Collisional Excitation and Weak Maser Action of Interstellar Methanimine

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Spectroscopy and Photochemistry; General Theory

Collisional Excitation and Weak Maser Action of Interstellar Methanimine Alexandre Faure, François Lique, and Anthony J Remijan J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01431 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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The Journal of Physical Chemistry Letters

Collisional Excitation and Weak Maser Action of Interstellar Methanimine Alexandre Faure,∗,† François Lique,∗,‡ and Anthony J. Remijan∗,¶ †Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France ‡LOMC - UMR 6294, Normandie Université, Université du Havre and CNRS, 25 rue Philippe Lebon, BP 1123 - 76 063 Le Havre cedex, France ¶National Radio Astronomy Observatory, 520 Edgemont Rd., Charlottesville, VA 22903, USA E-mail: [email protected]; [email protected]; [email protected]

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The Journal of Physical Chemistry Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The inelastic cross sections and rate coefficients for the rotational excitation of methanimine (CH2 NH) by cold H2 have been determined quantum mechanically based on a new highly correlated five-dimensional potential energy surface. This surface was fitted to more than 60 000 ab initio points with a root mean square error of ∼ 1-2 cm−1 in the region of the potential well whose depth is -374.0 cm−1 . The rotationally inelastic rate coefficients have been combined with spectroscopic data to generate the non-equilibrium spectrum of CH2 NH towards the interstellar molecular cloud Sgr B2(N). The transition 110 → 111 at 5.29 GHz is found to be inverted and the predicted weak maser emission spectrum is in excellent agreement with new observations performed with the 100-meter Green Bank Telescope.

Graphical TOC Entry

+ CH2NH

2

H2


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Complex organics are observed throughout the Universe, from Solar System objects to stars and galaxies. In the interstellar medium (ISM), more than 200 different (mostly organic) molecules have been detected, including biomolecule precursors such as formamide (NH2 CHO) and glycolaldehyde (CH2 OHCHO) (see e.g. Belloche et al. 1 ). Imines are of special interest because they are possible precursors of amino acids, 2 which have so far eluded detection in the ISM. 3 Amino acids are the building blocks of proteins and the study of their precursors may shed light about the origin of life in the Universe. Methanimine (CH2 NH), the simplest imine, was discovered in the ISM in 1973 towards the molecular cloud Sagittarius B2 (Sgr B2). 4 It was firmly identified thanks to the (hyperfine) multiplet structure of the 110 → 111 rotational line at 5.29 GHz. Since then, CH2 NH has been detected in many galactic and extragalactic sources (see Ref. 5 for a review). The formation of methanimine in the ISM is, however, matter of debate. Ion-molecule reactions are the dominant gas-phase processes at low temperatures and the formation of CH2 NH + might occur through the reaction CH+ 3 + NH2 →CH2 NH2 + H followed by the dissociative 6 recombination of CH2 NH+ 2 with an electron to produce CH2 NH. Neutral-neutral reactions

involving radicals such as NH + CH3 are other possible gas-phase formation pathways. 7 Finally, hydrogenation of solid HCN is a possible grain-surface route to CH3 NH2 where CH2 NH is a stable intermediate, as demonstrated experimentally. 8 In order to elucidate the chemistry of CH2 NH in the ISM, it is first crucial to observe multiple transitions in a large frequency range. This has been made possible through many laboratory studies of the rotational spectrum of methanimine (see Ref. 5 and references therein). As a result, CH2 NH has been detected towards Sgr B2 from centimeter 4 to submillimeter wavelengths. 9 The identification of many transitions is, however, not sufficient to derive accurate abundances because interstellar spectra are generally not at local thermodynamic equilibrium (LTE). Indeed, densities (i.e. pressures) in the ISM are such that the frequency of collisions is neither negligible nor large enough to maintain thermodynamic equilibrium. In such conditions, deriving column densities (i.e. abundances) requires to solve

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simultaneously the radiative transfer equation and a set of statistical equilibrium equations for the molecular levels. This in turn requires the availability of the state-to-state rate coefficients for collisional (de-)excitation. These collisional energy transfer rate coefficients are extremely difficult to measure in the laboratory and radiative transfer models rely almost exclusively on theoretical estimates. 10 In the case of CH2 NH, the only theoretical study was done for electron-impact excitation. 11 In the “dense” molecular ISM, however, the dominant colliders are hydrogen molecules (H2 ). In this Letter, we report the first potentiel energy surface (PES) for CH2 NH–H2 based on ∼ 66,000 high-level ab initio points. This PES was employed in quantum close-coupling calculations to determine rotationally inelastic cross sections in the energy range 2−200 cm−1 , from which rate coefficients were deduced in the temperature range 5−30 K. In addition, the spectrum of CH2 NH towards Sgr B2(N) at 5.29 GHz has been generated using radiative transfer calculations and it has been compared to new observations performed with the 100-m Robert C. Byrd Green Bank Telescope (GBT). The PES of the CH2 NH−H2 complex was computed in a body-fixed frame centered at the center of mass of CH2 NH, as defined in Ref. 12. Here the z- and x-axes correspond to the a- and b- principal inertia axes of the molecule, respectively, so that CH2 NH lies in the (x, z) plane. The intermolecular vector R connects the centres of mass of the CH2 NH and H2 molecules. The θ1 and φ1 angles define the rotation of vector R relative to the CH2 NH body-fixed axis system. The rotation of the H2 molecule is defined by angles θ2 and φ2 . The monomers were assumed to be rigid1 with geometries corresponding to the ground vibrational state: r(CN)=2.406 a0 , r(NH)=1.929 a0 , r(CH)=2.06 a0 , ◦ [ [ \cis =125.1◦ from the experimental results of Ref. 14 and r(HH) = HNC=110.4 ,HCH=117.0◦ ,NCH

1.44874 a0 from the calculations of Ref. 15. Ab initio calculations for the CH2 NH−H2 complex in its ground electronic state were carried out at the explicitly correlated coupled cluster 1

It was shown recently for the CO−H2 system that the use of ground vibrational state geometries in rigid-rotor PES is an excellent approximation to a full-dimensional approach, 13 which here would involve 15-dimensional calculations.

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with single, double and perturbative triple excitations [CCSD(T)-F12a] 16 level of theory with augmented correlation-consistent triple zeta (aVTZ) 17 basis set using the MOLPRO 2012 package. 18 Basis set superposition error (BSSE) was corrected using the Boys and Bernardi counterpoise scheme. 19 The size inconsistency caused by the F12 triple energy correction was corrected by subtracting from the ab initio interaction energies the asymptotic interaction energy at R = 1000 a0 which is 7.4796 cm−1 for all relative orientations. The performance of the CCSD(T)-F12a method was assessed by comparison with standard CCSD(T) results using double-, triple- and quadruple-zeta basis sets extrapolated to the complete basis set (CBS) limit. We have found that CCSD(T)-F12 calculations are within 1−2 cm−1 of CCSD(T)/CBS(D,T,Q) results in the minimum region of the PES. The calculations were carried out for a large random grid of angular orientations: for each value of R, varied from 4.0 to 15.0 a0 , the energies of 3000 mutual orientations were calculated. The energies were leastsquares fitted to an angular expansion of 251 terms (see computational details). The global minimum of the (fitted) PES occurs at R = 5.77 a0 , θ1 = 83◦ , φ1 = 0◦ , θ2 = 117◦ , φ2 = 0◦ with a dissociation energy of De = 374.0 cm−1 . In this planar geometry, the complex has an approximate T-shape with H2 almost perpendicular to the C=N bond. In Fig. 1, we present two contour plots of the CH2 NH−H2 (fitted) PES in this region. We can observe that the PES is highly anisotropic at this distance, with only a small attractive region where θ1 ∼ 80◦ . The CH2 NH−H2 PES was employed in quantum-mechanical scattering calculations to compute rotationally inelastic cross sections. We used the (time independent) close-coupling formalism for collisions of an asymmetric top rigid rotor and a linear rigid rotor, as described in Ref. 20. All calculations were performed with the OpenMP extension2 of the version 14 of the MOLSCAT code. 21 The coupled differential equations were solved using the hybrid modified log-derivative Airy propagator from 3 to a maximum of 200 a0 (at low energy) with a step size lower than 0.25 a0 . The rotational constants of CH2 NH were fixed at their 2

See http://ipag.osug.fr/∼faurea/molscat/index.html

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Figure 1: Potential energy cuts of the 5D CH2 NH−H2 PES. The intermolecular distance is fixed at R = 5.77 a0 and φ2 = 0◦ , corresponding to the equilibrium values of the complex. Left panel: φ1 = 0◦ . Right panel: θ2 = 117◦ . The minimum in the two plots is -374.0 cm−1 at θ1 = 83◦ . Energy contours in cm−1 . experimental values 22 A0 = 6.54490 cm−1 , B0 = 1.15552 cm−1 and C0 = 0.979062 cm−1 . The rotational constant of H2 was taken as B0 = 59.322 cm−1 . The rotational energy levels of CH2 NH are labeled by three quantum numbers: the angular momentum j1 and the pseudo-quantum numbers ka and kc which correspond to the projection of j1 along the axis of the smallest and largest moments of inertia, respectively. The lowest 8 levels of CH2 NH are displayed in Fig. 2. The rotational energy levels of H2 are designated by j2 . Due to the large well depth in the CH2 NH−H2 PES (374 cm−1 ) and the relatively dense rotational spectrum of CH2 NH, close-coupling calculations were highly demanding both in terms of memory and CPU time. In practice, calculations were performed for total energies between 2 and 200 cm−1 , with an energy grid adjusted to properly sample the low-energy resonances. The projectile H2 was restricted to para-H2 (j2 = 0), which is the dominant form of H2 in the cold interstellar medium. 23,24 The basis set included levels j1 = 0 − 12 and j2 = 0, 2 with rotational energies (CH2 NH plus H2 ) less than a threshold EMAX=600 cm−1 . This cutoff was necessary to limit the number of coupled-channels below 6,000 while preserving convergence to within ∼10% for all transitions among the first 15 rotational levels of CH2 NH, i.e. up to

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-1

Level energy (cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

_

61.2

62.8

_

__

303

168

202

_

211 212

110 111

56.5

5 17.5

_ _

93.1

101

1.82

0

000

ka=0

ka=1

Figure 2: Lowest 8 levels of CH2 NH, with energies taken from the CDMS catalog. 22 For each level, the strongest radiative transitions are indicated by arrows and the numbers give the corresponding Einstein coefficient (in units of 10−6 s−1 ) taken from Ref. 22. The spectrum consists of a-type (∆ka = 0) and b-type (∆ka = ±1) transitions with corresponding dipole moments µa = 1.340 D and µb = 1.446 D. the level 220 at 28.3 cm−1 . Rate coefficients were obtained in the temperature range 5–30 K by integrating the cross sections over Maxwell-Boltzmann distributions of relative velocities. Cross sections and rate coefficients for the lowest 4 transitions out of the ground state 000 are presented in Fig. 3 as function of collisional energy and temperature, respectively. Many resonances are observed in the cross sections, as expected from the deep potential well. We can also notice that the favored transitions are 000 → 101 and 000 → 202 , corresponding to the usual propensity rule ∆j1 = 1, 2 and ∆ka = 0. In addition, for the ka = 1 doublet, the lower level is found to be favored. This propensity was also observed for higher ka = 1 doublets and this corresponds to j1 being preferentially oriented along the direction of the greatest moment of inertia (the c−axis). This result is observed in other molecules and is responsible, in particular, of the anti-inversion of the doublet 110 −111 in interstellar H2 CO. 23 Here, however, because both collisional and radiative transitions between the ka = 1 and ka = 0 ladders are allowed (in contrast to H2 CO), the above propensity is in competition with inter-ladder transitions. In particular the spontaneous decay rate from the 111 to 000 level is about 1.6 times that from the 110 to the 101 level (see Fig. 2), which favors inversion 7



of the doublet, as in the case of methyl formate (HCOOCH3 ). 25 The strong emission of the intrinsically weak 110 → 111 line, as first detected by Godfrey et al., 4 was thus attributed to a population inversion rather than an anomalously high abundance. 26 The lack of collisional data, however, has precluded so far any definite conclusion. Using our rate coefficients, the critical density3 of the upper level 110 can be estimated as ∼ 1.5×105 cm−3 which means that non-LTE effects are expected at densities in the range 103 − 107 cm−3 . However, only nonLTE radiative transfer calculations can predict the actual rotational populations of CH2 NH for a given set of physical conditions, as illustrated below. 10

-9

100

000→101

10

000→111

1

000→101

3 -1

2

Rate coefficient (cm s )

000→202 Cross section (Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.1

10

000→202

-10

000→111 10

-11

000→110

000→110

0.01

0

10

20 30 40 50 -1 Collision energy (cm )

60

10

-12

5

10

15 20 Temperature (K)

25

30

Figure 3: Cross sections (left panel) and rate coefficients (right panel) for excitation out of the 000 level to levels 101 , 202 , 111 and 110 due to para-H2 (j2 = 0) collisions. The star forming region Sgr B2 is an exceptionally massive cloud complex in the Galactic Center, where shocks and supersonic turbulence are ubiquitous. Towards the north core of Sgr B2 (Sgr B2(N)), the continuum emission is produced by a complex region of ionized gas (so-called HII region). A detailed description of this source can be found in Ref. 27. We focus below on the 110 → 111 transition of CH2 NH at 5.29 GHz. This line was first observed in 1973 by Godfrey et al. 4 towards Sgr B2 with the 3.80 beam (at 5.29 GHz) of the Parkes 64-meter telescope. New observations towards Sgr B2(N) were performed with 3

The critical density defines the density at which the collisional rate out of the upper state of a transition equals the spontaneous radiative rate.

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the 2.30 beam of the GBT. The multiplet was detected with a high signal-to-noise ratio, as displayed in Fig. 4. The transition frequencies have been shifted to the laboratory rest frame using the nominal source velocity of +64 km.s−1 . Weaker transitions with a velocity component of 82 km.s−1 (-0.32 MHz) are also observed, as found in several other molecules with the GBT. 28 These two velocity components correspond to two molecular clouds lying superimposed along the same line of sight. Radiative transfer calculations were performed with the non-LTE RADEX program 29 based on the escape probability formalism for a uniform sphere. The code was employed to i ) and opacity (τi ) for each hyperfine transition compute the line excitation temperature (Tex

i = 1, 6 of the 110 → 111 line. The two velocity components were computed separately. The hyperfine energy levels and radiative rates were taken from the CDMS catalog. 22 The hyperfine-resolved rate coefficients were obtained from the rotational rate coefficients using the statistical approximation, which has been shown to be reliable at low opacities. 30 The kinetic temperature and density of H2 were fixed at T =30 K at nH2 = 104 cm−3 , respectively, for each velocity component. These values, derived by Faure et al. 25 from their modeling of the weak HCOOCH3 masers, correspond to a relatively cold and dilute gas surrounding the north core, in the foreground of the HII region. The line widths were taken as 15 and 10 km.s−1 for the low- and high-velocity components, respectively. 27 The column density of CH2 NH was adjusted for each velocity component to best reproduce the observational spectrum. The solution of the radiative transfer equation was expressed as the radiation temperature, as in Ref. 25:

∆TR∗ (ν) = [Jν (Tex ) − Jν (TCM B ) − Tc (ν)](1 − e−τ (ν) ),

(1)

where Jν (T ) = (hν/kB )/(ehν/kB T − 1), ν is the frequency of the transition (5.29 GHz), Tcmb = 2.725 K is the temperature of the cosmic microwave background and Tc (ν) is the main beam background continuum temperature of Sgr B2(N), as measured by the GBT,

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which is ∼36 K at 5.29 GHz. The total opacity τ (ν) in Eq. 1 is the sum over the two velocity components and the 6 hyperfine transitions, assuming individual opacities are gaussian. The resulting composite line (with 8 resolved components) is compared to the observation in Fig. 4 where a remarkable agreement is obtained. The best fit was found for CH2 NH column densities of 2.5±0.5×1014 and 1.0±0.2×1014 cm−2 for the low- and high-velocity components, respectively. As expected, the 110 → 111 transition is inverted with an excitation temperature of -0.48 K (equal for each hyperfine transition within 0.01 K). We have checked that this population inversion occurs for H2 densities in the range 6×102 −6×106 cm−3 , as anticipated, meaning this is a very robust phenomenon. We have also plotted the emergent spectrum in LTE conditions with the same column densities. A very faint absorption (the spectrum has been multiplied by a factor of 10) is predicted in this case, demonstrating that the weak inversion, by amplifying the strong background continuum radiation, is essential to produce the emission of the otherwise undetectable 5.29 GHz line. The derived CH2 NH column densities correspond to low fractional abundances relative to H2 (f (H2 ) . 10−10 , assuming a H2 column density of 3 × 1024 cm−2 as in Ref. 31). They are in particular lower than the value derived by Halfen et al. 32 (9.1 ± 4.4 × 1014 cm−2 ) from a spectral survey of emission lines at higher frequencies (>70 GHz), which probe another extended, warmer and denser, component. Methanimine is also detected in a compact component, the so-called “hot core” of Sgr B2(N) where the column density is ∼ 1018 cm−2 . 1 A more complete treatment is now required to model all detected lines, in absorption and emission, in order to improve the determination of the abundances and physical conditions in both the extended cool and warm components. This will be presented in a future dedicated work.

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Radiation temperature (K)

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0.4

observation non-LTE model LTE model(×10)

0.3 0.2 0.1 0

-1

+64 km.s

-0.1

-1

+82 km.s

-0.2 5.288

5.289

5.290 5.291 Frequency (GHz)

5.292

Figure 4: Observational and model spectra of methanimine 110 → 111 transition at 5.29 GHz towards Sgr B2(N). Relative intensities of the (partially resolved) hyperfine structure in the optically thin limit are shown at the bottom. The nominal source velocity is +64 km.s−1 . A second velocity component is resolved at +82 km.s−1 . The non-LTE model predicts a population inversion with a negative excitation temperature Tex = −0.48 K. The LTE model spectrum has been multiplied by a factor of 10 to show it more clearly.

Computational details The analytical expansion for an asymmetric-top-linear molecular system can be written as: 12

V (R, θ1 , φ1 , θ2 , φ2 ) =

X

vl1 m1 l2 l (R)tl1 m1 l2 l (θ1 , φ1 , θ2 , φ2 ),

(2)

where the functions tl1 m1 l2 l (θ1 , φ1 , θ2 , φ) are products of spherical harmonics, as given explicitly in Eqs. (5-6) of Ref. 33. The indices l1 , m1 and l2 refer to the (θ1 , φ1 ) and (θ2 , φ2 ) dependence of the PES, whereas l runs from 0 to the sum of l1 and l2 . The expansion coefficients vl1 m1 l2 l (R) were obtained through a least-squares fit on the random grid of 3000 angular geometries at each intermolecular separation (22 radial grid points in the range R = 4 − 15 a0 ). All anisotropies up to l1 = 14, l2 = 6 and l = 20 were included, resulting in 3054 expansion functions. We then selected only significant terms using a Monte Carlo error estimator (defined in Ref. 34), resulting in a final set of 251 expansion functions with anisotropies up to l1 = 13, l2 = 6 and l = 16. The root mean square was found to be lower 11



than 2 cm−1 in the long-range and minimum regions of the PES (R > 5.75 a0 ). In these regions, the mean error on the expansion coefficients vl1 m1 l2 l (R) is smaller than 1.25 cm−1 . A cubic spline radial interpolation of these coefficients was finally employed over whole grid of intermolecular distances and it was smoothly extrapolated (using exponential and power laws at short- and long-range, respectively) in order to provide continuous radial coefficients adapted to quantum close-coupling calculations.

Acknowledgement This work was supported by the French program Physique et Chimie du Milieu Interstellaire (PCMI) funded by the Conseil National de la Recherche Scientifique (CNRS) and Centre National d’Etudes Spatiales (CNES). F.L. acknowledges the Institut Universitaire de France for financial support. We thank Joanna Corby for stimulating discussions initiating this work. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. The Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

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ity of methanimine (CH2 NH), ammonia (NH3 ), and hydrogen cyanide (HCN). Astron. Astrophys. 2011, 535, A47. (3) Snyder, L. E.; Lovas, F. J.; Hollis, J. M.; Friedel, D. N.; Jewell, P. R.; Remijan, A.; Ilyushin, V. V.; Alekseev, E. A.; Dyubko, S. F. A Rigorous Attempt to Verify Interstellar Glycine. Astrophys. J. 2005, 619, 914–930. (4) Godfrey, P. D.; Brown, R. D.; Robinson, B. J.; Sinclair, M. W. Discovery of Interstellar Methanimine (Formaldimine). Astrophys. Lett. 1973, 13, 119–121. (5) Dore, L.; Bizzocchi, L.; Degli Esposti, C. Accurate rotational rest-frequencies of CH2 NH at submillimetre wavelengths. Astron. Astrophys. 2012, 544, A19. (6) Turner, B. E.; Terzieva, R.; Herbst, E. The Physics and Chemistry of Small Translucent Molecular Clouds. XII. More Complex Species Explainable by Gas-Phase Processes. Astrophys. J. 1999, 518, 699–732. (7) Suzuki, T.; Ohishi, M.; Hirota, T.; Saito, M.; Majumdar, L.; Wakelam, V. Survey Observations of a Possible Glycine Precursor, Methanimine (CH2NH). Astrophys. J. 2016, 825, 79. (8) Theulé, P.; Borget, F.; Mispelaer, F.; Danger, G.; Duvernay, F.; Guillemin, J. C.; Chiavassa, T. Hydrogenation of solid hydrogen cyanide HCN and methanimine CH2 NH at low temperature. Astron. Astrophys. 2011, 534, A64. (9) Persson, C. M.; Hajigholi, M.; Hassel, G. E.; Olofsson, A. O. H.; Black, J. H.; Herbst, E.; Müller, H. S. P.; Cernicharo, J.; Wirström, E. S.; Olberg, M. et al. Upper limits to interstellar NH+ and para-NH2 − abundances. Herschel-HIFI observations towards Sgr B2 (M) and G10.6-0.4 (W31C). Astron. Astrophys. 2014, 567, A130.

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(10) Roueff, E.; Lique, F. Molecular Excitation in the Interstellar Medium: Recent Advances in Collisional, Radiative, and Chemical Processes. Chemical Reviews 2013, 113, 8906– 8938. (11) Wang, K.; Meng, J.; Baluja, K. L. Electron collisions with H2 CNH using the R-matrix method. European Physical Journal D 2015, 69, 78. (12) Phillips, T. R.; Maluendes, S.; McLean, A. D.; Green, S. Anisotropic rigid rotor potential energy function for H2 O-H2 . J. Chem. Phys. 1994, 101, 5824–5830. (13) Faure, A.; Jankowski, P.; Stoecklin, T.; Szalewicz, K. On the importance of fulldimensionality in low-energy molecular scattering calculations. Scientific Reports 2016, 6, 28449. (14) Pearson, R.; Lovas, F. J. Microwave spectrum and molecular structure of methylenimine (CH2 NH). J. Chem. Phys. 1977, 66, 4149–4156. (15) Bubin, S.; Adamowicz, L. Variational calculations of excited states with zero total angular momentum (vibrational spectrum) of H2 without use of the Born-Oppenheimer approximation. J. Chem. Phys. 2003, 118, 3079–3082. (16) Knizia, G.; Adler, T. B.; Werner, H.-J. Simplified CCSD(T)-F12 methods: Theory and benchmarks. J. Chem. Phys. 2009, 130, 054104–054104. (17) Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007–1023. (18) Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M.; Celani, P.; Györffy, W.; Kats, D.; Korona, T.; Lindh, R. et al. MOLPRO, version 2012.1, a package of ab initio programs. 2012; see http://www.molpro.net (accessed May 27, 2018).

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Collisional Excitation and Weak Maser Action of Interstellar Methanimine

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