Edited by: Majdi Hochlaf, Université Paris Est Marne la Vallée, France
Reviewed by: Ryan C. Fortenberry, University of Mississippi, United States; Jacek Antoni Klos, University of Maryland, United States
This article was submitted to Astrochemistry, a section of the journal Frontiers in Chemistry
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Theoretical–computational studies together with recent astronomical observations have shown that under extreme conditions in the interstellar medium (ISM), complexes of noble gases may be formed. Such observations have generated a wide range of possibilities. In order to identify new species containing such atoms, the present study gathers spectroscopic data for noble gas hydride cations, NgH+ (Ng = He, Ne, Ar) from high-level
Given the extreme conditions of temperature and pressure, the interstellar medium (ISM) is a perfect framework to find unconventional molecules that are unthinkable in the Earth's atmosphere. Such example is the noble gas (Ng) hydride cations, NgH+ (Fortenberry,
The presence of the HeH+ and ArH+ molecules in ISM has been recently reported for first time in the planetary nebula NGC 7027 (Güsten et al.,
The study of ArH+ complex started in 1970, when for first time, the potential energy curve (PEC) of its fundamental electronic state have been reported (Roach and Kuntz,
The interest in the HeH+, discovered in the laboratory in 1925 (Hogness and Lunn,
With respect to the heavier noble gases, Ne is the fifth most abundant element in the universe, while Kr is so rare, and Xe is rarer still in the ISM (Rogers et al.,
Thus, the purpose of this research is to provide potential curves obtained from benchmark
All
For all configurations studied, the basis set superposition error (BSSE) was corrected by the counterpoise method (Boys and Bernardi,
In order to spectroscopically characterize these noble gas cations and their more abundant isotopologues, it is necessary to obtain an accurate PEC. To do this, the computed PECs are compared with the most recent theoretical and experimental ones available. In total, 200 points along
We first performed optimization calculations for each NgH+ molecule at CCSD(T)/AV6Z level of theory, and the obtained equilibrium bondlengths
Equilibrium bondlengths,
The rather short bondlengths range from 0.774461, 0.991304, and 1.281013 Å, and the exceptionally high vibrational frequencies between 3219 and 2718 cm−1 going from HeH+ to ArH+, respectively, indicate the clearly dominant covalency of these molecules. Thus, by considering the equilibrium geometries from the above CCSD(T)/AV6Z optimizations, we carried out single point calculations at different levels of theory, such as MP2, CCSD(T), CCSD(T)-F12, and MRCI+Q, employing large AVXZ (X = Q, 5, 6) basis sets, and then extrapolations to CCSD(T)/CBS limit considering both two- and three-step schemes (Schwartz,
Comparison of total energy values (in a.u.) at equilibrium distance of R obtained in the present work from the indicated calculations and the best estimates of previous studies.
Literature | −2.9786667 |
−128.902477 |
−527.179256 |
−2.97868906 |
−128.944424 |
−527.210000 |
|
−2.97870262 |
−128.943538 |
−527.204368 |
|
−2.978706591 |
|||
−2.978708310771 |
|||
MP2/AVQZ | −2.97119612 | −128.92535770 | −527.19676773 |
MP2/AV5Z | −2.97212128 | −128.93866766 | −527.20640683 |
MP2/AV6Z | −2.97249327 | −128.94360982 | −527.21174138 |
CCSD(T)/AVQZ | −2.97753886 | −128.93261021 | −527.22479619 |
CCSD(T)/AV5Z | −2.97822081 | −128.94453910 | −527.23319916 |
CCSD(T)/AV6Z | −2.97846538 | −128.94853590 | −527.23725238 |
CCSD(T)−F12/AVQZ | −2.97854415 | −128.94837833 | −527.22436255 |
MRCI+Q/AV6Z | −2.97846538 | −128.94851552 | −527.24011465 |
CCSD(T)/CBS[Q56] | −2.97860770 | −128.95086138 | −527.23961265 |
CCSD(T)/CBS[56] | −2.97872479 | −128.95363280 | −527.24247792 |
In
Total
Total
In the HeH+ case, the CCSD(T)/CBS[56] potential energies show very small differences with the high accurate Born-Oppenheimer potential reported by (Pachucki,
An important aspect of the potential curves, with strong influence on bound and quasi-bound states in the dissociation limit, is the correct behavior at such asymptotes. At large intermolecular distances, the ground NgH+(X1Σ+) states dissociate to Ng(1S0) + H+, with the ion-induced dipole interaction between the Ng atom and the proton being the leading long-range potential term. In
In turn, we will also discuss the energetics of the simplest pathways for their formation given by the following gas phase reactions:
In
Formation energies at T = 0 K (in kcal/mol) for Ng–H+ complexes at the indicated levels of theory, and their comparison with recently reported experimental/theoretical data.
−47.05/−47.05/−47.05(−42.55) | −42.5 |
|
−51.51/−52.02/−52.47(−48.40) | −47.5 |
|
−92.94/−93.28/−93.57(−89.73) | −88.2 |
|
−300.13/−300.25/−300.41(−295.91) | −295.9 |
|
−236.53/−236.88/−237.35(−233.28) | −231.2 |
|
−143.86/−144.26/−144.74(−140.90) | −138.0 |
|
17.48/17.33/17.12(17.91) | 19.6 |
|
11.53/11.53/11.55(11.91) | 14.6 |
|
−29.12/−29.15/−29.18(−29.05) | −26.1 |
|
−191.48/−191.60/−191.76(−190.03) | −191.7 |
|
−127.18/−127.47/−127.80(−125.64) | −127.0 |
|
−34.51/−34.84/−35.25(−32.86) | −33.8 |
The computations predict that the formation of all NgH+ molecules is more favorable through reaction (2), then follows the reaction (4) for HeH+ and NeH+, while for ArH+ is the reaction (1) the second more favorable pathway. However, the most likely formation pathways will not only follow thermodynamic results but kinetic patterns. The Ng atoms are likely not going to ionize first and will require some leaving group to carry about the excess energy kinetically. Hence, mechanism (3) is the most likely pathway to occur, and the mechanism (1) follows as the second-most likely. Further, in astrophysical environments, depending on the regions of ISM that such molecules have been observed, it proves the main corresponding mechanism of their formation, and numerous investigations have been reported (Zygelman et al.,
The calculated ground electronic state CCSD(T)/CBS[56] and MRCI+Q interaction energies as a function of
CCSD(T)/CBS[56] (solid lines) and MRCI+Q (dashed lines) interaction energies
The dipole moment values for HeH+ and NeH+ show an almost linear dependence as
In
Equilibrium distances (R
CCSD(T)/CBS[56] | 0.7745 | 16456.95 | 0.71 |
MRCI+Q/AV6Z | 0.7745 | 16457.88 | 1.64 |
Theory (Orville-Thomas, |
0.774 | 16477.9 | 21.66 |
Theory (De Fazio et al., |
0.7747 | 16460.1 | 3.86 |
Theory (Pachucki, |
0.7743 | 16457.1 | 0.86 |
Expt. (Coxon and Hajigeorgiou, |
0.7743 | 16456.24 | - |
CCSD(T)/CBS[56] | 0.9913 | 18486.02 | 136.02 |
MRCI+Q/AV6Z | 0.9913 | 18519.54 | 169.54 |
Theory (Rosmus, |
0.9959 | 18357 | 7.0 |
Theory (Pendergast et al., |
0.9917 | 18551 | 201.0 |
Theory (Civiš et al., |
0.9912 | 18519.7 | 169.7 |
Theory (Gerivani et al., |
0.9927 | 18449 | 90.0 |
Expt. (Ram et al., |
0.9912 | 18350 | - |
CCSD(T)/CBS[56] | 1.2810 | 32695.50 | 231.49 |
MRCI+Q/AV6Z | 1.2810 | 32811.50 | 347.50 |
Theory (Stolyarov and Child, |
1.2790 | 33391.3 | 927.30 |
Theory (Alekseyev et al., |
1.2680 | 34601.2 | 2137.20 |
Theory (Abdoulanziz et al., |
1.2801 | 32576.7 | 112.70 |
Theory (Coxon and Hajigeorgiou, |
1.2803 | 32460 | - |
Expt. (Hotop et al., |
1.2806 | 32464 | - |
Despite that NeH+ have not been observed in the ISM yet, there are various
Previous theoretical studies on the ground state ArH+ have also determined equilibrium energies and bondlengths from MP2, CCSD(T), and MRCI calculations (Hirst et al.,
On the basis of the present CCSD(T)/CBS[56] PECs, vibrational bound state calculations were carried out, aiming to investigate the effect of the potential form on the vibrational states, and to further validation of the interactions by comparisons of the obtained spectroscopic constants with available experimental data taken into account ZPE effects. Given the importance of different isotopes, due to their abundance in ISM, and thus their potential detection in a variety of astrophysical environments, we decide to consider the 3He, 4He, 20Ne, 21Ne, 22Ne, 36Ar, 38Ar, 40Ar isotopes for the Ng atoms, and D, H for the hydrogen one. In
The CCSD(T)/CBS[56] potentials support 12 (υ = 0–11) vibrational levels for the hydrogenated 3He/4HeH+ species in agreement with the most accurate theoretical data (Stanke et al.,
In
Potential energy curves of ground state NgH+ molecules together with the radial distributions for all calculated vibrational bound states.
In turn, in
Vibrational υ → υ′ frequencies (in cm−1) of all computed bound states for the indicated NgH+ isotopes, and comparison with available best known or experimental values.
1 → 0 | 2911.0174/2910.8698 | 2911.425 | 2677.86(1984.59)/2672.50 | 2678.80(1985.65)/2673.45 | 2589.2803 | 2592.392 |
2 → 1 | 2604.2053/2604.1468 | 2604.561 | 2453.41(1866.36)/- | 2453.37/(1865.27)/2448.98 | 2470.4824 | 2472.665 |
3 → 2 | 2295.6350/2295.5776 | 2296.111 | 2230.5 | 2230.44(1749.87)/2227.03 | 2354.5593 | 2357.226 |
4 → 3 | 1982.1338/1982.0808 | 1982.784 | 2007.28(1632.08)/2004.84 | 2241.3801 | 2247.186 | |
5 → 4 | 1660.4510/1660.3924 | 1661.280 | 1781.92(1514.50)/1780.51 | 2130.7724 | 2135.512 | |
6 → 5 | 1327.9060/1327.8469 | 1328.951 | 1551.91(1397.74)/1551.56 | 2025.643 | ||
7 → 6 | 984.4969/984.4453 | 985.727 | 1315.69(1279.01)/1316.48 | 1919.666 | ||
8 → 7 | 639.3449/640.3172 | 640.638 | 1071.45(1158.99)/1073.43 | 1815.963 | ||
9 → 8 | 327.4952 | 328.578 | 819.97(1036.13)/823.51 | 1711.330 | ||
10 → 9 | 116.2242 | 116.541 | 568.98(910.73)/573.10 | 1608.228 | ||
11 → 10 | 24.4392 | 24.438 | 337.29(782.23)/341.55 | 1505.493 | ||
12 → 11 | 162.387(650.554)/165.697 | 1401.692 | ||||
13 → 12 | 61.5322(518.061)/63.331 | 1296.496 | ||||
14 → 13 | 16.911(386.962)/17.597 | 1188.398 | ||||
15 → 14 | 1076.222 | |||||
16 → 15 | 958.158 | |||||
17 → 16 | 832.442 | |||||
18 → 17 | 697.400 | |||||
19 → 18 | 552.743 | |||||
20 → 19 | 402.814 | |||||
21 → 20 | 261.787 | |||||
22 → 21 | 151.511 | |||||
23 → 22 | 80.784 | |||||
24 → 23 | 39.183 | |||||
25 → 24 | 16.050 | |||||
26 → 25 | 4.662 |
Finally, the calculated molecular spectroscopic constants of the present CCSD(T)/CBS[56] PECs, such as binding energies D0, equilibrium vibrational frequencies ω
The present study is focused on the computational characterization of noble gas hydride NgH+ (Ng = He, Ne, Ar) cations, the simplest noble gas-containing molecules. Our results provide benchmark data on the underlying interactions and spectroscopic constants, determined from high-level and well-converged
Two of these molecules, in particular 4HeH+ and 36ArH+/38ArH+ isotopes, have been already detected in the ISM, and has been recently extensively studied, in relation with their formation and destruction mechanisms. Here, we presented new spectroscopic data on binding energies and vibrational transitions from quantum calculations for all known stable isotopic structures in ISM and on earth of the lighter NgH+ molecules. These data were compared with the corresponding values reported in previous studies available, and it was found that they could serve as a benchmark for their ground electronic states.
As the accuracy issues have profound implications in developing chemoinformatics models, such reference datasets can serve to guide and cross-check computational approaches for building up predictive data-driven models for larger cationic noble gas hydrides, e.g., Ng
The original contributions presented in the study are included in the article/
All authors have contributed to the work and approved it for publication.
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.
We would like to thank Raúl Rodríguez-Segundo and José A. Torres for useful discussions on DENEB software. The authors thank to the Centro de Calculo del IFF/SGAI-CSIC and CESGA-Supercomputing centre for allocation of computer time, and the CSIC (URICI) open access publication support initiative for the partial support of the publication fee. We acknowledge financial support by the Comunidad de Madrid grant Ref: IND2018/TIC-9467, MINECO grant No. FIS2017-83157-P, and COST Action CA18212(MD-GAS).
The Supplementary Material for this article can be found online at: