A global \textit{ab initio} dipole moment surface for methyl chloride
Alec Owens, Sergei N. Yurchenko, Andrey Yachmenev, Jonathan Tennyson, Walter Thiel
AA global ab initio dipole moment surface for methylchloride
Alec Owens a,b , Sergei N. Yurchenko a , Andrey Yachmenev a , JonathanTennyson a , Walter Thiel b a Department of Physics and Astronomy, University College London, Gower Street,WC1E 6BT London, United Kingdom b Max-Planck-Institut f¨ur Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 M¨ulheim ander Ruhr, Germany
Abstract
A new dipole moment surface (DMS) for methyl chloride has been generatedat the CCSD(T)/aug-cc-pVQZ(+d for Cl) level of theory. To represent theDMS, a symmetry-adapted analytic representation in terms of nine vibra-tional coordinates has been developed and implemented. Variational calcu-lations of the infrared spectrum of CH Cl show good agreement with a rangeof experimental results. This includes vibrational transition moments, abso-lute line intensities of the ν , ν , ν and 3 ν bands, and a rotation-vibrationline list for both CH Cl and CH
Cl including states up to J = 85 andvibrational band origins up to 4400 cm − . Across the spectrum band shapeand structure are well reproduced and computed absolute line intensitiesare comparable with highly accurate experimental measurements for certainfundamental bands. We thus recommend the DMS for future use. Keywords:
Line-lists, Radiative transfer, Databases, HITRAN
Email address: [email protected] (Alec Owens)
Preprint submitted to JQSRT August 17, 2018 a r X i v : . [ phy s i c s . c h e m - ph ] A ug . Introduction The proposal of methyl chloride as a potential biosignature gas [1–3]in the search for life outside of the Solar System has ignited interest in itsinfrared spectrum. There is now considerable motivation for a comprehensiverotation-vibration line list of CH Cl. Since methyl chloride is known tocontribute to ozone depletion, any such line list would undoubtedly be usefulin terrestrial studies. Its importance as an atmospheric molecule is confirmedby the huge number of recent spectroscopic studies [4–31].The HITRAN database [32] has the most detailed coverage with over212 000 lines for the two main isotopologues, CH Cl and CH Cl (hence-forth labelled as CH
Cl and CH
Cl). This includes rovibrational tran-sitions up to J = 82 and covers the 0–3200 cm − region. However, thereare deficiencies and we will see in Sec. 4.3 that HITRAN is missing a bandaround 2880 cm − . Some line positions and intensities are also from theo-retical predictions using a fairly old, empirically refined anharmonic forcefield [33]. Given the numerous high-resolution studies since then, notablyin the 3 . µ m region [4] (included in HITRAN2012) and in the 6 . µ m re-gion [14], improvements can be expected in the coverage of CH Cl. Anothervaluable resource is the PNNL spectral library [34] which covers the 600 to6500 cm − region at a resolution of around 0 .
06 cm − for temperatures of 5,25 and 50 ◦ C. Other databases such as GEISA [35] include CH Cl but thedatasets are not as extensive, whilst the JPL [36] catalog has been incorpo-rated into HITRAN.Intensity information is vital for practical applications such as atmo-spheric modelling or remote sensing. The six fundamental bands of CH Clhave all been considered at some stage [4, 14, 37–50]. Notably, absoluteline intensities have been measured for the ν , ν and 3 ν bands in the 29202o 3100 cm − range [4], and for over 900 rovibrational transitions in the ν band [14]. These two studies are the most reliable and complete line inten-sity measurements for both CH Cl and CH
Cl to date. From a theoreticalperspective, calculations of dipole moment derivatives and infrared intensitieshave been reported [27, 33, 51–57]. However, we are unaware of any globalDMS which could be used for intensity simulations of the rotation-vibrationspectrum of CH Cl.Previously we reported [58] two state-of-the-art ab initio potential energysurfaces for the two main isotopologues of methyl chloride. Variational cal-culations of the vibrational J = 0 energies and equilibrium geometry showedexcellent agreement with experimental results. Building on this work, wepresent a new nine-dimensional ab initio DMS which has been computedusing high-level electronic structure theory. A symmetrized molecular bond(SMB) representation for XY Z-type molecules has been implemented intothe nuclear motion code TROVE [59] to represent the DMS analytically.Comprehensive calculations of the rotation-vibration spectrum are then car-ried out to evaluate the quality of the DMS. The work presented here rep-resents the next step towards generating a complete rovibrational line listapplicable for elevated temperatures.The paper is structured as follows: In Sec. 2 the electronic structure cal-culations and analytic representation of the DMS are described. Details ofthe variational calculations are given in Sec. 3. In Sec. 4 the DMS is evalu-ated against a range of experimental measurements as well as the HITRANand PNNL spectroscopic databases. Results include vibrational transitionmoments, absolute line intensities of the ν , ν , ν and 3 ν bands, and anoverview of the rotation-vibration spectrum for states up to J = 85 in the0–6500 cm − frequency range. Concluding remarks are offered in Sec. 5.3 . Dipole Moment Surface The first derivative of the electronic energy with respect to external elec-tric field strength defines the electric dipole moment of a molecule. Work-ing in a Cartesian laboratory-fixed
XY Z coordinate system with origin atthe C nucleus, an external electric field with components ± .
005 a.u. wasapplied along each axis and the respective dipole moment component µ A for A = X, Y, Z determined using finite differences. Calculations were car-ried out at the CCSD(T) [coupled cluster with all single and double excita-tions and a perturbational estimate of connected triple excitations] level oftheory with the augmented correlation consistent quadruple zeta basis set,aug-cc-pVQZ(+d for Cl) [60–63], in the frozen core approximation. MOL-PRO2012 [64] was used for all calculations.The DMS was evaluated on a nine-dimensional global grid of 44 ,
820 pointswith energies up to hc ·
50 000 cm − ( h is the Planck constant and c is thespeed of light). The grid included geometries in the range 1 . ≤ r ≤ .
95 ˚A,0 . ≤ r i ≤ .
45 ˚A, 65 ≤ β i ≤ ◦ for i = 1 , , ≤ τ jk ≤ ◦ with jk = 12 ,
13. Here, the nine internal coordinates are: the C–Cl bond length r ; three C–H bond lengths r , r and r ; three (cid:54) (H i CCl) interbond angles β , β and β ; and two dihedral angles τ and τ between adjacent planescontaining H i CCl and H j CCl. The grid utilized for the DMS is the same asthat used for the PESs previously reported [58].
Before fitting an analytic expression to the ab initio data it is necessary toestablish a suitable molecule-fixed xyz coordinate system. Methyl chlorideis a prolate symmetric top molecule of the C (M) symmetry group [65].4here are six symmetry operations { E, (123) , (132) , (12) ∗ , (23) ∗ , (13) ∗ } whichmake up C (M). The cyclic permutation operation (123) replaces nucleus 1with nucleus 2, nucleus 2 with nucleus 3, and nucleus 3 with nucleus 1; thepermutation-inversion operation (12) ∗ interchanges nuclei 1 and 2 and invertsall particles (including electrons) in the molecular centre of mass; the identityoperation E leaves the molecule unchanged. The symmetrized molecularbond (SMB) representation has been successfully applied to molecules of C (M) symmetry [66, 67] and this approach is employed for the presentstudy.We first define unit vectors along each of the four bonds of CH Cl, e i = r i − r C | r i − r C | ; i = 0 , , , , (1)where r C is the position vector of the C nucleus, r the Cl nucleus, and r , r and r the respective H atoms. The ab initio dipole moment vector µ isprojected onto the molecular bonds and can be described by molecule-fixed xyz dipole moment components, µ x = 1 √ µ · e ) − ( µ · e ) − ( µ · e )) , (2) µ y = 1 √ µ · e ) − ( µ · e )) , (3) µ z = µ · e . (4)Symmetry-adapted combinations have been formed for µ x and µ y and thesetransform according to E symmetry, while the µ z component is of A sym-metry. The advantage of the SMB representation is that the unit vectors e i used to define µ for any instantaneous positions of the nuclei are related tothe internal coordinates only.To construct the three dipole surfaces corresponding to the componentsgiven in Eqs. (2) to (4), a numerical, on-the-fly symmetrization procedure5as been implemented. This is similar to the approach employed for thePES [58] but because µ is a vector quantity we have to consider the trans-formation properties of the dipole moment components themselves. For µ z ,which points along the C–Cl bond, the process is trivial owing to its A symmetry and invariance to the C (M) symmetry operations. Building ananalytic expression follows the same steps as the PES. For the two E sym-metry components, µ x and µ y , the construction is more subtle and they mustbe treated together.We consider an initial (reference) term in the dipole expansion belongingto µ x , µ x µ y = µ initial x,ijk... , (5)where µ initial x,ijk... = (cid:0) ξ i ξ j ξ k ξ l ξ m ξ n ξ p ξ q ξ r (cid:1) . (6)This term has maximum expansion order i + j + k + l + m + n + p + q + r = 6,and is expressed in terms of the nine coordinates, ξ = (cid:0) r − r ref0 (cid:1) , (7) ξ j = (cid:0) r i − r ref1 (cid:1) ; j = 2 , , , i = j − , (8) ξ k = ( β i − β ref ) ; k = 5 , , , i = k − , (9) ξ = 1 √ τ − τ − τ ) , (10) ξ = 1 √ τ − τ ) . (11)Here, τ = 2 π − τ − τ and the reference structural parameters r ref0 =1 . r ref1 = 1 . β ref = 108 . ◦ . Note that the values of r ref0 , r ref1 and β ref were optimized during the fitting of the DMS.The action of a symmetry operation X = { E, (123) , (132) , (12) ∗ , (23) ∗ , (13) ∗ } on Eq. (6) will (i) permute the expansion indices ijk . . . , to i (cid:48) j (cid:48) k (cid:48) . . . to pro-6uce a new expansion term and (ii) permute the unit vectors e i for i = 1 , , e x and e y molecule-fixed vectors and added to the respectivedipole moment components. The resulting components, µ (cid:48) x and µ (cid:48) y , reduceto µ (cid:48) x µ (cid:48) y = C µ X x,ijk... C µ X x,ijk... , (12)where C and C are constants associated with the acting C (M) symmetryoperation, and µ X x,ijk... is the new expansion term connected to Eq. (6) by thesymmetry operation X . Note that a contribution arises in µ (cid:48) y ( C (cid:54) = 0) dueto the projection operator acting on the two-component quantity ( µ x , µ y ).The steps are repeated for each symmetry operation of C (M) and theresults summed to produce a final dipole term (ignoring constants), µ final x,ijk... = µ Ex,ijk... + µ (123) x,ijk... + µ (132) x,ijk... + µ (12) ∗ x,ijk... + µ (23) ∗ x,ijk... + µ (13) ∗ x,ijk... , (13)which is best understood as a sum of symmetrized combinations of differentpermutations of coordinates ξ i . Likewise, a similar expression contributes to µ y . Although we have only considered an initial term belonging to µ x , thesame idea applies to initial terms belonging to µ y . Incorporating µ z into theprocedure is straightforward, thus enabling the simultaneous construction ofall three dipole moment surfaces of CH Cl. Each surface is represented bythe analytic expression µ total α ( ξ , ξ , ξ , ξ , ξ , ξ , ξ , ξ , ξ ) = (cid:88) ijk... F ( α ) ijk... µ final α,ijk... , (14)where some of the expansion coefficients F ( α ) ijk... are shared between the x and y components.A least squares fitting to the ab initio data utilizing Watson’s robustfitting scheme [68] was employed to determine F ( α ) ijk... for α = x, y, z . Weight7actors of the form [69], w i = tanh (cid:104) − . × ( ˜ E i −
15 000) (cid:105) + 1 . . × N ˜ E ( w ) i , (15)were used in the fitting, with normalization constant N = 0 . E ( w ) i =max( ˜ E i ,
10 000), where ˜ E i is the potential energy at the i th geometry aboveequilibrium (all values in cm − ). At geometries where r ≥ .
35 ˚A, or r i ≥ .
00 ˚A for i = 1 , ,
3, the weights were decreased by several ordersof magnitude. This was done because the coupled cluster method is knownto become unreliable at very large stretch coordinates, indicated by a T1diagnostic value > .
02 [70]. Whilst the energies are not wholly accurateat these points, they ensure the DMS maintains a reasonable shape towardsdissociation.The three dipole surfaces for µ x , µ y and µ z employed sixth order ex-pansions and used 175, 163 and 235 parameters, respectively. A combinedweighted root-mean-square (rms) error of 9 × − D was obtained for thefitting. Incorporating the analytic representation into variational nuclearmotion calculations is relatively straightforward and the implementation re-quires only a small amount of code. The dipole expansion parameters alongwith a FORTRAN routine to construct the DMS are provided in the supple-mentary material.
3. Variational calculations
The nuclear motion program TROVE [59] was employed for all rovibra-tional calculations and details of the general methodology can be found else-where [59, 66, 71]. Since methyl chloride has already been treated usingTROVE [58], we summarize only the key aspects of our calculations.8n automatic differentiation method [71] was used to construct the rovi-brational Hamiltonian numerically. The Hamiltonian itself was representedas a power series expansion around the equilibrium geometry in terms of ninevibrational coordinates. The coordinates used are almost identical to thosegiven in Eqs. (7) to (11), except for the potential energy operator whereMorse oscillator functions replace the linear expansion variables for stretch-ing modes. In all calculations the kinetic and potential energy operators weretruncated at 6th and 8th order, respectively. This level of truncation is ade-quate for our purposes (see Ref. [59] and [71] for a discussion of the associatederrors of such a scheme). Atomic mass values were employed throughout.Two purely ab initio
PESs [58], CBS-35 HL and CBS-37 HL , correspond-ing to the two main isotopologues, CH Cl and CH
Cl, have been utilizedfor the present study. The surfaces are based on extensive explicitly corre-lated coupled cluster calculations with extrapolation to the complete basisset (CBS) limit and include a range of additional higher-level energy correc-tions. The CBS-35 HL and CBS-37 HL PESs reproduce the fundamental termvalues with rms errors of 0 .
75 and 1 .
00 cm − , respectively. We are thereforeconfident that the DMS of CH Cl can be evaluated accurately in conjunctionwith these PESs.A multi-step contraction scheme [66] is used to construct the vibrationalbasis set and a polyad number truncation scheme controls its size. For CH Cl,we define the polyad number P = n + 2( n + n + n ) + n + n + n + n + n ≤ P max , (16)and this does not exceed a predefined maximum value P max . Here, the quan-tum numbers n k for k = 1 , . . . , φ n k for each vibrational mode. Multiplication with rigid-rotor eigenfunctions | J, K, m, τ rot (cid:105) produces the final symmetrized basis set for use in
J > K is the projection (in units of ¯ h ) of J onto the molecule-fixed z -axis, whilst τ rot determines the rotational parity as( − τ rot . As we will see in Sec. 4, different sized basis sets have been uti-lized in this work and this reflects the computational demands of variationalcalculations of rovibrational spectra.TROVE automatically assigns quantum numbers to the eigenvalues andcorresponding eigenvectors by analysing the contribution of the basis func-tions. To be of spectroscopic use we map the vibrational quantum numbers n k to the normal mode quantum numbers v k commonly used in spectroscopicstudies. For CH Cl, vibrational states are labelled as v ν + v ν + v ν +v ν + v ν + v ν where v i counts the level of excitation.The normal modes of methyl chloride are of A or E symmetry. The threenon-degenerate modes have A symmetry; the symmetric CH stretchingmode ν (2967 . / .
75 cm − ), the symmetric CH deformation mode ν (1354 . / .
69 cm − ) and the C–Cl stretching mode ν (732 . / .
03 cm − ).Whilst the three degenerate modes have E symmetry; the CH stretchingmode ν (cid:96) (3039 . / .
63 cm − ), the CH deformation mode ν (cid:96) (1452 . / .
16 cm − )and the CH rocking mode ν (cid:96) (1018 . / .
68 cm − ). The values in paren-theses are the experimentally determined fundamental frequencies for CH Cl/ CH
Cl [4, 22]. The additional vibrational angular momentum quantumnumbers (cid:96) , (cid:96) and (cid:96) are necessary to resolve the degeneracy of their respec-tive modes. 10 . Results As an initial test of the DMS we compute vibrational transition moments, µ if = (cid:115) (cid:88) α = x,y,z |(cid:104) Φ ( f )vib | ¯ µ α | Φ ( i )vib (cid:105)| . (17)Here, | Φ ( i )vib (cid:105) and | Φ ( f )vib (cid:105) are the initial and final state vibrational ( J = 0) eigen-functions, respectively, and ¯ µ α is the electronically averaged dipole momentfunction along the molecule-fixed axis α = x, y, z .Transition moments have been determined experimentally for the six fun-damental modes of CH Cl and these are listed in Table 1 along with ourcomputed values. Calculations employed a polyad truncation number of P max = 12 which is sufficient for converging µ if . Overall the agreement isencouraging and it indicates that the DMS should be reliable for intensitysimulations of the fundamental bands.For CH Cl, band strength measurements of the ν [43] and ν [45] bandshave been carried out but only minor differences were observed comparedto CH Cl [40, 44]. Likewise, as seen in Table 1 the computed transitionmoments for the fundamentals only marginally differ compared to CH
Cl.It seems the intensity variation from isotopic substitution in methyl chlorideis relatively small and in some instances almost negligible. A list of computedtransitions moments from the vibrational ground state for 79 levels up to4200 cm − is provided in the supplementary material. Note that for theequilibrium dipole moment of methyl chloride we calculate µ = 1 . µ = 1 . ν , ν , ν and ν bands Recently, absolute line intensities were determined for the ν , ν and3 ν bands around the 3 . µ m region [4] (included in HITRAN2012), and11 able 1: Calculated vibrational transition moments (in Debye) and frequencies (in cm − )from the vibrational ground state for CH Cl and CH
Cl.
Mode Sym. Experiment a Calculated µ calc if µ exp if Ref.CH Cl ν A b Elkins et al. [41] ν A c Blanquet et al. [49] ν A ν E d Elkins et al. [41] ν E ν E e Blanquet et al. [44]CH Cl ν A ν A ν A ν E ν E ν E a From Bray et al. [4] and Nikitin et al. [22]. b From Papouˇsek et al. [56] but derivedfrom band strength measurement of S v = 84 . ± . − atm − at 296 K [41]. c Value of µ exp ν = 0 . d From Papouˇsek et al. [56] butderived from band strength measurement of S v = 33 . ± . − atm − at 296 K [41]. e From Papouˇsek et al. [56] but derived from band strength measurement of S v = 15 . ± . − atm − at 296 K [44]. ν band in the 6 . µ m region [14]. To assess the DMS we compareagainst these works for both isotopologues up to J = 15. Calculating higherrotational excitation is computationally demanding (rovibrational matricesscale linearly with J ) so we set P max = 10 which is sufficient for reliableintensities. A study on the five-atom molecule SiH [73], which has similarconvergence properties with respect to P max , also employed P max = 10 toproduce intensities of the ν band with an estimated convergence error of 1%or less for transitions up to J = 16. Because the two ab initio PESs used inthis study, CBS-35 HL and CBS-37 HL , can at best only be considered accurateto about ± − , for illustrative purposes we have shifted computed linepositions to better match experiment in the following comparisons.Absolute absorption intensities have been simulated at room temperature( T = 296 K) using the expression, I ( f ← i ) = A if πc g ns (2 J f + 1) exp ( − E i /kT ) Q ( T ) ν if (cid:20) − exp (cid:18) − hcν if kT (cid:19)(cid:21) , (18)where A if is the Einstein A coefficient of a transition with frequency ν if between an initial state with energy E i , and a final state with rotationalquantum number J f . Here, k is the Boltzmann constant, T is the absolutetemperature and c is the speed of light. The nuclear spin statistical weightsare g ns = { , , } for states of symmetry { A , A , E } , respectively. Thesevalues have been calculated using the method detailed in Jensen and Bunker[74]. For the partition function we use values of Q ( T ) = 57 , .
728 and58 , .
711 for CH
Cl and CH
Cl, respectively [32]. Note that to ensurea correct comparison with the experimental studies of Bray et al. [4] andBarbouchi Ramchani et al. [14], the intensities of overlapping A and A spectral lines (listed as being of A symmetry) must be halved.In Fig. 1 we plot absolute line intensities for 126 transitions of the ν band and their corresponding residuals (cid:0) % (cid:2) obs − calcobs (cid:3)(cid:1) compared to measure-13 ray et al.TROVEWavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) Wavenumber (cm − ) % [ ( o b s - c a l c ) /o b s ] Figure 1: Absolute line intensities of the ν band for transitions up to J = 15 (left) andthe corresponding residuals (cid:0) % (cid:2) obs − calcobs (cid:3)(cid:1) (right) when compared with measurements fromBray et al. [4]. Transitions for both CH Cl and CH
Cl are shown and the intensitieshave not been scaled to natural abundance. For illustrative purposes TROVE line positionshave been shifted by − .
35 cm − . ments from Bray et al. [4]. The majority of computed intensities, althoughtending to be marginally stronger, are within the experimental accuracy of10% or better [75]. Calculated line positions had on average a residual errorof ∆ obs − calc = − .
35 cm − and this has been corrected for in Fig. 1. Simi-larly, computed intensities of the ν band shown in Fig. 2 are largely withinexperimental uncertainty. Here, line positions possessed a residual error of∆ obs − calc = − .
42 cm − .Line intensities of the 3 ν band are shown in Fig. 3. Excited modes areharder to converge and the size of the vibrational basis set at P max = 10means the respective rovibrational energy levels have a convergence error of1 . − for low J values (compared to errors of ≈ .
1, 0 . .
03 cm − for the ν , ν and ν bands, respectively). The effect is that computed lineintensities will have an uncertainty of around 5%. Even so, the agreement forthe 16 lines from Bray et al. [4] is good. Note that line positions displayed aresidual error of ∆ obs − calc = − .
23 cm − .14 ray et al.TROVEWavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) − ) % [ ( o b s - c a l c ) /o b s ] Figure 2: Absolute line intensities of the ν band for transitions up to J = 15 (left) andthe corresponding residuals (cid:0) % (cid:2) obs − calcobs (cid:3)(cid:1) (right) when compared with measurements fromBray et al. [4]. Transitions for both CH Cl and CH
Cl are shown and the intensitieshave not been scaled to natural abundance. For illustrative purposes TROVE line positionshave been shifted by − .
42 cm − . Bray et al.TROVEWavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) Wavenumber (cm − ) % [ ( o b s - c a l c ) /o b s ] Figure 3: Absolute line intensities of the 3 ν band for transitions up to J = 15 (left)and the corresponding residuals (cid:0) % (cid:2) obs − calcobs (cid:3)(cid:1) (right) when compared with measurementsfrom Bray et al. [4]. Transitions for both CH Cl and CH
Cl are shown and theintensities have not been scaled to natural abundance. For illustrative purposes TROVEline positions have been shifted by − .
23 cm − . arbouchi Ramchani et al. TROVE Wavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) − ) % [ ( o b s - c a l c ) /o b s ] Figure 4: Absolute line intensities of the ν band for transitions up to J = 15 (left) andthe corresponding residuals (cid:0) % (cid:2) obs − calcobs (cid:3)(cid:1) (right) when compared with measurements fromBarbouchi Ramchani et al. [14]. Transitions for both CH Cl and CH
Cl are shownand the intensities have not been scaled to natural abundance. For illustrative purposesTROVE line positions have been shifted by − .
40 cm − . A high-resolution study of the ν band measured absolute line intensitieswith an experimental accuracy of 5% or less, and line positions with anaverage estimated accuracy between 10 − to 10 − cm − . As shown in Fig. 4a significant number of computed line intensities are within experimentaluncertainty and agreement for the 256 transitions up to J = 15 is excellent.Here calculated line positions had a residual error of ∆ obs − calc = − .
40 cm − . The HITRAN database contains over 212 000 lines for CH Cl and consid-ers transitions up to J = 82. To compute such highly excited rovibrationalenergy levels it has been necessary to again reduce the size of the vibrationalbasis set. Calculations were carried out with P max = 8 and an upper energylevel cut-off of 8000 cm − . Subsequent transitions and intensities were com-puted for a 6300 cm − frequency window with a lower state energy thresholdof 4400 cm − . Information has undoubtedly been lost by introducing thesethresholds but the values were carefully chosen to keep this to a minimum.16uch restrictions also allow the straightforward calculation of high J valuesin a timely manner on compute nodes with 64 GB of RAM. Note that forpure rotational transitions in HITRAN the hyperfine structure has been re-solved [76]. Therefore, in order to have a reliable comparison for this spectralregion we scale our intensities by a factor of 1 / J = 85 for both isotopo-logues of methyl chloride. Computed intensities have been scaled to naturalabundance (0.748937 for CH Cl and 0.239491 for CH
Cl) and are com-pared against all available lines in the HITRAN database. Overall the agree-ment is pleasing, particularly given the reduced size of the vibrational basisset and energy level thresholds. Up to 3200 cm − the only noticeable missingband in HITRAN appears to be the 2 ν band around 2880 cm − shown inFig. 6. This is not expected to be important for atmospheric sensing.An improved spectroscopic line list in the range 1900–2600 cm − was re-cently published [23] and considered transitions up to J = 47 with absoluteline intensities possessing an estimated uncertainty of 20% or less. In Fig. 7 acomparison of this region, which is composed of several weak bands, is shownfor CH Cl. The DMS appears reasonable for much weaker intensities andthe overall band structure in this region is well reproduced. There are someirregularities between TROVE and Nikitin et al. [23]; we expect these arecaused by the low-level nature of our calculations and also the assignmentprocedure in TROVE. In future work we intend to carry out a more compre-hensive analysis of this region. Note that the computed TROVE line list hasnot been truncated at J = 47 for this comparison.Whilst spectral features above 3200 cm − are not as prominent there arenoticeable bands between 4300–4550 cm − and 5700–6200 cm − as shownin Fig. 8. Here we have compared against the PNNL spectral library [34]17 ITRANTROVEWavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) Figure 5: Overview of methyl chloride rotation-vibration line list up to J = 85 comparedwith all transitions in the HITRAN database [32]. Computed intensities have been scaledto natural abundance. Wavenumber (cm − ) A b s o l u t e i n t e n s i t y ( c m / m o l ec u l e ) ν band of methyl chloride. Computed intensities have been scaled tonatural abundance. - 2 1 - 2 2 - 2 3 - 2 4 - 2 5 W a v e n u m b e r ( c m - 1 ) n + n n + n + n n + n n + n ( E ) n + n n + n n + n n N i k i t i n e t a l . - 2 5 - 2 4 - 2 3 - 2 2 - 2 1
T R O V E + n n + n ( E ) n + n n + n n Absolute intensity (cm/molecule) Cl in the range 1900–2600 cm − compared withmeasurements from Nikitin et al. [23]. Computed TROVE transitions are up to J = 85whilst the results from Nikitin et al. [23] are up to J = 47. Note that a logarithmic scalehas been used for the y-axis. NNLTROVEWavenumber (cm − ) C r o ss - s ec t i o n ( c m / m o l ec u l e ) − ) C r o ss - s ec t i o n ( c m / m o l ec u l e ) Figure 8: Overview of simulated rotation-vibration spectrum in the 4300–4550 cm − (left)and 5700–6200 cm − (right) regions compared with the PNNL spectral library [34]. Com-puted intensities have been scaled to natural abundance. (overview of entire spectrum presented in Fig. 9). Cross sections have beengenerated at a resolution of 0 .
06 cm − and fitted using a Gaussian profilewith a half width at half maximum of 0 .
112 cm − . This line shape provides astraightforward and reasonable comparison [77], however, we expect a Voigtprofile dependent on instrumental factors would be more suitable.Looking at Fig. 8 it is clear that our calculations are becoming worse athigher energies and producing spurious intensities. This is to be expectedgiven the size of the vibrational basis set and thresholds imposed in our vari-ational calculations. For the complete spectrum in Fig. 9 the agreement withPNNL is encouraging but does indicate the need for improved computationsand line shape modelling.
5. Conclusions
A new nine-dimensional DMS for methyl chloride has been computedusing high-level ab initio theory and fitted with a symmetry-adapted ana-lytic representation. The DMS has been utilized to simulate the rotation-vibration spectrum of methyl chloride up to 6300 cm − . Overall, band shape20 NNLTROVEWavenumber (cm − ) C r o ss - s ec t i o n ( c m / m o l ec u l e ) Figure 9: Overview of methyl chloride rotation-vibration spectrum up to J = 85 comparedwith the PNNL spectral library [34]. Computed intensities have been scaled to naturalabundance. − –10 − cm/molecule have been reportedin the 11 590–11 760 cm − spectral region [26]. Presently we are unable toaccurately model such high frequencies; this is a major challenge for varia-tional calculations on small polyatomic molecules. We expect these issuesto be addressed during the construction of a comprehensive, hot line list forinclusion in the ExoMol database [80, 81]. Acknowledgements
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