Rotational Rest Frequencies and First Astronomical Search of Protonated Methylamine

We report first laboratory rest frequencies for rotational transitions of protonated methylamine, C H 3 N H 3 + , measured in a cryogenic 22-pole ion trap machine and employing an action spectroscopy scheme. For this prolate symmetric top molecule thirteen transitions between 80 and 240 GHz were detected in the ground vibrational state, covering J K = 2 K − 1 K up to J K = 6 K − 5 K with K = 0, 1, 2. Some transitions exhibit noticeable structure that is attributed to internal rotation splitting. As the CN radical and several of its hydrogenated and protonated forms up to methylamine, CH3NH2, are well known entities in the laboratory and in space, protonated methylamine, C H 3 N H 3 + , is a promising candidate for future radio astronomical detection.


INTRODUCTION
The cyano radical, CN, was one of the first molecules detected in the interstellar medium (McKellar, 1940). It is astrochemically linked to its hydrogenated and protonated forms, most of which have been detected in the interstellar medium, typically in the galactic center source Sgr B2, such as HCN (Snyder and Buhl, 1971), HNC (Snyder and Buhl, 1972;Zuckerman et al., 1972), HCNH + (Ziurys and Turner, 1986), and H 2 C NH (Godfrey et al., 1973). The terminal product of this hydrogenation series is methylamine, CH 3 NH 2 , which has been well characterized by laboratory spectroscopy (Ohashi et al., 1987;Ilyushin and Lovas, 2007;Motiyenko et al., 2014) and was first detetcted in Sgr B2 and Orion A in 1974 by Kaifu et al. (1974) and Fourikis et al. (1974).
In interstellar environments, molecules may also occur in their protonated forms, generated by a proton transfer from a proton donor like H + 3 , e.g. CO + H + 3 → HCO + + H 2 . Many of the simpler protonated species have been detected in the interstellar medium, such as HCO + (Buhl and Snyder, 1970), N 2 H + (Turner, 1974), HCNH + (Ziurys and Turner, 1986) and HOCO + (Thaddeus et al., 1981), whereas many of the more complex ones so far are only suspected to be present. Examples are CH 3 NH 3 + , as a product of proton transfer to methyl amine (see, e.g., the KIDA database; Wakelam et al., 2015) or from radiative association of NH 3 and CH 3 + (Herbst, 1985), but also protonated methanol, CH 3 OH + 2 (Jusko et al., 2019), and protonated methane, CH + 5 (Asvany et al., 2012;Asvany et al., 2015). In particular the latter two molecular ions have not yet been searched for in space because their laboratory microwave spectra are predicted to be quite irregular and still not known.
Following up on our recent work on the high-resolution rotational spectra of CN + (Thorwirth et al., 2019a) and CH 2 NH + 2 (Markus et al., 2019), in this study, we finally focus on the very last member of the CN hydrogenation/protonation chain, protonated methylamine, CH 3 NH 3 + . Upon protonation, methylamine, CH 3 NH 2 , an asymmetric top molecule featuring two internal large-amplitude motions (internal rotation and inversion), is converted into a much simpler symmetric top of C 3v point group symmetry, in which the CH 3 and the NH 3 groups assume a staggered configuration at the global energy minimum (see inset in Figure 1). Literature on the spectroscopy of CH 3 NH 3 + is extremely sparse, with only one experimental paper presenting low-resolution infrared (IR) features of the Ar-tagged species (Michi et al., 2003), and one work reporting ab initio values for its IR vibrational frequencies (Zeroka and Jensen, 1998). Therefore, the spectroscopic study in the present work was complemented with new high-level quantum-chemical predictions of the FIGURE 1 | Measurements of the J K ′ ← J K ″ (K 0, 1, 2) rotational transitions of CH 3 NH 3 + (red trace), recorded as depletion signal of the normalized CH 3 NH 3 + −He counts. The simulations (green sticks indicate nitrogen quadrupole hyperfine structure (hfs) and their convolution is given as black traces), based on a symmetric rotor model ( Table 1, fit I), indicate that the hyperfine splitting is not resolved and that discrepancies between the simulated and measured spectra, in particular the blue-shifted shoulders for K 0 and 1 (red trace), are most probably due to the neglect of torsional motion in the simulation.
Frontiers in Astronomy and Space Sciences | www.frontiersin.org February 2022 | Volume 8 | Article 805162 2 molecular structure and force field (see Section 3). The ion trap experiment is briefly described in Section 2. The experimentally derived rotational transitions of CH 3 NH 3 + as well as the ground state spectroscopic parameters are summarized in Section 4. A first astronomical search of CH 3 NH 3 + towards Sgr B2(N) and Sgr B2(M) is finally presented in Section 5.

EXPERIMENTAL METHODS
The rotational transitions of CH 3 NH 3 + have been measured using an action spectroscopic method which exploits the rotational state dependence of the ternary attachment of He atoms to cations at low temperature Brünken et al., 2017;Doménech et al., 2017;Jusko et al., 2017;Doménech et al., 2018a;Doménech et al., 2018b;Thorwirth et al., 2019a;Asvany et al., 2021). The experiment was performed in the 4 K ion trapping machine COLTRAP described by Asvany et al. (2010Asvany et al. ( , 2014. The ions were generated in a storage ion source by electron impact ionization (E e ≈ 26-30 eV) of the precursor gas mixture. This mixture consisted of methylamine, CH 3 NH 2 (Aldrich Chem. Corporation, CAS 74-89-5, 98%), and helium (Linde 5.0) which were admitted to the ion source via two separate leakage valves. CH 3 NH 3 + is generated by a reaction of the type CH 3 NH 2 + + CH 3 NH 2 → CH 3 NH 3 + + CNH 4 . A pulse of several ten thousand mass-selected parent ions (m 32 u) was injected into the 22-pole ion trap filled with about 10 14 cm −3 He at 4 K. At the beginning of the trapping time lasting 800 ms, CH 3 NH 3 + -He complexes formed by three-body collisions with He. The resonant absorption of the cw millimeter-wave radiation by the trapped cold CH 3 NH 3 + cations is detected by observing the decrease of the number of CH 3 NH 3 + -He complexes. A rotational line is thus recorded by repeating these trapping cycles (1 Hz) and counting the mass-selected CH 3 NH 3 + -He complexes (m 36 u) as a function of the millimeter-wave frequency. This millimeter-wave radiation was supplied by a multiplier chain source (Virginia Diodes, Inc.), covering the ranges 80-125 and 170-1100 GHz. This source was driven by a synthesizer (Rohde&Schwarz SMF100A), which was referenced to a rubidium atomic clock. The beam of the millimeter-wave source has been directed toward the ion trap via an elliptical mirror and a thin diamond vacuum window. The 160 GHz line of CH 3 NH 3 + was measured with a different multiplier chain (Radiometer Physics GmbH), covering the range of 110-170 GHz.

COMPUTATIONAL METHODS
As no previous high-resolution experimental data were available for CH 3 NH 3 + , spectroscopic searches and analysis were based on high-level quantum-chemical calculations performed here at the CCSD(T) level of theory (Raghavachari et al., 1989). Equilibrium geometries were calculated using analytic gradient techniques (Watts et al., 1992) and Dunning's correlation-consistent basis sets as large as cc-pwCVQZ (Peterson and Dunning, 2002). Anharmonic force fields to evaluate the zero-point vibrational contributions 1 2 i α A,B,calc i ( ΔA 0 , ΔB 0 ) to the equilibrium  (2007) and Borvayeh et al. (2008). b This study; A e , B e , eQq( 14 N) and dipole moment μ e calculated at the CCSD(T)/cc-pwCVQZ, level, zero-point vibrational corrections ΔA 0 , ΔB 0 and centrifugal distortion terms calculated at the CCSD(T)/cc-pVTZ, level. Torsional barriers V 3 evaluated from the CCSD(T)/cc-pwCVQZ energy difference of the staggered and eclipsed forms complemented with harmonic vibrational corrections evaluated at the CCSD(T)/cc-pVTZ level. c Calculated CH3NH3 + value further scaled with the ratio X exp /X calc of the corresponding parameter of C 2 H 6 . d Fit performed using an in-house program assuming a uniform uncertainty of 15 kHz. e Kept fixed. f C 2 H 6 : Kept fixed at value of A rotational constant; CH3NH3 + : Kept fixed at the customary value of A/(ρ(1 − ρ)). g Weighted rms, dimensionless.
Frontiers in Astronomy and Space Sciences | www.frontiersin.org February 2022 | Volume 8 | Article 805162 3 rotational constants were calculated using analytic secondderivative techniques (Gauss and Stanton, 1997;Stanton and Gauss, 2000) followed by additional numerical differentiation to calculate the third and fourth derivatives needed for the anharmonic force field (Stanton et al., 1998;Stanton and Gauss, 2000). These calculations were carried out using the frozen core (fc) approximation in combination with the cc-pVTZ basis set (Dunning, 1989).
All calculations were performed using the CFOUR program (Matthews et al., 2020) and strategies summarized elsewhere (Puzzarini et al., 2010). The computed spectroscopic parameters are listed in Table 1 that also provides scaled (best-estimate) parameters obtained from a comparison of experimental and calculated values of isoelectronic ethane, C 2 H 6 (see, e.g., Martinez et al. (2013) for a similar procedure used in the vinyl acetylene/protonated vinyl cyanide family of isoelectronic species). Additional results from the calculations are given in the Supplementary Material. An estimate of the torsional barrier height was obtained using the energy difference between the staggered and the eclipsed forms of CH 3 NH 3 + calculated at the CCSD(T)/cc-pwCVQZ level and under consideration of harmonic zero-point vibrational contributions calculated at the CCSD(T)/cc-pVTZ level. This procedure results in a barrier of V 3 1.98 kcal/ mol. A similar calculation of ethane, C 2 H 6 , yields 2.45 kcal/mol to be compared against an experimental value of 3.00 kcal/mol (Borvayeh et al., 2008). Using the ethane exp/calc-ratio of V 3 for the purpose of scaling, a best estimate value of 2.42 kcal/mol (846 cm −1 ) for the torsional barrier in CH 3 NH 3 + is obtained.

LABORATORY RESULTS AND SPECTROSCOPIC PARAMETERS
Using frequency predictions based on the new high-level quantumchemical calculations, the lines shown in Figure 1 were found subsequently during targeted spectroscopic survey scans. The spectra were recorded in individual measurements in which the frequency was stepped in an up-and-down manner several times. The frequency steps were typically 2 kHz, except for the J K 4 K ← 3 K measurement at 159 GHz, for which 10 kHz steps were applied. Such individual measurements were repeated typically ten times. In the depiction of Figure 1, all available spectra were accumulated and rebinned to a stepwidth of 10 kHz. This deep integration was necessary due to the comparably small signal strength (maximum depletion upon photon absorption is on the order of 2%), and due to somewhat noisy signal counts, which had its origin in ion source instabilities caused by the sticky consistency of the methylamine precursor. Also, during the measurements, care was taken to avoid power broadening. Thus, the linewidths were expected to be dominated by the Doppler broadening due to the kinetic temperature of the ions in the trap (nominal temperature T 4 K with some residual heating to typically 8 K), and a possible contribution due to non-resolved hyperfine splitting. The line patterns detected for a given rotational transition were in line with those expected for a prolate symmetric top molecule and at first sight, no further spectroscopic complexity, as could be expected for resolved nitrogen quadrupole hyperfine structure or torsional motion between the CH 3 and NH 3 subunits, was detected in individual measurements at our experimental conditions. For all individual measurements, the detected lines were fitted to Gaussian functions, from which line centers and their uncertainties were determined, and the first results were very similar to the frequencies quoted in Table 2 (Model I).
The measured frequencies of the pure rotational lines collected in Table 2 (Model I) were first fit with a standard symmetric rotor Hamiltonian using the PGOPHER program (Western, 2017), yielding the set of parameters for the ground state given in Table 1 (fit I). Since the transitions of a symmetric rotor obey the ΔK 0 selection rule, A and D K cannot be determined experimentally, and only B 0 , D J and D JK were derived in the leastsquares fitting procedure and are presented in Table 1. Computed parameters are also included in Table 1 for comparison. As can be seen, the overall agreement between the calculated and scaled bestestimate values and the experimental values is very good. A simulated stick spectrum and its convolution, based on fit I of Table 1 and accounting for the hyperfine structure due to the quadrupole moment of the 14 N nucleus (with spin I 1), are included in Figure 1. As the computed value eQq( 14 N) +158 kHz is very small (see also Table 1), it is not surprising that the hyperfine structure is not resolved in our experiment.
Closer inspection after co-addition of all spectra revealed some noticeable blue-shifted shoulders, as discernible in the accumulation of Figure 1. These are particularly evident in the spectra at 119 (J 3 K − 2 K ) and 159 GHz (J 4 K − 3 K ), but are also discernible in the weaker spectrum at 199 GHz (J 5 K − 4 K ). In the spectrum at 119 GHz (second panel in Figure 1 and close-up in Figure 2) both blue shoulders have an offset of about +170 kHz relative to the main peaks (K 0 and 1), and this offset is found to increase for the higher obtained by fitting multiple Gaussians to the spectra in Figure 1. The uncertainties (1 σ) are given in parentheses in units of the last significant digits. The assignment of Model I assumes a standard symmetric top Hamiltonian whereas that of Model II assumes a symmetric top featuring torsional splitting, see text for details.

Frequency
Model I Model II frequency transitions at 159 (≈+230 kHz) and 199 GHz (≈+290 kHz). While a detailed analysis is hampered by the overall poor signal-to-noise ratio of the spectra, a first analysis was performed here under the assumption that the spectra are affected by internal rotation, an effect that has rarely been observed previously for symmetric top molecules in their ground vibrational states (see, e.g., Ozier and Moazzen-Ahmadi, 2007, and references therein). As indicated in Figure 2, the structure of the J 3 K − 2 K spectrum may be decomposed into four features, two strong ones (the putative K 0 and 1 components used in the first fitting procedure in Table 1, fit I) each of which is accompanied by a weaker satellite that is found blue-shifted relative to the main component. Similar patterns are observed for the J 4 K − 3 K and J 5 K − 4 K transitions. Ideally, a suitable model Hamiltonian should be able to reproduce both the magnitude of the torsional splitting as well as the intensities of the individual spectroscopic components. First, the magnitude of the torsional splitting to be expected in CH 3 NH 3 + was estimated based on the so-called hybrid approach described elsewhere (Wang et al., 2001) using the dominant parameters (V 3 , ρ I α /I c , F A/(ρ × (1 − ρ)), F 3J , F 3K ) as calculated here and complemented with parameters taken from isoelectronic ethane (Borvayeh et al., 2008). Using this approach, the splitting was predicted in very good agreement with the experimental values. In analogy to other closely related symmetric top molecules such as methyl silane, CH 3 SiH 3 , each rotational transition of CH 3 NH 3 + with K 1, 2 is expected to split in up to three components (σ 0, +1, −1) whereas transitions with K 0 only split into two, σ 0, ±1 (Pelz et al., 1992;Ozier and Moazzen-Ahmadi, 2007). The symmetries and nuclear spin weights under consideration of torsional splitting that are needed for intensity estimates have been given, for example, in Pelz et al. (1992). From this, it is concluded that in the CH 3 NH 3 + -spectra two strong torsional components of the K 1-transitions (σ 0, 1) are too close in frequency to be spectroscopically resolved and thus only one strong (superposition of σ 0 and 1) and one weaker torsional component (σ − 1) are observed. The K 0 splitting is also (partly) resolved and both components assigned, a stronger (σ 0) and a weaker one (σ ±1), respectively. For the K 2 transitions, only one component (σ 0) can be assigned in the spectra obtained here with some confidence. Using this spectroscopic knowledge, the accumulated spectra as depicted in Figure 1 were refitted using multiple Gaussian components, and the final frequencies and their assignments are listed in Table 2, Model II. With this improved spectroscopic assignment, a second fit was performed (using an inhouse program and assuming a uniform frequency uncertainty of 15 kHz) leading to an alternative set of molecular parameters given in Table 1 (fit II). In this approach, owing to the limited amount of spectroscopic information available to constrain the internal rotation problem more rigorously, several parameters required in the theoretical description were kept fixed at values calculated quantum-chemically (ρ, F, V 3 ). In analogy to fit I, B 0 , D J , and D JK were varied in the least squares adjustment and additionally F 3J was released, resulting in a good fit result and agreement with the fit I and C 2 H 6 parameter sets. If released also, V 3 cannot be determined statistically from the present data set and changing its value from the scaled calculated value of 2.42 kcal/mol to the unscaled value of 1.98 kcal/mol has little impact on the overall fit quality but decreases the value of F 3J significantly to −87(3) MHz. Based on this new set of parameters and taking into consideration the proper spin statistical effects (e.g., Pelz et al., 1992), new simulations of spectra have been obtained that are shown in Figure 3. The agreement between the experimental spectra and the simulations is rather compelling and hence speaking very much in favor of internal rotation as to the cause of the peculiar lineshapes and splittings observed.

INTERSTELLAR SEARCH
The CH 3 NH 3 + spectral line transitions reported in Table 2 have frequencies > 40 GHz and constitute good targets to be searched  Table 1, Model II).
Frontiers in Astronomy and Space Sciences | www.frontiersin.org February 2022 | Volume 8 | Article 805162 5 for with facilities like ALMA (Atacama Large Millimeter/submillimeter Array; ALMA Partnership et al., 2015). While the low-energy transitions are not covered by current ALMA bands, the J 4 K → 3 K and J K 5 K → 4 K lines can be observed with the new ALMA band 5 receiver (covering a frequency range from 159 to 211 GHz), and the J K 6 K → 5 K transitions are observable with the commonly used band 6 receiver (211-276 GHz).
The detection of species closely related to protonated methylamine such as HCN, HCNH + or CH 3 NH 2 in the starforming region Sgr B2 (e.g., Schilke et al., 1991;Belloche et al., 2013) motivates the search for protonated methylamine in this region. We have made use of the ALMA spectral line survey published in Sánchez-Monge et al. (2017, see also Schwörer et al., 2019. The observations target the star-forming objects Sgr B2(N) and Sgr B2(M) and cover the whole ALMA band 6 with a spectral resolution of 0.7 km s −1 and an angular resolution of 0.′′4 (corresponding to 3300 au at the distance of the source). This high angular resolution allows to resolve the regions in more than 40 different dense cores (see Sánchez-Monge et al., 2017). Figure 4 presents the spectra extracted We mark with vertical lines the location of the CH 3 NH 3 + transitions.
We have selected objects in different evolutionary stages and with different physical properties. Cores AN02, AN17 and AM03  (2017). The baseline for each spectrum corresponds to a brightness temperature of 0 K, however, the spectrum of each source has been manually shifted by 60 K (with respect to the source below) for an easier visualization of the data. The intensities of some spectra have been divided by the factor indicated to the right. Grey solid and dashed vertical lines mark the transitions of CH 3 CN (J K 13 K − 12 K ), CH 13 3 CN (J K 13 K − 12 K ) and SO 2 (J Ka ,Kc 21 7,15 − 22 6,16 ). The blue vertical lines mark the 6 K → 5 K transitions of CH 3 NH 3 + .
The top panel shows the expected synthetic spectrum for CH 3 NH 3 + as observed with ALMA at 0.′′4 angular resolution and considering a column density of 5 × 10 14 cm −2 , a temperature of 225 K, and a linewidth of 5 km s −1 .
Frontiers in Astronomy and Space Sciences | www.frontiersin.org February 2022 | Volume 8 | Article 805162 7 correspond to dense cores dominated by dust but with a rich chemistry. In particular, core AN02 has been extensively studied in the literature in the search of new chemical species (e.g., Belloche et al., 2014). We have also included objects in which an embedded HII region has been found (e.g., AN10, AM06, AM15). The presence of the UV radiation from embedded massive stars ionizing the gas and resulting in HII regions can enhance the protonation of methylamine in the photon-dominated region around the HII region. As shown in Figure 4, no obvious features are detected at the frequencies of the tabulated CH 3 NH 3 + transitions, suggesting a low abundance of protonated methylamine in Sgr B2. We have determined an upper limit of ≈ 5 × 10 14 cm −2 to the column density of protonated methylamine. This is estimated based on a 3-sigma noise upper limit and assuming a gas temperature of 200-300 K (as derived from other molecular species in Sgr B2, Schwörer et al., 2019). This translates into an upper limit of the fractional abundance of ∼10 -10 . The high densities of the Sgr B2 region (∼ 10 5 -10 8 cm −3 ; see also Schmiedeke et al., 2016) can rapidly attenuate the radiation field and result in a low production of heavy ions like CH 3 NH 3 + . Moreover, the J 6 K → 5 K transitions are located close to bright CH 3 CN and CH 13 3 CN (J K 13 K → 12 K ) transitions and a strong SO 2 feature which may hinder the detection of the weaker CH 3 NH 3 + in chemically rich, embedded objects. Observations at other frequency ranges, as well as in other astronomical sources associated with highly ionized and less dense gas, may help in the detection of this species in space.

CONCLUSION AND OUTLOOK
In the present study, the pure rotational spectrum of protonated methyl amine, CH 3 NH 3 + , was observed for the first time. It is worthwhile to recall that upon protonation of CH 3 NH 2 , forming CH 3 NH 3 + , the complex dynamical behaviour of the former molecular system is largely simplified, because the inversion at the NH 2 group in CH 3 NH 2 is eliminated and only the torsional motion between CH 3 and NH 3 has to be potentially considered for the pure rotational spectrum of CH 3 NH 3 + in its ground vibrational state. In this study, a total of five pure rotational transitions from J 2 K − 1 K to J 6 K − 5 K and K up to 2 were identified. As indicated through complementary quantum-chemical calculations, explicit treatment of nuclear quadrupole hyperfine structure from the presence of the nitrogen nucleus was found to be negligible. While the strongest spectroscopic features in the spectrum can be assigned and fitted reasonably well in a straightforward fashion using a standard symmetric-top Hamiltonian, peculiar lineshapes and weak substructure identified in the spectra upon close inspection indeed required extension of the theoretical treatment to account for internal rotation. This refined model description permits very convincing reproduction of the experimental line profiles. A more comprehensive treatment of the internal rotational problem in CH 3 NH 3 + would certainly benefit from extension of the present work to a higher degree of rotational excitation but also from detection of vibrational satellites of CH 3 NH 3 + in torsionally excited states.
Future work towards the spectroscopic characterization of protonated amines offers many possibilities, not only in the millimeter-wave regime. For example, the low-resolution vibrational spectra of CH 3 NH 3 + and also protonated ethyl amine, C 2 H 5 NH 3 + , were observed recently in the range from 700 to 1750 cm −1 (Thorwirth et al., 2019b) using the FELion ion trap apparatus (Jusko et al., 2019). For the purpose of millimeter-wave radio astronomical searches of CH 3 NH 3 + the data presented here should already suffice. Although the column density of CH 3 NH 3 + in the interstellar medium may be some orders of magnitude lower than that of CH 3 NH 2 , the more favorable partition function of CH 3 NH 3 + will support radio astronomical detectability. In the search towards SgrB2 presented in this work CH 3 NH 3 + was unfortunately not found.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

AUTHOR CONTRIBUTIONS
PS: measurement, manuscript writing MT: measurement ST: quantum chemical computations, data evaluation, manuscript writing CE: data evaluation, manuscript writing AS-M: data evaluation, manuscript writing AS: data evaluation, manuscript writing PS: supervision SS: supervision, manuscript writing OA: measurement, data evaluation, manuscript writing, supervision.