Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the 2ν3 band (5853–6201 cm−1)

Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Contents lists available at ScienceDirect

Journal of Quantitative Spectroscopy & Radiative Transfer journal homepage: www.elsevier.com/locate/jqsrt

Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the 2ν3 band (5853–6201 cm
1) E. Starikova a,b,n, A.V. Nikitin a,b, M. Rey c, S.A. Tashkun a,b, D. Mondelain d,e, S. Kassi d,e, A. Campargue d,e, Vl.G. Tyuterev c a

Laboratory of Quantum Mechanics of Molecules and Radiative Processes, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia Laboratory of Theoretical Spectroscopy of IAO SB RAN, Av. 1, Akademician Zuev square, 634021 Tomsk, Russia GSMA, UMR CNRS 7331, Université de Reims Champagne Ardenne, Moulin de la Housse, BP 1039-51687 Reims Cedex 2, France d Université Grenoble Alpes, LIPhy, F-38000 Grenoble, France e CNRS, LIPhy, F-38000 Grenoble, France b c

a r t i c l e i n f o

abstract

Article history: Received 8 November 2015 Received in revised form 22 December 2015 Accepted 23 December 2015

The absorption spectrum of the 13CH4 methane isotopologue has been recently recorded by Differential Absorption Spectroscopy (DAS) at 80 K in the 5853–6201 cm
1 spectral range. An empirical list of 3717 lines was constructed for this spectral range corresponding to the upper part of the Tetradecad dominated by the 2ν3 band near 5987 cm
1. In this work, we present rovibrational analyses of these spectra obtained via two theoretical approaches. Assignments of strong and medium lines were achieved with variational calculations using ab initio potential energy (PES) and dipole moment surfaces. For further analysis a non-empirical effective Hamiltonian (EH) of the methane polyads constructed by high-order Contact Transformations (CT) from an ab initio PES was employed. Initially predicted values of EH parameters were empirically optimized using 2898 assigned line positions fitted with an rms deviation of 5  10
3 cm
1. More than 1860 measured line intensities were modeled using the effective dipole transition moments approach with the rms deviation of about 10%. These new data were used for the simultaneous fit of the 13 CH4 Hamiltonian parameters of the {Ground state/Dyad/Pentad/Octad/Tetradecad} system and the dipole moment parameters of the {Ground state-Tetradecad} system. Overall, 10 vibrational states and 28 vibration sublevels of the 13CH4 Tetradecad are determined. The comparison of their energy values with corresponding theoretical calculations is discussed. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Methane Isotopic shift Absorption spectroscopy Spectra analyses Variational calculations Ab initio intensities

1. Introduction Precise information on methane spectral transitions in the infrared is required for the modeling of absorption/ emission phenomena in various planetary atmospheres [1–3] and for other astrophysical applications [4]. Methane is also important in environmental sciences acting as a n Corresponding author at: Laboratory of Quantum Mechanics of Molecules and Radiative Processes, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russia. E-mail address: [email protected] (E. Starikova).

greenhouse gas in the Earth atmosphere [5]. The measurements of the 13C/12C isotopic abundance at various parts of the Universe would benefit from the use of accurate spectroscopic data for the methane isotopologues. It is well known that 12CH4 and 13CH4 bands exhibit polyad structures [6] because of approximate relation ω1  ω3  2ω2  2ω4 between harmonic frequencies of bending and stretching vibrations. Each polyad is defined by the integer polyad number P¼2(v1 þv3) þv2 þv4, where (v1,v2,v3,v4) are the principal vibrational normal mode quantum numbers. A major difficulty of methane spectra analyses is due to strong couplings among nearby

http://dx.doi.org/10.1016/j.jqsrt.2015.12.023 0022-4073/& 2016 Elsevier Ltd. All rights reserved.

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

2

vibration–rotation states within each polyad resulting to complicated accidental perturbations in line positions and intensities. A lot of efforts have been devoted to measurements and analyses of methane spectra in ranges of lower polyads [7–15] as well of isotopologues (Refs. [16–22] and references therein) using empirical polyad models, but many experimental methane spectra [23,24] corresponding to highly-excited polyads remained yet unassigned or only partly assigned. This is due to the limited extrapolation capabilities of the purely empirical approach. In case of 13CH4 the information included in available databases [25–27] is quite sparse beyond the Octad range (P¼3). On the other hand, recent progress in accurate variational predictions of rotationally resolved spectra of methane isotopologues [28–34] using potential energy surface (PES) [35] and ab initio dipole moment surfaces (DMS) [28], has allowed a breakthrough in our understanding of the near infrared absorption spectrum of methane. A complete assignment of the Icosad bands (P¼5) of the main isotopologue, 12CH4, has been recently achieved in the 6280–7800 cm
1 range [36] using theoretical lists [29,30]: among the 20 bands and the 134 sublevels involved in the 12CH4 Icosad system, 20 and 108 were identified for the first time, respectively. Concerning the Tetradecad range (P¼4) of the main isotopologue 12CH4, the previously available analyses have used experimental measurements recorded in support of the GOSAT mission [37,38] and also FTS measurement of Zurich group [15]. One of the advantages of variational global spectra calculations is that this permits a propagation of information on assigned bands of 12CH4 to less studied rare isotopologues via accurate predictions of isotopic shifts [32,37]. In Ref. [39], such procedure has been successfully applied in the 5560–6200 cm
1 region to FTS spectra of 13CH4 recorded with a short optical path (8.75 cm), at 180, 240 and 298 K. The 339 strongest 13CH4 transitions of the ν3 þ2ν4, ν2 þ ν3 þ ν4, 2ν3 and 2ν2 þ ν3 vibrational bands could be rovibrationnally assigned, relying on the isotopic shifts between the 12CH4 and 13CH4 vibrational levels, computed from an ab initio PES with accuracies of nearly one cm
1, at that time. Here, we consider a much more complete 13CH4 line list recently constructed in Grenoble by Differential Absorption Spectroscopy (DAS) at 80 K and 296 K in the high energy part of the Tetradecad (5853–6201 cm
1) [40]. The present work is devoted to the rovibrational assignment and modeling of the 80 K list including 3717 lines. As a result of the large extension of the experimental data set and of the increased accuracy of the theoretical predictions [32], the set of assignments is considerably enlarged (about 2900 assigned transitions). The positions and intensities of the assigned lines have been used for the first modeling of 13CH4 Tetradecad spectrum based on an effective Hamiltonian and effective dipole moment operators.

Fig. 1. Overview of the 13CH4 spectrum recorded at 6.0 Torr by DAS spectroscopy at 80 K [40]. The different colors correspond to different DFB laser diodes. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

cell cooled at liquid nitrogen temperature used to construct the 80 K list under analysis. We summarize here the experimental conditions of the recordings of Ref. [40]. The 13 CH4 sample (from Sigma Aldrich) has a chemical purity higher than 99% and a 13C enrichment higher than 99%. Several series of recordings were performed at 0.10, 0.25, 1.0 and 6.0 Torr. The 142 cm long absorption cell was used in a round trip configuration leading to absorption path length of 284 cm. The spectral coverage from 5853 to 6201 cm
1 was achieved using a series of 15 fiberconnected Distributed Feed-Back (DFB) diode lasers. For each laser diode, the recorded transmission spectrum was obtained as the ratio of a transmitted spectrum over a reference spectrum acquired simultaneously over the whole laser tuning range (about 30 cm
1). The achieved noise equivalent absorption of the spectra (αmin E1  10
7 cm
1) allowed us to measure lines with 80 K intensity at the 1  10
26 cm/molecule level. Fig. 1 shows an overview of the recordings at 6.0 Torr. The line centers and intensities were determined using an interactive least squares multi-line fitting program assuming a Voigt profile. The estimated uncertainty on the line centers is 1.5  10
3 and 2  10
3 cm
1, below and above 6150 cm
1, respectively. In the cases of isolated lines recorded with good signal to noise ratio, the uncertainty on the intensity values was estimated to be at the 2% level. Fig. 2 shows an overview of the DAS list constructed in Ref. [40] including 3717 lines, 2898 of them were rovibrationally assigned, as described below.

3. Rovibrational assignement The diagram of vibrational levels and sub-levels of the CH4 polyads computed [32] from the PES [35] is given in Fig. 3. Several previous analyses of the 13CH4 spectra up to the Octad range (3500–4700 cm
1) have been reported by Champion et al. [16], Niederer et al. [17,45] and Brown et al. [22]. The 5853–6200 cm
1 spectral interval considered in 13

2. Experiment The reader is referred to Refs. [40–44] for a detailed description of the DAS spectrometer and of the cryogenic

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

3

Fig. 2. Overview of the assigned transitions in the 13CH4 spectrum recorded at 80 K [40] between 5853 and 6201 cm
1. Different colors are used to indicate the different band systems contributing to the spectrum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

this work is the upper part of the Tetradecad dominated by the 2ν3 with the band center near 5987 cm
1. As mentioned above, prior to this work, the strongest lines of the 2ν3 (E) and 2ν3 (F2) sub-bands at 5987.0 and 6023.8 cm
1, respectively, and of the ν2 þ ν3 þ ν4, and 2ν2 þ ν3 band systems around 5820 and 6050 cm
1, respectively, were rovibrationally assigned [39]. Here we considerably extended the analysis of these band systems. In addition the weak 3ν2 þ ν4 and 4ν2 band systems, around 5880 and 6120 cm
1, respectively, are newly assigned. Although the vibrational centers of 2ν2 þ2ν4, ν1 þ ν2 þ ν4, 2ν1, ν1 þ ν3 bands are below the investigated range, some R-branch transitions corresponding to high J quantum numbers of these bands could be assigned. 3.1. Theoretical methods In order to extend rovibrational analyses of experimental DAS spectra described in the previous section we used two theoretical approaches. Assignments of strong and medium lines were achieved with variational calculations [32] using potential energy and dipole moment surfaces reported by Nikitin, Rey, Tyuterev [28,35] hereafter referred to as NRT PES and DMS. For further analysis a non-empirical effective Hamiltonian (EH) of the methane polyads constructed by high-order Contact Transformations (CT) [46] from the same NRT PES was employed. This approach permits quite accurate characterization of resonance coupling terms in order to avoid the well-known ambiguity of purely empirical EH models [47–49]. Computational algorithm of this method and comparisons with variational calculations and experimental methane data have been discussed by Tyuterev et al. [46]. The effective rovibrational Hamiltonian adapted to the polyad structure of the 12CH4 and 13CH4 isotopologues is expressed as: X H ef f ¼ HfPn g ¼ HfGSg þ H fDyadg þ H fPentadg þ H fOctadg þ H fTetradecadg n

ð1Þ where the subsequent terms of this expansion gather

Fig. 3. Scheme of vibrational level patterns of the 13CH4 polyads (left side), and vibration sublevels of the part of Tetradecad considered in this work (right side). At the right hand side panel, symmetry types (Td irreducible representations) of vibration sublevels, vibrational ranking numbers within the Tetradecad and the names of corresponding vibrational bands are shown.

operators specific to the successive polyads X Γ ΩðK;Γ Þ A1 ΓÞ H fP n g ¼ t nΩ1ðK; Þ n2 n3 n4 ;m1 m2 m3 m4 ðV n1 n2 n3 n4 ;m1 m2 m3 m4  R in the representation of the irreducible tensor operators (ITO) [6,50–55]. Vibrational ITO operators VΓ n1 n2 n3 n4 ;m1 m2 m3 m4 were constructed by recursive couplings of elementary creation and annihilation operators for each of four normal modes; and Γ is the irreducible representation of the Td point group. Rotational tensors RΩðK;Γ Þ are defined with the usual ITO convention generally applied for spherical tops [56,57]. The upper indices indicate the rotational characteristics of the considered term: Ω is the rotational power with respect to the angular momentum components; k is the tensor rank in the full rotation group. The rotational symmetry type coincides with the vibrational symmetry type to satisfy the invariance condition under the molecular point group operations. The procedure of the converting vibration-rotation terms from a standard Cartesian representation to the ITO representation for spherical top molecules has been described in detail in Refs. [52,53]. Effective dipole moment (EDM) expansion is represented in a similar manner as that of the Hamiltonian but the full symmetry type under the operations of Td group is different: it is A1 for the Hamiltonian terms and F1 for the dipole moment terms [6]. Different construction rules are possible [6,51,58]. Here we use the coupling scheme of Ref. [51] which has been implemented in the MIRS software [54,55] for high-resolution spectra calculations. The MIRS

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

4

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Fig. 4. Example of 13CH4 spectrum assignment near 6105.7 cm
1 using the SpectraPlot graphical method [62]. The bottom panel is the DAS spectrum recorded at 80 K [40]. Upper panel shows the quantum assignments predicted from the effective operator models. In the middle panel, the assigned lines of the experimental list [40] are presented.

algorithms and the computational code [54,55] permit treating in a similar way all symmetry groups and do not depend on the number of vibrational modes nor on the expansion order. Note that this ITO representation is somewhat different that implemented in the STDS Dijon program [58] in terms of the tensor coupling scheme and the symmetrized powers of elementary operators [51]. A major difference with previous works based on empirical STDS calculations is that our initial t-parameter values were first generated from ab initio PES using high-order contact transformations via MOL_CT program suite [46,59]. At the next step, initially predicted values of some diagonal EH parameters were empirically optimized using new experimental data that permitted assignments to be extended. Then a fine tuning of few coupling parameters was performed in order to better match the observed spectra. This approach has been already used in recent works by Nikitin et al. [60,61] for 12CH4 and by Brown et al. [22] for the 13CH4 Octad spectra. At all stages of the spectrum identification the visual control of assignment is important. On Fig. 4 we present an example of spectra assignment near 6105.7 cm
1 using the SpectraPlot program [62]. Preliminary empirical estimations for the lower state energy levels Eemp [40], previously obtained from the Boltzmann factor involved in two-temperature intensity measurements, gave useful hints in the assignment process. Even an approximate knowledge of Jemp allowed us to considerably narrow the search down. In total, 2898 lines were rovibrationally assigned to the Tetradecad bands that correspond to about 80% of integrated absorption in the 5853–6201 cm
1 region (Fig. 2).

At the final step all data available from the previous analyses [16,17,22,45] of the lower polyads involving the Dyad (900–1700 cm
1), Pentad (2000–3200 cm
1) and Octad (3500–4800 cm
1) together with our Tetradecad data were simultaneously included in the least-squares EH fit of line positions based on the vibrational extrapolation scheme [6]. 3.2. Data fit statistics The detailed statistics for our assigned transitions are summarized in Table 1. Although the rms fit deviation for our Tetradecad line positions was better than 0.005 cm
1, the obtained EH model has to be yet considered as a preliminary one. This is because we could not include in the fit the lines in the missing range 4800–5853 cm
1 for which experimental 13CH4 spectra are not available. A large part of predicted transitions of the 2ν2 þ2ν4, ν1 þ ν2 þ ν4, 2ν1, ν2 þ ν3 þ ν4, ν1 þ ν3 bands (Table 1(A)) is located in this range below 5853 cm
1 which has not been explored experimentally. In our DAS spectrum [40] we could mainly observe some R-branch transitions of these bands for medium J values. Many EH and EDM parameters specific to these five bands could not be experimentally refined. This also applies to the parameters of the resonance coupling between these five bands and the bands centered in the analysed range, which were also kept fixed to the theoretically predicted values. This affects the result of the observed transitions fit, which is represented in the sixth column of Table 1. The worst fit results correspond to very weak bands for which only a few transitions were observed. This is also the case of the bands having band centers below our experimental range (A-panel of Table 1).

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎ Table 1 Overview of the rovibrational assignments of the statistics. Band

Upper sublevel

5

CH4 spectrum at 80 K between 5853 and 6201 cm
1 and corresponding line position and intensity fit

13

Sub-band center (cm
1)

Positions Nb. data

Intensities Jmin, Jmax

(A) preliminary analysis of bands having center located in lower wavenumber range o 5853 cm
1 2ν2 þ2ν4 A1 5666.1 3 9, 9 ν1 þν2 þν4 F2 5717.3 6 8, 11 F1 5735.2 6 8, 8 2ν1 A1 5784.4 36 6, 10 a ν2 þν3 þν4 F2 1 5805.7 111 5, 11 F1 1b 5807.7 94 4, 12 E 1c 5814.7 22 3, 11 A1 5819.3 34 3, 11 E 2c 5825.1 54 3, 11 A2 5825.6 48 4, 11 a F2 2 5826.6 94 4, 11 b F1 2 5829.5 95 2, 11 ν1 þν3 F2 5849.67 135 1, 11 (B) analysis of bands located in the spectral range under investigation: 5853–6201 cm
1 3ν2 þν4 F2 1d 5858.7 90 1, 9 F1 1e 5872.05 81 2, 9 F2 2d 5886.709 92 0, 11 F1 2e 5901.43 63 1, 10 2ν3 A1 5930.3 14 4, 7 F2 5987.047 390 0, 12 E 6023.787 265 1, 12 ν1 þ2ν2 E 5951.564 192 1, 12 A1 5959.89 98 2, 10 2ν2 þν3 F2 1f 6044.927 190 0, 11 F1 6051.178 274 1, 11 F2 2f 6055.996 317 1, 11 4ν2 A1 6117.4 15 3, 7 E 1g 6119.1 47 1, 8 g E2 6124.7 32 1, 6 Total 2898

RMS (10


3

cm


1

)

Nb. data

RMS (%)

4.2 40.0 28.9 7.6 4.4 5.9 4.6 6.8 9.4 5.1 4.7 4.3 6.6

3 3 19 57 51 20 18 30 33 45 65 88

14.4 13.0 6.2 11.7 10.3 9.8 8.8 7.8 12.2 7.1 7.4 8.8

7.6 4.7 5.0 3.5 3.5 3.2 1.7 2.3 3.6 2.1 2.6 2.3 3.1 2.0 1.1 4.6

50 46 46 25 4 246 203 125 65 136 189 253 4 24 16 1864

10.5 10.6 11.1 8.3 8.9 9.7 10.0 9.7 9.6 8.6 10.5 9.1 14.3 10.8 12.5 9.7

Notes: The vibrational sublevels are enumerated here for each band for a given symmetry type. The ranking numbers within the Tetradecad are the following: a N ¼ 13 and N ¼14 for F2 1 and F2 2. b N ¼9 and N¼ 10 for F1 1 and F1 2. c N ¼9 and N ¼ 10 for E 1 and E 2. d N ¼16 and N ¼ 17 for F2 1 and F2 2. e N ¼ 11 and N ¼12 for F1 1 and F1 2. f N ¼19 and N ¼ 20 for F2 1 and F2 2. g N ¼ 13 and N¼ 14 for E 1 and E 2.

Fig. 5. Fit residuals for line positions (a) and intensities (b) in the 13CH4 Tetadecad region. Different colors are used to indicate the different band systems contributing to the spectrum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

6

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

Graphically, this is clearly seen in Fig. 5a. For these bands we estimate the band centers uncertainty varying between 0.2 and 0.5 cm
1. The assignments of the most of bands in the 5853– 6201 cm
1 range (Table 1(B)) are supported by the observation of J¼ 0 and J¼1 lines. In these cases the uncertainty estimation for the band centers is 0.003–0.005 cm
1. For other bands where less than 100 transitions were assigned we quoted two digits for their empirical center determination with the uncertainty estimation of 0.05–0.1 сm
1. In total, 250 effective Hamiltonian parameters were adjusted to 10259 observed transitions covering Dyad, Pentad, Octad [16,17,45] and the upper part of Tetradecad ranges, the latter one being assigned in this work. Among them, 54 parameters specific to the Tetradecad were fitted. Only two of them correspond to the resonance interaction between ν1 þ ν3 and 3ν2 þ ν4 bands. The remaining coupling parameters specific to the Tetradecad were not adjusted and held fixed to their initial values predicted from the PES using MOL_CT code [46,59].

Fig. 6. Histogram of the (J–Jemp) differences between the lower state J values determined by the 2T-method [63] and from more rigorous rovibrational assignments obtained in this work.

The intensities of 1864 selected transitions of the observed bands were used to derive the parameters of the effective dipole transition moment operator. This sample of line intensities could be reproduced with an rms deviation of 10%. In total, 36 transition moment parameters for the studied Tetradecad bands were fitted. Detailed intensity fit statistics for the two frequency ranges are given in Table 1. Fig. 5b displays the fit residuals for line intensities in the range 5853–6201 cm
1. A sample of the Supplementary file, given in Table 1A in Appendix A, includes the observed minus calculated positions and intensities (at 80 K) along with the quantum assignments and lower state energies and rovibrational assignments (the assignment notation format is described in notes after the Table).

Fig. 8. Comparison between the experimental spectrum of 13CH4 at 80 K (middle panel) with simulation based on the effective Hamiltonian/ Dipole moment models (upper panel) and with variational predictions using NRT PES [35] and ab initio DMS [28] (lower panel) in the 5853– 5900 cm
1 region of the Tetradecad.

Fig. 7. Reduced upper state energies of 13CH4 transitions from 5750 to 6200 cm
1. ‘Reduced energy’ is computed as the upper state energy of a J0 , C0 , K0 level minus B0J(J þ1), where B0 is the ground state rotational constant. Various colors correspond to mixing coefficients of normal mode wavefunctions due to resonance interactions. Left panel: all predicted energies up to J¼ 12. Right panel: the corresponding empirical energies obtained from the assigned lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

7

Fig. 9. Comparison between the DAS spectrum of 13CH4 at 80 K (middle panel) with simulation based on the effective Hamiltonian/Dipole moment models (upper panel) and with variational predictions using NRT PES [35] and ab initio DMS [29] (lower panel) in the 6040– 6130 cm
1 region of the Tetradecad.

3.3. Comparison with prior 2T-empirical determination of low J values In Ref. [40], the empirical values of the lower state energy level, Eemp, were systematically derived from the intensity ratios of the lines retrieved from the DAS spectra at 80 K and 296 K. This “2T-method” [41,42,63] allowed deriving 2782 lower state energy values, Eemp. The corresponding empirical values of the rotational quantum number, Jemp, were obtained from Eemp ¼B0 Jemp (Jemp þ1) where B0 ¼5.214 cm
1 is the 13CH4 ground state rotational constant. In the present work, 2898 lines were rovibrationally assigned, providing a set of 2336 lines in common for comparison of the J values. According to Fig. 6, 80% of the rounded Jemp values agree with our more rigorous assignments and 93% correspond to 1 oJem– Jo1. Most of the disagreements correspond to weak or blended lines, in particular to high J transitions with very small intensity at 80 K. 3.4. Energy levels and line lists A list of 8154 transitions of the bands under investigation was calculated for the range 5853–6200 cm
1 using the determined parameters of the effective Hamiltonian and of the transition moment. The intensity cut off was fixed to 1  10
28 cm/molecule, Jmax ¼12. Note that the sensitivity of the DAS spectra is at the 1  10
27 cm/ molecule (see Fig. 2). In the Supplementary materials we provide two line lists: the experimental one including our assignments (2898 lines) and the calculated one which is more complete (8154 transitions). The corresponding examples are given in Tables 1A and 2A of the Appendix A. In total 1744 rovibrational energy levels of the 13CH4 Tetradecad were determined from experimental spectra using our assignments. An overall comparison of the empirical level set with the calculated one is given in Fig. 7. The left

Fig. 10. (a) Comparison between the DAS spectrum of 13CH4 at 80 K (middle panel) with simulation based on the effective Hamiltonian/ Dipole moment models (upper panel) and with variational predictions in the 5920–6040 cm
1 region of the Tetradecad (lower panel). (b) Detailed comparison around 5986 cm
1 using two versions of variational calculations at the lower panel, both with ab initio NRT DMS [28]: dashed orange curves correspond to line positions directly computed from NRT PES [35] and blue solid curves to the spectrum computed with the Δ (12C-13C) isotopic shift corrections [32]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

panel displays all possible predicted values for 28 different vibrational sub-states while the right panel shows the individual Tetradecad levels corresponding to observed transitions. The synthetic spectrum of the bands simulated from this list leads to a good agreement with the experimental spectrum, as illustrated in Figs. 8–10.

4. Comparison with variational predictions and discussions Comparisons of our assigned experimental spectra split in lower, higher and middle ranges with variational spectra predictions using PES and DMS are shown in Figs. 8–10.

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

8

Table 2 Comparison of the empirically determined band centers of 12 C-13C. Band

Sublevel

13

Sub-band center (cm
1) α 13

CH4 with those predicted by direct variational calculations [32] and using isotopic shifts

Difference (direct calc)β (cm
1) 13

Empirical CH4 [15] þ Δ (iso-shifts)γ

CH4 Direct var. calc. [32]

5858.7 5872.05 5886.709 5901.43

5859.209 5872.483 5887.068 5901.805


0.5
0.43
0.359
0.38

A1 F2 E

5930.3 5987.047 6023.787

5930.091 5986.869 6023.736

ν1 þ 2ν2 E A1

5951.564 5959.89

2ν2 þ ν3 F2 1f F1 F2 2f

2ν3

4ν2

1d 1e 2d 2e

A1 E 1g E 2g

Difference (via iso-shifts)δ (cm
1)

12

Empirical

3ν2 þ ν4 F2 F1 F2 F1

Sub-band center (cm
1)

CH4

5858.82 5872.101 5886.734 5901.053


0.1
0.05
0.025 0.38

0.2 0.178 0.051

5937.879** 5987.052 6023.756


7.6*
0.005 0.031

5951.745 5959.806


0.181 0.08

5951.561 5957.287**

0.003 2.60*

6044.927 6051.178 6055.996

6045.103 6051.385 6056.318


0.176
0.207
0.322

6044.941 6051.206 6056.000


0.014
0.028
0.004

6117.4 6119.1 6124.7

6118.246 6119.872 6124.989


0.8
0.8
0.3

6122.749** 6119.526 6124.744


5.3*
0.4 0.0

**As stated in Ref. [15] for these bands there was not enough assigned lines and thus the empirical uncertainties could be large up to several wavenumbers. *These outliers could originate from large uncertainties of 12CH4 vibration levels marked by ** as noted in Ref. [15]. α Our empirical 13CH4 band center determinations in the range 5853–6201 cm
1 of the analyzed DAS spectra. β Our empirical centers minus directly calculated [32] from NRT PES [35]. γ Calculated by adding ab initio computed [32] isotopic shifts Δ ¼EV(13CH4)–EV(12CH4) to previously empirically determined 12CH4 band centers [15]. δ Discrepancies between our empirical 13CH4 band centers and the values given in the previous column γ. The ranking numbers, marked here by the d, e, f, g letters, are listed after Table 1.

Let us recall that the NRT PES [35] has been based on extended ab initio calculations at 20,000 nuclear configurations with a further four-parameters scaling using the four fundamental frequencies of 12CH4. The NRT DMS [28] is a pure ab initio surface computed on the same grid of nuclear configurations without any empirical corrections. Rey et al. [32] have converted these surfaces in the normal mode ITO representation for the 13CH4 isotopologue and calculated vibration-rotation spectrum up to the Octad range [32]. For the present study these variational predictions were extended to the Tetradecad of 13 CH4. The agreement with observations is very good, distinctions between experimental and predicted lists being hardly visible on the scale of the Figs. 8, 9 and 10a. Fig. 10b with the blown up scale gives an idea of the errors in line positions of the variational line list (dashed orange spectrum at the bottom panel). They amount in average to about 0.2 cm
1. These theoretical errors can be significantly reduced by applying the “isotopic-shift” method. In Ref. [32] it was shown that ab initio predictions of the isotopic shift Δ ¼ EV(13CH4)–EV(12CH4) in the lower spectral range were much more accurate than absolute values of predicted vibrational levels. This is because in firstprinciples calculations the mass-dependent effects result mainly from the kinetic part which is very accurately defined in the full nuclear motion Hamiltonian. Using this fact, we could obtain precise values for all 13CH4 band

centers by adding ab initio Δ values to the known experimentally determined 12CH4 band centers. In Table 2 we check this method for 13CH4 band centers determined in the considered spectral range. It is seen that the “isotopic-shift” method allowed us decreasing the prediction errors for most of bands, except those (marked by **) for which 12CH4 band centers have been poorly determined because of missing assignments in Ref. [15]. This suggests that “isotopic-shift” calculations could serve as useful criteria for the consistency of spectra analyses of two isotopic species. Another confirmation of the validity of this method is shown in Fig. 10b where isotopic shift corrections bring ab initio calculations (blue solid line spectrum at the lower panel) in a nearly perfect agreement with the experimental spectrum.

Acknowledgments The support of the LIA SAMIA between CNRS (France) and RFBR (Russia) is acknowledged. We acknowledge the support from IDRIS and CINES computer centers of CNRS France and of the computer center Reims-ChampagneArdenne, as well as of Tomsk State University D. Mendeleev funding program. A.N. thanks computer centers of ICM@MG SB RAS (Novosibirsk) and SKIF Siberia (Tomsk). This work was performed in the frame of the Labex OSUG@2020 (ANR10 LABX56).

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

9

Appendix A See Tables A1 and A2.

Table A1 Sample of Electronic Supplementary data. Observed ν0 cm

Intensity at 80 K
1

5855.2734 5855.3584 5855.3838 5855.4258 5855.4688 5855.5089 5855.5284 5855.5447 5855.6138 5855.6693

CH4 methane transitions with assignments in the 5853–6201 cm
1 region at 80 K.

13

Rotational Assignment

cm/molec

Low. state

3.753E
24 1.858E
22 5.001E
25 1.276E
25 1.286E
24 8.660E
26 2.693E
25 2.277E
25 8.534E
24 7.614E
23

0 0 0 0 0 0 0 0 0 0

7 4 6 5 8 8 8 7 5 3

A2 1 F1 1 F2 1 F1 1 F2 2 F2 1 F1 2 E1 E1 F2 1

Vibrational assignment

E lower

Up. state

Low. state

Up. state

cm

4 4 4 4 4 4 4 4 4 4

0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0111 F2 0111 F1 0111 F2 1010 F2 0111 F1 0111 F1 0111 E 0111 F2 2000 A1 0111 F1

219.930 104.780 219.925 157.132 376.844 376.803 376.822 293.184 157.144 62.880

7 A1 63 5 F2 121 7 F1 168 5 F2 146 9 F1 201 9 F1 201 9 F2 197 7 E 131 6 E 98 4 F1 101

A1 A1 A1 A1 A1 A1 A1 A1 A1 A1

Obs-Calc


1

10


3

cm


1


1.337
1.518 1.705 6.514 6.810 7.119
1.453 1.487
2.401
5.193

(Io
Ic)/Io %
1.1
1.3
23.4 6.4 7.7 3.0 6.1 5.1

Notes: in this table, the columns are: 1. νo: measured line positions. 2. I (80 K): measured line intensities in cm
1/(molecule cm
2) at 80 K. 3. Lower state rovibrational assignment are given by the vibrational polyad number P, the rotational quantum number J, the rovibrational symmetry type C (Td irreducible representation) and the rovibrational ranking index N. 4. Upper state rovibrational assignment in the same format. 5. Lower vibrational band assignment contains the principal vibrational quanta (v1,v2,v3,v4) and vibrational symmetry type CV (Td irreducible representation). 6. Upper vibrational band assignment in the same format. 7. E lower: lower energy value [in cm
1]. 8. Difference between measured and calculated line position included in the fit in 10
3 cm
1 units. 9. (Io
Ic)/Io*100 (%) is the relative difference between measured and calculated intensities included in the fit. These values appear for assigned lines if their measured intensities were included in the fit.

Table A2 Sample of Electronic Supplementary data. Calculated line list of the

CH4 methane transitions at 80 K for the 5853–6201 cm
1 region.

13

ν0

Intensity at 80 K

Rotational assignment

cm
1

cm/molec

Low. state

Up. state

5852.8585 5852.8742 5852.8793 5852.8864 5852.9022 5852.9049 5852.9142 5852.9604 5852.9650 5852.9962

1.07E
25 1.84E
26 8.01E
26 4.25E
24 6.99E
24 1.20E
26 5.68E
25 7.99E
28 4.78E
25 3.39E
26

0 0 0 0 0 0 0 0 0 0

4 7 F2 193 4 8 F1 216 4 9 E 130 4 4 E 81 4 3 F2 91 4 5 E 104 4 7 F2 193 4 10 F1 205 4 9 E 130 4 9 F2 193

7 8 8 4 3 6 7 9 8 8

F1 2 F2 1 E2 E1 F1 1 E1 F1 1 F2 1 E1 F1 2

V

V V V V V V V V V V

32 33 31 6 14 14 32 27 31 31

Vibrational assignment

E lower

Low. state

Up. state

cm
1

0000 0000 0000 0000 0000 0000 0000 0000 0000 0000

0111 F1 0111 A2 0111 F1 1010 F2 0301 F1 0301 F1 0111 F1 0202 E 0111 F1 0111 F1

293.192 376.803 376.839 104.781 62.879 219.924 293.137 470.742 376.753 376.822

A1 A1 A1 A1 A1 A1 A1 A1 A1 A1

Notes: in this table, the columns are: 1. νo: calculated line positions. 2. I (80 K): calculated line intensities in cm
1/(molecule cm
2) at 80 K. 3 Lower state rovibrational assignment are given by the vibrational polyad number P, the rotational quantum number J, the rovibrational symmetry type C (Td irreducible representation) and the rovibrational ranking index N. 4. Upper state rovibrational assignment in the same format. 5. V n is the number of vibrational subband in the MIRS [54,55] labeling. 6. Lower vibrational band assignment contains the principal vibrational quanta (v1,v2,v3,v4) and vibrational symmetry type CV (Td irreducible representation). 7. Upper vibrational band assignment in the same format. 8. E lower: lower energy value [in cm
1].

Appendix B. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j. jqsrt.2015.12.023.

References [1] Sromovsky LA, Fry PM, Boudon V, Campargue A, Nikitin A. Comparison of line-by-line and band models of near-IR methane absorption applied to outer planet atmospheres. Icarus 2012;218: 1–23.

[2] De Bergh C, Courtin R, Bézard B, Coustenis A, Lellouch E, Hirtzig M, et al. Applications of a new set of methane line parameters to the modeling of Titan's spectrum in the 1.58 μm window. Plan Space Sci 2012;61:85–98. [3] Hirtzig M, Bézard B, Lellouch E, Coustenis A, De Bergh C, Drossart P, et al. Titan's surface and atmosphere from Cassini/VIMS data with updated methane opacity. Icarus 2013;226:470–86. [4] Tinetti G, Encrenaz T, Coustenis A. Spectroscopy of planetary atmospheres in our Galaxy. Astron Astrophys Rev 2013;21:63. [5] Khalil M. Non-CO2 greenhouse gases in the atmosphere. Ann Rev Energy Environ 1999;24:645–61. [6] Champion JP, Loete M, Pierre G. In: Rao KN, Weber A, editors. Spectroscopy of the Earth's atmosphere and interstellar medium. San Diego: Academic Press; 1992. [7] Boudon V, Pirali O, Roy P, Brubach BJ, Manceron L, et al. The highresolution far-infrared spectrum of methane at the SOLEIL synchrotron. J Quant Spectrosc Radiat Transf 2010;111:1117–29.

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

10

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

[8] Hilico JC, Champion JP, Toumi S, Tyuterev VlG, Tashkun SA. New analysis of the pentad system of methane and prediction of the (pentad–pentad) spectrum. J Mol Spectrosc 1994;168:455–76. [9] Predoi-Cross A, Brown LR, Devi VM, Brawley-Tremblay M, Benner DC. Multispectrm analysis of 12CH4 from 4100–4635 cm
1: I. Selfbroadening coefficients (widths and shifts). J Mol Spectrosc 2005;232:231–46. [10] Devi VM, Benner DC, Smith MAH, Mantz AW, Sung K, Crawford TJ, et al. Self- and air-broadened line shape parameters in the ν2 þ ν3 band of 12CH4: 4500–4630 cm
1. J Quant Spectrosc Radiat Transf 2015;152:149–65. [11] Nikitin AV, Daumont L, Thomas X, Régalia L, Rey M, Tyuterev VlG, et al. Preliminary assignments of 2ν3–ν4 hot band of 12CH4 in the 2 μm transparency window from long-path FTS spectra. J Mol Spectrosc 2011;268:93–106. [12] Albert S, Bauerecker S, Boudon V, Brown LR, Champion JP, Loete M, et al. Global analysis of the high resolution infrared spectrum of methane 12CH4 in the region from 0 to 4800 cm
1. Chem Phys 2009;358:131–46. [13] Nikitin AV, Thomas X, Regalia L, Daumont L, Von der Heyden P, Tyuterev VlG. First assignment of the 5v4 and v2 þ 4v4 band systems of 12CH4 in the 6287–6550 cm
1 region. J Quant Spectrosc Radiat Transf 2011;112:28–40. [14] Daumont L, Nikitin AV, Thomas X, Régalia L, Von der Heyden P, Tyuterev VlG, et al. New assignments in the 2 μm transparency window of the 12CH4 Octad band system. J Quant Spectrosc Radiat Transf 2013;116:101–9. [15] Nikitin AV, Boudon V, Wenger Ch, Albert S, Brown LR, Bauerecker S, et al. High resolution spectroscopy and the first global analysis of the Tetradecad region of methane 12CH4. Phys Chem Chem Phys 2013;15:71–93. [16] Champion J-P, Hilico JC, Brown LR. The vibrational ground state of 12 CH4 and 13CH4. J Mol Spectrosc 1989;133(2):244–55. [17] Niederer HM, Albert S, Bauerecker S, Boudon V, Champion JP, Quack M. Global analysis of the infrared spectrum of 13CH4: lines in the region 0 to 3200 cm
1. Chimia 2008;62:273–6. [18] Nikitin A, Champion JP, Tyuterev VlG, Brown L, Mellau G, Lock M. The infrared spectrum of CH3D between 900 and 3200 cm
1: extended assignment and modeling. J Mol Struct 2000;517:1–24. [19] Nikitin AV, Brown LR, Féjard L, Champion JP, Tyuterev VlG. Analysis of the CH3D Nonad in the region 2000–3300 cm
1. J Mol Spectrosc 2002;216:225–51. [20] Nikitin AV, Champion JP, Brown LR. Preliminary analysis of CH3D from 3250 to 3700 cm
1. J Mol Spectrosc 2006;240:14–25. [21] Nikitin AV, Brown LR, Sung K, Rey M, Tyuterev VlG, MAH Smith, et al. Preliminary modeling of CH3D from 4000 to 4550 cm
1. J Quant Spectrosc Radiat Transf 2013;114:1–12. [22] Brown LR, Nikitin AV, Sung K, Rey M, Tashkun SA, Tyuterev VlG, et al. Measurements and modelling of cold 13CH4 spectra in the 3750– 4700 cm
1 region. J Quant Spectrosc Radiat Transf 2016, http://dx. doi.org/10.1016/j.jqsrt.2016.01.016. [23] Brown LR, Sung K, Benner DC, Devi VM, Boudon V, Gabard T, et al. Methane line parameters in the HITRAN2012 database. J Quant Spectrosc Radiat Transf 2013;130:201–19. [24] Ulenikov ON, Bekhtereva ES, Albert S, Bauerecker S, Niederer HM, Quack M. Survey of the high resolution infrared spectrum of methane (12CH4 and 13CH4): partial vibrational assignment extended towards 12,000 cm
1. J Chem Phys 2014;141:234302. [25] Rothman LS, Gordon IE, Babikov Y, Barbe A, Chris Benner D, Bernath PF, et al. The HITRAN2012 molecular spectroscopic database. J Quant Spectrosc Radiat Transf 2013;130:4–50. [26] Tyuterev VlG, Babikov YL, Tashkun SA, Perevalov VI, Nikitin A, Champion JP, et al. T.D.S. spectroscopic databank for spherical tops. J Quant Spectrosc Radiat Transf 1994;52:459–80. [27] Ba YA, Wenger C, Surleau R, Boudon V, Rotger M, Daumont L, et al. MeCaSDa and ECaSDa: Methane and ethene calculated spectroscopic databases for the virtual atomic and molecular data centre. J Quant Spectrosc Radiat Transf 2013;130:62–8. [28] Nikitin AV, Rey M, Tyuterev VlG. New dipole moment surfaces of methane. Chem Phys Lett 2013;565:5–11. [29] Rey M, Nikitin AV, Tyuterev VlG. First principles intensity calculations of the methane rovibrational spectra in the infrared up to 9300 cm
1. Phys Chem Chem Phys 2013;15:10049–61. [30] Rey M, Nikitin AV, Tyuterev VlG. Convergence of normal mode variational calculations of methane spectra: theoretical line list in the icosad range computed from potential energy and dipole moment surfaces. J Quant Spectrosc Radiat Transf 2015;164:207–20.

[31] Rey M, Nikitin AV, Tyuterev VlG. Theoretical hot methane line lists up to T ¼ 2000 K for astrophysical applications. Astrophys J 2014;789 (2):1–10. [32] Rey M, Nikitin AV, Tyuterev VlG. Predictions for methane spectra from potential energy and dipole moment surfaces: Isotopic shifts and comparative study of 13CH4 and 12CH4. J Mol Spectrosc 2013;291:85–97. [33] Rey M, Nikitin AV, Tyuterev VlG. Accurate first-principles calculations for 12CH3D infrared spectra from isotopic and symmetry transformations. J Chem Phys 2014;141:044316. [34] Rey M, Nikitin AV, Tyuterev VlG. First predictions of rotationally resolved infrared spectra of di-deuteromethane (12CH2D2) from potential energy and dipole moment surfaces. J Phys Chem A 2015;119:4763–79. [35] Nikitin AV, Rey M, Tyuterev VlG. Rotational and vibrational energy levels of methane calculated from a new potential energy surface. Chem Phys Lett 2011;501:179–86. [36] Rey M, Nikitin A, Campargue A, Kassi S, Mondelain D, Tyuterev VG. Ab initio variational predictions for understanding highly congested spectra: rovibrational assignment of 108 new methane sub-bands in the icosad range (6280–7600 cm
1). Phys Chem Chem Phys 2016;18:176–89. [37] Nikitin AV, Lyulin OM, Mikhailenko SN, Perevalov VI, Filipov NN, Grigoriev IM, et al. GOSAT-2009 methane spectral line list in the 5550–6236 cm
1 range. J Quant Spectrosc Radiat Transf 2010;111: 2211–24. [38] Nikitin AV, Lyulin OM, Mikhailenko SN, Perevalov VI, Filippov NN, Grigoriev IM, et al. GOSAT-2014 methane spectral line list. J Quant Spectrosc Radiat Transf 2015;154:63–71. [39] Nikitin AV, Mikhailenko S, Morino I, Yokota T, Kumazawa R, Watanabe T. Isotopic substitution shifts in methane and vibrational band assignment in the 5560–6200 cm
1 region. J Quant Spectrosc Radiat Transf 2009;110:964–73. [40] Campargue A, Lopez Segovia J, Béguier S, Kassi S, Mondelain D. The absorption spectrum of 13CH4 in the region of the 2ν3 band at 1.66 mm: empirical line lists and temperature dependence. J Quant Spectrosc Radiat Transf 2015;152:140–8. [41] Kassi S, Gao B, Romanini D, Campargue A. The near infrared (1.30– 1.70 mm) absorption spectrum of methane down to 77 K. Phys Chem Chem Phys 2008;10:4410–9. [42] Gao B, Kassi S, Campargue A. Empirical low energy values for methane transitions in the 5852
6181 cm
1 region by absorption spectroscopy at 81 K. J Mol Spectrosc 2009;253:55–63. [43] Sciamma-O'Brien E, Kassi S, Gao B, Campargue A. Experimental low energy values of CH4 transitions near 1.33 mm by absorption spectroscopy at 81 K. J Quant Spectrosc Radiat Transf 2009;110:951–63. [44] Campargue A, Wang L, Kassi S, Mondelain D, Bezard B, Lellouch E, et al. An empirical line list for methane in the 1.26–1.71 mm region for planetary investigations (T ¼ 80–300 K). Application to Titan. Icarus 2012;219:110. [45] Niederer HM, Wang X-G, Carrington T, Albert S, Bauerecker S, Boudond V, et al. Analysis of the rovibrational spectrum of 13CH4 in the Octad range. J Mol Spectrosc 2013;291:33–47. [46] Tyuterev VlG, Tashkun SA, Rey M, Kochanov RV, Nikitin AV, Delahaye T. Accurate spectroscopic models for methane polyads derived from a potential energy surface using high-order contact transformations. J Phys Chem 2013;117:13779–805. [47] Tyuterev VlG, Champion J-P, Pierre G, Perevalov VI. Parameters of reduced Hamiltonian and invariant parameters of interacting E and F2 fundamentals of tetrahedral molecules: v2 and v4 bands of 12CH4 and 28SiH4. J Mol Spectrosc 1986;120:49–78. [48] Perevalov VI, Tyuterev VlG, Zhilinskii BI. Ambiguity of spectroscopic parameters in the case of accidental vibration—rotation resonances in tetrahedral molecules. r2J and r2J2 terms for E/F2 interacting states. Chem Phys Lett 1984;104:455–61. [49] Perevalov VI, Tyuterev VlG, Zhilinskii BI. Reduced Hamiltonian for 0100 and 0001 interacting states of tetrahedral XY4 molecules: calculated r2J2 and r2J3-type parameters for v2 and v4 bands of methane. J Mol Spectrosc 1985;111:1–19. [50] Boudon V, Champion JP, Gabard T, Loëte M, Michelot F, Pierre G, et al. Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups. J Mol Spectrosc 2004;228:620–53. [51] Nikitin AV, Champion JP, Tyuterev VlG. Improved algorithms for the modeling of vibrational polyads of polyatomic molecules: application to Td, Oh, and C3v molecules. J Mol Spectrosc 1997;182:72–84. [52] Rey M, Nikitin AV, Tyuterev VlG. Ab initio ro-vibrational Hamiltonian in irreducible tensor formalism: a method for computing

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i

E. Starikova et al. / Journal of Quantitative Spectroscopy & Radiative Transfer ∎ (∎∎∎∎) ∎∎∎–∎∎∎

[53]

[54]

[55]

[56]

[57] [58]

energy levels from potential energy surfaces for symmetric-top molecules. Mol Phys 2010;108:2121–35. Rey M, Nikitin AV, Tyuterev VlG. Complete nuclear motion Hamiltonian in the irreducible normal mode tensor operator formalism for the methane molecule. J Chem Phys 2012;136:244106. Nikitin AV, Champion JP, Tyuterev VlG. The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules. J Quant Spectrosc Radiat Transf 2003;82:239–49. Nikitin AV, Rey M, Champion JP, Tyuterev VlG. Extension of the MIRS computer package for modeling of molecular spectra: from effective to full ab initio ro-vibrational hamiltonians in irreducible tensor form. J Quant Spectrosc Radiat Transf 2012;113:1034–42. Moret-Bailly J. Calculation of the frequencies of the lines in a threefold degenerate fundamental band of a spherical top molecule. J Mol Spectrosc 1965;15:344–54. Zhilinskii BI. Reduction of rotational operators to standard form. Opt Spectrosc 1981;51:262–3. Wenger C, Champion JP. Spherical top data system (STDS): a software for the simulation of spherical top spectra. J Quant Spectrosc Radiat Transf 1998;59:471–80.

11

[59] Tyuterev VlG, Tashkun SA, Seghir H. High-order contact transformations: general algorithm, computer implementation and triatomic tests. SPIE 2004;5311:164–75. [60] Nikitin AV, Thomas X, Regalia L, Daumont L, Rey M, Tashkun SA, et al. Measurements and modeling of long-path 12CH4 spectra in the 4800–5300 cm
1 region. J Quant Spectrosc Radiat Transf 2014;138: 116–23. [61] Nikitin A, Rey M, Tashkun S, Kassi S, Modelain D, Campargue A, et al. Analyses and modeling of the 12CH4 spectrum at 80K between 6539 and 6800 cm
1. J Quant Spectrosc Radiat Transf 2016;108:207–16. [62] Nikitin AV, Kochanov RV. Visualization and identification of spectra by the SpectraPlot program. Atmos Ocean Opt 2011;24:931–41. [63] Wang L, Kassi S, Liu AW, Hu SM, Campargue A. High sensitivity absorption spectroscopy of methane at 80K in the 1.58 mm transparency window: temperature dependence and importance of the CH3D contribution. J Mol Spectrosc 2010;261:41–52.

Please cite this article as: Starikova E, et al. Assignment and modeling of the absorption spectrum of 13CH4 at 80 K in the region of the.... J Quant Spectrosc Radiat Transfer (2016), http://dx.doi.org/10.1016/j.jqsrt.2015.12.023i