ions. The production of cold anions allows for more clearly defined ion energetics for the subsequent study of photoinduced processes. Alternatively, the ability to collisionally heat the ions allows investigation of the effects of internal excitation on dissociation dynamics and thermally activated processes.

To demonstrate the effectiveness of COAT, PPC spectroscopy was performed on O<sup>−</sup> 3 at 388 nm (Eh<sup>ν</sup> = 3.20 eV), just below the threshold for autodetachment of O<sup>−</sup> 2 (v ≥ 4) products which result from the photodissociation of O<sup>−</sup> 3 . The photoelectron spectrum of O<sup>−</sup> 3 at Eh<sup>ν</sup> = 3.20 eV show three concurrent photophysical processes: (1) photodetachment O3– + hν → O<sup>3</sup> + e <sup>−</sup>; (2) photodissociation/autodetachment O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> O − 2 ( <sup>2</sup>5) + O(3P), and (3) photodissociation O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup>−( <sup>2</sup>P) + O2( <sup>1</sup>1g) followed by the photodetachment O−( <sup>2</sup>P) + hν → O(3P) by a second photon. While all three processes are influenced by the internal excitation of the precursor anion, the most striking effect is observed in process (2). It is wellknown that vibrational excitation of O<sup>−</sup> <sup>2</sup> > 4 quanta results in autodetachment of the electron yielding O2( <sup>3</sup>Σ<sup>−</sup> g ) (Allan et al., 1996a; Matejcik et al., 1996; Goebbert and Sanov, 2009). Jarrold et al. recently observed the autodetachment of O<sup>−</sup> 2 as a result of photofragmentation of O<sup>−</sup> 3 to O<sup>−</sup> 2 (v > 4) + O at 355 nm (Eh<sup>ν</sup> = 3.49 eV) photon energy (Nestmann et al., 2005), and this process was further characterized at Eh<sup>ν</sup> = 3.20 eV in an initial report from our laboratory (Shen et al., 2017). The onset for the autodetachment channel lies 3.24 eV above O<sup>−</sup> 3 (X˜ <sup>2</sup>B1) as shown in **Figure 1**. Access to the autodetachment channel is therefore energetically accessible only when the precursor anion (O<sup>−</sup> 3 ) is vibrationally excited, making this an ideal candidate for testing the capabilities of COAT. The design and application of COAT in PPC spectroscopy is discussed in detail in the following sections, using O<sup>−</sup> 3 as an example of the ability to prepare either cold or hot ions to exert control over product channel pathways.

3 autodetachment channel.

## EXPERIMENTAL SETUP

The cryo-PPC spectrometer (Johnson et al., 2011) has been modified to include a new source chamber and a cryogenic octopole accumulation trap (COAT) as shown in **Figure 2**. The new modifications can be divided into three sections discussed in detail below: ion source, COAT trap design, and COAT operation.

#### Ion Source

A new source chamber was added to the existing PPC spectrometer to house a piezoelectric pulsed valve (PPV) with coaxial discharge plates and a Wiley-McLaren style mass spectrometer. This source chamber is pumped by an Edwards NEXT240 turbomolecular pump maintaining 10−<sup>4</sup> mbar pressure during operation. Ions are generated in a supersonic expansion from the PPV with a 1 keV electron beam counterpropagating down the expansion, oriented perpendicular to the ion beam axis of the PPC spectrometer. The ions are extracted from the expansion using three pulsed electrodes in a Wiley-McLaren configuration (Wiley and McLaren, 1955). A gear system was constructed to allow the distance between the PPV and the Wiley-McLaren plates to be adjusted, enabling extraction of different portions of the supersonic expansion. The first two plates (14 cm outside diameter with 2 cm inner diameter apertures) are spaced 6 cm apart between which the supersonic expansion propagates. The plates are pulsed with negative potentials giving ions an average of ∼225 eV translational kinetic energy while the third plate is typically held at −30 V. The ions are then guided through six focusing lens elements and one set of deflectors into COAT in the next chamber.

## Coat Trap Design

COAT is a linear octopole trap, as shown in **Figure 3**, based on a similar design used by Wester et al. (Otto et al., 2012). These devices have been known to be effective at cooling both external and internal degrees of freedom via buffer gas collisions (Gerlich, 1992; Wester, 2009; Otto et al., 2012; Redwine et al., 2013). For linear RF traps, the effective radial field is Veff(r) ∞ r n−2 , where r is the radius and n is the number of poles (Gerlich, 1992, 1995). The Veff plays a critical role in determining the trapping volume, as mentioned previously. An octopole configuration provides an optimal compromise in trapping volume by confining the ions along a smaller radius from the center of the trap, while

FIGURE 2 | Overview of the modified PPC spectrometer incorporating a new source and COAT. Labeled sections are as follows: (1) Source with pulsed valve/discharge assembly with Wiley-McLaren-style extraction. (2) COAT (3) Acceleration stack with potential switch. (4) Electrostatic chopper. (5) Pre-EIBT ion detector. (6) Electron Detector / EIBT. (7) Post-EIBT ion detector. (8) Neutral particle detector.

still allowing for facile extraction of the ions. This also allows for maximal laser overlap with the trapped ions for future IR excitation experiments.

The octopole trap is composed of RF rods with a 2.5 mm diameter arranged in a cylindrical array, with an inscribed inner diameter of 7.5 mm. The assembly (**Figure 3**) consists of four cylindrical rods mounted to each RF mount and assembled such that adjacent rods are mounted on opposing rod mounts. The trapping of ions in the radial direction is achieved by applying opposite RF phase to each RF rod mount giving adjacent cylindrical rods an alternating RF phase, generating an octopole field with a 4 MHz, 320 volt peak-to-peak RF waveform produced by a home-built RF generator (Jones et al., 1997; Jones and Anderson, 2000). Longitudinal confinement is achieved by endcaps on both sides of COAT with a 6 mm diameter opening which can be switched, using home built high voltage MOSFET switches, for loading, trapping, and extracting ions. Three equally spaced shaping electrodes surround the RF rods and, with limited field penetration, generate a potential field ramp to bias longitudinal storage of ions toward the exit endcap of the trap. The RF mounts, as well as the shaping electrodes, are all electrically isolated from the copper base of the trap by sapphire plates, taking advantage of sapphire's high thermal conductivity at cryogenic temperatures. The RF mounts along with a buffer gas shield surrounds the rods and shaping electrodes to provide a cold closed environment for collisional cooling. A thin layer of Apiezon N is used between all areas of mechanical contact to improve thermal conductivity at cryogenic temperatures.

The entire trap is mounted on a heating block that allows for variable temperatures between ∼10 and 300 K via heaters clamped around the heating block. The heating block, in turn, is mounted to the 2nd stage of a Sumitomo RDK-205D 4K Cryocooler cold head. COAT can be cooled to ∼17 K as measured by a silicon diode (LakeShore DT-471-CO) though it is an upper limit as H<sup>2</sup> freezes onto the electrodes of COAT indicating an inner surface temperature of ∼10 K. The 1st stage of the cold head is mounted to a thermal radiation shield (37 K) that encloses COAT. The buffer gas is pre-cooled to ∼40 K through a 3 mm diameter copper tube in thermal contact with the 1st stage of the cold head prior to injection into COAT through a hole in the base of the trap. The entire assembly is mounted on a movable flange on top of the COAT chamber allowing for the COAT to be aligned or moved out of the ion beam-line axis.

## Coat Operation

COAT is generally operated in one of three modes: cooling, heating or accumulation. The ability to heat and cool ions comes from controlling the initial translational energy of the precursor ions as they enter into COAT, as well as adjusting the duration of trapping. To reduce the initial translational energy of the ions entering the trap, the entire trap assembly is floated at an appropriate DC potential, and the incoming ions are focused into the trap using an entrance lens element. To further facilitate trapping and cooling of the ions, a pulse of pre-cooled buffer gas generated with a Gerlich-type valve (Gerlich et al., 2019) is used to raise the pressure in the trap to ∼10−<sup>2</sup> mbar prior to ion injection. Upon entering, the ions collide with buffer gas,

further reducing translational kinetic energy, and trapping them within COAT.

All source timing signals are controlled by a Stanford Research DG645 digital delay generator triggered by and prescaled to 1/100th of the laser repetition rate (1,037 Hz) while all COAT timings are controlled by a Quantum Composer 9,518 digital delay generator triggered off the prescaled signal. These timings control what mode COAT is run in: accumulation, cooling, or heating. In accumulation mode, the entrance endcap can be held at constant trapping voltage to facilitate accumulation of ions over multiple ion generation cycles. This can be synchronized with a faster rate of ion generation (20 Hz) and/or coupled with a longer EIBT trap time. In accumulation mode, only cold ions are available since most of the ions are trapped for a long period. In cooling and heating mode, the entrance endcap is switched from an attractive potential while loading ions to a repulsive potential to trap ions. This maximizes the quantity of ions entering the trap for a single cycle. A typical map of voltages on the essential elements is shown in **Figure 4** for the cooling/heating mode.

Within COAT, the ions undergo collisional cooling with the buffer gas for a pre-set period of time determined by whether or not vibrationally excited ions are desired. Shorter trapping time limits the thermalization and cooling of the ions, allowing the preparation of hotter ions. Increasing the trapping time allows thermalization of the trapped ions to the temperature of COAT. Similar traps have shown thermalization of the anions under similar pressures (∼10−<sup>2</sup> mbar) within 30 ms (Hock et al., 2012). Due to coupling with our EIBT, a trapping time of 80 ms is typical for maximizing the cooling time while still maintaining a 10 Hz duty cycle. After the set trapping time, the exit endcap is switched to an attractive potential to extract the ions from within COAT, and the ions guided into the next portion of the apparatus with three focusing elements.

The ions are then directed into a differentially pumped chamber where they are accelerated to a kinetic energy of 7 keV, re-referenced to ground (**Figure 2**, region 3), and mass selected by time of flight (**Figure 2**, region 4) for trapping within a cryogenically cooled electrostatic ion beam trap (EIBT) for 100 ms (**Figure 2**, region 6). This aspect of the experiment has been described in detail previously (Johnson et al., 2011). Within the EIBT, the ion packet is bunched and phase-locked to a 387.8 nm (Eh<sup>ν</sup> = 3.20 eV) laser pulse from a Ti:Sapphire regenerative amplifier (Clark MXR CPA-2000; 1.2 ps pulse width) at a repetition rate of 1,037 Hz using a field-programmable-gatearray-synced RF function generator (HP 3325). The oscillating ion packet interacts with the laser repeatedly over a 100 ms trapping period per experimental cycle, and the electron and neutral products are measured. The laser fluence is modulated by using a single 0.5 m focal length lens for high power density measurements vs. collimation with a 2.5:1 telescope on the 3.5 mm-diameter doubled output beam of the Ti:Sapphire laser. The power density for the collimated laser was estimated to be 2 × 10<sup>9</sup> W/cm<sup>2</sup> with the focused laser approximately 100x greater. Detached electrons are orthogonally extracted and mapped via velocity map imaging to a time and position sensitive detector. The center-of-mass eKE is determined from the three-dimensional electron velocity vector. Optimal resolution is achieved through selection of electrons with minimal zvelocities perpendicular to the detection plane as determined by the TOF of the center-of-mass for photoelectron detection by equatorially slicing the photoelectron spectra. This effect of slicing on the intensities in the photoelectron spectra was corrected for by dividing the sliced photoelectron spectrum by the energy-dependent acceptance function of the z-velocity slice (Bowen and Continetti, 2004). Calibration of O<sup>−</sup> 2 photoelectron spectra as well as the O<sup>−</sup> 2-photon events observed in the present experiments indicate 1eKE/eKE ∼4% full-width-at-halfmaximum (FWHM) at 1.74 eV for O−. After photodetachment, the resulting neutrals, no longer trapped within the EIBT, exit and impinge on a multiparticle time-and position-sensitive detector 1.3 m away from the laser interaction region (region 8), allowing determination of the product mass ratio and kinetic energy release (KER) for each event.

#### RESULTS

The capabilities of COAT are demonstrated here by comparing the signatures of the three concurrent photophysical channels occurring at Eh<sup>ν</sup> = 3.20 eV in the photoelectron spectra of O − 3 : (1) photodetachment O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup><sup>3</sup> <sup>+</sup> <sup>e</sup> <sup>−</sup>, (2) photodissociation/autodetachment O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup> − 2 ( <sup>2</sup>5g) + O(3P), and (3) photodissociation O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup>−( <sup>2</sup>P) + O2( <sup>1</sup>1g) followed by the photodetachment O−( <sup>2</sup>P) + hν → O(3P) by a second photon. The primary spectroscopic feature of channel (1) is a structured photoelectron spectrum in the 0.30–1.50 eV eKE range (Novick et al., 1979; Arnold et al., 1994; Garner et al., 1997; Mann et al., 2015). Channel (2) is observed in the spectra as a structured signal at low eKE (0.0– 0.4 eV) originating from sequential autodetachment of O<sup>−</sup> 2 (v′′ > 4). In addition, at high laser fluence there is also a 2-photon O − 2 (v′′ < 4) signal, observed as a broad baseline extending out to near the photon energy, produced by channel (2). In the second ion photodissociation channel (3), the photodissociation of O<sup>−</sup> 3 results in stable O−, which is then photodetached at high laser fluence and results in a peak at eKE = 1.74 eV. The effective laser fluence was changed in order to distinguish one and two photon processes. The features from these three channels exhibit varying intensities with different COAT temperatures, trapping times, and buffer gas identity. These features will be compared and interpreted with a temperature estimate for the photodetachment channel using a Franck-Condon simulation. Under no buffer gas conditions, as seen in the upper panel of **Figure 5** (purple trace) and the upper panel of **Figure 6** (black trace) no collisional heating or cooling takes place, which will be used as a reference for the initial internal excitation of the trapped anions.

#### Cooling

Over the course of an ion trapping cycle, ions within COAT collide with the pre-cooled buffer gas to remove both translational kinetic energy and internal energy, making the cooling performance dependent on buffer gas density and identity. The effects of varying buffer gas conditions can be seen in the total photoelectron spectra (electrons in coincidence

FIGURE 5 | The total photoelectron spectrum for O<sup>−</sup> 3 with different buffer gas and laser configurations is shown. Top panel (high laser fluence): spectra collected without buffer gas (purple trace), with H2/He buffer gas (blue trace) and with neat He buffer gas (black trace). Bottom panel (low laser fluence): Both O<sup>−</sup> 3 spectra collected at 17 K with 80 ms trapping time with either neat He buffer gas (black trace) or H2/He buffer gas (blue trace).

with both dissociative products and stable O3) in **Figure 5**. The peaks at low eKE (0.07, 0.19, and 0.32 eV) originate from the photodissociation/autodetachment O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> O − 2 ( <sup>2</sup>5) + O(3P) pathway (2) via photoexcitation to the <sup>2</sup>A<sup>2</sup> excited state as previously reported (Mann et al., 2015; Shen et al., 2017). At Eh<sup>ν</sup> <sup>=</sup> 3.20 eV, access to O<sup>−</sup> 2 (v′′ = 4,5,6) is energetically forbidden without vibrational excitation of O<sup>−</sup> 3 , as shown in the energetics diagram in **Figure 1**, so observation of vibrationally auto detaching O<sup>−</sup> 2 provides a sensitive test of parent anion internal energy. The peaks at eKE = 0.07 and 0.19 eV correspond to the vibrational autodetachment of O2(v′ = 0) + e <sup>−</sup> ← O − 2 (v′′ = 4,5) and are most prominent under no buffer gas conditions, indicating significant initial vibrational excitation in O<sup>−</sup> 3 .

Trapping the ions for 80 ms in COAT at a temperature <17 K significantly reduces the autodetachment channel when neat He (black trace) buffer gas was used and the channel is effectively eliminated when a 20:80 H2/He (blue trace) buffer gas mix was used. The temperatures noted are the measured temperatures of COAT, but their relation to the ion temperature is dependent on the duration of trapping to allow for thermalization. Even with longer trapping times there may be non-Boltzmann distributions of excitation in high-frequency vibrations. The 20:80 H2/He buffer gas mix cools the precursor ions more effectively than neat He due to collisional cooling being more effective with lighter buffer gases (Moriwaki et al., 1992, 1996). The empirical efficacy of He/H<sup>2</sup> gas mixtures for collisional cooling was first reported by Wang et al. in photoelectron spectroscopy studies (Wang and

FIGURE 6 | The total photoelectron spectrum for O<sup>−</sup> 3 with different temperatures, trap times, and laser configurations is shown. Top panel (high laser fluence): Spectra collected with short trapping times (500 µs) with higher (red trace) and lower (purple trace) entrance lens acceleration compared to no buffer gas (black trace). Bottom panel (low laser fluence): Short trapping time at cold temperatures (800 µs, 17 K, neat He buffer gas) shown in brown, longer trapping times at room temperature (30 ms, 300 K, neat He buffer gas) shown in black, long trapping times at cold temperatures (80 ms, 17 K, H2/He buffer gas) shown in blue.

Wang, 2008), and has also been found to be effective in other systems (Kamrath et al., 2011; Hock et al., 2012), including O<sup>−</sup> 3 as shown here.

The feature at 1.74 eV eKE is a result of (3) photodissociation O − <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup>−( <sup>2</sup>P) + O2( <sup>1</sup>1g) followed by sequential photodetachment O−( <sup>2</sup>P) + hν → O(3P) (Shen et al., 2017). As shown in the upper panel (**Figure 5**), using a focused laser the O<sup>−</sup> photodetachment signal is much stronger, while use of a collimated laser caused a significant decrease in this two photon signal, increasing the sensitivity to the hot bands in the stable channel. Upon cooling (**Figure 5**, upper panel, black line), the fraction of events resulting in channel (3) is reduced compared to the no-buffer-gas conditions (purple line) under similar laser fluence. The reduction in the signal under the H2/He condition is due to lower laser fluence rather than an effect of cooling.

The dominant channel observed in the total photoelectron spectra is the photodetachment (1) O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup><sup>3</sup> <sup>+</sup> e <sup>−</sup> yielding a structured photoelectron spectrum in the eKE range between 0.30 and 1.50 eV as shown in **Figure 5**. The photoelectron spectra are consistent with the electron affinity (EA) of O<sup>3</sup> previously determined to be 2.10 eV and a Franck-Condon vibrational progression in the totally symmetric v<sup>1</sup> and v<sup>2</sup> modes of the O3(X˜ <sup>1</sup>A1) ground state (Arnold et al., 1994). The vibrational energies for O<sup>−</sup> 3 have been previously reported (Arnold et al., 1994) and are summarized in **Table 1** with the 1 0 1 hot band location annotated in **Figure 5**. Under the coldest

TABLE 1 | Vibrational energies used in Franck-Condon simulation (Arnold et al., 1994).


conditions, the 1<sup>0</sup> 1 hot band is within the noise of the spectra indicating little if any population in the <sup>ν</sup><sup>1</sup> mode of O<sup>−</sup> 3 . Franck-Condon simulations (**Figure 7**) for the stable (1) O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> O<sup>3</sup> + e <sup>−</sup> channel have been carried out with PESCAL (Ervin et al., 1988) using single point calculations in Gaussian 03 (Frisch et al., 2004) with previously reported geometries (Arnold et al., 1994; Liang et al., 2007) and frequencies (**Table 1**) (Arnold et al., 1994). The Franck-Condon factors were calculated using the independent Morse oscillator approximation due to the strong effects of anharmonicity for transitions to high vibrational levels of O3. The simulated spectra were generated by convolving the stick spectra with a Gaussian convolution consistent with the 4% 1eKE/eKE resolution. The stick spectra were calculated at 0 K in all modes for cold conditions (top panel, ν1, ν2, ν<sup>3</sup> = 0 K) and a Boltzmann distribution for hot conditions (bottom panel, ν<sup>1</sup> = 2,000 K ν<sup>2</sup> = 1,500 K ν<sup>3</sup> = 0 K). The dominant progression is the ν<sup>1</sup> symmetric stretch populating O<sup>3</sup> vibrational states from ν<sup>1</sup> = 0 to ν<sup>1</sup> = 5 with the minor progression being combination bands of ν<sup>2</sup> = 1 with ν<sup>1</sup> = 0 to ν<sup>1</sup> = 5. The temperature of ν<sup>3</sup> was found to have no significant contribution to the spectra, consistent with previous assignments (Arnold et al., 1994), and was therefore left at 0 K. The 0 K simulation provides an acceptable match to the photoelectron spectrum under optimal cold conditions.

Overall COAT demonstrates the ability to thermalize the ions to a temperature cooler than through the use of supersonic expansion alone. This is consistent with similar accumulation traps that have been demonstrated to be effective at cooling and thermalizing both small (Hock et al., 2012) and large molecules (Boyarkin and Kopysov, 2014). As also found by other research groups ( Wang and Wang, 2008; Hock et al., 2012), the degree of cooling is dependent on the buffer gas with the mixture of He/H<sup>2</sup> being found to be more effective than neat He. The difference is observed as the suppression of pathway (2) and the significant reduction of pathway (3).

#### Heating

Upon loading into COAT, precursor anions collide with the buffer gas transforming translational kinetic energy into rovibrational heating of the ions. Total photoelectron spectra under various heating conditions are shown in **Figure 6** in contrast to the cooling conditions shown in **Figure 5**. These spectra are scaled to the 0–0 peak in the photodetachment channel (1) to more clearly distinguish the relative differences in dissociative events. Autodetachment peaks corresponding to electrons arising from O<sup>−</sup> 2 (v′′ = 4, 5, and 6), with peaks located at 0.07, 0.19, and 0.32 eV respectively, are clearly resolved under all hot conditions. While v′′ = 4 is observed under the conditions

of no buffer gas (**Figure 6**), top panel, black trace), a significant enhancement in intensity of the O<sup>−</sup> 2 (v′′ = 5,6) is observed under all hot COAT conditions (**Figure 6**). The sensitivity of the autodetachment channel to O<sup>−</sup> 3 vibrational excitation infers a strong coupling of vibrational excitation within the <sup>2</sup>A<sup>2</sup> excited state to highly vibrationally excited products (Shen et al., 2017). The expansion of the parent anion wavefunction upon vibrational excitation of O<sup>−</sup> <sup>3</sup> may lead to an increase in Franck-Condon overlap with the <sup>2</sup>A<sup>2</sup> excited state.

The ability to influence the dissociative pathways through heating the precursor ions is further demonstrated with channel (3). The 2-photon process is enhanced upon heating at similar laser power density. Under no buffer gas conditions (**Figure 6**), top panel, black trace) the amplitude for the O<sup>−</sup> photodetachment is lower than under heating conditions (red and purple traces). This is consistent with increased FC overlap with the <sup>2</sup>A<sup>2</sup> state upon photoexcitation increasing the fraction of events from channels (2) and (3). The primary parameters affecting the heating of the ions are settings that affect the kinetic energy of the precursor anion, and trapping times. Settings such as Wiley-McLaren ion extraction voltage, the COAT float voltage, as well as the COAT entrance lens voltage can increase the temperatures of the ions by accelerating to larger translational energies just prior to initial collisions within COAT.

The hottest conditions (**Figure 6**), upper panel, red trace) were achieved with a combination of short trapping time (500 µs), He buffer gas, and accelerating ions with the entrance lens just before trapping. This resulted in a significantly larger contribution from the autodetachment channel (2) as well as the O<sup>−</sup> photodissociation channel (3) with the 2-photon O<sup>−</sup> signal amplitude dominating over the stable channel. Reducing the entrance lens acceleration voltage (by ∼50 V) under the same source conditions (upper panel, purple line) still shows significant heating, but to a lesser degree as indicated by the amplitude of the autodetachment signal. The increased spectral congestion with the autodetachment channel is due to autodetachment to O2(v′ > 0), which has been previously reported in electron scattering experiments at high incident electron kinetic energy (Allan et al., 1996b). The dominant autodetachment channel produces O2(v′ = 0) + e <sup>−</sup> even as the precursor ions are heated to a higher degree, as evidenced by the resolved O<sup>−</sup> 2 (v′′ = 4,5,6) autodetachment peaks. This is in contrast to the DEA experiments carried out by Allan et al. where the distribution of autodetached electrons originate almost equally from the O2(v′ = 0) as from O2(v′ = 1) products as the impact electron kinetic energy increases. The difference may be a result of the internal energy distribution in collisionally activated precursor anions compared to the well-defined impact electron energy in the DEA experiments (Allan et al., 1996b). The increase in precursor ion temperatures does not appear to significantly increase the 2-photon signal from O<sup>−</sup> 2 (v′′ < 4).

Under collimated laser conditions, the shortened trapping time of 800 µs in COAT (**Figure 6**), lower panel, brown trace) yields a larger distribution of autodetachment electrons as well as hot bands in contrast to the cold spectra (**Figure 6**), lower panel, blue trace). This indicates a higher average ion temperature than the ions thermalized for 30 ms at 300 K as shown in **Figure 6** (bottom panel, black trace). Upon heating, the stable channel shows a significant increase in photodetachment hot bands, particularly for the 1<sup>0</sup> 1 and 1<sup>0</sup> 2 transitions. The amplitude for the hot bands in the bottom panel of **Figure 6** is consistent with the expected trend from the amplitude of the autodetachment channel, with the shorter 800 µs trapping time exhibiting prominent peaks for 1<sup>0</sup> 1 and 1<sup>0</sup> 2 hot bands. In the hottest spectrum (**Figure 6**), top panel, red trace) it can be seen that the 1<sup>0</sup> 1 hot band is nearly half the amplitude of the 0–0 transition in that spectrum. Additionally, a significant increase in spectral congestion due to sequence bands is observed, most notably in the hottest spectrum where the 1<sup>2</sup> 0 peak exhibits the largest amplitude in the stable spectra.

A Franck-Condon simulation with the temperature of the vibrational modes set to ν<sup>1</sup> = 2,000 K, ν<sup>2</sup> = 1,500 K is shown in **Figure 7**, providing an estimate for the temperature of the ions under the hottest conditions observed. These temperatures should be considered a lower limit to the ion temperature given that a significant fraction of the ions undergo photodissociation, which is not taken into consideration in the simulation. The temperature difference in vibrational modes is explained by the expected non-Boltzmann distribution of vibrational excitation due to collisional heating as well as the opening of the photodissociation/autodetachment pathway with parent ion vibrational excitation. This excitation introduces competition between the stable and dissociative channels. Additionally, it has been found that the bending mode (ν2) significantly contributes to channel (2) (Shen et al., 2017). The sequence bands shown in the Franck-Condon simulation show that significant spectral congestion is caused by transitions from excitation of the ν<sup>1</sup> and ν<sup>2</sup> modes with up to three quanta of excitation in the precursor anion.

The heating of ions using COAT is shown to have a dependency on the voltage settings just prior to their entry into COAT, as well as the trapping duration. Increasing the kinetic energy of the ions prior to their entry into COAT and shorter trapping times resulted in hotter ions. In the case of ozonide, pathways (2) and (3) are significantly increased along with an increase in spectral congestion for pathway (1). This demonstrates an effective way to exert control over the ion temperature to examine the effects of internal excitation on dissociation dynamics and thermally activated processes.

#### CONCLUSIONS

The addition of COAT to the PPC spectrometer enables the preparation of colder anions than achievable with a supersonic expansion alone, as well as the preparation of collisionally heated ions in a controlled manner. The elimination of the photodissociation/autodetachment channel (2) O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> O − 2 ( <sup>2</sup>5g, v > 4) + O(3P) channel demonstrates the ability for COAT to internally cool precursor anions. The enhancement of both channels (2) and (3) O<sup>−</sup> <sup>3</sup> <sup>+</sup> <sup>h</sup><sup>ν</sup> <sup>→</sup> <sup>O</sup>−( <sup>2</sup>P) + O2( <sup>1</sup>1g), as well as the appearance of hot bands in the photoelectron spectrum for channel (1), indicate that varying trapping conditions can also be used to produce hot precursor anions. Most importantly, COAT has demonstrated the ability to influence the dissociation dynamics of O<sup>−</sup> 3 . Cooling precursor ions to their vibrational ground states will be invaluable in future experiments, including studies of much larger systems that have not been sufficiently cooled by supersonic expansion

## REFERENCES


alone, such as the tert-butoxide anion (Shen et al., 2014). Wellcharacterized anion temperatures will also be integral for further laser excitation experiments, where the effects of direct infrared excitation of specific modes will be examined (Otto et al., 2014a,b; Ray et al., 2017). Of particular interest is cooling HOCO anions to their vibrational ground state prior to infrared photoexcitation. This will extend the work conducted on this system by studying how product branching ratios between OH + CO and H + CO<sup>2</sup> as well as tunneling rates for HOCO → H + CO<sup>2</sup> are impacted by controlled anion excitation (Lu et al., 2007; Johnson et al., 2014). Additionally, the ability to heat ions through collisional excitation can provide an approach for examination of thermally activated processes, providing increased flexibility in PPC spectroscopy.

## DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

## AUTHOR CONTRIBUTIONS

RC conceived the experiment. BS designed and assembled COAT. All authors assisted in modifying the PPC spectrometer to accommodate COAT and designed the experiments. BS, KL, and YB collected and analyzed the data. BS wrote the manuscript. KL, YB, and RC edited the manuscript.

## FUNDING

This material is based on work supported by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under award number DE-FG03-98ER14879.

## ACKNOWLEDGMENTS

We acknowledge helpful discussions with R. Otto, R.D. Thomas, and Joseph Taulane in the design and implementation of COAT.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Shen, Lunny, Benitez and Continetti. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Quantum Dynamics and Kinetics of the F + H<sup>2</sup> and F + D<sup>2</sup> Reactions at Low and Ultra-Low Temperatures

Dario De Fazio<sup>1</sup> , Vincenzo Aquilanti <sup>2</sup> and Simonetta Cavalli <sup>2</sup> \*

1 Istituto di Struttura della Materia, Consiglio Nazionale Delle Ricerche (CNR), Rome, Italy, <sup>2</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Perugia, Italy

Integral cross sections and rate constants for the prototypical chemical reactions of the fluorine atom with molecular hydrogen and deuterium have been calculated over a wide interval of collision energy and temperature ranging from the sub-thermal (50 K) down to the ultra-cold regimes (0.5 mK). Rigorous close coupling time-independent quantum reactive scattering calculations have been carried out on two potential energy surfaces, differing only at long-range in the reactants' channel. The results show that tunnel, resonance and virtual state effects enhance under-barrier reactivity giving rise to pronounced deviations from the Arrhenius law as temperature is lowered. Within the ultra-cold domain (below 1 mK), the reactivity is governed by virtual state effects and by tunneling through the reaction barrier; in the cold regime (1 mK–1 K), the shape resonances in the entrance channel of the potential energy surface make the quantum tunneling contribution larger so enhancing cross sections and rate constants by about one order of magnitude; at higher temperatures (above 10 K), the tunneling pathway enhanced by the constructive interference between two Feshbach resonances trapped in the reaction exit channel competes with the thermally activated mechanism, as the energy gets closer to the reaction barrier height. The results show that at low temperatures cross sections and rate constants are extremely sensitive to small changes in the long-range intermolecular interaction in the entrance channel of the potential energy surface, as well as to isotopic substitution.

Keywords: scattering resonances, tunnel effect, Wigner threshold law, kinetic isotope effect, cold and ultra-cold collisions

## 1. INTRODUCTION

The F + H<sup>2</sup> reaction has been extensively studied for many years from a variety of perspectives, as reported in numerous papers and reviews appeared in the literature (see e.g., Manolopoulos, 1997; Liu, 2001; Der Chao and Skodje, 2002; Althorpe and Clary, 2003; Qiu et al., 2006; Wang et al., 2018 and references therein). Its peculiarity of being accessible both to theory and to experiments makes it an important prototype to validate methodologies to be used for more complex hydrogen atom transfer reactions, that show up in many areas of chemistry, ranging from processes in space (Neufeld et al., 2005; Goumans and Kästner, 2010) to reactions in biological environments (Nagel and Klinman, 2006). The discovery of the interstellar HF molecule (Neufeld et al., 1997) and its recent observation in several astrophysical environments (see e.g., Emprechtinger et al., 2012 and references therein), has also made this system very appealing for astro-chemistry. The

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Balakrishnan Naduvalath, University of Nevada, Las Vegas, United States Bas Van De Meerakker, Radboud University Nijmegen, Netherlands

\*Correspondence:

Simonetta Cavalli simonetta.cavalli@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 05 February 2019 Accepted: 24 April 2019 Published: 14 May 2019

#### Citation:

De Fazio D, Aquilanti V and Cavalli S (2019) Quantum Dynamics and Kinetics of the F + H2 and F + D2 Reactions at Low and Ultra-Low Temperatures. Front. Chem. 7:328. doi: 10.3389/fchem.2019.00328 large chemical stability and large dipole moment of the HF molecule make it favorably detectable, so that it may serve as a tracer for molecular hydrogen within the diffuse interstellar medium (Sonnentrucker et al., 2010), a valid alternative to CO molecule, the main tracer of molecular gas. An account of the chemistry of the HF molecule is given in Zhu et al. (2002). Being the F + H<sup>2</sup> reaction the only source of interstellar hydrogen fluoride, reliable kinetic data at low temperatures are of course highly desirable. In recent years, the field of cold and ultra-cold chemistry has seen a considerable growth becoming a frontier both for applied and theoretical research in physics and chemistry (see e.g., Smith, 2008; Krems et al., 2009; Balakrishnan, 2016). The interested reader is directed to the recent review articles (Herschbach, 2009; Hutzler et al., 2012; Quemener and Julienne, 2012; van de Meerakker et al., 2012) for a detailed description of experimental and theoretical developments of the field of cold and ultra-cold molecules, and to (Lara et al., 2012; Tizniti et al., 2014; Costes and Naulin, 2016) for progress on chemical reactivity at low temperature.

The F + H<sup>2</sup> reaction and its isotopic counterpart F + D<sup>2</sup> are exothermic with a low energy barrier along the reaction path connecting reactants to products. At thermal or higher energies these reactions occur as thermally activated process. However, at sub-thermal energies the reaction gains access to quantum phenomena and the reactivity is higher than expected on the basis of classical theories. Quantum effects, such as scattering resonances, i.e., the formation of metastable states of the collision complex, and tunneling through the reaction barrier play a progressively larger role on the reactivity of these systems (see e.g., Althorpe and Clary, 2003 and references therein), as energy or temperature decrease. Quantum threshold effects manifest themselves only at very low temperature, typically 1 K or less, when the de Broglie wavelength becomes comparable to, or longer than, the distances between colliding species (Simbotin et al., 2011, 2014). Theoretical approaches based on classical mechanics fail to describe the under-barrier reactivity, and therefore a detailed understanding of dynamics and kinetics requires quantum mechanical treatments and realistic potential energy surfaces. For a survey of the commonly used scattering theory methods see Schatz (1996).

The analysis of the resonances for the F + H<sup>2</sup> reaction has been the subject of several previous theoretical and experimental works, for a recent review see Wang et al. (2018). Most of the effort has been devoted to understand the features above 20 meV coming from the large number of the metastable states supported by the van der Waals well in the exit channel (Manolopoulos, 1997; Der Chao and Skodje, 2002; Aquilanti et al., 2004). Nevertheless, it was also evident from experiments and theory (Takayanagi and Kurosaki, 1998; Aquilanti et al., 2005a) that resonances trapped by the van der Waals well in the entrance channel, although probably too narrow to be experimentally resolved, could play some role. In the following we show that the latter dominate the dynamics in the cold energy regime.

In this paper we investigate the dynamics and kinetics of the F + H<sup>2</sup> and F + D<sup>2</sup> reactions at low temperatures, in a wide interval extending from near absolute zero to 50 K, where quantum mechanical effects control chemical reactivity. The aim is to determine how large they are and where they show up. In the quantum mechanical low-temperature regime, chemical reactivity is most sensitive to the details of the potential energy surface and small changes in the entrance channel interaction can enhance cross sections and rate constants by orders of magnitude. To this purpose, numerically exact quantum scattering calculations of integral cross sections and rate constants have been carried out on two potential energy surfaces, the Stark and Werner potential energy surface (SW PES hereafter) (Stark and Werner, 1996) and PES-II (Aquilanti et al., 2001, 2005b), differing only in the long-range interaction of the F atom with the H<sup>2</sup> molecule. Namely, the entrance channel van der Waals well of the PES-II is deeper, wider and shifted to larger intermolecular distances than for the SW PES, see Aquilanti et al. (2005b) for more details.

In the last ten years new ab-initio potential energy surfaces have been published for this reaction: they are denoted FXZ (Fu et al., 2008), CSZ (Chen et al., 2015), LWAL (Li et al., 2007; Lique et al., 2011) PESs. Unlike the SW PES, these surfaces include the effect of spin-orbit coupling. However, as more extensively discussed in a previous paper (De Fazio et al., 2016), their reliability in describing the reaction dynamics in the cold and ultra-cold regimes is not as satisfactory as at higher energies. As is known, the neural network algorithm used in the fit of FXZ/CSZ PESs and the splines used to merge the three different local fits of LWAL PES can give rise to significant numerical instabilities when the ab-initio grid points are not dense enough, as they should be to push quantum scattering calculations down to the Wigner limit. The results of some test calculations below 1 K, have shown that none of them met the convergence requirements achieved with SW PES probably because of the artifacts of the fits to the ab initio points, and so we preferred not to present them. As pointed out in reference (Balakrishnan, 2016), the situation for the F + H<sup>2</sup> system is far from ideal. None of the available PESs provide an accurate treatment of the long-range interaction. As mentioned by the authors of both reference (Chen et al., 2015) and reference (Lique et al., 2011), further refinements in the description of the interaction around the van der Waals well in the entrance channel are needed in order to use CSZ and LWAL PESs in scattering calculations at energy below 0.1 meV.

The choice of PES-II is motivated by the recent experimental measurements (Tizniti et al., 2014) which have confirmed as realistic the description of the van der Waals region in the entrance channel, while the SW PES is used here for purpose of comparison with the results of other theoretical investigations. Further experimental evidences of the reliability of PES-II at low collision energies will be shown in the present article. The SW PES and PES-II have the same barrier height but a slightly different width. Thus, the comparison between the two PESs allows to assess the relevance that barrier width, other than barrier height and exo-ergicity, has on the intermolecular kinetic isotope effect of H-transfer reactions at low temperature.

The first quantum reactive scattering calculations for the F + H<sup>2</sup> system at ultra-cold temperatures were made more than 15 years ago (Balakrishnan and Dalgarno, 2001; Bodo et al., 2004). However, these papers presented only calculations with zero total angular momentum, so that reliable information was obtained only in the Wigner regime. Convergent rate constants, calculated by the hyper-quantization technique (Aquilanti et al., 1998), down to a few Kelvin, were published by our research group (Aquilanti et al., 2005b). Here, we extend this previous study at very low temperatures where the sensitivity to the entrance channel interaction is larger. Because of the relevance that the analysis of the kinetic isotope effect (KIE) has especially in organic chemistry and biochemistry (see e.g., Roston et al., 2013), the temperature dependence of the intermolecular kinetic isotope effect has also been assessed. The quantum dynamics and kinetics of the F + H<sup>2</sup> and F + D<sup>2</sup> reactions are predicted form first principles using a coupled channel method summarized in section 2. The effects of tunneling, resonances and isotope substitution on cross sections and rate constants are discussed in section 3; conclusions follow in section 4.

#### 2. CHEMICAL REACTIONS FROM FIRST PRINCIPLES: A SUMMARY OF THE THEORETICAL METHODOLOGY

Within the quantum mechanical time independent framework for studies of reaction dynamics, we use the Born-Oppenheimer separation of electronic and nuclear motion and solve the Schrödinger equation for the motion of nuclei

$$\left[-\frac{\hbar^2}{2\mu}\nabla^2 + V - E\right]\Psi = 0\tag{1}$$

controlled by the ground electronically adiabatic potential energy surface V, with µ being the reduced mass of the system and ∇ denoting the Laplacian operator, applying a convergent closecoupling technique. To describe the concerted bond breaking and bond forming taking place in the hydrogen atom transfer reaction, we use hyper-spherical coordinates: the hyperradius, ρ, playing the role of a reaction coordinate being capable to describe democratically both the reactants and products channels, and five angular variables. Alternative parameterizations of the hyperangles have been proposed, see references (Pack and Parker, 1987; Launay and Le Dourneuf, 1989; Aquilanti et al., 2000). The computer code (Skouteris et al., 2000) used to carry out scattering calculations implements the formalism in Delves hyper-spherical coordinates.

The wave function 9 is expressed in terms of eigenfunctions of the total angular momentum and internal states of the system. The integration over the angular variables leads to a multichannel scattering problem as a function of ρ

$$\left[\frac{d^2}{d\rho^2} + \frac{2\mu}{\hbar^2} \left(E - \epsilon\_n\right)\right] F\_{nn'}(\rho) - \sum\_{n'} W\_{nn'} F\_{nn'}(\rho) = 0 \tag{2}$$

where ǫ<sup>n</sup> are effective hyperspherical potentials potentials and Wnn′ is the coupling between them. The multichannel equations are then solved subject to scattering boundary conditions

$$F\_{nn'}(\rho) = 0 \quad \text{as} \quad \rho \to 0 \tag{3}$$

$$F\_{nn'}(\rho) \sim \frac{1}{2ik\_n} \left( \delta\_{nn'} \exp[-ik\_n \rho] - S\_{nn'}^{\;I}(E) \exp[ik\_n \rho] \right)$$

$$\text{as } \rho \to \infty \tag{4}$$

to yield the partial wave scattering matrix elements S J nn′(E) : these are the fundamental quantities for generating reactive transitions from an initial state n to a final state n ′ as a function of total energy. For specific total energy, E, and total angular momentum quantum number, J, the computer code [Skouteris et al. (2000)] provides the reactive scattering matrix. The square moduli of the S-matrix elements

$$P\_{nn'}^{J}(E) = |\, \mathcal{S}\_{nn'}^{J}(E) \mid^{2} \tag{5}$$

are state-to-state reaction probabilities yielding the products in the roto-vibrational state n ′ starting from the reactants in the roto-vibrational state n.

Quantum reactive scattering calculations serve to generate differential and integral cross sections as well as rate constants, the observable quantities in reaction dynamics and kinetics experiments. The comparison between experiments and theory supplies the most stringent test for the reliability of potential energy surfaces. Formulas used to calculate the cross sections and the rate constants shown in **Figures 1**, **2** are summarized in the following.

The initial state-selected total integral cross section at given values of the relative translational energy of reactants, E<sup>c</sup> , can be expressed as the sum of reaction probabilities

$$\sigma\_n(E\_c) = \frac{\pi}{g\_n k\_n^2} \sum\_{n'} \sum\_{J} (2J+1) \, P\_{nn'}^{J}(E) \tag{6}$$

over all the final states, n ′ , and the partial waves, J, accessible during the reaction, with g<sup>n</sup> and k<sup>n</sup> being the initial state degeneracy factor and wave vector, respectively. The dependence of the rate constant on temperature is calculated averaging σ<sup>n</sup> over the Maxwell-Boltzmann distribution of the initial translational energy

$$k\_n(T) = \left(\frac{2}{k\_B T}\right)^{3/2} \frac{1}{(\pi m)^{1/2}} \int\_0^\infty E\_c \,\sigma\_n(E\_c) \, \exp\{-E\_c/k\_B T\} \,\mathrm{d}E\_c \tag{7}$$

where k<sup>B</sup> is the Boltzmann constant and m is the reduced mass of the reactants. The thermal rate constant is the sum over all the initial states accessible at a given temperature T weighted for the relative population of the state n, where n ≡ (v, j) stands for the vibrational and rotational quantum numbers v, j of the molecule.

Quantum scattering calculations on SW PES and PES-II have been carried out using a parallelized variant of the computer code (Skouteris et al., 2000) implementing the Enhanced Renormalized Numerov method (Colavecchia et al., 2003) for the integration of the hyperradial multichannel equations in Equation (2) above, see references (De Fazio, 2014; De Fazio et al., 2016) for more details. These changes

make the code more efficient, especially at very low collision energies. The input parameters used in the production run are given in **Tables S1**, **S2**. After extracting the scattering matrix we calculate the total integral cross sections from Equation (6) and then perform the thermal averaging in Equation (7) to obtain the rate coefficients. These latter have been divided by the electronic partition function of the fluorine atom to account for its open-shell structure. As far as the temperature dependence of the electronic partition function is concerned, it has been properly taken into account in rate constant calculations. However, in the range of temperature investigated, it is essentially negligible (<0.001 %) and was not considered in the calculation of the tunneling correcting factor in Equation (12).

## 3. RESULTS AND DISCUSSION

The effects of quantum mechanical tunneling and resonances on reaction cross sections and rate constants of the title reactions are discussed in the following.

## 3.1. Reaction Cross Sections

The total integral cross sections (ics) of the F + H2(v = 0;j = 0) → HF + H and F + D2(v = 0;j = 0) → DF + D chemical reactions have been calculated in a wide collision energy interval ranging from the ultra-cold region to above the reaction barrier (10−<sup>6</sup> - 10<sup>2</sup> meV), as shown in **Figure 1**. In each panel, the results obtained using SW PES and PES-II are compared. In the right panel we also report the experimental values of reference (Che et al., 2007) with the relative error bars. The good agreement with PES-II results corroborates the reliability of this PES for describing the low collision energy dynamics of this system.

The ics have a very similar dependence on energy, with a minimum at about 4 meV and the appearance of narrow resonance patterns between 0.01 and 2 meV. However, the number of resonance peaks, their position and intensity vary markedly as the PES and the isotopic variant are changed. Broader resonance features also appear between 20 and 100 meV. Below 0.01 meV the ics increase smoothly with decreasing collision energy, quickly approaching the limiting behavior predicted by the Wigner's threshold law (Wigner, 1948). The broader peaks appearing above 20 meV have been analyzed in detail in previous papers (Castillo et al., 1996; Der Chao and Skodje, 2002; Aquilanti et al., 2004) which have provided a satisfactory description of the spectrum of metastable states of the F + H<sup>2</sup> reaction. In particular, the oscillations observed have been interpreted as an interference effect between two of them: a resonance trapped in the transition state region and the other one supported by the van der Waals well of the exit channel (Cavalli and De Fazio, 2007, 2011; Sokolovski et al., 2007b). A clear explanation of the oscillatory pattern in the integral cross section has also been given in terms of Regge oscillations (Sokolovski et al., 2007a).

#### 3.1.1. The Cold Collision Regime

As far as the sharp resonance peaks in the cold energy regime are concerned, we have found that they are narrow isolated resonances affecting just a single partial wave. From the analysis of the reaction probabilities, we have been able to label each peak with the value of the total angular momentum quantum number, J, at which the resonance state appears. As shown in **Figure 1**, in most cases the sequences of the J values labeling the resonances are not regular and many values are missing. This observation suggests that the observed patterns do not originate from the rotational levels of a single metastable state. To support this hypothesis, we have calculated the vibrational energies of the triatomic van der Waals complex in the entrance channel at selected J values, see **Table 1**. For the calculation of the rotovibrational energies we have used an adiabatic model. In brief, we have extended the J = 0 quasi-bound state calculations of Takayanagi and Kurosaki (1998) to larger values of J. The energies have been calculated by solving, at fixed J, a one-dimensional bound state problem in R, the intermolecular distance between the F atom and the H2/D<sup>2</sup> molecule. The matrix elements of the Hamiltonian have been evaluated numerically in a basis of asymptotic diatomic roto-vibrational functions. More details of the calculations done will be given elsewhere.

From the results of **Table 1**, we can see that the number of rotational levels for each vibrational state coincides, in all cases, with the lowest value of J in each rotational progression shown in **Figure 1**. The J- selected peaks appearing in the ics are therefore due to shape resonances trapped in the van der Waals welllocated in the entrance channel of the reaction: increasing the centrifugal energy the (quasi-)bound vibrational states escape from the well affecting the reactivity of the two successive partial waves. Thus, the number of bound vibrational states of the van der Waals complex determines the number of J progressions observed in each panel of **Figure 1**. These conclusions also explain why the number of peaks is different for each isotopic variant studied as well as for the two PESs: the number of resonance states is greater the stronger the long-range forces and the lower the vibrational frequency of the triatomic complex. The deeper and wider van der Waals well of PES-II supports more states that of SW PES: for example in the H<sup>2</sup> case two vibrational states are bound in PES-II and just one in SW PES. Moreover, the vibrational frequency decreases with the increase of the isotopic mass so that the number of bound states is larger for the F· · · D<sup>2</sup> van der Waals complex: three vibrational states are bound in PES-II and two in SW PES. Finally we note that these resonance features were also found in reference (Lique et al., 2011) but were erroneously attributed to Feshbach resonances in the exit van der Waals well.

#### 3.1.2. The Ultra-Cold Limit

In the ultra-cold energy range (below 0.001 meV) only J = 0 contributes to the partial wave expansion in Equation (6), so that the dependence of ics on collision energy follows the limiting behavior well-described by the Wigner's threshold law (Wigner, 1948):

$$
\sigma\_W = \frac{4\pi\hbar\beta}{k} \tag{8}
$$

where σ<sup>W</sup> denotes the ics in the Wigner regime, β is the imaginary part of the scattering length [Balakrishnan et al.

TABLE 1 | Roto-vibrational states of the three-atomic complexes F· · · H<sup>2</sup> and F· · ·D<sup>2</sup> supported by the entrance channel van der Waals well on SW PES and PES-II.


J and v are the total angular momentum and vibrational quantum numbers, respectively. E<sup>t</sup> and E<sup>b</sup> denote the total and the bound state energies (the zero energy is located at the bottom of the reactant valley).

(1997)] and k = √ 2mEc/h¯ is the reactants' wave number. Fitting the ics shown in **Figure 1** to Equation (8) we have obtained the values of the imaginary scattering lengths, see **Table 2**. Comparing the β values reported in the table, we see that the dispersion forces and isotopic substitutions influence both the collision energy of the onset of the Wigner regime and the magnitude of β. Because of the stronger long-range interaction potential of PES-II with respect to that of SW PES, the Wigner regime manifests itself to lower collision energy (approximately at 10−<sup>4</sup> meV for PES-II, as shown in **Figure 1**). The larger barrier width of PES-II reduces significantly the β values. Also, we can note that lighter isotopic substitution yields larger β values. Again, for the H<sup>2</sup> case the Wigner regime is encountered at higher energies although the effect is of minor entity than changing the entrance channel of the PES. However, the large differences found in the F + H<sup>2</sup> case, where β changes by more than one order of magnitude, suggest that tunneling cannot be the only reason of this different behavior between the PESs.

TABLE 2 | Values of the imaginary scattering length, β, in atomic units.


In reference Bodo et al. (2004), analyzing elastic and reactive J=0 reaction probabilities obtained with the SW PES, the authors were able to obtain the real and imaginary parts of the scattering length. The values obtained were a = (−2.0 − 6.3 × 10−<sup>2</sup> i)Å and a = (3.95 − 8.6 × 10−<sup>4</sup> i)Å for the FH<sup>2</sup> and FD<sup>2</sup> systems, respectively. Comparing with the values reported in **Table 2** we can see that the imaginary part of the scattering lengths is in perfect agreement with our results. The negative value obtained for the real part of the scattering length for H<sup>2</sup> is attributed to the presence of a virtual state associated with the van der Waals well in the entrance channel and located around 0.3 meV below the reactive threshold. Fingerprints of this effect can also be noted in the left panel of **Figure 1**, where the SW PES curve shows up a faster increase around to 0.01 meV before reaching the Wigner regime. Additional evidences will be given later. For the F+D<sup>2</sup> reaction, the positive value of the real part of the scattering length suggests that the scattering may be influenced by a resonance state. However, no structure has been detected in the reactive observables.

## 3.2. Reaction Rates at Low and Ultra-Low Temperatures

In **Figure 2**, the rate constants for the production of HF and DF molecules in the temperature range between 0.5 mK and 50 K are shown on log-log plots. Panels (A) and (B) show the results of quantum scattering calculations using SW PES and PES-II, respectively. As we can see from the figure, the kinetics of the two reactions studied is markedly influenced by resonance and tunnel quantum effects. The strong J-selected resonance features appearing in the cold collision domain, see **Figure 1**, survive to the Boltzmann averaging, see Equation (7) in section 2, giving a maximum at about 1 K. At lower temperature the rates decrease until they reach the Wigner regime at about 1 mK becoming independent of temperature. However, we can note that the SW PES curve in the left panel of **Figure 2** behaves differently from the other, showing a minimum around 0.1 K that is not present in the other curves. This is again a manifestation of the virtual state effect discussed in the previous section. As discussed in reference (Simbotin and Côté, 2015), in the presence of a virtual or a resonance state near to the reactive threshold, in the so called Near Threshold Resonance (NTR) regime, the rate constant scales with temperature as 1/T before reaching the Wigner limiting value. Depending on the proximity of the virtual/bound state to the channel threshold, the reaction rate may increase by orders of magnitude. In this case (see also Simbotin and Côté, 2015) the virtual state is not so near, so that the 1/T behavior is just barely apparent.

In the plots of **Figure 2** we can clearly distinguish three different regions as the temperature increases. Up to 1 mK the only pathway for the reaction is the tunneling through the barrier eventually enhanced by the virtual state effect. In the region intermediate between 1 mk and 10 K, the reactivity is additionally affected by the shape resonances in the entrance channel. Above 10 K, the scattering resonances trapped in the transition state and in the exit channel as well as the thermal activation mechanism cause a further increase in the rate coefficients.

In the so-called classical region, where the reactivity is dominated by the thermal activation pathway, the dependence of rate constants with temperature is described by the Arrhenius' law, predicting an exponential decrease of the reaction rate constants against reciprocal temperature

$$k = A \exp(-E\_a/RT) \tag{9}$$

where E<sup>a</sup> denotes the activation energy and A is the preexponential factor. When the reaction also proceeds through the tunneling mechanism, the rate constants are larger than this law would predict and concave Arrhenius plots are observed. For chemical reactions where the exchange of the light hydrogen atom represents the rate determining step, the deviations can be pronounced: they depend on the tunnel effect. As the temperature tends toward zero (below 1 mK), according to the Wigner law (Wigner, 1948), the rate constants

$$k\_W = \frac{4\pi\hbar\beta}{m} \tag{10}$$

become temperature independent. An extra factor of 1/2 must be inserted to account for the open-shell structure of the fluorine atom (Aquilanti et al., 2005b). The temperature, T<sup>c</sup> , at which the low- and high-temperature limits in Equations (9, 10) cross is defined as the cross-over temperature (Hänggi et al., 1990) delimiting the deep (T < Tc) and moderate (T<sup>c</sup> . T . 2 Tc) tunneling regimes. According to Christov (1997), at the temperature T = 2T<sup>c</sup> the tunneling and overbarrier mechanisms play the same role. In 1935 Bell found a formula bridging the low- and high-temperature limits of the rate coefficient

$$k\_Q = AQ \exp(-V^\*/RT) \tag{11}$$

where V ∗ is the reaction barrier height and

$$Q = \frac{T - T\_c \exp\left[V^\*(1/RT - 1/RT\_c)\right]}{T - T\_c} \tag{12}$$

is a tunneling correcting factor (Bell, 1980). The above expression, written so to emphasize its dependence on the crossover temperature, holds in the case of a truncated parabolic barrier, for more details see Cavalli et al. (2014). Toward the absolute zero, Equation (11) leads correctly to a nonvanishing and temperature independent expression while at high temperature E<sup>a</sup> = V ∗ and the Arrhenius rate expression (9) is recovered. For the F+H<sup>2</sup> reaction, the temperature dependence of the activation energy has been calculated using a phenomenological approach (Aquilanti et al., 2012) in the range 10–350 K.

The quantitative enhancement that resonances have on the tunneling can be defined in terms of a coefficient

$$\mathcal{V} = \frac{k}{k\_Q} \tag{13}$$

that we take to be the ratio of the numerically exact rate constant k, obtained from rigorous quantum scattering calculations, to the tunneling corrected rate constants kQ, calculated from Equation (11) using the Arrhenius parameters A and V ∗ reported in Persky and Kornweitz (1997). The values of T<sup>c</sup> have been obtained by imposing the limit for T = 0 of Equation (11) equal to Equation (10), namely:

$$T\_c = \frac{-V^\*}{R \ln[(4\pi\,\hbar\beta)/(mA)]}\,\,\,. \tag{14}$$

Using the values of the imaginary scattering length, β, reported in **Table 2**, we obtain T<sup>c</sup> ≃ 74.4 K and 67.7 K for F + D<sup>2</sup> SW PES and PES-II, respectively and T<sup>c</sup> ≃ 72.9 K for F + H<sup>2</sup> PES-II. Note that Equation (14) does not hold in presence of virtual state effects because the model used to obtain Equation (11) does not take it into account. For this reason we can not obtain T<sup>c</sup> and γ in the F+H<sup>2</sup> SW PES case. The temperature dependence of the γ coefficient is shown in **Figure 3**. Note that γ is always lager than one, as it should be. The pronounced peak at very low temperatures is the overall contribution of the J-selected shape resonances, while the shallow maximum above 10 K is due to the presence of a transition state resonance (Cavalli and De Fazio, 2007).

#### 3.2.1. Kinetic Isotope Effect

The ratio between the rates of the lighter and the heavier isotopic combinations is a measure of the inter-molecular kinetic isotope effect (KIE) (Steckler et al., 1985). The temperature dependence of KIE is shown in **Figure 4**. The rate constant of the F + H<sup>2</sup> reaction increases drastically as temperature decreases, so that in the ultra-cold regime the fluorine atom is about one hundred times more reactive with H<sup>2</sup> than with D<sup>2</sup> on SW PES. We note that this effect is about two orders of magnitude larger than the semi-classical limit (Bigeleisen, 1949), which applies above room temperature, where the tunnel effect is negligible and the main source of KIE comes from the difference among the reactants' zero point energies, the so-called primary KIE. At low temperatures (until 1 K), the features are markedly influenced by the tunnel effect giving an exponential enhancement (Bell, 1980) more evident in PES-II where the barrier is thicker. Below 1 K the KIE behavior in two PESs is very different: a typical sigmoid curve is observed on SW PES, while the resonance enhancement of the rates give rise to a maximum observed at about 1 K in the case of PES-II. This big difference is of course due to the presence of the virtual state effect that enhances selectively the F + H<sup>2</sup> rate of the SW PES curve, hiding also the smaller resonance KIE effect. Below 1 mK the rates are temperature independent and therefore also is the KIE.

## 4. CONCLUSIONS

The reactivity of the F atom with the H<sup>2</sup> and D<sup>2</sup> molecules in their ground roto-vibrational state has been investigated in the quantum mechanical low-temperature regime (0.5 mK–50 K), where because of the prominent role of tunneling and resonances, the rates show pronounced deviations from the Arrhenius law before they become independent of temperature near absolute zero according to the Wigner law. The latter, unlike the Arrhenius' law, predicts that chemical reaction rates do not tend to zero when collision energies become vanishingly small. Total integral cross sections and rate constants have been calculated by numerically exact quantum reactive scattering calculations carried out on two potential energy surfaces, the widely used SW PES and a variant of it referred to as PES-II, differing in the description of the van der Waals well in the reactants' channel. The results have shown that the small changes in the entrance channel interaction and the isotopic substitution lead to the enhancement of cross sections and rate coefficients by many orders of magnitude and induce an unexpected dependence of the intermolecular kinetic isotope effect on temperature.

A quantitative assessment of the extent of the roles of tunneling and resonances, as well as that of the energy region where these quantum effects show up, has been provided. We have shown that the wide interval of collision energies and temperatures analyzed can be adequately divided into smaller domains within which the reactivity is differently influenced by the different quantum mechanical effects: at ultra-cold energies, the title reaction and its isotopic variant occur only

via the tunneling pathway possibly enhanced by virtual state effects; in the cold collision regime, cross sections and rate coefficients are additionally affected by shape resonances in the entrance channel of the potential energy surface, that enhance the contribution of the tunnel effect; finally, as the collision energy gets closer to the height of the classical barrier, the tunneling enhanced by a resonance state trapped in the transition state region of the potential energy surface competes with the over-barrier mechanism.

The ultra-cold results obtained with the SW PES corroborate previous studies (Bodo et al., 2004; Simbotin and Côté, 2015) made with the same PES, namely that a virtual state in the reactants' van der Waals well deeply affects the ultra-cold reactivity of the F+H<sup>2</sup> reaction. However, no evidence of this effect is found in the PES-II calculations. The large difference in the KIE behavior between the two PES suggests that this is likely the most sensitive observable to emphasize these features.

## AUTHOR CONTRIBUTIONS

All authors listed have contributed equally to the work, and approved it for publication.

## REFERENCES


## ACKNOWLEDGMENTS

The authors thank the High Performance Computing center at CINECA for computer time awarded via the ISCRA programme and the SIR 2014 Grant RBSI14U3VF.

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00328/full#supplementary-material


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 De Fazio, Aquilanti and Cavalli. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Radiation Damage Mechanisms of Chemotherapeutically Active Nitroimidazole Derived Compounds

Jacopo Chiarinelli 1,2, Anna Rita Casavola<sup>1</sup> , Mattea Carmen Castrovilli <sup>1</sup> , Paola Bolognesi <sup>1</sup> , Antonella Cartoni 1,3, Feng Wang<sup>4</sup> , R. Richter <sup>5</sup> , Daniele Catone<sup>6</sup> , Sanja Tosic<sup>7</sup> , Bratislav P. Marinkovic<sup>7</sup> and Lorenzo Avaldi <sup>1</sup> \*

<sup>1</sup> CNR-Istituto di Struttura Della Materia (CNR-ISM), Area della Ricerca di Roma 1, Monterotondo Scalo, Italy, <sup>2</sup> Dipartimento di Scienze, Università di Roma Tre, Rome, Italy, <sup>3</sup> Dipartimento di Chimica, Sapienza Università di Roma, Rome, Italy, <sup>4</sup> Molecular Modelling Discovery Laboratory, Department of Chemistry and Biotechnology, Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, VIC, Australia, <sup>5</sup> Elettra-Sincrotrone Trieste, Trieste, Italy, <sup>6</sup> CNR-Istituto di Struttura Della Materia, Area della Ricerca di Tor Vergata, Rome, Italy, <sup>7</sup> Institute of Physics, Laboratory for Atomic Collision Processes, University of Belgrade, Belgrade, Serbia

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Radha Gobinda Bhuin, University of Erlangen Nuremberg, Germany Yujun Shi, University of Calgary, Canada

> \*Correspondence: Lorenzo Avaldi lorenzo.avaldi@ism.cnr.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 22 February 2019 Accepted: 24 April 2019 Published: 14 May 2019

#### Citation:

Chiarinelli J, Casavola AR, Castrovilli MC, Bolognesi P, Cartoni A, Wang F, Richter R, Catone D, Tosic S, Marinkovic BP and Avaldi L (2019) Radiation Damage Mechanisms of Chemotherapeutically Active Nitroimidazole Derived Compounds. Front. Chem. 7:329. doi: 10.3389/fchem.2019.00329 Photoionization mass spectrometry, photoelectron-photoion coincidence spectroscopic technique, and computational methods have been combined to investigate the fragmentation of two nitroimidazole derived compounds: the metronidazole and misonidazole. These molecules are used in radiotherapy thanks to their capability to sensitize hypoxic tumor cells to radiation by "mimicking" the effects of the presence of oxygen as a damaging agent. Previous investigations of the fragmentation patterns of the nitroimidazole isomers (Bolognesi et al., 2016; Cartoni et al., 2018) have shown their capacity to produce reactive molecular species such as nitric oxide, carbon monoxide or hydrogen cyanide, and their potential impact on the biological system. The results of the present work suggest that different mechanisms are active for the more complex metronidazole and misonidazole molecules. The release of nitric oxide is hampered by the efficient formation of nitrous acid or nitrogen dioxide. Although both metronidazole and misonidazole contain imidazole ring in the backbone, the side branches of these molecules lead to very different bonding mechanisms and properties.

Keywords: nitroimidazole, radiosensitizers, mass spectrometry, PEPICO experiments, appearance energy, DFT

## INTRODUCTION

The use of "high-throughput screening" methods for drug discovery allows to rapidly conduct a very broad and random screening over an enormous number of chemicals. However, in these procedures the very fundamental chemical and physical mechanisms that determine the activity of these compounds at the molecular level remain unknown. On the other hand, highly sensitive experimental techniques and accurate computational methods have been developed to provide a detailed description of model molecules and to link their electronic and geometric structure to their functions. This, in particular, is of paramount importance in the case of the molecular response of cells and their building blocks to radiosensitising drugs used to increase the potential of radiotherapy. Despite the fact that the typical energies used in radiotherapy are in the keV to MeV range it is well-documented (García Gómez-Tejedor and Fuss, 2012) that a large fraction of the radiation damage on biological systems is due to secondary processes releasing particles (electrons, ions, radicals) with a broad energy distribution, which can subsequently trigger the damaging of DNA and its surrounding environment. Slow electrons with energy of a few eV have been considered among the most active species (Boudaiffa et al., 2000; Michael and O'Neill, 2000). Thus, the potential impact of VUV based techniques is due to their possibility to provide detailed information on the electronic structure and fragmentation of valence orbitals, which are the ones mainly involved in the processes induced by low energy electrons. Photoelectronphotoion coincidence, PEPICO, experiments then, due to their energy selectivity, provide detailed insights on state-selected fragmentation, and therefore are particularly suited to identify the states involved in the production of specific fragments and the release of radicals.

The question is whether the fragmentation mechanisms and properties identified in the model systems are still active at macroscopic level in more complex and realistic systems.

In this work we present the results of a bottom-up approach, which goes from the model molecule to the real drugs used in therapy. Photoionization mass spectrometry (PIMS), photoelectron spectroscopy and photoelectron-photoion spectroscopic (PEPICO) technique, and computational methods have been combined to investigate nitroimidazole (NI) derived molecules. These molecules are used in radiotherapy thanks to their capability to sensitize hypoxic tumor cells to radiation by "mimicking" the effects of the presence of oxygen as a damaging agent (Wardman et al., 2007; Rockwell et al., 2009; Sonveaux et al., 2009; Wilson and Hay, 2011; Higgins et al., 2015). However, the detailed mechanisms of their operation at molecular levels are still unknown, making difficult any rationale in the design of more efficient and less toxic drugs for treatment. In our bottom-up approach we have investigated the building blocks of the molecules used in therapy: the 2- and 4(5)-NI molecules (Bolognesi et al., 2016; Cartoni et al., 2018). The main results of the investigation of the fragmentation patterns of the NI isomers are summarized in **Figure 1** where the mass spectra (bottom panel) of the 2-NI and 4(5)-NI and the potential energy surfaces (top panels) for the NO loss and further fragmentations are shown.

At first glance, the most evident observation in **Figure 1** is that the fragment at m/z 83 is one of the leading fragmentation channels in 2-NI, while it is almost absent in the 4(5)-NI sample. The m/z 83 fragment can be unambiguously attributed to the

FIGURE 1 | (Bottom panel) Mass spectra of 4(5)-NI [red line and inset (A)] and 2-NI molecules [gray, full area, and inset (B)] measured at 60 eV photon energy. The assignment of the main fragments is reported. (Top panels) Potential energy surfaces of the 2-NI and 5-NI, respectively, for the fragmentation of their corresponding molecular ions M<sup>+</sup> (m/z 113) calculated at the CCSD/6-311++G\*\*//B3LYP/6-311++G\*\* level of theory (Bolognesi et al., 2016). The molecular ion M<sup>+</sup> as well as the fragments [M-O]+, NO<sup>+</sup> 2 , HCN<sup>+</sup> 2 , NO+, and HCNH<sup>+</sup> are all radical ions; the radical symbol • as been omitted here and all over the paper for sake of simplicity.

loss of nitric oxide, which is particularly relevant for its potential implications in the biological context due to the well-recognized action of NO as a radiosensitiser and vasodilator (Wardman et al., 2007; Rockwell et al., 2009; Sonveaux et al., 2009). This may suggest that 2-NI is able to release a significantly larger amount of NO than 4(5)-NI, hence supporting the observation of its higher efficiency as radiosensityzer (Wardman et al., 2007). The quantum mechanical calculations (**Figure 1**, top panels) at the B3LYP/6-311++G ∗∗ level of theory for the geometry optimization and at the CCSD/6-311++G ∗∗ level for singlepoint energy calculation show that all of the nitroimidazole isomers are likely to release NO. However, in 4(5)-NI the subsequent fragmentation of the residual m/z 83 intermediate breaks the imidazole ring releasing HCN and CO molecules, while in 2-NI the higher kinetic stability of the ring leaves the intermediate intact. These results explain the different intensity of the fragments at m/z 83, 55, 30, and 28 observed in the mass spectra of both 2-NI and 4(5)-NI, respectively. From these evidences we determined that all the nitroimidazole isomers release the NO fragment with similar mechanisms. The released NO, being active for a short period of time after irradiation, could act by fixing dangling bonds in damaged DNA, making the damage permanent and by "favoring either drug delivery or the therapeutic efficacy of irradiation through transient tumor reoxygenation," as suggested by Sonveaux et al. (2009). In addition to the redox mechanism, this could provide explanation for the potential of all nitroimidazoles as radiosensitisers active on hypoxic tumors (Higgins et al., 2015). On the other hand, the release of carbon monoxide, CO, and hydrogen cyanide, HCN, more pronounced in 4(5)-NI isomers, may induce an opposite effect by efficiently attaching to hemoglobin (Berg et al., 2012) and inhibiting the cytochrome c oxidase in mitochondria (Yoshikawa and Caughey, 1990), respectively. Therefore, this effectively reduces the needed oxygenation and the overall radiosensitising effect.

Guided by these former results, in this work we have studied both experimentally and theoretically the fragmentation mechanisms of metronidazole [IUPAC name: 2-(2-methyl-5 nitro-1H-imidazol-1-yl) ethanol] and misonidazole [IUPAC name (RS)-1-methoxy-3-(2-nitroimidazol-1-yl)propan-2-ol]

of the metronidazole (left panel) and misonidazole (right panel) molecules. The labeling of each atom in the molecules is also shown.

(**Scheme 1**), the two radiosensitisers built on the 5-NI and 2-NI compounds, respectively, which are used in radiotherapy.

The experimental methods are described in section Experimental, while the theoretical ones are summarized in section Theoretical Methods. The experimental results are analyzed in section Results and discussed/interpreted with the support of the DFT theoretical calculations in section Discussion. Finally some conclusions are presented in section Conclusion. In the following the radical symbol • has been omitted for the sake of simplicity.

## EXPERIMENTAL

The experiments have been performed at the Circular Polarized (CIPO) and Gas Phase Photoemission (GAPH) beamlines of the Elettra synchrotron radiation source, Trieste (Italy). The characteristics of the beamlines have been described in details elsewhere (Derossi et al., 1995; Blyth et al., 1999) and will not be repeated here.

The metronidazole sample of analytical standard was purchased from Sigma-Aldrich, while the misonidazole one with 95% purity by Vinci-Biochem Srl. Both samples have been used without further purification. They are in the form of powders at standard ambient temperature and pressure, and they are evaporated in a furnace at about 150◦C. No evidence of sample dissociation is observed.

The Appearance Energy, AE, of the different fragments has been obtained by the measurement of the photoionization efficiency curves of the parent ion and selected fragments at the CIPO beamline using the aluminum normal incidence monochromator (NIM), that covers the photon energy range 5– 17 eV with a resolving power of about 1,000. The setup consists of five electrostatic lenses that focus and accelerate the ions from the region of interaction to the quadrupole mass spectrometer (QMS). This is a commercial QMS (10–4000 u, Extrel 150-QC 0.88 MHz) with a mass resolution M/1M of about 500. It is mounted perpendicularly to the photon beam and to the gas source. The photoionization efficiency curves were normalized to the photon intensity, measured simultaneously by a photodiode located at the end of the beamline. The photon energy was calibrated against the autoionization features observed in the Ar total photoionization spectrum between the 3p spin orbit components. In the photon energy scans up to 11.7 eV, a lithium fluoride filter was used to remove the second order radiation. Above this energy, the contribution of the second order radiation was evaluated by comparing the Ar<sup>+</sup> ion yield measured as a function of the photon energy to its ionization cross section (Marr and West, 1976). This second order contribution has been taken into account in the extraction of the photoionization efficiency curves (Castrovilli et al., 2014).

The photoelectron and mass spectra as well as the photoelectron-photoion coincidence, PEPICO, spectra have been measured at the GAPH beamline using a high vacuum chamber hosting a hemispherical analyzer (VG 220i) equipped with six channeltron dectectors and a custom made Wiley McLaren (Wiley and McLaren, 1955) time-of-flight (TOF) mass spectrometer mounted opposite to each other at the magic angle with respect to the polarization axis of the photon beam. The TOF mass spectrometer, working in conjunction with the "virtually" continuous ionization source provided by the multibunch operation mode of the synchrotron radiation, is operated in pulsed extraction mode. The repeller and extractor electrodes are polarized with antisymmetric voltages (manufacturer Directed Energy Inc., model PVM4210) driven by an external trigger, which provides a typical extraction field of 700 V/cm. The electron and ion mass analyzers can be operated independently, for photoelectron spectroscopy and photoionization mass spectrometry, respectively. In these operation modes (i) the hemispherical analyzer is normally operated with pass energy of 5 eV, corresponding to a kinetic energy resolution of about 150 meV or (ii) the extraction field of the TOF spectrometer is triggered using a 1 kHz pulse generator (Stanford Research Systems DG535) to extract the ions. The two analyzers can also be operated simultaneously for coincidence measurements. In this mode a residual penetration field from the drift tube of the TOF produces a kinetic energy shift of the photoelectron spectrum (easily taken into account by the calibration procedure) and a degradation of the energy resolution of the electron analyzer. Therefore, in the coincidence mode the electron energy analyzer has been operated at pass energy of 20 eV, with a gain in efficiency, but no further loss of resolution. The final energy resolution is estimated to be around 0.5 eV. In order to perform photoelectron-photoion coincidence spectroscopic measurements, the electronic chain

FIGURE 2 | Photoelectron spectrum (left panel), photoionization mass spectrum (bottom panel), and a set of PEPICO spectra (central panel) of metronidazole. The color code of the PEPICO spectra corresponds to the colored bars in the PES spectrum, which identify the different regions of the spectrum selected by the detection of the energy selected photoelectrons.

schematically reported in Figure 1 of Plekan et al. (2008) has been used for all detectors of the VG analyser. The three different types of measurement, that can be performed by this set-up, are illustrated in **Figure 2** where the photoelectron spectrum, the photoionization mass spectrum and a few PEPICO spectra of metronidazole measured at 60 eV photon energy are shown.

In the PEPICO measurements the selection of the kinetic energy of the detected photoelectron allows to make a state selected investigation of the fragmentation of the molecule as clearly shown in the central panel of **Figure 2**. From the spectra measured at different binding energies, BE, the branching ratio for the formation of a selected fragment vs. photon energy can be obtained. The procedures for the treatment of the PEPICO spectra, with the subtraction of the background due to the random coincidence and relative normalization have been described recently elsewhere (Chiarinelli et al., 2018) and therefore will not be repeated here.

In **Figure 2** each energy selected mass spectrum is characterized by only a few fragments as compared to the unselected mass spectrum (see bottom panel in **Figure 2**); the parent ion is observed only near the ionization energy of the molecule; only a few fragmentation channels at a time are associated with a selected electronic state of the cation although lower energy fragmentation channels are already energetically open.

## THEORETICAL METHODS

Quantum chemical calculations have been performed with Density Functional Theory (DFT). The geometries were optimized using the Becke, three-parameter, Lee-Yang-Parr (B3LYP) functional with the 6-311++G ∗∗ basis set. The frequency analysis was based on the normal mode harmonic approximation (Wong, 1996). All critical points were characterized as energy minima or transition state structures (TS) by calculating the harmonic vibrational frequencies at the same level of theory. They were also used to compute the zero-point and thermal energy corrections. The TS were unambiguously related to their interconnected energy minima by intrinsic reaction coordinates (IRC) calculations (Gonzalez and Schlegel, 1989, 1990).

The outer valence vertical ionization energies were calculated using the outer valence Green function OVGF/6-311++G ∗∗ methods (von Niessen et al., 1984; Ortiz, 1988), based on the optimized geometries using B3LYP/6-311++G ∗∗ .

The determination of the potential energy surfaces for the two flexible metronidazole and misonidazole compounds is very challenging, because rotations of their single C-N, C-C, and C-O bonds may produce a number of local minimum structures, i.e., conformers on their potential energy surfaces. All the possible stable conformers of a molecule may contribute

examples of the effect of the rotation on the structure.

to the measurement, based on Boltzmann's distribution at the temperature of the measurement. The search for all possibly stable conformers can be a daunting task. The structures and vibrational frequencies of the different structures in the potential energy surface of metronidazole and misonidazole for the electronic ground state were calculated using the Gaussian 09 program package (Frisch et al., 2009). High-level ab initio calculations have been done to map the potential energy surface for internal rotation of the molecules. Among the several rotational paths that the molecule can follow, here we have considered the ones which, leading to large potential energy barriers, are able to produce stable local minimum structures, i.e., conformers of the compounds. These rotational pathways are represented in the following figures. In the case of metronidazole the rotations around the N6-C5, which is the nitro and imidazole N-C bond and C10-C11 which is the ethanol backbone C-C bond, exhibit apparent energy barriers due to formation of the intramolecular hydrogen bonding. The relative potential energy scans were calculated rotating these two bonds, N6- C5 (dihedral angle O7N6C5C4), and C10-C11 (dihedral angle O12C11C10N1), respectively. The potential energy scans as a function of the dihedral angles are reported in **Figure 3**.

Optimizations of the structures are performed again at the local minima structures on the potential energy surface and the stable local minimum structures (conformers) are then found. The selected parameters which characterize the minimum structures conformer I (C10-C11) and conformer II (N6-C5) are collected in **Table 1SM**. We found that although conformers I and II obtained from rotation of the N6-C5 and C10- C11 bonds, respectively, are almost energy degenerate with a difference of 0.085 KJ/mol, they are different conformers as other properties such as dipole moments are very different. Vibrational frequency calculations were performed at the same level of the geometry optimization to characterize the stationary points as either minima or transition state structures (first-order saddle points). The frequencies calculated for the minimum structure conformers are all positive confirming that they are true minimum structures.

In the case of misonidazole the same high-level ab-initio calculations have been performed to map out the potential energy surface for internal rotation of the NO<sup>2</sup> group around the N6- C2 bond (**Figure 4A**), of the OCH<sup>3</sup> group around the C18-O21 bond (**Figure 4B**) and of the OH group around the C14-O16 bond(**Figure 4C**).

Once the minimum in the potential energy surface is found, we optimized it for the most stable structure. Due to intramolecular hydrogen bonding, the rotation of the OH group produces a conformer more stable than the rotation around

C14C18O21C22) (B) and C14-O16 (dihedral angle H17O16C14C11) (C) bonds, respectively. The red dots indicate the angle of rotation of the structure represented on the left hand side of the figure. They have been chosen as examples of the effect of the rotation on the structure.

the other bonds. As in the case of metronidazole, the energy differences between the analyzed conformers are in the range of few Kcal/mol. It means that already at room temperature there is a mix of different conformers. In the calculations only one structure, the most stable one resulting from the rotation of the C14-C16 bond (dihedral angle H17O16C14C11), is chosen as starting point of the fragmentation pathway. This may represent a strong limit, because some pathways might not be identified due to a different initial structure.

## RESULTS

The mass spectra of the metronidazole and misonidazole molecules measured at 60 eV photon energy are shown in **Figure 5**.

The metronidazole molecule is built on the 5-NI where the H bound to C2 is replaced by the methyl group CH<sup>3</sup> and the one bound to the N1 in the imidazole ring by a "short" ethanol tail (T<sup>1</sup> = CH2CH2OH, m = 45 Da) terminated by a OH group. In its

TABLE 1 | Experimental and theoretical values calculated at the B3LYP6-311++G\*\* level of the ionization potential, IP, of the parent ion and AE of some fragments of the metronidazole, and misonidazole.


In the case of metronidazole also the experimental data by Guo et al. (2012) have been reported. \*(Guo et al., 2012)

mass spectrum (bottom panel of **Figure 5**) the main features are at m/z 171 (parent ion M+), m/z 125, and 124 ([M-NO2] <sup>+</sup> and [M-HONO]+, respectively), around m/z 81 ([M-NO2-(T1-H)]<sup>+</sup> group), m/z 53 (corresponding to the opening of the imidazole ring following a further fragmentation of m/z 81), and around m/z 42 with the peak at m/z 45 assigned to the ethanol cation tail [T1] <sup>+</sup>. Below m/z 20 the peaks due to smaller fragments such as H2O and CH<sup>3</sup> are also observed.

The misonidazole molecule is built on the 2-NI where the H bound to the N1 of the imidazole ring is replaced by a "longer" tail (T<sup>2</sup> = CH2CH(OH)CH2OCH3, m = 89 Da) in which the propanol-2 is terminated by a methoxy group. The inspection of the mass spectra of misonidazole (top, red) and metronidazole (bottom, black) given in **Figure 5** shows that, although the two molecules share some common fragment groups, the relative intensities of the different fragments are very different. Two major differences are observed. One major difference in the two spectra is represented by the near absence of the parent ion in misonidazole; the other is that the very limited number of relevant fragments in the misonidazole spectrum or the number of intensive fragments in the metronidazole spectrum (bottom, black) indicate this molecule is more fragile. Therefore, the radiosensitizers engage with very different bonding mechanism. The parent ion M<sup>+</sup> at m/z 201 of misonidazole represents only a minor contribution to the mass spectrum and the main feature at m/z 45 can be assigned to the [CH2OCH3] <sup>+</sup> fragment and corresponds to a part of the tail T2. The other noticeable feature is represented by the group at about m/z 155 assigned to the [M-NO2] <sup>+</sup> fragment. All in all the [CH2OCH3] <sup>+</sup> fragment and the group at about m/z 155 contribute to about 50% of the spectrum at this photon energy.

As for as the comparison with the 2-NI and 4(5)-NI spectra reported in **Figure 1**, it is noticeable that the loss of the NO group ([M-NO]<sup>+</sup> with m/z 141 and 171 in the metronidazole and misonidazole, respectively) or the correlated product NO<sup>+</sup> (m/z 30) appear to be, if any, a minor channel.

Based on the observations from the mass spectra in **Figure 5**, in the PEPICO and AE measurements we concentrated our attention on the parent ion, the fragments corresponding to [M-NO2] <sup>+</sup> and [M-HONO]<sup>+</sup> and the m/z 45 fragment which may correspond to the tail [HOCH2CH2] <sup>+</sup> in metronidazole and a section of the tail [CH2OCH3] <sup>+</sup> in the misonidazole. In the case of the metronidazole we also investigated two other fragments at m/z 81 and 54. A detailed report of the AE and PEPICO measurements relative to all the fragments observed in the mass spectra will be reported in a separate publication (Bolognesi, in preparation).

The experimental and calculated AE values are collected in **Table 1**, while the branching ratio of the parent ion and different fragments derived from the PEPICO measurements are shown in **Figure 6**. In the bottom panel of the same figures the photoelectron spectrum of each molecule measured at 60 eV

FIGURE 6 | Branching ratio for the parent ion and a few fragments of metronidazole (left panel) and misonidazole (right panel) reported vs. the binding energy. The scale of the different branching ratios is indicated by the arrows. At the bottom of each figure the photoelectron spectrum of the molecule is reported. The vertical bars represent the binding energy of the cation states calculated using the outer valence Green function OVGF76-311++G\*\* method (von Niessen et al., 1984), see Supplementary Material.

is reported. The energies of the cation states calculated by the outer valence Green function OVGF6-311++G ∗∗ method (von Niessen et al., 1984) up to 15 eV are reported in **Figure 6** and tabulated in **Table 2SM**. The spectroscopic pole strengths calculated in the Green's function model are in the range of 0.85–0.91, suggesting that the independent particle picture is a good approximation in this energy region. In the region of BEs higher than 15 eV electronic configurations with relaxation, twohole-one-particle (2h-1p) and higher excitations may dominate the cationic states. These contributions, which represent the electronic correlation and relaxation, make the one-particle picture of the cationic states and/or vertical ionization process no more good approximations in this region. As a result, we concentrate on the outer valence region of the compounds in this section.

In both molecules the parent ions are possibly produced only via the ionization of the electrons on their highest occupied molecular orbital (HOMO) states. In the case of misonidazole the production of the parent ion competes already at threshold with dissociation channels involving the NO<sup>2</sup> and HONO losses, see also **Table 1**. The same channels are observed in the metronidazole at about 1 eV above the ionization threshold with the HONO fragment loss having its maximum branching ratio in the energy region of HOMO-1 to HOMO-3 orbitals The NO<sup>2</sup> loss channel is characterized by an AE very close to the one of the HONO loss, but becomes more effective at BE > 12 eV. The channel leading to the formation of the [CH2OCH3] <sup>+</sup> fragment, which appears to be the dominant channel in the fragmentation of misonidazole, has a measured AE in the proximity of the BE of the HOMO-1 state and already at a BE of 12 eV its branching ratio is about 0.5. The channel leading to the m/z 45 fragment in metronidazole, which corresponds to the loss of the tail bound to N1 in the imidazole ring, displays a higher AE (about 12.09 eV), but a lower branching ratio (maximum value of about 0.1). The AE of m/z 124 and 125 fragments measured by Guo et al. (2012) are also reported in **Table 1**. The two sets of experimental data agree within their respective uncertainties.

#### DISCUSSION

The mass spectrum of the metronidazole molecule has been previously measured by 75 eV electron impact (Linstrom and Mallard, 2008) and at a few photon energies between 9.5 and

13 eV by Guo et al. (2012) in the m/z range 100–180. All the previously observed fragments of metronidazole in the electron impact spectrum are also present in **Figure 5**. However, we noted that slightly different intensities for the bands centered at approximately m/z 125 and 81, respectively, are observed in this spectrum. In the outer valence region, the measurements by Guo et al. (2012) are consistent with the present PEPICO experiments. At 9.5 eV only the parent ion is produced in the photoionization event, while at 11 eV fragments corresponding to the NO2 and HONO losses at m/z 124 and 125 are observed as well as at the highest photon energy used (13 eV) also the fragments corresponding to m/z = 126 and 127. Pandeti et al. (2017) observed the loss of C2H4O (44 Da) at position N1 followed by the NO2 loss as the dominant fragmentation channels in a collision induced dissociation experiment of protonated metronidazole. Such a process in the present case would lead to prominent features at m/z 127 and 81, respectively. While the feature at m/z 81 is clearly observed in the mass spectrum in **Figure 5**, the other one seems to give a minor contribution to our spectrum.

Less information is available for the mass spectrum of misonidazole. Recently Feketeova et al. (2014) presented fragmentation spectra of protonated misonidazole in the m/z

FIGURE 8 | Fragmentation pathways in metronidazole leading from m/z 81 to the m/z 54 fragment and the neutral species HCN. The initial isomer is CH3CNCHCHN in pathway (A) and CH3CNHC2HN in pathway (B). The 1E values of the transition states refer to the IP.

range 60–205 obtained by collision and electron induced dissociation experiments. The assignment of the features observed in **Figure 5** has been done according to that work and for the low m/z region not covered by the study of Feketeova et al. (2014) the results of the competitive fragmentation modeling method (Allen et al., 2014) have been employed to assist the analysis.

Very rare photoelectron spectrum (PES) studies are available for metronidazole and misonimidazole. The PES of metronidazole was measured and interpreted by a comparison with a series of spectra of simpler methylnitroimidazoles by Kajfez et al. (1979). The spectrum was measured with a HeI discharge lamp with a resolution of about 35 meV. Despite the lower resolution all the features assigned by Kajfez et al. (1979) are also visible in the present study as given in **Figure 6** (see **Table 3SM**). The present measurement extends over a broader binding energy range up to 25 eV. To our knowledge no previous photoelectron spectrum of misonimidazole has been reported in the literature. The charge densities of the molecular orbitals in **Table 4SM** indicate that the HOMO is a π orbital located above and below the imidazole ring plane, while in the case of the HOMO-1 a contribution of σ type between C14 and C18 exists. In the comparison of the two experimental spectra the HOMO of the misonidazole appears to be stabilized (the BE being about 200 meV higher than in the metronidazole) while the theoretical predictions sets the BE of the HOMO of misonidazole about 100 meV below the metronidazole one, see **Table 2SM**. However, the differences are well within the accuracy of the approximation of the used theoretical method and the experimental uncertainties.

Let's now discuss the AEs and the ion yields determined in the energy selected PEPICO experiments. In the case of the metronidazole the parent ion (m/z 171) is observed (**Figure 6**) only in the region of the HOMO orbital. Already at about 1 eV above the ionization potential, IP, the state selected mass spectrum is dominated by the m/z 125 and 124 fragments, which correspond to the NO<sup>2</sup> and HONO losses, respectively. The process leading to the NO<sup>2</sup> elimination has been simulated. In this simulation as well as in all the others discussed later on in the text the full potential energy surface along the possible reaction coordinate has been explored. To simplify the representation in the figures only the transition states (TS) and the final optimized geometries of the products have been reported together with the relevant energies referred to the calculated adiabatic IP. The simulations summarized in **Figure 7**, right panel, shows that the process leading from the parent ion in its ground state to a charged fragment with m/z 125 and the NO<sup>2</sup> elimination needs to overcome a barrier of about 1 eV. The calculated AE is in satisfactory agreement with the measured value. The simulation also indicates that the NO<sup>2</sup> elimination leads to the formation of a by-cyclic structure in which O12 is bound to C5. This can be explained by considering as a starting configuration the conformer II (see **Table 1SM**) with the O12H group oriented toward the nitryl group.

This can be rationalized considering that the scans that lead to the identification of the conformer of minimum energy (see **Figure 3**), indicate that within an energy range of a few meV several conformers exist. As already mentioned, this

represents a severe challenge for the simulations, because the use of a conformer as a starting point of a scan may strongly influence the reaction path. Guo et al. (2012) studied the NO<sup>2</sup> loss and found that the cleavage of the C5-N6 bond is accompanied by an intramolecular hydrogen transfer. These authors considered three different formation pathways starting by two conformations of the parent ion, which differ by the orientation of the O12H hydroxil group with respect to the nitryl

group. In all cases the transition states involve the formation of a by-cyclic structure with energy barriers between 1.1 and 1.3 eV, which is consistent with the one calculated in the present work.

The same authors (Guo et al., 2012) proposed similar reactions for the HONO loss. When the hydroxyl group is located at the same side of the nitryl one the H atom of the hydroxyl group is transferred to the nytril one and an intramolecular ring-closing reaction occurs via the formation of the C11O12-C5 bond. When the hydroxyl group is located at the other side one H atom migrates from C10 to the nytril group. The calculated energy barrier of 0.72 eV and AE=9.20 eV for the first route are closer to the observed experimental value, thus it has been suggested as the most likely (Guo et al., 2012). Our extensive search for the transition state leading the HONO loss failed. The formation of the fragment at m/z 124 via the two successive losses of NO<sup>2</sup> and H lead to a calculated AE of about 17 eV, i.e., more than 7 eV higher than the experimental observation. Thus, while our experimental observation is in agreement with the one by Guo et al. (2012) and consistent with the predicted value by the same authors we can't confirm theoretically the reaction pathway they proposed.

On the left part of **Figure 7** the path leading to the loss of the tail T<sup>1</sup> (CH2CH2OH, 45 Da) by the C10-N1 rupture is illustrated. The simulation shows that at the rupture of the bond the formed structure is CH3CHOH, i.e., a H migration occurred. In this process the charge might be localized either on the heavier fragment, which includes the imidazole ring, or on the tail. Considering the relative intensity of the peaks at m/z 126 and 45 in **Figure 5**, it seems that the process leading to the CH3CHOH <sup>+</sup> fragment is the most likely one. The appearance energy of this latter process has been calculated to be 11.34 eV, i.e., 2.74 eV above the IP. The predicted value is about 1 eV lower than the observed one. Guo et al. (2012) in the measurement at photon energy of 13 eV observed a tiny feature assigned to m/z 126 and calculated the AE of that fragment at 12.21 eV. Even though in our experiment the branching ratio for that fragment is vanishing, we calculated its AE and found a value of 12.16 eV consistent with the one by Guo et al. (2012).

It is interesting to note that in the scan of the potential energy surface no paths leading to the isomerization of the NO<sup>2</sup> and the following NO loss, as observed in the 2- and 4(5)-NI, have been found. This is consistent with the experimental observation and represents a major difference in the fragmentation of the molecules studied here and their nitroimidazole model systems.

The other relevant fragment in the mass spectrum of metronidazole is at m/z 81, which results from the successive losses of NO<sup>2</sup> and CH2CHOH. Starting from the fragment m/z 125, the migration of H from the CH2OH group to the ring occurs, leading to a break of the double ring and subsequent elimination of CH2CHOH. The m/z 81 fragment, which can have two configurations with a H atom either bound to C5 or to N1 (**Figures 8A,B**, respectively), will further evolve with the formation of the fragment m/z 54 and the neutral species HCN (27 Da). Depending on the initial structure two interesting paths have been observed on the potential energy surface. In the first case (**Figure 8A**) a transition state at about 4.4 eV above the IP leads to the opening of the ring at the N3-C2 bond with the release of the HC4N3 group. In the second case (**Figure 8B**) one could have foreseen a direct elimination of HNC, but theoretical calculations demonstrate instead an unexpected mechanism. This involves two bond ruptures along the ring leading to HNC elimination as a first step. Then a closed structure with C4-C2 and C4-C5 bonds is formed (transition state at about 4.95 eV above the IP) and finally the HC5N1 group is lost. The predicted AEs for the m/z 54 fragment in both pathways are consistent with the experimental value, but the second one is closer to the experiment. Thus, it seems the most likely one.

In the case of the misonidazole fragmentation the NO<sup>2</sup> loss leading to fragment m/z 155 occurs via two transition states (see **Figure 9**) in which a H atom bond to C11 migrates from the tail to C2. The calculated AE is in satisfactory agreement with the measured value.

The reaction, that leads to the C5H6N3O<sup>3</sup> (156 Da) and H3COCH<sup>2</sup> (45 Da) moieties, can occur via two different paths of concerted mechanisms (**Figure 10**) depending on where the charge is localized. The path with the lower barrier (<1 eV) leaves the charge on the m/z 156 fragment, while the other path with a transition state of about 1.63 eV has the charge localized on the m/z 45 fragment. The mass spectrum at 60 eV (**Figure 5**) is dominated by this latter fragment and in the PEPICO spectra (**Figure 6**) the largest branching ratio is associated to this fragment, too. The observation that a channel not favored from an energetic point of view appears to be the dominant one in the experiment is unusual. It may be explained by the structure of the orbitals of the misonidazole. As seen in the bottom panel of **Figure 6** and in **Table 2SM** no ionic states exist at about 1 eV above the IP and the charge of the π HOMO is mainly distributed above and below the ring (**Table 4SM**). Vice versa the HOMO-1 binding energy is calculated to be at about 1.4 eV above the IP and its charge distribution displays a contribution along the C14- C16 σ bond (**Table 4SM**). Thus, the removal of one electron from this orbital may weaken the bond and lead to the release of the charged tail H3COCH<sup>+</sup> 2 .

It is interesting to observe that while in misonidazole the fragmentation channel leading to the [CH2OCH3] <sup>+</sup> m/z 45, i.e., the loss of a charged part of the tail T2, appears to be the dominant channel with an AE close to the energy of the HOMO-1 orbital, the loss of the tail, [CH2CH2OH]+, in metronidazole has a definitely higher AE (>12 eV) and it is characterized by a small branching ratio in the PEPICO measurements. This indicates that this low-lying fragmentation channel in misonidazole represents the most efficient channel for energy dissipation.

## CONCLUSION

The photoinduced fragmentation of metronidazole and misonidazole molecules has been studied. The combination of photoionization mass spectrometry, photoelectron spectroscopy, photoelectron-photoion coincidence spectroscopy, and computational spectroscopy has been used to investigate and characterize the main reaction/fragmentation channels observed in the mass spectra, which correspond to the elimination of the NO2 and HONO group in both molecules and the formation of the [CH2OCH3]+ ion in misonidazole. The preferential elimination of the nitro-group (-NO2) in both molecules supports the hypothesis (Adams et al., 2012) that the radiosensitizer effect is due to the complex redox chemistry, which, occurring after the selective binding of the nitroaromatic compounds to hypoxic cells, involves the reduction of the nitro-group to an amine (-NH2).

The message that can be derived from the present results is that although both metronidazole and misonidazole contain imidazole ring in the backbone, the side branches of these molecules lead to different bonding mechanisms and properties. Metronitrodazole is very fragile and a complex fragmentation process follows the initial ionization. Misonidazole on the other hand is relatively robust. Ionization and fragmentation may occur simultaneously, as the intensity of the molecular ion in the mass spectrum is very small. Then the preferential loss of the [CH2OCH3] <sup>+</sup> fragment, i.e., a part of the tail T2, acts as a protection of the ring against its opening and successive fragmentations. Therefore, if the therapeutic effect is linked to the nitroimidazole building block, then the efficient formation of the [CH2OCH3] <sup>+</sup> fragment may help to protect the ring and to preserve the therapeutic effect of the compound.

More complex fragmentation can be linked to toxicity, thus from this point of view metronizadole, which displays a very rich mass spectrum, seems to have a higher toxicity than misonidazole.

The observation that the NO loss, the most relevant channel discussed in the previous studies (Bolognesi et al., 2016; Cartoni et al., 2018) in the 2-NI and 4(5)-NI molecules, is a minor, if any, channel in these compounds used in radiotherapy, prevents a direct extension of the chemical physics mechanisms identified in the building block molecules to the real drugs adopted in the clinical use. However the complex metabolism, that determines the biotransformation of NO and its related oxides in vivo (Kelm, 1999) does not allow to make definitive conclusions.

The results of our study, which has followed a bottom-up approach, indicate that translating the findings of chemical physics experiment to chemotherapeutic compounds

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is not an easy task. However considering that nitro compounds have found and are finding clinical application (Overgaard, 2011; Wang et al., 2018) the understanding of their chemical physics properties, of the specific mechanisms of the interaction between radiation and chemotherapy and of how the chemical radiosensitizers actually work at the molecular level is a challenge that cannot be neglected.

### DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

#### AUTHOR CONTRIBUTIONS

PB, JC, RR, ST, BM, and LA performed the PEPICO experiments, while PB, MCC, and DC performed the AE measurements. ARC and AC performed the theoretical calculations and FW provided advices on the computational spectroscopy and interpretation of the spectra. PB, AC, JC, and MCC participated to the data analysis and interpretation. ARC, PB, and LA prepared the manuscripts. All the authors contributed to the interpretation of the results and the revision of the manuscript.

#### ACKNOWLEDGMENTS

We gratefully acknowledge the support from the Progetto di Grande Rilevanza of the Italian Ministero degli Affari Esteri e della Cooperazione Internazionale (MAECI) Italia-Serbia A nanoview of radiation-biomatter interaction. ST and BM acknowledge the support from MESTD project OI 171020.

#### SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00329/full#supplementary-material

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Chiarinelli, Casavola, Castrovilli, Bolognesi, Cartoni, Wang, Richter, Catone, Tosic, Marinkovic and Avaldi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# An Experimental and Theoretical Investigation of 1-Butanol Pyrolysis

Marzio Rosi <sup>1</sup> , Dimitris Skouteris <sup>2</sup> , Nadia Balucani <sup>3</sup> , Caterina Nappi <sup>3</sup> , Noelia Faginas Lago<sup>3</sup> , Leonardo Pacifici 2,3, Stefano Falcinelli <sup>1</sup> and Domenico Stranges <sup>4</sup> \*

<sup>1</sup> Department of Civil and Environmental Engineering, University of Perugia, Perugia, Italy, <sup>2</sup> Master-Up, Perugia, Italy, <sup>3</sup> Laboratory of Molecular Processes in Combustion, Department of Chemistry, Biology and Biotechnologies, University of Perugia, Perugia, Italy, <sup>4</sup> Department of Chemistry, University of Rome "La Sapienza", Rome, Italy

Bioalcohols are a promising family of biofuels. Among them, 1-butanol has a strong potential as a substitute for petrol. In this manuscript, we report on a theoretical and experimental characterization of 1-butanol thermal decomposition, a very important process in the 1-butanol combustion at high temperatures. Advantage has been taken of a flash pyrolysis experimental set-up with mass spectrometric detection, in which the brief residence time of the pyrolyzing mixture inside a short, resistively heated SiC tube allows the identification of the primary products of the decomposing species, limiting secondary processes. Dedicated electronic structure calculations of the relevant potential energy surface have also been performed and RRKM estimates of the rate coefficients and product branching ratios up to 2,000 K are provided. Both electronic structure and RRKM calculations are in line with previous determinations. According to the present study, the H2O elimination channel leading to 1-butene is more important than previously believed. In addition to that, we provide experimental evidence that butanal formation by H<sup>2</sup> elimination is not a primary decomposition route. Finally, we have experimental evidence of a small yield of the CH<sup>3</sup> elimination channel.

#### Edited by:

Ramesh L. Gardas, Indian Institute of Technology Madras, India

#### Reviewed by:

Mohammednoor K. Altarawneh, Murdoch University, Australia Barbara Michela Giuliano, Centro de Astrobiología (CSIC-INTA), Spain

\*Correspondence:

Domenico Stranges domenico.stranges@uniroma1.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 01 March 2019 Accepted: 23 April 2019 Published: 14 May 2019

#### Citation:

Rosi M, Skouteris D, Balucani N, Nappi C, Faginas Lago N, Pacifici L, Falcinelli S and Stranges D (2019) An Experimental and Theoretical Investigation of 1-Butanol Pyrolysis. Front. Chem. 7:326. doi: 10.3389/fchem.2019.00326 Keywords: combustion chemistry, pyrolysis, biofuels, ab initio calculations, rate constants

## INTRODUCTION

Combustion is a complex phenomenon that involves physical and chemical processes. Because of its importance in many human activities, a thorough characterization has been pursued for decades aiming at optimizing the performance of engines or heaters or other devices exploiting combustion systems (Gardiner, 2000). More recently, the recognition that pollutants are massively emitted from flames has stimulated a more accurate characterization of the combustion environments trying to reduce or minimize those harmful emissions (see, for instance, Battin-Leclerc et al., 2013 and references therein). Since pollutants are normally produced in trace amounts, an in-depth characterization is necessary that requires a chemical description of the elementary reactions occurring in flames at the atomistic level (see, for instance, Balucani et al., 2012a). As a result of such a cumulative effort, we have now a good knowledge of the elementary reactions lying at the heart of combustion of fossil fuels, although several problems remain (e.g., soot formation, NO formation). In the last decades, the advent of biofuels caused by the expected shortage of non-renewable fuels and by the search of carbon-neutral fuels has posed a new challenge to the chemical characterization of combustions as, typically, biofuels are constituted by more complex molecules than traditional fuels (Kohse-Höinghaus et al., 2010). Remarkably, most of the proposed biofuels are O-bearing organic compounds like alcohols, ethers and esters (Kohse-Höinghaus et al., 2010). While the use of biofuels seems to reduce the production of several pollutants which are typical of fossil fuels, their combustion generates a new group of pollutants which are instead absent in the case of fossil fuels, namely highly toxic aldehydes and ketones (Kohse-Höinghaus et al., 2010; Battin-Leclerc et al., 2013). Therefore, the work done for the characterization of fossil fuels combustion must be extended to the new fuels.

Among biofuels, a promising family of compounds are bioalcohols, which have been already used in several countries. In particular, 1-butanol is considered an excellent candidate for massive use, because of its high energy content, low water absorption, high miscibility with conventional fuels, and the possibility of being used in conventional engines (Kohse-Höinghaus et al., 2010). For this reason, 1-butanol combustion has been widely investigated and the global combustion properties, such as heat release and CO<sup>2</sup> emission, have been characterized (see, for instance Dagaut et al., 2009; Sarathy et al., 2009, 2012, 2014; Black et al., 2010; Grana et al., 2010; Harper et al., 2011; Cai et al., 2012; Yasunaga et al., 2012; Feng et al., 2017). Among the various elementary processes occurring when burning 1-butanol, its unimolecular high temperature decomposition is certainly important because of the high temperature conditions of combustion environments (Grana et al., 2010; Harper et al., 2011; Cai et al., 2012; Karwat et al., 2015). This has motivated numerous experimental and theoretical studies on the pyrolysis of butanol (see Cai et al., 2012, and references therein). The most comprehensive study is that by Cai et al. (2012) where a combined experimental and theoretical approach has been used. More precisely, rate coefficients of unimolecular reactions were calculated with the variable reaction coordinate-transition-state theory (VRC-TST) and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory on a newly derived potential energy surface while the experiments were performed in a flow reactor at a pressure ranging from 5 to 760 Torr with synchrotron VUV (Vacuum Ultra-Violet) photoionization mass spectrometry to identify the pyrolysis products. In spite of the use of such a sophisticated experimental technique, a model needed to be used to interpret the experimental results and it remained unclear whether some observed species are primary products of the unimolecular decomposition of 1-butanol or secondary products formed in the flow reactor. In the Laboratory of Molecular Processes in Combustion of the University of Perugia, we are now building an apparatus to perform experiments based on the flash pyrolysis technique and mass spectrometric detection by FUV (Far Ultra-Violet) ionization at 118.2 nm within the frame of the AMIS project (http://amis.chm.unipg. it). The same approach has already used by Chambreau et al. (2000), Chambreau et al. (2005), Weber et al. (2006), Morton et al. (2011), and Liu et al. (2018), while flash pyrolysis coupled to other detection techniques has been implemented by O'Keeffe et al. (2008), Vasiliou et al. (2009, 2011), Scheer et al. (2011, 2012), Urness et al. (2013), Prozument et al. (2014), Buckingham et al. (2016), Holzmeier et al. (2016), Porterfield et al. (2017), Vasiliou et al. (2017), Zhao et al. (2017), Abeysekera et al. (2018), and Ormond et al. (2018). The advantages of the flash pyrolysis technique is that the very limited residence time inside a SiC tube of ca. 2–2.5 cm, which can be resistively heated at temperatures as high as 1,500 K, allows one to better define the yield of the primary pyrolysis products (Guan et al., 2014; Weddle et al., 2018; Zagidullin et al., 2018) because the probability of secondary reactions involving pyrolysis products or even further pyrolysis of primary products are strongly reduced (Guan et al., 2014).

In this work, we report a test-case we have performed at the University of Rome where an apparatus exploiting flash pyrolysis with traditional electron impact mass spectrometry is operative (O'Keeffe et al., 2008). The apparatus has been used in the past to characterize the flash pyrolysis of azidoacetone, while its main applications have focused on the UV photodissociation of radicals produced by the pyrolysis of a suitable precursors (Stranges et al., 1998, 2008; Chen et al., 2010, 2011; Stranges and Ripani, 2012). Because of its relevance and relative simplicity, our test-case involved the flash-pyrolysis of 1-butanol. To the best of our knowledge this is the first experiment on the flash pyrolysis of 1-butanol. New physical insights emerged from this study concerning the importance of H2O-elimination and the possibility that 1-butanal is a primary product. We have also completed this study by performing dedicated new electronic structure calculations at the B3LYP and CCSD(T) levels of theory of the stationary points necessary to describe the unimolecular decomposition of 1-butanol. We have also calculated the energetics of previously ignored decomposition pathways involving the rupture of C-H and O-H bonds. These data have been used to perform RRKM estimates under the conditions of our experiments. A more detailed picture of the thermal decomposition of 1-butanol has emerged.

## EXPERIMENTAL METHOD

The experimental measurements in this work were carried out on a rotating source photofragment-translational spectrometer (at University of Rome "La Sapienza") which is normally utilized to study UV photodissociation processes. A drawing of this apparatus is shown in **Figure 1**. When it is utilized for pyrolysis experiments the source chamber is positioned at 0◦ so that the molecular beam direction is along the detector axis.

A 0.2% mixture of 1-butanol seeded in Ar was sent to a piezoelectrically activated pulsed valve (Proch and Trickl (1989) operated at a repetition rate of 100 Hz. This pulsed valve was coupled to a "flash-pyrolytic" source, already utilized to generate molecular beams of hydrocarbon free radicals (Stranges et al., 2008; Chen et al., 2011), and a drawing is reported in **Figure 2**.

The gas mixture (1.3 bar) was expanded through a resistively heated SiC tube (length 23 mm) inducing the thermal decomposition of the 1-butanol molecules. When the gas mixture exits the hot SiC tube it undergoes a supersonic expansion, resulting in internal cooling of the thermal decomposition products, which are thus stable to further dissociation during their flight time to the electron impact ionizer. This aspect gives a big advantage to this technique as compared to conventional pyrolysis methods. It is due to the short residence time of the

parent molecule in the pyrolysis zone (20–30 µs) together with the internal cooling of the nascent thermal products by the supersonic expansion. Therefore, in the case of pyrolysis of organic molecules, which proceeds via stepwise mechanisms, it is possible to isolate intermediate thermal decomposition products that are not observed using conventional oven techniques, providing a more detailed insight into the mechanisms involved.

The neutral molecules fly along the detector axis for 40 cm before reaching the ionizer where they are ionized by electron impact (70 and 100 eV electron energy), then the ions are mass selected by a quadrupole mass filter (Extrel 150QC) and counted by a Daly type counter. In order to minimize the background signal, mainly due to the residual gas, the surfaces of the ionizer region are cooled with liquid nitrogen allowing to reach a pressure of <1.0 × 10−<sup>11</sup> mbar.

Time-of-Flight (ToF) spectra at different mass to charge ratios, m/e, were recorded as a function of the electrical power dissipated through the SiC tube, by inserting a spinning slotted disk (200 Hz) into the molecular beam to select a "slice" (∼7.5 µs) of the gas pulse. These spectra were recorded and stored on a computer by using a Multi Channel Scaler (MCS-pci, EG&G Ortec). In order to obtain the mass spectra of the 1-butanol pyrolysis products it was preferred to integrate the ToF spectra recorded for different masses, by interrogating a very small part (∼7.5 µs) of the gas pulse, to obtain background modulation and subtraction. The power dissipated through the SiC tube was converted into temperature by measuring the beam velocity of a neat He beam at the same experimental conditions. The velocity of a supersonic ideal atomic beam is related to the temperature of the source (SiC tube) via the expression V = q 5RT m , where T is the source temperature, m is the mass of the gas, V is the atomic beam velocity, and R is the gas constant.

#### THEORETICAL METHODS

The potential energy surface of the species of interest was calculated employing a computational strategy which has already been utilized with success in several cases (see, for instance Leonori et al., 2009a,b; de Petris et al., 2011; Rosi et al., 2012; Skouteris et al., 2015; Troiani et al., 2017). In this scheme the lowest stationary points were optimized at the B3LYP (Becke, 1993; Stephens et al., 1994) level of theory in conjunction with the correlation consistent valence polarized set aug-cc-pVTZ (Dunning, 1989; Kendall et al., 1992). At the same level of theory we have computed the harmonic vibrational frequencies in order to check the nature of the stationary points, i.e., minimum if all the frequencies are real, saddle point if there is one, and only one, imaginary frequency. The assignment of the saddle points was performed using intrinsic reaction coordinate (IRC) calculations (Gonzalez and Schlegel, 1989, 1990). The energy of the main stationary points was computed also at the higher level

FIGURE 4 | Time of Flight spectra recorded at a temperature of 1,214 K for several mass-to-charge ratios. Each spectrum has been arbitrarily normalized after background subtraction.

FIGURE 5 | Time of Flight spectra recorded at a temperature of 1,355 K for several mass-to-charge ratios. Each spectrum has been arbitrarily normalized after background subtraction.

of calculation CCSD(T) (Bartlett, 1981; Raghavachari et al., 1989; Olsen et al., 1996) using the same basis set aug-cc-pVTZ. Both the B3LYP and the CCSD(T) energies were corrected to 298.15 K by adding the zero point energy and the thermal corrections computed using the harmonic vibrational frequencies evaluated at B3LYP/aug-cc-pVTZ level. Corrections to other temperatures were performed following the same procedure. For comparison purposes, some calculations were performed also at the Gaussian-3 (G3) (Curtiss et al., 1998) and Gaussian-3 using B3LYP structures and frequencies (G3B3) (Baboul et al., 1999) level. All calculations were done using Gaussian 09 (Frisch et al., 2009) while the analysis of the vibrational frequencies was performed using Molekel (Portmann and Lüthi, 2000; Flükiger et al., 2000-2002).

The rate constants for each unimolecular reaction in our scheme were calculated as a function of energy using the RRKM scheme (as in our previous works, see Balucani et al., 2009, 2010, 2012b; Leonori et al., 2009a, 2013), through the expression

$$k\left(E\right) = \frac{N(E)}{h\ \rho\left(E\right)}$$

where N(E) is the sum of states of the transition state, ρ(E) is the density of states of the reactant and h is Planck's constant. For the calculation of each density of states the rigid rotor/harmonic oscillator model was assumed. Even though the treatment of low-frequency modes as harmonic can lead to errors, we have chosen this strategy as the best alternative so as to keep the vibrational modes uncoupled and to avoid any arbitrariness in hindered rotor potentials. Moreover, tunneling was taken into account using the imaginary frequency of each transition state and modeling the potential energy as an Eckart barrier with the correct height (as calculated from the energy) and width (as calculated from the imaginary frequency). The RRKM code used is a home-made one developed by one of the authors and previously used in many systems.

In this way, for each unimolecular reaction in our scheme, we generate energy-dependent rate constants k(E) for a fixed range of energies, ranging from the lowest useful energy (the zeropoint energy of the 1-butanol species) up to 1,500 kJ mol−<sup>1</sup> . The hypothesis here is that, during the pyrolysis event, the energy of the molecule remains constant and statistically distributed among the degrees of freedom. Subsequently, for each product species, the corresponding energy-dependent rate constants were Boltzmann-averaged (using the density of states of 1 butanol and the corresponding partition function) to calculate temperature dependent rate constants up to 2,000 K for each species. Thus, we are assuming that, prior to the pyrolysis event, butanol molecules are thermalized by interaction with the environment.

Where no obvious transition state is indicated, we performed a variational transition state theory (VTST) calculation, calculating RRKM rate constants for a range of candidate transition states and choosing the minimum one. A full electronic calculation was performed for each candidate transition state, with no use of Lennard-Jones potentials for the long-range interactions.

## EXPERIMENTAL RESULTS

In **Figures 3**–**5** are reported the ToF spectra recorded at several mass-to-charge ratios, m/e, at the temperatures of 997, 1,214, and 1,355 K. Other spectra were recorded at lower temperatures, but in those cases the mass spectra derived by ToF integration are in all aspects similar to the one derived for 1-butanol at 300 K. Therefore, in those conditions no pyrolysis occurred inside the SiC tube.

To analyze the data and derive the mass spectra of the pyrolysis products alone, the contribution deriving from the nonpyrolyzed 1-butanol must be subtracted. The procedure normally used consists in recording the mass spectrum of the molecule to be pyrolyzed at room temperature and then subtracting this spectrum from those recorded at different temperatures by normalizing their weight to the signal of the parent peak. In the case of 1-butanol, this procedure is not possible because, as often happens for alcohols, the parent peak has a very low intensity compared to all the other masses present in the spectrum.

The procedure followed to subtract this contribution is based on the consideration that in the ToF spectra recorded at different temperatures for masses 57 and 72, the signal is absent. In the butanal (CH3CH2CH2CHO) mass spectrum (NIST-1 Chemistry Webbook)<sup>1</sup> the masses 72 and 57 are about 75 and 25% of the most intense peak (m/e = 44), respectively. This implies that the presence of butanal would be detectable even in small concentrations. We can therefore exclude the formation of CH3CH2CH2CHO and H<sup>2</sup> from the pyrolysis of 1-butanol under our experimental conditions.

If we exclude the presence of H and OH elimination reactions, since they are very endothermic, then the signals at m/e 55 and 56 are due only to 1-butanol and 1-butene. To determine their contribution in the ToF spectra we took advantage of their quite different fragmentation pattern for the two masses (m56 = 100% and m55 = 30% for 1-butanol, m56 = 40% and m55 = 20% for 1-butene) which allow to set up the following system of two equations:

$$\begin{aligned} \text{\%Py56} &= \text{C}\_1 \times \text{\%A56} + \text{C}\_2 \times \text{\%Bu56} \\ \text{\%Py55} &= \text{C}\_1 \times \text{\%A55} + \text{C}\_2 \times \text{\%Bu55} \end{aligned}$$

%Py56 and %Py55 represent the percentages of these two masses in the pyrolysis spectra (normalized to 100 for the most intense mass), %A56 and%A55 are the relative abundances of the two masses in the mass spectrum of 1-butanol (NIST-2 Chemistry Webbook)<sup>2</sup> , %Bu56 and %Bu55 are the relative abundances of the two masses in the mass spectrum of 1-butene (NIST-3 Chemistry Webbook)<sup>3</sup> , and C<sup>1</sup> and C<sup>2</sup> represent the apparent percentages of 1-butanol and 1-butene, respectively, present in the molecular beam.

The mass spectra of neat 1-butanol and 1 butene were measured under the same experimental conditions as pyrolysis but with the SiC tube at room temperature and then subtracted from the pyrolysis mass spectra. In this way the mass spectra relative to the other dissociation channels with lighter products were obtained.

To obtain the branching ratio between 1-butene and 1 butanol, their apparent percentages have to be corrected for the

<sup>1</sup>https://webbook.nist.gov/cgi/cbook.cgi?ID=C123728&Units=SI&Mask=200# Mass-Spec

<sup>2</sup>https://webbook.nist.gov/cgi/cbook.cgi?ID=C71363&Units=SI&Mask=200# Mass-Spec

<sup>3</sup>https://webbook.nist.gov/cgi/cbook.cgi?ID=C106989&Units=SI&Mask=200# Mass-Spec

different ionization cross section by electron impact: 11.74A<sup>2</sup> for 1-butene (NIST-4 Chemistry Webbook)<sup>4</sup> and 12.40A<sup>2</sup> for 1-butanol (Hudson et al., 2003).

The ratio between the signal attributed to butene and the undissociated remaining 1-butanol, N(butene)/N(1-butanol), is shown in **Figure 6**. Remarkably, N(butene)/N(1-butanol) keep on increasing with the temperature. If we compare the present trend with the butene signal recorded by Cai et al. (2012), it is clear that there is no secondary pyrolysis of butene or secondary reactions affecting its abundance in the pyrolyzed mixture. This can be taken as a confirmation that the experimental method employed here allows a better characterization of the primary events in the pyrolysis.

The remaining mass spectra at the three temperatures investigated, once the contributions of undissociated 1-butanol and main pyrolysis product 1-butene have been subtracted, are reported in **Figure 7**. As clearly visible, signals at m/e 42, 42, 33, 31, 29, 27, and 15 have been recorded. They correspond to both parent ions of pyrolysis products and their daughter species. Even though it is not possible to disentangle them with the present results, we note that the intensity of all peaks is increasing, thus testifying that the extent of 1-butanol pyrolysis increases with the temperature for all species.

## THEORETICAL RESULTS AND DISCUSSION

The optimized structure of the most stable isomers of 1 butanol is shown in **Figure 8**, while the optimized structures of the main saddle points localized on the investigated PES are reported in **Figure 9** and the optimized structures of the main fragmentation products in the hydrogen atom loss processes in **Figure 10**. **Table 1** reports the enthalpy changes and barrier heights of the main dissociation and isomerization processes for the 1-butanol. From **Table 1** we can see that there is a reasonable agreement between B3LYP and CCSD(T) energies. For this reason, we will consider only the more accurate CCSD(T) results. Preliminary partial calculations have been previously reported (Pacifici et al., 2015).

From **Figure 8** we can see that we have an isomer (a) which shows a C<sup>s</sup> symmetry and two other isomers, almost degenerate with (a), which show no symmetry. As we can see from **Table 1**, at B3LYP level (a) is the most stable species, while at CCSD(T) level (b) is the most stable isomer, but only by 0.3 kJ/mol with respect to (a). Being the energy differences among these species below the estimated accuracy of the calculations (±5 kJ/mol), we will refer all the following discussion to the most symmetric species (a). In (a) both the dihedral angles <sup>6</sup> HOCC and <sup>6</sup> OCCC are equal to 180.0◦ , while in (b) <sup>6</sup> HOCC is equal to −65.4◦ and <sup>6</sup> OCCC is equal to −62.6◦ and in (c) <sup>6</sup> HOCC is 61.6◦ and <sup>6</sup> OCCC is 177.6◦ . The dihedral angles are the main differences among these three isomers and, being the C—C and C—O bonds all single bonds, the isomerization saddles among these species are expected to be very low in energy. As we can see from **Table 1**, the isomerization of (a) to (c) is almost barrierless, while the isomerization of (a) to (b) shows a barrier of only 11.3 kJ/mol at CCSD(T) level. In **Figures 11**, **12** we have reported a schematic representation of the main dissociation channels of

<sup>4</sup>https://physics.nist.gov/cgi-bin/Ionization/table.pl?ionization=C4H8xx0

1-butanol. For simplicity, only the CCSD(T) energies are shown in the figure. In **Figure 11**, we have reported the dissociation processes which involve a transition state, while in **Figure 12** we have reported the dissociation processes which involve only the breaking of a bond and are, therefore, endothermic and do not show a transition state, since the geometrical rearrangement is not very pronounced. From **Figure 11**, we can see that 1 butanol can dissociate producing water, molecular hydrogen, formaldehyde and its isomer CHOH, both in the more stable trans and in the cis structure. All these reactions imply the presence of relatively high transition states. The dissociation of 1-butanol into CH3CH2CH<sup>3</sup> and CHOH imply a barrier of 340.6 kJ/mol for the formation of the trans species and 422.2 kJ/mol for the formation of the cis isomer. Both reactions are endothermic, the first by 276.1 kJ/mol and the second by 294.3 kJ/mol. After formation, CHOH cis can isomerize to the more stable (by 18.2 kJ/mol at CCSD(T) level) trans species but this reaction shows a barrier of 94.9 kJ/mol, being involved the breaking of a partial double bond. CHOH trans can also isomerize to the more stable (by 214.2 kJ/mol) formaldehyde species with a barrier of 127.5 kJ/mol. Formaldehyde can be formed also from 1-butanol, starting from isomer (b). This reaction which is endothermic by 62.2 kJ/mol shows a barrier as high as 365.1 kJ/mol. CH3CH2CH<sup>3</sup> and CH2O can isomerize to CH3CHCH<sup>2</sup> and CH3OH producing methanol. However, this reaction, endothermic by 36.0 kJ/mol, shows a barrier of 179.5 kJ/mol, as we can see from **Table 1**. The production of molecular hydrogen from 1-butanol is an endothermic reaction (by 72.8 kJ/mol) with a barrier as high as 356.1 kJ/mol. Water can be produced in two different reactions. The first one gives water and the more stable species CH3CH2CHCH2; this reaction is endothermic by only 38.1 kJ/mol and has a barrier of 276.6 kJ/mol. In the other reaction we have the formation of the less stable species CH3CH2CH2CH; this reaction shows a barrier of 339.7 kJ/mol, which is almost equal to the endothermicity of the process.

From **Figure 11** we can notice that the main dissociation channel should be the one leading to 1-butene and water since it shows the lowest barrier. Due to the relevance of this point, we decided to perform comparison calculations in order to check the reliability of our results, following also the useful suggestions of the referees. We computed the barrier for the dissociation reaction of (a) into 1-butene and water also at the G3 (Curtiss et al., 1998) and G3B3 (Baboul et al., 1999) level. From **Table 1** we can see that the barrier height for this reaction is 259.8 kJ/mol at B3LYP/aug-cc-pVTZ level and 276.6 kJ/mol at CCSD(T)/aug-ccpVTZ level. This discrepancy is expected since it is well-known that B3LYP usually tends to underestimate the energy of the transition states, although it provides a reasonable estimate of the optimized geometries. This is confirmed by the G3 method which provides for the same reaction a barrier height of 281.1 kJ/mol. At G3B3 level we computed a barrier height of 279.3 kJ/mol. Therefore, the values computed at CCSD(T)/aug-cc-pVTZ, G3 and G3B3 level differ by less than the estimated uncertainty (±5 kJ/mol) in the calculations. The CCSD(T)/aug-cc-pVTZ barrier height computed at the G3 (G3B3) optimized geometry is 279.0 (277.5) kJ/mol, confirming that the B3LYP provides a correct description of the optimized geometries, although it underestimates the energies of the transition states.

In **Figure 12** we have reported the main dissociation channels which do not show a transition state. All these reactions are highly endothermic. In particular, the hydrogen atom loss reactions show an endothermicity around or higher of 400 kJ/mol.

The same reaction has been previously investigated by Cai et al. (2012). The agreement between our results and Cai et al. investigation is very good, despite the different methodologies employed. The only significant difference is in the channels leading to HCOH because we considered both the formation of HCOH trans and cis, while Cai et al. (2012) considered only one species, without specifying which one they investigated.

Concerning the kinetics calculations, some details specific to the system considered should be mentioned. It was reasonably assumed that the reaction starts from an equilibrium population of the two 1-butanol conformers. Moreover, in the case of the production of the three interconvertible species CHOH(cis), CHOH(trans), and CH2O, it was assumed that an eventual equilibrium was reached between them. As a result, the rate TABLE 1 | Enthalpy changes and barrier heights (kJ/mol, 298.15 K) computed at the B3LYP/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory for selected dissociation and isomerization processes for the system CH3CH2CH2CH2OH.


constants for the production of these three species were summed together for each energy and, subsequently, this overall rate constant was partitioned between the three based on the density of states of each species for the particular energy considered. The rate coefficients for the most important channels are reported in **Figure 13**, while the relative branching ratios for the seven channels actually contributing up to 2,000 K are shown in **Figure 14**.

It can be seen that the most abundant channel by far is CH3CH2CHCH<sup>2</sup> + H2O. The reason for this is easily seen to be the fact that the barrier to this channel is the lowest one. Nevertheless, this barrier lies 276.6 kJ mol−<sup>1</sup> above the reactants and, as a result, the corresponding rate constant becomes relevant only above 1,000 K. Our rate coefficient for this channel is essentially identical to the one calculated by Cai et al. (2012), apart from the highest temperatures, where the rate coefficient seems to increase with a different slope. We suspect that this curvature of their rate constants at high temperatures may be due to the fact that Cai et al. only consider energies up to 600 kJ mol−<sup>1</sup> while we go up to 1,500 kJ mol−<sup>1</sup> . The next two channels, of similar abundance to each other (but much lower than the first one) are CH3CH2CH2CH + H2O and CH3CH2CH<sup>3</sup> + CH2O (which are not shown by Cai et al. in their Arrhenius plots). Even though the barrier to the first of the two is significantly lower than the barrier to CH2O formation, it should be remembered that the latter channel is in equilibrium with the formation of the CHOH (cis and trans) products, as CHOH isomerizes without losing energy. As the formaldehyde product lies much lower in energy than both CHOH species, it is almost exclusively favored at equilibrium and, thus, all rate constants leading to CHOH or CH2O essentially are rate constants for formaldehyde formation. In particular, the barrier leading to CHOH (trans) from the (a) conformer of butanol is essentially identical to the barrier leading to CH3CH2CH2CH + H2O and this explains the similar abundance of the two channels.

The next highest channel (of very similar abundance to the previous ones) is the formation of CH2CH2OH + CH3CH2, followed by the CH2OH + CH3CH2CH<sup>2</sup> one. Even though it is the second of these two channels that has the lowest energy barrier of the two, the first one is augmented by an increased density of states caused by low-frequency vibrational modes, i.e., an entropy effect. This inversion of the rate constants with respect to the potential barriers is also seen in the rate constants of Cai et al. For the same reason, the CH2CH2CH2OH + CH<sup>3</sup> channel, even though it has an energy barrier very similar to the CH2CH2OH + CH3CH<sup>2</sup> channel, is penalized by the high rotational constant of the methyl radical which drastically reduces its density of states. Again, this is also precisely the effect seen in the Cai et al. rate constants. The effect is seen even more clearly for the butanal + H<sup>2</sup> production channel (which is not considered by Cai et al.), whose rate constant is noticeably even lower than that of CH<sup>3</sup> production.

It is to be noted that the rate constants of Cai et al. (2012) for the last three channels mentioned (which have monotonic reaction paths), although very similar to ours, are consistently somewhat higher. As our rate constants have been computed variationally (choosing the minimal rate constant among various candidate transition states), we feel that such a difference may be due to an incomplete sampling of the configuration space by the authors.

Finally, the other channels we have computed (pertaining to OH and H elimination from the original butanol molecule) only play a minor role in the kinetics and we have deemed their rate constants undetectable by the present experiment. Therefore, the assumption used in the analysis of our experimental results is fully supported by the present calculations.

## CONCLUSIONS

The present experimental results clearly demonstrate that butene is an important pyrolysis product under the experimental conditions of our experiments. These results are confirmed by the theoretical calculations of the decomposition rate coefficients which identify 1-butene as the most important product in the temperature range spanned in our experiments. In addition to that, there is no experimental evidence that 1-butanal is formed by elimination of molecular hydrogen. Considering that butanal has a parent peak with a significant intensity at 70 eV, were it formed we should have seen it. Finally, our results indicate that methyl elimination is also occurring. As for the other channels, we have a clear indication that C-C bond breaking channels are occurring, but we are unable to quantify their yields as they interfere with each other because of dissociative ionization. Nonetheless, it is clear from the trend reported in **Figure 14** that the extent of pyrolysis and the impact of the other channels is increasing with the temperature.

Our theoretical investigation is in line with previous characterization and is in agreement with the experimental results. The H-elimination channels have been reported here for the first time, but, as expected because of their high energy levels, they do not contribute significantly to the process.

## DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

## AUTHOR CONTRIBUTIONS

DoS, NB, SF, and CN performed the experiments and the experimental data analysis. MR and LP performed the electronic structure calculations. DiS and NF performed the kinetics calculations. The manuscript was written by NB, DiS, DoS, and MR.

## FUNDING

This work was financially supported by Sapienza University of Rome (Progetti di Ricerca, 2017), Fondazione Cassa Risparmio Perugia Italy (Project code: 2014.0253.021 Scientific and Technological Research) and the University of Perugia (Fondo Ricerca di Base 2017). Partial support from COST Action CM1404 (Chemistry of Smart Energy Carriers and Technologies—SMARTCATS) is also acknowledged.

## ACKNOWLEDGMENTS

We gratefully acknowledge the Università degli Studi di Perugia and MIUR for financial support to the project AMIS, through the program Dipartimenti di Eccellenza−2018–2022.

## REFERENCES


studied by pyrolysis in combination with molecular beam mass spectrometric techniques. J. Chem. Phys. 112, 3086–3093. doi: 10.1021/jp077406j


using density-functional force-fields. J. Phys. Chem. 98, 11623–11627. doi: 10.1021/j100096a001


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Rosi, Skouteris, Balucani, Nappi, Faginas Lago, Pacifici, Falcinelli and Stranges. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Radicals and Ions Formed in Plasma-Treated Organic Solvents: A Mechanistic Investigation to Rationalize the Enhancement of Electrospinnability of Polycaprolactone

#### Edited by:

Antonio Barbon<sup>2</sup>

Nathalie De Geyter <sup>1</sup>

Stefano Falcinelli, University of Perugia, Italy

#### Reviewed by:

Davide Bassi, University of Trento, Italy James M. Farrar, University of Rochester, United States

#### \*Correspondence:

Ester Marotta ester.marotta@unipd.it

†These authors share first authorship

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 07 March 2019 Accepted: 26 April 2019 Published: 16 May 2019

#### Citation:

Grande S, Tampieri F, Nikiforov A, Giardina A, Barbon A, Cools P, Morent R, Paradisi C, Marotta E and De Geyter N (2019) Radicals and Ions Formed in Plasma-Treated Organic Solvents: A Mechanistic Investigation to Rationalize the Enhancement of Electrospinnability of Polycaprolactone. Front. Chem. 7:344. doi: 10.3389/fchem.2019.00344 <sup>1</sup> Research Unit Plasma Technology, Department of Applied Physics, Faculty of Engineering and Architecture, Ghent University, Ghent, Belgium, <sup>2</sup> Department of Chemical Sciences, Università degli Studi di Padova, Padua, Italy

, Rino Morent <sup>1</sup>

, Agata Giardina<sup>2</sup>

, Cristina Paradisi <sup>2</sup>

,

, Ester Marotta<sup>2</sup>

\* and

Silvia Grande1†, Francesco Tampieri 2†, Anton Nikiforov <sup>1</sup>

, Pieter Cools <sup>1</sup>

This paper reports and discusses the beneficial effects on the quality of electrospun polycaprolactone nanofibers brought about by pretreatment of the solvent with non-thermal plasma. Chloroform/dimethylformamide 9:1 (CHCl3:DMF 9:1) and pure chloroform were pretreated by a few minute exposure to the plasma generated by an atmospheric pressure plasma jet (APPJ). Interestingly, when pure chloroform was used, the advantages of plasma pretreatment of the solvent were way less pronounced than found with the CHCl3:DMF 9:1 mixture. The chemical modifications induced by the plasma in the solvents were investigated by means of complementary analytical techniques. GC-MS revealed the formation of solvent-derived volatile products, notably tetrachloroethylene (C2Cl4), 1,1,2,2-tetrachloroethane (C2H2Cl4), pentachloroethane (C2HCl5), hexachloroethane (C2Cl6) and, in the case of the mixed solvent, also N-methylformamide (C2H5NO). The chlorinated volatile products are attributed to reactions of ·Cl and Cl-containing methyl radicals and carbenes formed in the plasma-treated solvents. ·Cl and ·CCl<sup>3</sup> radicals were detected and identified by EPR spectroscopy analyses. Ion chromatography revealed the presence of Cl−, NO<sup>−</sup> 3 , and HCOO<sup>−</sup> (the latter only in the presence of DMF) in the plasma-treated solvents, thus accounting for the observed increased conductivity and acidification of the solvent after plasma treatment. Mechanisms for the formation of these solvent derived products induced by plasma are proposed and discussed. The major role of radicals and ions in the plasma chemistry of chloroform and of the chloroform/dimethylformamide mixture is highlighted. The results provide insight into the interaction of plasma with organic solvents, a field so far little explored but holding promise for interesting applications.

Keywords: non-thermal plasma (NTP), plasma jet in liquid, chloroform, dimethylformamide (DMF), spin-trapping

## INTRODUCTION

It was recently reported that the application of nonthermal plasma leads to remarkable improvements in the electrospinnability of polymer solutions to form nanofibers (Shi et al., 2011; Colombo et al., 2014; Grande et al., 2017; Rezaei et al., 2018b) but no explanation was given for the origin of these effects.

Electrospinning is an efficient and powerful fabrication process to obtain high quality nanofibers with a wide range of diameters, from several micrometers down to a few tens of nanometers (Frenot and Chronakis, 2003; Reneker and Yarin, 2008). Because of its ease of use and versatility, this technique has led to an exponential increase in the production of nanofibers and their application in many different fields such as filtration (Shabafrooz et al., 2014), sensors (Huang et al., 2003), electronics (Long et al., 2012), and biomedicine (Venugopal and Ramakrishna, 2005). A typical electrospinning process involves the application of a high voltage (HV) between a tip, from which the polymer solution is extruded, and a collector (Bhardwaj and Kundu, 2010). The HV acting on free charges present in the polymer solution attracts the liquid toward the collector generating a jet which upon evaporation of the solvent leads to the formation of fibers on the collector itself (Teo and Ramakrishna, 2006). Various parameters influence the properties and quality of electrospun nanofibers, a major role being played by the characteristics of the polymer solution, notably its electrical conductivity, viscosity and surface tension. Indeed, a commonly used strategy to enhance the electrospinnability of polymer solutions consists in increasing the solution conductivity with additives such as salts or polar organic solvents (Hsu and Shivkumar, 2004; Qin et al., 2007; Ryu and Kwak, 2013). However, the use of additives can affect the chemical composition and properties of electrospun nanofibers and pose safety and environmental issues (Zong et al., 2002; Hsu and Shivkumar, 2004).

Non-thermal plasma is a partially ionized gas in nonequilibrium thermal state in which the electrons temperature is much higher than that of ions and neutrals. Such plasmas are conveniently generated by electrical discharges in a gas at room temperature and atmospheric pressure. When applied in contact with liquids, the discharges generate intense UV radiation, shock waves and active radicals, which can induce variations of the chemical composition of the liquid itself as well as directly affect any organic or biological material present in the system (Bruggeman and Leys, 2009; Bruggeman et al., 2016). Many electrode configurations and experimental set-ups have already been employed to work with liquids (Bruggeman et al., 2016), but only a few studies involve organic solvents for polymer solution modification (Shi et al., 2011; Colombo et al., 2014; Grande et al., 2017; Rezaei et al., 2018b).

In previous work by some of the authors of this paper, an atmospheric pressure plasma jet (APPJ), explicitly designed to ensure a close and intense contact between the plasma plume and the liquid (Grande et al., 2017; Rezaei et al., 2018a,b), was used to treat solutions of polycaprolactone (PCL) or polylactic acid (PLA) in solvent mixtures of chloroform (CHCl3) and N,N-dimethylformamide (DMF) (Grande et al., 2017; Rezaei et al., 2018b). It was found that plasma treatment of these solutions before electrospinning leads to nanofibers of better quality, i.e., with a bead-free morphology and uniform diameter, than obtained in control experiments without plasma. The analysis of the polymers by size exclusion chromatography (SEC) and X-ray photoelectron spectroscopy (XPS) showed that the molecular weight and the surface chemical composition of electrospun PCL nanofibers were not significantly affected by the APPJ treatment. Significant changes were instead observed in some important solution properties, notably conductivity and viscosity, both of which were found to increase after plasma treatment, and pH, which instead decreased. Thus, the enhanced electrospinnability was mainly attributed to these modifications.

Analogous improvements in the quality of electrospun fibers were obtained by plasma pretreatment of PLA solutions (Rezaei et al., 2018a,b). Interestingly, some improvement was also observed when the pure solvent, or solvent mixture, was treated with plasma prior to the addition of PLA (Rezaei et al., 2018a). Building on these promising results we studied the behavior of PCL in two organic solvents, pure chloroform and CHCl3:DMF 9:1 mixture, with the dual objective of verifying the scope and generality of the phenomenon observed for PLA and, more importantly, of studying in detail what happens to the organic solvent when it is treated with plasma. The latter subject is of great interest per se, as our present knowledge of the interaction between plasma and organic solvents and of its outcomes is very limited. Analyses were thus performed both on the nanomaterials produced and on the solvents. The quality and morphology of electrospun PCL nanofibers obtained according to various experimental protocols were investigated by means of SEM analysis, while plasma treated solvents were analyzed by gas chromatography coupled with mass spectrometry (GC-MS), by EPR spectroscopy, with the use of spin traps, and by ion chromatography, to gather information on the ions formed in the plasma-treated solvents. The combination of these techniques provided a powerful diagnostic array to gain insight into the complex mechanisms induced by plasma treatment. Comparison of the results obtained with pure CHCl<sup>3</sup> and with a CHCl3:DMF 9:1 mixture turned out to be particularly informative.

## MATERIALS AND METHODS

#### Materials

PCL pellets (M<sup>n</sup> = 80,000 g/mol), chloroform (CHCl3, > 99%), N,N-dimethylformamide (DMF, > 99%) N-tert-butyl-αphenylnitrone (PBN, 98%), sodium carbonate (Na2CO3), sodium bicarbonate (NaHCO3), sodium nitrate (NaNO3), potassium chloride (KCl), and formic acid (HCOOH) were purchased from Sigma-Aldrich and used without further purification. Argon gas (Alphagaz 1) was purchased from Air Liquide. Ultrapure grade water (milliQ water) was obtained by filtration of deionized water with a Millipore system.

## APPJ Treatment of PCL Solvents

The plasma source used in this work to treat PCL solvents is an APPJ specifically designed for liquid treatment. The set-up was already described in detail in a previous work (Grande et al., 2017). In short, the plasma was generated inside a thin quartz capillary fed by an argon flow. A tungsten needle was placed within the capillary and acted as high-voltage electrode, while a ring-shaped copper grounded electrode was placed around the quartz capillary at 4.5 cm from the tip of the tungsten needle. A constant argon flow of 1 standard liter per minute (slm) was sent through the capillary. Successively, the discharge was ignited by applying an AC high voltage (fixed frequency of 50 kHz) to the high-voltage electrode with a peak-to-peak value of 7.6 kV. A small reactor chamber, which can contain the solvents, was placed on top of the capillary exit by fixing a quartz tube with an inside and outside diameter of 13 mm and 20 mm respectively to a stainless-steel flange possessing a small opening where the APPJ quartz capillary can be inserted. The distance between the top of the grounded electrode and the bottom of the stainless-steel flange was maintained at 0.5 cm to ensure electrical isolation. For all experiments, a fixed liquid sample volume of 10 mL was introduced into the reactor chamber using a glass syringe. Afterwards, the top of the reactor chamber was covered with a stainless-steel flange containing a small opening of 2 mm acting as gas outlet, thereby limiting solvent evaporation during plasma treatment. In this work, pure CHCl<sup>3</sup> and a mixture of CHCl3:DMF (9:1 v/v) were exposed to the APPJ for a fixed plasma exposure time of 3 min. This treatment time was chosen based on the results obtained in plasma treatment of the polymer solutions (Grande et al., 2017). Under those conditions, it was observed that extending the treatment time beyond 3 min did not bring any further improvement on the morphology of electrospun nanofibers. Thus, the same treatment time was applied in this study to allow for a direct comparison of the results obtained with the two plasma activation protocols.

To electrically characterize the plasma, the voltage applied to the needle electrode was measured using a high voltage probe (Tektronix P6015A) while the charge on the electrodes was obtained by measuring the voltage over a capacitor of 10 nF placed in series with the grounded electrode. The obtained voltage-vs.-charge plot was visualized using a PC oscilloscope (Picoscope 3204A) enabling the construction of a Lissajous figure. From the area enclosed by this figure, the electrical energy consumed per voltage cycle Eel could be estimated. The electrical power Pel was then obtained by multiplying the electrical energy with the frequency of the feeding voltage, which is equal to 50 kHz in this work, and was found to be 4.8 W.

The Ar streamed samples, used as control, were prepared under the same conditions as the plasma treated samples except for the fact that plasma was turned off. After 3 min of Ar streaming of the mixture CHCl3:DMF 9:1 the remaining liquid volume was 8 mL.

## Preparation and Electrospinning of PCL Polymer Solutions

Five percent w/v PCL polymer solutions were prepared by dissolving PCL pellets in pristine and plasma-treated CHCl<sup>3</sup> as well as the pristine and plasma-treated CHCl3:DMF mixture. Subsequently, the differently prepared PCL solutions were stirred at room temperature for 3 h and electrospun. In this study, a bottom-up electrospinning process was performed using a customized Nanospinner 24 electrospinning machine (Inovenso, Turkey). In a first step, the PCL polymer solution under study was loaded into a 5 mL standard syringe connected to a bluntended copper needle and placed into a syringe pump (NE-300 Just InfusionTM syringe pump). This syringe pump controlled the flow rate of the polymer solution through a polyethylene tube (inner diameter: 2 mm) ending in an aluminum pipe containing a single brass nozzle with an inner diameter of 0.8 mm. During the electrospinning process, the flow rate of the polymer solution was maintained at 0.1 mL/min. The metallic nozzle was placed vertically below a rotating stainless-steel collector (100 rpm) at a distance of 20 cm. During electrospinning, a DC high voltage of 30 kV was supplied to the nozzle, while the rotating cylinder was grounded. PCL nanofibers were subsequently collected on an aluminum sheet placed on top of the collecting cylinder.

## Characterization of the Electrospun PCL Nanofibers by SEM

The surface morphology of the PCL nanofibers was imaged using a JEOL JSM-6010 PLUS/LV scanning electron microscope (SEM). SEM images were acquired with an accelerating voltage of 5 or 7 kV, after coating the samples with a thin layer of gold making use of a sputter coater (JFC-1300 autofine coater, JEOL).

#### Chemical Characterization of Pristine and Plasma-Treated Solvents GC-MS

GC-MS analyses of the PCL liquid solvents under study (CHCl<sup>3</sup> and a 9:1 mixture of CHCl3:DMF) before and after plasma treatment were carried out with an Agilent Technologies instrument (GC System 6850 Series, Mass Selective Detector 5973) using an HP-5ms column (30 m × 0.25 mm internal diameter). One microliter samples were injected and analyzed with the following temperature program: 50◦C for 5 min, 50- 200◦C at 15◦C/min and 200◦C for 5 min.

#### Ion Chromatography, Conductivity and pH

To quantify the ionic species in the liquid solvents, 5 mL of MilliQ water was added to 5 mL solvent into a separating funnel. Afterwards, the aqueous phase was analyzed by ion chromatography using a Dionex-ICS-900 instrument equipped with a Dionex IonPac AS22 column. A mixture of 4.5 mM Na2CO<sup>3</sup> and 1.4 mM NaHCO<sup>3</sup> was used as eluent at a flow rate of 1.2 mL/min. Standard solutions of KCl and NaNO<sup>3</sup> were used to obtain calibration lines for chloride and nitrate ions, respectively.

The conductivity of the aqueous phase was also determined using a FiveEasyTM conductivity meter (Mettler Toledo) equipped with an InLab720 conductivity probe operating in a conductivity range of 0.1 to 500 µS/cm, while the pH of the aqueous phase was obtained making use of a FiveEasyTM pH meter equipped with an InLab Science Pro-ISM pH probe.

#### Spin-Trapping Experiments

The spin-trapping measurements have been performed at room temperature using an X-band Bruker ELEXSYS spectrometer equipped with an ER 4103TM cylindrical mode resonator for aqueous and high-dielectric samples. In a first step, a solution of PBN 1.0·10−<sup>2</sup> M was prepared in chloroform and subsequently treated in the plasma reactor for 3 min. Immediately after plasma treatment, the solution was transferred to an EPR flat cell (500 µL capacity) and rapidly introduced in the EPR spectrometer. EPR spectra were collected at room temperature, at different delays after the introduction of the sample in the spectrometer, in order to follow the time evolution of the EPR signals; each spectrum was the average of 10 scans. The acquisition parameters were: modulation frequency 100 kHz, scan range 100 G, modulation amplitude 1.5 G, receiver gain 60 dB, microwave frequency 9.77 GHz (scaling of the field has been used), power attenuation 18 dB, time constant, 5.12 ms, scan time 41.94 s, conversion time 40.96 ms. All EPR spectra have been reproduced using EPR WinSim software in order to isolate and identify all the radical species (Duling, 1994).

## RESULTS

## SEM Analysis of Electrospun PCL Nanofibers

The APPJ (Grande et al., 2017), briefly described in the Experimental Section, was used to treat the pure solvents (CHCl<sup>3</sup> and the CHCl3:DMF 9:1 mixture), after which PCL was dissolved in the plasma-treated solvents. The obtained PCL solutions were

subsequently electrospun and SEM analyses were carried out of electrospun PCL nanofibers obtained under different conditions. **Figure 1** reports SEM images obtained for these experiments and for controls run without plasma pretreatment of the solvents. Specifically **Figures 1A,B** show the SEM images of electrospun fibers obtained when PCL was dissolved in pristine and in plasma-treated CHCl3, respectively. In both cases, non-uniform PCL fibers with a large amount of beads can be observed, but the average size of the beads appears to be smaller in the plasma treated samples. The SEM images relative to the electrospun PCL fibers obtained when PCL was dissolved in untreated and plasma-treated CHCl3:DMF 9:1 are reported in **Figures 1C,E**, respectively.

These images clearly reveal the dramatic improvement in the nanofibers quality achieved by plasma treatment of the solvent preliminary to addition of PCL and electrospinning of the solution. The obtained sample consisted of a uniform and almost bead-free mesh. A control experiment was carried out to determine the possible contribution to the effects observed in **Figure 1E** by modifications of the solvent composition due to vapor stripping by the argon flow used to sustain the discharge during plasma treatment. **Figure 1D** shows a SEM image of the sample obtained in this experiment, which was carried out with the plasma switched off and flowing argon for a time long enough to achieve the same volume reduction as obtained in experiments with "plasma on." It is seen that without plasma, non-uniform PCL fibers containing a large number of beads were obtained. However, the beads are definitely smaller compared to those in the untreated control sample (**Figure 1C**). This improvement can be ascribed to the different ratio of the two solvents in the final solution which was used to electrospin the fibers shown in **Figure 1D**. This effect is the result of the two solvents different evaporation rates and the consequent increase in the relative amount of DMF with respect to the 9:1 ratio in the original mixture.

## Chemical Analysis of Plasma-Treated Solvents

#### GC-MS Analyses

To investigate possible modifications of the solvent composition and the formation of new volatile organic compounds due to the plasma treatment, GC-MS analyses of untreated and plasma-treated CHCl<sup>3</sup> and CHCl3:DMF (9:1) were performed. **Figure 2** reports the chromatograms of CHCl<sup>3</sup> before and after 3 min plasma treatment, respectively. In the chromatogram of untreated CHCl<sup>3</sup> some impurities were detected and are labeled as in. After CHCl<sup>3</sup> was treated with plasma for 3 min, four additional peaks (A to D) were detected in the chromatogram. Based on the analysis of their mass spectra, reported in **Figure 2**, and comparison with reference spectra (Linstrom and Mallard, 2019), these additional peaks could be ascribed to chlorinated ethanes (1,1,2,2-tetrachloroethane, pentachloroethane, and hexachloroethane) and tetrachloroethylene. The anomalous isotopic distribution observed in some of our spectra are due to low signal intensities.

**Figure 3** shows the chromatograms of the pristine and plasma-treated CHCl3:DMF 9:1 mixture, respectively. **Figure 3** shows an additional impurity found in DMF, labeled as i4, which could be identified as formamide from its mass spectrum. In the chromatogram of plasma-treated CHCl3:DMF 9:1, the same peaks as detected in the chromatogram of plasma-treated CHCl<sup>3</sup> can be observed, except for the peak attributed to tetrachloroethylene, which was hidden by the broad peak due to DMF. Moreover, the relative ratio between the peaks of the three chloroethanes (B, C, and D) was different with respect to the case in which these were formed by plasma treatment of pure CHCl3. In particular, hexachloroethane was no longer the major chloroethane formed and the relative amount of 1,1,2,2-tetrachloroethane was significantly higher. An additional peak was also detected in the chromatogram of plasma-treated CHCl3:DMF (peak E in **Figure 3**), which could be attributed, on the basis of its MS spectrum, to N-methylformamide.

#### Ion Chromatography, Conductivity and pH

As ascertained in previous publications (Šunka et al., 1999; Rezaei et al., 2018a,b), the plasma treatment of polymer solutions

TABLE 1 | Extracted water: conductivity, pH and concentration of chloride and nitrate from different solvents.


induces an increase in electrical conductivity of the liquids. In this work, we investigated whether this increase also occurs when the solvents are treated by plasma in the absence of polymers. **Table 1** shows the conductivity of the aqueous phase used for the extraction of water soluble species from the treated solvents (as described in the experimental part). For pure CHCl<sup>3</sup> a large increase in conductivity was indeed observed after plasma treatment. In the case of the CHCl3:DMF 9:1 solvent mixture, a tremendous increase in conductivity was induced by plasma treatment of the pristine mixture. In contrast, only a slight increase was observed after argon streaming of CHCl3:DMF (**Table 1**), confirming that the increase in conductivity was really due to plasma treatment. To identify and quantify the ions responsible for the solution conductivity, ion chromatography was applied.

The ion chromatograms of untreated and plasma-treated chloroform are shown in **Figure 4A**. The untreated sample

gave only a small peak in the chromatogram, corresponding to chloride ions (Cl−). Quantitative analyses showed that the intensity of this peak and the corresponding concentration in solution was considerably higher after plasma treatment (**Table 1**). In addition, because of the plasma treatment, a peak due to nitrate ions (NO<sup>−</sup> 3 ) also appeared in the ion chromatogram. NO<sup>−</sup> <sup>3</sup> was most likely present due to the interaction of the discharge with residual environmental air, which could be mixed in the solvent during the treatment.

The ion chromatograms of the untreated, argon-streamed and plasma-treated CHCl3:DMF mixture are shown in **Figure 4B**. Similar to pure chloroform, the untreated and argon-streamed samples only showed a small peak corresponding to Cl−, while the plasma-treated sample revealed a significantly larger Cl<sup>−</sup> peak and the formation of nitrate ions. Moreover, compared to plasma-treated chloroform, one additional peak appeared in the chromatogram of the plasma-treated solvent mixture, which could be ascribed to formate (HCOO−). Also in this case, the concentration of chloride ions has been quantified (**Table 1**). Compared to pure treated chloroform, the amount of Cl<sup>−</sup> was one order of magnitude higher when DMF was added to chloroform. On the contrary, the concentration of nitrates remained more or less the same, confirming the hypothesis that nitrates were formed from residual environmental air in the plasma set-up.

The pH of the aqueous extracts from the organic solvents used in this study was also determined before and after plasma treatment. The results, summarized in **Table 1**, clearly showed a decrease of the solution pH induced by plasma treatment. The observed increased acidity could be directly linked to the increased concentration of chloride and to the formation of nitrate and formate ions, considering that these species were produced in their acidic form.

#### Spin-Trapping Experiments

Spin-trapping experiments have been performed to detect and identify radicals in solution. A spin trap is a diamagnetic compound (most commonly an organic nitroso or nitrone compound) that can react with a radical species to form a paramagnetic adduct with a lifetime long enough to be detected by EPR spectroscopy (Alberti and Macciantelli, 2009). The spintrapping analysis of the plasma treated solvents has already been presented in detail in a previous work (Rezaei et al., 2018a). Here we supplemented that analysis with some new results obtained by spin-trapping experiments done in pure chloroform.

A 1.0·10−<sup>2</sup> M chloroform solution of spin-trap PBN (N-tert-Butyl-α-phenylnitrone) was treated in the plasma reactor for the desired time and, immediately after the treatment, analyzed by EPR. As an example, the cw-EPR spectrum of a solution treated with plasma for 3 min is reported in **Figure 5A**. The careful reproduction of the experimental spectrum by means of an appropriate simulation software (Duling, 1994) revealed that the spectrum is the sum of different contributions, as presented in **Figure 5B**, with the relative hyperfine interaction values (ai) which are also summarized in **Table 2**. Comparison of these hyperfine values with data reported in the literature (Davies and Slater, 1986) enabled us to identify the various

TABLE 2 | Hyperfine coupling constants for the relative nuclei of the contributions displayed in Figure 5B used for the simulation of spectrum Figure 5A.


components (see the first column of **Table 2**, and the attributed structures in **Figure 5B**). Please note that for the adduct PBN-Cl (formed by trapping a Cl atom), the simulation takes into account the presence of both <sup>35</sup>Cl and <sup>37</sup>Cl isotopes in fixed natural abundance (76 and 24%, respectively) (Davies and Slater, 1986); for them, a( <sup>37</sup>Cl)/a( <sup>35</sup>Cl) = gN( <sup>37</sup>Cl)/gN( <sup>35</sup>Cl). The acyl nitroxide has been observed in other works (Ohto et al., 1977; Niki et al., 1983) and is attributed to an oxidation product of the spin-trap (Davies and Slater, 1986), likely formed by reaction of PBN with some oxidizing reactive species of the plasma.

We followed the time evolution of the cw-EPR spectrum, by acquiring spectra at different delay times after the end of the treatment. No further species were observed, but the relative weight of the three species changed in time, as reported in **Figure 5C**. Specifically, the signals due to the PBN-CCl<sup>3</sup> and PBN-Cl adducts decreased in time whereas that assigned to the PBN=O adduct increased. The overall intensity did not significantly change in 10 min, but a substantial decay of all adducts intensities was observed after 20 min. Possibly the PBN=O adduct was produced because of exposure to air, but we cannot exclude other mechanisms of production. For instance, a similar rise of the PBN oxidation products has been found for a system in which Cl radicals were produced (Callison et al., 2012). In that case the authors invoked as a possible mechanism the reaction of PBN with relatively long lived molecular chlorine, produced from atomic chlorine.

## DISCUSSION

Considering all the species detected using the various techniques employed in this study, it is possible to outline the major chemical processes taking place when the argon plasma jet is applied to chloroform and to chloroform containing 10% DMF. It is reasonable to assume that these chemical processes occur in the argon plasma bubbles where chloroform and dimethylformamide will also be present as gases due to the evaporation induced by the discharge. The stable products formed within the gas phase are then transferred into the liquid. The formation of chloroethanes is attributed to radical recombination reactions, specifically two ·CCl<sup>3</sup> radicals in case of hexachloroethane (Shilov and Sabirova, 1959; Michael et al., 1993), one ·CCl<sup>3</sup> and one ·CHCl<sup>2</sup> radical in case of pentachloroethane and two ·CHCl<sup>2</sup> radicals in case of 1,1,2,2-tetrachloroethane, as shown in reactions 1–3. Perchloroethane, Cl3C-CCl3, was the most abundant chloroethane detected by GC-MS analysis in plasmatreated chloroform. The ·CCl<sup>3</sup> radical was indeed observed by EPR spectroscopy in a freshly plasma treated sample of pure chloroform. In contrast, Cl2HC-CHCl<sup>2</sup> was barely detectable in the GC-MS chromatogram suggesting that the ·CHCl<sup>2</sup> radical was present in lower concentration than ·CCl3. This conclusion is consistent with the fact that this radical was not observed by EPR analysis.

$$2\cdot \text{CCl}\_3 \rightarrow \text{Cl}\_3\text{C}-\text{CCl}\_3 \tag{1}$$

$$\cdot \text{CCl}\_3 + \cdot \text{CHCl}\_2 \rightarrow \text{Cl}\_3\text{C}-\text{CHCl}\_2 \tag{2}$$

$$2\cdot \text{CHCl}\_2 \rightarrow \text{Cl}\_2\text{HC}-\text{CHCl}\_2\tag{3}$$

The formation of tetrachloroethene can be ascribed to the recombination of two :CCl<sup>2</sup> carbene units (4) (Won and Bozzelli, 1992).

$$\text{2:CCl}\_2 \rightarrow \text{Cl}\_2\text{C=CCl}\_2 \tag{4}$$

According to the literature, the formation of :CCl<sup>2</sup> from chloroform can occur either via loss of ·H from ·CHCl<sup>2</sup> (5) (Won and Bozzelli, 1992) or via chloroform dissociation into :CCl<sup>2</sup> and HCl (6) (Semeluk and Bernstein, 1954). The formation of hydrogen chloride was indeed verified experimentally by the measurement of the solution pH (H+) and ion chromatography (Cl−).

$$\cdot \text{CHCl}\_2 \rightarrow \cdot \text{H} + \cdot \text{CCl}\_2 \tag{5}$$

$$\text{CHCl}\_3 \rightarrow : \text{CCl}\_2 + \text{HCl} \tag{6}$$

In the literature :CCl<sup>2</sup> and HCl are reported to be the main products of chloroform thermal decomposition (Semeluk and Bernstein, 1954; Chuang and Bozzelli, 1986) but also of its decomposition induced by non-thermal plasma (Foglein et al., 2005; Gaikwad et al., 2013). In the case of the APPJ used in this work, thermal dissociation is highly unlikely because the gas temperature was too low. We thus believe that chloroform/electron interactions are responsible for the formation of :CCl<sup>2</sup> and HCl.

Chloroform thermal decomposition (Semeluk and Bernstein, 1954) or chloroform excitation by interaction with electrons, photons or Ar metastables (Yang et al., 1994) can also induce the homolytic dissociation of a C-Cl bond (7), and, less likely, of the C-H bond (8). We succeeded in detecting two of the radicals formed in these reactions, notably ·Cl and ·CCl3, by spin trapping and EPR analysis. Evidence for the formation of the third, ·CHCl2, was provided by the observation of Cl3C-CHCl<sup>2</sup> and Cl2HC-CHCl<sup>2</sup> among the products of plasma treatment. Failure to detect CHCl<sup>2</sup> by EPR analysis could be attributed to its low concentration in the system.

$$\cdot \text{CHCl}\_3 \xrightarrow{\text{e}^- \text{ or } \text{hv or Ar}^\*} \cdot \text{Cl} + \cdot \text{CHCl}\_2 \tag{7}$$

$$\cdot \text{CHCl}\_3 \xrightarrow{\text{e}^- \text{ or } \text{hv or Ar}^\*} \cdot \text{H} + \cdot \text{CCl}\_3 \tag{8}$$

Reaction (8) is less probable than reaction (7) due to the higher dissociation energy of the C-H bond with respect to the C-Cl bond [average bond dissociation energies for C-H and C-Cl bonds are 4.13 eV e 3.43 eV, respectively (Weissman and Benson, 1983)]. Thus, an alternative source of ·CCl<sup>3</sup> must be considered to account for its higher abundance than ·CHCl2, specifically the reaction of ·Cl with chloroform, which proceeds via hydrogen abstraction (9) (Orlando, 1999).

$$\cdot \text{Cl} + \text{CHCl}\_3 \rightarrow \cdot \text{CCl}\_3 + \text{HCl} \tag{9}$$

When DMF was added to chloroform and the mixture CHCl3:DMF 9:1 was subjected to plasma treatment, two significant changes in the product distribution were observed: the concentration of Cl<sup>−</sup> increased by a 10-fold factor and Cl3C-CCl<sup>3</sup> was no longer the most abundant chloroethane produced, the area of its chromatographic peak becoming similar to those of Cl3C-CHCl<sup>2</sup> and Cl2HC-CHCl2. The latter observation implies that in the mixed solvent the ·CHCl<sup>2</sup> radical was formed in similar concentration as ·CCl3. All these observations are rationalized if one considers that in the presence of DMF another important process takes place, i.e., dissociative electron attachment to chloroform (10). The products of this reaction are indeed chloride and ·CHCl2, as known from literature (Scheunemann et al., 1980; Matejcik et al., 1997). The promotion of this process in the presence of DMF could be attributed to the well-known ability of DMF to solvate and stabilize ions, especially anions.

$$\cdot \text{CHCl}\_3 + \text{e}^- \rightarrow \text{Cl}^- + \cdot \text{CHCl}\_2 \tag{10}$$

Thus, reaction (10) accounts for both the increase of recombination products Cl3C-CHCl<sup>2</sup> and Cl2HC-CHCl<sup>2</sup> with respect to Cl3C-CCl<sup>3</sup> and the increase of chloride ions observed in the mixture CHCl3:DMF 9:1 with respect to pure CHCl3. It cannot be excluded that dissociative electron attachment may also occur in the liquid phase involving solvated electrons, formed at the gas/liquid interface and reacting there or within the solvent in the first layers in contact with the gas. It is known, indeed, that solvated electrons undergo efficient dissociative electron attachment reactions with chlorinated organic compounds in aqueous media producing chloride (Lichtscheidl and Getoff, 1976; Naik and Mohan, 2005; Yuan et al., 2015) and that they are also involved in organic solvents.

Two additional species observed in the presence of DMF are N-methylformamide and formic acid. N-methylformamide may originate from thermal or electron induced decomposition of DMF via homolytic dissociation of the N-C bond (11a), followed by hydrogen abstraction from chloroform (11b). As for formic acid, we believe it formed via hydrolysis of DMF which can occur in the presence of traces of water with acid catalysis. The presence of traces of water was previously detected by the appearance of the OH signal in the emission spectroscopy spectrum acquired during the plasma treatment of the mixture CHCl3:DMF 9:1 (Grande et al., 2017).

HC(=O)N(CH3)<sup>2</sup> + e <sup>−</sup> <sup>→</sup> HC(=O)N·(CH3) + ·CH<sup>3</sup> <sup>+</sup> <sup>e</sup> <sup>−</sup> (11a) HC(=O)N·(CH3) + CHCl<sup>3</sup> → HC(=O)NH(CH3) + ·CCl<sup>3</sup> (11b)

Finally, another process which must be considered is the ionization of the solvent. Considering the lower ionization energy of chloroform (EI = 11.37 eV) and of DMF (EI = 9.13 eV) with respect to that of argon (EI = 15.76 eV) (Linstrom and Mallard, 2019), it is expected that both solvents undergo ionization via charge exchange with argon ions (12a and 13a). The resulting radical cations can dissociate leading to CHCl<sup>+</sup> 2 and ·Cl (12b) and to HC(=O)N+(CH3) and ·CH<sup>3</sup> (13b), respectively.

$$\text{CHCl}\_3 + \text{Ar} \cdot ^+ \rightarrow \text{CHCl}\_3 \cdot ^+ + \text{Ar} \tag{12a}$$

$$\text{CHCl}\_3\text{\text{\textdegree\textdegree}} + \text{CHCl}\_2^+ + \cdot \text{Cl} \tag{12b}$$

$$\text{HC(=O)N(CH\_3)}\_2 + \text{Ar} \cdot ^+ \rightarrow \text{HC(=O)N(CH\_3)}\_2 \cdot ^+ + \text{Ar} \quad \text{(1.3a)}$$

$$\text{HC(=O)N(CH\_3)\_2\cdot ^+} \rightarrow \text{HC(=O)N}^+\text{(CH}\_3) + \cdot \text{CH}\_3 \quad \text{(13b)}$$

Since the proton affinity of CCl<sup>2</sup> (8.92 eV) is lower than that of DMF (9.19 eV) (Hunter and Lias, 1998), proton transfer from CHCl<sup>+</sup> 2 to DMF in the gas phase is thermodynamically favored and expected to be kinetically very fast (14). It is worth noting that reaction (14) may thus contribute to the acidification of the solution and provide a direct entry, in the presence of water traces, to acid catalyzed hydrolysis of DMF.

$$\text{CHCl}\_2^+ + \text{HC(=O)N(CH\_3)\_2} \rightarrow \text{:CCl}\_2 + \text{HC(=O)NH}^+ \text{(CH}\_3\text{)\_2} \text{ (14)}$$

#### CONCLUSIONS

All the experimental results obtained in the work described here fit nicely into a coherent mechanistic picture. We can thus compare and rationalize the effects of plasma treatment of CHCl<sup>3</sup> and of the CHCl3:DMF 9:1 mixture, which are useful solvents for the production of nanofibers by electrospinning of polymer solutions. It was found that plasma induces the formation of hydrogen chloride, a process which is more pronounced in the CHCl3/DMF solvent mixture than in pure CHCl3. The

#### REFERENCES


detection of tetrachloroethene and of chloroethanes, the products of recombination of :CCl2, ·CCl<sup>3</sup> and ·CHCl<sup>2</sup> radicals, allowed us to identify the major reaction pathways of chloroform in the absence and in the presence of DMF and, specifically, to underline the prominent role of DMF in the global process. These findings are valuable per se, considering the present lack of data and knowledge on the interaction of non-thermal plasma with organic solvents and on its consequences. They also explain the beneficial effect on PCL electrospinning, observed when the solvent, a CHCl3:DMF 9:1 mixture, was preliminarily treated by plasma prior to the addition of the polymer. It is thus proven that pretreatment of the solvent is an interesting possibility for electrospinning and it is expected that other applications might take advantage of this novel approach.

#### DATA AVAILABILITY

All datasets generated for this study are included in the manuscript and/or the supplementary files.

#### AUTHOR CONTRIBUTIONS

ND and RM conceived the research project. SG, FT, AN, AG, AB, and EM designed and performed the experiments and analyzed the data. SG, FT, AB, CP, and EM wrote the paper. All authors discussed the results and revised the paper.

## FUNDING

This research has received funding from the European Research Council (ERC) under the European Union's Seventh Framework Program (FP2007-2013): ERC Grant Agreement number 335929 (PLASMATS) and University of Padova (grant P-DiSC #05BIRD2017-UNIPD). PC would like to thank the Special Research Fund of Ghent University for financing his post-doctoral grant.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Grande, Tampieri, Nikiforov, Giardina, Barbon, Cools, Morent, Paradisi, Marotta and De Geyter. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Molecular Beam Scattering Experiments as a Sensitive Probe of the Interaction in Bromine–Noble Gas Complexes

David Cappelletti <sup>1</sup> \*, Antonio Cinti <sup>1</sup> , Andrea Nicoziani <sup>1</sup> , Stefano Falcinelli <sup>2</sup> and Fernando Pirani <sup>1</sup>

<sup>1</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Perugia, Italy, <sup>2</sup> Dipartimento di Ingegneria Civile ed Ambientale, Università degli Studi di Perugia, Perugia, Italy

This paper reports for the first time molecular beam experiments for the scattering of He, Ne, and Ar by the Br<sup>2</sup> molecule, with the aim of probing in detail the intermolecular interaction. Measurements have been performed under the experimental condition to resolve the glory pattern, a quantum interference effect observable in the collision velocity dependence of the integral cross section. We analyzed the experimental data with a reliable potential model defined as a combination of an anisotropic van der Waals component with the additional contribution due to charge transfer and polar flattening effects related to the formation of an intermolecular halogen bond. The model involves few parameters, whose values are related to fundamental physical properties of the interacting partners, and it allows an internally consistent comparison of the stability of the gas-phase adducts formed by Br<sup>2</sup> moiety with different noble gases as well as homologous complexes with the Cl<sup>2</sup> molecule. The same model appears to be also easily generalized to describe the interaction of diatomic halogen molecules in the excited B(35) electronic state where the halogen bond contribution tends to vanish and more anisotropic van der Waals components dominate the structure of the complexes with noble gases.

Keywords: halogen bond, charge transfer, molecular beam scattering, bromine, noble gases

## INTRODUCTION

The knowledge of the nature and the characterization of the role of the intermolecular halogen bond (XB) is presently recognized to be of great relevance in many areas of fundamental and applied research, including materials engineering, biochemistry, molecular recognition, drug design, and supra-molecular Chemistry (Gilday et al., 2015; Han et al., 2017).

In order to disentangle the effect of the XB on the molecular dynamics, it is necessary to identify the interaction components involved and to provide their radial and angular dependences. This information, seldom available in the literature, can obtained by investigating in detail prototypical systems, whose features are necessary to formulate interaction models useful for the description of the force fields in systems at increasing complexity and of applied interest (Cappelletti et al., 2015).

The weakly bound complexes Ng–X2, formed by a noble gas (Ng) and a di-halogen molecule X<sup>2</sup> (X=Cl, Br, I), have been considered as prototypes of particular relevance for investigating energy transfer mechanisms and for the characterization of the fundamental role of the intermolecular

#### Edited by:

Doo Soo Chung, Seoul National University, South Korea

#### Reviewed by:

Imran Khan, Sultan Qaboos University, Oman Siddharth Surajbhan Gautam, The Ohio State University, United States Jacek Antoni Klos, University of Maryland, College Park, United States

> \*Correspondence: David Cappelletti

david.cappelletti@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 04 February 2019 Accepted: 23 April 2019 Published: 17 May 2019

#### Citation:

Cappelletti D, Cinti A, Nicoziani A, Falcinelli S and Pirani F (2019) Molecular Beam Scattering Experiments as a Sensitive Probe of the Interaction in Bromine–Noble Gas Complexes. Front. Chem. 7:320. doi: 10.3389/fchem.2019.00320

**226**

interaction components (Baturo et al., 2017; Li et al., 2017) leading to the formation of the weak intermolecular halogen bond (Desiraju et al., 2013). Moreover, for the identification of basic selectivity in energy transfer processes, the X<sup>2</sup> moiety has been considered both the ground (X <sup>2</sup>Σ<sup>+</sup> g ) and in the excited (B <sup>3</sup>5u) electronic state (Janda et al., 1998; Rohrbacher et al., 2000; Delgado-Barrio et al., 2006; Beswick et al., 2012), and related potential energy surfaces (PES) have been classified as X (ground) and B (excited).

Extensive spectroscopic and theoretical studies (see, for instance, Jahn et al., 1996; Buchachenko et al., 2000; Prosmiti et al., 2002a,b; de Lara-Castells et al., 2004; Boucher et al., 2005; Garcia-Vela, 2005; Carrillo-Bohórquez et al., 2016) have been devoted to the characterization of the stability of the Ng–Br<sup>2</sup> adducts in the limiting collinear and T-shaped configurations and of the predissociation dynamics induced by electronic, vibrational, and rotational excitations.

Nowadays, it is clear that in the ground-state PES, both the collinear and T-shaped isomers have comparable binding energy and are separated by a significant saddle region. By contrast, in the electronically excited PES, the T-shaped configuration is the most stable one, as typical of most of the atom-diatom complexes bound by van der Waals (vdW) forces (de Lara-Castells et al., 2004; Garcia-Vela, 2005; Pirani et al., 2019). The origin of this difference in the topography of the PES is still being debated because it depends on a delicate balance between the involved interaction components. In particular, open questions concern the proper identification of the principal interaction terms, their modeling, and their dependence on the atomic or molecular partners involved within the complex.

Recently, we performed an integrated experimental/theoretical investigation on Ng–Cl<sup>2</sup> systems with the goal of adequately addressing some of the abovementioned open questions (Nunzi et al., 2019; Pirani et al., 2019). In particular, we have found that for such systems, the most relevant features of the X ground-state PESs are mainly determined by the anisotropic halogen bond components, which operate even in the case of the lightest He–Cl2. Such components concur to stabilize the collinear configuration selectively by charge transfer (CT) and polar flattening (PF) effects, which are specific interaction features of XB. Ab initio calculations have revealed that both CT and PF contributions miss in the electronic excited B PESs, where the formed adducts show typical vdW behavior. This observation is consistent with the behavior of other atom–diatom systems, as Ng–O<sup>2</sup> and Ng–N<sup>2</sup> complexes, dominated by size repulsion and dispersion/induction attraction (Aquilanti et al., 1995).

The present manuscript reports and discusses the results of a new experimental investigation, focused on the X ground PES of the He–, Ne–, and Ar–Br<sup>2</sup> systems, carried out with the molecular beam (MB) technique applied under the same conditions of recent experiments on Ng–Cl2. The analysis of these new scattering data has been performed by extending the methodology applied to the rationalization of data measured for homologous systems formed with the Cl<sup>2</sup> moiety (Nunzi et al., 2019; Pirani et al., 2019). In particular, the main components, characterizing the interaction potential between Ng and Br2, have been identified and their radial angular dependences represented through the adoption of semi-empirical/empirical equations involving only a few parameters, each one with a defined physical meaning. As for Ng–Cl<sup>2</sup> systems, we have found that X groundstate PES in Ng–Br<sup>2</sup> adducts is mainly determined by anisotropic halogen bond components, concurring to stabilize selectively the collinear configuration by CT and PF effects. The model has also been applied to predict the behavior of Kr– and Xe–Br<sup>2</sup> systems, for which MB experiments cannot be carried out under sufficiently high angular and velocity resolution conditions, obtainable for lighter Ng atoms, which are proper to resolve quantum interference effects in the scattering. Such an extension has been achieved by simply exploiting the change of parameters involved when one is moving along the Ng–Br<sup>2</sup> homologous family of systems. Finally, the features the obtained PES have been compared with results from the literature.

## EXPERIMENTAL APPARATUS AND SCATTERING RESULTS

Gas-phase scattering experiments have been carried out in order to measure the velocity dependence of the integral cross section. The availability of the projectile (here, He, Ne, and Ar) in a large speed range is of great relevance to perform measurements as a function of the collision velocity. On the other hand, the choice of temperature and pressure of the target with a defined mass [here, Br<sup>2</sup> (X,1Σ<sup>+</sup> g )] is crucial to achieve in the experiments angular and velocity resolution conditions proper to resolve quantum interference effects, as those giving the "glory" oscillations, observable in the velocity dependence of the integral cross section. The collected experimental results probe in detail, and an internally consistent way, the absolute scale of the interaction both at long and intermediate distance ranges, where, respectively, the attraction dominates and the potential well occurs (Pirani and Vecchiocattivi, 1982; Pirani et al., 2008). Therefore, such results provide direct information on some basic features of the X PESs and allow a direct comparison with other X PESs, recently characterized in detail for the corresponding Ng–Cl<sup>2</sup> systems (Nunzi et al., 2019; Pirani et al., 2019).

The experiments have been performed with an MB apparatus, with the objective of measuring the total (elastic + inelastic) integral cross section Q as a function of the selected MB velocity v. Such an apparatus has been extensively described in the past (Aquilanti et al., 1992; Cappelletti et al., 2002, 2015, 2016a,b). Briefly, it is composed of a set of differentially pumped vacuum chambers, where MB, in the present case formed by Ng atoms, is generated by the gas expansion from a nozzle, maintaining its temperature in the range of 77–600 K and total pressure in the source within 7–20 mbar, in order to avoid cluster formation and to cover a wide range of collision velocities. Under such conditions, the MB emerges with near-effusive or moderate supersonic character, and it is analyzed in velocity by a mechanical selector and collides at a "nominal" velocity, v, with the stationary target gas (Br2) contained in the scattering chamber at a pressure not larger than 2 × 10−<sup>4</sup> mbar in order to assure the occurrence of single collision events. The chamber is kept at room temperature to avoid condensation effects of the target gas on the walls and to maintain a sufficiently high rotational temperature of the target molecules. The latter condition is critical to limit anisotropy effects in the scattering and then to better resolve frequency and amplitude of the glory oscillatory pattern. MB is detected downstream by a quadrupole mass spectrometer, coupled with an ion counting device. At each selected velocity, v, of the projectile atoms, the quantity to be measured is the MB attenuation I/I0, where I represents the MB intensity detected with the target in the scattering chamber (filled at the chosen pressure) and I<sup>0</sup> that without it (empty chamber). From the measurement of the ratio I/I0, it is possible to determine the value of the integral cross section Q(v) through the Lambert–Beer law: calibration methodology and reference data are given in Nenner et al. (1975), Aquilanti et al. (1976), Pirani and Vecchiocattivi (1977).

The Q(v) values, measured for He–, Ne–, and Ar–Br<sup>2</sup> systems as a function of the selected MB velocity v, are reported in **Figure 1**. In all cases, the cross sections are plotted as Q(v)· v 2/5 to emphasize the "glory" quantum interference and to more efficiently analyze the scattering cross sections in terms of a smooth component and an oscillating part. The He–, Ne– , and Ar–Br<sup>2</sup> systems exhibit absolute scales of the observables and interference patterns that are very different, thus revealing significant variations in the intermolecular interactions.

The analysis of Q(v) (see next sections) provided a quantitative characterization of the strength of the intermolecular interaction both at long range, obtained from the velocity dependence of the average value of Q(v), and in the potential well region, probed by the resolved glory structure (Pirani and Vecchiocattivi, 1982; Pirani et al., 2008).

During the analysis, center-of-mass (CM) cross section values have been calculated within the semi-classical Jeffreys– Wentzel–Kramers–Brillouin approximation (Child, 1974) from the assumed intermolecular interaction potential V (see next section), and afterwards convoluted in the laboratory frame to make a direct comparison with the measured Q(v) (Cappelletti et al., 2002).

During a trial-and-error procedure, the parameters defining the basic features of V have been tested and fine-tuned in order to obtain the best comparison between experimental and calculated data. This phenomenological analysis (see the next section) has been guided also by available results obtained in the past on a large variety of atom–molecule systems (Pirani et al., 2019).

#### POTENTIAL PARAMETRIZATION AND DATA ANALYSIS

For the Ng–Br<sup>2</sup> systems, we adopted a formulation of PES based on what recently developed for the homologous systems with Cl<sup>2</sup> (Nunzi et al., 2019). In particular, the total intermolecular potential V has been defined as the sum of three contributions, identified as vdW, VvdW, three bodies, V3B, and CT, VCT, each one related to fundamental features of the partners involved in the interaction.

FIGURE 1 | Integral cross sections Q(v) for Ng atom projectiles colliding at each selector velocity with Br<sup>2</sup> targets. Data are plotted as Q(v)· v 2/5 to emphasize the glory patterns. Solid line: cross sections calculated with the full PES, including in the formulation of the various interaction components taken into account in the data analysis. Dashed line: calculation with the spherically averaged PES.

The electronic polarizability is the fundamental chemical– physical property determining both dispersion/induction attraction and Pauli (exchange or particle size) repulsion and can be employed in semi-empirical correlation formulas (Cambi et al., 1991) for the modeling of a large variety of non-covalent intermolecular interactions. Accordingly, the anisotropic VvdW component has been represented in terms of two pairwise additive potential contributions, Ng–Br<sup>i</sup> , where the Br<sup>i</sup> interaction centers coincide with the bromine atoms of the Br<sup>2</sup> molecule. As emphasized for the representation of Cl atoms in Cl<sup>2</sup> (Nunzi et al., 2019), also for these "effective" Br atoms, involved in a stable Br–Br chemical bond, we assumed an anisotropic component of the electronic polarizability different from that of the isolated Br atom. On the other side, the value obtained by summing the average polarizability of the "effective" Br atoms is kept consistent with that of the Br<sup>2</sup> molecule (Maroulis and Makris, 1997). To adequately describe the repulsion contributions related to the strongly anisotropic Br<sup>2</sup> electron density, mostly determined by the outer valence electrons in the π <sup>∗</sup> molecular orbitals, we included in the formulation of V a three-body term, V3B. Finally, a third interaction component, VCT, has been included and associated with CT effects, which directly influences the formation of the intermolecular bond (Pirani et al., 2000; Belpassi et al., 2009; Cappelletti et al., 2012).

Therefore, assuming as R the distance between Ng and the CM of Br2, and as θ the angle between the vector **R** and the Br–Br bond axis (see **Figure 2**), for the Ng–Br<sup>2</sup> adducts in the X ground states, we defined the anisotropic intermolecular potential V(R, θ) as the combination of three main components:

$$V(R,\theta) = V\_{vdW}\left(R,\theta\right) + V\_{CT}\left(R,\theta\right) + V\_{\text{3B}}\left(R,\theta\right) \tag{1}$$

Such components indirectly include the role of less important contributions.

In more detail, VvdW has been represented as the sum of two Ng–Br<sup>i</sup> (i= a, b) pairwise additive contributions:

$$V\_{\rm vdW}(R,\theta) = V\_{\rm Ng-Br\_{a}}(r\_{a},\varphi\_{a}) + V\_{\rm Ng-Br\_{b}}(r\_{b},\varphi\_{b}) \tag{2}$$

where a and b identify the two different Br atoms,r<sup>a</sup> and r<sup>b</sup> are the distances between Ng and Bra/Br<sup>b</sup> , and φaand φ<sup>b</sup> are the angles

TABLE 1 | Potential parameters (ε, ACT, A3B in meV, and r<sup>m</sup> in Å) employed for the formulation of the Ng–Br atom–atom pairwise interaction for Ng–Br2 systems in the (X1Σ + g ) ground and (B350u+) excited states.


Data for He–, Ne–, and Ar–Br2(X) have been determined from the experimental best fit; the others (in italics) are from model calculations (see text).

(a)The β parameter of the ILJ function (see text) has been fixed to 7.0 for all atom–atom pairs. The maximum estimated uncertainty is about 5% for ε, 2% for rm, and 15% for ACT and A3B.

(b)The β parameter of the ILJ function (see text) has been fixed to 7.0 for all atom–atom pairs. The maximum estimated uncertainty is about 10% for ε and 3% for rm.

between **r**a**/r**<sup>b</sup> and the Br<sup>2</sup> bond axis. Accordingly, each atom– atom pair term has been formulated as an improved Lennard Jones (ILJ) function (Pirani et al., 2008):

$$V\_{N\circ-Bri}(r\_i,\varphi\_i) = \varepsilon(\varphi\_i) \left[ \frac{6}{n\left(r\_i,\varphi\_i\right) - 6} \cdot \left(\frac{r\_m(\varphi\_i)}{r\_i}\right)^{n(r\_i,\varphi\_i)} \right]$$

$$-\frac{n(r\_i,\varphi\_i)}{n\left(r\_i,\varphi\_i\right) - 6} \cdot \left(\frac{r\_m(\varphi\_i)}{r\_i}\right)^6 \right] \tag{3}$$

where the ε(ϕi) and rm(ϕi) parameters are generated by the following relationships:

$$\varepsilon(\varphi\_i) = \varepsilon\_{\parallel} \cdot \cos^2(\varphi\_i) + \varepsilon\_{\perp} \cdot \sin^2(\varphi\_i) \tag{4}$$

$$r\_m(\varphi\_i) = \|r\_{m\parallel} \cdot \cos^2(\varphi\_i) + r\_{m\perp} \cdot \sin^2(\varphi\_i) \tag{5}$$

The symbols k and ⊥ refer, respectively, to the parallel (ϕ<sup>i</sup> =0) and perpendicular (ϕ<sup>i</sup> = π/2) configurations within each Ng– Br<sup>i</sup> pair. The factor n(r<sup>i</sup> , ϕi), which modulates simultaneously the "fall off " of the repulsion and the radial dependence of the intermediate and long-range attraction, depends on β, an additional parameter related to the hardness of both partners (Capitelli et al., 2007). It is expressed as,

$$m(r\_i, \varphi\_i) = \beta + 4 \cdot \left(\frac{r\_i}{r\_m(\varphi\_i)}\right)^2 \tag{6}$$

Note that the partial long-range attraction coefficient, C6<sup>i</sup> = ε (ϕi) · r 6 <sup>m</sup> (ϕi), provides the asymptotic behavior of each ILJ

FIGURE 3 | Comparison for Ne–Br2 system between experimental cross section data, plotted as Q(v)· v <sup>2</sup>/<sup>5</sup> and reported as a function of the molecular beam (MB) velocity v, and calculations performed considering the interaction in the three selected limiting configurations (colored lines), the infinite-order sudden (IOS) approximation (dotted line), and the full treatment employed for the data analysis (solid line, see text).

contribution, while the global attraction coefficient is simply given as the sum of the two angular averaged C6<sup>i</sup> components.

The values of the ε and r<sup>m</sup> parameters have been predicted in an internally consistent way for the three Ng–Br<sup>2</sup> systems from the polarizability components (Cambi et al., 1991). They have been tested, and when necessary, fine-tuned, by exploiting the comparison of calculated cross sections with experimental results. During the analysis, the additional constraint of providing global average asymptotic attractions in substantial agreement (within about 10%) with those reported by Olney et al. (1997) has been imposed. As previously done for other systems involving other halogen atoms (Bartocci et al., 2015; Cappelletti et al., 2015; Nunzi et al., 2019), the zero-order values of r<sup>m</sup> <sup>k</sup> have been decreased by about

interactions are reported for comparison (black dashed lines).

4% to account for the PF effect in the X ground state of Br2. Such an effect must be related to the peculiar electronic charge distribution of Br along the Br–Br bond direction pointing at the approaching Ng in the collinear isomer (see next section). The decreasing of r<sup>m</sup> <sup>k</sup> has been accompanied by an of e<sup>k</sup> in order to maintain the C<sup>6</sup> coefficient constant.

The second term in Equation 1, V3B(R, θ), has been formulated as,

$$V\_{\rm 3B} \left( R, \theta \right) = -A\_{\rm 3B} \left( \sin 2\theta \right)^2 \cdot e^{-3.0 \cdot R} \tag{7}$$

and it has been enclosed to properly represent the angular dependence of the full PES, especially in the proximity of the

TABLE 2 | Potential well depth (ǫ, in meV) and well location r<sup>m</sup> (in Å) for the Ng–Br<sup>2</sup> complexes for the (X1<sup>Σ</sup> + g ) ground and (B350u+) excited states of Br<sup>2</sup> representative of the intermolecular bond stability and length in the three basic configurations.


\*Average of A′ and A ′′ PES.

Data for He–, Ne–, and Ar–Br2(X) have been determined from the experimental best fit, the others (in italics) from a semi-empirical model or ab initio calculations (see text).

Finally, the third term, VCT(R,θ), has been defined as,

$$V\_{CT}(R,\theta) = \sum\_{i=a,b} A\_{CT} \cdot \cos^4(\varphi\_i) \cdot e^{-3.0 \cdot r\_i} \tag{8}$$

The dynamical treatment used for the data analysis, adopted for many other atom–molecule systems and summarized in the **Supporting Information** (SI), allows a good reproduction of the measured cross sections for all the investigated systems by mostly adjusting A3B and ACT values, while keeping unaltered (or variable in limited ranges) the other parameters. The final values are reported in **Table 1**.

#### DISCUSSION

Cross sections, calculated with the full PES based on the potential parameters of **Table 1**, are compared with the experimental data in **Figure 1**. In the same figure is also reported, as a dashed line, a calculation based on the spherically averaged PES. In **Figures 3**, **4**, some details are given on the dynamical model employed and on the sensitivity of the experiment to the PES features. Results are presented for the case of Ne–Br2, chosen as a representative. Specifically in **Figure 3**, scattering cross sections derived from selected cuts of the PESs are reported together with those obtained combining them according to those obtained according to the IOS (infinite-order sudden) approximation and to the dynamical regime adopted, whose details are reported by Nunzi et al. (2019) and also summarized in **Supporting Information**.

The IOS calculations are very sensitive to the anisotropy of the PES and must be considered correct to describe the scattering when the collisions are "sudden": this typically occurs at high relative collision velocities. The data treatment exploited in the present work combines the IOS results with cross sections calculated with the spherically averaged PES, probed in the present investigation by collisions confined at low velocities (see **Figure 1**) by means of a switching function operative in the intermediate velocity range (see the **Supplementary Information**). Therefore, this treatment exploits the concept that present observables are basically determined by anisotropic elastic collisions and that inelastic events, occurring at orbital angular momentum values smaller than those probed by the present experiments, play a minor role (Aquilanti et al., 1998). The combined calculations reproduce the amplitude satisfactorily and the frequency of the glory patterns very well, experimentally resolved for all investigated systems, and this represents an important reliability test for all proposed PESs. They have been formulated in an internally consistent way and using few parameters, all related to basic physical properties of the interacting partners. In particular, the parameters that define VvdW depend on the polarizability components of Br<sup>2</sup> and scale also according to that of Ng, while the significant effect of V3Bmanifests along the direction of π <sup>∗</sup> molecular orbitals, occupied by more outer electrons of Br2.

In **Figure 4**, we report the results of a sensitivity test for the Ne–Br<sup>2</sup> case. In particular, a calculation has been performed with a PES including the term and the PF effect (VvdW, blue dotted) and further adding the three-body term (VvdW + V3B, green dashed). These incomplete PESs fail in reproducing the correct location of the calculated glory interference extrema.

The average strength of VCT increases from He to Ar, accordingly with the ionization potential of Ng. It must also depend on the electron affinity of Br2, which is slightly larger with respect to that of Cl2. Moreover, its angular dependence is strongly modulated by the PF and by the so-called σ-hole in the electron density of the halogen molecule (Clark et al., 2007; Kol and Hobza, 2016).

In order to illustrate the main basic features of the PESs characterized in this paper, the interaction energy for selected configurations of Ng–Br<sup>2</sup> systems is plotted as a function of the Ng–Br<sup>2</sup> distance, R, in **Figure 5**.

These results can be compared with those obtained for the analogous Ng–Cl<sup>2</sup> systems recently (Nunzi et al., 2019; Pirani et al., 2019). When passing from Cl<sup>2</sup> to Br<sup>2</sup> adducts, the relative anisotropy, obtained by scaling the absolute anisotropy for the average interaction, is very similar, but the absolute interaction is higher for the Br<sup>2</sup> family. The variation can be attributed to the simultaneous increase of all the basic

the angular variable θ are reported for the Ne–Br2(X) case.

components, here represented as VvdW, V3B, and VCT, due to the combined change of electronic polarizability and of the extension of external charge distribution when moving from Cl<sup>2</sup> to Br2.

In **Table 2**, the main features of the obtained PESs, namely, binding energy and equilibrium distance for the three basic configurations of each system, are given for the noble gas–Br2(X) systems. In the table are also reported significant results from the literature, mostly from ab initio calculations, available for the He, Ne, and Ar cases.

Within the same approach, we have also predicted the interaction parameters for Kr–Br<sup>2</sup> and Xe–Br<sup>2</sup> systems, whose values have been enclosed in **Tables 1**, **2**. Specifically, the vdW r<sup>m</sup> , ε, and the A3B parameters of Kr– and Xe– cases (**Table 1**) have been obtained by a direct scaling of those of the lighter rare gases' parameters, utilizing the noble gas polarizabilities and correlation formulas of general validity (Cambi et al., 1991). The CT parameter ACT has been obtained through correlation formulas for the CT component (see Pirani et al., 2000 and references therein), utilizing the ionization potential of the noble gases and the electron affinity of the halogen molecule (Pirani et al., 2000).

The agreement with literature data is, in general, very good. The present results for the He–Br<sup>2</sup> and Ne–Br<sup>2</sup> cases show slightly deeper well depths.

The minimum energy path, MEP, describing the angular dependence of the binding energy evaluated at each equilibrium distance is given in **Figure 6**. The MEP has been easily obtained here by exploiting the adopted analytical formulation of the interaction.

The angular trend of the interaction component VvdW, V3B, and VCT, is reported for Ne–Br<sup>2</sup> in **Figure 7**. From the figure, it can be clearly seen that VvdW alone would provide a T-shaped configuration (θ=90◦ ) much more stable than the collinear (θ =0 ◦ ); on the other side, the VCT term is responsible for the change in stability of the collinear configuration with respect to the perpendicular one. The effect of the V3<sup>B</sup> term manifests itself at an intermediate angle and affects mostly the relative stability of the saddle configuration.

The phenomenological approach has also been extended to obtain, within the same framework adopted for the systems involving Cl2, an analytical formulation of the PESs for the complete family of the Ng(<sup>1</sup> S0)–Br2(B <sup>3</sup>50u+) systems. Upon excitation in the triplet B state, leading an electron from the π ∗ to the σ <sup>∗</sup> molecular orbital, a consistent charge rearrangement is attained in the Br<sup>2</sup> molecule, accomplishing an increase in the polarizability and its anisotropy with respect to that of the ground state. Since the excitation energy for Br<sup>2</sup> is very similar to that of Cl2, we assumed for Br<sup>2</sup> the same change in polarizability as for Cl2, for which reliable values are available (Beneventi et al., 1993; Nunzi et al., 2019; Pirani et al., 2019). For the ground electronic state of Br2, the average polarizability value and its anisotropy have been taken from the literature (Maroulis and Makris, 1997). The interaction potential in the triplet B state has been modeled by considering exclusively the occurrence of a vdW interaction, which can be represented with a pairwise additive approach. The potential parameters (r<sup>m</sup> , ε) have been estimated on the basis of polarizability and correlation formulas (Cambi et al., 1991).

The estimated parameters for the excited B state are reported in **Table 1**. For the He–Br<sup>2</sup> system, the relative anisotropy of the present PES for the B state (i.e., the difference between perpendicular and parallel configuration divided by the average value) is in good agreement with that obtained by ab initio calculations (de Lara-Castells et al., 2004; Garcia-Vela, 2005).

In conclusion, we have found, trough a detailed experimental investigation, that the noble gas–Br adducts are affected by a selective emergence of the intermolecular halogen bond, as recently demonstrated for the companion noble gas–Cl<sup>2</sup> systems (Nunzi et al., 2019; Pirani et al., 2019). In particular, it has been confirmed that for these systems, XB's peculiar effect comes into play only in the collinear configuration of the ground-state PES. The obtained results extend the phenomenology and knowledge of the intriguing weak XB.

The present study also provided a simple and accurate analytical formulation of the PESs, describing the intermolecular interaction both in the ground X and in the excited electronic B state of Br2. The PES has been represented as a combination of three basic interaction components, each one modulated by few and well-defined physical parameters. The model potential provided the force fields in the full space of the relative configurations and is then suitable for molecular dynamics simulations of fundamental phenomena, such as energy transfer processes.

## AUTHOR CONTRIBUTIONS

DC and FP contributed conception and design of the study. DC, FP, and SF conducted data collection and analysis. DC wrote the first draft of the manuscript. DC and FP wrote sections of the manuscript. All the authors contributed to the development of the experimental facility and analysis instruments. All authors contributed to manuscript revision, read and approved the submitted version.

## ACKNOWLEDGMENTS

DC, AN, AC, and FP thank MIUR and the University of Perugia for financial support through the AMIS project (Dipartimenti di Eccellenza−2018–2022).

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00320/full#supplementary-material

## REFERENCES


J. Chem. Phys. 116, 9249–9254. doi: 10.1063/1.1473800


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Cappelletti, Cinti, Nicoziani, Falcinelli and Pirani. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A Fast Transient Absorption Study of Co(AcAc)<sup>3</sup>

Luisa Ferrari <sup>1</sup> , Mauro Satta<sup>2</sup> , Amedeo Palma<sup>3</sup> , Lorenzo Di Mario<sup>1</sup> , Daniele Catone<sup>1</sup> , Patrick O'Keeffe<sup>4</sup> , Nicola Zema<sup>1</sup> , Tommaso Prosperi <sup>1</sup> and Stefano Turchini <sup>1</sup> \*

<sup>1</sup> CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma Tor Vergata, Rome, Italy, <sup>2</sup> CNR-ISMN, Chemistry Department, Università di Roma Sapienza, Rome, Italy, <sup>3</sup> CNR-ISMN, Area della Ricerca di Roma 1 - Montelibretti, Rome, Italy, <sup>4</sup> CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1 - Montelibretti, Rome, Italy

The study of transition metal coordination complexes has played a key role in establishing quantum chemistry concepts such as that of ligand field theory. Furthermore, the study of the dynamics of their excited states is of primary importance in determining the de-excitation path of electrons to tailor the electronic properties required for important technological applications. This work focuses on femtosecond transient absorption spectroscopy of Cobalt tris(acetylacetonate) (Co(AcAc)3) in solution. The fast transient absorption spectroscopy has been employed to study the excited state dynamics after optical excitation. Density functional theory coupled with the polarizable continuum model has been used to characterize the geometries and the electronic states of the solvated ion. The excited states have been calculated using the time dependent density functional theory formalism. The time resolved dynamics of the ligand to metal charge transfer excitation revealed a biphasic behavior with an ultrafast rise time of 0.07 ± 0.04 ps and a decay time of 1.5 ± 0.3 ps, while the ligand field excitations dynamics is characterized by a rise time of 0.07 ± 0.04 ps and a decay time of 1.8 ± 0.3 ps. Time dependent density functional theory calculations of the spin-orbit coupling suggest that the ultrafast rise time can be related to the intersystem crossing from the originally photoexcited state. The picosecond decay is faster than that of similar cobalt coordination complexes and is mainly assigned to internal conversion within the triplet state manifold. The lack of detectable long living states (>5 ps) suggests that non-radiative decay plays an important role in the dynamics of these molecules.

Keywords: fast transient absorption, TDDFT (time-dependent density functional theory) calculations, femtosecand laser pulses, metal complexes, charge - transfer

## INTRODUCTION

Transition metal complexes are of paramount importance in chemical and biological photochemical processes (Ruggiero et al., 2014) involving the conversion of the energy of visible light into chemical energy and the activation of redox-states for catalysis (Prier et al., 2013). Indeed, it is desirable to study the early formation of optically excited states, to explore the possibility of triggering and tailoring the electronic and structural properties of this class of compounds. Moreover, the spreading of the population of the excited electrons into different relaxation channels plays a key role in smart sensors and ultrafast devices (Wada, 2004).

#### Edited by:

Stefano Falcinelli, University of Perugia, Italy

#### Reviewed by:

Nadja Doslic, Rudjer Boskovic Institute, Croatia Franco Vecchiocattivi, University of Perugia, Italy

> \*Correspondence: Stefano Turchini stefano.turchini@ism.cnr.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 07 February 2019 Accepted: 29 April 2019 Published: 21 May 2019

#### Citation:

Ferrari L, Satta M, Palma A, Di Mario L, Catone D, O'Keeffe P, Zema N, Prosperi T and Turchini S (2019) A Fast Transient Absorption Study of Co(AcAc)3. Front. Chem. 7:348. doi: 10.3389/fchem.2019.00348

The development of femtosecond laser sources gave rise to a revolution in the comprehension of the fate of excited electrons and provided a microscopic basis for already established theories such as molecular internal vibration relaxation (Grossmann, 2013), mostly based on the analysis of the photo fragmentation processes (Wada and Tanaka, 2013). Moreover, the advent of ultrafast X-ray facilities provided new insight into electronic and structural dynamics of transition metal complexes (Huse et al., 2011; Chergui, 2018). To this end future perspectives are strongly related to the ultrafast application of VUV-Soft X-ray PhotoElectron Spectroscopy studies in the gas phase, to our knowledge still lacking in the field of metal complexes, and the application of theoretical state of the art methods to characterize the dynamics of the electronic structure (Squibb et al., 2018).

The dynamics studies usually are modeled by excitation following the Franck-Condon approximation, which takes place in about 1 fs (Demtröder, 2008), then three different relaxation processes occur (Tramer et al., 2010). Internal conversion (IC) allows the de-excitation to a different electronic state within the same spin multiplicity. Intersystem crossing (ISC) is the mechanism characterized by a change of spin of the relevant electronic states. IC and ISC are first-order perturbation theory processes, their decay mode can be modeled by exponential functions and their rate is inversely proportional to the energy difference of the involved states (Bixon and Jortner, 1968). Vibrational cooling (VC), which is usually the fastest process, represents the de-excitation from the highest excited to the lower vibrational levels within the same electronic state; the decay is generally associated with energy dissipation toward the surrounding medium and can be modeled by perturbation theory using a bath Hamiltonian (Fujisaki et al., 2006).

Transition metal complexes present a manifold of low-lying excited states with a high density of states that enables them to efficiently harvest light; in a narrow interval of energy (hundreds of meV) the excited electronic states display different electronic character, inducing a great variety of de-excitation pathways and reactivity processes after optical excitation. Moreover, in transition metal compounds the spin-orbit coupling term of the Hamiltonian is strong because of the open d-shell of the metal and it favors a fast ISC with the subsequent formation of long living states. This is in contrast to organic molecules where ISC is generally slower than IC (Tramer et al., 2010). The strong spinorbit term alters the hierarchy of the perturbations and makes the distinction between ISC and IC fuzzier. It is reasonable to assume that these two processes could occur in the same time scale and, consequently, convoluted, although in a quantummechanical picture the relative strength between the non-Born-Oppenheimer terms and the spin-orbit does not allow us to consider the two processes separated in terms of perturbation theory. The presence of ISC is generally associated with long living states that de-excite by phosphorescence decay.

The existence of two time scales related to fast and slow relaxation processes reflects different photochemical and photophysical phenomena. The fast evolution after photoexcitation displays intramolecular processes that dramatically change the electronic and structural properties in a very selective pathway; this can be tailored by tuning the excitation energy and the vibrational composition of the excited state. On the other hand, relaxed fully thermalized excited states with lifetimes greater than the diffusion time scale provide the basis for slow photochemistry reactions that are not thermodynamically accessible in the ground state. Moreover, the electronic character of the excited states provides different chemical selectivity with respect to the ground state.

In metal complexes the tailoring of ISC by tuning the excitation channel can dramatically change the ratio between the fluorescence and phosphorescence relaxation channels (Hsu et al., 2012), with potential applications in sensor design.

The relevance of ISC in transition metal complexes dynamics has been extensively studied (Vlcek, 2000; McCusker, 2003; ˇ Wagenknecht and Ford, 2011). Fluorescence up-conversion measurements on [Ru(bpy)3] <sup>2</sup><sup>+</sup> display ISC for metal to ligand charge transfer (MLCT) states: <sup>1</sup>MLCT → <sup>3</sup>MLCT with τ =40 ± 15 fs, while IC displays a time scale of the order of picoseconds (Bhasikuttan et al., 2002). On the other hand, fast transient absorption spectroscopy (FTAS) measurements assign a τ≈100 fs for the overall formation of the <sup>3</sup>MLCT (Damrauer et al., 1997). [Fe(II)(tren(py)3)]2<sup>+</sup> shows ISC characteristic time constant less than 1 ps (Monat and McCusker, 2000). To establish the <sup>5</sup>T<sup>2</sup> character of the long living state, the difference of absorption spectra of Fe(II) complexes with <sup>5</sup>T<sup>2</sup> (high-spin) and <sup>1</sup>A<sup>1</sup> (low spin) ground state provided a reference for the time-resolved excited state spectrum. The assignment of <sup>5</sup>T<sup>2</sup> to <sup>1</sup>A<sup>1</sup> conversion was recently found by a variable temperature FTAS study of [Fe(bpy)3] <sup>2</sup>+-type complexes and [Fe(terpy)2] <sup>2</sup><sup>+</sup> (Carey et al., 2019). FTAS studies on Co(III) compounds have been presented (McCusker et al., 1993): [Co(en)3](ClO4)3, [Co(tpen)](C1O4)3, and [Co(tppn)](C1O4)<sup>3</sup> show biphasic relaxation kinetics; in the case of [Co(tpen)]3<sup>+</sup> excited-state decay is expressed by two time constants τ<sup>1</sup> = 4 ± 2 ps and τ<sup>2</sup> = 44 ± 5 ps, for [Co(tppn)]3<sup>+</sup> τ<sup>τ</sup> = 3 ± 1 ps and τ<sup>2</sup> = 51 ± 3 ps, while the data for [Co(en)3] 3+ give τ<sup>τ</sup> = 2 ± 1 ps and τ<sup>2</sup> = 450 ± 100 ps. For [Co(tpen)](C1O4)<sup>3</sup> and [Co(tppn)](C1O4)<sup>3</sup> the experimental data suggest a lifetime of the <sup>1</sup>LMCT (ligand to metal CT) state less than 1 ps. No fluorescence yield was observed for the three compounds. Regarding the kinetics of the non-radiative decay, the relation between photochemical properties and ligand field excited state character leads to the assignment of the lowest lying excited state as <sup>5</sup>T<sup>2</sup> for the octahedral Co(III) complexes considered. Cr(III)(AcAc)<sup>3</sup> has been thoroughly studied by means of FTAS (Juban and McCusker, 2005) and shows the formation of the <sup>2</sup>E<sup>2</sup> state from LMCT and ligand-field excitation. The ligand field excitation presents a monophasic decay of τ<sup>1</sup> = 1.1 ± 0.1 ps for every excitation and pump wavelength, LMCT excitation exhibits τ<sup>τ</sup> = 50 ± 20 fs and τ<sup>2</sup> = 1.2 ± 0.2 ps, associated with charge transfer to ligand field manifold ISC and VC to <sup>2</sup>E2, respectively. Transient infrared spectroscopy points out that 70-85% of the ground state population of Cr(acac)<sup>3</sup> recovers with a time constant of 15 ps, and the remaining population is described by the lifetime of the <sup>2</sup>E state (Maçôas et al., 2007).

These results clearly indicate the action of fast intersystem crossing and reverse the usual sketch of ISC being the slowest process.

We present a FTAS study of Co(AcAc)3, where AcAc is the Acetylacetone molecule, a diketone moiety which forms complexes with transition metal atoms. This is a transition metal complex currently employed as a catalyst for the formation of C–C bonds and oxidation reactions (Ishii et al., 1996). This compound has closed shell with D<sup>3</sup> symmetry point group and allows reliable and accurate quantum chemistry calculations. The electronic structure of the molecule was characterized by photoelectron and circular dichroism photoelectron spectroscopy (Catone et al., 2012, 2013) with good agreement of theory with spectroscopic data.

By means of density functional theory (DFT) and time dependent density functional theory (TDDFT) quantum chemistry calculations, we provide a picture of the structural and electronic properties involved in the ultra-fast dynamics, discussing the ligand-field and the charge transfer states excitation. Ligand-field approach is very important for a qualitative assignment of electronic character and symmetry of excited states. DFT and TDDFT calculations provide a more precise characterization of the ligand to metal and metal to ligand excited states. FTAS data will be discussed in view of these results.

The aim of the present work is to investigate the interplay between ISC and the other relaxation processes on the basis of the calculated electronic structure and spectroscopic data.

#### EXPERIMENTAL DETAILS

FTAS is a pump-probe methodology that measures the difference in absorption between the excited state and the ground state taken at different time delays after the optical excitation at a defined wavelength.

The pump was generated by an optical parametric amplifier (OPA) fed by the 800 nm radiation of an amplified Ti:Sapphire laser with a pulse length of 35 fs and a repetition rate of 1 kHz, and the probe was a white light supercontinuum generated in a commercial transient absorption spectrometer (FemtoFrame II-IB photonics). The probe wavelengths ranged between 400 and 750 nm while the pump-probe delay time was scanned up to 100 ps, with an overall temporal instrument response function described by a Gaussian peak with FWHM of 50 fs. Co(AcAc)<sup>3</sup> (Sigma Aldrich, purity 99.99%) was diluted in acetonitrile (ACN). Two different concentrations were used in the pumpprobe experiments on Co(AcAc)3: 0.01 M (excitation wavelength 365 and 390 nm) and 0.05 M (excitation wavelength 580 and 650 nm). Typical pump laser fluence was 500–2500 µJ/cm<sup>2</sup> . The measurements were carried out in a quartz cell with path length 1 mm. A blank pump-probe experiment was performed to seek non-linear contributions of the solvent in the experiment. We paid attention to minimize cross-phase modulation structures in the transient spectrum by choosing a suitable pump fluence, although for low pump absorption it was not possible to eliminate it completely. The chirp of the FTAS signal was corrected by an alignment based on a polynomial fit. Since the transient absorption slowly varies as a function of the wavelength, to increase the signal to noise ratio the temporal cuts were averaged ±5 nm around the chosen wavelength. No FTAS signal was detected in the 800–1600 nm region of probe wavelength. Measurements were taken at the magic angle between the linear polarization vectors of pump and probe radiation. Further details of the experimental set-up can be found in previous publications (Catone et al., 2018; Fratoddi et al., 2018).

## COMPUTATIONAL DETAILS

The description of the geometries and of the electronic structures of the gas phase and of solvated complex has been carried out using DFT formalism coupled with the polarizable continuum model (PCM) based on reaction field calculations and the integral equation formalism (Tomasi et al., 2005; Scalmani and Frisch, 2010). The excited states have been studied within the TDDFT approach (Bauernschmitt and Ahlrichs, 1996). The hybrid exchange-correlation functional Becke (Becke, 1993), three-parameter, Lee-Yang-Parr (Vosko et al., 1980; Lee et al., 1988; Stephens et al., 1994) has been adopted together with the split-valence double-zeta Pople basis set (Hariharan and Pople, 1973; Francl et al., 1982) with the addition of extra functions as established by Barone et al. (Barone et al., 2008) to be used in the frame of effective discrete/continuum solvent models. TDDFT and the chosen basis set are a good compromise between accuracy and computer time consuming for these complexes. TDDFT with B3LYP has been successfully used in the literature to characterize the electronic structure in similar calculations (Savarese et al., 2012, 2014; Catone et al., 2018).

The geometries were fully optimized for the ground states of the singlet, triplet and quintet spin configurations; at each of these geometries the first twenty excited electronic states have been computed. In order to have a picture of the excitation of the singlet, triplet and quintet states during the vertical transition from the initial geometry of the ground state, we have calculated the singlet, triplet, quintet excited electronic levels at the singlet minimum energy geometry. All the calculations were performed using the Gaussian code (Frisch et al., 2016).

The ISC processes have been described by estimating the relative non-radiative lifetimes computed by means of spin-orbit coupling matrix elements. In particular, we have used ADF (2018) code to calculate the spin-orbit coupling as a perturbation to a scalar relativistic calculation of TDDFT excitation energies for the gas phase. The TDDFT has been performed using the B3LYP functional, in analogy with our results obtained by Gaussian code, with double zeta polarization basis set on H, C, and O atoms, whereas the Co basis set is double zeta with 1s, 2s, 2p frozen core.

The number of singlet excited states considered was 20 for the singlet, and 60 for the triplet due to degeneracy. The spin-orbit coupling matrix was computed at the geometry corresponding to vertical transition from the equilibrium geometry of the electronic ground state. Several unsuccessful attempts to follow the geometry relaxation of the singlet electronic excited states were performed resulting in several singlet-singlet crossings along the optimization paths which at the end always lead to the first singlet excited state. The spin-orbit coupling matrix was

computed at five different geometries only for the first singlet excited state, taking the geometries from the optimization of the first singlet excited state performed by Gaussian code.

The ISC non-radiative lifetimes τ NR i , where i is the ith singlet excited state, have been computed following the Fermi golden rule with a Franck-Condon weighted density of states (FCWD), which assumes an equal vibrational structure between the involved electronic states (Valiev et al., 2018):

$$\mathbf{1}/\tau\_{\mathbf{i}}^{\mathbf{NR}} = \frac{2\pi}{\hbar} \sum\_{\mathbf{j}} \mathbf{SO}\_{\mathbf{ij}}^2 \frac{\Gamma}{\left(\Delta \mathbf{E}\_{\mathbf{ij}}^2 + \frac{\Gamma^2}{4}\right)}.$$

with the relaxation width of the vibronic levels Γ taken as 10<sup>14</sup> s −1 , which is a condition generally fulfilled in experimental studies of luminescence properties (Valiev et al., 2018), SOij are the spin- orbit matrix element coupling the ith singlet state with the jth triplet state, and 1Eij is the corresponding energy difference.

#### RESULTS AND DISCUSSION

The structure of the Co(AcAc)<sup>3</sup> complex is shown in **Figure 1**, while the most significant geometrical parameters are reported in **Table 1** for the minimum energy geometries of the three spin configurations.

It is worth noting that while in the singlet and quintet configuration the three rings are all planar and the symmetry of the system remains D3, in the triplet case one of the rings is bent ( C-O-Co-O 25.1◦ and 25.0◦ for the gas phase and ACN solvent, respectively) lowering the symmetry of the system. The minor changes in the geometrical parameters reported in **Table 1** for the three different spin configurations should take place during the ISC relaxation dynamics following the initial excitation. In the case of the gas-phase complex the calculations show (see **Figure 2**) that the triplet ground state is about 1 eV above the singlet ground state, while the quintet ground state is slightly higher than the triplet state. For the triplet spin configuration (right part of **Figure 2**) the energy level distribution is quite uniform: about 20 levels in an energy interval of 3 eV. In contrast, for the quintet spin case (left part of **Figure 2**), there is an energy gap of about 2 eV between the ground and first excited state, above which there is a quite uniform distribution of the density of states (DOS) up to 5.5 eV. In order to have a qualitative picture of the dynamics involving ISC, we report the singlet, triplet and quintet excited energy levels calculated at the geometry of the singlet ground state minimum energy (central part of **Figure 2**). In the energy gap between the first singlet excited state and the ground state energy (about 2 eV), there are several other energy levels of the triplet and quintet states. An analogous quite high DOS is calculated up to 5 eV above the ground singlet state, thus supporting the possibility of a complex intersystem evolution of the wavepacket produced by the initial vertical photo-excitation.

In the ACN solvent (see **Figure 3**) the quintet ground state minimum energy is lower than that of the triplet, and it is about 0.8 eV above the singlet ground state. The DOS for the singlet, triplet and quintet states are similar to each other, in particular the DOS calculated in the geometry of the singlet ground state minimum energy are quite similar to those calculated in the gas phase, while for quintet the density of state changes significantly. The large difference between the quintet energy calculated in the gas phase and ACN is related to the high polarizability of these spin states with respect to triplets and singlets.

The electronic scheme of octahedral metal complexes is ruled by ligand field splitting of the d electrons. Tanabe-Sugano d<sup>6</sup> diagrams assign <sup>1</sup>A<sup>1</sup> character to the ground state, with excited states in order of energy <sup>3</sup>T1, <sup>3</sup>T2, <sup>1</sup>T<sup>1</sup> (Griffith, 1961). The energy of the <sup>5</sup>T<sup>2</sup> with respect to singlet and triplets states depends on the ratio 1/B of the crystal field parameters, where 1 is the octahedral energy splitting and B the Racah electron repulsion parameter. **Figure 4** reports the one electron picture of the <sup>1</sup>A1, <sup>3</sup>T1, <sup>5</sup>T<sup>2</sup> octahedral ligand field states along with the excited states involving the ligand. The D<sup>3</sup> point group symmetry splits the above octahedral states, however in this work we shall relate each state to the original octahedral symmetry in order to simplify comparison with the literature.

**Figure 5** reports the experimental absorption of Co(AcAc)<sup>3</sup> along with the theoretical oscillator strength calculations in ACN. The spectrum shows a broad band centered at 2.1 eV, where the d-orbital excited states of the Co are relevant, and a steep rise starting at 2.4 eV, associated with the LMCT manifold. **Table 2** displays the TDDFT excitation energies, the irreducible representations and oscillator strengths calculated for ACN; the numeric label in the table will be used in the discussion to identify the states. In order to have a good agreement with the experiment a rigid shift of 0.2 eV toward lower energies is applied to the calculated data. This shift value is compatible with the accuracy of

TABLE 1 | Most significant geometrical parameters for the singlet, triplet and quintet ground state minimum energy and first excited state singlet level for Co(AcAc)3 in the gas phase and in ACN solvent.


Distances in Angstrom, angles in degrees.

the TDDFT method. The oscillator strengths of quasi-degenerate states have been summed.

In the photon energy range 1.8-2.7 eV the envelope of d-d transitions is reproduced by the transition to excited states 1-3. The octahedral <sup>1</sup>T<sup>1</sup> state is split by the D<sup>3</sup> symmetry group into an A state (1) and double degenerate E states (2,3) at calculated excitation energies 2.23 and 2.29 eV, respectively. The charge transfer states <sup>1</sup>LMCT are represented by an A state at 2.88 eV (4), associated with zero oscillator strength, and a pair of doubly degenerate E states at 3.11 eV (5,6) and 3.28 eV (7,8), respectively.

The excitation (1A<sup>1</sup> → <sup>1</sup>LMCT) produces a marked ligandto-metal character for the complex both in the gas phase and solvated in ACN, as **Figure 6** shows (excitation at 5 (3.11 eV), 6 (3.11 eV), 7 (3.29 eV), 8 (3.29 eV) in ACN), where there is a charge transfer from the three organic ring molecules of AcAc to the cobalt central atom. This electronic rearrangement does not invert the net charge transfer which occurs in the ground state of the metal complex, where about 0.5 e of charge is transferred from

FIGURE 4 | Schematic diagram of one electron excited states for a d<sup>6</sup> orbital configuration in an octahedral field (lower row) and LMCT states with the transfer of one electron from the ligand to the metal states (upper row).

the metal atom to the ligands. The yellow iso-density surfaces represent an enrichment of the electron charge density upon excitation, whereas the blue iso-surfaces indicate a depletion

TABLE 2 | Theoretical transition energies, wavelengths and oscillator strengths of optically excited states for Co(AcAc)3 in ACN.

−0.2 eV to improve the accord with experimental data. The oscillator strengths

of quasi-degenerate states have been summed.


in the electronic charge density, as reported in **Figure 6**: in particular there is a rearrangement of the electron charge density over the p MOs of the oxygen atoms, while the CH groups are net charge donors during this electronic transition with a reduction in the p MOs charge density. The excitation at 3.11 eV (399 nm) produces a charge electron density shift from the rings to a d<sup>z</sup> 2 MO of the central Co atom both in the gas phase and in the ACN solvent (see **Figure 6**). In one case of excitation at 3.29 eV (excitation 7 in **Table 2**) the charge density is shifted into a dxy MO of Co, while in the other excitation at 3.29 eV (excitation 8 in **Table 2**) the density shift is from the ring to a d<sup>z</sup> <sup>2</sup> MO of Co. The amount of the charge density shift is higher in the transition at 3.29 eV (377 nm) with respect to that at 3.11 eV (399 nm). Since it is difficult to exactly locate the energy position of the

FIGURE 6 | Iso-surface of the change in electron densities upon vertical transitions of optically excited states (singlet) for Co(AcAc)3 in the gas phase (left side) and ACN solvent (right side). In yellow the positive value iso-surface are represented, while with the blue are indicated the negative value ones. The iso-surface threshold is fixed to 0.0025 a.u. The energy of the excitation and the numeric label of the state (see Table 2) are reported.

<sup>1</sup>LMCT in the experimental spectrum, we chose two wavelengths for the pump to excite electronic states with reasonable excess energy: 5 and 6 at 390 nm (photon energy 3.18 eV) and 7 and 8 at 365 nm (photon energy 3.40 eV). For the excitation of the ligandfield state two wavelengths were chosen for the pump: 580 nm (2.13 eV) near the maximum of the ligand-field state absorption and 650 nm (1.91 eV) at the onset of the absorption curve.

**Figure 7** reports the transient absorption (TA) spectra (1A in the figure) in the 400-750 nm probe wavelength range at different delay times after the excitation at the chosen wavelength. The

spectra taken at 365 and 390 nm (**Figure 7** upper panels) display similar shape and time dependent behaviors. The TA spectra show positive values associated with a dominant contribution of the excited state absorption and two clearly defined broad bands, approximately centered at 480 and 700 nm. Two distinct time dependent regimes can be identified by analyzing the temporal evolution. Although the bands do not evolve in shape and wavelength position as a function of time, there is a clear evolution in their branching ratio. In the time range 0.1–1 ps the branching ratio between the maxima of the two structures monotonically decreases from roughly 1.3 to 1 and remains almost constant for t > 1 ps. The change in absorption suggests that the formation time of the population of the electronic state, which decays to the ground state, is about 1 ps. The lack of the appearance of new structures and of meaningful shifts of the maxima, together with the recovery of the kinetic traces back to 1A = 0, are strong indications that the molecule preserves its electronic structure and no photodegradation occurs. The dynamics of the Co(AcAc)<sup>3</sup> fades out at about 5 ps and long living state are absent at every pump wavelength employed. **Figure 8** reports the time evolution of the TA spectra at fixed probe wavelengths (520 and 710 nm) as a function of the delay time for excitations at 365 and 390 nm. The cuts are characterized by a swift rise, clearly

revealed within the temporal resolution of the pump-probe system.

The curves were fitted with a biphasic exponential function one related to the ultrafast rise time and the other related to the slower picosecond relaxation process. In the fit the temporal instrument response function (50 fs) was taken into account. In **Table 3** the time constants of the two processes are reported as a function of selected probe energies around the maxima of the two broad structures. For both pumps at 365 and 390 nm the time constants only very weakly depend on the probe wavelengths and substantially agree within the fit error. For the 390 nm excitation the averaged fit values are τ<sup>1</sup> = 0.08 ± 0.04 ps for the rise and τ<sup>2</sup> = 1.5 ± 0.3 ps for the decay, and for 365 nm excitation the value are τ<sup>1</sup> = 0.07 ± 0.04 ps and τ<sup>2</sup> = 1.5 ± 0.3 ps.

We now connect the phenomenological data analysis to a model of the dynamics of the Co(AcAc)<sup>3</sup> LMCT excited states and assign the hierarchy of the processes governing the dynamics of the molecule excitation. According to the literature ISC is the most likely fastest process. A previous FTAS study of Co(III) compounds (McCusker et al., 1993) proposed two mechanisms to understand the possibility to access different spin configurations. The first mechanism is ISC, while the second one points out that the LMCT transition alters the charge of the Co(III) ion that



τ<sup>1</sup> and τ<sup>2</sup> are related to the lifetime of the rise and of the decay of the photoinduced absorption at the indicated wavelength, respectively. The rise is within the temporal resolution after 580 and 650 nm excitation for the 460 and 520 nm probe wavelength. After 650 nm excitation at the probe wavelength of 680 nm the fit of the lifetime was not possible due to the residual intensity of the pump.

assumes a Co(II) character. Due to known instability of Co(II) low-spin states the metal ion could provide a swift transition lowspin → high-spin. Both processes lead to the same final state: in the former case the mechanism has a molecular nature, in the latter is based on the metal ion.

In view of these results we suggest that the origin of the rise time lies in an ISC that takes place on time scale of the order of tens of fs (Bhasikuttan et al., 2002) which depopulates the <sup>1</sup>LMCT in favor of different spin states. The sum of the manifold of these processes gives rise to the phenomenological fast onset. It is worth noticing that the variety of the states involved causes different probed dynamics that is reflected in the slightly different response of the states to the photon energy of the probe pulse. Hence the spread of the τ<sup>1</sup> values is related to the time scale of the different dynamics of the population of the states composing the early dynamics of ISC.

To test the hypothesis of the population of the lowest triplet and quintet levels, we compare the TA spectra after a time delay greater than 2 ps with the TDDFT calculations of the absorption spectra of the lowest energy levels of triplet and quintet states. **Figure 9** reports the calculated spectra of triplet and quintet lowest states together with the experimental TA spectrum measured 3 ps after 390 nm excitation. The oscillator strengths are converted into absorption by convolution with a gaussian function with a standard deviation of 100 meV. In the comparison a rigid shift of 300 meV toward lower photon energies was applied. There is a clear accord in the branching ratio between the two most intense triplet transitions

and the experimental curve. Although the absolute energy is slightly miscalibrated and the lack of vibrational calculations hinders the comparison, the energy difference of the calculated triplet transitions is 0.5 eV where the experimental energy difference between the experimental bands is about 0.7 eV, with a reasonable accord taking into account the accuracy of the TDDFT. This result sheds light on the process of the formation of the population of the states stemming from ISC suggesting the assignment of a predominant triplet character to the TA spectrum. According to these calculations, in the energy range investigated (1.5-3 eV) the ground state quintet oscillator strengths are one order of magnitude less favored than those of the triplets, and hence TA spectra are less sensitive to quintet transitions contributions. For this reason the presence of population in the quintet lowest level cannot be excluded.

VC occurs on the same time scale as the ISC and should be considered in the formation of the triplet (quintet) state. In the case of Co(AcAc)3, according to DFT calculations, the ground states of triplet and quintet states present an elongation of the Co-O bond length in the interval 0.1–0.2 Å associated with a lower symmetry with respect to the octahedral coordination. The elongation of the RCo−<sup>O</sup> bond length is then related to the fastest processes. A similar elongation is found by means of Xray TA for Fe-N bond of [FeII(mbpy)3] <sup>2</sup><sup>+</sup> in acetonitrile for the photoinduced high spin (HS) <sup>5</sup>T<sup>2</sup> state (Liu et al., 2017).

In order to study the relaxation following the excitation processes, we have reported the geometrical optimization of the first singlet excited state in **Figure 10**. The higher energy curves (shown as colored lines) refer to higher singlet electronic states. The optimization steps corresponding to the sample geometry structures used to compute the spin-orbit coupling matrix and ISC lifetimes are shown as rhombuses. Here, the electronic excited states.

first point of the optimization steps represents the vertical excitation corresponding to the geometry of the equilibrium structure of the ground singlet state. It can be seen that the initial degeneracy, associated with the D<sup>3</sup> symmetry, is removed during the relaxation path. After the 7th point of the optimization steps the energy remains almost constant, with a variation less than 30 meV with respect to the asymptotic energy corresponding to the equilibrium structure of the first excited singlet state. The higher energy singlet curves have a complex behavior along the relaxation path, and are characterized by several crossings, which open the way to a non-radiative decay by conical intersection from the singlet high energy states toward the lower excited singlet states.

**Figure 11** reports the calculated lifetime τ for the singlet – triplet ISC of the optically active first four singlet excited states calculated at the geometry of the vertical transition (step 1 in **Figure 11**). Only for the 1 <sup>1</sup>A state the dependence of ISC lifetimes on the optimization steps is reported. The 1 <sup>1</sup>A ISC lifetime weakly depends on the optimization step and beyond step 7 there is no substantial change in the geometry of the complex, and consequently the change in the spin-orbit coupling matrix is negligible. It is worth noticing that for the excited states corresponding to the LMCT the τ related to the vertical transition geometry is within the range 0.1 – 1.0 ps, while in the ligand field case is faster and presents values in the range 0.01-0.02 ps.

The ISC calculations performed offer a quantitative basis for the analysis of the experimental lifetimes.

The fast experimental lifetime τ<sup>1</sup> = 0.08 ± 0.04 ps after excitation at 390 nm is in good agreement with that expressed by the 2 <sup>1</sup>E state about 0.1 ps, suggesting a fast singlet-triplet ISC.

The 3 <sup>1</sup>E state presents a τ about 1 ps at the geometry of the vertical transition and the measured lifetime τ<sup>1</sup> = 0.07 ± 0.04 ps at 365 nm suggests an IC transition toward the first excited singlet state and then a fast ISC with lifetime about 20 fs from 1 <sup>1</sup>A.

However, we cannot exclude a fast geometry relaxation on this particular electronic state that lower the ISC lifetime to tens of fs. The dynamics expressed by the time constant τ<sup>2</sup> contains the last part of the dynamics, the relaxation toward the lowest levels of the triplet state and, successively, to the ground states. Although, as explained above, the excited states populated with the pumps at 390 nm and 365 nm present a different interpretation in the dynamics, the information condensed in the time constants does not present a difference within experimental error.

The proposed dynamics is summarized in the Jablonski diagram reported in **Figure 12**, where the relaxation paths of <sup>1</sup>LMCT (2 <sup>1</sup>E) and <sup>1</sup>LMCT (3 <sup>1</sup>E) are shown.

To complete the study of the dynamics with excited states associated to the ligand-field excitation, the same analysis was performed for pump wavelengths of 580 and 650 nm. The spectral features of the absorption difference, plotted at different delay time (**Figure 7** lower panels), have a comparable behavior with the 390 and 365 nm analysis; two broad bands are present and positive values in the investigated range. In particular, the TA spectra measured after 580 nm excitation exhibit the same qualitative evolution of the branching ratio of the LMCT excited spectra for a time delay greater than 2 ps. For the spectra obtained with a pump at 650 nm the branching ratio analysis is hampered by the presence of the residual pump signal. However, the band at lower wavelength appears to be extended toward the blue with respect to the LMCT case. **Table 3** reports the time constants of the two processes as a function of selected probe energies for pump wavelengths of 580 and 650 nm, respectively. It is worth noticing that the fast rise measured in the previous case (τ<sup>1</sup> = 0.07 ± 0.04 ps) is observed only in the band centered at about 700 nm, while it is within the temporal resolution of the experimental system in the band in the range 450–600 nm.

At excitation wavelength of 580 nm the slow lifetime constant associated to the averaged fit values is τ<sup>2</sup> = 1.6 ± 0.2 ps for the low wavelength band (450–600 nm) and τ<sup>2</sup> = 2.0 ± 0.2 ps for the

FIGURE 12 | Jablonski diagram with the sketch of the excited state dynamics. The arrows explain qualitatively the dynamics: absorption transitions (green arrows), internal conversion (yellow arrows), intersystem crossing (light blue arrows), vibrational cooling (dark blue arrows), non-radiative decay toward the ground state (violet arrow). After ligand field excitation (1T1), VC and ISC occur with an overall lifetime 0.07 ± 0.04 ps and, successively, IC toward the lower triplet state and relaxation toward the ground state with a lifetime 1.8 ± 0.3 ps. The same dynamics is proposed for the <sup>1</sup>LMCT (2 <sup>1</sup>E) excitation, with VC and ISC (1LMCT → <sup>3</sup>LMCT) overall lifetime 0.08±0.04 ps, and IC and non-radiative relaxation overall lifetime 1.5 ± 0.3 ps. For <sup>1</sup>LMCT (3 <sup>1</sup>E) excitation the calculations assign an ISC lifetime about 1 ps, slower than the experimental rise time 0.07 ± 0.04 ps. A fast IC toward the first singlet excited state and a fast singlet-triplet ISC is suggested to be associated with the fast experimental lifetime. The decay toward the ground state is sketched by IC within the triplet states and non-radiative decay with lifetime 1.5 ± 0.3 ps.

high wavelength band (650–750 nm). For excitation at 650 nm the averaged lifetime constants are τ<sup>2</sup> = 1.5 ± 0.2 ps and τ<sup>2</sup> = 2.1 ± 0.2 ps for the low and high wavelength bands, respectively.

It is impossible to disentangle the decay time constant of the two relaxation channels and we assign an overall averaged value to the decay time constant in the ligand field excitation case τ<sup>2</sup> =1.8±0.3.

The calculated singlet – triplet ISC τ for the ligand field states is in the range of 10 – 20 fs and confirms this phenomenological picture. In the low wavelength band the rise time is faster than the time resolution of the system and is compatible with an ISC of few tens of fs, while the high wavelength band probably contains information about VC relaxation.

The relaxation channels above discussed are reported in the Jablonski diagram in **Figure 12** ( <sup>1</sup>T<sup>1</sup> excitation).

Comparing the results obtained in this study on Co(AcAc)<sup>3</sup> with the Cr(AcAc)<sup>3</sup> (Juban and McCusker, 2005) case, the

#### REFERENCES

ADF. (2018). SCM, Theoretical Chemistry, eds E. J. Baerends, T. Ziegler, A. J. Atkins, J. Autschbach, O. Baseggio, D. Bashford, et al. (Amsterdam: Vrije Universiteit). Available online at: http://www.scm.com

Barone, V., Cimino, P., and Stendardo, E. (2008). Development and validation of the B3LYP/N07D computational model for structural parameter and dynamics of these molecules exhibits similar time constants and interpretations. Indeed, the order of magnitude of the time scale of the ISC presents a slight dependence on the different electronic and spin character of the transition (quadruplet to doublet in Cr(AcAc)<sup>3</sup> and singlet to triplet in Co(AcAc)3).

#### CONCLUSIONS

The FTAS study of Co(AcAc)<sup>3</sup> displayed a very fast de-excitation dynamics characterized by a distribution of processes with lifetime constants on the scale 1-2 ps.

On the grounds of the TDDFT analysis we identified different processes associated with these dynamics. An elongation of Co-O bond length with reduction of octahedral symmetry subsequent to the LMCT excitation can be associated with the early stage of dynamics. The transient absorption spectra for delay times greater than 2 ps reveal the features of the absorption of the lowest triplet state. It is worth noticing that the findings of TDDFT theory can help to connect the phenomenological analysis to a microscopic model. A TDDFT calculation and a parametrized model was used to calculate singlet-triplet ISC lifetime at the vertical geometry, with values in the range 10-20 fs for LF states and 0.1-1 ps for LMCT states.

To summarize the dynamics, the formation of the population of the triplet involves different concomitant processes, such as vibrational relaxation, geometry distortion, intersystem crossing. The microscopic processes included in the fast time constant are the vibrational cooling and the intersystem crossing, while the slower lifetime decay involves the journey toward the lowest triplet state and the final relaxation to the ground states.

We believe that the characterization of the dynamics of metal complexes is desirable in view of possible spintronic applications that nano-fabrication could provide. The LMCT fast de-excitation with a short transient in the triplet state could be exploited in single molecule devices such as spinvalves.

#### AUTHOR CONTRIBUTIONS

MS and AP performed the theoretical calculations. The remaining authors performed the experiments and the data analysis. All the listed authors equally contributed to the scientific discussion and the writing of the manuscript.

#### ACKNOWLEDGMENTS

We gratefully acknowledge the support of NVIDIA Corporation with the donation of the Titan V GPU used for this research.

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catalytic system: N-Hydroxyphthalimide (NHPI) Combined with Co(acac)n (n = 2 or 3). J. Org. Chem. 61, 4520–4526. doi: 10.1021/JO9 51970L


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The handling editor declared a past co-authorship with one of the authors DC.

Copyright © 2019 Ferrari, Satta, Palma, Di Mario, Catone, O'Keeffe, Zema, Prosperi and Turchini. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Full Dimensional Potential Energy Function and Calculation of State-Specific Properties of the CO+N<sup>2</sup> Inelastic Processes Within an Open Molecular Science Cloud Perspective

Andrea Lombardi 1,2 \*, Fernando Pirani <sup>1</sup> , Massimiliano Bartolomei <sup>3</sup> , Cecilia Coletti <sup>4</sup> and Antonio Laganà2,5,6

<sup>1</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Perugia, Italy, <sup>2</sup> Consortium for Computational Molecular and Materials Sciences (CMS)2 , Perugia, Italy, <sup>3</sup> Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Madrid, Spain, <sup>4</sup> Dipartimento di Farmacia, Università "G. d'Annunzio" Chieti-Pescara, Chieti, Italy, <sup>5</sup> CNR ISTM-UOS Perugia, Perugia, Italy, <sup>6</sup> Master-UP srl, Perugia, Italy

#### Edited by:

Xi Zhang, Shenzhen University, China

#### Reviewed by:

Thuat Thanh Trinh, Norwegian University of Science and Technology, Norway Sugata Chowdhury, National Institute of Standards and Technology (NIST), United States

\*Correspondence:

Andrea Lombardi andrea.lombardi@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 08 February 2019 Accepted: 18 April 2019 Published: 22 May 2019

#### Citation:

Lombardi A, Pirani F, Bartolomei M, Coletti C and Laganà A (2019) Full Dimensional Potential Energy Function and Calculation of State-Specific Properties of the CO+N2 Inelastic Processes Within an Open Molecular Science Cloud Perspective. Front. Chem. 7:309. doi: 10.3389/fchem.2019.00309 A full dimensional Potential Energy Surface (PES) of the CO + N<sup>2</sup> system has been generated by extending an approach already reported in the literature and applied to N2-N<sup>2</sup> (Cappelletti et al., 2008), CO2-CO<sup>2</sup> (Bartolomei et al., 2012), and CO2-N<sup>2</sup> (Lombardi et al., 2016b) systems. The generation procedure leverages at the same time experimental measurements and high-level ab initio electronic structure calculations. The procedure adopts an analytic formulation of the PES accounting for the dependence of the electrostatic and non-electrostatic components of the intermolecular interaction on the deformation of the monomers. In particular, the CO and N<sup>2</sup> molecular multipole moments and electronic polarizabilities, the basic physical properties controlling the behavior at intermediate and long-range distances of the interaction components, were made to depend on relevant internal coordinates. The formulated PES exhibits substantial advantages when used for structural and dynamical calculations. This makes it also well suited for reuse in Open Molecular Science Cloud services.

Keywords: intermolecular interactions, molecular energy transfer, rate constants, molecular beams, astrochemistry, carbon monoxide, planetary atmospheres

## 1. INTRODUCTION

The presence of significant traces of CO in gaseous systems in which molecular nitrogen N<sup>2</sup> is an abundant component is a frequent situation in astrochemistry, plasma chemistry and combustion. Besides obvious implications for combustion and CO<sup>2</sup> plasmas, CO plays an important role in planetary atmospheric chemistry (He et al., 2017), and it has been detected in Titan, Triton, and Pluto as a stable minor constituent (Lellouch et al., 2010), contributing to the energy balance of the planet and the chemistry of small organic molecule formation. For example, recent studies consider the contribution of CO to the formation and role of atmospheric hazes present in a number of solar system and exoplanetary atmospheres (He et al., 2017) and, particularly, hydrocarbon hazes, which

**248**

have substantial radiative heating and cooling effects in such atmospheres, as observed for Saturn's moon Titan (Tomasko et al., 2008; He et al., 2017; Hörst et al., 2018) and for Jupiter's stratosphere (Zhang et al., 2015) (not to mention the role of CO in the Earth's atmosphere chemistry). Organic hazes are particularly interesting due to astrobiological implications, such as the potential for Titan's atmosphere to contain the building blocks of life (Hörst, 2012; Fabiano et al., 2017). It was recently shown in a series of atmosphere simulation experiments using gas mixtures of CO, CH4, and N<sup>2</sup> (Hörst et al., 2018) that the inclusion of CO has a dramatic effect on the gas phase chemistry as well as on the density and composition of the solid material that is formed. In this respect, CO can actually be seen as the smallest molecule that could serve as a source of oxygen and carbon in space and planetary atmospheres.

The knowledge of the intermolecular interactions involving carbon monoxide and nitrogen (as well as methane) is generally required in the above mentioned fields to correctly assess their role in the chemical kinetics of gaseous environments. A fundamental issue is the accurate representation of the set of energy transfer processes involving CO in the various kinetic models used to study the gaseous mixtures.

Collisions between molecules promote transfer of energy amongst translational, rotational and vibrational degrees of freedom, determining the molecular state population. Dynamics simulations based upon quantum, classical and semiclassical scattering calculations permit one to obtain cross sections and thermal or state-to-state rate coefficients (Lombardi et al., 2013, 2015, 2016a; Celiberto et al., 2016). The resulting data, refined and complemented by experimental data (whenever available) can be used to set up relevant parts of kinetic models (Kustova and Kremer, 2014), routinely used in many research fields to simulate complex environments such as combustion mixtures, plasmas, atmospheres and molecular clouds in in the interstellar medium (Bacmann et al., 2002). The energy transfer processes in each collision event, being generally strongly state-specific, are sensitive to the initial quantum states of the involved molecules. Therefore, energy exchange kinetics is better accounted for by appropriate sets of state-to-state rate coefficients, rather than averaged. Indeed, state-to-state coefficients are entirely necessary when non-equilibrium conditions prevail. In those cases, the collection of reliable energy transfer cross sections and rate coefficients is the true accuracy-determining step of the modeling (Kustova and Nagnibeda, 2012; Kustova and Kremer, 2014).

In turn, the accuracy of whatever rate coefficient obtained by calculations depends on the realism of the underlying dynamics simulations, which essentially means a very accurate description of the intermolecular interactions, occurring at long- and midrange distances, with the energy exchanges being to a large extent due to such forces. Finally, the need for accuracy has to be contrasted with the computational demand of campaigns of massive state-to-state coefficient calculations. In this respect, flexible and easy to reuse potential energy surface formulations play an important role in the cooperative assemblage of simulations of chemical processes based on atomistic approaches. However, most of the structural and dynamics data available in popular data banks, of interest in several fields, including astrochemistry, combustion and plasmas, lack solid validation and are sometimes even totally arbitrary. A typical weakness of the mentioned data consists of the fact that even those originating from high-level ab initio calculations might be lacking sufficient accuracy in the long-range region. For this purpose, we currently check the suitability of the proposed PESs for carrying out calculations of the detailed probabilities, cross sections and rate coefficients for inelastic processes of the title systems.

Our work, however, due to the general high demand of computational resources that kinetics and dynamics simulations generate, has also the broader prospective aim of building MOlecular Simulator Enabled Cloud Services (MOSEX) (Vitillaro and Laganà, 2018) meant to provide the Molecular Science Community with a Cloud service (Laganà et al., 2018b) by offering the provision of accurate estimates of molecular properties generated in (often collaborative) experiments and validated by high-level theory (also often collaborative) simulations.

Accordingly, the purpose of the present work is threefold. First is to illustrate the development of an accurate full dimensional PES describing the intermolecular interactions of CO-N<sup>2</sup> systems. This is done by extending a well established semiempirical approach, based on a bond-bond description of the interactions (see e.g., Cappelletti et al., 2008; Faginas Lago et al., 2013 and references therein).

Second is to discuss a dynamical preliminary validation of the proposed PES through application to the case of the basic Vibration-Vibration (VV) energy exchange processes of CO in nitrogen-containing mixtures: CO(1)+N2(0) → CO(0)+N2(1) and N2(1)+CO2(0) → N2(0)+CO2(1).

Third is to report on the progress made in providing calculated scattering properties as a service to the community using the so-called Grid Empowered Molecular Simulator (GEMS) (Laganà et al., 2010; Manuali et al., 2010; Rampino et al., 2012a) through the activities of the Virtual Organization (VO) COMPCHEM (Laganà et al., 2010) first and of the Chemistry Molecular and Materials Science and Technologies (CMMST) Virtual Research Community (VRC) (Laganà, 2012) later.

The paper is therefore organized as follows. Section 2 is devoted to the description, formulation and optimization of the proposed CO+N<sup>2</sup> PES. Section 3 is devoted to illustrating the quantum-classical calculations and related results. Section 4 is devoted to illustrating the implemented Open Molecular Science Cloud prototype.

## 2. THE POTENTIAL ENERGY SURFACE

In this section we discuss the formulation of the PES of the CO-N<sup>2</sup> system used for the calculations and briefly illustrate as well its optimization and extension to flexible monomers. The approach we use is based on the so called bond-bond method (Cappelletti et al., 2008), a valuable feature of which is the choice of expressing the potential function parameters in terms of bond properties and parameters characterizing the internal molecular structure, such as charge distributions and polarizabilities. Since the energy functions depend on parameters having a well-defined physical meaning, these are portable in different molecular environments as building blocks of force fields of, in principle, whatever complexity, as testified by the application of the method to a variety of systems (see e.g., Albertí et al., 2011; Albertí and Faginas Lago, 2012; Bartolomei et al., 2012; Lombardi et al., 2012, 2016b; Falcinelli et al., 2013; Pacifici et al., 2013; Faginas-Lago et al., 2014a,b, 2015; Yeamin et al., 2014). It is worth mentioning that this aspect of the method is a pivotal element for our strategy of developing in order to provide rich and diverse data sets of molecular properties as a cloud service.

#### 2.1. The Representation of the PES

The intermolecular potential energy, Vinter, of the two interacting molecules, CO and N2, is formulated as a combination of two effective interaction components:

$$V\_{inter} = V\_{vdW} + V\_{elect}.\tag{1}$$

where VvdW and Velect represent the van der Waals (size repulsion plus dispersion-attraction) and the electrostatic interaction components, respectively. Velect originates from the anisotropic molecular charge distributions of the two bodies, which asymptotically tend to the sum of the (permanent) quadrupole- (permanent) quadrupole and dipole-quadrupole interactions. Both VvdW and Velect depend on the distance R between the centers of mass of the two molecules (say a for CO and b for N2), and on the Jacobi angular coordinates 2a, 2<sup>b</sup> and 8 describing the a − b mutual orientation as well (see **Figure 1**). In the present work we will consider a series of limiting configurations of the interacting molecules, specifically (2a,2<sup>b</sup> ,8)=(90◦ , 90◦ , 0 ◦ ), (90◦ , 90◦ , 90◦ ), (90◦ , 0◦ , 0◦ ), (0◦ , 90◦ , 0◦ ), (180◦ , 90◦ , 0◦ ), (0◦ , 0◦ , 0◦ ) and (180◦ , 0◦ , 0◦ ), which will be referred to as H, X, Ta, Tb<sup>1</sup> , Tb<sup>2</sup> , I<sup>1</sup> and I2.

The van der Waals term, VvdW of Equation (1), is expressed as a sum of the noncovalent contributions V i vdW as follows,

$$V\_{vdW}(R) = \sum\_{i=1}^{4} V\_{vdW}^{i} \left( r\_i \right), \tag{2}$$

where r<sup>i</sup> is the distance between different interaction centers of the involved molecules, which here are chosen to coincide with the constituting atoms (see **Figure 1**). Accordingly, the sum of Equation (2) runs over all four atom pairs of the CO-N<sup>2</sup> complex (see **Figure 1**). It must be emphasized here that in the present

work the bond-bond formulation is replaced by the pseudoatompseudoatom one in order to properly account for the variation of the anisotropy with the atom-atom distance and the polarizability consistent with the diatom (Pirani et al., 2019).

The explicit form of V i vdW is obtained using the Improved Lennard-Jones (ILJ) potential function (Pirani et al., 2008):

$$\frac{V\_{\rm vdW}^i(r\_i, \cdot)}{\varepsilon} = f(\mathbf{x}\_i) = \left[ \frac{6}{n(\mathbf{x}\_i) - 6} \left( \frac{1}{\mathbf{x}\_i} \right)^{n(\mathbf{x}\_i)} - \frac{n(\mathbf{x}\_i)}{n(\mathbf{x}\_i) - 6} \left( \frac{1}{\mathbf{x}\_i} \right)^6 \right] \tag{3}$$

where x<sup>i</sup> is the reduced distance defined as

$$\alpha\_i = \frac{r\_i}{R\_m}.\tag{4}$$

and ε and R<sup>m</sup> are, respectively, the well depth and position of the corresponding pair interaction. Note that the ILJ function (Pirani et al., 2008) is more realistic than the original Lennard-Jones (12,6) one, with a much more accurate size repulsion (first term within the square brackets) and the long range dispersion attraction tail (second term within the square brackets) (Pirani et al., 2004; Lombardi and Palazzetti, 2008).

The exponent n in Equation (3) is expressed as a function of x<sup>i</sup> using the following empirical equation (Pirani et al., 2004):

$$n(\mathbf{x}\_i) = \beta + 4.0x\_i^2. \tag{5}$$

in which β is a parameter depending on the nature and the hardness of the interacting particles. For the present system, β has been set equal to 8 (a value typical of van der Waals interactions in neutral-neutral systems) for all atom-atom pairs.

The relevant ε and R<sup>m</sup> parameters are directly related to the molecular polarizability of the involved partners, and a zerothorder estimate of them can be obtained from correlation formulas (Pirani et al., 2001, 2019; Cappelletti et al., 2008) which exploit "effective" atomic polarizability.

In this way a tentative full dimensional PES is generated and related ε and R<sup>m</sup> parameters can be fine-tuned by fitting experimental data and by comparing model predictions with accurate ab initio electronic structure calculations (see below).

The Velect term of Equation (1) has been formulated as a sum of Coulomb potentials as follows:

$$V\_{\text{elect}}(\mathbb{R}, \Theta\_a, \Theta\_b, \Phi) = \sum\_{jk} \frac{q\_{ja} q\_{kb}}{r\_{jk}} \tag{6}$$

with qja and qkb being point charges (located on the monomers a and b, respectively, and having values consistent with the corresponding calculated molecular dipole and quadrupoles) and rjk being the distance between them.

Such a formulation of Velect must be used for cases in which the molecular dimensions are not negligible with respect to the intermolecular distance R (Maitland et al., 1987). For both monomers a linear distribution of charges as that used in a previous work, see Lombardi et al. (2016b), has been adopted,

which consists of three charges placed on the atoms and on the molecule center of mass.

For charge values q<sup>i</sup> (as well as for the corresponding position ri), we took for N<sup>2</sup> the values reported in Lombardi et al. (2016b) while for CO we obtained them by exploiting corresponding dipole and quadrupole moment calculations (see below) together with simple geometrical considerations (see **Appendix A**). A comparison of the van der Waals and electrostatic interaction contributions to the intermolecular potential energy, for the various configurations of the two interacting molecules is reported in **Figure S1** of the Supplementary Material.

#### 2.2. The Optimization of the PES

The above-mentioned adopted values of ε and R<sup>m</sup> (hereinafter called "predicted") were fine-tuned by carrying out a comparison with ab-initio estimates of the intermolecular part of the interaction and an analysis of the second virial coefficient data (see next section). Predicted and optimized values for the case of rigid monomers are given in **Table 1** together with the other parameters used to formulate the intermolecular potential.

In **Figure 2** the main features of the intermolecular potential Vinter calculated for seven selected geometries of the interacting system at the CCSD(T) level of theory (see next section) are reported. Although such results will be discussed in more detail later, it is worth pointing out here that, as shown by the figure, the stability ranking of the investigated geometries on the empirical PES model globally agrees well with that of the ab initio values.

In order to carry out the fine tuning of the parameters of the semiempirical functional representation of the PES, we followed the procedure already employed in Bartolomei et al. (2012); Lombardi et al. (2016b), and we first investigated the dimer formation for two rigid monomers (with bond lengths and angles fixed at their equilibrium values). In this perspective, we performed CCSD(T) intermolecular potential calculations

TABLE 1 | Optimized Rm (Å) and ε (meV) parameters and (within parentheses) predicted values estimated for rigid momomers at the equilibrium bond length req (Å) and by considering atomic "effective" polarizabilities αx values (Å<sup>3</sup> ).


<sup>a</sup>From Linstrom and Mallard (2018). <sup>b</sup>present work. <sup>c</sup>From Bartolomei et al. (2011). <sup>d</sup>From Appendix B of Cappelletti et al. (2008). <sup>e</sup>From Lombardi et al. (2016b).

for the H, X, Ta, Tb<sup>1</sup> , Tb<sup>2</sup> , I1, and I<sup>2</sup> configurations of the dimer (see section 2.1), as a function of the distance R of the two monomers. Results are reported in **Figure 2** where they are compared with the corresponding empirical PES energy profiles. The supermolecular CCSD(T) energies were calculated using the MOLPRO package (Werner et al., 2006) and corrected using the counterpoise method (Boys and Bernardi, 1970; van Lenthe et al., 1987) in order to remove the basis set superposition error. For all supermolecular calculations, the Dunning's augcc-pVTZ basis set (Kendall et al., 1992) was used together with the bond function set [3s3p2d1f] developed by Tao Tao and Pan (1992) and placed on the midpoint of the intermolecular distance R that was varied in the range 2.5–8 Å. In order to assess the convergence of the supermolecular energies with the basis set, additional calculations using the aug-cc-pVQZ plus bond functions (see above) basis set were also performed for the usual dimer configurations around their minima. The corresponding results, compared in **Table 2** with those obtained using the less extended basis set, show deviations of about 0.1–0.2 meV. The C-O and N<sup>2</sup> bond lengths of the linear monomers were set equal to 1.1283 Å (Linstrom and Mallard, 2018) and 1.1007 Å (Bartolomei et al., 2011), respectively.

In order to carry out a comparison with the flexible monomer empirical potential (to be described below), further CCSD(T) calculations were carried out by considering a maximum variation of 10% in the bond length of one of the two monomers. Such small deformations did not alter the single determinant character (Lee and Taylor, 1989) of the used wavefunctions and allowed the use of the CCSD(T) method also for the deformed arrangements. The ab initio interaction profiles related to flexible monomers, reported in the following, have been compared with the results of the model potential in **Figures 6**, **7**, to prove the validity of the model predictions.

In order to introduce into the empirical model potential the dependence of the electrostatic component Velect (see Equation 1) on monomer deformations, the variation of the CO and N<sup>2</sup> molecular multipole moments with the internal coordinates (and consequently, also that of the related charge distributions) was introduced. As for N2, the molecular multipoles and the related point charge dependence as those adopted in Lombardi et al. (2016b) were used. In the case of CO, as previously done for CO<sup>2</sup> (Bartolomei et al., 2012) and N<sup>2</sup> (Lombardi et al., 2016b), multireference ACPF (Averaged Coupled Pair Functional) calculations were performed as a function of the stretching for the molecular dipole and quadrupole moments by following the guidelines reported in Bartolomei et al. (2011). In particular, the molecular orbitals in the ACPF calculations were all taken to be these natural ones from the complete active space self-consistent field (CASSCF) reference wave functions. Therefore, the considered active space (CAS) was assumed to distribute 10 electrons in the orbitals indicated as (2, 3, 4)σ<sup>g</sup> (2, 3, 4)σu(1, 2)πu(1, 2)π<sup>g</sup> . The 1σg1σ<sup>u</sup> core molecular orbitals were fully optimized, while being constrained to be doubly occupied and excluded from the used CAS. The Dunning's aug-cc-pV5Z basis set (Kendall et al., 1992) was employed and the calculations were performed using the MOLPRO package (Werner et al., 2006).

TABLE 2 | Equilibrium distance (Re) and binding energy (De) for the present rigid monomers empirical and ab initio PESs considering selected geometries of the CO-N2 dimer (see Figure 2).


For the model empirical PES the reported values correspond to those obtained with the optimized and predicted (in parenthesis) R<sup>m</sup> and ε parameters of Table 1. For the ab initio PES the reported values correspond to those obtained with two different basis sets (see text): aug-cc-pVTZ plus bond functions and aug-cc-pVQZ plus bond functions (in parentheses).

The parameters of the rigid monomers defining the empirical PES were optimized in order to best fit at the same time the measured second virial coefficients and the ab initio interaction energies. It is worth pointing out here that, given the physical ground of the procedure, both the number of parameters allowed to vary in the fit and their interval of variation are rather small. As an example, the long-range dispersion attraction coefficient values, defined as ε·R 6 <sup>m</sup> were allowed to vary within a 10% interval of their initial value (see also Appendix A of Cappelletti et al., 2008). Moreover, it is also worth pointing out here that, due to some inter-dependencies, the final best fit values of the adjustable parameters usually differ only by a few percent from the initial ones (see **Table 1** for ε and Rm). The main features (equilibrium distance R<sup>e</sup> and binding energy D<sup>e</sup> for selected dimer geometries) of the optimized and predicted empirical PES's are reported in **Table 2**, and it can be seen that the small variations of the optimized ǫ and R<sup>m</sup> (see **Table 1**) lead in general to a less attractive potential. **Table 2** shows also that while optimized and predicted parameter values are both able to satisfactorily reproduce the relative stability of the limiting configurations (see **Table 2**), the former are closer to ab initio results, especially for the most attractive dimer geometries. However, it can also be noticed that the model PES is not capable of predicting the T<sup>a</sup> configuration as the most stable of those here considered; nevertheless, it has to be stressed that the ab initio energy difference between the Ta, Tb<sup>1</sup> , and Tb<sup>2</sup> configurations is quite low and less than 1 meV (see **Table 2**) and that the very few parameters of the model PES do not allow the description of this very fine behavior.

As anticipated above, to validate and optimize the rigid rotor PES, second virial coefficient (B(T)) values, including first quantum correction Bq1(T) to the classical estimate Bcl(T) (Pack, 1978) (B(T) = Bcl(T) + Bq1(T)), were also computed. The calculations evidence that quantum corrections are smaller than 1% even for temperature values as low as 200 K. A comparison of calculated B(T) values with experimental measurements (Jaeschke et al., 1988; McElroy and Buchanan, 1995) over the temperature range 273 < T < 350 K is given in **Figure 3**.

The figure shows that the predicted PES results underestimate the experimental data in the considered range of temperature, while those referring to the optimized PES lie between the two sets of the measured values. This behavior suggests that, in agreement with the above reported analysis for the ab initio energy values, the predicted PES provides an interaction that is too attractive, which indeed can be properly corrected by tuning the involved ε and R<sup>m</sup> parameters.

A further check of the reliability of the empirical PES is reported in **Figure 4**, where the related spherical averaged potential is compared with an accurate ab initio estimate at the MP4 level and obtained from Karimi-Jafari et al. (2011). Again, it has to be pointed out that although the predicted PES shows a 15% deeper well, it becomes practically negligible after optimization.

## 2.3. Extension of the PES to Consider Flexible Monomers

The parametrization of the empirical PES has been generalized by properly introducing the dependence of VvdW and Velec (see Equation 1) on the molecular elongation. Specifically, the variation of the electric multipole affecting Velec has been obtained as indicated above, while the change of the molecular polarizability has been taken into account for the modulation of the VvdW potential parameters.

For the N<sup>2</sup> monomer deformation, the empirical bond length dependence of the molecular polarizability α as reported in Appendix B of Cappelletti et al. (2008) is used, while for the corresponding point charges distribution dependence the analytic formulas given in Appendix A of Lombardi et al. (2016b) are employed.

In the case of the CO monomer we used the empirical bond length dependence of the polarizablity α as reported in **Appendix A**, which is shown here in the lower panel of **Figure 5** together with previous ab initio estimates. In addition, for the CO permanent dipole quadrupole dependence on the bond length, an appropriate representation can be obtained from the analysis of present ab initio results reported in the upper panels of **Figure 5**. To this end, ab initio data were fitted using suitable analytic functions providing the radial dependence of point charges on the CO bond length r, as shown in detail in **Appendix A**.

The effect of the stretching of a single monomer on the complex interaction predicted by the adopted potential formulation is illustrated in **Figures 6**, **7**. In all cases the plots of the CCSD(T) values, obtained for rigid and flexible molecules, are also reported for comparison: it can be appreciated that the elongation of one monomer provokes the same trends in both PESs for the stability of the considered interaction profiles, confirming therefore the reliability of the adopted empirical model.

### 3. QUANTUM CLASSICAL CALCULATIONS FOR VIBRATIONAL ENERGY TRANSFER PROCESSES

As a premise to this section, we remark that, when collisions involve more than three atoms, it is impractical to ground realistic simulations and the related systematic computations on full dimensional quantum methods, solving the associated Schrödinger equations, since their efficiency is strongly dependent by the number of degrees of freedom. Although work is constantly being done to achieve the feasibility of exact

FIGURE 5 | CO electric dipole (µ) and quadrupole (Q) moments as well as molecular polarizability (α¯) plotted as a function of the interatomic distance r. Full squares refer to present ab initio values obtained as detailed in the text, while solid lines correspond to analytic fits (see text and Appendix A). Open circles in the lowest panel refer to previous ab initio estimations at the CCSD(T) level from Maroulis (1996). The vertical line indicates the CO equilibrium distance.

quantum calculations (e.g., through new coordinates and basis sets Aquilanti et al., 2000, 2002, 2004a,b, 2006; Sevyuk et al., 2005; Castro Palacio et al., 2007; Barreto et al., 2011, 2012; Palazzetti et al., 2011), these remain mainly limited to three-atom systems. For energy transfer, reactive and photodissociating systems involving triatomic and larger molecules, or for the simulation of more complex environments such as gaseous mixtures and flows, classical trajectories are widely employed to interpret experimental results, saving computing time (see e.g., Lombardi et al., 2010; Aquilanti et al., 2011; Palazzetti et al., 2013; Nakamura et al., 2015).

Semiclassical methods are also available (Laganà et al., 2003; Faginas-Lago and Laganá, 2005; Lago et al., 2005; Faginas-Lago et al., 2006, 2010; Faginas et al., 2008; Rampino et al., 2012b), but these won't be considered here.

geometries of a pair of rigid monomers (black lines) and of a rigid N2 plus a stretched CO (the bond length has been elongated of 10% with respect to equilibrium) monomer (red dashed lines). Empirical PES results are plotted in the lower panel while those corresponding to the ab initio calculations are plotted in the upper panel.

On the other hand, an efficient and accurate method for calculating cross sections and rate coefficients for the exchange of vibrational quanta of energy upon inelastic collisions for the process:

$$\text{CO}(\nu\_i) + \text{N}\_2(\nu\_i') \to \text{CO}(\nu\_f) + \text{N}\_2(\nu\_f'),$$

is the Quantum Classical (QC) one introduced and developed by G.D. Billing (see Billing, 1984a, 1987) by combining quantum mechanics treatments (for selected bound degrees of freedom) with classical mechanics ones (for the remainder).

The QC method is still one of the most efficient tools to calculate large numbers of accurate rate coefficients for processes involving vibrational energy transfer. The detailed description of the method goes beyond the aim of the present work. The formulation used here is essentially the one described in detail in Coletti and Billing (1999), Coletti and Billing (2000), Coletti and Billing (2002), Billing et al. (2003), and Fioccola et al. (2017), to which the reader is referred for the relevant mathematical derivation. In this paper we give only the formulation of the basic properties.

#### 3.1. The Main Features of the Adopted Quantum Classical Method

plotted in the upper panel.

According to the QC approach, the quantum mechanical timedependent Schrödinger equation for the nuclear motion is solved for the degrees of freedom of the system playing the most relevant role in vibration-to-vibration (VV) quantum energy exchange, vibrations and roto-vibrational couplings, by a coupled equations method to obtain the quantum transition amplitudes avv′(t), where v and v ′ are the initial vibrational quantum numbers of the diatoms. The vibrational wavefunction is initialized as the product of the Morse functions φ 0 v (rCO)φ 0 v ′(rN<sup>2</sup> ) for the two infinitely separated diatoms, whose parameters are given in **Table 3**, and is expanded as:

$$\Psi = \sum\_{\mathbf{v}, \mathbf{v}'} a\_{\mathbf{v}\mathbf{v}'} (\mathbf{t}) \phi\_{\mathbf{v}} (r\_{\text{CO}}) \phi\_{\mathbf{v}'} (r\_{\text{N}\_2}) \exp\left[ -\mathbf{i} \hbar^{-1} (E\_{\mathbf{v}} - E\_{\mathbf{v}'}) \mathbf{t} \right] \tag{7}$$

where E<sup>v</sup> and E<sup>v</sup> ′ are the vibrational energies of the oscillators in their initial states. The remaining degrees of freedom are treated classically by integrating the corresponding set of Hamilton equations of motion in an effective potential defined as the Ehrenfest average of the interaction potential.

The quantum transition amplitudes av<sup>f</sup> <sup>v</sup> ′ f (t) can then be used to calculate either specific state-to-state vibrational/rotational

TABLE 3 | Morse and vibrational parameters for CO and N2.


transitions cross sections, σv<sup>i</sup> jiv ′ i j ′ <sup>i</sup>→v<sup>f</sup> j f v ′ f j ′ f , or Monte Carlo averaged cross sections over the Boltzmann distribution of the initial rotational angular momenta j and j ′ for CO and N2, respectively:

$$\sigma\_{\nu,\mathbf{v}'}(U,T\_0) = \frac{\pi \hbar^6}{8\mu (kT\_0)^3 I\_{CO} I\_{N\_2}} \times \tag{8}$$

$$\int\_0^{l\_{\text{max}}} \int\_0^{j\_{\text{max}}} \int\_0^{j' \max} \, \text{d}j \, \text{d}j' \, \text{d}l \, (2j+1)(2j'+1)$$
 $(2l+1)N^{-1} \sum |a\_{\nu \nu'}|^2$ 

where T<sup>0</sup> is an arbitrary reference temperature, which cancels out in the formulation of rate constants (Equation 9), ICO and IN<sup>2</sup> are the moments of inertia of the diatoms, U is the classical energy, obtained by subtracting from total energy the vibrational energy of the two diatoms, U = E−E<sup>v</sup> −E<sup>v</sup> ′ , jmax and j ′ max are the upper limit for the randomly chosen rotational quantum numbers for the diatoms, lmax the upper limit for the angular momentum and µ is the reduced mass of the system.

From such averaged cross sections, rate coefficients for vibrational relaxation kvv′(T) (see e.g., Coletti and Billing, 2002; Billing et al., 2003) can be derived as follows:

$$k\_{\nu\nu'}(T) = \left(\frac{8kT}{\pi\mu}\right)^{1/2} \left(\frac{T\_0}{T}\right)^3 \int\_{\epsilon\_{\rm min}}^{\infty} \mathrm{d}\left(\frac{\overline{U}}{kT}\right) \mathrm{e}^{-\overline{U}/kT} \sigma\_{\nu,\nu'}(T\_0, \overline{U}), \tag{9}$$

where ǫmin = 0 for exothermic and ǫmin = 1E for endothermic processes and U is the symmetrized classical energy (Billing, 1984b):

$$
\overline{U} = U + \frac{1}{2}\Delta E + \frac{\Delta E^2}{16U} \tag{10}
$$

which has been introduced to restore, in an approximate fashion, the quantum mechanical detailed balance principle (Billing, 1984a,b, 1987).

In the present treatment the anharmonic vibrational energy is formulated as:

$$E\_{\nu\_i} = \hbar\omega\_{\rm ef}\left(\nu\_i + \frac{1}{2}\right) - \hbar\omega\_{\rm ef}\chi\_{\rm ef}\left(\nu\_i + \frac{1}{2}\right)^2 + \hbar\omega\_{\rm ef}\wp\_{\rm ef}\left(\nu\_i + \frac{1}{2}\right)^3 \tag{11}$$

where ωei is the wavenumber for the i-th oscillator and xei and yei are the anharmonicity constants (see **Table 3** for the values employed in the calculation for N<sup>2</sup> and CO).

#### 3.2. Results and Discussion

QC rate coefficients have been computed for the exothermic exchange of a single vibrational quantum of energy between the first excited vibrational level v ′ <sup>i</sup> = 1 of N<sup>2</sup> (N2(1)) and the ground vibrational level v<sup>i</sup> = 0 of CO (CO(0))

$$\text{CO(0)} + \text{N}\_2\text{(1)} \rightarrow \text{CO(1)} + \text{N}\_2\text{(0)} + 187.45 \text{cm}^{-1}$$

and for the endothermic exchange of a single vibrational quantum of energy between the first excited vibrational level v<sup>i</sup> = 1 of CO (CO(1)) and the ground vibrational level v ′ <sup>i</sup> = 0 of N<sup>2</sup> (N2(0))

$$\text{CO(1)} + \text{N}\_2\text{(0)} \rightarrow \text{CO(0)} + \text{N}\_2\text{(1)} - 187.45 \text{cm}^{-1}$$

and in the temperature range 80–3,000 K, by running trajectories at 15 initial values of total classical energy comprised between 50 cm−<sup>1</sup> and 15,000 cm−<sup>1</sup> , with a more frequent sampling driven toward lower energies. For each energy value, 2,000 trajectories were considered, which should ensure an accuracy for rate constants of ∼ 20% at lower temperatures and ∼ 15% at higher ones.

For each trajectory, the impact parameter was randomly chosen between 0 and 10 Å , and the initial separation between the colliding partners was set equal to 15 Å. In the expansion (7) a total of 36 vibrational states was included, i.e., those consisting of a band of energy 1E up to 14,000 cm−<sup>1</sup> .

**Figures 8**, **9** show the dependence of the computed QC rate coefficients on the temperature for the exothermic CO(0)+N2(1)→ CO(1)+N2(0) and the endothermic CO(1)+N2(0) → CO(0)+N2(1) processes, respectively.

For comparison, the same Figures show the experimental data (Sato et al., 1969; von Rosenberg et al., 1972; Mastrocinque et al., 1976; Allen and Simpson, 1980), when available, together with previous theoretical results (Kurnosov et al., 2003).

Rate coefficients computed at some selected temperature values are also reported in **Tables 4**, **5**.

The behavior of the QC rate coefficient plots computed on our PES shown in **Figures 8**, **9** for both processes agrees well with the experimental ones over the whole temperature range. More in detail, deviations by a maximum factor of 3 are found at the lowest values of T, where the experimental data are more bound to be affected by lower accuracy, although the corresponding slope is well reproduced. Indeed the calculated and experimental value of β in the Arrhenius expression k(T) = A exp(− β RT ) for the T range 80–300 K differs for little less than 10%.

In the case of the exothermic VV exchange, where experimental data are available in a wider range of temperatures up to 3,000 K, the behavior at low temperatures is the same as for the endothermic process, but the deviation between calculated and experimental rate coefficients is found to decrease

FIGURE 8 | Rate coefficients (logarithmic scale) plotted as a function of temperature for the CO(0)+N2(1)→ CO(1)+N2(0) transition. Present work results (solid line) compared to the experimental ones up to 300 K of Allen and Simpson (1980) (red circles), those obtained by laser-induced fluorescence (blue triangles) (Mastrocinque et al., 1976) and the high temperature ones of Sato et al. (1969) (green squares). The close area represents rate coefficients obtained in von Rosenberg et al. (1972) by shock wave in the range 1,000–2,000 K.

to ∼ 20% at temperatures larger than 1,000 K (**Figure 8**). Thus, the agreement between theoretical and experimental data is rather good in the whole temperature range. Agreement at higher temperatures (superior than in previous theoretical determination) is an indication that the basic contributions to the interaction are well described. The slightly larger discrepancy at low temperature can be attributed either to the lower accuracy of low-temperature experiments or to the neglecting of a proper quantum treatment for rotations which might play a role in the vibrational energy exchange process at low collision energies.

## 4. THE PROTOTYPING OF THE OPEN MOLECULAR SCIENCE CLOUD SERVICE

In this section the present implementation of the abovementioned MOSEX [MOlecular Simulator Enabled Cloud Services (MOSEX) (Vitillaro and Laganà, 2018)], which aimed to support research in computational simulations of molecular scattering processes, is illustrated with particular focus on related progress in the following:


## 4.1. Networking and Networked Software Applications

Networking and assembling networked software applications for the Molecular science community begun within COST

TABLE 4 | Experimental and calculated rate constants, in cm<sup>3</sup> s −1 , for the exothermic CO(0)+N2(1)<sup>→</sup> CO(1)+N2(0)+187.45 cm−<sup>1</sup> process.


(www.cost.eu/) Action D23 (METACHEM) and D37 (Grid Computing in Chemistry: GRIDCHEM). In METACHEM the activities of various Molecular Science research laboratories were networked on a shared computing platform made of a geographically distributed cluster of heterogeneous computers operating as a single virtual parallel machine (Foster and Kesselman, 1999). In the following Action GRIDCHEM Grid solutions and paradigms for molecular science research developed by D23 were consolidated on the grid. GRIDCHEM leveraged the creation and the use of distributed computing infrastructures (the "Grid") to drive collaborative computer modeling and simulation in chemistry toward "new frontiers in complexity and a new regime of timeto-solution" (GRIDCHEM, 2006–2010). At more infrastructural level, the European projects EGEE (Enabling Grids for EsciencE, https://cordis.europa.eu/project/rcn/87264\_en.html), first, and the EGI (European Grid Infrastructure, https://en.wikipedia.org/wiki/European-Grid-Infrastructure),

next, provided various disciplines, including Molecular Science, with a world class level platform for computational collaborations. In particular, during EGEE-III, the first pilot computational application called GEMS (Laganà et al., 2010) designed to enable the distributed calculation of cross sections and rate coefficients starting from the ab initio computation of the electronic structure of the molecular system followed by the fitting of the computed ab initio points using a combination of analytic formulae into a proper functional representation of the interaction in short, intermediate and long-range regions—was implemented. This allows at present routine computation of reactive and nonreactive properties of elementary systems based on the desired number of molecular geometries (Storchi et al., 2006) and collisional paths (Gervasi and Laganà, 2004) by distributing them on the grid. The scheme of the most recent evolution of GEMS toward the atomistic simulation of the kinetics of more complex systems, together with the related "data analysis and validation" and "open archive and reuse" in a cloud service perspective, is sketched in **Figure 10**.

TABLE 5 | Experimental and calculated rate constants, in cm<sup>3</sup> s −1 , for the endothermic CO(1)+N2(0)<sup>→</sup> CO(0)+N2(1)-187.45 cm−<sup>1</sup> process.


The molecular science community has been accordingly organized into the COMPCHEM (Laganà et al., 2010) VO first and in the CMMST (Chemistry, Molecular and Materials Science a Technologies) VRC (Virtual Research Community) (https://wiki.egi.eu/wiki/Towards\_a\_CMMST\_VRC) later. On a national basis, then, the different disciplinary communities were gathered in Joint Research Units (JRU), for example in Italy with IGI (http://www.italiangrid.it), in order to give a higher local momentum to networked applications. In this spirit, the following activities were pursued in networked Molecular Sciences:


management for training and education in sciences and technologies;

• turn (in collaboration with partner SMEs), the versatility of the adopted e-infrastructure tools, the richness of the developed CMMST knowledge and the credit mechanism supporting the synergistic operating into a business model, enabling an efficient transfer of the activities to the market, thereby ensuring business sustainability by leveraging synergistic models.

## 4.2. Assembling Cloud Computing Infrastructures

The cloud-oriented computing infrastructure developed for our calculations is an embryonic platform of the Beowulf type running under the OpenStack platform sketched in the lower side of Figure 3 of Vitillaro and Laganà (2018) named HERLA (https://en.wikipedia.org/wiki/Beowulf\_cluster). HERLA has been established at the Dipartimento di Chimica, Biologia e Biotecnologia (DCBB) of the University of Perugia. The platform consists of a couple of HPC clusters, (CG/training) and (FE/research) running Scientific Linux 6.x with two distinct access nodes. The clusters are connected using NIS in a singleimage system and are used first for students' training (CG) and second for scientists' research (FE). The management of Herla is presently carried out by the CMS<sup>2</sup> Consortium (http://www.cms-2.org/index.php) of the University of Perugia, CNR-ISTM - Perugia unit and the two companies Master-UP s.r.l. and Molecular Horizon s.r.l. Recently, cloud images of HERLA (VHERLA) have been created and deployed in a storage system (CEPH located at DCBB). This effort was meant to support as well the activities of the School on Open Science Cloud (SOSC17) held in Perugia on June 2017 in collaboration with the Department of Physics and Geology (DFG) and INFN Perugia (running under the INFN OpenStack platform sketched in the lhs upper side of Figure 3 of Vitillaro and Laganà, 2018).

Later, as sketched in the rhs side of Figure 4 of Vitillaro and Laganà (2018), the images of VHERLA were allocated to the OpenStack GARR Cloud platform in Palermo within the project "cnr-istm" and were used to install the version VHERLA(GARR-CLOUD) hscw (http://hscw.herla.unipg.it/ganglia/?p=2&c=FrontEnd) bearing the following features: Access node hscw (2 core, 4Gb RAM, 200Gb storage) and Cluster (7 nodes, 96 cores, 360Gb RAM, 700Gb storage). The Access node hscw, can be reached at the IP address [90.147.189.20] via SSH and the following 7 nodes, 96core, 380Gb, 512Gb scratch are defined at Torque(PBS)/MAUI as [Intel Xeon E3-12xx v2(Ivy Bridge)/2.6Ghz]. This allowed the generation of a virtual cluster for Molecular Sciences that has also been used for the training of the Students of the XIII EM TCCM (European Master in Theoretical Chemistry and Computational Modeling) Intensive Course (http://wwwold.chm.unipg.it/chimgen/mb/theo2/TCCM2018/EM-

TCCM2018/EM-TCCM/Welcome.html) with details at the following reference web page: http://hscw.herla.unipg.it URL.

## 4.3. Developing a Sustainable Operational Model

As to the operational model we have already developed a sustainable open collaborative user/producer (Prosumer), whose prototype has been first implemented for running the ECTN (European Chemistry Thematic Network (http://ectn.eu/)) EChemTest e-tests based on the use of the educational LibreEOL (https://echemtest.libreeol.org) and GLOREP (https://glorep.unipg.it/) services Laganà et al., 2018a. An important feature of the Prosumer model adopted for EChemTest was the containment of costs by leveraging the fact that the ECTN member HEIs running e-test Self Evaluation Sessions (SES)s for the assessment of the Chemistry competences of their own students already act at the same time as consumers of EChemTest services and as producers of Question and Answers (Q&A)s, assessors of students' competences, designers and developers of e-learning materials (a typical cluster of the horizontal type) for the harmonization at the European level of the assessment of Molecular Science competences. This behavior is quite usual in education and research activities in which knowledge is a common good to be at the same time produced and consumed.

The only additional action needed to the end of making the prosumer model sustainable was to assign to a company the role of market spinner. For EChemTest this role was taken by Master-Up s.r.l. thanks to its nature as a former spinoff of the University of Perugia (started in the year 2004 out of the aggregation of some members of the Chemistry Department and the Mathematics and Informatics Department who were experts in molecular dynamics simulations and computer science) devoted to design, production and marketing services for technological innovation as its main goal. As a matter of fact, the mission of Master-Up has been since the very beginning the design and development of cloud services for molecular sciences and technologies. In the particular case of EChemTest, the Prosumer model has led to the production in the year 2018 of 2622 SESs, with an increase of 5 percent over the previous year. Further efforts have also been spent in the period up to January 2019 for the implementation of the already mentioned MOlecular Simulator Enabled Cloud Services (MOSEX), a European Open Science Cloud Pilot designed as a follow-up of the EGI COMPCHEM VO activities for the following applications:


## 5. CONCLUSIONS

In this work we have presented an accurate full dimensional potential energy surface for the CO-N<sup>2</sup> system, characterized by an extension of the bond-bond formulation of the intermolecular interactions. The PES, intended for use in dynamics simulations aimed at calculating sets of accurate state-to-state rate coefficients, has been validated by performing Quantum-Classical dynamics simulations of the CO-N<sup>2</sup> vibrational energy exchange, with outcoming rate coefficients in substantial agreement with experimental data on a wide range of temperatures. The generation of large pools of kinetics data and accurate molecular properties to feed databases employed in astrochemical models, plasma chemistry and combustion studies, is a current challenge for theoretical and computational chemistry, with a strong multidisciplinary character. Here we suggest to set up cloudoriented computing infrastructures based on collaborative computer modeling and simulations to gather communities and boost efforts.

## AUTHOR CONTRIBUTIONS

AaL and AoL conceived and supervised the study and wrote the manuscript. FP and MB formulated the PES and performed ab initio calculations. CC performed dynamics simulations based on the Quantum Classical method, obtaining the theoretical rate coefficients.

## ACKNOWLEDGMENTS

The authors thank MIUR and Perugia University for financial support through the AMIS project (Dipartimenti di Eccellenza 2018–2022). Financial support from VII FP (Egi-Inspire, Phys4Entry) and COST (Action CM901) is acknowledged. AaL and FP thank the Italian MIUR for funding through the program PRIN 2015 (contract 2015F59J3R\_002). AaL also thanks the Dipartimento di Chimica, Biologia e Biotecnologie for funding under the program Fondo Ricerca di Base 2017. The work was also financially supported by Fondazione Cassa Risparmio Perugia (Codice Progetto: 2015.0331.021 Ricerca Scientifica e Tecnologica). MB was supported by the Ministerio de Ciencia, Innovación y Universidades (Spain, grant FIS2017-84391-C2-2-P). Calculations have been made possible by the support of the Virtual Organization COMPCHEM and allocated computing time from the OU Supercomputing Center for Education & Research (OSCER) at the University of Oklahoma (OU).

## SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fchem. 2019.00309/full#supplementary-material

## REFERENCES


Its Applications - ICCSA 2016, volume 9786 of Lecture Notes in Computer Science, ed O. E. A. Gervasi (Cham: Springer), 246–257.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Lombardi, Pirani, Bartolomei, Coletti and Laganà. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

#### APPENDIX A

## Dependence of the CO Polarizability and Permanent Multipoles on the Monomer Bond Length

The radial dependence of the CO average polarizability α¯ (in Å<sup>3</sup> ) is defined by the following empirical equations given in terms of n, an effective bond order, r, the bond length, and req its equilibrium value (see **Table 1**):

$$\bar{\alpha}(r) = \left(0.5733n + 0.8400\right) \left\{ 1 + \frac{1}{3} \left(\frac{r}{r\_{eq}} - 1\right) \right.$$

$$\exp\left[1.0961\left(\frac{r}{r\_{eq}} - 1\right) \left(1 - 0.4682r\right) \sqrt{\frac{r}{r\_{eq}}}\right] \tag{A1}$$

where the effective bond order reads

$$n = 3 - \left(\frac{0.6538 \frac{r}{r\_{eq}} + 1.3076}{1 + 0.8770r^2}\right) \exp\left[-0.9635 \, r \left(\frac{r}{r\_{eq}} - 1\right)\right] \tag{A2}$$

The dependence of α¯ on r is reported in the bottom panel of **Figure 5** where a comparison with previous ab initio estimates is also provided.

The atomic polarizabilities related to the C and O atoms are obtained as

$$\alpha\_C = 0.66 \,\bar{\alpha}, \,\, \alpha\_O = 0.33 \,\bar{\alpha}$$

while that for the N atom (αN) is assumed to be half the N<sup>2</sup> molecular polarizability which is obtained from the Appendix B of Cappelletti et al. (2008).

The atomic polarizabilities of the involved molecular partners are then used to obtain the R<sup>m</sup> and ε interaction parameters for each atoma-atom pair<sup>b</sup> as follows Pirani et al. (2001):

$$R\_m = 1.767 \frac{\alpha\_a'^{1/3} + \alpha\_b'^{1/3}}{(\alpha\_a \alpha\_b)^{0.095}} \text{ Å} \tag{A3}$$

with α ′ <sup>C</sup>= 1.382 αC, α ′ <sup>O</sup>= 1.382 α<sup>O</sup> and α ′ <sup>N</sup>= 1.65 αN, and

$$
\varepsilon = 0.72 \frac{C\_{disp}}{R\_m^6} \text{ meV} \tag{A4}
$$

being

$$C\_{\rm disp} = 15.7 \times 10^3 \frac{\alpha\_d \alpha\_b}{(\alpha\_d / N\_a)^{1/2} + (\alpha\_b / N\_b)^{1/2}} \text{ meV}^6$$

an efficient dispersion coefficient depending on the numerical coefficients NC, N<sup>O</sup> and N<sup>N</sup> with the meaning of the total atomic effective electron numbers which assume the 4, 6, and 4.4 values, respectively.

The radial dependence of the CO molecular dipole (µ(r)) is formulated as

$$\mu(r) = \mu(r\_{eq}) - 1.250(r - r\_{eq}) + 0.210(r - r\_{eq})^2$$

$$+ 0.420(r - r\_{eq})^3 - 0.015(r - r\_{eq})^4 \tag{A5}$$

where µ(req) represents the dipole moment at req.

That of the CO molecular quadrupole (Q(r)) is expressed as

$$Q(r) = Q(r\_{eq}) + 2.250(r - r\_{eq}) + 0.680(r - r\_{eq})^2$$

$$-0.490(r - r\_{eq})^3 - 1.580(r - r\_{eq})^4 + 0.400(r - r\_{eq})^5 \quad \text{(A6)}$$

being Q(req) the quadrupole moment at req.

Such polynomial representations provide results in atomic units which reproduce the ab initio data illustrated in the top and intermediate panels of **Figure 5**.

From the above relationships we obtain the molecular charge distribution as

$$q\_O = \frac{Q(r) + \mu(r) \cdot r\_C}{r\_C \cdot r\_O + r\_O^2},\tag{A7}$$

$$q\_C = \frac{-\mu(r) + q\_O \cdot r\_O}{r\_C},\tag{A8}$$

and

$$q\_{cm} = -q\_O - q\_C,\tag{A9}$$

where qO, qC, and qcm are point charges on the oxygen and carbon atoms and CO center of mass (CM), respectively, and rO, r<sup>C</sup> are atom positions with respect to CM.

# Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Valter H. Carvalho-Silva<sup>1</sup> \*, Nayara D. Coutinho<sup>2</sup> \* and Vincenzo Aquilanti 2,3 \*

<sup>1</sup> Grupo de Química Teórica e Estrutural de Anápolis, Campus de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás, Anápolis, Brazil, <sup>2</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Perugia, Italy, <sup>3</sup> Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, Rome, Italy

#### Edited by:

Antonio Aguilar, University of Barcelona, Spain

#### Reviewed by:

Luca Evangelisti, University of Bologna, Italy Ernesto Garcia, University of the Basque Country, Spain

#### \*Correspondence:

Valter H. Carvalho-Silva fatioleg@gmail.com Nayara D. Coutinho nayaradcoutinho@gmail.com Vincenzo Aquilanti vincenzoaquilanti@yahoo.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 26 March 2019 Accepted: 10 May 2019 Published: 29 May 2019

#### Citation:

Carvalho-Silva VH, Coutinho ND and Aquilanti V (2019) Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity. Front. Chem. 7:380. doi: 10.3389/fchem.2019.00380 Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Keywords: transitivity plot, Aquilanti-Mundim (AM) formula, Nakamura-Takayanagi-Sato (NTS) formula, Volgel-Fulcher-Tammann (VFT) formula, viscosity and diffusion

## INTRODUCTION

To understand and control the physical chemistry of materials in an ample variety of environments that may be encountered in basic and applied scientific research, information on the kinetics of the involved elementary processes and their role in global mechanisms is needed: of particular interest are the rates, and often in a wide range of conditions—specifically of temperature. Theoretical and computational studies are of increasing utility, especially in the cases where experimental results are difficult to obtain, or the measurements are difficult to interpret. Examples span all of chemistry: from the long list that is continuously updated, we refer here to some selected cases from: combustion chemistry (Atkinson, 1986); condensed-phase (Limbach et al., 2006), atmospheric and astrochemical reactions (Smith, 2008; Sims, 2013); processes involved in preservation and aging of food and drugs (Darrington and Jiao, 2004; Peleg et al., 2012) as well as in basic geochemical (e.g., Giordano and Russell, 2018) and biochemical environments (e.g., Klinman and Kohen, 2013; Warshel and Bora, 2016).

A variety of techniques has been applied with remarkable success in several scenarios to investigate the mechanisms to both calculate and interpret the kinetics of reactive processes at a microscopic level (Sikorski et al., 2004; Pu et al., 2006; Wang et al., 2012; Hassanali et al., 2014; Coutinho et al., 2015a; Santin et al., 2016; Roy et al., 2017). From the early Arrhenius (1889) and Eyring (1935) formulations, demands emerge for interpretative theoretical tools to study the kinetics of chemical reactions and to phenomenological account of reaction rate data as generated from exact quantum benchmarks or from approximate semiclassical and classical trajectory approaches.

The seminal phenomenological description of the reaction rate constants, date of birth of theoretical chemical kinetics as a science, can be traced back to 1889 with the empirical formulation of the Arrhenius formula (Arrhenius, 1889; Laidler, 1987).

$$k = A e^{\frac{-E\_0}{RT}},\tag{1}$$

where R is the gas constant and T is the absolute temperature. The pre-factor A (often found to be temperature independent) has sometimes been given the meaning and the name of a "frequency factor." The quantity E<sup>a</sup> is termed the "energy of activation" of the reaction; according to the Arrhenius interpretation, it represents the energy that the molecule in the initial state of the process must acquire before it can take part in the reaction, whether it be a physical or a chemical process. In the Arrhenius plane prompted by Equation (1) the logarithm of a reaction rate constant, ln k(T) is plotted against reciprocal temperature, <sup>1</sup> T : for systems that obey the Arrhenius law, Equation (1), a linear behavior is observed.

Formulations from first principles of theoretical reaction rates only became realistic after the advent of quantum and statistical mechanics. The Eyring formulation (∼1935) proposes a consistent and predictive theory for the kinetic reaction rate constant: the celebrated Transition-State Theory (TST) (Eyring, 1935; Glasstone et al., 1941) provided the basis for the understanding of many phenomena and triggered most of the subsequent proposals for the understanding of physicochemical rate processes. However, as traditionally implemented, TST is unable to cope with systems with strong deviation from Arrhenius behavior (Masgrau et al., 2003). The chemical reactions for which quantum tunneling effects play an important role are those where Arrhenius plots show a concave curvature (Limbach et al., 2006; Silva et al., 2013; Sanches-Neto et al., 2017): this is the most important case of sub-Arrhenius kinetics for elementary reactions, but in complex processes it may show up, e.g., when concurrent reactions contribute to the mechanism (Hulett, 1964; Perlmutter-Hayman, 1976; Vyazovkin, 2016).

Eyring himself amplified the scope of his TST beyond elementary reactions proposing a formulation for including the description of viscosity and diffusion of fluids in physicochemical rate processes (Glasstone et al., 1941). However, an ample set of old and more recent data in wide ranges of temperature has been showing again and again a strong convex curvature in Arrhenius plot for both viscosity and diffusion in fluids (Angell, 1995; Coutinho et al., 2015b; Giordano and Russell, 2018). There are examples of super-Arrhenius kinetics, rare for elementary processes (Truhlar and Kohen, 2001), but that in complex processes are common, in particular when consecutive reactions contribute to the mechanism (Hulett, 1964; Perlmutter-Hayman, 1976; Vyazovkin, 2016): these are characteristic cases of super-Arrhenius kinetics for which the traditional Eyring's transitionstate formulation fails. However, the TST connection between the potential energy surface profile with the phenomenological apparent activation energy through Tolman Theorem (Tolman, 1920), serves as a guide toward an interpretation of deviation from Arrhenius behavior.

In previous work (Aquilanti et al., 2017b, 2018) evidence emerged for introducing the phenomenological Transitivity function γ (T) which regulates transit in physicochemical transformations and can be put into a relationship with traditional and recent reaction rate constant formulas available in the literature. With respect to other popular phenomenological approaches, ours arguably offers flexibility for the description of the experimental data over a wide range of temperature alternative to other formulas, that were applied to various sets of problems, ranging from particle diffusion and viscosity in supercooled liquids and glasses (Angell, 2002; Stillinger and Debenedetti, 2013) to food and drug preservation and aging processes (Peleg et al., 2012).

The still popular Kooij formula (Kooij, 1893) involving an arbitrary T <sup>n</sup> parameter multiplying the pre-factor A has no justification and is often unable to reproduce observations. Kooij formulation has to be discouraged and is physically unrealistic. It should be abandoned because: (i) at high temperature, the Arrhenius Activation energy is not recovered; (ii) at intermediate temperatures, the non-Arrhenius description is illusory valid only in extremely narrow ranges and is mathematically arbitrary; (iii) at low and ultra-low temperatures, there is consensus that non-Arrhenius behavior is pronounced, and the Kooij formula tends to Arrhenius law in clear disagreement with transitivity concept. Also, the Arrhenius-Break Temperature (ABT) formulation (Kumamoto et al., 1971; Kubo, 1985) is often one commonly used: it involves two additional parameters beyond Arrhenius and may turn out misleading from an interpretative viewpoint—when possible, it should be avoided in compacting data for modeling.

The suitability of the transitivity function is being checked against a variety of phenomenological examples with respect to its power to account for deviation from Arrhenius behavior. Here, we will show details on the treatment for amplifying the insight in various directions (section Transitivity Defined). In the subsequent section, specifically regarding the super-Arrhenius case, we establish the connections with the Vogel-Fulcher-Tammann treatments (VFT) (see Vogel, 1921; Fulcher, 1925; Tammann and Hesse, 1926) via the transitivity function. We also generalize the sub-Arrhenius case discussing in a uniform way the trend toward Wigner' limit (Wigner, 1948), yielding Nakamura-Takayanagi-Sato (NTS) formula (Nakamura et al., 1989) and Aquilanti-Sanches-Coutinho-Carvalho (ASCC) (Coutinho et al., 2018b) at low temperature. In section Transition-State Theory Extended to Moderate Tunneling (d-TST), the sub-Arrhenius case appropriate for extending the Transition-State Theory of Eyring (the d-TST formalism) is accounted for, as introduced and applied recently (Claudino et al., 2016; Carvalho-Silva et al., 2017; Sanches-Neto et al., 2017). A special attention will be devoted in section Viscosity and Diffusion From the Transitivity Function to a derivation of the temperature dependence of viscosity of fluids from the transitivity function γ according for the super-Arrhenius behavior and establishing the connection with the diffusion coefficient through the Stokes-Einstein equation. The final section is devoted to additional and concluding remarks.

#### TRANSITIVITY DEFINED

#### The Transitivity Plot

In this section, we will show how the properly defined "Transitivity" function γ (T) regulates the transit in physicochemical transformations: in other words, it controls the rate of passage with no bias from the transition-state hypothesis. In the 1976 article of Berta Perlmutter-Hayman (Perlmutter-Hayman, 1976) the concept of apparent activation energy E<sup>a</sup> has been considered in a very deep detail: in her spirit 20 years later, the International Union of Pure and Applied Chemistry (Laidler, 1996) recommended the now accepted definition:

$$E\_a(T) = RT^2 \frac{d \ln k(T)}{\text{d }T} = -R \frac{\text{d} \ln k(T)}{\text{d }\left(\frac{1}{T}\right)}\tag{2}$$

To be consistent with Equation (1), the assumption of constancy for E<sup>a</sup> can be taken as valid for physicochemical processes, at least for the temperature range of interest but deviation occur. According to our classification of d-Arrhenius cases (Silva et al., 2013; Aquilanti et al., 2017a), the deviations are considered as exhibiting sub-, super-, or anti-types of behavior.

An initial step in order to find out how to account in a simple form for these deviations, we search for a functional dependence of E<sup>a</sup> according to a large variety of cases accumulated from experiments and simulations. In her thorough study, a few decades-old, Perlmutter-Hayman (Perlmutter-Hayman, 1976) considered a large body of documentation where the dependence were regarded either as

$$E\_{\rm a} \nu \text{s. } T \text{ or } E\_{\rm a} \text{ } \nu \text{s. } 1/T \text{,} \tag{3}$$

the latter form clearly inspired by the Arrhenius plot. We have been showing ample phenomenological evidence and deep theoretical motivation (Aquilanti et al., 2017b) of the insight to be gained by studying

$$\frac{1}{E\_a} \text{ } \text{vs } \frac{1}{T}, \tag{4}$$

i.e., to study the behavior of the reciprocal the activation energy studied against reciprocal of absolute temperature. Therefore, from now on, we find convenient to adopt the usual definition in statistical mechanics, of the parameter β = 1 RT sometime referred to as "the coldness" (e.g., Müller, 1971) and often referred as to the Lagrange parameter, because of its ubiquitous role in statistical mechanics where it occurs in optimization procedures involving the Lagrange multipliers.

From a decade-old work (Aquilanti et al., 2010), the observation arose that the reciprocal of E<sup>a</sup> vs. the reciprocal of absolute temperature yielded an approximate linearization by the d parameter (italic symbol for the linearization parameter should not be confused with the roman d denoting differentials). Writing as customary the Arrhenius-Eyring energy barrier, ε ‡ , as essentially an energetic obstacle toward reaction, we have

$$\frac{1}{E\_a} = \frac{1}{\varepsilon^\ddagger} - \frac{d}{RT} \,. \tag{5}$$

Introducing the "transitivity" function through the identifications

$$\mathcal{V}\left(T\right) \equiv \frac{1}{E\_a\left(T\right)}\,,\tag{6}$$

and also putting

$$
\alpha = 1/\varepsilon^{\ddagger},
\tag{7}
$$

Equation (5) takes the simple form

$$
\gamma \; (\beta) = \alpha - d\beta. \tag{8}
$$

In general, as discussed in preceding work (Aquilanti et al., 2017b), a linear γ dependence from β may be only valid in a specific range around a value β0; on a wider range, we can always assume that the function is well-behaved, namely that it has a Laurent power expansion,

$$\gamma\left(\beta\right) = \sum\_{n=-\infty}^{\infty} c\_n \left(\beta - \beta\_0\right)^n. \tag{9}$$

where the c<sup>n</sup> coefficients are related to n-order derivatives of γ (β) with respect to β, taken at β0.

The task of a theory of the kinetics of chemical reactions is therefore focused at that of providing a set of such coefficients to connect to experimental or computationally generated k (T) via Equations (2 and 6). Advantages now are shown for the introduction of the "Transitivity Plot," defining as the plane γ vs. β, which gives insight into the idea of the "canonical" dependence of the γ function in regulating transitions in physicochemical processes (see **Figure 1**).

Consistently with the established nomenclature, one gets a positive linear dependence of γ (β) for sub-Arrhenius (and negative for super-Arrhenius, d > 0): this according to experimental and theoretical evidence from many sources (Aquilanti et al., 2010; Silva et al., 2013). Defining in the transitivity plot α = 1 ε ‡ , Equation (7), as a horizontal line (the Arrhenius line), the line of deviations from Arrhenius around β<sup>0</sup> forms δ angle which can show sub- or super-Arrheniustype of behavior, corresponding to anticlock—and clockwise direction from the β axis, respectively, yielding an expression corresponding to Equation (8),

$$
\gamma = \alpha + \beta \tan \delta; \text{ -} \tan \delta = d,\tag{10}
$$

FIGURE 1 | The transitivity plane, γ = 1 Ea vs. β = 1 RT serves to give a geometrical meaning to the phenomenological parameters occurring in the study of non-linear Arrhenius plots. The Arrhenius behavior is given as corresponding to a line parallel to the β axis starting at α = 1 ε ‡ and corresponds to a constant apparent activation energy Ea. The well-known double dagger notation was introduced by Eyring (Eyring, 1935; Glasstone et al., 1941). Deviations from Arrhenius behavior gives to the γ function straight line dependence at small β a direction forming the δ angle, which it is connected to the d parameter of the Aquilanti-Mundim (AM) law. At low temperatures as the "coldness" variable β increases, the transitivity function tends to characteristic ultra-cold limiting values: (i) for d < 0 (sub-Arrhenius) it tends to the Wigner limit and (ii) for d > 0 (super-Arrhenius), γ , namely the propensity for reaction to occur, vanishes in β † , γ β † = 0 : the corresponding energy and temperature parameters are denoted by a single dagger, ε †and T † , respectively, as detailed below.

where d < 0 (δ > 0) corresponds to the sub- case while d > 0 (δ < 0) corresponds to the super-Arrhenius case. Rarer cases are found for which d > 0 and α < 0, and are referred as corresponding to anti-Arrhenius behavior (e.g., Coutinho et al., 2015a).

The expression for the rate constant can be retrieved, integrating (10) from Equation (2). Introducing an integrating factor, A that accounts for a value for γ at the reference value, e.g., β = 0: we obtain the Aquilanti-Mundim (AM) or d-Arrhenius formula in the form:

$$k\left(\beta\right) = A \left(1 + \tan \delta \,\frac{\beta}{\alpha}\right)^{-\cot \delta},\tag{11}$$

Through Equations (7, 10) and introducing the Lagrange parameter, we finally obtain the AM formula

$$k\left(T\right) = A\left(1 - d\frac{\mathcal{E}^{\frac{\ddagger}{\xi}}}{RT}\right)^{\frac{1}{d}},\tag{12}$$

in the usual notation (Aquilanti et al., 2010). The Arrhenius law k (T) = A exp −E<sup>a</sup> RT is obtained in two well-defined cases at β → 0 (high temperature limit) and at d → 0 (the "thermodynamic" limit) (Aquilanti et al., 2018).

#### Limiting Behaviors for the Transitivity Function at Low and High Temperature

In the AM formulation for k, Equation (12), when d or tan δ tends to zero, one gets the exponential Arrhenius behavior through the Euler limit as detailed in Aquilanti et al. (2018). In this limit, to first order, the transitivity function deviate linearly from constancy (the Arrhenius behavior) as described by the AM formula. When β increases (low temperature):


We are now in the position to look at the d-parameter from alternative perspectives. For super-Arrhenius cases, the β

exhibited assuming ε ‡ 1 = ε ‡ 2 in Equation (26).

endpoint, β † , marks the final low-temperature range for the system to be "active": energetically, the introduction of the corresponding energy ε † = RT† , permits the identification

$$d = \frac{\varepsilon^{\ddagger}}{\varepsilon^{\ddagger}}.\tag{13}$$

For sub-Arrhenius, the connection of d with features of the potential energy barrier permits to describe quantum tunneling in elementary chemical reactions (see e.g., Silva et al., 2013 and next section).

Additional insight to the AM formula in Equation (5) for d < 0 is obtained when β tends to infinity yielding,

$$\lim\_{\beta \to \infty} \nu \,\, \nu \,\, (\beta) = -d \,\, \beta. \tag{14}$$

Going back to the rate constant, integrating (14) from Equation (2), we obtain

$$\lim\_{\beta \to \infty} k\left(\beta\right) = A\left\|\beta^{\frac{1}{4}}\right\|,\tag{15}$$

formally appearing as the venerable Esson-Harcourt formula (Laidler, 1984), and in consonance with the Wigner limit restricted to the case of thermoneutral reactions at ultralow temperature (Takayanagi, 2004). Nevertheless, for d > 0 a minimum and constant reactivity is obtained for β † ,

$$k\left(\boldsymbol{\beta}\right) = A \left(\boldsymbol{\beta}^{\dagger}\right)^{\frac{\boldsymbol{e}^{\dagger}}{\boldsymbol{e}^{\dagger}}}.\tag{16}$$

In Equation (16), when ε † tends to infinity, k (β) = A respecting the Arrhenius limit (most other formulations do not).

After the description of the sub- and super-Arrhenius cases in the limit d →0 at large β, we turn now to consider the limiting behavior as β → 0, namely at high temperature. In most cases, the generic behavior is considered to be the tendency to the Arrhenius as a limit: situations may occur where this assumption has been relaxed [important examples are protein folding (Chan and Dill, 1998; Wallace et al., 2002) and reactions in sub- or super-critical solvent (Christensen and Sehested, 1983; Lukac, 1989; Marin et al., 2003)]. We can take advantage of the following useful expansion (Abe and Okamoto, 2008; Tsallis, 2009):

$$k\left(\beta\right) = A\left(1 - d\varepsilon^{\frac{\varphi}{\beta}}\beta\right)^{\frac{1}{d}} = A\varepsilon^{-x^{\frac{\varphi}{\beta}}\beta} \left[1 - \frac{1}{2}d\varepsilon^{\frac{\varphi}{\beta}}\beta^2 - \frac{1}{3}d^2\varepsilon^{\frac{\varphi}{\beta}}\beta^3\right]$$

$$-\frac{1}{8}\left(2d - 1\right)d^2\varepsilon^{\frac{\varphi}{\beta}}\beta^4 + \mathcal{O}\left(\beta^6\right)\Big].\tag{17}$$

Therefore, Arrhenius behavior is recovered both as β and d tend to zero independently:

$$\lim\_{\substack{d \to 0 \\ \text{const } \beta}} k\left(d, \beta\right) = \lim\_{\substack{\beta \to 0 \\ \text{const } d}} k\left(d, \beta\right) = A \ e^{-\varepsilon^\sharp \beta}. \tag{18}$$

## PHENOMENOLOGICAL MODELS OF TEMPERATURE DEPENDENCE OF REACTION RATE CONSTANTS THROUGH THE TRANSITIVITY FUNCTION

The previous development opens the way to the next step of our study, the examination and classification through the transitivity concept of previous phenomenological proposals, assessing relationships between them and also attempting at giving a physicochemical meaning to their empirical parameters. As a bonus, more physically motivated formulas can be generated.

From Equations (2, 6), it is possible to build up the theoretical apparatus to connect experimental or computationally generated reaction rate constants to the transitivity function and vice-versa. Below traditional and recent phenomenological reaction rate constant formulas and transitivity function are presented to deal with sub- and super-Arrhenius behavior with larger deviations than those not accounted for the AM d-Arrhenius formula (see **Figure 2**): VFT, ASCC, and NTS. The basic expression

$$k\left(\beta\right) = \exp\left(-\int\_{\beta\_0}^{\beta} \frac{\mathrm{d}\beta}{\mathcal{V}}\right). \tag{19}$$

Can be employed, where clearly, A = k (β0) represents the initial condition (again, the differential under the integral sign is denoted by the roman letter d to avoid confusion with d in italic for the deviation parameters).

#### Vogel–Fulcher–Tammann (VFT) Formula

It is insightful to obtain the expression for the transitivity function for perhaps the most popular equation for modeling super-Arrhenius behavior, the Vogel–Fulcher–Tammann (VFT) formula (Vogel, 1921; Fulcher, 1925; Tammann and Hesse, 1926), here written as a rate constant in an Arrhenius-like fashion, but involving one additional parameter:

$$k\left(T\right) = A \exp\left(\frac{B}{T - T\_0}\right) \tag{20}$$

where A, B, and T<sup>0</sup> are the fitting parameters: they are often designated, respectively being often denoted as the pre-factor, pseudo-activation energy and VFT-temperature, respectively. It is noteworthy, that in the polymer and food science community (Angell, 1997; Peleg et al., 2002; Coutinho et al., 2015b) Equation (20) is also known as the Williams-Landel-Ferry (WLF) equation: see (Williams et al., 1955; Dudowicz et al., 2015) where the equivalence among the respective parameters is demonstrated explicitly.

The VFT transitivity function is obtained directly from the definition through the analytical logarithmic differentiation of Equation (20) with respect to β: The result is

$$\gamma\left(\beta\right) = \frac{1}{RB} - \frac{2T\_0}{B}\beta + \frac{RT\_0^2}{B}\beta^2,\tag{21}$$

That can be worked out in a more compact representation,

$$\gamma\left(\beta\right) = \frac{1}{RB} \left(1 - RT\_0 \beta\right)^2. \tag{22}$$

Here, formula (22) adds insight on the VFT parametrization for γ by a summarizing comparison with the Arrhenius and with the AM formulations for the transitivity function: the following general expression,

$$\gamma\_n(\boldsymbol{\beta}) = \frac{1}{\varepsilon\_n^{\frac{\hat{\boldsymbol{\gamma}}}{\hat{\boldsymbol{\gamma}}}}} \left(1 - d\_n \varepsilon\_n^{\frac{\hat{\boldsymbol{\gamma}}}{\hat{\boldsymbol{\gamma}}}} \boldsymbol{\beta}\right)^n \tag{23}$$

covers three cases for different values of n: (i) for n = 0 one recovers Arrhenius formula, (ii) for n = 1 the AM formula is obtained, and (iii) for n = 2 one gets the VFT (and WLF) formula. From **Figure 1**, in the transitivity plane, a geometrical interpretation can be given and leads to

$$\tan \delta = \frac{\mathrm{d}\wp\_n(\beta)}{\mathrm{d}\beta} \tag{24}$$

in limiting case of β tending to zero,

$$\lim\_{\beta \to 0} \frac{\mathrm{d}\varphi\_n(\beta)}{\mathrm{d}\ \beta} = \lim\_{\beta \to 0} -\frac{n d\_n \left(1 - d\_n \varepsilon\_n^{\frac{\gamma}{\gamma}} \beta\right)^n}{1 - d\_n \varepsilon\_n^{\frac{\gamma}{\gamma}} \beta} = -n d\_n \tag{25}$$

and the comparison between n =1 (AM) and n = 2 (VFT) parametrizations is shown to be

$$d\_1 = 2d\_2 \text{ or } \frac{\varepsilon\_1^\dagger}{\varepsilon\_1^\dagger} = 2\frac{\varepsilon\_2^\dagger}{\varepsilon\_2^\dagger}. \tag{26}$$

See details in **Figure 2**, where the ASCC and NTS formulas, to be discussed next, are also considered.

#### Deep Tunneling and the ASCC Formula

As reported in the earlier literature (Bell, 1980; Christov, 1997), the degree of concavity in the Arrhenius plot can be correlated with the assessment of the role of tunneling in chemical reactions: the definition of a "crossover temperature,"

$$T\_c = \frac{\hbar \nu^\ddagger}{R},\tag{27}$$

permits to conventionally establish (within some arbitrariness) the ranges of tunneling regimes for a specific imaginary frequency at the top of the barrier point, consistently denoted by a double dagger, ν ‡ : classical (T > 4Tc), negligible(4T<sup>c</sup> > T > 2Tc) , moderate (2T<sup>c</sup> > T > Tc) and deep (T<sup>c</sup> > T) regimes. The ranges of tunneling regimes are indicative of the importance of quantum tunneling to affect rate constants in particular cases. From a mathematical viewpoint, the AM formulation has clear limitations in the description of the deep tunneling regime toward the Wigner limit (Wigner, 1948)

$$\lim\_{T \to 0} k(T) \propto T^0 \tag{28}$$

Details pertinent to the present discussion can be found in a very useful reference (Takayanagi et al., 1987).

As a counterpart for sub-Arrhenius behavior of the super-Arrhenius VFT formula, it is argued that cases of deep tunneling can be dealt by introducing a modified form of the AM formula (Coutinho et al., 2018b), defined as Aquilanti-Sanches-Coutinho-Carvalho (ASCC) expression:

$$k\left(T\right) = A\left(1 - \frac{d\varepsilon^{\ddagger}}{k\_B T + h\upsilon^{\ddagger}}\right)^{\frac{1}{d}},\tag{29}$$

where d = − 1 3 hν ‡ 2ε ‡ 2 as reported in Silva et al. (2013) and references therein. Here, the formulation introduces the three A, ε ‡ and ν ‡ parameters and reproduces the Wigner limit at low temperature, β → ∞. The ASCC transitivity function can be worked out considering the logarithmic differentiation of Equation (29) with respect to β and the result is

$$\gamma \left( \beta \right) = \frac{1}{\varepsilon^{\ddagger}} - \frac{d\varepsilon^{\ddagger} - 2h\nu^{\ddagger}}{\varepsilon^{\ddagger}} \beta + \frac{h\nu^{\ddagger} \left( d\varepsilon^{\ddagger} - h\nu^{\ddagger} \right)}{\varepsilon^{\ddagger}} \beta^2,\tag{30}$$

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or in a more compact representation,

$$\mathcal{V}\left(\boldsymbol{\beta}\right) = \frac{1}{\varepsilon^{\ddagger}} \left[1 + h\boldsymbol{\nu}^{\ddagger}\boldsymbol{\beta}\right] \left[1 - \left(d\varepsilon^{\ddagger} - h\boldsymbol{\nu}^{\ddagger}\right)\boldsymbol{\beta}\right] \tag{31}$$

For small values of dε ‡ , an analogous to VFT formula is recovered, see Equation (22). The ASCC formula was initially applied in Coutinho et al. (2018b) for astrochemical reactions in extremely cold environments generated by "exact" benchmark quantum dynamics. More results of applications will be given elsewhere for a variety of processes that involve deep tunneling.

#### Nakamura-Takayanagi-Sato (NTS) Formula

A flexible approach to describe the deep tunneling phenomenology was proposed 30 years ago by Nakamura et al. (1989) and Sato (2005): their formula evolves smoothly behavior down to low temperature and with respect to the tendency toward the Wigner limit (Wigner, 1948):

$$k\left(T\right) = A \exp\left[-\frac{\varepsilon^{\frac{\gamma}{\xi}}}{R\left(T^2 + T\_0^2\right)^{\frac{1}{2}}}\right],\tag{32}$$

where A, ε ‡ and T<sup>0</sup> are the parameters. Again, ε ‡ is essentially the fitting parameter bearing connection with the barrier height along the minimum energy pathway to reaction.

Also, in this case, we can work out the Nakamura-Takayanagi-Sato transitivity function

$$\gamma\left(\beta\right) = \frac{1}{\varepsilon^{\frac{\star}{2}}} \left[1 + (RT\_0)^2 \,\beta^2\right]^{\frac{3}{2}} \tag{33}$$

#### BEYOND EYRING

#### Transition-State Theory Extended to Moderate Tunneling (d-TST)

Eyring's Transition-State Theory (TST) and its variants are frequently used to compute rates of chemical reactions typically assuming a well-defined activated complex. The theory has been the object of a number of studies yielding a variety of formulations based on the concept of an equilibrium between the reactants and the activated complex, all assumed with Boltzmann distributions of the internal degrees of freedom. The rate of transformation is, then, obtained by a combining of thermodynamics, kinetics, quantum chemistry, and statistical mechanics arguments. The authoritative textbook is (Glasstone et al., 1941). For a general bimolecular reaction, such as R<sup>1</sup> + R<sup>2</sup> −→ TS‡ −→ Products, it is necessary to compute the Q1, Q<sup>2</sup> , and Q ‡ partition functions of R1, R<sup>2</sup> and of the transition state, respectively. However, the conventional TST is not able to account for low temperature curvatures in the Arrhenius plot, particularly when due to quantum tunneling through the reaction barriers (for the viscosity of fluids see next section). To account for the quantum tunneling in chemical reactions, the transitivity function is modeled in analogy with the AM formula, yielding the deformed-Transition-State Theory (d-TST) (Carvalho-Silva et al., 2017):

$$k(T) = \frac{RT}{h} \frac{Q^\ddagger}{Q\_1 Q\_2} \left(1 - d \frac{\varepsilon^\ddagger}{RT}\right)^{\frac{1}{d}}, \quad d = -\frac{1}{3} \left(\frac{h\nu^\ddagger}{2\varepsilon^\ddagger}\right)^2,\tag{34}$$

where h is the Planck's constant and ε ‡ is the effective height of the energy barrier, given by the sum of the harmonic zero-point energy correction and the height of the potential energy barrier. This formulation uniformly covers the range from classical to moderate tunneling regimes but is inadequate for deep tunneling. The proposed variant of transition-state theory permits comparison with experiments and tests against alternative formulations (see e.g., Claudino et al., 2016; Santin et al., 2016; Sanches-Neto et al., 2017).

#### Viscosity and Diffusion From the Transitivity Function

Eyring's proposal of a kinetic rate theory was also amplified toward the description of viscosity and diffusion of fluids in physicochemical processes (Eyring, 1936; Glasstone et al., 1941). Eventually, it turned out that the theory was unable to describe processes in a wide temperature range, in particular when presenting a convex curvature in the Arrhenius plot. In the present context, this is a manifestation of super-Arrhenius kinetics (Truhlar and Kohen, 2001; Coutinho et al., 2015b; Giordano and Russell, 2018). To describe deviations from Arrhenius of the rates of reaction in fluids, we take into account later developments by Kramers (1940) and Collins and Kimball (1949), involving viscosity and diffusion.

To account for the temperature dependence of viscosity in cases clearly exhibiting super-Arrhenius behavior, we introduce a treatment using the transitivity function concept. From the defining, Equations (2) and (6) we obtain the differential equation,

$$\frac{\text{d}}{\text{d}\,\beta}k\,(\beta) - \frac{1}{\text{y}\,(\beta)}k\,(\beta) = 0.\tag{35}$$

For β<sup>0</sup> = 0 as the lower limit of integration range and the restriction to only two terms of the Taylor–McLaurin series of Equation (9), we obtain the AM transitivity function, where α < 0 represents an energetic propensity toward to evolution of the fluid. The d is again the deformation parameter, playing an analogous role to that amply discussed previously: the result is an AM-like formula for viscosity (Aquilanti et al., 2017b),

$$
\eta\_{\varepsilon}(\beta) = \eta\_{o} \left( 1 + d\varepsilon^{\ddagger} \beta \right)^{\frac{1}{d}},\tag{36}
$$

here η<sup>o</sup> is introduced as a counterpart of Arrhenius prefactor A and is the viscosity when the temperature tends to infinity (β → 0). At low temperature, in viscous processes the apparent activation energy turns out to increase indefinitely and consequently the propensity to proceed to a kinetic transition approaches zero, γ → 0: so we establish a direct relationship for the d parameter (analogous to the cases dealt in section Limiting Behaviors for the Transitivity Function at Low and High Temperature):

$$d = \frac{RT^{\dagger}}{\varepsilon^{\ddagger}},\tag{37}$$

and T † is identified as a phenomenological "freezing" temperature of the process, namely the critical temperature (to be connected with that of glass transition, see Aquilanti et al., 2017b), where the kinetic energy of the fluid particles is too low for the process to be turned on. In the early approach by Eyring (1936) and Glasstone et al. (1941), it was argued that the ε ‡ parameter be empirically put into relationship with the energy of vaporization of the fluid, 1Hvap, and intuitively connected with the work required to make a hole of molecular size.

Using the Kauzmann-Eyring pre-factor η<sup>0</sup> = Nah V¯ (Kauzmann and Eyring, 1940; Glasstone et al., 1941), where N<sup>a</sup> is the Avogadro number and V is the molar volume, and Equation (37) for d, we finally obtain,

$$\eta\left(T\right) = \frac{N\_a h}{\overline{V}} \left(1 + \frac{T^\dagger}{T}\right)^{\frac{s^\ddagger}{RT^\dagger}}.\tag{38}$$

when T † tends to zero, the Arrhenius-Eyring exponential formula for viscosity is recovered, η (T) = Nah V exp ε ‡ RT† through the Euler limit.

The deviation from Arrhenius behavior in the temperature dependence of diffusion can now be evaluated from Equation (39) through the Stokes-Einstein equation(Einstein, 1905).

$$D(T) = \frac{k\_B T}{6\pi r} \frac{1}{\eta(T)}\tag{39}$$

where r is the hydrodynamic radius (Henriksen and Hansen, 2008). This treatment of course does not provide further insight into these amply investigated issues, but points at a simple and perhaps useful physical interpretation of a long-standing as well recent intriguing rate phenomena. From a general perspective, the theory encourages considering wide ranges of available data on geochemistry (Giordano and Russell, 2018), supercooled liquids science (Angell, 1995) and biochemistry (Kohen et al., 1999) and digging for hidden insights. Preliminary searches, to be published, turned on successful.

#### ADDITIONAL AND FINAL REMARKS

This paper applies thoroughly the transitivity concept to a set of topics, completing the presentation of the theory outlined in Aquilanti et al. (2017b). A separated paper (Machado et al., submitted) presents the code developed for the implementation to a set of cases of interest in physicochemical kinetics where the need for deviation from Arrhenius behavior is demanded: applications of our formulation can be accessed in the homepage of our computational code—Transitivity (www.vhcsgroup.com/ transitivity), where manual, installation video, and specific examples are provided. Further remarks follow:

#### Ab initio "Exact" Quantum Dynamics

In principle, this is the most valuable source of kinetics data but still limited to simple benchmark cases. For full formulations of the reaction kinetics, following the microcanonical path along a quantum chemically or empirically generated potential energy surface, high-level computational effort is demanded. It typically proceeds according to these steps: a) calculation of the intermolecular interactions involved in a reactive process with a high-level of accuracy, b) dynamical evolution in phasespace configurations from the solution of quantum equations of motion, c) identification of reactive trajectories, with consequent calculation of the quantum scattering matrix, cumulative reaction probability and cross sections. Finally, the Boltzmann weight averaging over a large span of kinetics energies yields the canonical expressions of kinetic variables as a function of temperature. These severe prescriptions have been able to provide the exact calculation over a given potential energy surface for reaction rate constants of only a limited number of reactive systems: in fact, the complexity of the programming and the computationally demanding requirements and computational demand strongly limit the study of reactive processes involving only a few atoms. Additional reactions involving isotopic exchange among three hydrogen atoms, exemplary benchmarks to be cited are the three-body reactions: F + H<sup>2</sup> (Aquilanti et al., 2005), F + HD (De Fazio et al., 2006; Cavalli et al., 2014), H + HeH<sup>+</sup> (De Fazio, 2014) see also and references therein.

#### First-Principles Molecular Dynamics

Another viable path is becoming possible thanks to improvements in computational facilities, in order to access at kinetic information through first-principles molecular dynamics simulations. However, computationally severe storing and time constraints permitting to obtain myriads of "onthe-fly trajectories" require a great effort toward the aim of generating realistic reactive kinetic data: this in spite of the fact that a wide research activity has been pursued, aiming at developing techniques capable of accurately predicting kinetic reaction rate constants from molecular dynamics simulations. Among examples that have been tackled in recent years, we cite (Pomerantz et al., 2005; Coutinho et al., 2015a; Döntgen et al., 2015; Fleming et al., 2016; Wu et al., 2019) and references therein. However, calculation of reaction rate constants has been limited by the arduous procedures both to accurately characterize reactive activated complexes of many body systems and to overcome the inherent difficulties of producing a number of trajectories with statistical consistency and reasonable completeness in the filling of the dynamically relevant parts of the phase-space. Recently, several works have been yielding values with reliable accuracy: overestimates due to limited sampling of phase-space, when experimental values are available for comparison, may exploit empirical calibration (Coutinho et al., 2016, 2017, 2018a).

#### Phenomenological Considerations and the Role of the Transitivity Concept

Experimentally and computationally generated kinetic data for polyatomic molecules provide reaction rate constants with the implicit fingerprint of the microscopical variables at work in the reactive process (Angell, 1995; Kohen et al., 1999; Limbach et al., 2006; Giordano and Russell, 2018; Capitelli and Pietanza, 2019, and references therein). Application of the techniques discussed in previous remarks is tremendously laborious for many-body systems: when the Arrhenius law is not obeyed at low temperature transitivity function guides us to an as a fruitful and consistent approach. As discussed in this article the approach turns out to be a powerful tool, capable of establishing a connection between canonical data and microcanonical information, permitting comparisons among apparently uncorrelated formulations: it also allows interpretation of empirical parameters, for example for the AM, ASCC, VFT and NTS formulas considered in this paper. Previous (Tsallis and Bukman, 1996; Lenzi et al., 2001; JiangLin et al., 2006; Zhou and Du, 2013) and concomitant (Zhou and Du, 2014; Guo and Du, 2015; Rosa et al., 2016; Junior et al., 2019) efforts have been dedicated to provide also a connection of anomalous kinetic diffusion effects while surmounting a potential barrier via variants of Fokker-Planck equation, tackling a class of phenomenologically physicochemical diffusion process.

#### Conclusion and Perspectives

In order to extend the validity of the Arrhenius rate law, the introduction of the deformation parameter d not only phenomenologically mimics the low temperature dependence of rate constants, but its relevance in producing physical insight is now amply demonstrated. The statistical mechanics aspects are

#### REFERENCES


now firmly established (Aquilanti et al., 2017b, 2018) capitalizing on various investigations inspired openly or implicitly on a Maxwellian approach: several examples in the literature have been inspiring the transfer from thermodynamics to the field of kinetics assuming procedures for taking the "thermodynamic limit." Venerable papers are (Jeans, 1913; Condon, 1938; Kennard, 1938; Landau and Lifshitz, 1958), and recent ones (Tsallis, 1999; Biró et al., 2014; Aquilanti et al., 2017b).

#### DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

#### AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

#### ACKNOWLEDGMENTS

VHC-S thanks Brazilian agency CNPq for the research funding programs [Universal 01/2016—Faixa A−406063/2016-8] and Organizzazione Internazionale Italo-Latino Americana (IILA) for Biotechnology Sector-2019 scholarship. VA and NDC acknowledge the Italian Ministry for Education, University and Research, MIUR, for financial support: SIR 2014 Scientific Independence for young Researchers (RBSI14U3VF).


Bell, R. P. (1980). The Tunnel Effect in Chemistry. London: Champman and Hall.


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Carvalho-Silva, Coutinho and Aquilanti. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Stereodynamical Effects by Anisotropic Intermolecular Forces

Daniela Ascenzi <sup>1</sup> \*, Mario Scotoni <sup>1</sup> , Paolo Tosi <sup>1</sup> , David Cappelletti <sup>2</sup> and Fernando Pirani <sup>2</sup>

<sup>1</sup> Dipartimento di Fisica, Università di Trento, Trento, Italy, <sup>2</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, Perugia, Italy

Electric and magnetic field gradients, arising from sufficiently strong anisotropic intermolecular forces, tend to induce molecular polarization which can often modify substantially the results of molecular collisions, especially at low rotational temperatures and low collision energies. The knowledge of these phenomena, today still not fully understood, is of general relevance for the control of the stereo-dynamics of elementary chemical-physical processes, involving neutral and ionic species under a variety of conditions. This paper reports on results obtained by combining information from scattering, spectroscopic and reactivity experiments, within a collaboration between the research groups in Perugia and Trento. We addressed particular attention to the reactions of small atomic ions with polar neutrals for their relevance in several environments, including interstellar medium, planetary atmospheres, and laboratory plasmas. In the case of ion-molecule reactions, alignment/orientation is a general phenomenon due to the electric field generated by the charged particle. Such phenomenon originates critical stereo-dynamic effects that can either suppress (when the orientation drives the collision complex into non-reactive or less reactive configurations), or enhance the reactivity (when orientation confines reagents in the most appropriate configuration for reaction). The associated rate coefficients show the propensity to follow an Arrhenius and a non-Arrhenius behavior, respectively.

#### Edited by:

Alkwin Slenczka, University of Regensburg, Germany

#### Reviewed by:

Fuminori Misaizu, Tohoku University, Japan Sonia Melandri, University of Bologna, Italy

\*Correspondence: Daniela Ascenzi daniela.ascenzi@unitn.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 03 February 2019 Accepted: 15 May 2019 Published: 31 May 2019

#### Citation:

Ascenzi D, Scotoni M, Tosi P, Cappelletti D and Pirani F (2019) Stereodynamical Effects by Anisotropic Intermolecular Forces. Front. Chem. 7:390. doi: 10.3389/fchem.2019.00390 Keywords: alignment, orientation, stereo-dynamics, ion-molecule reactions, astrochemistry

## INTRODUCTION

The focus of the present work is on investigating the role of electric and magnetic field gradients, arising from anisotropic intermolecular forces, which can induce molecular polarization (i.e. alignment/orientation of rotational angular momentum / bond direction of a molecule along a preferential axis) as a consequence of collisions with other atoms or molecules. Deep knowledge of these phenomena, today still not fully understood, is of general relevance to control the stereodynamics of elementary chemical-physical processes, occurring both in gaseous and condensed phases under a variety of conditions (Vattuone et al., 2004, 2009, 2010; Gerbi et al., 2006). In particular, understanding the mode-specificity in reaction dynamics of open-shell atoms, free radicals, molecules, atomic and molecular ions, under hyper-thermal, thermal, and subthermal conditions is of fundamental importance for catalysis, plasmas, photodynamics as well as interstellar, and low-temperature chemistry (see for instance Aquilanti et al., 2005; Chang et al., 2013; Li et al., 2014; Rösch et al., 2014; Balucani et al., 2015).

The possibility of aligning or orienting molecules by collisions in gaseous streams may also have some implications in unraveling the origin of chiral discrimination and chiral selectivity emerging in vortices formed both in the liquid and in the gas phase (Lombardi and Palazzetti, 2018, and references therein; Su et al., 2013).

On the basis of the experimental findings, achieved in the last 25 years by the authors, it is proper to distinguish:

Molecular alignment determined by weak van der Waals forces: It arises as a combined effect of several elastic/inelastic collisions occurring along preferential directions in environments where anisotropic velocity distributions are operative;

Molecular orientation controlled by anisotropic intermolecular forces of intermediate strength: Such phenomenon manifests even during single collision events, when the molecules are in low rotational states;

Molecular orientation induced by anisotropic intermolecular forces of high strength: It becomes dominant in each collision event under an ample variety of conditions.

The abovementioned classification is proposed on the basis of the results obtained exploiting different but complementary experimental techniques, in the Perugia and Trento laboratories, as well as an integrated experimental-theoretical approach. This paper focuses on selected results highlighting the role of molecular polarization, induced in a natural way by weak, intermediate and strongly anisotropic forces, on the reaction stereo-dynamics under a variety of conditions, including those of applied interest.

## RESULTS AND DISCUSSION

## Molecular Alignment by Weak Anisotropic Forces

Molecular alignment induced by weak anisotropic van der Waals (vdW) forces emerges in supersonic expansions leading to the formation of seeded molecular beams, where hundreds of collisions between seeded molecules and lighter (hence faster) carrier atoms occur preferentially in the forward direction of the expansion. Value and direction of the relative collision velocity, also defined as velocity slip, play a crucial role in determining important selectivities in the involved elastic and inelastic collisions. To correctly identify the microscopic phenomena, it is useful to distinguish two different regions of the expansion zone. The first one is confined in the proximity of the source nozzle, where the velocity slip and gas density are both sufficiently high to promote, in addition to many-body elastic events, also inelastic collisions leading to both molecular rotational excitation and relaxation. The second zone is localized at larger distances from the nozzle, where gas density and velocity slip exhibit decreased values, and only elastic and inelastic processes at low energy (rotational relaxation) can occur. In the last region, where only two-body collisions are present, the promoted microscopic events can be classified in terms of the orbital angular momenta (or impact parameters b in a classical picture) involved (see the upper panel of **Figure 1**). Hence, the degree of achieved molecular alignment is expected to depend on the geometric features of the nozzle, on the pressures used in the source and on the resolution conditions adopted in the experiments. We have found that polarization effects are more evident when the angular cone probed around the beam axis becomes narrower, suggesting that the observed phenomena arise from marked stereodynamical effects (Pirani et al., 2001, 2003).

spectrometer). In this conceptual scheme a common MBS and velocity selection is exploited for the successive (A) magnetic analysis or (B) scattering experiment. In the magnetic analysis (A) the MB transmittance IB/I0 varies with the molecular velocity and paramagnetism. In the scattering experiments (B) the beam attenuation I/I0 varies with the molecular velocity and intermolecular forces that drive the scattering.

In the Perugia apparatus, two different experiments have been exploited as probes of the alignment in the produced molecular beams [see (A,B) in **Figure 1**], as detailed in (Aquilanti et al., 1994, 1995a,b, 1997). The probe experiments were performed at a considerable distance from the beam source and after a detailed velocity selection of the formed molecular beam (MB). The first experiment, applicable exclusively to paramagnetic molecules, exploits beam transmittance measurements across a Stern-Gerlach magnetic selector. This device probes the magnetic sublevel population of the molecules in the achieved final states and velocity. The second experiment, of more general applicability, involves measurements of beam intensity attenuation by collisions with an atomic or molecular target. The attenuation value, depending on the strength of the intermolecular interaction driving the scattering, is expected to vary with the relative orientation of the two colliding partners, hence on the helicity states populated by the projectile molecules.

The O<sup>2</sup> molecule is an open shell species with total spin quantum number S = 1. The magnetic analysis performed on O<sup>2</sup> seeded beams showed that molecules achieve a high and anomalous paramagnetism, related to a non-statistical distribution of their magnetic sublevels. The paramagnetic degree is found to increase with the final speed reached by the molecules within the same velocity distribution, and with the pressure employed in the source (Aquilanti et al., 1994, 1995a). In other words, molecules in a supersonic MB are preferentially confined

FIGURE 2 | Upper relative O2 intensity (open circles) as a function of the molecular velocity for a He seeded supersonic beam (with 2.5% O2 in He). The fitted velocity distribution (colored continuous line) gives a translational temperature of ∼2 K. Black squares represent the molecular polarization degree as quantitatively obtained in Aquilanti et al. (1994). The color code (red = no alignment, blue = high alignment) is a qualitative aid for the eye, also employed in the next figure (Figure 3). Lower angular momentum coupling for the <sup>16</sup>O16O diatomic molecule in the ground <sup>3</sup>P g electronic state. The spin-rotational sublevels, relevant for cold supersonic beams (Ttras of few Kelvin), are indicated. In the right side of the panel the case of a collision complex of O2 with a rare gas is represented. Herein, the electron spin is decoupled from the rotational angular momentum (see text).

in the edge-on configuration (upper panel, **Figure 1**, where the formation of zero helicity state is depicted), and the faster ones exhibit the highest polarization degree (upper panel, **Figure 2**). Crucial for the interpretation of experimental findings is to recall that the rotation-electronic angular momentum coupling for O<sup>2</sup> is best described by Hund's case b. Besides, O<sup>2</sup> molecules in seeded beams nearly exclusively populate the ground rotational state defined by the quantum number K = 1 and the associated angular momentum **K** couples with **S** to give the well-known spin-rotational sublevels, identified by J (**J**=**K**+**S**), as indicated in **Figure 2**. The analysis of the O<sup>2</sup> beam paramagnetism, based on a non-statistical distribution of spin-rotation sublevels, suggested that the fastest molecules achieve a high simultaneous/combined polarization of **K** and **S** (Aquilanti et al., 1999).

The same analysis provided an average rotational alignment of O<sup>2</sup> and a source pressure dependence similar to those from previous experiments on closed-shell molecules (see Aquilanti et al., 1995a and references therein). However, an open question concerns the microscopic mechanism leading to the simultaneous alignment of **K** and **S**. In particular, the focus is on the behavior of the electronic spin **S** that couples with other angular momenta exclusively via magnetic interactions. During a scattering event leading to a collision complex (**Figure 2**), the intermolecular electric field strength is sufficient to decouple **K** from **S**, and the field anisotropy (or gradient) tends to form states with zero helicity. Under such conditions, the single quantization axis for **S** is the direction of the orbital angular momentum of the collision complex. After the collision, **K** couples again with **S** and a polarization transfer between **K** and **S** can occur. Although observed in other phenomena (Ramsey, 1955; Bhaskar et al., 1982; Happer et al., 1984; Sofikitis et al., 2007) involving rotational, nuclear and electronic spin angular momentum couplings, probably all implications of the polarization transfer on the molecular dynamics are still not fully understood.

The investigation of O<sup>2</sup> in several seeded beams showed that the achieved alignment degree is nearly independent of the type of lighter carrier species and that a proper scaling factor is the reduced speed (or speed ratio), defined as the ratio between the selected molecular velocity and the peak velocity of the MB. Therefore, merely exploiting the velocity selection technique, it has been possible to sample, in a controlled way, molecules flying at the same speed but having a different alignment degree (Aquilanti et al., 1994, 1995a). Accordingly, it was possible to measure, at the same collision velocity, crosssection anisotropy arising from the different alignment degree of projectile molecules with respect to the collision direction (see **Figure 3**). In particular, using Kr and Xe atoms as targets, scattering cross sections have been measured (Aquilanti et al., 1998) selecting specific speed ratios, related to molecules flying in the tail, peak, near the head and in the head of several seeded beams. This sampling allowed to quantify:


The combined analysis of beam paramagnetism and scattering experiments confirmed the dependence of the O<sup>2</sup> molecular alignment on the speed ratio and allowed to obtain intermolecular potential energy surfaces (PESs) in the anisotropic and weakly interacting O2-Kr and O2-Xe systems.

In a similar manner, by exploiting the combination of velocity selection with scattering experiments, the cross section anisotropy in collisions of diamagnetic N<sup>2</sup> projectiles with Xe target were measured (Aquilanti et al., 1997). Correspondence of the measured anisotropy has also been found (Vattuone et al., 2010) with literature data on the scattering of oriented NO molecules by Xe (Reuss, 1975; Thuis et al., 1979). Such authors controlled the NO orientation by the external electric fields of an hexapole. Moreover, in the N<sup>2</sup> experiments, the use of a defined PES allowed extracting information on the molecular alignment degree, that exhibits a speed ratio dependence very similar to that of O2.

Within a Trento-Perugia collaboration, a combined study making use of scattering experiments and spectroscopic probes has been performed on seeded beams of hydrocarbon molecules (Pirani et al., 2001, 2003). The use of two different and independent techniques, probing two different observables

related to molecular orientation, has provided interesting insights in the alignment processes of such molecules. The scattering technique, already described, uses the total integral cross section dependence on the relative orientation of the projectile molecule with respect to the target one. The spectroscopic technique is based on the dependence of the intensity of some rovibrational transitions on the relative orientation between the transition dipole moment of the molecule and the light polarization vector.

Benzene has been the first examined system (Pirani et al., 2001, 2003). It is a planar molecule exhibiting a strong dependence of the scattering cross section on the orientation of the molecular plane with respect to the velocity direction. The spectroscopic experiment probed a C-H stretching transition whose dipole moment lies in the molecular plane. Hence, by analyzing the absorption intensity as a function of the angle between the light polarization vector and the velocity vector of the molecule, the amount of anisotropy in the molecular orientation states was quantified.

In this investigation both techniques gave the same indication: after supersonic expansion there is a net deviation of the scattering and optical observables from the values expected in case of isotropic distribution of orientation (i.e., flying) modes: the states with molecular plane parallel to the velocity direction (frisbees) are considerably more probable than those having the molecular plane perpendicular to it (flywheels).

The combined experiment gave also relevant clues on final velocity dependence, previously discussed, and on the angular cone amplitude around the beam axis sampled after the supersonic expansion, confirming that, also for large molecules, the alignment process is dependent on stereodynamical processes due to collisions during beam expansion.

## Molecular Orientation by Intermediate Strength Forces

In the last 10 years, particular attention has been addressed to the scattering of water molecules by several targets (Cappelletti et al., 2012) and to develop model potentials describing the interaction of H2O molecules in neutral and ionic clusters (Albertí et al., 2009). Water is a polar species having a permanent electric dipole moment equal to 1.85 Debye, and it exhibits electronic polarizability very close to that of Ar. MB scattering experiments with a series of hydrogenated polar molecules have been performed in order to systematically investigate the phenomenology associated to anisotropy effects in collisions of polar hydrogenated molecules, as a function of the product of their permanent electric dipoles. Integral cross-section Q(v) values, measured for the D2O-D2O, D2O-ND3, D2O-H2S, and ND3-H2S colliding pairs, have been reported and discussed (Roncaratti et al., 2014a,b) in comparison with those of reference systems Ar-Ar, Ar-Kr, Ar-Xe, and Kr-Xe.

The choice of reference systems has been suggested by the following similarities in the polarizability values: Ar (1.6 Å<sup>3</sup> ) and water (1.5 Å<sup>3</sup> ), Kr (2.5 Å<sup>3</sup> ) and ammonia (2.2 Å<sup>3</sup> ), Xe (4.0 Å 3 ), and hydrogen sulfide (3.8 Å<sup>3</sup> ). The isotropic polarizability, related to the particle size and to the probability of induced electric dipole formation, represents a proper scaling factor of both average size repulsion and of dispersion/induction attraction. It should be noted that, when dealing with molecules, the overall polarizability includes contributions from the constituent atoms as well as from bonds. Therefore, each pair of investigated molecular and atomic reference systems is expected to exhibit the same isotropic van der Waals interaction. Measured scattering results clearly indicate that all systems formed by two hydrogenated polar molecules exhibit much larger crosssections Q(v), well outside the experimental uncertainty, than those of the corresponding reference atomic ones. In particular, we evaluated that the cross section ratios of the polar pairs vs. the corresponding reference systems are (on average) ∼2.5 for D2O-D2O, ∼1.7 for D2O-ND3, ∼1.4 for D2O-H2S, and ∼1.2 for ND3-H2S. These Q(v) ratios show a clear linear dependence on the product of the dipole moments of the colliding partners, suggesting an appreciable role of the electrostatic component of the intermolecular potential on the investigated experimental observables (Roncaratti et al., 2014a,b). A negligible role is expected for collisions with randomly oriented partners, since the electrostatic component vanishes. This is a clear evidence that, during collisions between polar molecules, the latter do not maintain random orientations and are not freely rotating, but tend to be trapped in pendular states, where they experience a much stronger interaction than that obtained by averaging over all relative configurations.

The transition from free rotors to pendular states is promoted by the coupling between the molecular permanent dipole moments within the field gradient due to the anisotropic intermolecular potential. The phenomenon, occurring in the timescale of ps (i.e., similar to the time required for a collision at thermal energies) couples more effectively molecules with very similar rotational periods and populating low lying rotational states (Roncaratti et al., 2014a,b). Under such most favorable conditions, the coupling originates the so-called synchronized dance of water molecules (see **Figure 4**), a phenomenon crucial to describe the passage of water molecules in carbon nanotubes and cellular channels.

Further experimental investigations, integrated by advanced theoretical calculations, have been also extended to mixed (prototype) systems, formed by polar molecules—noble gas atom pair, to characterize selectivities in the formation of weak intermolecular hydrogen bond (Cappelletti et al., 2012).

molecules both in J = 1 is depicted. The coupling induces a local modification of the molecular modes, clearly evidenced when the relative motion of the two dipoles is projected on the Y-t plane. The collision complex dynamics is driven by an effective electrostatic dipole-dipole interaction. Most part of its influence manifests in the time scale from −1 to +1 ps.

## Molecular Orientation by Strong Intermolecular Forces

In the case of ion-molecule reactions, alignment/orientation is a general phenomenon due to the electric field generated by the charged particle. Stereo-dynamic effects related to long-range anisotropic interactions have been observed in several systems, with different outcomes on reaction probability. A pertinent example is given by the (Ar-N2) <sup>+</sup> system, whereby a reasonable description of the charge-transfer dynamics can only be achieved by accounting for the spin–orbit interaction, the molecular anisotropy and the electronic anisotropy related to the open-shell nature of Ar<sup>+</sup> (Candori et al., 2001, 2003).

In general, when alignment/orientation drives the collision complex into the most appropriate configurations for reaction, an enhancement of reactivity is possible. It is the case of the H<sup>+</sup> <sup>2</sup> + H<sup>2</sup> → H + <sup>3</sup> + H reaction, for which an enhancement of the rate coefficient with respect to the classical Langevin-capture behavior at low collision energies has been attributed to anisotropic modification of the long-range scattering potential due to interaction between the H<sup>+</sup> 2 charge and the rotational quadrupole moment of the ground state of ortho-H<sup>2</sup> (Allmendinger et al., 2016).

On the other hand, when long-range interaction potentials reorient the reacting couple, either in a non-reactive or in a configuration unfavorable for reaction, the overall reaction probability will be suppressed, as in the case of the Hatom transfer reaction between H<sup>2</sup> and H2O+. In the latter

symmetric atomic orbital of He<sup>+</sup> and the inner valence orbital of DME from which the electron is extracted.

system, the most attractive orientation, governed by charge and dipole-quadrupole/induced multipole interactions, is not the most favorable for H atom transfer. Thus reorientation of H2O+, facilitated by rotational excitation, is necessary to promote reactivity (Li et al., 2014). Hence, rate constants can show an Arrhenius dependence (i.e., a positive dependence on T) even in the case of barrierless and exothermic processes, as observed in the reactions of Ar<sup>+</sup> and N<sup>+</sup> 2 ions with diatomic interhalogens ICl and ClF (Shuman et al., 2017).

Differences in the long-range ion-molecule interaction potentials are also at the basis of the different bimolecular reactivity observed by different rotational isomers (conformers) of a polyatomic molecule in the gas phase. By elegantly exploiting an experimental technique based on the spatial separation of conformers having significantly different electric dipole moments in a MB via electrostatic deflection (i.e., the use of inhomogeneous electric fields), the specific chemical reactivity of two conformers of 3-aminophenol with cold Ca<sup>+</sup> ions in a Coulomb crystal was observed (Chang et al., 2013; Rösch et al., 2014), thus demonstrating the possibility of controlling reactivity through selection of conformational states.

A recent investigation from our laboratories focused on the study of some ion-molecule reactions of relevance to assess the competition and balance of phenomena occurring in many gaseous and plasma environments, ranging from the ionospheres of planets and the interstellar medium (Balucani et al., 2015) (low temperatures) to laboratory plasmas for technological applications (much higher temperatures). In particular, collisions with He<sup>+</sup> are an important pathway for the decomposition of "complex organic molecules" (COMs, i.e., molecules containing at least six atoms) in various astronomical environments (Balucani et al., 2015; Ascenzi et al., 2019). Since dimethyl ether (DME) and methyl formate (MF) are among the most abundant COMs, experiments have been performed on the reactivity of He<sup>+</sup> ions with such neutrals, using a Guided Ion Beam Mass Spectrometer, which allows measurements of reactive cross sections and branching ratio (BR) as a function of the collision energy (Cernuto et al., 2017, 2018). Due to the large dipole moments exhibited by the neutral collision partners (1.30 Debye for DME and 1.77 Debye for MF) the studied systems present large interaction anisotropies that can induce strong stereodynamical effects and influence the outcome of reactive collisions. The experimental evidence is that the electron exchange processes are completely dissociative, leading to extensive fragmentation of the neutral partner, and cross section trends with collision energies are at odds with those expected from simple capture models. By investigating the nature of the non-adiabatic transitions between the reactant and product potential energy surfaces using an improved Landau-Zener model, we were able to identify three critical elements at the basis of such discrepancy:


#### PES Anisotropy

For both DME and MF the interaction anisotropy in the entrance channels is such that one (two for the MF case) deep potential wells (with depth in the range 1.3–1.7 eV) are present for selected configurations: namely when the He<sup>+</sup> ion approaches the molecule from the O atom side, on the plane defined by the C atoms and the ethereous O atom (see **Figure 5**, top panel). As a consequence, the reaction dynamics is substantially limited to a few geometries confined around the most stable configurations of the collision complex. The rather large interaction anisotropy induces pronounced orientations of the polar neutrals in the electric field generated by He+, which are mostly operative at low collision energies. While the neutrals are free to rotate at large distances, as the colliding partners come closer, the rotation of the polar molecule becomes partially hindered by the intermolecular electric field gradient associated with the interaction anisotropy. Hence, at short distances, the collision complex is confined within pendular states, a particular case of bending motion (see **Figure 5**, bottom left panel). Such orientation effects can influence the dynamic of the chargeexchange process by channeling most of the neutral molecules in narrow angular cones confined around the most attractive configurations of the interacting systems. Similar effects have been also observed at the interface between the gas and liquid phase for solutions containing cations and anions (Gisler and Nesbitt, 2012).

#### Crossings Among Entrance and Exit Diabatic PESs

Due to the large differences in ionization energy (IE) between He (IE = 24.59 eV) and DME (IE = 10.025 eV) or MF (10.835 eV),

## REFERENCES

Albertí, M., Aguilar, A., Cappelletti, D., Lagana, A., and Pirani, F. (2009). On the development of an effective model potential to describe water analysis of the interaction PESs shows that the (diabatic) reactant surfaces do not cross the product surfaces correlating asymptotically with the ground state of DME<sup>+</sup> and MF+. Thus, He<sup>+</sup> captures an electron from an inner valence orbital of the neutral molecules, forming the molecular cation in a highly excited state, that quickly dissociates.

#### Symmetry of the Electron Density Distributions

The symmetry of the electron density distribution of the molecular orbitals from which the electron is removed turns out to be a further major point affecting the probability of electron transfer to He+, since it affects the overlap integral between the orbitals involved in the electron exchange. In both DME and MF cases, at least one of the molecular orbitals that are expected, in terms of crossing positions, to give the most significant contribution to charge transfer, presents a small overlap with the spherically symmetric atomic orbital of He+( 2 S1/2), as pictorially shown in the bottom right panel of **Figure 5**. This effect originates the paradox that the most attractive geometry is the least efficient for charge transfer, and the reactions are increasingly driven by the Coriolis coupling (i.e., the coupling between the rotational angular momentum of nuclei in the collision complex and the orbital angular momentum of the electron) rather than by orbital overlap. Using such a combined experimental and theoretical methodology we have been able to provide new values for the temperature dependent rate coefficients and branching ratios of the reactions of He<sup>+</sup> with the two important COM, dimethyl ether and methyl formate (MF). Our results will be relevant for a correct modeling of the chemical kinetics in various regions of the interstellar space, such as prestellar cores and hot corinos (Ascenzi et al., 2019).

In conclusion, all the experimental findings, characterized in several experiments carried out within the Perugia-Trento collaboration, can be rationalized in a unifying picture that considers the sterodynamics of gas phase collisions controlled by anisotropic forces of different strength.

#### AUTHOR CONTRIBUTIONS

FP and DA wrote the first draft of the manuscript. PT, MS, and DC wrote sections of the manuscript. All authors contributed to manuscript revision, read and approved the submitted version and contributed conception and design of the study.

#### ACKNOWLEDGMENTS

DC and FP thank MIUR and the University of Perugia for financial support through AMIS project (Dipartimenti di Eccellenza−2018–2022). DA, MS, and PT acknowledge support from the Department of Physics of the University of Trento.

interaction in neutral and ionic clusters. Int. J. Mass Spectrom. 280, 50–56. doi: 10.1016/j.ijms.2008.07.018

Allmendinger, P., Deiglmayr, J., Hçveler, K., Schullian, O., and Merkt, F. (2016). Observation of enhanced rate coefficients in the H<sup>+</sup> <sup>2</sup> + H<sup>2</sup> → H + <sup>3</sup> + H reaction at low collision energies. J. Chem. Phys. 145:244316. doi: 10.1063/1.497 2130


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Ascenzi, Scotoni, Tosi, Cappelletti and Pirani. This is an openaccess article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Molecular Dynamics of CH4/N<sup>2</sup> Mixtures on a Flexible Graphene Layer: Adsorption and Selectivity Case Study

Jelle Vekeman1,2, Noelia Faginas-Lago1,3 \*, Andrea Lombardi 1,3 , Alfredo Sánchez de Merás <sup>4</sup> , Inmaculada García Cuesta<sup>4</sup> and Marzio Rosi <sup>5</sup>

<sup>1</sup> Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Perugia, Italy, <sup>2</sup> Instituto de Ciencia Molecular, Universidad de Valencia, Valencia, Spain, <sup>3</sup> Consortium for Computational Molecular and Materials Sciences (CMS2), Perugia, Italy, <sup>4</sup> Departamento de Química Física, Universidad de Valencia, Valencia, Spain, <sup>5</sup> Dipartimento di Ingegneria Civile e Ambientale, Università degli Studi di Perugia, Perugia, Italy

#### Edited by:

Doo Soo Chung, Seoul National University, South Korea

#### Reviewed by:

Piotr Gauden, Nicolaus Copernicus University in Torun, Poland ´ Jean-Marc Simon, Université de Bourgogne, France

> \*Correspondence: Noelia Faginas-Lago noelia.faginaslago@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 07 February 2019 Accepted: 14 May 2019 Published: 03 June 2019

#### Citation:

Vekeman J, Faginas-Lago N, Lombardi A, Sánchez de Merás A, García Cuesta I and Rosi M (2019) Molecular Dynamics of CH4/N2 Mixtures on a Flexible Graphene Layer: Adsorption and Selectivity Case Study. Front. Chem. 7:386. doi: 10.3389/fchem.2019.00386 We theoretically investigate graphene layers, proposing them as membranes of subnanometer size suitable for CH4/N<sup>2</sup> separation and gas uptake. The observed potential energy surfaces, representing the intermolecular interactions within the CH4/N<sup>2</sup> gaseous mixtures and between these and the graphene layers, have been formulated by adopting the so-called Improved Lennard-Jones (ILJ) potential, which is far more accurate than the traditional Lennard-Jones potential. Previously derived ILJ force fields are used to perform extensive molecular dynamics simulations on graphene's ability to separate and adsorb the CH4/N<sup>2</sup> mixture. Furthermore, the intramolecular interactions within graphene were explicitly considered since they are responsible for its flexibility and the consequent out-of-plane movements of the constituting carbon atoms. The effects on the adsorption capacity of graphene caused by introducing its flexibility in the simulations are assessed via comparison of different intramolecular force fields giving account of flexibility against a simplified less realistic model that considers graphene to be rigid. The accuracy of the potentials guarantees a quantitative description of the interactions and trustable results for the dynamics, as long as the appropriate set of intramolecular and intermolecular force fields is chosen. In particular it is shown that only if the flexibility of graphene is explicitly taken into account, a simple united-atom interaction potential can provide correct predictions. Conversely, when using an atomistic model, neglecting in the simulations the intrinsic flexibility of the graphene sheet has a minor effect. From a practical point of view, the global analysis of the whole set of results proves that these nanostructures are versatile materials competitive with other carbon-based adsorbing membranes suitable to cope with CH<sup>4</sup> and N<sup>2</sup> adsorption.

Keywords: adsorption, molecular dynamics, ab-initio potential, flexible graphene, ab initio calculations

## 1. INTRODUCTION

Graphene has often been investigated as a possible material for the separation of small gases (Du et al., 2011; Wang et al., 2016; Raghavan and Gupta, 2017). Due to its unique structure and electronic properties on one hand and to its cheapness and stability on the other, it has been shown to outperform other candidate materials such as metal organic frameworks (MOF) in multiple studies (Thierfelder et al., 2011; Kumar et al., 2013; Wu et al., 2015). Usually, in molecular dynamics studies, the inherent internal flexibility of the graphene sheet is neglected by fixating the sheet within the simulation box. In reality, however, the sheet will have vibrations and other internal movement both in and out of the plane that might influence the adsorption capacity of the sheet (Deng and Berry, 2015; Bianco et al., 2018; Zhang et al., 2018). Indeed, in previous studies, we found that the adsorption of methane, nitrogen and carbon monoxide separately simulated as pure gases adsorbing on graphene was influenced by the introduction of a intramolecular force field in the graphene sheet in comparison to its rigid form (Vekeman et al., 2018b; Wilson et al., 2018; Vekeman et al., in press). In this work, we follow up on these previous works with a classical molecular dynamics study of the methane/nitrogen gas mixture in order to assess the influence of flexibility on the separation of both gases. In a similar way as in these previous works, we will use three intramolecular force fields —including stretch, bending and torsional terms—found in the literature that we have implemented and compare their performance to the typically modeled rigid sheet fixed in the simulation box (Walther et al., 2001; Kalosakas et al., 2013; Fthenakis et al., 2017).

Furthermore, we will evaluate the performance of different molecular gas models by comparing the estimates obtained from both united-atom and atomistic models for methane and nitrogen (Do and Do, 2005). The united-atom model, reducing the molecule to a sphere, is expected to be a cheap, yet reliable model, while the atomistic one, considering explicitly all interatomic interactions, will be more expensive and more accurate (Vela and Huarte-Larrañaga, 2011; Apriliyanto et al., 2018). The choice between these types of models is thus often a balancing of accuracy and computational cost and therefore their comparison is critical to make informed decisions (Lucena et al., 2010). In previous works, we have derived intramolecular potentials specifically designed for the adsorption of nitrogen and methane on graphene (Vekeman et al., 2018a,b). We based these potentials on the Improved Lennard-Jones potential (ILJ) (Pirani et al., 2004, 2008) as these have shown to outperform the very popular Lennard-Jones (LJ) potential (Pacifici et al., 2013; Faginas-Lago et al., 2015, 2016).

As the use of fossil fuels is causing more and more problems for the environment, a possible alternative on the short term is methane (Harfoot et al., 2018). It is more abundant on earth, cheaper and more easily implemented than not yet completely matured techniques such as hydrogen driven processes (Marques et al., 2018; Rogelj et al., 2018). Existing applications running on fossil fuels, such as cars, can indeed relatively easy and cheaply be adapted to run on natural gas instead (Menon and Komarneni, 1998; Choi et al., 2016). Nitrogen is often encountered as an unwanted impurity in natural gas that needs to be removed efficiently before use (Cavenati et al., 2004). On the other hand, postcombustion fuel gas mixtures contain both methane and nitrogen gas among others and the removal of methane of these mixtures is crucial to limit the release of methane into the atmosphere (Shao et al., 2011; Apriliyanto et al., 2018). It is thus clear that the CH4/N<sup>2</sup> is a gas mixture highly relevant for industrial applications.

The aim of this paper is then to study the separating ability of graphene for the CH4/N<sup>2</sup> mixture at room temperature with a focus on the influence of intramolecular force fields in the graphene sheet and the molecular models used for the gas molecules. Section 2 will shortly highlight the computational details of this work, section 3 will be dedicated to the used force fields and the results will be described in section 4. Finally, the conclusions will be presented in section 5.

## 2. COMPUTATIONAL DETAILS

We have performed molecular dynamics simulations using DL\_POLY v2.2 (Smith et al., 2002) placing a graphene sheet in the middle of a simulation box. We applied periodic boundary conditions in the 3 dimensions allowing sufficient space in the z-direction for assuring that the different copies of the graphene sheet did not interact and to allow gas molecules enough space to escape the graphene sheet. In the x- and ydirection the box size was adapted to a graphene sheet of 840 carbon atoms with an average C-C distance of 1.42 Å , such that there were no defects upon applying the periodic boundary conditions. The box size was thus 51.65 Å × 42.6 Å × 40 Å . All simulations were carried out at 300K in the NVE and the NVT ensembles, using a Hoover thermostat with a relaxation constant of 0.5 ps in the latter case. A cutoff distance of 18 Å was used for all interaction types and a timestep of 1 fs for a simulation time of which 150,000 were for equilibration. Such equilibration time was determined following a well-established procedure previously developed (Faginas-Lago et al., 2017). Convergence was checked by monitoring the time evolution of the energy and temperature. The geometry of gas molecules were optimized at the B3LYP/6-31G\*\* (Hehre et al., 1972; Becke, 1993) level and assumed rigid during the simulations.

## 3. FORCE FIELDS

In this work, we used intermolecular potentials based on the ILJ potential (Pirani et al., 2004, 2008) to describe the interactions between different gas molecules on one hand and the interactions between the gas molecules and the graphene sheet on the other (Vekeman et al., 2018a,b). Furthermore, we implemented intramolecular interaction potentials in DL\_POLY v2.2. (Smith et al., 2002) to model the flexibility of the sheet. The used force fields are described in detail in the following sections.

#### 3.1. Intermolecular Potentials

For the intermolecular force fields, we assume that the interaction can be described by an electrostatic and a non-electrostatic part that are independent from each other

$$\begin{split} V\_{\text{tot}}(\mathcal{R}) &= V\_{\text{nlec}}(\mathcal{R}) + V\_{\text{elec}}(\mathcal{R}) \\ &= V\_{\text{IIJ}}(\mathcal{R}) + V\_{\text{Coul}}(\mathcal{R}). \end{split} \tag{1}$$

For the non-electrostatic part, we used the ILJ potential (Albertí and Lago, 2012, 2013; Faginas-Lago et al., 2016) which has the following form

$$V(R) = \epsilon \left[ \frac{m}{n(R) - m} \left( \frac{r\_0}{R} \right)^{n(R)} - \frac{n(R)}{n(R) - m} \left( \frac{r\_0}{R} \right)^m \right],\tag{2}$$

where,

$$n(R) = \beta + 4\left(\frac{R}{r\_0}\right). \tag{3}$$

The potential contains four parameters, one of which, m, is fixed depending on the interacting species, in this case, 6, as the species are neutral molecules (Pirani et al., 2008). Furthermore ǫ and r<sup>0</sup> are the well depth and the equilibrium distance, respectively, and have the same meaning as in the standard LJ potential. β is an extra parameter that allow for the tuning of the ILJ potential at long and short interaction distances, where the LJ potential is known to underperform (Albertí et al., 2012; Lago et al., 2013; Faginas-Lago et al., 2015; Faginas Lago, N. et al., 2009). This parameter is loosely related to the hardness of the interacting molecules.

The parameters that were used for the graphene-gas and the gas-gas interactions have been obtained by fitting the ILJ potential, supplemented with a Coulombic sum, to high-level interaction energies at DFT level of the respective systems. The obtained potentials were then benchmarked against DFT and CCSD(T) results as was explained in previous publications (Vekeman et al., 2018a,b). From the results in these articles, here, for both methane and nitrogen, a united-atom and an atomistic model were selected with corresponding partial charges and used for simulations; the used parameters can be found in **Table 1**. The united-atom model treats the gas molecule as a sphere by putting just one interaction center on the center of mass of the molecule. The atomistic model, on the other hand, puts an interaction center on all atoms of the molecule leading to a higher accuracy, but as well a higher computational cost. For the methane molecule in the united-atom approach, charges calculated by the Hirshfeld population analysis (Hirshfeld, 1977) were used placing a negative charge of –0.148 e on the carbon atom and positive charges of 0.037 e on the hydrogen atoms. For the atomistic approach on the other hand, the best performance was given by not including any charges at all. For the nitrogen molecule, the Cracknell scheme (Cracknell et al., 1996) gave the best performance for both the united-atom and the atomistic approach. In this scheme, both a negative charge of –0.373 e and a positive charge of 0.373 e are positioned on either TABLE 1 | Interaction parameters for the ILJ potential used in this work to represent the intermolecular potentials in a united-atom or fully atomistic representation.


For methane in the united-atom approach, the Hirshfeld charge scheme was used, whereas for nitrogen in both approaches, the Cracknell scheme was used (Vekeman et al., 2018a,b). Cm referst to the center of mass of the respective molecules.

side of the nitrogen atoms outside of the molecule with the positive charges separated by 1.694 Å and the negative charges by 2.088 Å . The graphene sheet is always represented atomistically by interaction centers on all carbon atoms while electrostatic interactions are neglected. Figurative representations of the used molecular models can be found in **Figure 1**.

A final remark on the used potentials is that, despite the fact that in order to preserve a possible physical interpretation of the β parameters their values must be restricted, we have chosen not to restrict them in order to better describe the potential surfaces determined at the DFT level of theory in previous papers (Vekeman et al., 2018a,b). This same approach has been also used in other works by the ILJ developers (Pacifici et al., 2013; Faginas-Lago et al., 2015, 2016).

#### 3.2. Intramolecular Potentials

Intramolecular potentials were introduced in the graphene sheet as mentioned before. In particular, we compared the performance of three different force fields. Firstly we have taken the force field originally developed for carbon nanotubes by Walther et al. (2001)

$$\begin{split} U\_1(r\_{ij}, \theta\_{ijk}, \phi\_{ijkl}) &= K\_{Cr1} (e^{-\gamma\_1(r\_{ij} - r\_{C1})} - 1)^2 \\ &+ \frac{1}{2} K\_{C\theta 1} (\cos \theta\_{ijk} - \cos \theta\_{C1})^2 \\ &+ \frac{1}{2} K\_{C\phi 1} (1 - \cos(2\phi\_{ijkl})). \end{split} \tag{4}$$

This force field contains a stretching, a bending and a torsional term and will be denoted field 1 from now on. The parameters are given as follows: KCr<sup>1</sup> = 114.46 kcal mol−<sup>1</sup> , γ<sup>1</sup> = 2.1867 Å−<sup>1</sup> , rC<sup>1</sup> = 1.418 Å , KCθ<sup>1</sup> = 134.369 kcal mol−<sup>1</sup> rad−<sup>2</sup> , θC<sup>1</sup> = 120◦ and KCφ<sup>1</sup> = 6.004 kcal mol−<sup>1</sup> .

Secondly, we took the force field by Kalosakas et al. specifically developed for graphene (Kalosakas et al., 2013)

$$\begin{split} U\_2(r\_{ij}, \theta\_{ijk}) &= K\_{Cr2} (e^{-\gamma\_2 \left(r\_{ij} - r\_{C2}\right)} - 1)^2 \\ &+ \frac{1}{2} K\_{C\vartheta 2} (\cos \theta\_{ijk} - \frac{2\pi}{3})^2 \\ &+ \frac{1}{2} K\_{C\vartheta 2}' (\cos \theta\_{ijk} - \frac{2\pi}{3})^3, \end{split} \tag{5}$$

where the parameters are given as KCr<sup>2</sup> = 131.429 kcal mol−<sup>1</sup> , γ<sup>2</sup> = 1.960 Å−<sup>1</sup> , rC<sup>2</sup> = 1.420 Å , KCθ<sup>2</sup> = 161.401 kcal mol−<sup>1</sup> rad−<sup>2</sup> and K ′ Cθ2 = 92.232 kcal mol−<sup>1</sup> rad−<sup>3</sup> . This field, denoted field 2 from now on, only takes into account stretching terms and bending terms. However, later on, the same authors extended the field with a torsional term and this constitutes the third field, referred to as field 2 m (field 2 modified) from now on in this work (Fthenakis et al., 2017)

$$\begin{split} U\_3(r\_{ij}, \theta\_{ijk}, \phi\_{ijkl}) &= K\_{Cr3} (e^{-\gamma\_3 \left(r\_{ij} - r\_{C3}\right)} - 1)^2 \\ &+ \frac{1}{2} K\_{C\theta 3} (\cos \theta\_{ijk} - \frac{2\pi}{3})^2 \\ &+ \frac{1}{2} K'\_{C\theta 3} (\cos \theta\_{ijk} - \frac{2\pi}{3})^3 \\ &+ \frac{1}{2} K\_{C\phi 3} (1 - \cos(2\phi\_{ijkl})). \end{split} \tag{6}$$

This field has the same parameters as field 2 with the addition of one extra parameter: KCφ<sup>3</sup> = 5.304 kcal mol−<sup>1</sup> . Observe that this field 2 m should be considered as the most adequate of the three as it has been specifically developed for graphene and includes the full set of parameters needed to describe the intramolecular motions of the sheet. In fact, it reproduces very accurately the out-of-plane acoustic and optical modes of graphene's phonon dispersion as well as all phonons with frequencies up to 1,000 cm−<sup>1</sup> (Fthenakis et al., 2017). Anyway, at least in what adsorption concerns, the differences in the results from the three fields are certainly very small, as shown below.

The performance of these three force fields will then be compared to a completely rigid graphene represented as a sheet without intramolecular force field, so explicitly freezing the positions of all carbon atoms. The rigid graphene will be denoted as field 0.

#### 4. RESULTS

Our previous work on pure methane and pure nitrogen adsorption on a flexible graphene sheet (Vekeman et al., in press) has clearly shown that graphene has more affinity for the adsorption of methane than for nitrogen and, thus, it can be expected that graphene could serve as a separator for both gases. Furthermore we found that the atomistic model predicted a much stronger methane adsorption than the united-atom model, while for nitrogen these results were quite similar. The united-atom model, on the other hand, showed a lower methane uptake when neglecting the intramolecular movements of the graphene sheet, while there was a smaller discrepancy in these results for the atomistic model.

Since the stronger affinity of graphene for methane than for nitrogen was clearly proven in this previous work, we expect that the graphene sheet could effectively separate this gas mixture. Therefore, in a first set of simulations we have adopted a protocol where we randomly allocated 100 gas molecules (50 CH<sup>4</sup> + 50 N2) over the graphene sheet. The molecules were placed such that at least 5 Å were left in between the different molecules, the edges of the box and the graphene sheet to avoid instantaneous, strongly repulsive interactions at the start of the simulation. We then ran one NVE simulation to allow the system to relax to a physically viable conformation and used the resulting output as input for a first NVT simulation. After this NVT simulation, we kept the molecules that were adsorbed (see below) and deleted the ones that were not. Subsequently, we randomly distributed 100 new gas molecules (50 CH<sup>4</sup> + 50 N2) over the remaining system from the previous simulation to run a new NVT simulation. This protocol was repeated until convergence of the amount of adsorbed molecules. As such, this protocol gives an indication of the amount of molecules that saturates the first adsorption layer and it allows comparison for the different intramolecular force fields and molecular models under study.

As a criterion for adsorption, we considered all molecules closer than 4.6 Å to the graphene sheet to be adsorbed, where the average of the carbon positions in the graphene sheet was used as the zero line. This distance was chosen based on preliminary studies in which the z-density profiles indicated the presence of a first adsorption layer below the distance of 4.6 Å for all studied gases. Similar z-density profiles can be found below where this can be verified.

**Table 2** shows the results for the simulations of the adsorption of the methane/nitrogen mixture on the graphene sheet using united-atom models for both gas molecules. The table shows the total amount of molecules that was present and the molar fraction that was adsorbed, methane and nitrogen combined. Then it shows the molar fraction of methane or nitrogen molecules that was present at the start of each respective simulation as Xinitial and the molar fraction of the respective molecules that was subsequently adsorbed at the end of this simulation as Xadsorbed.

Looking at the total amount of molecules that gets adsorbed it is seen that in the initial simulations, most of the molecules are adsorbed (76% for the sheet assumed rigid, 84% for field 1 and field 2 and 89% for field 2 m.), while this fraction lowers in subsequent simulations. In the first simulations, the amount of molecules that is introduced in the system is not enough to fully saturate the graphene sheet and thus most molecules stay will adsorb onto the sheet. When more molecules are gradually introduced, the graphene sheet gets quickly saturated and more molecules will be forced to stay in gas phase in equilibrium with the adsorbed molecules. A closer inspection of the results for methane and nitrogen within the mixture reveals a changing methane/nitrogen ratio from one simulation to the next. Indeed, it can be seen that in the first simulations, a substantial amount of nitrogen molecules is adsorbed on the graphene sheet (66% without intramolecular force field for graphene, 70% with field 1 and field 2 and 78% with field 2 m), while in subsequent simulations, they are steadily removed from the adsorbed layer. The methane molecules are adsorbed preferentially, but in the first simulations there are not enough molecules to completely saturate the graphene sheet allowing nitrogen molecules to adsorb as well. When more methane molecules are added, they occupy more and more space on the graphene surface allowing less space to nitrogen, which is forced to stay in gas phase. In the end, a situation is reached where about 70% of the molecules in the simulation are methane molecules and 30% are nitrogen, consistent over the four graphene sheets. Adding to this, the fraction of methane molecules that adsorbs is much larger than the fraction of nitrogen molecules, giving a first indication that indeed the graphene sheet is well capable of separating methane and nitrogen from each other.

Examining the influence of the flexibility of the graphene sheet on the adsorption, clear differences between the results for the different models are found. First of all, the fraction of the total amount of molecules that is adsorbed if the flexibility of the sheet is not accounted for (about 60%) is lower than when it is explicitly included (about 65%). As methane is dominantly present in the mixture, this result is clearly a reflection of the results for methane within the mixture. While the simulation predicts an adsorption of about 70% of the available methane (note that the initial mole fraction is similar for all fields), the flexible ones increases the prediction to up about 80% of the available methane. For nitrogen, the difference is smaller and anyway with less influence TABLE 2 | Simulation results for the methane/nitrogen mixture using a united-atom approach for the four intramolecular force fields considered in this work.


Results are represented for the total amount of molecules (methane + nitrogen) and the separate methane and nitrogen adsorption within the mixture. Xadsorbed indicates the molar faction of the adsorbed molecules.

on the total result since the initial fraction is much lower. Keeping in mind that for the pure methane, the united-atom model predicted a lower uptake on the rigid sheet (Vekeman et al., in press) and the dominance of methane in the CH4/N<sup>2</sup> mixture, this results is no surprise. Dreisbach et al. (1999) reported a slowly rising, while converging, methane mole fraction in the methane/nitrogen mixture with a result of 0.733 at 59.8 atm (the highest pressure they measured). In addition, Sudibandriyo et al. (2003) reported a very similar methane mole fraction of 0.732 at the same pressure, while reporting 0.744 at 70 atm. These results coincide very well with our simulations at similar pressures.

The results in **Table 3**, using the atomistic model for both methane and nitrogen, predict an even more efficient separation. The mole fraction of methane within the mixture reaches values of 0.80 for the rigid model and 0.85 for the flexible ones. The methane is now so strongly adsorbing to the graphene sheet that effectively all nitrogen molecules are forced into gas phase, leaving adsorbed mole fractions close to 0.00 for the flexible representation and 0.07 for the rigid ones. Although methane still


TABLE 3 | Simulation results for the methane/nitrogen mixture using an atomistic approach for the four intramolecular force fields considered in this work.

Results are represented for the total amount of molecules (methane + nitrogen) and the separate methane and nitrogen adsorption within the mixture.

dominates the total results, the mole fraction of total molecules that adsorbs is lower, because there is always a portion of nitrogen molecules that never adsorbs. As stated previously, we found in previous work (Vekeman et al., in press) that the methane adsorption predicted by the atomistic model was stronger than for the united-atom model explaining the stronger preference for methane over nitrogen using the atomistic model. This also explains the lower dependence of the adsorption on the flexibility of the graphene sheet as was found for the atomistic pure methane adsorption, as indeed the different intramolecular force fields—or even its complete absence—have little influence in the adsorption when the atomistic model is used.

Once the saturation point of the graphene sheet was known for the different gas molecules on the different sheets, we were interested to study how the molecules distribute themselves in function of the amount of molecules present in the system. In a second protocol, we therefore ran independent simulations with different, predefined amounts of molecules. More specifically, we ran simulations with 150, 250, and 350 molecules randomly distributed over the graphene sheet, i.e., 75 CH<sup>4</sup> + 75 N2, 125 CH<sup>4</sup> + 125 N<sup>2</sup> and 175 CH<sup>4</sup> + 175 N2, respectively. In all cases an NVE simulation was run first to allow the system to relax, after which an NVT simulation was run as a production run. This protocol allows to look at how the adsorption process changes as a function of the amount of molecules introduced into the simulation box. The expected separation of the gases is visible in the screenshots of the simulations with 350 molecules in **Figure 2**. The methane molecules form a clear adsorption layer on the sheets, while the nitrogen molecules stay in gas phase. While there are some nitrogen molecules entering the adsorption layer and some methane molecules in gas phase, the screenshots once again suggest that the separation is quite effective.

**Figure 3** shows the z-density profiles of the methane adsorption within the methane/nitrogen mixture using a unitedatom and an atomistic model for the three different amounts of molecules (150, 250 and 350) of the second protocol. Starting by the united-atom model, it is encountered that—in accordance with the isotherms discussed below and the previously discussed results—when assuming the graphene to be rigid, it adsorbs less methane than the considered flexible sheets. The fact that the adsorption peaks of flexible graphene are lower than those of the rigid one is compensated by a larger broadness, making them of slightly larger area. Indeed, because of the movement of the graphene sheet, the layer will move slightly along, leading to the spread of the molecules along the z-coordinate. After the first very strong adsorption layer, there appears to be a start of a second adsorption layer that arises only in the simulation with 350 molecules. In the two simulations with less molecules (150 and 250 molecules), all methane molecules can be accommodated in the first adsorption layer and no second adsorption layer is observed. For the atomistic model, however, all the methane molecules are adsorbed in the first layer, even for the simulation with 350 molecules. Indeed, it is seen that all 175 methane molecules are adsorbed in the first adsorption layer, no second layer or gas phase being present. Furthermore, the quantities adsorbed by rigid and flexible sheets are almost coincident, with adsorption peaks slightly higher and broader in the case of rigid graphene sheets. Globally, and comparing the two different models, it is once again clear that the atomistic model predicts a larger methane adsorption than the united-atom model.

The z-density profile for the nitrogen molecules from the same simulations are found in **Figure 4** for both the unitedatom and the atomistic approach. In general, it can be seen that indeed less nitrogen is adsorbed in the first adsorption layer than methane due to the strong competition of the latter. On the other hand, the nitrogen molecules organize themselves in a relatively strong second adsorption layer that is, however, still smaller than the first adsorption layer. Furthermore, there are plenty of nitrogen molecules that are still present in the gas phase as is visible from the area under the curve at distances larger than 10 Å.

For the united-atom model, it is noteworthy to see that the first adsorption layer does not grow upon adding more molecules to the system, the height of the first adsorption peak is as high as in the two subsequent simulations. Whereas the remaining nitrogen molecules stay in gas phase for the simulation with 150 molecules, in the other two simulations (250 and 350 molecules) a strong second adsorption layer is formed. As before, the assumed rigid sheet adsorbs slightly less nitrogen molecules than the flexible sheets.

FIGURE 2 | Screenshots of the simulations of the methane/nitrogen mixture on the four graphene sheets using the atomistic model and with 175 methane and 175 nitrogen molecules in the system. From left to right: field 0, field 1, field 2, and field 2 m. Nitorgen atoms are colored in blue, carbon atoms in dark gray and hydrogen atoms in light gray.

Looking at the simulations with the atomistic model, the behavior changes quite a bit: the first adsorption layer for nitrogen is smaller for the simulation with the most (350) molecules compared to the other simulations with 150 and 250 methane molecules. This is a consequence of the strong methane adsorption predicted by the atomistic model: the stronger competition allows less nitrogen molecules to enter the first adsorption layer. In the simulation with 150 molecules, the first adsorption layer is not yet completely saturated by methane and nitrogen is allowed space in the first adsorption layer. As the amount of molecules increases, less and less space remains available for nitrogen and the first adsorption peak of nitrogen decreases as a result. Already in the simulation with 150 molecules, there is a small second adsorption layer present, which increases strongly upon increasing the amount of molecules in the system. In the simulation with 350 nitrogen molecules, there are very little nitrogen molecules present in the first adsorption layer, but there is a relatively large second adsorption layer and subsequent gas phase.

Due to the changing widths of the adsorption peaks—due to the internal graphene movement—in **Figures 3**, **4**, it is hard to compare the results for the different fields visually. Instead, visualization is eased by building the adsorption isotherms shown in **Figures 5**, **6** for methane and nitrogen, respectively. With this aim, the area under the peaks in **Figures 3**, **4**, as well as some equivalent ones determined at different initial number of molecules, were determined. In these figures, the calculated points are plotted together with their fitting to the simple Langmuir equation to give an estimated adsorption isotherm. For the methane molecule, as expected, there is a different behavior for the united-atom and the atomistic models. The former shows clear differences depending on wether the flexibility of graphene is or is not accounted form, the capacity of adsorption increasing with the introduced degree of flexibility in accordance

with previous results. The opposite behavior is observed for the atomistic models, although the influence of the explicit inclusion of flexibility is now very small. Once again, the atomistic model predicts a larger uptake of methane molecules than the unitedatom model combined with a much slower convergence rate.

For nitrogen, it can be seen that the united-atom model predicts a converged adsorption within the investigated pressure range due to the strong methane competition. The rigid model predicts a slightly lower uptake and slower convergence than the flexible ones. For the atomistic model it is striking that,

due to the very strong methane adsorption, the simulation with 350 molecules has very little nitrogen adsorbed on the sheet leading to a very low uptake. For this reason, we have fitted the Langmuir isotherm using only the first two simulation results as it is not intended to describe such a sudden drop in the uptake. Furthermore, the drop is caused by the methane more than by the nitrogen itself. The atomistic model predicts a very slightly lower uptake of nitrogen in the rigid simulation than when considering the flexible representations. As was expected, more nitrogen is adsorbed using the united-atom model than the atomistic model,

FIGURE 5 | Adsorption isotherms using the united-atom model (Left) and the atomistic model (Right) for the adsorption over graphene of the methane in the mixture for the four considered models of flexibility of the sheet. In both cases the uptake of methane is plotted against the total pressure of the gas in equilibrium.

because the methane is less strongly attracted to the graphene sheet in that case.

Kumar and Rodríguez-Reinoso (2013) have investigated the adsorption of the methane/nitrogen mixture on different carbonbased materials related to graphene: a slit-pore, a carbon nanotube, a carbon foam and a randomized carbon structure. Their grand canonical Monte Carlo simulations were performed in the pressure range between 0 and 50 atm, but with the important difference compared to us that they considered 90/10 and 95/5 methane/nitrogen mixtures. Their methane results were quite similar to ours, especially for the carbon foam, which showed an adsorption of about 14 mmol/g at 50 atm. The adsorption isotherm is, furthermore, very similar in shape to our equivalent atomistic model. The randomized carbon adsorption isotherm has an uptake of 10 mmol/g at 50 atm, while the carbon nanotube and the slit-pore show lower methane uptakes. For the nitrogen molecule, however, their results are somehow different in the sense that they predict the nitrogen uptake to be an order of magnitude lower than that of methane, while in our work the difference is less pronounced. Note that this seemingly big difference can be easily explained by the lower percentages (5 and 10 %) of nitrogen in their mixtures, to be compared with ours (50 %). While this had little influence on the methane molecule, being the dominant adsorbate, it is much more influential on the nitrogen adsorption. Vandenbrande et al. compared different molecular models and experimental results for different MOFs finding the highest methane uptake to be about 18 mmol/g at 70 atm. Moreover, this theoretical result well overestimated the associated experimental number of about 8 mmol/g (Vandenbrande et al., 2017). Similar conclusions are

found in the work by Becker et al. where the highest methane adsorption was found to be just above 12 mmol/g (Becker et al., 2017). As such, our results suggest that graphene outperforms many of the investigated MOFs for which adsorption results have been reported in the literature as was also indicated by Kumar et al. (2013) and Wu et al. (2015).

Finally, we have calculated the selectivity as follows

$$S\_{\rm AB} = \frac{\left(\frac{\chi\_{\rm A}}{\chi\_{\rm B}}\right)\_{\rm adorbed}}{\left(\frac{\chi\_{\rm A}}{\chi\_{\rm B}}\right)\_{\rm bulk}},\tag{7}$$

where, x is the mole fraction adsorbed of the specified molecule, while y is the mole fraction in the bulk of the specified molecule.

**Figure 7** shows how the separation capacity of graphene for the methane/nitrogen mixture varies with pressure depending both on the way in which the flexibility of graphene is considered and on the used intermolecular model. For the united-atom molecule, the rigid representation behaves again somewhat different than the flexible ones. Whereas the flexible models show a linear rise of the selectivity within the pressure range that was investigated, the rigid simulation shows a slightly curved increase which crosses the flexible curves at around 35 atm. Within the pressure range considered here, the deviation is more evident at low pressures and, indeed, the overestimation produced by completely neglecting the intramolecular motion of graphene is above 10%. Contrarily, the atomistic model, shows little influence of the flexibility with an exponential increase with rising pressure. As was seen previously, the stronger attraction of the atomistic methane strongly favors the methane adsorption leading to an even higher selectivity. An important point to note is the fact that completely neglecting the atomic structure of the gases leads to a clear underestimation of the selectivity of graphene. In fact, even though the effect is not so exaggerated at low pressures, at higher pressures the selectivity predicted by the oversimplified united-atom model is sensibly less than half the determined by the atomistic model. At any rate, the selectivity is good in all cases and rises with rising pressure since more methane molecules enter the system, pushing the nitrogen molecules out of the adsorption layer.

Even though (Dreisbach et al., 1999) have not explicitly reported selectivities for their carbon pores, the methane uptake is about five times higher at 60 atm than the nitrogen uptake as was the case in the work of methane/nitrogen adsorption on wet Tiffany coals by Fitzgerald et al. (2005). Both results are in agreement with the selectivities from our atomistic models in this work, which represents another argument justifying the superiority of such model over the simple united-atom one. In particular, it is noteworthy to stress that the latter produces values of the selectivity that are approximately half of those predicted by the atomistic model. Moreover, it is also significant the deviationespecially at low pressures-of the rigid graphene model with respect to the flexible ones when using the united-atom approach to describe the gas molecules.

#### 5. CONCLUSIONS

In this work, we have studied the influence of the flexibility of the graphene sheet on its separation ability of the methane/nitrogen gas mixture. The flexibility was introduced via three intramolecular force fields taken from the literature, two of which contained stretching, bonding and torsional terms, while a third one lacked the latter contribution. Two fields were specifically designed for graphene, while a third one was originally intended for use on carbon nanotubes. Furthermore we studied the different behavior of a united-atom model and an atomistic model during these simulations.

In general, we have confirmed that graphene shows a strong preference for methane over nitrogen. Using both models, the methane posed a strong competition toward the nitrogen and pushed the nitrogen out of the first adsorption layer, forcing it to form a second adsorption layer or go into gas phase. This effect was found stronger for the atomistic gas models than for the united-atom models, which is expected to give a poorer representation as it does not takes into account orientation effects. The difference, which is at times large, calls for care when assuming united-atom models in these types of simulations.

Concerning the treatment of flexibility, we showed that, indeed, it influences the behavior of the graphene sheet as a separator of the methane/nitrogen gas mixture. For the unitedatom model, neglecting the flexibility of the graphene sheet leads to predict lower methane uptakes that if such flexibility is taken into account. The atomistic model on the other hand predicted a slightly higher methane uptake. Similar results were found for nitrogen, leading to the conclusion that for the united-atom model, a lower amount of gas molecules in general is predicted to be adsorbed if the sheet is supposed to be rigid. The atomistic model, on the other hand, predicts a larger general gas adsorption also on the considered rigid graphene sheet. Observing the combination of these results in the selectivity of the four models of the intramolecular motions of graphene, we find that the united-atom model in conjunction with the rigid representation predicts the lowest selectivity for the methane/nitrogen mixture in the largest portion of the pressure range investigated, while the atomistic model shows very similar behavior for the rigid and the flexible graphene models. Moreover, since graphene is, in fact, flexible, it is then clear that in order to safely disregard its internal movements an atomistic model is definitely required, the simplified united-atom model being absolutely inadequate. On the other hand, if the flexibility of graphene is explicitly accounted for by means of the appropriate force field -the field

#### REFERENCES


2 m (Fthenakis et al., 2017) conceptually being the one of choice-, both atomistic and united-atom models provide very similar results.

#### AUTHOR CONTRIBUTIONS

JV, IG, and AS ran the first principles calculations and developed the subsequent interaction force field. NF-L, AL, and MR developed and ran the theoretical and molecular dynamics calculations.

#### FUNDING

The project leading to this publication has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 642294.

#### ACKNOWLEDGMENTS

NF-L and AL thank MIUR and the University of Perugia for the financial support of the AMIS project through the Dipartimenti di Eccellenza programme. NF-L also acknowledges the Fondo Ricerca di Base 2017 (RICBASE2017BALUCANI) del Dipartimento di Chimica, Biologia e Biotecnologie della Università di Perugia for financial support. AL acknowledges financial support from MIUR PRIN 2015 (contract 2015F59J3R\_002) and the Dipartimento di Chimica, Biologia e Biotecnologie (Fondo Ricerca di Base 2017).


quantum chemistry and molecular dynamics. J. Phys. Chem. A 120, 6451–6458. doi: 10.1021/acs.jpca.5b12574


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Vekeman, Faginas-Lago, Lombardi, Sánchez de Merás, García Cuesta and Rosi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Compendium of the Reactions of H3O<sup>+</sup> With Selected Ketones of Relevance to Breath Analysis Using Proton Transfer Reaction Mass Spectrometry

Michaela Malásková1†, David Olivenza-León2†, Felix Piel 3,4†, Paweł Mochalski 1,5 \*, Philipp Sulzer <sup>3</sup> , Simone Jürschik <sup>3</sup> , Chris A. Mayhew1,2 and Tilmann D. Märk 3,4

#### Edited by:

Amala Dass, University of Mississippi, United States

#### Reviewed by:

Michael H. Nantz, University of Louisville, United States Renato Zenobi, ETH Zürich, Switzerland

> \*Correspondence: Paweł Mochalski pawel.mochalski@uibk.ac.at

†Early Stage Researchers who have contributed equally to the measurements, data analyses and contribution to the completion of this paper

#### Specialty section:

This article was submitted to Analytical Chemistry, a section of the journal Frontiers in Chemistry

Received: 08 March 2019 Accepted: 17 May 2019 Published: 13 June 2019

#### Citation:

Malásková M, Olivenza-León D, Piel F, Mochalski P, Sulzer P, Jürschik S, Mayhew CA and Märk TD (2019) Compendium of the Reactions of <sup>H</sup>3O<sup>+</sup> With Selected Ketones of Relevance to Breath Analysis Using Proton Transfer Reaction Mass Spectrometry. Front. Chem. 7:401. doi: 10.3389/fchem.2019.00401 1 Institute for Breath Research, Fakultät für Chemie und Pharmazie, Leopold-Franzens-Universität Innsbruck, Dornbirn, Austria, <sup>2</sup> Molecular Physics Group, School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom, <sup>3</sup> IONICON Analytik Gesellschaft m.b.H., Innsbruck, Austria, <sup>4</sup> Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria, <sup>5</sup> Institute of Chemistry, Faculty of Mathematics and Natural Sciences, Jan Kochanowski University, Kielce, Poland

Soft chemical ionization mass spectrometric techniques, such as proton transfer reaction mass spectrometry (PTR-MS), are often used in breath analysis, being particularly powerful for real-time measurements. To ascertain the type and concentration of volatiles in exhaled breath clearly assignable product ions resulting from these volatiles need to be determined. This is difficult for compounds where isomers are common, and one important class of breath volatiles where this occurs are ketones. Here we present a series of extensive measurements on the reactions of H3O<sup>+</sup> with a selection of ketones using PTR-MS. Of particular interest is to determine if ketone isomers can be distinguished without the need for pre-separation by manipulating the ion chemistry through changes in the reduced electric field. An additional issue for breath analysis is that the product ion distributions for these breath volatiles are usually determined from direct PTR-MS measurements of the compounds under the normal operating conditions of the instruments. Generally, no account is made for the effects on the ion-molecule reactions by the introduction of humid air samples or increased CO<sup>2</sup> concentrations into the drift tubes of these analytical devices resulting from breath. Therefore, another motivation of this study is to determine the effects, if any, on the product ion distributions under the humid conditions associated with breath sampling. However, the ultimate objective for this study is to provide a valuable database of use to other researchers in the field of breath analysis to aid in analysis and quantification of trace amounts of ketones in human breath. Here we present a comprehensive compendium of the product ion distributions as a function of the reduced electric field for the reactions of H3O+. (H2O)<sup>n</sup> (n = 0 and 1) with nineteen ketones under normal and humid (100% relative humidity for 37 ◦C) PTR-MS conditions. The ketones selected for inclusion in this compendium are (in order of increasing molecular weight): 2-butanone; 2-pentanone; 3-pentanone; 2-hexanone; 3-hexanone; 2-heptanone; 3-heptanone; 4-heptanone; 3-octanone; 2-nonanone; 3-nonanone; 2 decanone; 3-decanone; cyclohexanone; 3-methyl-2-butanone; 3-methyl-2-pentanone; 2-methyl-3-pentanone; 2-methyl-3-hexanone; and 2-methyl-3-heptanone.

Keywords: ketones, breath analysis, PTR-MS, reduced electric field, fastGC

## INTRODUCTION

Depending on the actual mass resolution, current proton transfer reaction mass spectrometers (PTR-MS) are easily capable of separating many protonated isobaric compounds through a peak fitting procedure providing their mass separation is at least 0.01 Da. The selectivity of PTR-MS can be further improved by the manipulation of the ion-molecule chemistry that occurs between a reagent ion and a given isobar in the drift tube to produce different product ions. This can be achieved by (i) changing the reagent ion, examples for which have been presented in the literature for explosives (Sulzer et al., 2013; Agarwal et al., 2014), or psychoactive substances (Acton et al., 2014; Lanza et al., 2015), and/or (ii) the collisional processes in the drift tube through changing the reduced electric field. Changes in the reduced electric field (the ratio of the electric field strength, E, to the gas number density, N, in the drift tube) to alter the product ion distributions have been demonstrated in the areas of homeland security, e.g., detection of chemical warfare agents (Petersson et al., 2009), explosives (Mayhew et al., 2010; Sulzer et al., 2012, 2013), and rape drugs (Jürschik et al., 2012), and in environmental science, e.g., the identification of monoterpenes (Materic et al., 2017 ´ ).

This application of changing collisional processes through changes in the reduced electric field to enhance compound selectivity has led to the development of a computer- controlled fast switching drift tube voltage (González-Méndez et al., 2018) and the adaptation of a radio frequency ion-funnel drift tube (González-Méndez et al., 2016).

Although today there are several ways to enhance the selectivity of PTR-MS for isobaric compounds, distinguishing isomeric compounds is still more of an issue. With no preseparation of isomeric compounds, rarely can isomers be easily identified using PTR-MS through differences in product ion distributions, even if the ion-molecule chemistry occurring in the drift tube of PTR-MS is manipulated in a structured way. One study has demonstrated how reactions of O<sup>+</sup> 2 and NO<sup>+</sup> can be used to distinguish two isomeric mephedrone substitutes (4 methylethcathinone and N-ethylbuphedrone) whereas reactions with H3O<sup>+</sup> could not (Lanza et al., 2013). However, such examples in ion-isomer chemistry are usually the exception rather than the rule.

Isomers of ketones are so far difficult to identify unambiguously with a PTR-MS instrument. Pre-separation offered by standard gas chromatography (GC) techniques can be used, but they take away the main advantage of PTR-MS, namely its real-time analytical capabilities. The recent development of fast gas chromatography (fastGC) coupled to PTR-MS provides a compromise between real-time measurements, ensuring reasonably fast analysis (within approximately 90 s), whilst still taking advantage of limited pre-separation of compounds to improve the analytical specificity of PTR-MS (Ruzsanyi et al., 2013; Romano et al., 2014; Anderson, 2015).

In this paper we have used the fastGC PTR-MS technique in order to accurately determine the product ion distributions for a large selection of ketones as a function of reduced electric field so that we can unambiguously determine their product ions, without any concerns from impurities in the samples. Ketones have been selected for this study, because they form a common class of compounds found in breath, blood and urine (de Lacy Costello et al., 2014), and their detection holds many possibilities for non-invasive diagnostic and monitoring procedures in health services. One example is the diagnosis of ketosis, resulting from the elevation of ketone bodies in the blood. Detecting changes in ketone concentrations could thus be used to diagnose diabetic ketosis. A key ketone found in high concentrations in breath is acetone, the production of which (as for most ketones) is linked to fat metabolism, and hence its detection in breath could provide a window to predict fat loss (Anderson, 2015). Given the importance of acetone in the breath, it has been investigated numerous times with PTR-MS, and hence acetone does not form part of this current study. Less attention has been given to other ketones in PTR-MS studies. Hence this investigation has focused its attention on other important breath ketones, although generally found in much lower concentrations in the breath than for acetone. This has produced a wealth of new data, providing a useful database of the product ion distributions resulting from the reactions of H3O<sup>+</sup> and H3O+. (H2O) with ketones using PTR-MS.

Awareness of possible changes in the reaction processes occurring in the drift tube of a PTR-MS instrument resulting from changes in humidity have been known for some time (Warneke et al., 2001; Tani et al., 2003, 2004). Breath samples are humid, and thus product ion distributions determined under the "normal" operating conditions of PTR-MS (e.g., using purified air or nitrogen as the buffer gas in the drift tube) may not be a true reflection of those associated with a humid gas sample in the drift tube. This is because it can be expected that a higher humidity associated with breath samples (100% relative humidity at 32– 34◦C) will affect the product ion distributions through changes in the energy associated with the collisional processes. Furthermore, if protonated water clusters can react with a breath volatile via proton transfer, far less energy will be available in the reaction than for that associated with H3O+, and with higher humidity comes a greater production of protonated water clusters for a given reduced electric field. This effect will generally be more important at low reduced electric field values (i.e., < ∼120 Td, 1 Td = 10−<sup>17</sup> V cm<sup>2</sup> ) when collisions will lead to less break-up of the protonated water clusters to H3O<sup>+</sup> and neutral water(s). Moreover, if the protonated water clusters cannot react with a volatile, then a reduction in the sensitivity of detection of that compound results. Finally, differences in product ion

distributions will arise if secondary processed occur, such as when primary product ions react with water.

A review of the literature shows that PTR-MS product ion distributions of compounds of interest to breath research are generally determined under the "normal" operating conditions, i.e., where the humidity in the drift tube is determined by the diffusion of water from the discharge region into the drift tube, which will be less than that associated with a breath sample. An objective of this work is to improve our knowledge on the effects of humidity on product ion distributions.

The first studies associated with investigating the effects of humidity on reaction processes in PTR-MS focused on sensitivity issues. For example, Warneke et al. (2001) showed how the sensitivity for the detection of benzene and toluene at fixed reduced electric fields decreased with increasing humidity, owing to unreactive H3O+.(H2O)<sup>n</sup> clusters. Hence, de Gouw et al. (2003) suggested employing a humidity factor to determine the concentrations of a compound if it reacts with protonated water clusters, a factor which takes into account the efficiencies of the proton transfer reaction and the transmission of H3O+.(H2O) relative to that of H3O+. These factors were determined and used to correct for the influences of humidity on the detection sensitivity for methanol, acetonitrile, acetaldehyde, acetone, benzene and toluene by de Gouw and Warneke (2007). A PTR-MS investigation of the effects of humidity on the product ion distributions resulting from the reactions of H3O<sup>+</sup> with two sesquiterpenes (α-cedrene and longifolene) was undertaken by Demarcke et al. (2009). In that study, no substantial influence of the humidity in the drift tube on the product ion yields was observed. More recently, the effects of humidity on product ion distributions have been investigated for α-pinene, δ-limonene, and longifolene by Kari et al. (2018) at two different E/N values (80 Td and 130 Td) (Kari et al., 2018), and for more than 20 volatile organic compounds (VOCs), including aldehydes, ketones, aromatic compounds and hydrocarbons by Trefz et al. (2018) at one fixed E/N (139 Td) (Trefz et al., 2018). In the former study, no significant changes in the product ion distributions were observed. However, Trefz et al. reported large differences in VOC intensities between "dry" and "humid" samples. Thus, the effect of humidity appears to depend very much on the volatile chemical compound.

In this paper we present details on the reactions of H3O<sup>+</sup> and associated water clusters with a selected number of ketones over a large reduced electric field range of 100–220 Td, and compare product ions obtained under "normal" and "humid" operating conditions of the drift tube. This work demonstrates that changes in product ion distributions do occur for fixed E/N for different humidities, and hence it clearly demonstrates that humidity effects should be considered when relying on product ion distributions for undertaking breath research with a PTR-MS.

#### MATERIALS AND METHODS

#### Sample Preparation

Samples were prepared in two different ways depending on the humidity of the measurement.

For measurements under normal conditions, an open glass vial containing a ketone was purged with high purity N<sup>2</sup> (Alphagaz 1, Air Liquide GmbH., Austria), which had been previously passed through a P300-1 Filter (VICI AG, Switzerland) for purification (6.0). The vial was then covered with parafilm. Using a glass syringe a quantity of headspace was taken from the vial through the parafilm. This headspace containing the ketone and N<sup>2</sup> was then injected into a PTFE bag filled with 3L of dry 6.0 N2, which was already connected to the inlet of the PTR-ToF-MS instrument. This injected volume into the bag varied from 5 µL to 10 mL, depending on the volatility of the ketone.

Humid samples were prepared using a Liquid Calibration Unit (LCU, IONICON Analytik GmbH, Austria). The LCU generates defined gaseous concentrations from aqueous solutions of volatile and semi-volatile organics. A description of the LCU has already been provided in detail by Fischer et al. (2013). Briefly, a homebuilt liquid flow controller injects a defined flow into a nebuliser (X175, Burgener Research Inc., United Kingdom). Vaporization of the aqueous solution produces micro droplets, which are evaporated in a heating chamber maintained at 100◦C. The heating chamber is being constantly flushed by a buffer gas, e.g., zero air or N2, diluting the organic sample and thus generating a continuous stream of a defined trace gas mixture.

For this study, to generate the humid samples, 16 mL glass vials, kept at a constant temperature of 30◦C, were filled with a trace quantity of a ketone [1–10 µL (depending on the volatility of the ketone)] diluted in 100 mL of purified water. A sample flow of this ketone/water mixture at 35 µL/min was diluted in a N<sup>2</sup> flow of 950 mL/min to achieve a 5% absolute humidity. The combined flow was then directly connected to the fastGC inlet system of the PTR-ToF-MS instrument.

For both the dry and humid measurements, the dilution of the samples were prepared to yield a concentration of the ketone in the drift tube to be approximately 100 ppbv.

The experiments presented here were done through an automated measurement procedure. This consisted of background measurements for 5 min. For the dry mixtures, this involved the PTFE bag filled only with purified N2. For the humid standards this step involved a vial containing only purified water. Next, the prepared samples were directed to the drift tube for a 2-min stabilization period, which was next followed by 2 min and 40 s of fastGC measurement at an E/N of 180 Td to help identify the product ions produced in the drift tube for a given ketone and a 26-min E/N set of measurements over the range 100–220 Td in steps of 10 Td (1 min each), in both directions, to provide two data sets.

#### FastGC PTR-ToF-MS

Details of PTR-ToF-MS and methods of operation have been reviewed extensively in the literature (Ellis and Mayhew, 2014), and therefore only brief details are required here. For this study, measurements were taken using a PTR-TOF 8000 with a fastGC add-on (IONICON Analytik GmbH, Austria) (Jordan et al., 2009; Graus et al., 2010). Briefly, water vapor is introduced into a hollow cathode discharge to generate H3O+.(H2O)<sup>n</sup> (n = 0, 1, 2, . . . ), initially through electron ionization of water and subsequent ion-molecule reactions with water. These reagent ions are then

TABLE 1 | Product ions identified and their associated product ion branching ratios (percentages) measured at reduced electric fields of 100, 140, and 180 Td resulting from the reactions of H3O<sup>+</sup> with several ketones.


(Continued)

#### TABLE 1 | Continued


Values for the product ion branching percentages are given whilst operating the drift tube under "normal" conditions and under "humid" (breath humidity) conditions. Errors in the branching percentages are estimated to be <20%.

3

transferred to the drift tube via a focusing lens. The distribution of the protonated water clusters in the reaction region depends on the E/N value and the humidity in the drift tube as shown in **Figure 1**.

These reagent ions are then transported down the drift tube under the influence of the uniform electric field. Analytes are injected into the drift tube through an inlet pipe. Proton transfer from hydronium to the analyte takes place within the drift tube if the proton affinity (PA) of the analyte is higher than that of water (PA(H2O) = 691 kJ mol−<sup>1</sup> ). Proton transfer can be nondissociative and dissociative. However, it should be stressed that fragmentation of the protonated molecule can be a barrierless process and occur spontaneously, or it can be induced by the collision of the reagent ions with analyte and/or charged analyte with the buffer gas.

For all measurements the drift tube was kept at a pressure of 2.3 mbar, with both the inlet system and drift tube being maintained at 100◦C. The collisional energies of the reagent and product ions were controlled by the value of the reduced electric field. For this study we kept the drift tube at constant pressure and temperature (and hence constant N), and changed the drift tube voltage to alter the value of E/N. The drift voltage could be changed from 410 V up to a maximum of 890 V. For the applied values of the drift tube pressure and temperature these values correspond to an E/N range from 100 to 220 Td.

Using a dry buffer gas in the drift tube of a PTR-MS instrument does not mean that it is operated under dry conditions, since some amounts of water vapor diffuse from the hollow cathode. This condition will be denoted as "normal" operating condition later in this paper. When a water saturated buffer gas was used, this is referred in the text as operating the drift tube under "humid" conditions.

FastGC was used to separate analytes of interest from possible contaminants in the produced standards. The fastGC add-on used in this study is a modification of the setup used by Romano et al. (2014) and Ruzsanyi et al. (2013). Therefore, only the modifications relevant for this study will be provided here. An MXT-1 column (10 m × 0.53 mm, film thickness 0.25µm, dimethyl polysiloxane phase, Restek, USA) was used. The samples were injected into a 0.5 ml sample loop made of passivated stainless steel. A custom-made valve block consisting of four three-way valves and a needle valve has been replaced by a 10-port passivated valve (VICI AG, Switzerland) and a three-way gas valve made from polyether ether ketone (PEEK) was used. All parts of the inlet system are installed within the oven that houses the drift tube to prevent cold spots. This revised setup enabled constant filling of the sample loop and constant backflushing of the capillary column with the carrier gas. 8 ml/min and 20 ml/min of 6.0 N<sup>2</sup> were used as carrier gas and make-up gas, respectively. A voltage ramp of 0.5 V/s from 10 V up to 80 V was applied raising the temperature of the capillary column from room value up to 240◦C.

#### Chemicals

The following liquid substances were purchased from Sigma-Aldrich: 2-pentanone (98%), 3-pentanone (99%), 2-hexanone (98%), 3-hexanone (98%), 3-heptanone (analytical standard), 4-heptanone (98%), 2-nonanone (99%), 3-nonanone (99%), 2 decanone (98%), cyclohexanone (99.8%), 3-methyl-2-pentanone (99%), 2-methyl-3-pentanone (97%), 2-methyl-3-hexanone (98%), and 2-methyl-3-heptanone (99%). 2-butanone (99.5%), 2-heptanone (98.5%), and 3-methyl-2-butanone (98.5%) were purchased from Honeywell. 3-octanone (99%) and 3-decanone (97%) were purchased from Acros Organics and SAFC, respectively. These were used with no further purification.

#### Data Analysis

The "PTR-MS Viewer" (IONICON Analytik GmbH, Austria) was used to identify peaks in the mass spectra and to extract peak data. Raw peak data, i.e., data not corrected for transmission factors, were normalized to 1 million reagent ions and had any backgrounds subtracted. By using the "raw" data, the product ion distributions we have determined here can be more easily compared with other measurements using different PTR-MS instruments. However, we emphasize that the product ion distributions that have been determined for the selection of ketones chosen for this study have to be taken with some caution if a PTR-TOF 8000 is not being used, and that researchers need to determine product ion distributions for their own instruments and conditions.

#### RESULTS AND DISCUSSION

**Table 1** presents a summary of the product ion distributions (percentages) for all the ketones investigated in this study at three selected reduced electric fields, namely 100 Td, 140 Td, and 180 Td under normal and humid conditions. These values give a good representation of all product ions observed and quickly illustrate the effects of humidity on the product ion distributions, if any. The table starts with the thirteen linear chained ketones in order of molecular weight (MW), followed by the one cyclic ketone (cyclohexanone), and finishing with five non-linear ketones, also presented in order of increasing nominal MW, and, for low E/N (see **Figure 1**), from reactions of H3O+.H2O with those ketones whose proton affinities are greater than that associated with (H2O)<sup>2</sup> (808 kJ mol−<sup>1</sup> ), i.e., 2-butanone (827 kJ mol−<sup>1</sup> ), 2-pentanone (833 kJ mol−<sup>1</sup> ), 3-pentanone (837 kJ mol−<sup>1</sup> ), and 3-methyl-2-butanone (836 kJ mol−<sup>1</sup> ).

The dependence of the product ion branching percentages as a function of E/N are shown graphically in **Figure 2**. The chemical formulae of the product ions given in **Table 1** and **Figure 2** have been tentatively identified via the exact m/z (to 2 decimal places) and isotope (13C) intensities. Only product ions who make a contribution to the branching percentage of at least 3% at any reduced electric field value are included in the table and figure.

Below approximately 140 Td, the protonated parent is the dominant product ion observed for all ketones. This is in reasonable agreement with other PTR-MS studies. For example, in the study by Buhr et al. (2002) at one reduced electric field of approximately 140 Td, the authors showed that proton transfer from H3O<sup>+</sup> to ketones will predominantly be non-dissociative, regardless of chain length. This limited dissociation observed in PTR-MS for reduced electric fields below 140 Td also agrees with studies using the thermalized conditions in Selected Ion Flow Tube—Mass Spectrometry (SIFT-MS) (Spanel et al., 1997; Smith et al., 2003, 2019), and suprathermal Selected Ion Flow Drift Tube (SIFDT) investigations (Specyvyi et al., 2017).

Above 140 Td, fragmentation of the protonated parent is observed, a fact that was not reported by Buhr et al. for 2 butanone, 2-hexanone, 2-heptanone, 3-heptanone, 4-heptanone, 3-octanone, 2-nonanone, and 2-decanone, for which only the protonated parent is observed. Limited fragmentation is, however, reported by Buhr et al. at 140 Td for 2-pentanone, with a product ion being observed at m/z 45, which we also observe and assign it to be C2H5O<sup>+</sup> (protonated acetaldehyde) although it is found with a much higher relative intensity compared to the protonated parent in our study than found by Buhr et al. This difference in intensity is most probably associated with differences in the transmission of ions, because Buhr et al. used a quadrupole mass spectrometer.

In the present study, significant percentages of hydrocarbon ions, CnH<sup>+</sup> <sup>m</sup>, are seen. This agrees with another E/N study of the ketones, 2-butanone, 2-pentanone, 2-hexanone, 2 heptanone, and cyclohexanone by Pan et al. (2017), who used a dipolar proton transfer reaction (quadrupole) mass spectrometer. Their study, which covered the reduced electric fields of approximately 50–110 Td, reported the m/z values of the product ions we have found, but observed substantially more fragmentation than we detected, even at their low E/N values. The amount of fragmentation reported at low E/N (as low as 50 Td) by Pan et al. is surprising, given that at these E/N values the reagent ion signal in our instruments would be protonated water clusters. This again illustrates that care must be taken when comparing results from different PTR-MS instruments.

In our study, typically 2–7 fragmentation channels have been observed. However, many of them were significant only at higher reduced electric field values. For instance, C3H + 3 and C3H + 5 ions occur only for E/N values higher than about 150 Td. Thus, for E/N values up to about 130 Td, the protonated molecules are dominant having well-above 80% branching percentages associated with that channel. Interestingly, the highest number of fragmentation channels was noted for 3-hexanone (7 channels) and C7 ketones; 2-heptanone (5 channels), 3-heptanone (6 channels), 4-heptanone (5 channels), and 2-methyl-3-hexanone (6 channels). As expected, heavier ketones are found to fragment considerably less.

For several ketones, the proton transfer process is followed by the elimination of an H2O molecule leading to the observed hydrocarbon ions CnH + 2n−1 . However, these channels have small associated branching percentages, and at higher values of the reduced electric field undergo further fragmentation.

The channel leading to the C2H5O<sup>+</sup> ion is very abundant in fragmentation patterns of C5 and C6 ketones. Interestingly, the mass spectra of C8 and C9 ketones do not have oxygencontaining fragmentation channels.

High humidity reduces the fragmentation of ketones. Interestingly, this effect is most evident for the E/N values of 150– 160 Td. For example, the abundance of the protonated parent ion of 2-pentanone under normal conditions for 150 Td is 47%; whereas, in humid air, it has a branching percentage of 69%. The analogous values for 3-nonanone are 48 and 79%, respectively. This interesting dependence can be attributed to the formation of considerable amounts of protonated water clusters, which can react with ketones of interest. Consequently, far less energy is available for fragmentation in such reactions than for those associated with H3O+. At the higher E/N values formation of water clusters is suppressed and, thereby, the positive effect of humidity on having reduced fragmentation is weakened. The general effect of the higher humidity is to shift the product ion branching percentage curves by approximately 20 Td to higher E/N.

To illustrate the quality of the data, a mass spectrum recorded at 180 Td for 3-hexanone is provided in **Figure 3**. This highlights some product ions which are associated with the volatile, but are not included in the tabulation or **Figure 2**, because their contributions to the total relative abundance are <3% for any reduced electric field value.

#### CONCLUSIONS

This work provides a large body of data and an extensive library of product ion distributions as a function of reduced electric field for the reactions of H3O+.(H2O)<sup>n</sup> (n = 0 and 1) with a selection of ketones using the powerful analytical technique of PTR-ToF-MS. Although the study was originally conceived owing to the importance of ketones in the breath, and the need to determine what product ions should be monitored using PTR-MS, these results should be of interest to researchers working in other areas such as the environmental sciences and atmospheric chemistry.

A key outcome from this work is that product ion distributions at any specific reduced electric field can only be used to provide an indication of what ion-molecule channels are occurring. Detailed branching percentages are only specific to a given PTR-MS instrument and then under the specific operational conditions, not least the humidity present in the drift tube, as demonstrated in the results from this study.

Of the ketone isomers investigated in this study, it is apparent that it is not possible to provide any selectivity by manipulating

#### REFERENCES


the ion chemistry through changes in the reduced electric field. For this to be accomplished, the use fast gas chromatography coupled to PTR-MS is needed when analyzing gas samples that contain a mixture of ketone isomers, as often occurs in breath samples.

In the context of the ketones analyses in real breath samples by PTR-MS, the functional isomers of species from this chemical family (such as e.g., aldehydes) also need to be considered and investigated as their protonated forms cannot be separated from the respective protonated ketones. The ketones' PTR-MS analyses in the presence of their functional isomers require further studies. However, it is worth mentioning here, that aldehydes undergo significant fragmentation in the PTR-MS instruments and the abundance of their protonated parent ions is usually very small (<10%) (Buhr et al., 2002; Schwartz et al., 2009). Consequently, the presence of aldehydes in the breath sample can only have minor influence on the parent ions of the respective ketones.

#### DATA AVAILABILITY

The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.

#### AUTHOR CONTRIBUTIONS

MM, DOL, and FP are Early Stage Researchers employed on the EU IMPACT ITN. They contributed equally to the experimental measurements, data analyses and contribution to the completion of this paper. PM proposed the study. PM, PS, SJ, CAM, and TDM contributed equally to the writing of the paper.

#### ACKNOWLEDGMENTS

We thank the Marie Skłodowska-Curie Actions Innovative Training Network: Ion-Molecule Processes for Analytical Chemistry Technologies (IMPACT) (www.impact-h2020itn.com) which has supported this research through the European Commission's HORIZON 2020 Programme under Grant Agreement Number 674911. The first three authors of this paper, MM, DOL, and FP are Early Stage Researchers in this IMPACT network.


mass spectrometry. Int. J. Mass Spectrom. 369, 81–86. doi: 10.1016/j.ijms.2014. 06.006


**Conflict of Interest Statement:** FP and TDM was employed by company IONICON Analytik Gesellschaft m.b.H.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Malásková, Olivenza-León, Piel, Mochalski, Sulzer, Jürschik, Mayhew and Märk. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# A New Insight on Stereo-Dynamics of Penning Ionization Reactions

Stefano Falcinelli <sup>1</sup> \*, Fernando Pirani <sup>2</sup> , Pietro Candori <sup>1</sup> , Brunetto G. Brunetti <sup>2</sup> , James M. Farrar <sup>3</sup> and Franco Vecchiocattivi <sup>1</sup>

*<sup>1</sup> Department of Civil and Environmental Engineering, University of Perugia, Perugia, Italy, <sup>2</sup> Department of Chemistry, Biology and Biotechnologies, University of Perugia, Perugia, Italy, <sup>3</sup> Department of Chemistry, University of Rochester, Rochester, NY, United States*

#### Edited by:

*Doo Soo Chung, Seoul National University, South Korea*

#### Reviewed by:

*Koichi Ohno, Tohoku University, Japan Balakrishnan Naduvalath, University of Nevada, Las Vegas, United States*

> \*Correspondence: *Stefano Falcinelli stefano.falcinelli@unipg.it*

#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *11 January 2019* Accepted: *31 May 2019* Published: *18 June 2019*

#### Citation:

*Falcinelli S, Pirani F, Candori P, Brunetti BG, Farrar JM and Vecchiocattivi F (2019) A New Insight on Stereo-Dynamics of Penning Ionization Reactions. Front. Chem. 7:445. doi: 10.3389/fchem.2019.00445* Recent developments in the experimental study of Penning ionization reactions are presented here to cast light on basic aspects of the stereo-dynamics of the microscopic mechanisms involved. They concern the dependence of the reaction probability on the relative orientation of the atomic and molecular orbitals of reagents and products. The focus is on collisions between metastable Ne<sup>∗</sup> ( <sup>3</sup>P2,0) atoms with other noble gas atoms or molecules, for which play a crucial role both the inner open-shell structure of Ne<sup>∗</sup> and the HOMO orbitals of the partner. Their mutual orientation with respect to the intermolecular axis controls the characteristics of the intermolecular potential, which drives the collision dynamics and the reaction probability. The investigation of ionization processes of water, the prototype of hydrogenated molecules, suggested that the ground state of water ion is produced when Ne<sup>∗</sup> approaches H2O perpendicularly to its plane. Conversely, collisions addressed toward the lone pair, aligned along the water C2v symmetry axis, generates electronically excited water ions. However, obtained results refer to a statistical/random orientation of the open shell ionic core of Ne<sup>∗</sup> . Recently, the attention focused on the ionization of Kr or Xe by Ne<sup>∗</sup> , for which we have been able to characterize the dependence on the collision energy of the branching ratio between probabilities of spin orbit resolved elementary processes. The combined analysis of measured PIES spectra suggested the occurrence of contributions from four different reaction channels, assigned to two distinct spin-orbit states of the Ne<sup>∗</sup> ( <sup>3</sup>P2,0) reagent and two different spin-orbit states of the ionic M+( <sup>2</sup>P3/2,1/2) products (M = Kr, Xe). The obtained results emphasized the reactivity change of <sup>3</sup>P<sup>0</sup> atoms with respect to <sup>3</sup>P2, in producing ions in <sup>2</sup>P3/<sup>2</sup> and <sup>2</sup>P1/<sup>2</sup> sublevels, as a function of the collision energy. These findings have been assumed to arise from a critical balance of *adiabatic* and *non-adiabatic effects* that control formation and electronic rearrangement of the collision complex, respectively. From these results we are able to characterize for the first time, according to our knowledge, the state to state reaction probability for the ionization of Kr and Xe by Ne<sup>∗</sup> in both <sup>3</sup>P<sup>2</sup> and <sup>3</sup>P<sup>0</sup> sublevels.

Keywords: Penning ionization, stereo-dynamics, metastable atoms, transition state, electron spectroscopy, crossed molecular beams

## INTRODUCTION

Penning ionization is a reaction that occurs between an excited atom X<sup>∗</sup> and another partner M forming an excited collision complex (X···M)<sup>∗</sup> . This complex, being immersed in the ionization continuum, spontaneously auto-ionizes

$$\text{(\text{ $X}$ ^\* + M \rightarrow \text{( $X\cdots M$ )}^\* \rightarrow \text{( $X\cdots M$ )}^+ + \text{ e}^- \rightarrow \text{ ion products}$$

leading to various ionic products, since in Penning ionization reactions the intermediate ionic complex (X···M)<sup>+</sup> can evolve producing different final ions: M<sup>+</sup> Penning ions, XM<sup>+</sup> associate ions, and—in the case of molecular targets—rearrangement and dissociative ionizations are also possible (Niehaus, 1973; Brunetti and Vecchiocattivi, 1993; Siska, 1993). In particular, ionization occurs when (X···M)<sup>∗</sup> exhibits a lifetime, with respect to autoionization, shorter than the collision time, typically in the order of ∼10−<sup>12</sup> s. Moreover, Penning ionization, collisional autoionization, and chemi-ionization are often considered to be synonyms of this kind of reactions (Niehaus, 1973; Brunetti and Vecchiocattivi, 1993; Siska, 1993).

A scheme of a typical molecular beam experiment, for the investigation of Penning ionization processes under single collision condition, is reported in **Figure 1A**. The used setup in our experiments is a crossed beam device already outlined in previous papers (Brunetti et al., 1998, 2006). Three differentially pumped vacuum chambers during the experiment are maintained at a pressure ranging between ∼10−<sup>7</sup> and 10−<sup>8</sup> mbar. Two chambers are used to produce a beam of metastable rare gas atoms, mainly He<sup>∗</sup> and Ne<sup>∗</sup> , employing either electron bombardment and microwave discharge beam sources specially developed in our laboratory. In a third chamber the metastable atoms beam induces the single reactive collision event under study, crossing at right angle a secondary effusive beam of target particles that, in the case of the present experiments, are of Kr, Xe atoms, or of H2O molecules. Mass spectrometric determinations can be performed extracting product ions, coming out from the monitored auto-ionization process, by an ion optics device and filtering them by a quadrupole mass spectrometer placed below the scattering volume. A channel electron multiplier detects selected ions, recording their relative abundances. For the collection of emitted electrons and the measure of their kinetic energy content, realizing a real spectroscopy of the transition state of the studied reactions, we use a dedicated and specially designed hemispheric electrostatic analyzer located above the scattering center.

Usually, studies are carried out using metastable He<sup>∗</sup> (2 <sup>1</sup> S0, 3 S1) with the electron configuration (e.c.) 1s 2s, Ne<sup>∗</sup> ( <sup>3</sup>P2,0) with e.c. 2p<sup>5</sup> 3s or Ar<sup>∗</sup> ( <sup>3</sup>P2,0) atoms having e.c. 2p<sup>5</sup> 3s, since they are characterized by an energy high enough to ionize most atoms or molecules and also possess a life-time longer than the collision time, even in slow collisions. The formed charged products are typically detected and analyzed in energy (the electrons) and mass (the ions) as a function of the collision energy (Niehaus, 1973; Brunetti and Vecchiocattivi, 1993; Siska, 1993).

These barrier-less reactions play an important role in biology, physics and chemistry of plasmas, planetary atmospheres, and interstellar environments (Falcinelli et al., 2015a, 2016a). They are driven by an optical potential W, defined as combination of a real, V<sup>t</sup> , and an imaginary part, Ŵ, which determine: (a) the dynamics of reactants approach and products separation, (b) the triggering of the electronic rearrangement within the transition state, respectively (Niehaus, 1973; Brunetti and Vecchiocattivi, 1993; Siska, 1993; Biondini et al., 2005a,b). More specifically, the imaginary part plays a crucial role in describing the disappearance probability of reactants, with their transformation into the final ionic products (Falcinelli et al., 2013). Accordingly, W is defined as

$$\mathbf{W} = \mathbf{V}\_t - \frac{\hbar}{2}\boldsymbol{\Gamma} \tag{1}$$

The strength of both these components is expected to vary with the center-of-mass separation (or intermolecular distance) R and with the relative orientation of two involved partners, since the spontaneous electron ejection driving the process can be strongly stereo-selective, as suggested by the cartoon in **Figures 1B,C** (Falcinelli et al., 2018a,b).

In previous investigations both real and imaginary components were usually considered to vary only with the separation distance, that is assuming a simple radial dependence, due to the lack of detailed information on the interaction anisotropy (related to the relative orientation of the approaching reactants and removing products), and on the stereo-selectivity of the electronic coupling within the collision complex (Gregor and Siska, 1981; Falcinelli et al., 2016b). Under such an assumption, the analysis of the experimental findings provided only semi-quantitative information on the average strength of both real and imaginary components. A first remarkable attempt has been performed by Siska with the adoption of the Tang-Toennies (TT) potential model for ion-atom interaction (Tang and Toennies, 1984; Siska, 1986). The same procedure has been extended by Ohno et al. to describe the radial dependence of the interaction in the exit channel of auto-ionization promoted by He<sup>∗</sup> ( 1 S, <sup>3</sup> S)-Ar collisions and assuming the anisotropy in the exit channel according to the criteria proposed by Morgner and coworkers (Hoffmann and Morgner, 1979; Ohno et al., 1996). The adopted methodology allowed these authors to obtain the branching ratio for the two Ar+( <sup>2</sup>P3/2) and Ar+( <sup>2</sup>P1/2) exit channels. Furthermore, Ohno et al. demonstrated that the stereodynamics in the collisional auto-ionization processes critically depends on anisotropic characteristics of the interaction potentials of either X<sup>∗</sup> + M and X + M<sup>+</sup> entrance and exit channels, respectively. For such a purpose they developed a collision-energy/electron-energy resolved two-dimensional Penning Ionization Electron Spectroscopy (2D-PIES) technique (Ohno et al., 1996). In particular, stimulated by the 2D-PIES of He<sup>∗</sup> (2 <sup>3</sup> S)-N2, CO, and CH3CN systems, Ohno and coworkers performed reliable ab initio calculations for both anisotropic entrance and exit potentials as well as for ionization probabilities (Yamazaki et al., 2002). After that, a series of important papers were published by Ohno group on this direction (Yamazaki et al., 2002, 2005, 2007; Ohno, 2004; Khishimoto and Ohno, 2007).

More recently, in our laboratory we are working to develop a more general exhaustive approach able to describe in an

internally consistent way both the entrance (X<sup>∗</sup> + M) and exit channels (X + M+), where either the real V<sup>t</sup> and the imaginary Γ parts of the optical potential [see Equation (1)] are both anisotropic and interdependent on the selective charge transfer (CT) component triggering the process. This is a new and original approach including the reactions induced by He<sup>∗</sup> collisions as a particular case of more general phenomena. The basic novelty consists on the following two main points: (i) The radial dependence of the real part of the potential [V<sup>t</sup> in the Equation (1)], both in the entrance and exit channels, is represented by an Improved Lennard Jones Potential model (ILJ) defined by few parameters related to basic physical properties of the interacting particles (Pirani et al., 2008). Its reliability, tested on high resolution scattering and spectroscopic experiments as well as by ab initio calculations, has been found to be comparable and even better with respect to that of multiparameter functions, widely used in the past, as the TT model (Falcinelli et al., 2017); (ii) The description of the anisotropy in both channels in terms of the same components related to the selective dependence of CT on the half-filled P orbital alignment within the intermediate collision complex; (iii) The internally consistent representation of both real V<sup>t</sup> and imaginary Γ parts of the optical potential [see Equation (1)] which, for the first time, has been considered not independent (as it has been done until now) but interdependent being related to the selectivity of CT. Other relevant works in the stereodynamical investigation of auto-ionization processes have been carried out by Ohno and coworkers on the He<sup>∗</sup> molecule systems where the He<sup>∗</sup> is an isotropic reagent and the dependence on the features of the involved molecular orbitals has been characterized (Ohno, 2004; Yamazaki et al., 2005, 2007; Horio et al., 2006; Khishimoto and Ohno, 2007). Important contributions have been also provided by the Kasai group on the dependence of reactions on the orientation of symmetric top molecules investigated in detail considering Ar<sup>∗</sup> as an isotropic collisional partner (Yamato et al., 2000; Brunetti et al., 2001; Ohoyama et al., 2001).

More recently, significant investigations were performed by Narevicius and coworkers (Henson et al., 2012; Pawlak et al., 2017; Bibelnik et al., 2019) and by Osterwalder and coworkers (Jankunas et al., 2014; Gordon et al., 2017; Zou et al., 2018), studying Penning ionization processes in the sub-thermal collision energy regime by merged-beams technique. These authors pointed out important stereodynamical implications in Ne∗+ND<sup>3</sup> system (Gordon and Osterwalder, 2019), quantum state controlled cross sections for Penning and associative ionization in Ne<sup>∗</sup> ( <sup>3</sup>P2)-Ar collisions (Gordon et al., 2018), and the observation of orbiting resonances in the He<sup>∗</sup> -Ar and H<sup>2</sup> Penning ionization reactions (Henson et al., 2012).

Therefore, important questions still remain opened: they concern the modulation of the reaction probability by the relative orientation of atomic/molecular orbitals more directly involved in the processes. A correct approach should assume quantized spatial orientations along the intermolecular electric field direction that selectively correlate with specific configurations of the collision complex, the only ones effective in leading to final products.

Target of this paper is to report on recent our advances on the characterization, for some prototypical systems, of radial and orientation dependences of both real and imaginary components of the optical potential. In particular, molecular beam experiments have been performed, measuring the energy dependence of total and partial (for the formation of product ions in specific states) ionization cross sections [σ(E)] and of energy spectra of emitted electrons. In particular, being the reaction probability highest at the closest approach of the colliding partners, Penning Ionization Electron Spectra (PIESs) can be considered as a sort of "transition state spectroscopy" (Hotop et al., 1979; Morgner, 1985; Benz and Morgner, 1986).

The analysis of experiments, performed with Ne<sup>∗</sup> ( <sup>3</sup>PJ) atoms and hydrogenated molecules, like water and ammonia (Ben Arfa et al., 1999; Brunetti et al., 2013; Falcinelli et al., 2016a,b, 2017), provided the dependence of the optical potential of the systems on the separation distance and on the orientation of the molecular orbitals interested in the ionization (see **Figure 1C**). However, these results did not include any dependence on the atomic orbital orientation/alignment, since they were referred to a statistical average over all the atomic sublevels of open-shell Ne<sup>∗</sup> . The dependence on the atomic orbital orientation, which is quantized and masked by spin-orbit electronic couplings within the open-atom structure of reagents and products, cannot considered a trivial question.

Our recent investigations focused on the energy analysis of electrons emitted in collisions between Ne<sup>∗</sup> ( <sup>3</sup>PJ) and Kr and Xe atoms under controlled kinetic energy conditions (Falcinelli et al., 2018a,b). The contributions of the different fine structure sublevels, both in the entrance and exit channels, have been separated and their collision energy dependence resolved. The analysis of the experimental findings permitted us to extract direct information on the role of the atomic anisotropy within the collision complex, determining relevant details of both real and imaginary components of the interaction. In particular, it has been emphasized that electronic rearrangements control adiabatic and non-adiabatic effects both in the entrance and exit channels and, mostly, in the transition state. It has been found that, while adiabatic effects influence essentially the anisotropy of the real part of the potential, non-adiabatic effects mostly control the imaginary part (Falcinelli et al., 2018a,b). However, their contributions must be not fully independent since they are simultaneously related to: (a) external electronic orbital polarization, (b) changes in the electronic angular momentum couplings and (c) selectivity of CT contributions.

The combination of all this information, representing a substantial advancement with respect to the previous works, has been here adopted to provide for the first time, on our knowledge, the state-to-state reaction probability of the system Ne<sup>∗</sup> ( <sup>3</sup>PJ)-Kr.

In the following, we start from a summary of the main results obtained on the study of orientation effects of the H2O molecular orbitals, involved in the collisional ionization by Ne<sup>∗</sup> ( <sup>3</sup>PJ) atoms and then we discuss the Ne<sup>∗</sup> ( <sup>3</sup>PJ)-Kr case with the determination of the Γ components associated to the state to state processes, i.e., Ne<sup>∗</sup> ( <sup>3</sup>P0)—Kr+( <sup>2</sup>P3/2), Ne<sup>∗</sup> ( <sup>3</sup>P0)— Kr+( <sup>2</sup>P1/2), Ne<sup>∗</sup> ( <sup>3</sup>P2)—Kr+( <sup>2</sup>P3/2), and Ne<sup>∗</sup> ( <sup>3</sup>P2)—Kr+( <sup>2</sup>P1/2), including all the multiplicity of states in entrance and exit channels (Falcinelli et al., 2016a,b).

#### THE Ne<sup>∗</sup> -MOLECULE CASE

A wide literature is available on Penning ionization studies involving He<sup>∗</sup> and Ne<sup>∗</sup> metastable atoms as ionizing agents of simple hydrogenated molecules, as water (Yee et al., 1976; Cermák and Yencha, 1977; Sanders and Muschlitz, 1977; Ohno et al., 1983; Haug et al., 1985; Mitsuke et al., 1989; Ishida, 1996).

Collisions between Ne<sup>∗</sup> and H2O have been investigated in detail also by our group and **Figure 2A** reports measured absolute total and partial ionization cross sections for the formation of [H2O(X or A)]<sup>+</sup> product ions, as a function of the collision energy (Balucani et al., 2012; Brunetti et al., 2012). They exhibit different values but similar energy dependence. The branching ratio (BR) was estimated by the areas of PIES peaks, also reported in **Figure 2B**, related to the formation of H2O<sup>+</sup> in the ground X respect to the first excited A electronic state (Balucani et al., 2012; Brunetti et al., 2012; Falcinelli et al., 2016a,b). On this ground, BR is found to be of about 0.3. A similar procedure has been adopted to obtain BR for other hydrogenated molecules (Falcinelli et al., 2015b, 2016b).

In the analysis of experimental data, the Γ component of the optical potential that depends on the overlap integral between orbitals exchanging the electron has been represented by an exponential decreasing function of R. Its angular dependence, modulated by trigonometric functions, has been derived from Legendre polynomials (or spherical harmonics) (Falcinelli et al., 2016b). In the adopted Γ formulation both dependences of the overlap integrals on R and on the shape of involved molecular orbitals have been enclosed. According to the guidelines described in Falcinelli et al. (2016b), we have assumed:

$$\Gamma\left(\mathbb{R}, \theta, \phi\right) = A e^{-bR} \cos^2 \theta \tag{2}$$

for the removal of one electron from the almost pure p orbital, that is perpendicularly to the molecular plane of H2O, with subsequent formation of the ground X electronic state of ionic molecular product. In order to describe the electron ejection from the molecular orbital with cylindrical symmetry, aligned along the C2<sup>v</sup> axis of H2O, which determines the formation of H2O+(A), the following formulation has been adopted (Falcinelli et al., 2016b):

$$\Gamma\left(\mathcal{R}, \theta, \phi\right) = A e^{-bR} \sin^2\theta \sin^2\phi \tag{3}$$

The Equation (2) holds only for 180◦≤φ≤360◦ , and outside such a range Γ becomes zero. The polar coordinate system is defined as illustrated in **Figure 2D**.

During the analysis, the strength of the binding energies, predicted by the real part of the optical potential for the most relevant limiting configurations of the Ne<sup>∗</sup> -H2O collision complex (Brunetti et al., 2013; Falcinelli et al., 2016a) (see also **Figure 2F**), has been tested on some features of PIES, including also the shift respect to the peak positions measured in pure photo-ionization events by Ne(I) photons. In addition, only the A and b parameters of Γ components have been varied in order to reproduce the absolute value of total and partial ionization cross sections and their energy dependence (Falcinelli et al.,

polar plot of the imaginary component of the optical potential for the production of A (black) and X (red) states of the H2O<sup>+</sup> product ion. (F) A contour map of the real part of the optical potential on the molecular plane (for details see Falcinelli et al., 2016a,b).

2016b). The angular dependence of the Γ components, defined by Equations (2) and (3) for three different distances chosen in the range of the classical turning points mainly probed in the investigated collision energy range, are also given in **Figure 2E**.

Furthermore, the combined characterization of imaginary and real parts of the optical potential permitted us to evaluate, at each collision energy, the value of partial ionization cross sections for the formation of product ions in different electronic states as a function of the polar angles (Falcinelli et al., 2016b). The obtained results emphasized the selectivity in the formation of the product ions in the different electronic states and provided crucial information on the stereo-dynamics of the auto-ionization reactions involving water, that is probably the most important prototype of hydrogenated molecules. In particular, this investigation clearly indicated that the reactions occur only for specific orientations of water molecule with respect to the approaching Ne<sup>∗</sup> atom. The convergence of calculated and measured cross sections and the reproduction of the BR, as deduced from the ratio of measured peaks in PIES, allowed us to estimate also the "effective" angular cones of approach where the reaction has the highest probability to occur, whose shapes are depicted in **Figure 2C** (Falcinelli et al., 2016a,b).

In spite of the clarification of these stereo-dynamical effects for atom-molecule collisions, a more detailed treatment should consider that the inner shell ionic core of the Ne<sup>∗</sup> atom exhibits a half filled p orbital and this exclusively promotes the reaction. Therefore, the lacking of its alignment along the R direction hinders the reactivity, and then in the simulations angular cone acceptances must widen in order to provide expected cross section values.

The characterization of the selective role of half-filled atomic orbitals has been the target of our most recent research (Falcinelli et al., 2018a,b), focused on metastable atom-atom systems, which represent the simplest case of stereo-selective chemical reactions. For such systems, it has been possible to investigate in detail the role of inner half-filled orbital and of its spatial quantized orientations.

#### THE Ne<sup>∗</sup> -ATOM CASE

As mentioned above, previous studies on atom-atom and simple atom-molecule systems (Hotop and Niehaus, 1968; Hotop et al., 1971; West et al., 1975; Gregor and Siska, 1981; van den Berg et al., 1987; Aguilar Navarro et al., 1992; Brunetti et al., 1993), carried out through the measurement of energy dependence of ionization cross sections, provided only estimates of the two terms, the real V<sup>t</sup> and the imaginary Γ parts, of the optical potential [see Equation (1)] in their isotropic radial dependence. Recent more advanced experiments with state selected Ne<sup>∗</sup> beams (Gordon et al., 2017; Zou et al., 2018) provided the collision energy dependence of associative to Penning branching ratio for individual sublevels of Ne<sup>∗</sup> ( <sup>3</sup>P2), an important observable, due to its expected dependence on the spatial quantization of open-shell structures within the collision complex.

Following previous pioneering experiments (Tang et al., 1972; West et al., 1975; Martin et al., 1978; Neynaber and Tang, 1979a,b), we have measured and analyzed important features of PIES spectra (Brunetti et al., 2006; Falcinelli et al., 2018a,b), in Ne<sup>∗</sup> - Kr, Xe experiments, providing new and complementary information on the role of adiabatic and non-adiabatic electronic effects controlling structure and reactivity of the intermediatetransition state of the systems.

Obtained PIESs for Ne<sup>∗</sup> -Kr, Xe, as a function of collision energy, are reported in **Figure 3**, where all peaks are shown to be globally shifted respect to the canonical Ne(I) photoionization spectra. The shift is known to originate by the effective real potential that controls energy and structure of the collision complex. In particular, the electron emission mostly occurs from the collision complex in proximity of the closest intermolecular distance, where the time spent by the system is longer, the interaction stronger, and the reaction probability is highest. Therefore, the shift is directly related to the stability of the collision complex in the achieved configuration, depending on the different orientations permitted to the half-filled orbital of the metastable atom and on the critical balance of attractive and repulsive interactions involved.

As reported in recent papers (Falcinelli et al., 2018a,b), the combined analysis of measured PIES spectra, plotted in **Figure 3**, suggested the occurrence of contributions from four different reaction channels, assigned to two different spin-orbit states of the Ne<sup>∗</sup> ( <sup>3</sup>P2,0) reagent and two different spin-orbit states of the ionic M+( <sup>2</sup>P3/2,1/2) products (M = Kr, Xe). The relative probability of these four channels has been extracted by fitting the PIES spectra with four different Gaussian functions to which we have imposed the following two conditions: (i) all used functions have the same width; (ii) their relative peak position is shifted taking into account for the spin-orbit spacing of Ne<sup>∗</sup> . The relative probability of the four channels has been then related to the relative height of the four peaks of the spectra.

The obtained results emphasized the reactivity change of <sup>3</sup>P<sup>0</sup> atoms with respect to <sup>3</sup>P2, in producing ions in <sup>2</sup>P3/<sup>2</sup> and <sup>2</sup>P1/<sup>2</sup> sublevels, as a function of the collision energy. These findings have been assumed to arise from a critical balance of adiabatic and non-adiabatic effects that control formation and electronic rearrangement of the collision complex, respectively.

While the anisotropy of the real part of W [see Equation (1)] depends on the effectiveness of adiabatic effects, strength and selectivity of the imaginary component are more directly affected by non-adiabatic effects. The latter, however, cannot be considered fully independent on the adiabatic ones, since all effects are simultaneously affected by relevant changes in the electronic configurations probed by the system.

The peak positions of PIES spectra, with respect to those from Ne(I) photoionization, and their shifts with the increase of the collision energy, are found to arise from different critical balances between attractive and repulsive components of the real potential. Therefore, in the entrance channels the potential formulation must take into account that the long range interaction is confined in the non-covalent neutral atom-neutral atom type, depending on the spherical electronic polarizability of both atoms, where that of Ne<sup>∗</sup> is the highest one being determined by the outer weakly bound electron in the 3s orbital. In the range of intermediate and short distances we have the gradual/adiabatic formation of the complex [(Ne-M)+] e∗, where the open shell (Ne-M)<sup>+</sup> ionic adduct is surrounded by the floppy cloud of the outer electron in excited Rydberg states. We can define a first critical distance, R0, being the internuclear separation where the two configurations have the same importance and consequently an intermediate situation takes place. The R<sup>0</sup> value must be almost the same for Ne<sup>∗</sup> -Ar, Kr, Xe systems, since they are primarily affected by the larger size Ne<sup>∗</sup> metastable atom (or by its polarizability), whereas it should increase when atoms with higher polarizability are involved, as is the case of He<sup>∗</sup> ( 1 S0).

In order to cast light on the contribution of adiabatic and non-adiabatic effects, exploiting the analysis of the experimental observables, it has been fundamental to evaluate preliminary all relevant features of effective interaction potentials controlling

the molecular dynamics both in the entrance and in exit channels. For their proper formulation, whose details are given in Falcinelli et al. (2018a,b), we have exploited a phenomenologicalsemiempirical method developed in our laboratory that combines information from theoretical approaches, useful to describe the collision events of open shell P-state atoms with closed shell partners, with results of scattering experiments performed with atomic beams selected in their spin-orbit sublevels J (Aquilanti et al., 1982, 1988, 1989, 1997; Pirani et al., 2000).

The rationalization of all experimental and theoretical findings suggested us (Falcinelli et al., 2018a,b) some crucial characteristics of adiabatic and non-adiabatic effects, summarized as it follows. Adiabatic effects determine:


5) The selective bond stabilization by CT of quantum molecular states of defined symmetry, arising from the configuration interaction between entrance and exit channel states differing for one electron exchange, that represents for such systems the main contribution to the interaction anisotropy at short range (Pirani et al., 2000).

Non-adiabatic effects relate to:


The simultaneous consideration of all these features suggested (Falcinelli et al., 2018a,b) that the electronic rearrangement triggering the transition from entrance to exit channels can involve two different complementary mechanisms. They are the following:

i) A direct mechanism. It is stimulated by nuclear vibrationelectronic orbital motion couplings. It causes a homogeneous electron exchange, involving two coupling terms, pointed out as A6−6 and as A5−5 on the basis of the symmetry of either initial and final states of the system involved in the electron exchange. Such mechanism is expected to be more efficient at short distances where the molecular character is more defined and/or the quantized spatial orientations of the half-filled orbitals are more effective. A value of 5 has been used for the A6−6/A5−5 ratio, following the suggestion of Krauss (1977) analyzing the different overlap integral, for the same value of R, between atomic orbitals giving molecular states of 6 and 5 character that are implicated in the CT.

ii) An indirect mechanism, supporting a heterogeneous electron exchange. Such a mechanism induces a mixing of 6 and 5 character and is promoted by the spin-orbit interaction as well as by the nuclear rotation-electronic orbital motion (also called as Coriolis coupling). It includes also possible contributions from cloud rearrangements of the outer excited electron, taking into account of radiative effects in previous developed treatments (Miller and Morgner, 1977; Gregor and Siska, 1981). Two possible coupling terms, A6−5 and A5−6, identified on the basis of the symmetry of the initial and final states are involved in this second mechanism. Also in this case, for the same reasons discussed above in the direct mechanism, the A6−5/A5−6 ratio has been fixed equal to 5.

The peak ratio dependence on the collision energy allowed us to characterize the relative role of the two mechanisms, defined as A6−5/A6−6 ratio (Falcinelli et al., 2018a,b). Moreover, the above considerations on the role of adiabatic and non-adiabatic effects suggest that A6−6, and consequently A5−5, must be rather proportional to the bond stabilization contribution by CT (Aquilanti et al., 1997; Falcinelli et al., 2017). Such contribution, that arises from the configuration interaction between quantum states of ionic adducts, having the same symmetry and associated to entrance and exit channels, must be also crucial in promoting the reactivity. Moreover, the proportionality is expected to depend mostly on the overlap integral between wave functions describing the ejected electron in the initial-excited and in the final-continuum state (Gregor and Siska, 1981). Since here the involved orbitals are rather diffuse, such proportionality can be assumed constant, that is independent of R (no radial dependence), at least in range of distances of interest. The value of the constant is expected to depend essentially on the characteristic of the electron wave function in initial excited state.

Assuming a proportionality constant equal to ½ for all processes promoted by Ne<sup>∗</sup> ( <sup>3</sup>P2,0), from the knowledge of the bond stabilization by CT, we have derived a simple relation providing the radial dependence of A6−6. In the case of Ne<sup>∗</sup> -Kr system (the treatment can be easily extended to other Ne<sup>∗</sup> -Noble gas cases) it has been assumed the form

$$A\_{\Sigma - \Sigma}(meV) = 3.35 \times 10^6 \text{ }e^{-4.32R} \tag{4}$$

where R is given in Å.

From the collision energy dependence of the A6−5/A6−6 ratio, we estimated also the following less pronounced, radial dependence for A6−5

$$A\_{\Sigma - \Pi} \ (meV) = 335 \ e^{-1.40R} \tag{5}$$

where R is again in Å.

The additional A5−5 and A5−6 couplings have been so indirectly characterized according to the criteria discussed above. The Γ components, depending on the symmetry of the states involved, must correspond to the so obtained coupling terms.

#### DISCUSSION AND CONCLUSIONS

Our investigation suggests a tentative comparison and a combined discussion of the most important findings presented in the previous sections for both the different type of prototype systems. The results for metastable atom-hydrogenated molecule systems, concerning the selective formation of product ions in the different electronic states (see **Figure 2**), provided crucial information on the stereo-dynamics of these important autoionization reactions, especially emphasizing the dependence of the reaction probability on the molecular orientation. The adopted treatment allowed also to estimate of the magnitude order of angular cones where the processes are mainly confined. Such cones amount to about 1–2 sr, corresponding to an aperture of about 30–60 degrees. Note that the results reported in a previous paper (Falcinelli et al., 2016b) are relative values and they must be multiplied for 4π to give absolute angular cones in radiants. The so obtained cones must be taken as effective, since their values are the result of an average over the investigated energy range. Furthermore, natural molecular orientation effects should reduce the angular cone of acceptance around the direction of the most favorable configurations: they can become operative during the collision of polar molecules, as for example H2O, and are induced by electric field gradients in strongly anisotropic intermolecular potentials. These effects should increase when the collision energy decreases, especially in

FIGURE 4 | Comparison of the radial dependence of the average Γ value obtained for two prototype systems: *Dashed line*—the Ne\*-H2O case, discussed in the text and giving the ground electronic state of water ion; *Full* lines—the Ne\*-Kr case, obtained by Gregor and Siska (1981) where black, red, and blue colors represent average value, lower and upper limits, respectively. For the same system the circles are the results of the present investigation.

the sub-thermal energy range (Chang et al., 2013; Jankunas et al., 2014; Cernuto et al., 2017, 2018).

Adopting the potential parameters reported in Falcinelli et al. (2016b) it becomes possible to determine both the highest value of the strength of Γ , associated to the most reactive configuration, and its value estimated by averaging over the full space of the relative configurations, where the most relevant contribution comes from the angular cone where the formation of a final ionic product in a specific state is favored. Considering an R value of 3Å, the highest Γ value that controls the formation of water ion both in the ground and in excited electronic state, amounts to about 70 meV, respectively, while the value averaged over the complete range of configurations reduces to about 7 and 4 meV, respectively. Similar estimates apply to other hydrogenated molecules as ammonia and hydrogen sulfide (Falcinelli et al., 2014, 2016a,b). For some comparisons with results presented below, the radial dependence of the average component giving the ground state of water ion is plotted in **Figure 4**.

For atom-atom cases, the Γ components, identified here with the A6−6(R), A5−5(R), A6−5(R), and A5−6(R) coupling terms, obtained according to the method summarized in the previous section, are plotted in **Figure 5**. Such components suggest that the dependence of the indirect mechanism by the internuclear distance R appears to be much less evident than the case of the direct mechanism. For this reason, the indirect mechanism becomes less relevant when the collision energy increases (or when the probed separation distance decreases), since the direct mechanism is favored by the more pronounced molecular character attained by the initial states.

The Γ components, evaluated in previous studies and showing only a radial dependence (Gregor and Siska, 1981), must

FIGURE 5 | The *A*6−6(R) (full black) *A*5−5(R) (dashed black), *A*6−5(R) (full red) and *A*5−6(R) (dashed red) coupling terms determining *direct and indirect mechanism*s in auto-ionization reactions of Ne\* -Kr system. Open and closed red circles represent the <sup>Γ</sup> components associated to <sup>3</sup>P0- <sup>2</sup>P3/<sup>2</sup> and <sup>3</sup>P0- <sup>2</sup>P1/<sup>2</sup> state to state processes; Open and closed blue triangles represent the <sup>Γ</sup> components associated to <sup>3</sup>P2- <sup>2</sup>P3/<sup>2</sup> and <sup>3</sup>P2- <sup>2</sup>P1/<sup>2</sup> state to state processes. Note that in the exit channels the reaction probability is weighted on the different degeneracy of J = 3/2 and J = 1/2 states of the ionic product.

considered as effective-average radial terms. An important test of our methodology can be achieved by performing a weighted sum of the obtained coupling terms by taking into account for the statistical populations of <sup>3</sup>P<sup>2</sup> and <sup>3</sup>P<sup>0</sup> fine levels of Ne<sup>∗</sup> reagent, the degeneracy of the different quantum states accessible to the colliding system and the dependences of the 6 and 5 character of each state on R. The average Γ values so obtained are reported in **Figure 4**, where they are compared with those of Ne<sup>∗</sup> -water, to emphasize that the strength is in the same scale, and with the empirical function obtained by Gregor and Siska (1981) for the same system. The very good agreement obtained authorized us to attempt a de-convolution of Γ in order to determine the stateto state Γ components. The obtained results, plotted in **Figure 5**, show a well evident dependence of the reaction probability on the fine level of both reagents, including <sup>3</sup>P0, and products.

It should be emphasized that the methodology proposed by us allows to characterize both the real and the imaginary parts of the optical potential within the same internally consistent framework, that takes into account properly all the features of P atom interaction and of its collision dynamics. Next steps concern the extension of the methodology to other atom-atom systems and to the obtaining the dependence of Γ on both J and Ω quantum numbers of reagent and products, which is of interest for the investigation of quantum effects in the coherent control of collision processes, promoting both Penning and associative ionization, from under ultra-cold up to thermal conditions (Arango et al., 2006a,b).

Moreover, our investigation on atom–atom auto-ionization reactions, takes into account for the first time in the PIES analysis of experimental spectra both decoupling schemes of the electronic angular momentum and the Coriolis coupling effects, providing new insights on the microscopic electron rearrangements within the transition state of autoionization reactions. In particular, both real and imaginary parts of the optical potential [see Equation (1)] have been reported in an internally consistent way being related to basic selectivities of CT. On this ground the electronic rearrangements have been classified as adiabatic and nonadiabatic effects: they are controlled by the anisotropy of specific interaction components and consequently their characterization is of relevance to rationalize also the behavior of atom-molecule systems. In particular, it has to be noted that orientation effects of polar molecules can spontaneously takes place, making accessible only some specific geometries of the transition state. This can occur at low collision energies, where non-adiabatic contributions tend to vanish, and under these conditions the reaction probability should be almost independent on the collision energy (Jankunas et al., 2014).

In conclusion, we proposed a new and original method to fully describe, and including in a more general picture, the stereodynamics of the state to state auto-ionization reactions. For such a purpose we exploited the ample phenomenology achieved in the last 30 years by our group on the selective collision dynamics of open-shell atoms. Furthermore, our model appears to be able also to clarify in detail the role of electronic rearrangements within the transition state of many other types of chemical processes, that are more difficult to characterize.

## AUTHOR CONTRIBUTIONS

All authors planned experiments and made discussion about the results. SF and PC managed the experiments. SF, FV, and FP analyzed the results. All authors participated in writing the manuscript.

## REFERENCES


## ACKNOWLEDGMENTS

This work is dedicated to our colleague and friend Jaime De Andres whose memory and love for science will inspire our future research. FP acknowledges funding from MIUR, Ministero dell'Istruzione, dell'Università e della Ricerca, PRIN 2015 (STARS in the CAOS—Simulation Tools for Astrochemical Reactivity and Spectroscopy in the Cyberinfrastructure for Astrochemical Organic Species, 2015F59J3R).


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<sup>+</sup> CHCl<sup>3</sup> <sup>→</sup> CHCl<sup>+</sup> <sup>2</sup> + Cl + e <sup>−</sup> + Ar. J. Chem. Phys. 113, 6673–6676. doi: 10.1063/1.1311614


alcohols and ethers. J. Electron Spectrosc. Relat. Phenom. 8, 291–312. doi: 10.1016/0368-2048(76)81013-4

Zou, J., Gordon, S. D. S., Tanteri, S., and Osterwalder, A. (2018). Stereodynamics of Ne(3P2) reacting with Ar, Kr, Xe, and N2. J. Chem. Phys. 148:164310. doi: 10.1063/1.5026952

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Falcinelli, Pirani, Candori, Brunetti, Farrar and Vecchiocattivi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

## State-Selected Reactivity of Carbon Dioxide Cations (CO<sup>+</sup> 2 ) With Methane

Daniela Ascenzi <sup>1</sup> \*, Claire Romanzin2,3, Allan Lopes <sup>2</sup> , Paolo Tosi <sup>1</sup> , Jan Žabka<sup>4</sup> , Miroslav Polášek <sup>4</sup> , Christopher J. Shaffer 5† and Christian Alcaraz 2,3

<sup>1</sup> Department of Physics, University of Trento, Trento, Italy, <sup>2</sup> Laboratoire de Chimie Physique, Bât. 350, UMR 8000, CNRS-Univ. Paris-Sud and Paris Saclay, Centre Universitaire Paris-Sud, Orsay, France, <sup>3</sup> Synchrotron SOLEIL, L'Orme des Merisiers, Saint-Aubin—BP 48, Gif-sur-Yvette, France, <sup>4</sup> J. Heyrovský Institute of Physical Chemistry of the Czech Academy of Sciences, Prague, Czechia, <sup>5</sup> Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences, Prague, Czechia

#### Edited by:

Ramesh L. Gardas, Indian Institute of Technology Madras, India

#### Reviewed by:

Aparna Shastri, Bhabha Atomic Research Centre (BARC), India Naved I. Malek, Sardar Vallabhbhai National Institute of Technology Surat, India

#### \*Correspondence:

Daniela Ascenzi daniela.ascenzi@unitn.it

#### †Present address:

Christopher J. Shaffer, Sherwin Williams, VAST R&D, Minneapolis, MN, United States

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 25 February 2019 Accepted: 15 July 2019 Published: 02 August 2019

#### Citation:

Ascenzi D, Romanzin C, Lopes A, Tosi P, Žabka J, Polášek M, Shaffer CJ and Alcaraz C (2019) State-Selected Reactivity of Carbon Dioxide Cations (CO<sup>+</sup> 2 ) With Methane. Front. Chem. 7:537. doi: 10.3389/fchem.2019.00537 The reactivity of CO<sup>+</sup> <sup>2</sup> with CD<sup>4</sup> has been experimentally investigated for its relevance in the chemistry of plasmas used for the conversion of CO<sup>2</sup> in carbon-neutral fuels. Non-equilibrium plasmas are currently explored for their capability to activate very stable molecules (such as methane and carbon dioxide) and initiate a series of reactions involving highly reactive species (e.g., radicals and ions) eventually leading to the desired products. Energy, in the form of kinetic or internal excitation of reagents, influences chemical reactions. However, putting the same amount of energy in a different form may affect the reactivity differently. In this paper, we investigate the reaction of CO<sup>+</sup> <sup>2</sup> with methane by changing either the kinetic energy of CO<sup>+</sup> 2 or its vibrational excitation. The experiments were performed by a guided ion beam apparatus coupled to synchrotron radiation in the VUV energy range to produce vibrationally excited ions. We find that the reactivity depends on the reagent collision energy, but not so much on the vibrational excitation of CO<sup>+</sup> 2 . Concerning the product branching ratios (CD<sup>+</sup> 4 /CD<sup>+</sup> 3 /DOCO+) there is substantial disagreement among the values reported in the literature. We find that the dominant channel is the production of CD<sup>+</sup> 4 , followed by DOCO<sup>+</sup> and CD<sup>+</sup> 3 , as a minor endothermic channel.

Keywords: vibrational excitation, plasma, astrochemistry, Mars atmosphere, synchrotron radiation, ion-molecule reaction, CO2 dissociation

## INTRODUCTION

The chemistry of the CO<sup>+</sup> 2 cation attracts much attention because of the presence of this ion in planetary atmospheres (with particular reference to the Earth and Mars Matta et al., 2013; Tenewitz et al., 2018 as well as in laboratory plasmas for energetic and environmental applications Snoeckx and Bogaerts, 2017). In the latter field, the efficient conversion of greenhouse gases into valueadded chemicals is a central topic in current research on renewable and sustainable energies (Wang et al., 2017). In particular, the hydrogenation of CO<sup>2</sup> by technologies based on green electricity allows both the storage of renewable energy in value-added compounds and recycling CO2, thus paving the way to decarbonise the energy system. Non-thermal plasmas have been explored for their capability to activate very stable molecules with the potential of achieving a higher energy efficiency compared to purely thermal processes (Scapinello et al., 2016; Martini et al., 2018). To improve the performances and to control the outcome of plasma-based processes, insight into the physical and chemical mechanisms at play is desired. According to a chemical kinetic model of the plasma-based dry reforming (Snoeckx et al., 2013), a key role is played by the reaction of CO<sup>+</sup> <sup>2</sup> with CH4. However, as described below, there is considerable uncertainty on the branching ratio, so that a reinvestigation of the reaction is desirable. Also, because vibrationally excited levels of CO<sup>+</sup> 2 can be populated in plasmas, this study aims at investigating the effect of the vibrational excitation of the CO<sup>+</sup> 2 cation on the reaction with CH4.

Energy, in the form of kinetic or internal motion of the reagents, is the driving force of chemical reactions. However, putting the same amount of energy in a different form (i.e., translational, vibrational, rotational or electronic energy) may affect the reactivity differently. For ion-molecule reactions, some state-selected experiments have shown that for endothermic charge-transfer (CT) processes, vibrational excitation is more effective than translational energy in driving the reactions (Viggiano and Morris, 1996). However, in other cases, the effect of vibrational excitation is more varied (see for example Candori et al., 2003; Boyle et al., 2011; Chang et al., 2012; Bell and Anderson, 2013a,b; Bell et al., 2014 and reference therein).

The effect of the internal excitation of CO<sup>+</sup> 2 in reactions with small molecules has been addressed in previous studies. It was found that the vibrational excitation of CO<sup>+</sup> 2 increases the reactivity with O<sup>2</sup> and NO (Alge et al., 1981; Durup-Ferguson et al., 1983; Derai et al., 1985; Ferguson et al., 1992; Nicolas et al., 2002), while it decreases the rate coefficient for the reaction with H<sup>2</sup> (Albritton, 1979; Borodi et al., 2009). However, no previous studies exist in which the CO<sup>+</sup> 2 cation is generated with a precise amount of internal energy (i.e., state-selection of a specific vibrational state) and reacted with CH4.

#### PREVIOUS STUDIES OF THE CO<sup>+</sup> <sup>2</sup> + CH<sup>4</sup> REACTION

The reaction of CO<sup>+</sup> <sup>2</sup> with methane in the gas phase has been studied by several groups, with the earliest experimental results dating back to the late 60s (Anicich, 2003). Rate constant and product branching ratio measurements were made using drift techniques, either flow drift tubes (FDT) (Rakshit and Warneck, 1980; Durup-Ferguson et al., 1983) or selected ion flow tube (SIFT) (Smith et al., 1978; Copp et al., 1982), ion cyclotron resonance (ICR) techniques (Huntress et al., 1980) and ion beam methods (Tsuji et al., 1994). Earlier determinations where done using high-pressure mass spectrometry (HPMS) (Harrison and Myher, 1967; Chong and Franklin, 1971; Kasper and Franklin, 1972) and electron space charge traps (SCT) (Ryan and Harland, 1974). The most relevant results are summarized in **Table 1**.

It has been shown that the reaction proceeds at thermal energy with a rate constant close to the Langevin collision rate constant kL=1.1 × 10−<sup>9</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·s −1 (Durup-Ferguson et al., 1983). There is fair agreement (within the experimental errors) among the total rate constants measured at thermal energies (in the range 280–340 K for the data reported in **Table 1**), with the exception of the HPMS study by Kasper and Franklin (1972), that gives a rate constant value more than a factor two higher than the others. The values for the branching ratios are quite scattered, with HOCO<sup>+</sup> being dominant in all studies except (Durup-Ferguson et al., 1983), where the CT is the only observed channel.

## MATERIALS AND METHODS

The experiments have been performed using the CERISES apparatus, an associated experiment to the SOLEIL synchrotron radiation facility. Since the set-up was described in details previously (see Alcaraz et al., 2004; Cunha de Miranda et al., 2015), only the most relevant details will be given here. CERISES is a guided ion beam tandem mass spectrometer composed of two octopoles located between two quadrupole mass spectrometers in a Q1-O1-O2-Q2 configuration that permits investigation of bi-molecular reactions of mass-selected ions. By measuring the yields of parent- and product-ions, absolute reaction cross sections, branching ratios and product velocity distributions as a function of the collision energy are derived.

Vibrational state selection of CO<sup>+</sup> 2 is performed via the Threshold Photoelectron Photoion Coincidence (TPEPICO) method (Baer and Guyon, 1986) using the ion source of CERISES and the DESIRS beamline. The undulator based DESIRS beamline (Nahon et al., 2012) provides tunable radiation in the vacuum ultraviolet (VUV) range from about 5 eV to 40 eV. Photons at the desired wavelength are selected and scanned simultaneously with the undulator peak energy by a normal incidence monochromator equipped with a low dispersion uncoated SiC grating (200 grooves/mm) optimized to provide photon flux in the 10<sup>12</sup> photon/s to 10<sup>13</sup> photon/s range with an energy resolution down to 1 meV in the 5 eV to 20 eV range. In the present experiments, the photon energies (Ephot) required to produce the parent ion by photoionisation are in the range 13.7– 18.3 eV. Depending on the operation mode, the monochromator slits were set in the range 25 to 400µm, corresponding, at these photon energies, to a resolution of 3 to 44 meV.

In the TPEPICO mode, the CO<sup>+</sup> 2 ions are extracted in coincidence with threshold photoelectrons. Threshold photoelectrons are filtered first through geometrical discrimination of energetic photoelectrons by using a small extraction field of ≈ 1 V/cm and an extraction hole of 2 mm in diameter. Further time discrimination of energetic photoelectrons is made possible by recording the photoelectron arrival time on the detector and setting a time gate of 10 ns corresponding to the arrival time of threshold photoelectrons. The overall resolution of threshold electrons is about 25 meV. The source pressure and VUV flux are set to limit the false coincidence (FC) rate in the order of 10%. The FC are measured for each TPEPICO point for parent and product ions by replacing the true photoelectron signal by an arbitrary trigger. The FC contribution is then subtracted from the ion count signal. Some measurements have been carried out in the DC mode, i.e., without state-selection but with parent ions in a distribution of excitation that can vary with the photon energy.


TABLE 1 | Summary of existing experimental determinations of rate constants and branching ratios for the reaction of CO<sup>+</sup> 2 with CH4.

<sup>a</sup>Rate constants at thermal energy.

<sup>b</sup>Reaction with CD<sup>4</sup> to give CO2D <sup>+</sup> exclusively.

Prior to the reactivity experiment, the threshold photoelectron spectrum of CO<sup>2</sup> has been measured using the CERISES set up in the 13.7–18.3 eV photon energy range corresponding to the X <sup>2</sup>5g(3/2, 1/2) ground state (I.E.=13.778 eV), the first excited state A <sup>2</sup>5 <sup>u</sup>(3/2, 1/2) with I.E.= 17.313 eV, up to the beginning of the B2P<sup>+</sup> u state of the ion (I.E.=18.076 eV). For high-resolution VUV TPES spectra of CO<sup>2</sup> with the complete assignment of the spectral features to specific internal modes of the CO<sup>+</sup> 2 ion, the reader is referred to the papers by Baer and Guyon (1986), Merkt et al. (1993), Liu et al. (2000a,b). In **Figure 1** we report our measured TPES spectrum in the VUV region where reactivity experiments have been performed. The red dashed lines indicate the photon energies chosen for the production of state-selected CO<sup>+</sup> 2 in the TPEPICO mode, while the black arrows point to the photon energies at which reactivity studies have been performed in the DC mode (without state-selection).

Following the assignment of Liu et al. (2000a), the photoelectron band at Ephot = 13.78 eV corresponds to the transition CO<sup>+</sup> 2 (0,0,0) X25g,3/<sup>2</sup> ← CO2(0,0,0) X16<sup>+</sup> g , hence producing the CO<sup>+</sup> 2 cation in its electronic ground state with no vibrational excitation, hereafter indicated as (0,0,0). The band at Ephot = 13.84 eV corresponds to one of the four vibronic components of the transition CO<sup>+</sup> 2 (0,1,0) X25<sup>g</sup> ← CO2(0,0,0) X <sup>1</sup>P<sup>+</sup> g , more precisely either the <sup>2</sup>15/<sup>2</sup> or <sup>2</sup>6<sup>+</sup> component that we cannot distinguish at our limited resolution (see Liu et al., 2000a paper for the attribution of the four components), thus generating the CO<sup>+</sup> 2 cation in its electronic ground state with one quantum of vibrational excitation in the bending ν<sup>2</sup> mode, hereafter indicated as (0,1,0). The band at Ephot = 13.95 eV corresponds to the overlap of two transitions, namely CO<sup>+</sup> 2 (1,0,0) X <sup>2</sup>5g,1/<sup>2</sup> ← CO2(0,0,0) X <sup>1</sup>6<sup>+</sup> g and CO<sup>+</sup> 2 (0,0,1) X <sup>2</sup>5g,3/<sup>2</sup> ← CO2(0,0,0) X16<sup>+</sup> g , and therefore leads to CO<sup>+</sup> 2 in the X state with one quantum of vibrational excitation in either the symmetric (ν1) or the antisymmetric (ν3) stretching vibration, hereafter indicated as (1,0,0) + (0,0,1).

A sufficient number of ion counts on the threshold electron signal have been observed to perform reactivity experiments with the state-selected cations at the three photon energies (red lines in **Figure 1**) corresponding to the vibronic bands giving CO<sup>+</sup> 2 with either no or low vibrational excitation. The intensity of other vibronic bands corresponding to higher internal excitation of CO<sup>+</sup> <sup>2</sup> was not sufficient to study reactivity in coincidence. For this reason, we decided to perform some measurements not in the coincidence mode, i.e., without pure state-selection but with parent ions in a distribution of excitation that can vary with the photon energy. Two photon-energies were chosen: at <sup>E</sup>phot <sup>=</sup> 13.48 eV, corresponding to the CO<sup>+</sup> 2 (0,0,0) X25g,3/<sup>2</sup> ← CO2(0,0,0) X16<sup>+</sup> g transition, the CO<sup>+</sup> 2 cation will be produced with no vibrational excitation; at Ephot = 16.48 eV, corresponding to a strong resonant autoionization transition via Rydberg states converging to the B˜ state of CO<sup>+</sup> 2 , the latter will be produced in the X electronic state but with a broad distribution of internal energies, hence in a mixture of low and high vibrational excitation (see Baer and Guyon, 1986 for details).

Deuterated methane (CD4) was used for the reactivity study, to avoid partial mass overlap between the strong parent ion peak at m/z 44 and the one due to the product of the H-atom transfer process at m/z 45. CD<sup>4</sup> pressure in the scattering cell was kept in the range 1–2 × 10−<sup>4</sup> mbar throughout the experiments. Some considerations on possible isotope effects arising when CD<sup>4</sup> is replaced by CH<sup>4</sup> are addressed in the Conclusions.

#### RESULTS AND DISCUSSION

#### Results in the DC Mode

As already mentioned in the previous section, in the DC mode we have measured absolute values of the cross sections as a function of the collision energy ECM at two selected photon energies: Ephot = 13.78 eV (no vibrational excitation of the CO<sup>+</sup> 2 cation) and Ephot = 16.48 eV (some excitation to high vibrational levels). The main reaction products observed are due to the CT and deuterium-atom-transfer channels (1) and (2), respectively:

$$\rm{CO}\_2^+ + \rm{CD}\_4 \rightarrow \rm{CO}\_2 + \rm{CD}\_4^+ \tag{1}$$

$$\rightarrow \text{ DCO}\_2^+ + \text{CD}\_3 \tag{2}$$

Also, small amounts of CD<sup>+</sup> 3 , and minimal amounts of CD3CO<sup>+</sup> 2 are detected and attributed to the following channels (3), (4) and (5):

$$\text{CO}\_2^+ + \text{CD}\_4 \rightarrow \text{CD}\_3^+ + \text{DOCO} \tag{3}$$

$$\rightarrow \text{ CD}\_3^+ + \text{D} + \text{CO}\_2 \tag{4}$$

$$\rightarrow \text{ CD}\_3\text{CO}\_2^+ + \text{D} \tag{5}$$

Using literature values (taken from NIST Chemistry Webbook<sup>1</sup> , with the exception of some products as specified in the following) for the standard enthalpies of formations (1fH◦ ) of reagents and products we can assess that both channels (1) and (2) are exothermic, while channels (3) and (4) are endothermic. In particular, the CT channel (1) has a reaction enthalpy 1rH◦ = −1.17 eV, while 1rH◦ for (2) is equal to −1.26 eV, assuming that HOCO<sup>+</sup> has the structure of the hydroxyformyl cation (Holmes et al., 2006). The production of CD<sup>+</sup> 3 can derive either from D<sup>−</sup> transfer process (3) or from dissociative CT (4). In the former case, the DOCO radical might be formed in association with the methyl cation, and the overall process is calculated to be endothermic by about 0.56 eV, using the heat of formation of HOCO as reported in Francisco et al. (2010). In the latter case, the methyl cation derives from dissociation of the CT product and the process is endothermic by about 0.61 eV.

The CD3CO<sup>+</sup> 2 formation can be due to D loss from the ionmolecule adduct CO<sup>+</sup> 2 -CD<sup>4</sup> (reaction 5). We can attempt to estimate the reaction enthalpy of (5) assuming that CD3CO<sup>+</sup> 2 has the structure of the methoxycarbonyl cation [an average value for its heat of formation 1fH◦ (CH3OCO+) is 5.57±0.19 eV, as reported in Holmes et al., 2006] to get 1rH◦ = −1.10 eV. We note in passing that the adduct CO<sup>+</sup> 2 -CD<sup>4</sup> was not observed,

FIGURE 2 | Reactive cross sections for products CD<sup>+</sup> 4 (uncorrected, black circles), DOCO<sup>+</sup> (uncorrected, red squares), CD<sup>+</sup> 3 (green diamonds), and CD<sup>+</sup> 5 (blue triangles) measured as a function of the collision energy (ECM) in the DC mode at a photon energy Ephot = 13.78 eV. The open black circles and open red squares are the CD<sup>+</sup> 4 and DOCO<sup>+</sup> cross sections corrected to include the contribution of secondary reactions leading to CD<sup>+</sup> 5 . The dotted line represents the CD<sup>+</sup> 4 cross sections corrected for the instrumental effect due to decreased collection efficiency at low ECM (see text for details). Error bars on all the data are about 30%: for the sake of clarity only two error bars are reported, at arbitrarily chosen low and high collision energy values.

as expected, as the CD<sup>4</sup> pressure in the scattering cell used throughout the experiments (about 2 × 10−<sup>4</sup> mbar) was too low to allow for secondary collisions for its stabilization.

Cross sections for products CD<sup>+</sup> 4 , DOCO<sup>+</sup> and CD<sup>+</sup> 3 as well as CD<sup>+</sup> 5 (from secondary reactions of the primary CD<sup>+</sup> 4 and DOCO<sup>+</sup> products) measured as a function of the collision energy when the reagent CO<sup>+</sup> 2 ion is in its ground vibrational state (i.e., at Ephot = 13.78 eV) are reported in **Figure 2**, while results for Ephot = 16.48 eV are shown in **Figure 3**. The cross section for CD<sup>+</sup> <sup>5</sup> was measured to correct the absolute value of the cross section for reactions (1) and (2) due to product ion losses via the highly efficient secondary reactions operative at the deuterated methane pressures used:

$$\rm{CD}\_4^+ + \rm{CD}\_4 \rightarrow \rm{CD}\_5^+ + \rm{CD}\_3 \tag{6}$$

$$\rm{DOCO}^{+} + \rm{CH}\_{4} \rightarrow \rm{CD}\_{5}^{+} + \rm{CO}\_{2} \tag{7}$$

with k = 1.1×10−<sup>9</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·sec−<sup>1</sup> for reaction (6) (Anicich, 2003) and k = 7.2 × 10−<sup>10</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·sec−<sup>1</sup> for reaction (7) (Anicich, 2003). The measured CD<sup>+</sup> 5 yields have been redistributed among the CD<sup>+</sup> 4 and DOCO<sup>+</sup> products on the basis of the CD<sup>+</sup> 4 /DOCO<sup>+</sup> yield ratio (that changes with collision energy from ∼2 at low energies up to ∼7 at high energies) and of the different rate coefficients for reactions (6) and (7). In **Figures 2**, **3** the uncorrected and corrected cross sections for CD<sup>+</sup> 4 are labeled as "CD<sup>+</sup> 4 " and "CD<sup>+</sup> 4 corr" respectively, and the same notation is used for DOCO+.

The sudden increase in the cross section shown for CD<sup>+</sup> 4 and CD<sup>+</sup> 5 products at ECM ∼ 0.3 eV (clearly visible in the

<sup>1</sup>NIST Chemistry WebBook, NIST Standard Reference Database Number 69 (2017), eds. P.J. Linstrom, and W.G. Mallard (Gaithersburg, MD: National Institute of Standards and Technology), 20899.

FIGURE 3 | Reactive cross sections for products CD<sup>+</sup> 4 (uncorrected, black circles), DOCO<sup>+</sup> (uncorrected, red squares), CD<sup>+</sup> 3 (green diamonds), and CD3CO<sup>+</sup> 2 (magenta triangles) measured as a function of the collision energy (ECM) in the DC mode at a photon energy Ephot = 16.48 eV. The open black circles and open red squares are the CD<sup>+</sup> 4 and DOCO<sup>+</sup> cross sections corrected to include the contribution of secondary reactions leading to CD<sup>+</sup> 5 (data not shown). The dotted line represents the CD<sup>+</sup> 4 cross sections corrected for the instrumental effect due to decreased collection efficiency at low ECM (see text for details). Error bars on all the data are about 30%: for the sake of clarity only two error bars are reported, at arbitrarily chosen low and high collision energy values.

data of **Figure 2**, but also present in the data of **Figure 3**) is an instrumental effect due to a decrease in the collection efficiency for "slow" products. In particular, when product ions are produced at very low velocities in the lab frame, they have a chance to move backwards in the 1st octopole (O1) in the opposite direction from the parent ions, and they then face the last electrode before this octopole, L3, which is set to a potential of −0.4 V. As these ions are produced in O1, their fate depends on their initial kinetic energy and the relative values of the O1 and L3 potentials. At high collision energies, the mean potential of O1 is very low (negative values) and all product ions going back in O1 are reflected on L3 and later detected. At low collision energies, the O1 potential can be higher than that of L3, and backward product ions can be lost, accounting for the step in the product yield observed below collision energies of ∼0.3 eV. To correct for such effect, we have rescaled the data measured at ECM ≤ 0.3 eV by a fixed multiplication factor, chosen equal to 1.12 to match the data measured at ECM < 0.3 eV with those measured at higher collision energy. Implicit in this way of rescaling data is the assumption that the number of product ions lost at low collision energy is independent on the collision energy. The corrected data (reported only for CD<sup>+</sup> 4 cross sections corrected for the presence of secondary reactions leading to CD<sup>+</sup> 5 ) are shown as dashed lines in **Figures 2**, **3**.

According to the above-mentioned thermochemistry, the formation of CD<sup>+</sup> 3 via either (3) or (4) is endothermic and the cross-section for its formation, when CO<sup>+</sup> 2 is generated with no vibrational excitation (see green diamonds in **Figure 2**), shows the expected threshold behavior, with an appearance energy compatible with the endothermicity. Above threshold, the cross section increases accordingly with collision energy. The small amount of signal observed below the threshold is an artifact due to the tail of the very intense mass peak at 20 m/z (CD<sup>+</sup> 4 ). Data measured at Ephot = 16.48 eV show non-negligible cross sections even at low ECM, thus indicating that vibrational excitation of the CO<sup>+</sup> 2 cation can promote the endothermic channel.

At Ephot = 13.78 eV and at the CD<sup>4</sup> pressure used, the yield of CD3CO<sup>+</sup> <sup>2</sup> was below the detection limit, while at Ephot = 16.48 eV it was possible to measure a cross section for this very minor channel (data for CD3CO<sup>+</sup> 2 in **Figure 3** are multiplied by 300 to be able to show them in the same scale of the other products).

In **Table 2** results at the two photon energies are summarized by reporting the branching ratios (BRs) for the observed product channels and the energy-dependent rate constants. BR for the ith channel have been calculated from the absolute cross sections according to the expression:

$$BR\left(i\right) = \frac{\sigma\_i}{\sum \sigma\_i}$$

The energy-dependent total rate constants ktot(Eave) have been estimated using the expression ktot(Eave) = hVi · σtot, were σtot is the total reaction cross section (i.e., P σi), as measured in this work (see data in **Figures 3**, **4**) and <v> is the average relative velocity that can be estimated from the collision energy ECM (see Ervin and Armentrout, 1985 and Nicolas et al., 2002 for a more detailed treatment). While the total rate constants do not change (within the error bars) when increasing the amount of internal excitation of the CO<sup>+</sup> 2 cation (compare the values at different photon energies but same Eave), a slight change in the BRs is observed when increasing the collision energy, which favors the production of CD<sup>+</sup> 4 (and CD<sup>+</sup> 3 ) over that of DOCO+.

Interestingly, our results for the branching ratios (see **Table 2**) show reaction (1) to be the dominant channel at all the explored collision energies, in net disagreement with some of the existing values for the branching ratios (see **Table 1**). As already mentioned, in fact, in the literature there is a spread of the branching ratios for reaction (1) and (2) ranging from 1:0 (Durup-Ferguson et al., 1983) to 0.6:0.4 (Smith et al., 1978), to 0.5:0.5 (Copp et al., 1982), to 0.28:0.72 (Tsuji et al., 1994) and 0.25:0.75 (Huntress et al., 1980), and finally to 0:1 (Harrison and Myher, 1967; Rakshit and Warneck, 1980). We provide here some explanations for the differences observed between our experiment and previous ones:

1. In addition to working with CD4, in our experiment we perform a mass selection of the parent ion before reaction. In this way, we eliminate the contribution due to the <sup>13</sup>CO<sup>+</sup> 2 parent ion that appears at the same m/z as the HOCO<sup>+</sup> product (from residual not fully deuterated methane) and represents ∼1% of the parent ion intensity. Additionally, our experimental procedure consists in measuring both parent and product ion yields first with the target gas in the collision cell, secondly with the target gas in the chamber. In this way, we correct for any contribution of "impurities" coming from the source at the same mass as the product (namely <sup>13</sup>CO<sup>+</sup> 2 /HOCO+). In one of the


TABLE 2 | Energy-dependent rate constants and branching ratios (BRs) for the title reaction measured in the DC mode at two different values of photon energies (Ephot) and average collision energies (Eave).

<sup>a</sup>Total (i.e., summed over all the product channels) rate constant (in cm<sup>3</sup> ·molecule-1 ·s -1) at the specified average collision energy Eave, estimated as detailed in the text.

earlier papers (Tsuji et al., 1994), the experiment is performed without parent ion mass selection, and no correction for <sup>13</sup>CO<sup>+</sup> 2 is mentioned. Hence the claimed HOCO<sup>+</sup> branching ratio (0.72) is most likely overestimated. In Durup-Ferguson et al. (1983), the parent ion mass selection is performed, although no indication is given about the mass resolution. In Rakshit and Warneck (1980), a mixing of CO<sup>+</sup> 2 , CO2CO<sup>+</sup> 2 and H2O<sup>+</sup> parent ions are used. The values from Huntress et al. (1980) are given without any experimental details, for which a reference is given to an earlier paper (Huntress, 1977) where the ICR set-up is described. However, the earlier paper does not contain data for the title reaction, and it is impossible to infer whether and how the <sup>13</sup>CO<sup>+</sup> 2 contribution was taken into account.

2. In our experiment, we keep the target gas pressure as low as possible to limit the number of secondary reactions. Some of the earlier works (Harrison and Myher, 1967; Kasper and Franklin, 1972; Tsuji et al., 1994) have a pressure in the reaction cell higher than ours by a factor 30-50, with about the same cell length. Such differences may lead to underestimating the BR for CH<sup>+</sup> 4 if secondary reactions are not adequately accounted for (as done in our study).

3. In our experiment, we use a pure target gas, while some of the earlier works perform mass spectrometry studies in mixtures of gases. If some CO<sup>2</sup> is present in the region where CH<sup>+</sup> 4 products are generated by the CO<sup>+</sup> <sup>2</sup> <sup>+</sup> CH<sup>4</sup> reaction, the CH<sup>+</sup> 4 will be easily consumed by the efficient reaction CH<sup>+</sup> <sup>4</sup> + CO<sup>2</sup> → HOCO<sup>+</sup> + CH<sup>3</sup> (k = 1.2 × 10−<sup>9</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·s −1 ) that will produce HOCO+, leading to a negative bias in the CH<sup>+</sup> 4 /HOCO<sup>+</sup> ratio. This is an issue in Rakshit and Warneck (1980) as highlighted by Copp et al. (1982), where CO<sup>2</sup> is present in the reaction cell, as well as in Ryan and Harland (1974), where mixing of CH4 and CO<sup>2</sup> occurs in the reaction region, in Tsuji et al. (1994), Harrison and Myher (1967) and Kasper and Franklin (1972).

4. In our experiments we mass select ionic products. Hence we can directly give BRs among different channels. In some of the flow/drift tube experiments, the reaction rate constants are measured by observing the decline of the primary ion signal upon addition of the neutral gas. For instance, in Durup-Ferguson et al. (1983) no mention is made about the mass detection of products, as if the authors have assumed the exclusive formation of CH<sup>+</sup> 4 via non-dissociative CT, not considering the possibility that HOCO<sup>+</sup> might be produced.

#### Results in the TPEPICO Mode

In the TPEPICO mode, we recorded cross sections for the reaction of CO<sup>+</sup> 2 ions in the (0,0,0) ground state and in two vibrationally excited states: (0,1,0) with one quantum of bending vibration and [(1,0,0) + (0,0,1)] corresponding to a combination of the symmetric and antisymmetric stretching vibration. Cross sections were measured for products CD<sup>+</sup> 4 , DOCO<sup>+</sup> and CD<sup>+</sup> 3 as well as CD<sup>+</sup> 5 (from secondary reactions of the primary CD<sup>+</sup> 4 products, see above). The ion yield for product CD3CO<sup>+</sup> <sup>2</sup> was too low to be detectable in coincidence. For most of the other products, reactive cross sections were measured at two different collision energies ECM = 0.17 ± 0.02 eV and 1.34 ± 0.01 eV and results are shown in **Figures 4**, **5**. Despite the larger uncertainties (due to the low S/N ratio in the coincidence mode) cross section measurements are consistent with results obtained in the DC mode. In particular, when converting cross sections reactions leading to CD<sup>+</sup>

5 .

reported in **Figure 4** for CO<sup>+</sup> 2 at low collision energy and in the (0,0,0) ground state we obtain the following BRs: CD<sup>+</sup> 4 (0.75 ± 0.25), DOCO<sup>+</sup> (0.25 ± 0.11) and CD<sup>+</sup> 3 (0.00 ± 0.03), entirely consistent, within the error bars, with the data obtained in the DC mode (see **Table 2**, second column from the left).

In addition, the TPEPICO results confirm that cross sections for the exothermic CT (1) and deuterium-atom-transfer (2) channels change very little with increasing vibrational excitation, and the increase is more evident in data taken at high collision energy (**Figure 5**). Cross sections for the endothermic channel leading to CD<sup>+</sup> 3 increase with collision energy but they do not seem to depend strongly on the internal excitation of the ionic parent, at least for the low internal excitations here explored (i.e., maximum one quantum of vibrational excitation).

The observed small dependence of reactions (1) and (2) from CO<sup>+</sup> 2 vibrational excitation requires some consideration. First of all, we note that our result is in agreement with a previous study (Durup-Ferguson et al., 1983) in which a drift tube technique is used, and the dependence of the reaction rate constant on the internal energy of the ions is examined by varying the mass of the buffer gas. Despite the limitations of the technique compared to our truly state-selection method, in Durup-Ferguson et al. (1983) the non-dissociative CT giving CH<sup>+</sup> 4 plus CO<sup>2</sup> is found to occur at near the collision rate and to have little energy dependence and no measurable vibrational dependence.

We also note that, differently from the CH<sup>4</sup> case, vibrational excitation of CO<sup>+</sup> 2 ions was found to enhance the CT reaction probability with O<sup>2</sup> (Durup-Ferguson et al., 1983; Ferguson et al., 1992; Viggiano and Morris, 1996; Nicolas et al., 2002). To rationalize such results, it should be considered that the two systems present several differences:

• CT channels have different exothermicities (−1.17 eV for CH<sup>4</sup> and −1.71 for O2).

• The CT rate constant is substantially larger for CH<sup>4</sup> (k = 0.3– 1 × 10−<sup>9</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·s −1 , see values in our **Table 1**) than for O<sup>2</sup> (k ∼ 5 × 10−<sup>11</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·s −1 ).

The inefficiency of the CT with O<sup>2</sup> is attributed to the nonresonant character of the reaction, i.e., to the fact that Franck-Condon factors for O<sup>2</sup> ionization at the ionization potential of CO<sup>2</sup> (13.78 eV) are close to zero (see for instance Wacks, 1964). On the other hand, it is known that for CH<sup>4</sup> the Franck-Condon factors are low at the ionization threshold and increase reaching a maximum in the region 13.5–14.5 eV (see for instance Stockbauer and Inghram, 1971). Thus, while in the CH<sup>4</sup> case CT can occur efficiently at long range via the direct mechanism previously described, for O<sup>2</sup> it should involve the formation of a collision complex. As tentatively explained and demonstrated in Ferguson et al. (1992), in the O<sup>2</sup> case a small amount in the stretching excitation of CO<sup>+</sup> 2 can lead to an increase in the CT probability. Hence, CH<sup>4</sup> and O<sup>2</sup> are quite different reaction systems, and in the latter case, the effect of CO<sup>+</sup> 2 excitation could be more pronounced than for a reaction already at the Langevin limit (as in CH4).

More generally, the dynamics of CT processes is regulated by crossings among entrance and exit potential energy surfaces. When such crossings are occurring at distances for which the probability of electron transfer from one adiabatic PES to the other is unfavorable, the CT cross section will be very small even for exothermic processes (according to the Landau-Zener model for CT probability). The fact that increasing the vibrational excitation of the cation does not increase the CT cross section can be related to the fact that the crossing probability does not change much when increasing the vibrational excitation of CO<sup>+</sup> 2 , even though the exothermicity increases. Unfortunately, modeling the dynamics occurring on a CO<sup>+</sup> 2 - CH<sup>4</sup> multidimensional potential energy surface which includes vibrational excitation of CH<sup>4</sup> is not an easy task, and it is beyond the scope of our paper. We hope that our results will stimulate theoreticians and experts in ab-initio calculations to use this system as a test bench for theory.

#### CONCLUSIONS

The reactivity of CO<sup>+</sup> <sup>2</sup> with deuterated methane has been investigated experimentally by guided ion beam mass spectrometric techniques by changing either the kinetic energy of CO<sup>+</sup> 2 or its vibrational excitation (using synchrotron radiation in the VUV energy range to produce vibrationally excited reagent ions). The main products are CD<sup>+</sup> 4 , DOCO+, and CD<sup>+</sup> 3 and reactivity is found to depend on the reagent collision energy, but not so much on the vibrational excitation of CO<sup>+</sup> 2 .

An interesting issue is whether reaction rates and dynamics change or remain the same when CD<sup>4</sup> is replaced by CH4. We do not expect charge transfer cross sections to be affected by a strong kinetic isotope effect (KIE). On the other hand, one can foresee a kinetic isotope effect in the H/D atom transfer channel leading to HOCO+/DOCO+. In particular, according to the semi-classical theory of primary KIE a normal effect (i.e., kH/k<sup>D</sup> > 1) is expected in the transfer of an H/D atom due to the vibrational zero-point energy differences for each of the vibrational modes of the reactants and transition state. Despite the limited mass resolution in our experimental set-up, we have managed to perform some tests using CH<sup>4</sup> in the reaction cell and measuring BRs and cross sections at a fixed collision energy of 0.11 eV in the DC mode at a photon energy Ephot = 13.78 eV (i.e., same conditions of **Figure 2**). Products are observed at m/z values corresponding to CH<sup>+</sup> 4 , CH<sup>+</sup> 5 , and HOCO+. By correcting for secondary reactions (as detailed in the text) we obtain a BR of 0.74:0.26 = CH4+: HOCO<sup>+</sup> and a total cross section of 199 (±30%) Å<sup>2</sup> , corresponding to an energy-dependent rate constant of (2.68 ± 0.8) × 10−<sup>9</sup> cm<sup>3</sup> ·molecule−<sup>1</sup> ·s −1 to be compared with the CD<sup>4</sup> value of (1.8 ± 0.5) × 10−<sup>9</sup> at similar Eave (see our results in **Table 2**) and the BR of 0.63:0.36 = CD<sup>+</sup> 4 : DOCO+. This means a positive KIE kH/k<sup>D</sup> = 1.5(±0.6). On the other hand, our results show that when CD<sup>4</sup> is replaced by the lighter isotopolog, the CT is more favored than the H atom transfer. This effect can be explained assuming that the different vibrational spacings in CD4/CH<sup>4</sup> might change the Franck-Condon factors and the efficiencies of non-adiabatic transition probability among the entrance and exit potential energy surfaces. We note that in a similar reacting system CN<sup>+</sup> plus CH4/CD<sup>4</sup> a KIE in the total rate coefficient similar to the one observed in our case has been reported, namely kH/k<sup>D</sup> = 1.55 (±0.66) (Raksit et al., 1984).

To put our results into the context of plasma chemistry used for the conversion of CO<sup>2</sup> in carbon-neutral fuels (Snoeckx et al., 2013; Snoeckx and Bogaerts, 2017), both the products (CH<sup>+</sup> 4 and HOCO+) of the reaction of CO<sup>+</sup> <sup>2</sup> with CH<sup>4</sup> eventually lead to the production of CH<sup>+</sup> 5 and CH3, as shown in the following scheme:

$$\text{CO}\_2^+ + \text{CH}\_4 \rightarrow \underset{\text{иO}\text{CO}^+}{\text{CO}\_2} \begin{array}{c} \text{CO}\_2 + \text{CH}\_4^+ \\ \text{Cu} \end{array} \tag{1}$$

$$\text{CO}\_2^+ + \text{CH}\_4 \rightarrow \begin{array}{c} \text{CO}\_2 + \text{CH}\_4\\ \text{HOCO}^+ + \text{CH}\_3 \end{array} \tag{2}$$

$$\text{CH}\_4^+ + \text{CH}\_4 \rightarrow \text{CH}\_5^+ + \text{CH}\_3 \tag{8}$$

$$\rm CH\_4^+ + CO\_2 \rightarrow HOCO^+ + CH\_3 \tag{9}$$

$$\rm{HOCO}^{+} + \rm{CH}\_{4} \rightarrow \rm{CH}\_{5}^{+} + \rm{CO}\_{2} \tag{10}$$

#### REFERENCES


Thus the energy initially used to ionize CO<sup>2</sup> is transferred to CH<sup>4</sup> to form CH<sup>+</sup> 4 , CH<sup>+</sup> 5 and CH3. Only processes (2) and (9) lead to HOCO<sup>+</sup> that, in addition to react with CH4, giving back CO2, can also recombine with electrons to yield CO plus OH.

#### DATA AVAILABILITY

The datasets generated for this study are available on request to the corresponding author.

## AUTHOR CONTRIBUTIONS

DA, CA, and PT contributed conception and design of the study. CA, CR, and JŽ planned and developed the experimental set-up. DA, CR, CA, AL, JŽ, MP, and CS contributed to data acquisition, data analysis, and interpretation of results. DA wrote the first draft of the manuscript. DA, PT, and CA wrote sections of the manuscript. All authors contributed to manuscript revision, read and approved the submitted version.

#### ACKNOWLEDGMENTS

We thank the DESIRS beamline team, L. Nahon, G. Garcia, N. De Oliveira, and J.-F. Gil, for assistance during the synchrotron measurements and the technical staff of SOLEIL for running the facility under projects n◦ 20140033 and 20150468. CA and CR acknowledge the synchrotron SOLEIL for the support to the associated CERISES setup since 2008 and subsistence expenses during beamtime periods. DA acknowledges financial support from the EU-TNA program during beamtime n◦ 20140033. JŽ and MP acknowledge support from the Czech Science Foundation project No. 17-14200S. DA and PT thanks the Department of Physics of the University of Trento for support.


N + 2 (X <sup>2</sup>Σ<sup>+</sup> g ; v<sup>+</sup> = 0–2; N<sup>+</sup> = 0–9) + Ar. J. Chem. Phys. 137:104202. doi: 10.1063/1.4750248


beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL. J. Synchrotron Rad. 19, 508–520. doi: 10.1107/S0909049512010588


**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Ascenzi, Romanzin, Lopes, Tosi, Žabka, Polášek, Shaffer and Alcaraz. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Angular Distribution of Ion Products in the Double Photoionization of Propylene Oxide

Stefano Falcinelli <sup>1</sup> \*, Marzio Rosi <sup>1</sup> , Fernando Pirani <sup>2</sup> , Davide Bassi <sup>3</sup> , Michele Alagia<sup>4</sup> , Luca Schio4,5, Robert Richter <sup>6</sup> , Stefano Stranges 4,7, Nadia Balucani <sup>2</sup> , Vincent Lorent <sup>8</sup> and Franco Vecchiocattivi <sup>1</sup>

<sup>1</sup> Department of Civil and Environmental Engineering, University of Perugia, Perugia, Italy, <sup>2</sup> Department of Chemistry, Biology and Biotechnologies, University of Perugia, Perugia, Italy, <sup>3</sup> Department of Physics, University of Trento, Trento, Italy, 4 IOM-CNR Tasc, Trieste, Italy, <sup>5</sup> Department of Basic and Applied Sciences for Engineering (SBAI), University of Rome "Sapienza", Rome, Italy, <sup>6</sup> Elettra-Sincrotrone Trieste, Trieste, Italy, <sup>7</sup> Department of Chemistry and Drug Technologies, University of Rome "Sapienza", Rome, Italy, <sup>8</sup> Laboratoire de physique des lasers, Université Paris 13 (UP13) - Institut Galilée - CNRS LPL UMR7538, Villetaneuse, France

#### Edited by:

Michal Fárník, J. Heyrovsky Institute of Physical Chemistry (ASCR), Czechia

#### Reviewed by:

Mauricio Federico Erben, National University of La Plata, Argentina Lionel Poisson, UMR9222 Laboratoire Interactions, Dynamiques et Lasers (LIDYL), France

> \*Correspondence: Stefano Falcinelli stefano.falcinelli@unipg.it

#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

Received: 07 February 2019 Accepted: 29 August 2019 Published: 11 September 2019

#### Citation:

Falcinelli S, Rosi M, Pirani F, Bassi D, Alagia M, Schio L, Richter R, Stranges S, Balucani N, Lorent V and Vecchiocattivi F (2019) Angular Distribution of Ion Products in the Double Photoionization of Propylene Oxide. Front. Chem. 7:621. doi: 10.3389/fchem.2019.00621 A photoelectron-photoion-photoion coincidence technique, using an ion imaging detector and tunable synchrotron radiation in the 18.0–37.0 eV photon energy range, inducing the ejection of molecular valence electrons, has been applied to study the double ionization of the propylene oxide, a simple prototype chiral molecule. The experiment performed at the Elettra Synchrotron Facility (Trieste, Italy) allowed to determine angular distributions for ions produced by the two-body dissociation reactions following the Coulomb explosion of the intermediate (C3H6O)2<sup>+</sup> molecular dication. The analysis of the coincidence spectra recorded at different photon energies was done in order to determine the dependence of the β anisotropy parameter on the photon energy for the investigated two-body fragmentation channels. In particular, the reaction leading to CH<sup>+</sup> <sup>3</sup> <sup>+</sup> <sup>C</sup>2H3O<sup>+</sup> appears to be characterized by an increase of <sup>β</sup>, from <sup>β</sup> <sup>≈</sup> 0.00 up to β = 0.59, as the photon energy increases from 29.7 to 37.0 eV, respectively. This new observation confirms that the dissociation channel producing CH<sup>+</sup> 3 and C2H3O<sup>+</sup> final ions can occur with two different microscopic mechanisms as already indicated by the bimodality obtained in the kinetic energy released (KER) distributions as a function of the photon energy in a recent study. Energetic considerations suggest that experimental data are compatible with the formation of two different stable isomers of C2H3O+: acetyl and oxiranyl cations. These new experimental data are inherently relevant and are mandatory information for further experimental and theoretical investigations involving oriented chiral molecules and linearly or circularly polarized radiation. This work is in progress in our laboratory.

Keywords: double photoionization, molecular dications, coincidence technique, propylene oxide, chiral, synchrotron radiation, angular distribution, astrochemistry

## INTRODUCTION

In life science a basic role is played by the left-right dissymmetry, at a macroscopic as well as at the microscopic level. In terrestrial life the unknown origin of homochirality and of the enantio-selectivity in biochemical processes involving chiral molecules are among the most intriguing aspects in natural phenomena (Engel and Macko, 1997; Pizzarello and Groy, 2011). Therefore, a big role is played by the investigation of molecular enantiomeric nature on various fields of chemistry, as for example the heterogeneous enantioselective catalysis, the photochemical asymmetric synthesis, the study of drug activity and enzymatic catalysis, the chiral surface science involving supramolecular assemblies.

Nowadays, and already for several decades, a wide number of experiments are carried out world-wide using circularly polarized tunable light sources of high intensity as synchrotron radiation and, in order to detect chirality in molecules, imaging photoelectron circular dichroism (Turchini et al., 2004; Stranges et al., 2005; Piancastelli et al., 2007; Alberti et al., 2008; Janssen and Powis, 2014). Moreover, techniques of molecular alignment with the pioneering work done by Zare et al. (Sinha et al., 1974; Caldwell and Zare, 1977) and by B. Friedrich and D. R. Herschbach (Friedrich and Herschbach, 1991; Friedrich et al., 1991) have been found of great relevance to control the stereodynamics of elementary chemical processes occurring in the gas phase and at surfaces, and are arguably crucial in chirality issues (Falcinelli et al., 2018a). In particular, previous studies (Caldwell and Zare, 1977; Karny et al., 1978; Sanders and Anderson, 1984; Pullman et al., 1990; Aquilanti et al., 1994) indicate that molecular directionality and alignment should strongly amplify dichroism and provide stereodynamical mechanisms for discrimination of enantiomers, other than via circularly polarized light (Herwig et al., 2013; Pitzer et al., 2013; Tia et al., 2017). Very recently, in our laboratory we are working, to couple a mechanical molecular velocity selector, specifically constructed ad hoc (able to control the velocity dependence of the molecular alignment) with a PEPIPICO (photo-electronphoto-ion-photo-ion coincidence) imaging device, in order to be used with a synchrotron radiation (Falcinelli et al., 2018a), delivering tunable intense photon sources with high degree of both linearly and circularly polarized light of both helicities. Double photoionization studies on propylene oxide enantiomeric molecules have been done by exploiting Auger spectroscopy (Piancastelli et al., 2007; Alberti et al., 2008). In these experiments, using high photon energy synchrotron radiation (in the 289–380 eV energy range), the authors indirectly estimated the first double ionization threshold, allowing the observation of a weak circular dichroism effect (Alberti et al., 2008). In our recent experimental work performed at the Synchrotron Radiation Facility of Elettra (Trieste, Italy) we were able to identify six two body fragmentation channels produced by double photoionization of propylene oxide in the 18.0– 37.0 eV photon energy range, including their relative threshold energies (Falcinelli et al., 2018a). Such two body fragmentation channels involve the direct ejection of two valence electrons, and allowed us to determine with more accuracy the first double photoionization energy of propylene oxide, obtaining the values of 28.3 ± 0.1 which is 0.9 eV below the previous indirect estimation of 29.2 eV by Auger spectroscopy (Piancastelli et al., 2007; Alberti et al., 2008).

Recently, using the photoelectron circular dichroism (PECD) as an established technique for chiral differentiation, interesting PECD data have been recorded in single photoionization experiments on enantiomerically pure trifluoromethyl-oxirane and methyl-oxirane (Garcia et al., 2014).

In 2016 propylene oxide has been discovered as the first chiral molecule in space by McGuire et al. by means of astronomical detection in absorption toward the Galactic center (McGuire et al., 2016). This important result highlights the relevance of a deep and full investigation of the possible fragmentation processes following the microscopic fragmentation dynamics by Coulomb explosion of propylene oxide (C3H6O)2<sup>+</sup> molecular dications produced by VUV double photoionization.

After the pioneering work of Hipple concerning the spontaneous dissociation processes of ions (Hipple, 1948), the importance of the fragmentation dynamics following single and double photodissociation photoionization processes has been investigated in a number of papers, respectively by R. N. Zare, who first fully described the dynamics of molecular photodissociation (Zare and Herschbach, 1962, 1963; Zare, 1972; Greene and Zare, 1982), and by J. H. D. Eland et al. (Eland and Treves-Brown, 1992; Field and Eland, 1993; Eland, 2006). Following such basic contributions, various authors contributed to this Research Topic (Fišer et al., 2009; Price et al., 2017), also highlighting the role of singly and doubly charged ions in the chemistry of upper planetary atmospheres (Thissen et al., 2011; Falcinelli et al., 2014, 2016a) and in space (Ascenzi et al., 2004; Bartolomei et al., 2008; Skouteris et al., 2015). Furthermore, dissociation dynamics of multiply charged ions has been studied [see for example Geronés et al. and references therein (Geronés et al., 2007)] with related implications on chemistry of the interstellar medium (Geronés et al., 2012). In particular, molecular metastable dications have attracted the attention of the scientific community after the pioneering valence bond calculations on He2<sup>+</sup> 2 carried out by Linus Pauling in 1933 (Pauling, 1933), since the possibility to be used as species able to store energy at a molecular level (Nicolaides, 1989; Boldyrev and Simons, 1992; Falcinelli et al., 1996; Tosi et al., 1999). These species can in principle be used as a new kind of alternative propellants since they are able to release a considerable amount of energy (up to about 10 eV) following their unimolecular fragmentation process by Coulomb explosion. In fact, this released amount of energy is exceptionally high being much greater than the energy obtainable from other important gasphase reactions such as the one involving H<sup>2</sup> and O<sup>2</sup> producing water which is exothermic by ∼2.52 eV (Nicolaides, 1989).

In this paper, a double photoionization study of propylene oxide—a prototype chiral molecule—is presented. The results of this experiment provide a solid basis to plan more ambitious future studies capable to highlight possible differences characterizing the interaction of polarized light with chiral systems, such as the angular distribution of both photoemitted electrons and produced ions. In order to achieve such a goal, first of all, we have recently started by the use of linearly polarized synchrotron radiation, such as the one available at the Circular Polarization (CiPo) beamline at the ELETTRA Synchrotron Facility of Trieste (Italy). We performed double photoionization experiments involving a racemic mixture of propylene oxide, using the same ARPES (Angle-Resolved PhotoEmission Spectroscopy) apparatus (see next section) successfully employed in previous studies at the Elettra "GasPhase" beamline, since almost two decades (Alagia et al., 2002, 2004a,b,c, 2011a,b, 2013a; Falcinelli et al., 2017a,b). Even if the use of a racemic mixture of propylene oxide could appear as a limitation in our experiment, the recorded data here presented are very important for further experimental investigations involving single enantiomers that are planned in next future. In this preliminary work we were able to identify the most abundant two-body fragmentation channels produced by the photodissociation process of the neutral molecular C3H6O precursor. In such an experiment the use of a single photon with an energy content around the threshold of the double photoionization of the molecule under study is able to extract a pair of valence electrons. This allows the formation of an intermediate molecular dication able to dissociate by Coulomb explosion, as we have discussed in our previous investigations (Alagia et al., 2004a, 2006a, 2007, 2010; Falcinelli et al., 2014, 2016a,b), even if a debate is still open on whether the multiply charged molecule obeys pure Coulomb explosion model during its breakup or not (Sheehy and DiMauro, 1996; Mathur, 2004). Preliminary data already published on the double photoionization of propylene oxide concern: (i) the threshold energy for the recorded six two-body dissociation channels producing C2H + 4 /CH2O+, C2H + 3 /CH3O+, CH<sup>+</sup> 2 /C2H4O+, CH<sup>+</sup> 3 /C2H3O+, O+/C3H + 6 , and OH+/C3H + 5 ion pairs; (ii) their relative cross sections as a function of the investigated photon energy; and (iii) the kinetic energy released (KER) distributions of each ion pair products as a function of the photon energy (Falcinelli et al., 2018a). In the present paper we report on the angular distributions of ion pair products formed in the two-body fragmentation reactions mentioned above. The measured angular distributions as a function of the photon energy (in the range of 18.0–37.0 eV) and the determination of the related anisotropy parameter β allowed us to confirm the existence of two possible microscopic mechanisms for the fragmentation channel producing CH<sup>+</sup> 3 /C2H3O<sup>+</sup> ion pairs, as highlighted by the bimodality behavior in the recorded KER distributions already published (Falcinelli et al., 2018a) and by recent energetic considerations based on the high level coupled-cluster single and double plus perturbative triples CCSD(T) preliminary calculations (Falcinelli et al., 2019b).

## EXPERIMENTAL

Experiments have been carried out at the ELETTRA Laboratory, using the ARPES end station at the CiPo beamline. For a detailed description of the beamline and the end station the reader can refer to Derossi et al. (1995) and Alagia et al. (2006a, 2013b), respectively. Main characteristics of the used PEPIPICO time-of-flight technique have been described in previous studies producing and characterizing dications in the double photoionization of various neutral precursor molecules (Alagia et al., 2006b, 2009; Falcinelli et al., 2016b). Here, only a brief summary is given of the used experimental apparatus, and related procedures.

The operating pressure of the ARPES end station is 10−<sup>7</sup> - 10−<sup>8</sup> mbar. The high intensity energy tunable synchrotron light beam crosses at right angle an effusive molecular beam of propylene oxide. Product ions and photoelectrons produced by each double photoionization event are detected in coincidence. The experiment used a synchrotron light scanned in the 18.0–37.0 eV investigated photon energy range at the "CiPo" beamline with the light polarization vector which is in the synchrotron ring plane and perpendicular to the used timeof-flight (TOF) mass spectrometer. The Normal Incidence Monochromator (NIM), equipped with two different (2,400 l/mm gold and 1,200 l/mm aluminum coated) holographic gratings, allows to cover the 8.0–37.0 eV energy range. The resolution over this range is about 2.0–1.5 meV. The use of the NIM geometry was adopted to reduce spurious effects, due to ionization by photons from higher orders of diffraction. The adoption of the NIM at the "CiPo" beamline, together with the emission spectrum of the electromagnetic wiggler allows to probe a lower photon energy range with respect to the linearly polarized light available at the "GasPhase" beamline. Despite that the "CiPo" beamline can provide both linearly and circularly polarized radiation, since the present experiment involved a racemic mixture of propylene oxide precursor molecules, we recorded the angular distributions of produced ion pairs employing the linearly polarized component. The use of circularly polarized light could be relevant in future experiments when we will try to record possible differences in the angular and energy distribution of fragment ions at different photon energies, employing the two different enantiomers of propylene oxide.

In the experiment we monitored (i) the incident photon flux; (ii) the gas pressure, and (iii) the ion yields for each investigated channel, which are divided for the total ion yield when we are interested to obtain the branching ratios as a function of the photon energy (Falcinelli et al., 2018a). The effusive molecular beam is produced by a 1.0 mm stainless steel needle nozzle fed by a racemic mixture−99% nominal purity—of commercial propylene oxide. At 20◦C propylene oxide is liquid, and its vapor pressure is 0.59 bar. A needle valve is placed between the glass cylinder containing the propylene oxide and the nozzle to optimize the molecular beam source pressure.

The electron-ion-ion coincidence technique was used to detect photoions in coincidence with photoelectrons, ejected from the photoionized neutral molecular precursor. The ion extraction and detection system, as well as the data analysis procedure, have been described in detail elsewhere (Lavollée, 1999; Alagia et al., 2012a). Such a device was especially designed to properly measure the cation photofragment momentum vectors in many body dissociation processes (Lavollée, 1999), and consists of a TOF spectrometer equipped with a position sensitive detector which is composed of a stack of three impedance matched micro-channel-plates (MCP) with a multi-anode array arranged in 32 rows and 32 columns.

In general, our experiments concern the double ionization of simple molecules using a photon energy around the ionization threshold. In such conditions we are able to detect and analyse with a momentum matching procedure (see below) only the twobody fragmentation channels following the Coulomb explosion of the intermediate molecular dication. In particular, by a careful analysis of the coincidence plots recorded for each investigated photon energy we are able to obtain both KER and angular distribution maps of the product ions coming from the Coulomb explosion of the intermediate molecular dication formed by the double photoionization of the neutral propylene oxide precursor. Exploiting a procedure, suggested by Lundqvist et al. (1995) and by Field and Eland (1993), the kinetic energy of the final products, released into the two photofragment ions, as well as the lifetime of the intermediate dication can be extracted, as we have done in the case of the Coulomb explosion of (N2O)2<sup>+</sup> and (CO2) <sup>2</sup><sup>+</sup> dications following the double photoionization of nitrous oxide (Alagia et al., 2006a) and carbon dioxide (Alagia et al., 2009) molecules, respectively. In particular, this goal can be obtained exploiting a momentum matching analysis on the peak for each ion pair in the coincidence spectra measured at all the investigated photon energies (Falcinelli et al., 2018a). The adopted computational procedure used a momentum matching filter to discriminate true coincidences related to each recorded fragmentation channels, produced by Coulomb explosion of the intermediate propylene oxide (C3H6O)2<sup>+</sup> dication. Typical coincidence plots obtained in our PEPIPICO experiment are shown in **Figure 1A** is related to an accumulation run performed at a photon energy of 27.5 eV, which is below the double ionization threshold energy (28.3 eV) of propylene oxide, where only the signal due to single ionization events can be observed (**Figure 1B**) is an ion-ion coincidence plot recorded at a photon energy of 37.0 eV where the signals of the double coincidences are well-evident as the diagonal traces centered at the crossing of the two different arrival times of fragment product ions to the ion position MCP detector. **Figure 1B** is only a portion of the full recorded coincidence spectrum. In this plot the diagonal traces are related to the double coincidences signal of the two-body fragmentation channels. In particular, the yellow dashed oval in **Figure 1B** points out the region used for the evaluation of both KER and angular distributions in the case of the two fragmentation channels leading to C2H + 3 /CH3O<sup>+</sup> and C2H + 4 /CH2O<sup>+</sup> ion pairs. In the plot the double coincidences are reported as a function of the two arrival times (indicated in ns) of ions to the ion imaging detector which are produced from the same double photoionization event followed by Coulomb explosion of the intermediate (C3H6O)2<sup>+</sup> dication. Such dots are extracted and discriminated from either background and single ionization signals in order to be used in the momentum matching filter analysis isolating only pulses due to true double coincidences. To achieve this goal the succeeding analytical condition has been employed:

$$s \le \frac{\sqrt{\mathbf{p}\_{\mathbf{x}1,2}^2 + \mathbf{p}\_{\mathbf{y}1,2}^2 + \mathbf{p}\_{\mathbf{z}1,2}^2}}{|\mathfrak{p}\_1| + |\mathfrak{p}\_2|} \tag{1}$$

Where **px1,2**, **py1,2**, and **pz1,2** stand for the sum of projections of **p<sup>1</sup>** and **p<sup>2</sup>** momentum vectors of the final **1** and **2** ion pairs produced by the two-body fragmentation processes following the double photoionization of the neutral precursor molecule. In the analytical procedure, in which TOF and position on the detector of the arrival ion allow us to extract, without ambiguity, complete information concerning the linear momentum (**px**, **py**, **p<sup>z</sup>** ) for each product ion, and consequently its angular and energy distribution, we used a value of S ≤ 0.1 in order to fully subtract the false coincidences. Such a condition (S ≤ 0.1) allowed us to subtract the background signal in the relative cross section for each recorded two-body fragmentation channel. In particular, S = 0.1 is an empirical factor which is the result of a compromise between a good statistics of the recorded signal and the background subtraction. Following such a procedure we were able to extract the KER distributions of any pair of fragment ions formed in two-body dissociation processes generated by double photoionization of any neutral precursors. For such a purpose we used the well-tested method suggested by Lundqvist et al. (1995) already successfully applied in analogous experiments involving different systems (Alagia et al., 2011a,b, 2012a,b; Falcinelli et al., 2016b). As an example, **Figure 1C** reports a portion of total KER distribution (with an energy resolution of ∼ 0.2 eV) for the production of CH<sup>+</sup> 3 /C2H + 3 ion pair products formed in the double dissociative photoionization of propylene oxide at a photon energy of 35.0 and 37.0 eV. To have an overview of recorded KER distributions for all investigated fragmentation channels produced in the double-photoionization experiments of propylene oxide molecules as a function of the photon energy in the 18.0–37.0 eV range the reader can refer to a recently published paper (Falcinelli et al., 2018b).

#### RESULTS AND DISCUSSION

Previous experiments performed at the ELETTRA Synchrotron Facility, allowed us to perform a direct measurement of the first double photoionization energy for propylene oxide: 28.3 ± 0.1 eV (Falcinelli et al., 2018a). Six different two-body fragmentation channels were recorded in our mass spectra in the investigated photon energy range (18–37 eV) with their respective relative abundances and threshold energies, as it follows:


The highest abundance of the Reaction (2) is due to the direct breaking of the two C−O and C−C bonds in the central C atom of the intermediate (C3H6O)2<sup>+</sup> molecular dication. As already discussed in detail in a previous paper where relative cross sections as a function of the photon energy are reported

a photon energy of 27.5 eV, below the double ionization threshold energy (28.3 eV), where is only present the signal due to single ionization events together with some background. (B) Is a spectrum recorded at a photon energy of 37.0 eV where the signal of the double coincidences is well-evident (the diagonal traces in the figure—see text); the yellow dashed oval points out the region of the coincidence spectrum used for the evaluation of both KER and angular distributions in the case of the two fragmentation channels leading to C2H + 3 /CH3O<sup>+</sup> and C2<sup>H</sup> + 4 /CH2O<sup>+</sup> ion pairs. (C) A portion of total KER distribution for the production of CH<sup>+</sup> 3 /C2H3O<sup>+</sup> ion pair products formed in the double dissociative photoionization of propylene oxide at a photon energy of 35.0 and 37.0 eV. The best fit (full line) of experimental data (open circles) is obtained using the sum of two different Gaussian functions (dashed lines) highlighting a bimodality generated by the presence of two different reaction mechanisms (Falcinelli et al., 2018a).

and discussed for all Reactions (2)–(7) (Falcinelli et al., 2018a), this main important Reaction (2) results in the formation of the most abundant C2H + 4 produced ion in single ionization experiments on propylene oxide, together with CH2O<sup>+</sup> being identified in previous experiments by others authors (Gallegos and Kiser, 1961; Liu et al., 1999). On the other hand, the twobody dissociation Reactions (6) and (7) are characterized by a concerted fragmentation with a hydrogen migration. Such a microscopic mechanism seems to be difficult to achieve in the case of the hydrogen shift toward the oxygen atom [Reaction (7)], as indicated by the low percentage formation of about 0.17%, but it appears of considerable amount for Reaction (6) which involves hydrogen migration toward the carbon atom, being the second more probable recorded fragmentation reaction with its 18.7%. In particular, in the case of the Reaction (6) in order to confirm this hypothesis it would be very useful to carry out an experiment with selectively deuterated propylene oxide (Otley et al., 2011). Future investigations in this direction are planned by our research group at the ELETTRA Synchrotron Facility.

It has to be noted that the CH<sup>+</sup> 3 formation by Reaction (4) could involve two different microscopic mechanisms as already mentioned in a recent paper (Falcinelli et al., 2018a), where the reported KER distributions of CH<sup>+</sup> <sup>3</sup> <sup>+</sup> <sup>C</sup>2H3O<sup>+</sup> final ions clearly show a bimodal behavior. In that paper we anticipated that further experiments were needed in order to clarify the two different microscopic paths involved. With this aim we have performed the present experiment based on the measure of the angular distributions of all ion pair products produced by Reactions (2)–(7) with respect the polarization vector of the used synchrotron radiation. For this purpose we have used the PEPIPICO technique and the related data analysis procedure described in the previous section has been widely employed by our research group during the last 15 years studying the dissociative double photoionization of different simple molecules, as: (i) N2O, where we found a very strong anisotropy distribution for both ion pair products of the two dissociative channels leading to N++ NO<sup>+</sup> and O<sup>+</sup> + N + 2 indicating that N2O molecules ionize when their axis is parallel to the light polarization vector, and the fragment ions are separating in a time shorter than the dication rotational period of about 10−<sup>11</sup> s (Alagia et al., 2007); (ii) CO<sup>2</sup> with the production of intermediates CO2<sup>+</sup> 2 dications having a lifetime of ∼3.1 µs which form O<sup>+</sup> ions with a very high kinetic energy content able to explain their escape from the upper atmosphere of Mars (Alagia et al., 2010; Falcinelli et al., 2016a); and (iii) C2H<sup>2</sup> where a quite evident change in the anisotropy β parameter (see below) related to the symmetric CH++ CH<sup>+</sup> fragmentation reaction indicating that two microscopic mechanisms involving several electronic states of the intermediate C2H 2+ <sup>2</sup> molecular dication are operative (Alagia et al., 2012b). Recently others research groups using the same PEPIPICO technique performed interesting experiments studying the photodissociation of simple organic molecules, as alcohols (Bava et al., 2015), carboxylic acid (Arruda et al., 2016), and perfluoropropionic acid (Martínez et al., 2018).

Using our ions position sensitive detector we obtained two dimensional (2D) images which are related to the photoelectronion-ion coincidence dots on the recorded coincidence plots at each investigated photon energy as those reported in **Figures 1A,B**. As already mentioned above, such dots are generated from pulses of dissociation products recorded as a function of their arrival time and position on the MCP detector plane. The recorded 2D images display the projection of the 3D distributed ion products on the plane of the MCP, and their best fit simulation procedure allowed us to determine the so called anisotropy parameter β according to the following equation (Zare, 1972; Dehmer and Dill, 1978; Ashfold et al., 2006):

$$\mathbf{I}\left(\theta\right) = \frac{\sigma\_{\text{tot}}}{4\pi} \left[\mathbf{1} + \frac{\beta}{2} \left(\mathbf{3}\cos^2\theta - \mathbf{1}\right)\right] \tag{8}$$

The important physical meaning of such an equation concerns the evaluation of the β term whose determination is crucial to obtain a complete description of the microscopic stereodynamics of fragmentation processes in double photoionization experiments involving linearly polarized light, as the one presented here. In fact, in Equation (8), the differential and total cross sections of the two-body fragmentation process under study are **I(**θ**)** and σ**tot**, respectively; θ represents the angle between the light polarization vector direction and the velocity vector of the recorded fragment ion. In general, the anisotropy parameter can assume values in the −1 ≤ β ≤ 2 range, depending on the recorded distribution of the final fragment ions. In particular, β = 0 characterizes an isotropic distribution of ions, while when β ranges from −1 up to 2 this means that the emission of product ions, generated by Coulomb explosion of the intermediate molecular dication, changes gradually from a direction perpendicular to the polarization vector of the light (β = −1), to a parallel direction (β = 2). **Figures 2**–**7** show the angular intensity distributions [which is the I(θ) sin(θ) product] of final ions of all detected dissociative channels with the exception of Reaction (7) which is too weak

to allow a reliable data analysis. The curves in red color are the result of a best fit simulation procedure on the experimental data based on Equations (1) and (8) satisfying the conservation of the total angular momentum of two fragment ions. The error in the measurement of the β anisotropy parameters and related angular distributions of **Figures 2**–**7** is of about 0.04–0.06 units of β being of the same order of magnitude of the dots dimensions, respectively. In order to control the reliability of our experiment, we started with the measurement of the angular distribution for Reactions (2) and (4) that were already determined in a previous experimental attempt (Falcinelli et al., 2019b) obtaining β parameters in very good agreement with the previous ones. After this preliminary check, we recorded new data of angular distribution of final ion pairs for all two-body dissociation Reactions (2)–(7) (see **Figures 2**–**7**).

Equation (8) giving the related anisotropy parameter β (see text).

**Figure 2** shows the angular distributions for product ions of Reactions (2)–(6) at a fixed photon energy of 37.0 eV with the determination of the relative β values by a fitting simulation

procedure based on Equations (1) and (8), as discussed above. It clearly appears that at this photon energy all the recorded angular distributions are characterized by a slight anisotropic behavior with a preferential direction of the product ions emission (from the Coulomb explosion of the intermediate (C3H6O)2<sup>+</sup> molecular dication) which is characterized by a parallel component respect to the polarization vector of the used synchrotron radiation. This is confirmed by the obtained β values ranging between 0.59 and 0.65. The only exception is given by the Reaction (5) whose angular distribution appears to be substantially isotropic with a β value almost zero (β = 0.08 ± 0.06). On the other hand, **Figures 3**–**7** report the angular distributions for ion pair products of Reactions (2)–(6) as a function of the photon energy at 29.7, 30.6, 31.8, 33.5, 35.0, and 37.0 eV. In the case of the Reaction (5), the **Figure 3** clearly shows

appear to be almost isotropic in the whole investigated photon energy range

an isotropic distribution of product ions in the whole investigated photon energy range, with a recorded anisotropy parameter β which is almost zero for each analyzed angular distribution. Conversely, the other two-body fragmentation channels [see Reactions (2)–(4), and (6)] appear to be characterized by two different contributions being active in their respective angular distributions of ion pair products (see **Figures 4**–**7**): an isotropic contribution which is dominant at lower photon energies (near the threshold energy of the respective channel) with β ≈ 0.00, and one anisotropy component (with ions emission preferentially in a parallel direction respect to the polarization vector of the light) increasing as the photon energy increases (with β reaching the values ranging between 0.59 and 0.65 at 37.0 eV, the highest investigated photon energy). This observation is an indication

(all β values are ∼ 0.0).

text). For this two-body fragmentation channel the angular distributions of ion products appear to be almost isotropic up to a photon energy of 33.5 eV, whereas at higher photon energy an anisotropic component (β > 0.0), which increases as the photon energy increases, must be included in order to obtain a best fit simulation of the experimental data (see text).

that for Reactions (2)–(4), and (6) the intermediate molecular dication of propylene oxide (C3H6O)2<sup>+</sup> at low photon energies, near the threshold (on average up to about 31.0 eV), should be formed in its ground electronic state characterized by a lifetime longer than its typical rotational period of the order of 10−<sup>10</sup> - 10−<sup>12</sup> s (Dantus et al., 1990) with a consequent isotropic fragment ions formation by a slow Coulomb explosion (β ≈ 0.00 in the related recorded angular distributions of **Figures 4**–**7**). As we have already discussed in previous papers (see for example: Alagia et al., 2007), when an anisotropy appears on the angular distribution of ionic fragments recorded in our PEPIPICO experiments, it is the consequence of the fulfillment of two main conditions: (i) the photon absorption must occur when the molecular orbitals involved in the double photoionization have the most favorable alignment respect to the vector's direction of

linearly polarized light; (ii) the separation of two ionic fragments following the dissociative double photoionization should take place in time shorter than the rotational period of the molecular dication which is involved in the Coulomb explosion.

Conversely, at higher photon energy values (in general for hν ≥ 31.8 eV) it should be possible the formation of excited vibronic states of the (C3H6O)2<sup>+</sup> dication having shorter lifetimes determining the opening and progressive increase of an anisotropic component in the recorded angular distributions (with a respective gradual increase of the anisotropy parameter toward positive values up to roughly about 0.7). Since our experiment probes a time window from about 50 ns up to 2.5 µs, depending on the used experimental set up (Alagia et al., 2012a), in the absence of evidences in our recorded coincidence plots for any traces due to metastable species (Alagia et al., 2012a,b; Falcinelli et al., 2018a), we can only fix an upper limit of ∼50 ns for the lifetime of the intermediate

FIGURE 7 | Angular distributions of C2H + 4 /CH2O<sup>+</sup> ion pair products formed by Reaction (2) as a function of the photon energy. Dots intensity in the ordinate axis are in arbitrary units, and the error bars are omitted for clarity being of the same order of magnitude of the dot dimensions. On the right side is also reported the anisotropy parameter β referred to related panels (see text). For this two-body fragmentation channel the angular distributions of ion products appear to be almost isotropic up to a photon energy of 30.6 eV, whereas at higher photon energy an anisotropic component (β > 0.0), which increases as the photon energy increases, must be included in order to obtain a best fit simulation of the experimental data (see text).

propylene oxide (C3H6O)2<sup>+</sup> molecular dication formed in our experimental conditions. In the case of our experiment, observed anisotropies represent also a probe that the main fragmentations occur before the randomization of molecular dication direction due to its rotational temperature. According to suggestions by Felker and Zewail (1987), for the present molecular systems the time scale of such randomizations, evaluated considering the rotational temperature and the average rotational molecular constant, assumes the maximum value of few tens of ps. However, our argumentation is only speculative, and, unfortunately, we cannot do something better at this stage of the data analysis. Specific theoretical calculations able to determine structure, energy and symmetry of dication states as well as the electronic

state of fragmentation ion products, energy barriers with their dependence on the geometry of the intermediate state should be

(2)–(6) as a function of the investigated photon energy (see text).

very important. It has to be noted that in such a general behavior [within which we can include all the investigated processes except for Reaction (7)] the Reaction (4) producing CH<sup>+</sup> <sup>3</sup> <sup>+</sup> <sup>C</sup>2H3O<sup>+</sup> shows a different trend. In fact, looking at the **Figure 5** it can be seen that the angular distribution of ion products preserves a clear isotropic character with a β ≈ 0.00 up to the recorded distribution at a photon energy of 33.5 eV, which is a value quite larger (of about 2.5–3.0 eV) than all the other analyzed cases. **Figure 8** reports the anisotropy β parameter obtained from our data analysis (see **Figures 2**–**7**) as a function of the investigated photon energy range for all recorded two-body dissociation channels [see Equations (2)–(6)] with the only exception of Reaction (7) since, as mentioned above, the collected signal was too low not allowing a meaningful analysis of the data. From the figure it is evident that the Reaction (4), the one characterized by a bimodal trend in the KER distributions (see **Figure 1C**), is also the unique two-body dissociation process for which the β parameter starts an anisotropic behavior at a photon energy higher than ∼32.0 eV. All the other recorder fragmentation channels, with the exception of Reaction (5) for which β is almost zero at all investigated photon energies, show a different trend with an anisotropic behavior that appears for lower photon energy values (hν ≥ 30.6 eV). This particular behavior could be a confirmation of the possibility that two different microscopic mechanisms are operative for such a two-body fragmentation process as we have discussed in a previous paper (Falcinelli et al., 2018a) where a bimodal behavior was found in the total KER distributions recorded for CH<sup>+</sup> <sup>3</sup> <sup>+</sup> <sup>C</sup>2H3O<sup>+</sup> ions produced in Reaction (4) (Falcinelli et al., 2018a,b, 2019b). A portion of such distributions is reported in **Figure 1C** for two different photon energy values (35.0 and 37.0 eV) and clearly show a bimodality being the experimental data best fitted by a sum of two Gaussian functions whose peak maxima are separated by ≈ 2.1 eV. It is interesting to note that previous ab initio molecular orbital calculations allowed Nobes et al. (1983) to determine structures and stabilities of various C2H3O<sup>+</sup> isomers. These authors found that only three different isomers of C2H3O<sup>+</sup> can be stable and observable species in gas-phase experiments. They are shown in **Figure 9**. In order of their decreasing energetic stability, the most stable is the acetyl cation [CH3−C = O]<sup>+</sup> (structure I in **Figure 9**) which is followed by the hydroxyvinyl cation [CH<sup>2</sup> = C−OH]<sup>+</sup> (structure II in **Figure 9**), and finally the less stable is the oxiranyl cation [CH2−CH−O]<sup>+</sup> (see structure III in **Figure 9**). The first two isomers are characterized by a linear structure, while the oxiranyl is a cyclic isomer with a triangular [C···O···C] ring (Nobes et al., 1983), as it is shown in **Figure 9**. Immediately after the publication of these calculations, experiments were performed by Burgers et al. demonstrating the unequivocal identification of all three mentioned C2H3O<sup>+</sup> isomers in gas-phase (Burgers et al., 1983). It has to be noted that the difference in the energetic stability between the most stable acetyl cation and the two other isomers is not very different. The acetyl cation is ≈ 1.87 eV more stable respect to the hydroxyvinyl cation, while the oxiranyl cation is located at ≈ 2.53 eV above

FIGURE 9 | Semiquantitative energetic schematic diagram showing the two alternative microscopic mechanisms for the unimolecular fragmentation of the intermediate propylene oxide (C3H6O)2<sup>+</sup> dication forming the two more probable C2H3O<sup>+</sup> isomers (see Reaction (4) in the text): the oxiranyl cation (structure III) and the acetyl cation (structure I). In the figure is reported also the third possible stable C2H3O<sup>+</sup> isomer, the hydroxyvinyl cation (structure II) whose energetic level is ∼1.7 eV above the most stable acetyl cation, and for this reason appears less probable to be formed (see text).

the acetyl one (see **Figure 9**) (Nobes et al., 1983). Both pairs of energy values are very close to the difference between peak maxima of the two Gaussian functions used to best fit our recorded KER (see **Figure 1C**). In particular, this energetic value of about 2.1 ± 0.3 eV is the difference in the translational energy of the two possible C2H3O<sup>+</sup> ions produced via two different microscopic mechanisms, following the Coulomb explosion of the intermediate (C3H6O)2<sup>+</sup> dication. It seems to fit better with the formation of: (i) the linear acetyl cation with a higher translational energy content (to which are associated the KER distributions centered at about 6.1 eV in **Figure 1C**), since it is the more stable isomer one; (ii) the cyclic oxiranyl isomer (to which are related the less intense KER distributions of **Figure 1C** located at about 4.0 eV) which is produced with a lower kinetic energy respect to the previous one, being ∼2.53 eV less stable than the other. Obviously, we cannot exclude the possible formation of hydroxyvinyl cation, even if the two following considerations make this hypothesis less probable: (i) its production from the Coulomb explosion of the (C3H6O)2<sup>+</sup> dication should involve a hydrogen shift toward the O atom of the propylene oxide ring resulting in its breakage and openness; (ii) the energetic difference of ∼1.87 eV in the stability between acetyl and hydroxyvinyl isomers as calculated by Nobes et al. (1983) do not fit properly with the difference in the translational energy characterizing the formation of C2H3O<sup>+</sup> ions coming out by the two different recorded mechanisms: the bimodality in the total KER distributions displays that the difference in the translational energy of the two formed C2H3O<sup>+</sup> isomers (one of which is always the more stable acetyl cation) could reach an upper limit of about 4.1–4.2 eV which is reasonable in the case of the oxiranyl cation formation, but it appears too high for the possible formation of the hydroxyvinyl isomer. It has to be noted that in the microscopic fragmentation dynamics of the intermediate (C3H6O)2<sup>+</sup> dication a H-migration could be possible prior to dissociation. In order to clarify this point, the estimation of the H-migration rate toward the formation of the two different C2H3O<sup>+</sup> final isomers, and the assessment of the role of electronically excited states of (C3H6O)2<sup>+</sup> dication should be very important. To this aim further experimental (for example, using labeled isotopic variants of propylene oxide) and accurate theoretical efforts are mandatory.

In order to clarify this qualitative speculation it should be highly helpful to perform further theoretical calculations on the structure and energetic stability of the intermediate propylene oxide dication, as well as of all possible ionic species that can be formed following its unimolecular two-body fragmentation by Coulomb explosion. Similar calculations have been carried out in our laboratory for simpler systems (Teixidor et al., 2003; Candori et al., 2007; Leonori et al., 2009a,b; Rosi et al., 2012; Skouteris et al., 2015).

## CONCLUSIONS

This study is important as no data on the propylene oxide (C3H6O)2<sup>+</sup> molecular dication energetics and on its nuclear dissociation dynamics are available. This information is required for further experimental and theoretical investigations of the interaction between chiral molecules and linearly or circularly polarized radiation in future projects. In order to investigate in detail stereodynamical mechanisms for the discrimination of enantiomers, a future extension of our experiments will aim at identifying possible differences in the angular and energy distribution of fragment ions and ejected photoelectrons, observable at different photon energies, coming out from the interaction of circularly polarized synchrotron light with propylene oxide and other simple chiral molecules, such as the 2-butanol, available as enantiomerically pure. The present paper reports on the measure of angular distributions of ion products as a function of the photon energy for each investigated two-body fragmentation channels produced in a double photoionization experiment involving propylene oxide.

All recorded angular distributions are characterized by a slight anisotropic behavior with a preferential direction of the product ions emission which is characterized by a parallel component respect to the polarization vector of the used synchrotron radiation. This is confirmed by the obtained β values ranging between 0.59 and 0.65. The only exception is given by the Reaction (5) whose angular distribution appears to be substantially isotropic with a β value almost zero (β = 0.08 ± 0.06).

The data analysis allowed the determination of the anisotropy parameter β for each investigated dissociation reaction as well as its behavior as the photon energy changes over the 18.0– 37.0 investigated range. This seems to be consistent with the hypothesis of the possibility of two different microscopic mechanisms for the fragmentation channel producing CH<sup>+</sup> 3 /C2H3O<sup>+</sup> ion pairs, already observed in their KER distributions in recent experiments (Falcinelli et al., 2018a,b). On the basis of previous theoretical calculations (Nobes et al., 1983) and experimental evidences (Burgers et al., 1983), we can argue that following the double photoionization of propylene oxide, different electronic states of the intermediate (C3H6O)2<sup>+</sup> dication could be formed with their subsequent two-body fragmentation toward the final formation of different stable isomers of C2H3O+. From energetic considerations on our recorded data, the more probable microscopic mechanism seem to be those that lead to the formation of the acetyl and oxiranyl pair of isomers. Moreover, we cannot exclude

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the formation of the third stable possible C2H3O<sup>+</sup> isomer, the hydroxyvinyl cation, even if it appears less probable. To understand comprehensively the microscopic dynamics of fragmentation of doubly photoionized propylene oxide, three are the possible strategies to follow: (i) to perform further experiments using isotopically labeled precursor molecules; (ii) to carry out theoretical calculations on structure and energetic stability of either propylene oxide (C3H6O)2<sup>+</sup> dication and final ions coming out from its Coulomb explosion; (iii) to adopt a new original methodology developed by our research group in order to fully describe the stereodynamics of dissociative double ionization reactions as recently applied to depict the reactivity of auto-ionization processes at a state to state level (Falcinelli et al., 2018c, 2019a). Our research group will be involved in both these directions during next future.

## AUTHOR CONTRIBUTIONS

SF, MA, and LS analyzed the results. All authors planned and managed the experiment, made discussion about the results and participated in writing the manuscript.

## FUNDING

Financial support from MIUR, Ministero dell'Istruzione, dell'Università e della Ricerca, PRIN 2015 (STARS in the CAOS − Simulation Tools for Astrochemical Reactivity and Spectroscopy in the Cyber infrastructure for Astrochemical Organic Species, 2015F59J3R). Support from Italian MIUR and University of Perugia (Italy) is acknowledged within the program Dipartimenti di Eccellenza 2018–2022.

## ACKNOWLEDGMENTS

This work was dedicated to our colleague and friend Jaime De Andres whose memory and love for science will inspire our future research. The scientific staff of CiPo and GasPhase beamlines of the Elettra Synchrotron Facility (Trieste, Italy) are gratefully acknowledged.

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Falcinelli, Rosi, Pirani, Bassi, Alagia, Schio, Richter, Stranges, Balucani, Lorent and Vecchiocattivi. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.