Van Der Waals Interaction of HNCO and H2: Potential Energy Surface

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Van Der Waals Interaction of HNCO and H: Potential Energy Surface and Rotational Energy Transfer Emna Sahnoun, Laurent Wiesenfeld, Kamel Hammami, and Nejmeddine Jaïdane J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00150 • Publication Date (Web): 26 Feb 2018 Downloaded from http://pubs.acs.org on February 28, 2018

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The Journal of Physical Chemistry

Van der Waals interaction of HNCO and H2: Potential energy surface and rotational energy transfer Emna Sahnoun,†,‡ Laurent Wiesenfeld,∗,†,¶ Kamel Hammami,‡ and Nejmeddine Jaidane‡ †Univ. Grenoble-Alpes, CNRS, IPAG, 38000 Grenoble, France ‡LSAMA, Université de Tunis El Manar, Tunis, Tunisia ¶ Université Paris-Saclay, CNRS, Laboratoire Aimé-Cotton, 91405 Orsay, France E-mail: [email protected]

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Abstract Isocyanic acid (HNCO) is the most stable of all its isomers; it has been observed repeatedly in many different conditions of the Interstellar Media, and its chemistry is poorly known. In order to quantitatively estimate the abundance of HNCO with respect to other organic molecules, we compute its rotational quenching rates colliding with H2 , the most common gas in the gaseous Interstellar Media. We compute ab initio the van der Waals interaction HNCO-H2 , in the rigid molecules approximation, with a CCSD(T)-F12a method. On the fitted ab initio surface, inelastic scattering crosssections and rates are calculated for a temperature range of 7-200 K, with CoupledStates quantum time-independent formalism. The critical densities are high enough to yield rotational temperatures of HNCO differing significantly from the kinetic temperature of H2 , especially so for the shorter wavelengths observed at the ALMA interferometer. It is found that the quenching rates for collisions with ortho- or para-H2 differ greatly, opening the possibility of far from equilibrium populations of some rotational levels of HNCO.

1 Introduction Recent years have witnessed a surge in the sensitivity, dynamical range, and spectroscopic precision of mm and sub-mm observatories, among those, the IRAM 1 and ALMA 2 instruments. It is nowadays possible for astrophysicists to observe in great details many molecules, including organic molecules with large molecular weight/small rotational constants at temperatures ranging from a few Kelvin to several hundreds of Kelvin. Because of the extended frequency range of instruments at the backend of telescopes on the ground (up to approx. 270 GHz -IRAM or 850 GHz -ALMA), many rotational transitions of many molecular species may be recorded.

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1.1 Astrophysical context Molecular rotational lines are usually observed in emission, and relating the intensity of the emission line to the column density or volume density of the emitter is no trivial task. 3 It has been known for long 4 that the optical nonlinear properties of the emitting gas has to be described in details, in order to understand the line shapes, intensities and self-absorption properties. Hence, the excitation mechanisms of molecular levels has to be described quantitatively, as vivid examples and reference databases shows readily. 5–7 Excitation of molecular levels is possible through photonic or molecular collisional processes. For photons, excitation occurs by absorption of the black-body Cosmic Microwave Background (CMB) radiation (T (CMB) ∼ = 2.725 K) or by warmer black-body photons originating possibly from dust, or else, by particular infra-red lines. Similarly, photonic quenching occurs both by spontaneous and induced emission, the former dominating the latter in the optically thin emission limit. For a polar molecule M under study, let us consider 2 rotational levels for sake of simplicity, i and f , with Ei > Ef . Suppose that spontaneous emission is the main process, for the transition i → f , Einstein coefficient Af i . Let kf i (T ) be the collisional quenching rate for the same transition, and n(H2 ), the volume density of the main collider, here H2 . We have the following (ni , nf are volume densities of M, levels i or f ): dni = −Af i ni − kf i n(H2 )ni + kif n(H2 )nf , dt

(1)

where kf i and kif are proportional, thanks to the microscopic-reversibility principle. A collider critical density n∗ (T ) is defined as:

n∗ (H2 , T ) =

Af i . kf i (T )

(2)

If colliders densities are similar to n∗ , photonic and collision processes are in competition in the excitation/ quenching of rotational levels of M. For n(H2 ) n∗ (H2 ), the kinetic

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temperature of H2 and the internal rotational temperature of M are equal; this is what is usually called as Local Thermodynamical Equilibrium (LTE) Much more detailed discussion may be found in Ref. 8. Consequently, in order to perform a quantitative determination of densities of the molecule M, one has to know the excitation/quenching conditions, and the critical densities of its various transitions. This amounts to measuring or computing the rotational rates of excitation/quenching for the observed molecule M diluted in the dominant gas, usually H2 and possibly atomic H, He, and electrons. On the one hand, measuring those rates (the rates of excitation for isolated collisions M-H2 ) is a difficult task seldom doable. 9,10 One of the only absolute rate measurements is the pressure broadening, indirectly related to both elastic and inelastic scattering. 11,12 On the other hand, computation of those rates has been performed for many decades, since the pioneering work of computing the CO-He collision. 13 Nowadays, computing rates for complex organic molecules (in Astrophysical parlance, organic molecules with at least five atoms, and at least two C, N, and/or O atoms) is made possible, 14–16 thanks to vast improvements in the determination of the non- reactive intermolecular potential energy surface (PES) and the powerful computers capable of performing quantum dynamics on those PES. The present paper is part of such an effort, devoted to a particularly interesting molecule, isocyanic acid (HNCO).

1.2 Astrochemical context Isocyanic acid, HNCO, is the simplest molecule containing all three common “heavy” elements known in astrophysics, more precisely, all three common nuclei

12

C,

14

N,

16

O. It has

been observed in many environments, for many decades. 17–25 Its chemistry is not clearly understood, nor is it confirmed whether it has a role in the synthesis of formamide NH2 COH, considered as a plausible parent molecule for bio-organic chemistry in astrophysical media. 22–24,26,27 Hence, a detailed understanding of its abundance in various media is of great interest, in order to constrain different chemical models, and to try and correlate its abun4


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dance with other molecules abundances. Isocyanic acid HNCO is the most stable of the four isomers (HNCO, HCNO, HOCN, HONC), 28 the former three being observed in interstellar media. 20,29,30 The deuterated isotopologue DNCO has also been observed. 31 Because of its very peculiar rotational spectroscopy (see below, section 4.1), HNCO displays no simple relation between upper level energy and transition frequency. HNCO is one prominent example where excitation conditions of the rotational lines vary considerably, within the same range of observed frequency, or when switching of frequency ranges for the same emitting medium. Knowing the collision conditions for HNCO is essential for understanding spectral line shapes and intensities. While some data exist for the collision of HNCO with He (see Green in 7) , they were derived under very severe approximations and were shown to be inadequate for understanding a batch of observations (E. Caux, private communication). Also, some partial HNCO-He collisions studies have been published by some of the present authors. 32 In order to go beyond these quenching rates and to be fully relevant for astrochemical modelling, the necessary ingredients are computed in this paper: (i) the computation of the PES of the HNCO-H2 interaction is described in section 2; (ii) its fitting upon a polyspheric expansion 33,34 is described in section 3; (iii) the quantum dynamical derivation of the inelastic cross sections is described in section 4. It must be born in mind that we do not aim here at spectroscopic precision, as for example in the earlier work on the H2 O-H2 collisions. 35 The goal of this computation is to deliver quenching and excitation rates to astrophysical modellers, who routinely need these with a moderate precision. 36,37 We shall pursue all of our computation with this aim of a more modest precision in mind. The paper finishes with some comparison with earlier results and a discussion, section 5 .

5



2 Potential energy surface 2.1 Geometries For astrophysical applications, we are interested in studying low- to medium-temperature collisions, 7 K . T . 200 K. Hence, we keep both molecules HNCO and H2 rigid. Indeed the lowest vibrational constant of HNCO is measured at ν5 = 577.5 cm−1 (ν5 is the HNC bend) and the torsional vibration (depart from planarity) is at ν6 = 659.8 cm−1 . The rigid rotator approximation is thus valid for low collisional energies, strictly speaking. DNCO has even lower frequencies, with the DNC bend at ν5 ' 460 cm−1 , limiting slightly more the rigid rotor approximation. However, because of the small values of vibrational excitation cross sections (and rates), a few orders of magnitude below those for rotational excitation at moderate energies, 38,39 it remains sensible to use the rigid-rotor approximation to values up to a few hundreds of wave-numbers above the ν5 threshold. We use the following geometry for HNCO, taken at average value for vibrational ground state (distances in bohr, angles in degrees): 40 r(HN) = 1.9137, r(NC) = 2.3007, r(CO) = 2.2028; the in-plane angles are α(HNC) = 124.0, α(NCO) = 172.1; the molecule has been experimentally determined as planar. The ground state average distance for the hydrogen molecule is r(HH) = 1.449. The geometry for the scattering system is shown schematically in figure 1. For technical reasons internal to the scattering code, the orientation of HNCO is as follows. The frame of reference is similar to the one used for water-H2 scattering, 35 with the Gx1 y1 z1 axes attached to the principal axes of inertia of HNCO; the plane of the molecule is in the Gx1 z1 plane, the Gz1 axis roughly along the OCN direction. The hydrogen molecule center of mass is located with the spherical coordinates R, θ1 , φ1 . The orientation of the H2 molecules in the G0 x2 y2 z2 frame (parallel to the Gx1 y1 z1 frame) is given by the two spherical angles θ2 , φ2 . G and G0 are respectively the HNCO and H2 center of masses. The rigid-rotor interaction PES is thus a 5-dimensional surface.

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z1

z2

H N

θ2,φ2 x2

y2

θ1,φ1 y1

x1

C O

Figure 1: Coordinates of the HNCO-H2 system. Gx1 y1 z1 is attached to the principal axes of inertia of HNCO. The G0 x2 y2 z2 axes are parallel to the Gx1 y1 z1 axes. θ and φ angles are spherical angles.

2.2 Ab initio computations The ab initio interaction energies are computed at the CCSD(T)-F12a level, via the supermolecular approach, using the MOLPRO2011 package. 41 Basis Set Superposition Error was corrected, using the Boys-Bernardi scheme. The interaction energy E(int) is taken as (X denoting the total base, including both HNCO and H2 ):

EX (int) = EX (HNCO, H2 ) − EX (HNCO) − EX (H2 ).

(3)

The CCSD(T)-F12a method is used with the augmented correlation-consistant polarized basis set, (aug-cc-pVXZ), where X = D, T, Q, ... denotes the order the basis. Because of the length of the computation, the basis X is chosen at the DZ level, with some points computed at the TZ level, for sake of comparison. Previous studies showed that results obtained from this approach are close to those deduced using the standard coupled cluster CCSD(T) aug-cc-pVTZ techniques, with a sizable reduction in CPU time. 42 Also, high precision of the CCSD(T)-F12 methods is known, with the AVDZ basis computation being already

7


of high quality. 43 Before using the mono-configurational method, a preliminary complete active space self-consistent field calculation is performed. It shows that the weight of the dominant configuration is greater than 0.93 for all orientations, thereby validating the monoconfigurational overall computation. We use of the F12a variant of the F12 formalism, better suited for smaller basis sets. 43 The CCSD(T)-F12a being not size-consistent, one has to subtract the value of the residual interaction at large distance. For distances larger than 30 bohr, isotropic value of EVDZ (int) = 0.25 cm−1 has to be subtracted from the interaction energy. HNCO having a important departure from rod-like geometry, the PES determination necessitates approximately 2 500 ab initio points/distance, and a grand total of 427 250 points. The computation at the aVTZ level, about 10 times slower, would have become prohibitively long. We discuss the loss of precision in the discussion section 5 The interaction energy is carried out in C1 symmetry group, for a random grid of the 4 angles θ1 , φ1 , θ2 , φ2 . Using a random grid of the angles has the distinctive advantages of: (i) getting rid of any oscillatory unwanted description of the fits, because of the maximum angular frequency described by the regular grid, and (ii) allowing for a Monte-Carlo-based fit of the potential, as described in the next section. The PES is found to have a global minimum of E(int) ' −235.26 cm−1 , for the configuration R = 7.9, θ1 = 32, φ1 = 90, θ2 = φ2 = 90 (the H2 molecule perpendicular to the HNCO plane, and the center of H2 in the rough direction of the H atom of HNCO). We present several cuts of the 5D PES in figure 2. To be complete, it is important to ensure that the long range description of the PES is sufficiently precise; In order to do so, we compare in figure 3 the ab initio AVDZ-F12a potential V (with the correction at infinity to have it tend to zero) with an analytical approximation of V , which we call Vanal. . Vanal. is found by a multipolar expansion of the interaction energy, taking into account both static and induced multipoles on HNCO and H2 . We make use of formulas from, 44 with numerical values for HNCO taken from 32 and for H2 from. 44 In Fig. 3, squares denote the actual value of |V |, as computed here, and

8


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|V | = |(V − Vanal. )|. One sees that the error is very small, much smaller than all other approximations made in computing V .

3 Fits In order to use the PES in subsequent quantum dynamical computations, we need an analytical form of the PES, depending on the (θ1 , φ1 , θ2 , φ2 ) angles in the following functional form. At a given distance R, we have in the coupled representation: 33

V (R, θ1 , φ1 , θ2 φ2 ) =

X

Vl1 ,m1 ,l2 ,l Tl1 ,m1 ,l2 ,l (θ1 , φ1 , θ2 φ2 ),

(4)

l1 ,m1 ,l2 ,l

with the polyspheric representation of T , see Ref. 33, eq(4) and proper normalization, see Ref. 35, eq(6) .

(2l1 + 1) 2 (1 + δm1 ,0 )

1/2

Tl1 ,m1 ,l2 ,l (θ1 , φ1 , θ2 φ2 ) = ×   X  l1 l2 l  (l +m +l +l)   Yl,r (θ1 , φ1 )Yl2 ,r2 (θ2 , φ2 ) δm1 ,r1 + (−1) 1 1 2 δ−m1 ,r1 r1 r2 r r1 ,r2 where Ylm (θ, φ) are spherical harmonics, δij is a Kronecker symbol and

.

.

.

.

.

.

(5)

is a 3-j

symbol, with r + r1 + r2 = 0. Because of the elongated shape of the HNCO molecule, fitting the PES with spherical functionals is a difficult task. We must resort to a scaling of the potential values, in a manner similar to what had been done previously. 16,45 The goal is to retain original ab initio values for the useful part of the PES (where the scattering occurs) and scale the higher potential values in order to be able to fit. The scaling procedure is as follows, with Vs , the scaled

9



13

13

11

11 -159.1

-140.6

-104.7 R(Bohr)

9

Ra

Ra

R(Bohr)

-174.0

7

-160.1

9

7

5

5 0

90

180

θ 1(deg)

270

360

0

(a) PES cut for φ1 = 0, θ2 = 90, φ2 = 90 (Molecule H2 perpendicular to the plane of HNCO). Minimum of the potential for R = 7.90, θ1 = 32.

13

-150.5

-175.9

(b)

90

270

360

180

-161.1

-235.2

135

-199.8 φ 2(deg)

-154.5

180

θ1(deg)

(b) PES cut for φ1 = 0, θ2 = 90, φ2 = 0 (both molecules in the same plane).

11

9

Ra

Ra

(c)

-219.1

(a)

-235.2

R(Bohr)

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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7

90

45

5 0

90

180 θ 1(deg)

270

0

360

(c) PES cut for φ1 = 0, θ2 = 0, φ2 = 0 (both molecules in the same plane).

0

45

90 θ 2(deg)

135

180

(d) PES cut around the minimum, R = 7.90, θ1 = 32, φ1 = 0, orientation of H2 varying.

Figure 2: All figures: red dotted lines, attractive potential; blue continuous line, repulsive potential. All figures in the plane of the HNCO molecule. Energies in cm−1 , distances in bohr, angles in degrees.

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Figure 3: Quality of the long distance computation. Squares, absolute values of the ab initio potential. Crosses, |V |, see text. Black symbols, θ1 = θ2 = φ1 = φ2 = 0; red symbols, same, with φ2 = 90 deg; blue symbols, θ1 = θ2 = 90 deg, φ1 = φ2 = 0. potential and Va the ab initio value.VT 1 < VT 2 are the two threshold values:

Vs =

Vs = VT 1 + (VT 2 − VT 1 ) × S Vs =

where S(u) =

2 π

sin

for Va ≤ VT 1

Va

VT 1 +

π 2

sin

π u 2

2 π

Va −VT 1 VT 2 −VT 1

(VT 2 − VT 1 )

for VT 1 < Va ≤ VT 2

(6)

for Va > VT 2 .

is a switching function with continuous third derivative. The

best fit with acceptable thresholds was found with VT 1 = 1000 cm−1 and VT 2 = 5000 cm−1 . The fit was performed by minimizing the number of angular functions, with the method outlined in 34 . Using a random distribution of angles allows to begin with as few orientations as possible, and increasing that number when the fit becomes both precise (enough terms in the expansion), and reliable (enough ab initio points to define all terms, that is, about 4 times as many points as terms). Best compromise between number of points/distance, precision of the fit and number of fitting functions was found for the following maximum values: l1 ≤ 15, m1 ≤ 6, l2 ≤ 2, l ≤ 17. Note that all permissible m1 are not used, because of

11



the weak anisotropy in φ1 . With these limitations the number of fitting functions amounts to 215. For R ≥ 5.5 bohr, the fit is better than 1%. A somewhat larger error is found for lesser values of R, thereby limiting the precision of the fit at higher collisional energies. Errors on the fit are depicted in figure 4. One sees that the error remains below 1%, except near the zero value of Viso =

1 V , 4π 0000

equation (4). Some erratic behavior is observed around

R = 10 bohr, but with errors below 1%. The ab initio points and/or the fit coefficients, together with the routines need to construct the fitted PES are available from the authors upon simple request.

Figure 4: Quality of the fit, as a function of distance. Blue crosses, |Viso |, in cm−1 ; red circles, error on the fits, as the rms of the residuals, see eq(9), 35 in cm−1 ; black filled diamonds, ratio rms/|Viso |.

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4 Dynamics Scattering dynamics is performed by solving the time-independant Schrödinger equation, in the coupled- channel or coupledstates formalisms. The OpenMP version of the Molscat code was used for that purpose. 46 In what follows, we denote by JKa Kc the rotational quantum numbers of HNCO, by J2 , the rotational quantum number of H2 . Jtot is the partial total angular momentum a conserved quantity.

4.1 Spectroscopy In order to compute the scattering cross sections, the spectroscopy of HNCO must be reproduced by the code with precision. HNCO is an asymmetric rotor, with the rotational constant for rotation along Oz much larger to the two other rotation constants, both nearly equal. We made use of the following rotational Hamiltonian (note the peculiar order of the rotational constants, 40 and ordered this way for technical reasons special to the molscat code: H = AJx2 + BJy2 + CJz2 + DJ J 4 + DJK J 2 Jz2 + DK Jz4 + HK Jz6 ,

(7)

with (in cm−1 ) : A = 0.369314, B = 0.3639144, C = 30.6494, DJ = 1.1675 × 10−7 , DJK = 3.1184 × 10−5 , DK = 0.2019, and HK = 9.5162 × 10−3 . Note that without the HK term, spectroscopy would be wrong above about 100 cm−1 . The next term, LK Jz8 , was not necessary in order to reproduce the rotational spectrum accurately. The rotational constant for H2 was taken at B = 60.853 cm−1 . We computed collisional rates connecting the 68 first levels, E ≤ 150 cm−1 , J ≤ 19. The average error for these 68 levels is h|Ecomp − Eexp |i = 0.04 cm−1 (maximum error, 0.157 cm−1 , for J = 7, Ka = 2, Kc = 1, 2). The spectrum of HNCO is schematically depicted in figure 5. A complete list of computed and experimental levels are given in the supplementary materials. As we examine the set of levels in figure 5, we note that HNCO behaves nearly like a set of rod-like molecules, for each value of Ka , separated by more than 30 cm−1 . In particular, the 13



JKa =0 Kc =J ladder behaves like a rod, with the radiative transition ∆J = −1 being readily observed on the sky. Note also that some transitions ∆J = +1, ∆Ka = −1, ∆Kc = +1 are also observable with the high-frequency telescopes, like ALMA.

HNCO levels, JKaKc 150 22

1

32

2

125 Energy (cm−1)

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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2

100

2 0

32

1

42

2

42 52

5 3

3

2 4

62

62

5

72

5

82

72

6

82

6

Transition > 300GHz

4

131 121

75

101

9

50 11

0

25 0

Transition 20 K, lower levels), and possibly within a factor 2-3 for higher transitions and temperatures. It must emphasized here that, except for ortho-to-para H2 ratios indirect measures, which need much greater precisions, this precision is sufficient for most LVG/nonLTE modelling of HNCO abundances in all usual ISM conditions. More than the absolute precision of the rates are the relative values of importance. The isotopically substituted DNCO molecule has been observed and is one of the tracers of chemical history. 31 It is of great interest to try and estimate relative abundances of DNCO vs. HNCO, with the possible help of relevant collision coefficients. Because of the weak influence of the outer H atom on the rotational/inertial properties of HNCO, it is expected that the D ↔ H substitution would not affect meaningfully the rates presented here, all the more because of their moderate precision. The scaling is inexistant, with reduced masses

19



Figure 8: Quenching rates for HNCO colliding with para-H2 and ortho-H2 (this work), form 0 0 the level 100 10 to J0J 0 , J < 10. Collider para-H2 in black circles, ortho-H2 in red diamonds. Temperatures, 160K.

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Figure 9: Critical density of collider, eq.(2), as a function of the transition frequency. Green circles, helium rates, scaled; black circles, para-H2 ; red circles, ortho-H2 , this work. Temperature is 160 K.

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nearly equal (µ(HNCO − H2 ) = 1.911 and µ(DNCO − H2 ) = 1.913), and the center of mass moving by approximately 0.07 bohr. The hyperfine splittings of the HNCO spectrum, due to the nuclear spin of

14

N, have not

been observed, to the best of our knowledge, since observations occur for values of J 1, where hyperfine effects become very small. The PES determined here could however be the basis for computations of anomalous hyperfine lines intensities, a precious tool for estimating optical depth (like in HCN observations 52 ). We have computed all transitions between rotational levels below E = 150 cm−1 , for Ecoll ≤ 600 cm−1 and rates for T ≤ 200K. The rates computed here differ systematically from earlier He rates, but not in a dramatic way for para-H2 . More interestingly, the large difference in rates between the ortho-H2 and para-H2 rates may result in large differences of abundance estimates, depending on the collider gas kinetic temperatures. This set of rates should greatly help in understanding the many observations of HNCO, because of the high critical densities for transitions in the mm to sub-mm ranges. It is hoped that these rates will help in determining the mostly unknown chemistry of the ubiquitous HNCO molecule.

Acknowledgement The authors acknowledge useful discussions with E. Caux, C. Ceccarelli, B. Lefloch, A. Faure, and M. Hochlaf. ES thanks COST Action CM1401 ’Our Astrochemical History’ and the Tunis El Manar University for travel support. LW thanks the PALMS Labex, Université Paris-Saclay for extensive stay support, as well as the Tunis El Manar University, and the CNRS national program ’Physico-Chimie de la Matière Interstellaire’ for partial support. Computations were performed on the CIMENT infrastructure (https://ciment.ujfgrenoble.fr), which is supported by the Rhône-Alpes region (GRANT CPER07 13 CIRA).

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Supporting Information Available Spectroscopy The following table gives the full list of HNCO rotational levels considered in this work, with experimental and computed levels, as well as the J, Ka , Kc corresponding quantum numbers. Table 1: HNCO rotational levels. Energies in cm−1 . Experimental values from 40 Level

Ecomp

Eexp

J

Ka

Kc

1

0

0

0

0

0

2

0.7332

0.7332

1

0

1

3

2.1997

2.1997

2

0

2

4

4.3994

4.3993

3

0

3

5

7.3322

7.3322

4

0

4

6

10.9983

10.9983

5

0

5

7

15.3975

15.3975

6

0

6

8

20.5299

20.5299

7

0

7

9

26.3955

26.3954

8

0

8

10

30.8209

30.8087

1

1

1

11

30.8263

30.8140

1

1

0

12

32.2818

32.2697

2

1

2

13

32.2980

32.2857

2

1

1

14

32.9941

32.9940

9

0

9

15

34.4732

34.4611

3

1

3

16

34.5056

34.4932

3

1

2

17

37.3950

37.3831

4

1

4

18

37.4490

37.4366

4

1

3

23



Page 24 of 32

. . . continued 19

40.3258

40.3257

10

0

10

20

41.0473

41.0355

5

1

5

21

41.1283

41.1157

5

1

4

22

45.4300

45.4183

6

1

6

23

45.5434

45.5307

6

1

5

24

48.3905

48.3904

11

0

11

25

50.5431

50.5316

7

1

7

26

50.6943

50.6814

7

1

6

27

56.3865

56.3752

8

1

8

28

56.5809

56.5679

8

1

7

29

57.1882

57.1881

12

0

12

30

62.9604

62.9493

9

1

9

31

63.2034

63.1901

9

1

8

32

66.7189

66.7188

13

0

13

33

70.2645

70.2537

10

1

10

34

70.5615

70.5480

10

1

9

35

76.9825

76.9824

14

0

14

36

78.2990

78.2885

11

1

11

37

78.6554

78.6416

11

1

10

38

87.0637

87.0535

12

1

12

39

87.4849

87.4708

12

1

11

40

87.9789

87.9788

15

0

15

41

96.5587

96.5488

13

1

13

42

97.0501

97.0356

13

1

12

43

99.7082

99.7080

16

0

16

44

106.7839 106.7744 14

1

14

24


Page 25 of 32 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


. . . continued 45

107.3508 107.3360 14

1

13

46

112.1702 112.1700 17

0

17

47

117.7392 117.7301 15

1

15

48

118.3871 118.3720 15

1

14

49

120.7087 120.5521

2

2

1

50

120.7087 120.5521

2

2

0

51

122.9076 122.7511

3

2

2

52

122.9076 122.7511

3

2

1

53

125.3648 125.3646 18

0

18

54

125.8395 125.6830

4

2

3

55

125.8395 125.6830

4

2

2

56

129.5044 129.3480

5

2

4

57

129.5044 129.3480

5

2

3

58

129.4246 129.4159 16

1

16

59

130.1590 130.1434 16

1

15

60

133.9021 133.7459

6

2

5

61

133.9022 133.7459

6

2

4

62

139.0328 138.8767

7

2

6

63

139.0329 138.8768

7

2

5

64

139.2921 139.2919 19

0

19

65

141.8401 141.8319 17

1

17

66

142.6662 142.6502 17

1

16

67

144.8964 144.7405

8

2

7

68

144.8965 144.7406

8

2

6

25



Rates The full rate table (7113 lines) is available in the LAMDA format and as an ascii file at the following url: xxxx.

References (1) http://iram-institute.org/ . (2) https://almascience.nrao.edu/documents-and-tools . (3) van der Tak, F. F. S.; Black, J. H.; Schoeier, F. L.; Jansen, D. J.; van Dishoeck, E. F. Astron. Astroph. 2007, 468, 627–U261. (4) Elitzur, M. Astronomical masers. Annual Reviews in Astonomy and Astrophysics 1992, 30, 75–112. (5) Faure, A.; Remijan, A. J.; Szalewicz, K.; Wiesenfeld, L. Weak Maser Emission of Methyl Formate toward Sagittarius B2(N) in the Green Bank Telescope PRIMOS Survey. Astrophys. J. 2014, 783, 72. (6) Dubernet, M.-L.; Alexander, M. H.; Ba, Y. A.; Balakrishnan, N.; Balança, C.; Ceccarelli, C.; Cernicharo, J.; Daniel, F.; Dayou, F.; Doronin, M. et al. BASECOL2012: A collisional database repository and web service within the Virtual Atomic and Molecular Data Centre (VAMDC). Astron. Astroph. 2013, 553, A50. (7) Schöier, F. L.; van der Tak, F. F. S.; van Dishoeck, E. F.; Black, J. H. An atomic and molecular database for analysis of submillimetre line observations. Astron. Astroph. 2005, 432, 369–379. (8) Goldsmith, P. F.; Langer, W. D. Population Diagram Analysis of Molecular Line Emission. Astrophys. J. 1999, 517, 209–225. 26


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The Journal of Physical Page Chemistry 32 of 32 1 2 3 4 5 6 7


Van Der Waals Interaction of HNCO and H2: Potential Energy Surface

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