Accurate Infrared Line Lists for 20 Isotopologues of CS2 at Room Temperature

To facilitate atmospheric and spectroscopic studies of carbon disulfide, or CS2, in both planetary and exoplanetary atmospheres, we adopt the “Best Theory + Reliable High-resolution Experiment” algorithm to generate semiempirical IR line lists for the 20 most abundant CS2 isotopologues, denoted as Ames-296K. The IR lists are computed using the Ames-1 potential energy surface, refined using the experimental transition set and an ab initio dipole moment surface fitted from CCSD(T)/aug-cc-pV(T/Q/5+d)Z dipoles extrapolated to a one-particle basis set limit. The IR lists cover the range of 0–10,000 cm−1, with an S 296K cutoff at 10−31 cm−1/molecule·cm−2 (abundance included). A “natural” IR line list at 296 K includes about 10 million lines of the 20 isotopologues, with their intensities scaled by the corresponding abundances. The zero-point energy, partition functions, and abundances are reported for each isotopologue. The energy levels in the global effective Hamiltonian model for 12C32S2 are adopted to improve the line position accuracy. This new IR list for the main isotopologue is denoted as A+I.296K. Reliable HITRAN2020 line positions are also utilized to improve the accuracy of the 32S12C34S, 32S12C33S, and 32S13C32S isotopologue line lists. The final composite line list is validated against Pacific Northwest National Laboratory experimental cross sections, showing excellent agreement. The agreement supports the quality of the composite line list and the power of synergy between experiment and theory. The new data are proposed for use in updating and expanding the CS2 data in HITRAN and other high-resolution IR databases. Supplementary files are available in Zenodo and AHED.


Introduction
CS 2 is a volatile, flammable, colorless, and highly toxic substance with a boiling point of 319.5 K. Due to its significant roles in Earth's atmosphere, e.g., in aerosols, volcanic activity, and combustion processes, it has attracted numerous IR spectral studies since the 1930s (e.g., Sanderson 1936;Plyler & Humphreys 1947;Foss Smith & Overend 1971;Maki & Sams 1974;Khalil & Rasmussen 1984).Beyond Earth, it is also part of the sulfur-bearing astrochemistry of astronomical objects (Mifsud et al. 2021), including Venus (Mahieux et al. 2023), Jupiter (Atreya et al. 1995), and comets (Jackson et al. 2004;Calmonte et al. 2016).CS 2 is also expected to contribute to the sulfur chemistry and photochemistry of exoplanets, and to act as a strong absorber or even a potential biosignature molecule (Domagal-Goldman et al. 2011) in the exoplanet transmission spectrum.However, until recently it was not available in any popular astronomical or atmospheric high-resolution IR databases, and only medium-resolution spectra in the range of 600-6400 cm −1 existed in the PNNL spectroscopic database of experimental cross sections (Johnson et al. 2004;Sharpe et al. 2004).To address this issue, the 2020 version of the HITRAN database (Karlovets et al. 2021;Gordon et al. 2022) was expanded to include the four most abundant isotopologues of CS 2 based on a global semiempirical model.Even more recently, a new global effective Hamiltonian model (Tashkun 2022) was published for 12 C 32 S 2 , the main isotopologue.The addition of this molecule to HITRAN has resulted in its first detection in the atmosphere of Venus (Mahieux et al. 2023) and the sub-Neptune exoplanet TOI-270 d (Holmberg & Madhusudhan 2024) and has enabled more CS 2 combustion studies (Peng et al. 2022).
Compared to CO 2 , CS 2 has longer bonds (r CS = 1.554Å), heavier mass, and a smaller rotational constant B 0 = 0.109 cm −1 .The symmetric stretch ν 1 at 658 cm −1 is IR inactive, the linear bend ν 2 at 397 cm −1 is weak (5 km mol −1 ), and the antisymmetric stretch ν 3 at 1535 cm −1 is very strong (567 km mol −1 ).Due to a much higher density of states, the rovibrational resonances within the vibrational polyads exhibit a high level of complexity, starting with polyad number P = 2ν 1 + ν 2 + 4ν 3 .Some of the earlier studies focused on the "hot" bands.For example, Bernath et al. (1981) reported laser-Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Concurrently, there have been several attempts at empirical potential energy surface (PES) or quartic force field (QFF) refinements, but not for the generation of IR line lists.The Murrell & Guo (1987) PES was refined in 1999 by Zúñiga et al. (1999), reducing the σ rms to 0.3-0.6 cm −1 for vibrational states up to 5000 cm −1 .In 1995, Kolbuszewski et al. (1995) reported a Morse oscillator and rigid bender function-based PES fitted with rovibrational data up to 5000 cm −1 , with σ rms = 2.12 cm −1 .The first high-quality ab initio QFF was reported also in 1995 by Martin et al. (1995).This QFF was refined in 2002 by Zúñiga et al. (2002) using the vibrational data up to 13,000 cm −1 in Brasen & Demtröder (1999), Liou &Huang (1999), andPique et al. (1992), with δ = 0.1-0.4cm −1 for P < 28 states or ∼1 cm −1 for P = 30-34 states.Also in 2002, Zhou et al. (2002) reported a QFF refined with 86 vibrational levels below 6000 cm −1 , with σ rms = 0.20 cm −1 .Both refined QFFs were used to compute and assign >2000 vibrational levels up to 20,000 cm −1 , and to investigate the evolution of Fermi resonances and quantum number stability (Zhou et al. 2002;Zúñiga et al. 2002).Since 2002, no more efforts to obtain a spectroscopically accurate CS 2 PES have been reported, e.g., the neural-network-based global ab initio PES from Pradhan et al. (2013) was developed for dynamics, so it was not empirically corrected.
The CS 2 list in HITRAN2020 included more than 83,000 transitions of the four most abundant isotopologues: 12 C 32 S 2 , 32 S 12 C 34 S, 32 S 12 C 33 S, and 13 C 32 S 2 , which were generated (see Karlovets et al. 2021) in the range of 0-6470 cm −1 and J up to 150, using the PGOPHER program to fit thousands of measured line positions and transition dipole moments.Due to the fact that CS 2 is often used as a calibration gas, the line positions of CS 2 have been measured in many works with very high precision, and therefore the effective model is based on a large subset of high-quality data (see, for instance, Wells et al. 1988 andKarlovets et al. 2020).Much less data existed for intensity/transition dipole moment values for most of the bands.Empirical scaling of intensities was done for many bands in order to better match the PNNL cross sections.This approach however is not ideal as in PNNL spectra, many hot and combination bands from different isotopologues are blended together; therefore it is not always easy to judge what the relative contributions of different bands are at a certain wavenumber.Additionally, the intensity model could not include the Herman-Wallis effect for most of the bands.Furthermore, for the bands not covered by PNNL, scaling was not possible.For instance, for the bending ν 2 fundamental, a rather dated and imprecise measurement had to be used (Person & Hall 1964).Having a theoretically computed and validated line list will certainly help to alleviate these issues.Air-and self-broadening parameters were also semiempirically modeled from experimental data.
In this study, room-temperature rovibrational IR line lists for CS 2 isotopologues, denoted as Ames-296K, are first developed through the "Best Theory + Reliable High-resolution Experiment" (BTRHE) strategy (Huang et al. 2021) to enhance the HITRAN database and better meet the needs of atmospheric studies.This strategy has been successfully utilized in previous studies on H 2 O (Partridge & Schwenke 1997), NH 3 (Huang et al. 2008(Huang et al. , 2011;;Sung et al. 2012), and CO 2 (Huang et al. 2012(Huang et al. , 2017(Huang et al. , 2022)), among others.The strength of BTRHEbased line lists is both the reliable reproduction of existing data and the reliable prediction of uncharacterized lines.The Ames-296K line lists include the 20 most abundant CS 2 isotopologues formed by nonradioactive isotopes 32/33/34/36 S and 12/13 C, from 12 C 32 S 2 to 13 C 36 S 2 .Following the trend of maximizing the synergy between experiment and theory, the Ames line lists are enhanced by adopting experiment-based energy levels and line positions.Both qualitative and quantitative comparisons are presented against published studies, and IR simulations with line-broadening half-widths are assessed with respect to the PNNL spectra.These line lists will fill the need for CS 2 IR data in both planetary and exoplanetary atmospheric research, and provide more reliable predictions for missing bands, weak bands, and minor-isotopologue bands.
The paper is organized as follows.Section 2 introduces the methodology and technical details of ab initio calculations, the PES and its refinement, the dipole moment surface (DMS), the rovibrational calculations, the integration with effective Hamiltonian (H eff ) models, and the line profile modeling.Section 3 reports the details of the Ames-1 PES, the Ames-296K line lists, and line lists updated with more accurate line positions.Section 4 compares the IR simulations to HITRAN and PNNL spectra, focusing on points of intensity agreement and disagreement.Section 5 gives a summary on the status of CS 2 line lists and a plan for future improvements.Please note that this paper is the first one in a series, and future generations of IR line lists will be reported in due course using more accurate PESs and DMSs, for both higher energies and higher temperatures.

Methods
An introduction to the BTRHE algorithm can be found in Huang et al. (2021).It starts with pure ab initio PESs fitted from energies computed at different levels of electronic structure methods and a basis with a least-squares fitting deviation σ rms ∼ 0.1-0.2cm −1 or better, to fully utilize the information obtained from high-quality electronic structure calculations.After comparison with experimental vibrationalband origins, one PES is selected for semiempirical refinement with respect to reliable high-resolution experimental rovibrational line positions or energy levels.Line positions are computed as the difference between rovibrational energy levels computed on a successfully refined PES, which usually means accurate reproduction of existing data and reliable prediction of missing data.High-quality ab initio DMSs enable the computation of transition dipole elements and IR intensities for rovibrational transitions using wave functions obtained on the refined PES.The final compilation of IR line lists consists of the line position and lower-state energy E″ in cm −1 , the IR intensity in cm −1 /molecule•cm −2 , and the Einstein A 21 coefficients in s −1 .The line profile parameters (namely the air-broadened half-widths and their temperature dependencies, as well as the self-broadened half-widths) for each transition can be calculated (as a function of the rotational index m; here m = −J for P-branches, J + 1 for R-branches, and J for Qbranches) using the Padé approximants provided in Karlovets et al. (2021).For validation purposes the line list is converted to HITRAN format and is used as an input to the HITRAN Application Interface (HAPI; Kochanov et al. 2016) to calculate the cross sections at experimental conditions of the PNNL spectra.

Ab Initio PES
The pure ab initio PES we choose for refinements is denoted as Ames-0.It is fitted from frozen-core CCSD(T)/aug-cc-pV(Q +d)Z energies computed using MOLPRO 2015.1 (Werner et al. 2012(Werner et al. , 2020) ) on 3303 grid points with energies up to 90,000 cm −1 , of which 2541 points are below 30,000 cm −1 .Seven additional points are added to the fit to ensure it is globally positive for following rovibrational calculations using the VTET (Schwenke 1996) program.
The total potential energy function is divided into long-range and short-range terms.The long-range part includes Morsetype potential for two C-S bond stretches, and a cosine potential term for bending motion.The short-range part of the potential is a 12th-order polynomial expansion of 252 coefficients multiplied with a damping function defined with δr CS and δ∠ SCS displacements.The formulae below use angstrom (Å) and radian units: The weighting function, w i , is defined to focus on the energy range below 30,000 cm −1 , similar to those in previous studies (Huang et al. 2012(Huang et al. , 2014(Huang et al. , 2023b)).There are 1655, 2197, and 2541 grid points up to 10,000 cm −1 , 20,000 cm −1 , and 30,000 cm −1 , respectively.Correspondingly, the mean deviation |δ| is 0.12, 0.16, and 0.18 cm −1 , and the rms error σ rms is 0.17, 0.23, and 0.28 cm −1 , respectively.The overall relative fitting deviations are ∼0.005%(mean) and ∼0.009% (σ rms ), with values slightly reduced at higher energy cutoffs.The evolution of the mean and rms of δ is plotted in Figure 1.

Ab Initio DMS
CCSD(T)/aug-cc-pV(T/Q/5+d)Z calculations are carried out to determine the numerical gradients of electronic groundstate energies in the finite electric field of ±0.0001 au.The computed dipoles are least-squares fitted to pseudocharges on the S nuclei using a polynomial expanded in C-S bond displacements and (1 + cos∠θ S-C-S ), assuming the carbon atom is centered at the origin so the charge on its nuclei has no impact on the molecular dipole.Related symmetries are automatically built into this representation: The Ames-1 DMS reported in this paper uses an eighth-order polynomial of 165 coefficients.For 2197 points in the range of 0-20,000 cm −1 , there are 2165 nonzero dipole x-components from −0.13 to 1.21 au, and 1965 nonzero dipole y-components from 0.007 to 0.51 au.Their average absolute deviations are 2.6 × 10 −6 au and 1.4 × 10 −6 au, respectively, and the σ rms are 7.2 × 10 −6 au and 4.3 × 10 −6 au, respectively.In total, the center half of their fitting deviations is in the range of −6.1 to 4.4 × 10 −7 au.The center half of the relative fitting deviations is −0.00051% to 0.00061%.
We initially consider fitting the DMS over a greater energy range and using higher-order polynomials, but that leads to intensity noise beyond 10,000 cm −1 .With the current fit, the magnitude of the intensity noise below 10,000 cm −1 is estimated to be less than 10 30,000 1.002002002 2.002002002 max 30,000, .
range of 0-10,000 cm −1 , the mean absolute fitting deviation and σ rms are 0.76 × 10 −6 au and 1.38 × 10 −6 au, respectively.A DMS upgrade is underway to further improve the quality and fitting accuracy in the range of 0-10,000 cm −1 , for more robust line intensity calculations with future PESs.The distribution of fitting deviations is given in the left panel of Figure 2, and the δ and δ% statistics are given in the right panel, in the range of 0-30,000 cm −1 .

Rovibrational Spectroscopy Calculation
Quantum mechanical calculations for rovibrational energy levels and IR transition intensities are carried out on the Ames-1 PES and DMS using a parallel version of the VTET program (Schwenke 1996) in the range of J = 0-200 for all 20 CS 2 isotopologues, within the Born-Oppenheimer approximation frame.We use hyperspherical Radau coordinates and a body frame with a maximum bending quantum number of 240.The angular matrix elements of the PES are analytically determined after a 241-term Legendre expansion of the PES, with an average deviation between the reexpansion and original values of less than 10 −12 au.The contracted basis functions are optimized for each JPS block.The cutoff for solving the onedimensional stretching Schrödinger equations is 0.20 Hartree, i.e., 43,895 cm −1 (1 Hartree = 219,474.63067cm −1 ), with error criterion 10 −8 for determining the number of optimized quadrature points (Schwenke 1992).For each J z , we keep coupled contracted functions with energies below 0.15 au.The bending and stretching functions are coupled to form the final CI matrices, including all functions whose sum of energies is less than 0.15 au.The matrix size is limited to 90,000.Eigenvalues up to 0.1 Hartree (21,947 cm −1 ) for the main isotopologue (222), and up to 0.07 Hartree (15,363 cm −1 ) for minor isotopologues, are extracted and the corresponding wave functions are saved for intensity calculations.
Please note that these calculations use nuclear masses, specifically 21,868.661757346au for 12 C, 23,697.665732302 au for 13 C, 58,265.519335475au for 32 S, 60,087.291861156 au for 33 S, 61,903.633127069au for 34 S, and 65,547.977387426 au for 36 S.
Our intensity calculations use 24-point optimized quadrature for stretches, and analytical angular integrals using a 60-term associated Legendre expansion of the dipole surface.The expansion coefficients are determined from 72-point Gauss-Legendre quadrature.Room-temperature calculations generate all the IR transitions with E′ ∼13,700 cm −1 above zero-point energy (ZPE) and S 296K > 10 −36 cm −1 /molecule•cm −2 .The final Ames-296K IR line lists report those transitions with S 296K 10 −31 cm −1 /molecule•cm −2 in the range of 0-10,000 cm −1 .

PES Refinement
Nonlinear refinement is carried out on the 22 short-range polynomial coefficients C ijk , where i + j + k 4. The refined coefficient set is used to compute new energies on the same set of grid points.The new energies are then refit to get the new PES coefficient set for the final refined PES.Selected energy levels based on HITRAN2020 (Gordon et al. 2022) and a few high-lying vibrational-band origins (J = 0) (Brasen & Demtröder 1999) form the initial reference set of levels.The pure experimental transition set published with Karlovets et al. (2021) is a valuable reference.Including the band origins of minor isotopologues may provide quality constraints and prevent overrefinements or unreasonable minimum geometries.The weights of those reference energy levels at higher energy are raised to minimize the J dependence of E′ deviations.
During the process, some HITRAN data are identified as forbidden by nuclear spin statistics, which means they do not exist and should be excluded from refinement, e.g., odd J levels of the 00 0 2, 02 0 0, 12 0 0, 20 0 0, and 30 0 0 bands of the main isotopologue (222), the 02 0 0 band of 232, J = 10-99 related 21 1 1 ← 12 0 1 transitions of 232, and R36 and P36 of the 00 0 3 band of the 224 isotopologue.Note that Tashkun (2022) also reported violating transitions or levels for the main isotopologue.Another piece of missing information is the e/f labeling for transitions, but most of the labels can be deduced sequentially from the transition network.We also run into ambiguities at certain high J and high energy levels.Later we restrict the vibrational quanta and corresponding J ranges up to those in the experimental set of transitions in Karlovets et al. (2021), e.g., J max = 164 for the ground state of 222, and J max = 122 for the 0111 state of 222.The final reference set for Ames-1 refinement includes 319 levels of 222 with J max = 150 and E max = 6790 cm −1 , plus 14 levels of 224 and 30 levels of 232.The levels of 224 and 232 are added mainly for safety constraints at high J 95, i.e., to avoid overrefinements and maintain reasonable rotational constants.The reference levels have J-dependent weights defined as w i ≈ 1.0 + 0.03•J, except the weights are reduced to 0.001-0.05for five levels with δE around 0.03-0.10cm −1 .The reference level set and the refinement input/output are reported in the Zenodo and AHED repositories.
Figure 3 shows the difference between E Ames and the reference level set along increasing wavenumbers and increasing J.In the range of 0-7000 cm −1 , the unweighted mean ± σ rms fitting errors are −0.002± 0.017 cm −1 (222), −0.021 ± 0.012 cm −1 (224), and 0.0006 ± 0.011 cm −1 (232).For most of the 12 C 32 S 2 levels carrying relatively larger differences with HITRAN, we find satisfactory agreement with the global H eff model, e.g., at 1790 cm −1 for the J = 95 level of 0220f, at 3370 cm −1 for the J = 98 level of 0221f, at 4947 cm −1 for the J = 5 level of 0113f, at 4955 cm −1 for the J = 10 level of 0113e, and at 3020 cm −1 for the J = 80 level of 0221f.Experimental levels at higher energy will be included in the future, e.g., 7000-15,000 cm −1 .
The equilibrium geometry on the Ames-0 and Ames-1 PESs has r CS = 1.55797Å and 1.55275 Å, respectively.The r CS equilibrium value determined from experiments (Bernath et al. 1981) is 1.5526 Å.The agreement probably can be further improved, but we expect it to be sufficient at this first stage.The three harmonic frequencies at the minimum geometry on the Ames-1 PES are 397.94,672.47, and 1558.72 cm −1 , compared to 397.55, 671.31, and 1556.74cm −1 on the Ames-0 PES.

Integration with Effective Hamiltonian
A popular method for improving semiempirical line lists is to utilize more accurate line positions derived from experimentaldata-based Hamiltonian models.In 2022, Tashkun (2022) from the V.E.Zuev Institute of Atmospheric Optics (IAO) group reported a global modeling of 12 C 32 S 2 line positions in the range of 240-12,000 cm −1 using nonpolyad effective Hamiltonian (H eff ) models.More than 13,000 measured line positions were fitted to 99 Hamiltonian model parameters, resulting in a dimensionless σ rms of 1.65 with respect to the experimental uncertainty.Compared to those of high-resolution experiments between 240 and 6466 cm −1 , the H eff -based line positions have an σ rms as small as 0.0013 cm −1 .This is 1 order of magnitude more accurate than Ames-1 PES based line positions.A comparison between H eff and HITRAN was reported, which also revealed deficits in the HITRAN data.For example, HITRAN included five nonexistent 12 C 32 S 2 bands between the vibrational ground state and 02 0 0, 20 0 0, 12 0 0, 30 0 0, and 00 0 2.These bands involve odd J levels of l = 0 vibrational states, but their nuclear spin statistical weights should be zero for symmetric isotopologues.
Tashkun's H eff model is utilized to generate a list of 12 C 32 S 2 rovibrational levels in the range of 0-9000 cm −1 , with polyad number P max = 40, angular moment quantum number l 2 max = 40, and rotational quantum number J max = 200.This list is matched to Ames-1 PES based levels using an iterative search algorithm.A compact computer program for pairing the levels is provided in supplementary Zenodo and AHED repositories.
The minor-isotopologue line positions in HITRAN2020 are also based on effective Hamiltonians, so they are adopted in the enhancement stage after the Ames-296K line list generation.See the details in Section 3.

Ames-1 PES Based Energy Levels and Line Positions
Rovibrational energy levels and transition wavenumbers computed on the Ames-1 PES refinement are compared to those in HITRAN.As we report in Figure 3 (right panel), the δE = E Ames − E HITRAN differences for most bands have negligible J dependence in the range of J = 0-80.For J = 80-150 levels, δE rises more quickly in certain bands, as illustrated in Figure 4 (left panel).Our analysis shows that most of those deviations indicate the difference between high-J extrapolations of E Ames and E HITRAN .The Ames versus HITRAN line comparison and matches adopt the following restrictions: |δE′| < 0.5 cm −1 , |δE″| < 0.5 cm −1 , and exact agreement on J′, J″, and e/f symmetry.After removing accidental matches due to nearly degenerate energy levels,  and a few outliers due to significant overextrapolations or symmetry violations, we are able to match 70,781 out of 83,420 lines in HITRAN, including 36,679 lines for 222, 6185 lines for 224, 3054 lines for 223, and 23,940 lines for 232.For these matched IR transitions, line position differences are plotted in Figure 4 (right panel), with a mean ± σ rms of 0.006 ± 0.044 cm −1 (222), 0.000 ± 0.040 cm −1 (224), 0.012 ± 0.048 cm −1 (223), and 0.004 ± 0.030 cm −1 (232).These statistics are roughly consistent among the four isotopologues.Note that they also include those relatively larger δE differences due to overextrapolations.Figure 4 (right panel) looks similar to Figure 5 in Tashkun (2022) for the main isotopologue, and our |δE| differences are just restricted within ±0.5 cm −1 .
The line position agreement is determined by the accuracy and consistency of upper and lower energy levels, which rely on vibrational-band origin agreement and the J dependence of corresponding levels.Obviously, the extrapolation at high J has a significant impact on the δE statistics for the energy levels.For J = 0-99, the δE of 2851 matched levels varies from −0.055 cm −1 to 0.119 cm −1 , with mean ± σ rms = 0.0005 ± 0.019 cm −1 .For J = 0-150, the δE range of 4408 matched levels expands to −0.253 cm −1 -0.613 cm −1 , with mean ± σ rms = 0.020 ± 0.079 cm −1 .Note that with respect to E HITRAN , the δE of our high-J extrapolations and the Tashkun H eff model extrapolations may carry opposite signs for certain states, e.g., Some bands in HITRAN were originally fitted only with e components, e.g., the 1220 band (Tashkun 2022).As shown in Figures 4 and 5 (left panels), this leads to unusually large discrepancies on 1220f transitions.The 1220f levels are not included in the statistics given above.In Figure 5 (left panel), the 0113e/f−0110e/f band in HITRAN accidentally uses a wrong lower-state energy E″ for J′ = 4-13 transitions.Corresponding 0113e/f levels that are affected by the E′ inconsistency of nearby Jʼ should also be excluded from comparison.Our calculation indicates the 0313e levels have strong perturbations at J = 54-56, but this is beyond the range of experimental data.Accordingly, the agreement on nearby J levels deteriorates upon the perturbation.There is a ∼0.16 cm −1 wide gap for δE near J = 56.In contrast, we find better agreement when comparing E Ames (0313e) to global H eff model energies.As shown in Figure 5 (left panel), the δ Ames-Heff differences are continuous through all J, and they are much more consistent between e/f branches.A small bump of ∼0.03 cm −1 appears between J = 54 and J = 68, indicating that the coupling between the 0313 and 3202 states has similar but slightly different descriptions between the H eff model and this work.
The significant δE disagreement and overextrapolationrelated discrepancies are mostly localized and isotopologuedependent.In other words, the large δE deviations of a specific band are usually isolated, not consistent through all isotopologues.For example, the 3001e and 0330e states of the 13 C-substituted 232 isotopologue have δE of ±0.2-0.3 cm −1 in the range of J = 100-150.The δE of the 1001e levels of the 33 S-substituted 223 isotopologue rises quadratically from less than 0.05 cm −1 at J = 90 to more than 1.0 cm −1 at J = 150.The δE of the 0220e levels of the 34 S-substituted 224 isotopologue also have similar divergence beyond J = 90 (see Figure 5, right panel).These unusual δE will require special treatment when experiment data or models are adopted to enhance the  prediction accuracy of Ames-1 PES based line positions.In comparison, the δE of 0113f in Figure 5 (left panel) has nearly linear J dependence starting from the lowest J.More interestingly, the E Ames and global H eff (222) energies show highly consistent agreement in the whole range of J = 0-150 and beyond, with negligible J dependence for the 0220, 0221, 0113, and 1220 states.See the green lines in Figure 5 (both panels).These observations partially support the quality and consistency of the Ames-1 PES refinement.

Partition Function
The CS 2 ZPE, degeneracy g, and partition function Q/g at 296 K are summarized in Table 1 for the 20 most abundant isotopologues, among which there are eight symmetric isotopologues, and 12 asymmetric isotopologues.The degeneracy g is computed as the product of 2I + 1, where the nuclear spin quantum number is I( 32/34/36 S) = 0, I( 33 S) = 3/2, I( 12 C) = 0, and I( 13 C) = 1/2.The Ames-1 PES based partition functions (Q Ames ) converge to better than 99.99% at 296 K, and are highly consistent through all isotopologues.The HITRAN partition functions (Gamache et al. 2021) for asymmetric isotopologues (224 and 223) are 0.45% higher than the Q Ames values.The differences possibly result from the Q HITRAN model approximations.In contrast, the Q HITRAN for symmetric isotopologues (222 and 232) are 27%-29% higher than the corresponding Q Ames values.For the main isotopologue (222), Tashkun's effective Hamiltonian model (Tashkun 2022) gives Q Heff = 1346.5257.It is in nearly perfect agreement with Q Ames = 1346.5210,with a difference of less than 0.0004%.We estimate the Q Ames for other minor isotopologues should have similar accuracy at 296 K, i.e., better than 99.998%.Interestingly, and fortunately, the line list in Karlovets et al. (2021) was computed using HITRAN2016/TIPS2017 (Gamache et al. 2017), which have values (Laraia et al. 2011) much closer to the ones reported here.In a convergence test, the energy cutoff of 0.10 au (adopted for 222) or 0.07 au (adopted for minor isotopologues) leads to a Q Ames (296 K) difference less than 10 −10 , which is totally negligible.

Ames-296K IR Line Lists for 20 Isotopologues
The partition function values in Table 1 are used in the calculations for the Ames-296K IR line lists of 20 CS 2 isotopologues.Figure 6 gives an overview of the 222 (#1), 224 (#2), 232 (#4), and 234 (#6) isotopologue spectral simulations with a Gaussian convolution full width at half-magnitude (FWHM) = 1 cm −1 , and their intensity as scaled by the terrestrial abundances.Take the 222 spectra (red) as an example: The first peak at 95 cm −1 is the ν 3 ← 2ν 1 hot band, followed by ν 1 ← ν 2 at 260 cm −1 and the linear bending fundamental ν 2 at 396 cm −1 .The strongest band is the antisymmetric stretching mode fundamental ν 3 at 1540 cm −1 .It leads to a series of cold bands from ν 3 + ν 1 , ν 3 + 2ν 2 , ν 3 + 2ν 1 , and ν 3 + ν 1 + 2ν 2 to ν 3 + 4ν 2 , ν 3 + 3ν 1 , ν 3 + 2ν 1 + 2ν 2 , and ν 3 + ν 1 + 4ν 2 , etc. Their peak magnitude decreases along with a rising polyad number.The 3ν 3 band at 4570 cm −1 leads to another peak series extending beyond 7000 cm −1 , with a similar pattern of intensity reduction.The 5ν 3 band at 7549 cm −1 starts a new series covering the strongest bands between 7500 cm −1 and 10,000 cm −1 .Please note that the CS 2 hot band series have intensities decreasing slowly when the vibrational quanta increase, and they also have small redshifts with respect to the original cold bands rising from the vibrational ground state.This means one needs many more hot bands and hot transitions to converge the total intensity in a spectral window.For example, we recommend using 10 −35 cm −1 /molecule•cm −2 or a lower cutoff to ensure the S total in a 1 cm −1 window converges to the 10 −31 cm −1 /molecule•cm −2 level.
When an 32 S atom is replaced by an 33/34/36 S isotope, the symmetry is broken, and more bands become IR active.For example, the 2ν 3 bands of the 224 isotopologue appear at 3043 cm −1 (see Figure 6) with S max = 1.2 × 10 −24 cm −1 / molecule•cm −2 for transition P31.Because the 3ν 3 band is 25 times stronger than 2ν 3 , overall the perturbation of 33/34/36 S substitution and symmetry breaking on IR spectra is not really significant, and is only noticeable in a few valleys at lower energy, e.g., below 5000 cm −1 .As a result, in Figure 6, apparently nearly all major features of 224 and 234 are under the counterparts of 222 and 232 (with higher abundances), especially in the range of 7000 cm −1 above.

Ames-296K "Natural" Line List
The individual Ames-296K IR line lists of the 20 CS 2 isotopologues are combined to generate a "natural" IR line list, in which their intensities are scaled by the abundances given in Table 2. Compared to those of other triatomic molecules like H 2 O and CO 2 , the abundances of minor isotopologues are higher by about 1 order of magnitude.Consequently, the intensity contributions from many symmetric and asymmetric minor isotopologues are critical for any highly accurate IR simulation or analysis.As demonstrated in the bottom panel of Figure 6, the ratio of intensity contributions in a 1 cm −1 window from the 224 and 232 isotopologues may easily reach 0.5-1.0, or 50%-100%.
The terrestrial "natural" abundance values for the first four isotopologues, from 222 to 232, are taken from HITRAN2020.The abundance values for the other isotopologues are estimated using the following isotopic ratios: 12 C: 13 C = 0.9893 : 0.0107, and 32 S: 33 S: 34 S: 36 S = 0.9493 : 0.0076 : 0.0429 : 0.0002.The sum of the 20 abundance values in Table 2 is 1.000122.The 0.000122 residual is due to the differences between the HITRAN terrestrial abundances and our isotopic-ratio-based abundance estimations.Its impact on the spectrum simulation or overall consistency can be safely ignored.On the other hand, the #20 (636) isotopologue has a very low abundance at the 10 −10 level.Because the next minor isotopologue ( 14 C-substituted 242) probably has an abundance at the 10 −12 level, and all other excluded isotopologues carry either 14 C or radioactive 35 S, we believe the Ames-296K lists are sufficient to meet the needs of most practical applications in atmospheric and spectroscopic studies at room temperature.
This "natural" line list has 9,874,405 transitions with abundance-scaled S 296K > 10 −31 cm −1 /molecule•cm −2 .An overview spectrum is also given in Figure 6, with Gaussian convolution FWHM = 1 cm −1 .The isotopic shifts of some band origins are comparable to IR-band spacings, resulting in spectral regions dominated by minor-isotopologue intensities.For example, the IR absorptions of 13 C-substituted CS 2 (232) are the main contributors at 820, 1467, 2240, and 2876 cm −1 , and at the strong band series of 4410, 5035, 5620 cm −1 , etc. Please note that multiple isotopologues may have comparable intensity contributions in a spectral range, indicating higher importance for some less abundant isotopologues.For example, in the "natural" line list, the 2ν 3 band series of 224 and the ν 3 + 4ν 2 band series of 232 accidentally overlap at 3040 cm −1 , with comparable intensities.
As a result, the intensity contributions from many symmetric and asymmetric minor isotopologues are critical for any highly accurate IR simulation or analysis.After running more tests, we conclude that the six most abundant isotopologues are required Intensities are scaled by their terrestrial abundances.The Gaussian convolution uses FWHM = 1 cm −1 .The "natural" CS 2 line list of 20 isotopologues is plotted as a black line in the top panel.At the bottom, the ratios of four isotopologue intensities to the total intensity in the "natural" list are presented, as examples for the significance of minor-isotopologue contributions.A complete overview of the 20 isotopologue line lists is available at https://huang.seti.org/CS2/cs2.html.
to guarantee >90% intensity coverage at 296 K for all cm −1 intervals between 0 and 10,000 cm −1 : 222 > 224 ≈ 232 > 223 ≈ 234 > 424, sorted by their contribution to the intensity completeness.The weights of the 222, 224, 232, and 234 isotopologues in the intensity sums are plotted in the bottom panel of Figure 6.The ratio of intensity contributions in a 1 cm −1 window from the 224 and 232 isotopologues may easily reach 0.5-1.0, or 50%-100%.Many more isotopologues will be needed to ensure 99% intensity-or for narrower spectral windows, e.g., 0.1 cm −1 .Therefore, we should include more minor isotopologues in highly accurate terrestrial analyses and IR simulations.Currently, there are only four isotopologues in HITRAN2020.Here we recommend the Ames "natural" list as a valuable guide, which can help scientists to decide which isotopologues to consider in future experimental analyses.

A+I.296K List for 222 Isotopologue
The differences δ = E Ames − E Heff for energy levels under 4500 cm −1 are in the range of 0-5 cm −1 .From 5000 to 9000 cm −1 , the discrepancy rises quickly, and the δ range expands to −35 to 5 cm −1 .Due to the Ames-1 PES deficiencies, the vibrational quanta of ν 2 and ν 1 have significant impact on the δ differences.In general, higher ν 1 quanta are associated with larger E Heff -E Ames differences (or −δ), and higher ν 2 quanta are connected to a wider δ range (e.g., −25 to 5 cm −1 ) by forming a larger polyad between nν 1 and 2nν 2 .Beyond 5000 cm −1 , the impact of nν 1 differences outweighs the impact of nν 2 differences.
An important question is how to evaluate if matches are reliable or correct.After trials and failures, we have learned to monitor the pattern of energy differences, δ = E Ames − E Heff , in matched pairs.The inset graph of Figure 7 plots the δ in the range of 0-4000 cm −1 , where we can see many black strips parallel to the horizontal axis and the baseline δ = 0.Each strip represents a vibrational state, and its δ has small or negligible J dependence.That is why they are parallel along the energy (J) coordinate.The separations between the strips show the deviations of vibrational-band origins growing at higher vibrational quanta and higher energy.If a δ series crosses those strips along a tilted or nearly perpendicular direction, they are likely outliers due to mismatches.Then we need to identify the source of the mismatches, modify the program accordingly, rerun the matching program, and check again, until the obvious δ outliers are fixed.Therefore, further details of this process are usually dependent on the molecule, PES, energy range, effective Hamiltonian model, and variational calculations.
At higher energies, it is more difficult to identify and remove all mismatches or irregularities, as shown in Figure 7 above 5000 cm −1 .The δ strips are still parallel to one another but exhibit positive J dependence of a few wavenumbers, and there are recognizable thin hairs crossing the strips.For this reason, energy-level matches and replacements above 7000 cm −1 may  Notes.The number of lines in the individual isotopologue line list (10 −31 cm −1 /molecule•cm −2 , 100% abundance) is also given for comparison.See text for more details.
contain a relatively higher percentage of mismatches, though most replacements are still reliable.The impact of potential mismatches is expected to be negligible or small at room temperature.Future matches at high energies should also consider the high density of states and convergence of variational CI calculations.This will be more important for line lists targeting a higher temperature.If an Ames-2 PES refinement yields better agreement with the H eff model, the chances of mismatches may be significantly reduced at higher energies.One potential solution is to refine the ab initio PES with respect to the global H eff levels, as we did for the CO 2 line list (Huang et al. 2023a).The numbers of 12 C 32 S 2 (222) levels computed on the Ames-1 PES at each J and parity symmetry block are plotted in Figure 8 as black squares.The maximum number is between 700 and 900 and near J = 18.These levels are matched to their counterparts in the global effective Hamiltonian model.The matching rate varies between 91% and 100%.In total, 185,022 out of 190,529 levels are matched-an overall matching rate of 97.1%.
In the Ames-296K line list for the main isotopologue, the E Ames energies are replaced by the H eff model energies for their counterparts in matched pairs (if available).After the replacements, the new line list of 222 is denoted as A+I.296K,where "A" and "I" refer to "Ames" and "IAO," respectively.Therefore, the A+I.296K line list integrates the experimentbased 12 C 32 S 2 line positions with ab initio intensity predictions computed on a PES semiempirically refined with experiment data and a high-quality ab initio DMS.

HITRAN-based Line Positions for 224, 223, and 232
After the significant enhancement of line position accuracy for 222 transitions, it would be ideal if the transitions of other important minor isotopologues could have similar improvements.For the 224, 223, and 232 isotopologues, we choose to combine the Ames-296K intensity predictions with the highly accurate upper and lower rovibrational state energies in HITRAN2020.But due to the overextrapolations of local H eff models (e.g., those illustrated in Figure 5) and other factors, the line position of certain bands requires extra attention and band/ J/isospecific adjustments.These adjustments are determined based on the isotopologue consistency and the linear J dependence of δ deviations, which we usually find with line lists constructed with BTRHE or like algorithms.Therefore, the reliable δ Heff (Ames versus H eff ) of the main isotopologue (222) or the δ HITRAN (Ames versus HITRAN) of lower J or from other isotopologues may be used as alternatives for the unreliable δ HITRAN , when necessary.Below is a list of our special adjustments, and our corrected energy E′ equals E Ames minus the adjustment δ HITRAN .In addition to the overextrapolation of H eff models at high J, some adjustments are due to missing data, or less accurate data in HITRAN.The accuracy of these adjustments, or predictions, will be judged by future experiments.
For the 223 isotopologue, we use δ HITRAN (224) for J 77 levels of the 1001e state, half of δ HITRAN for J 66 levels of the 0003e state, and the δ HITRAN average of the J = 144 and J = 146 levels of the 0003e state for its J = 145 level.For the 224 isotopologue, the δ HITRAN of the 0110e and 0113e levels are used for the δ HITRAN of their corresponding 0110f and 0113f levels (assuming E Ames has similar accuracy for the e/f branches); for the 0220e state the mean value of δ HITRAN computed from the J = 2-77 levels is adopted for the δ HITRAN of J > 80 levels; and for the 0003e state the δ HITRAN of the J = 10, 14, 24, 29, and 81 levels are interpolated from the δ HITRAN values of their neighboring J levels.For the 232 isotopologue, the 0330e state uses the mean value of δ HITRAN computed from the J = 3-61 levels as the adjusted δ HITRAN for J 63 levels, and the 3001e state uses the average δ HITRAN of the J = 109 and J = 113 levels as the adjusted δ HITRAN for the J = 111 level.

Results and Discussion: Line Shape and Validation
In order to validate the new line list against the PNNL spectra, we supplement it with air-broadening parameters, and their temperature dependencies are calculated using the Padé approximants reported in Karlovets et al. (2021).These approximants are based on fits to experimental data from Misago et al. (2007, 2009) and Kongolo Tshikala et al. (2012, 2014).A short Python program is given in the Zenodo and AHED repositories.The cross sections derived from this and the HITRAN2020 line list are calculated (and convoluted) using HAPI (Kochanov et al. 2016) assuming the same conditions reported in PNNL.These experimental cross sections are at 298.1 K and 1 atm of buffer nitrogen (N 2 ) gas and are recorded with 0.112 cm −1 resolution using a Fourier transform spectrometer.Comparisons demonstrate a substantial improvement in all observed bands when using the new line list with respect to the HITRAN2020 data.Figure 9 shows the region of strongest absorption, which is mainly due to the ν 3 band.The top panel shows a weaker absorption due to isotopologues (primarily 13 CS 2 , which is shifted more relative to 12 C-containing isotopologues), while the bottom panel shows the region underlying the stretching fundamental band of the principal isotopologue.While the fundamental provides the strongest contribution to the absorption for all isotopologues, there are multiple hot bands that contribute significantly to the total absorption, most notably the ν 2 + ν 3 − ν 2 band.
Figures 10 and 11 provide comparison in the regions of strongest hot bands and combination bands.While sometimes residuals are comparable in general the new line list is a clear improvement.Remaining differences can be attributed to the fact that we use air (i.e., a mixture of nitrogen and oxygen) instead of pure nitrogen when calculating broadening effects, while also ignoring the effect of line mixing that would be especially pronounced in the Q-branches due to a higher density of lines.Due to the fact that the PNNL data below 1 × 10 −22 cm 2 molecule −1 are contaminated by noise, we do not show detailed comparisons with weaker bands, but inspection of the spectrum also gives an idea of improvement.

Summary and Future Work
The Ames-0 PES and Ames-1 PES refinement were finalized in 2020-2021, after Karlovets et al. (2021) was published.In 2021 December, the first set of Ames-296K line lists were put online at https://huang.seti.org/CS2/cs2.htmlfor the five most abundant isotopologues, but they were computed using the old DMS that exhibited intensity noise above 10,000 cm −1 .In 2022 June, those line lists were recomputed using the updated VTET program to fix the small intensity gap at J = 0 and oscillations in the Q-branch, and using the final Ames-1 DMS of 165 coefficients to minimize intensity noise.Tashkun independently published the global effective Hamiltonian model in late 2022.In 2023 June, the matches between the Ames-1 PES levels and the global effective Hamiltonian model were completed, and the A+I.296K line list for the main isotopologue 222 was put online.Reliable HITRAN levels of 224, 232, and 223 were also utilized to further enhance the quality of the natural CS 2 line list.From 2022 July to 2022 September, the number of minor isotopologues included in the Ames "natural" CS 2 line list expanded from 12 to 20.The "natural" list was finalized in 2023 December.
The timeline above explains why this paper is the first of the series for CS 2 IR line lists.Obviously, future Ames PES refinements should incorporate experimental data for higher energy levels, especially the ν 2 and ν 1 overtone-related bands.It may be necessary to investigate different representations for the short-range part of the potential energy, and to determine a reliable set of vibrational-band origins up to 12,000 cm −1 or higher.A reliable estimate is preferred for the accuracy and uncertainty of rovibrational experimental data beyond 10,000 cm −1 .These parts are in preparation.On the other hand, intensity calculations can be improved by more accurate DMS fitting and more robust ab initio calculations.For example, more ab initio points and higher fitting weights will reduce the fitting error in certain energy ranges and generate more accurate higher-order dipole terms, which may have noticeable impact on the intensity of some hot bands or higherorder vibrational excitations.We have started working on this aspect.A more accurate DMS fitting with more advanced ab initio calculations is expected in 2024.Another major direction of enhancements is to collaborate with experimentalists in unexplored spectral regions or conditions.
The dissociation temperature of CS 2 is higher than 1000 K, with CS and S 2 as the main products.A line list suitable for higher temperature will be helpful.However, the very high density of states of CS 2 beyond 10,000 cm −1 provides a challenge to the convergence of rovibrational energy levels and subsequent intensity calculations, due to a large variational configuration-interaction (CI) basis, a large number of roots, and the fact that even more hot band series must be included to ensure the intensity sum is satisfactorily converged.This direction will be explored stepwise with discretion.For example, a line list for 500 K should converge well before a line list for 1000 K is computed.
Related data files have been uploaded to online databases, including PESs, DMSs, line lists, and ORIGIN project files for figures and some analyses presented in this paper.They are available on Zenodo at doi:10.5281/zenodo.10715006,and on AHED at doi:10.48667/8h4w-8p21.
Due to the clear improvements demonstrated here we propose to use the line list (or parts of it) calculated in this work in future updates of the HITRAN database.

Figure 1 .
Figure1.Statistics of fitting deviation |δ| in the least-squares fit of the pure ab initio PES selected for refinement.Legend: "avg" is the average absolute value (filled square), "rms" is the rms error (σ rms , half-filled circle) in each energy interval of 1000 cm −1 , and the "accu" open symbols indicate the accumulated deviations from 0 cm −1 .

Figure 2 .
Figure2.Left: fitting residual δ (left y, in atomic units) and relative deviation δ% (right y, in percentage) of Ames-1 DMS least-squares fit; right: mean and σ rms statistics on the δ and δ% of the dipole x-and y-component in each 1000 cm −1 interval, and accumulated values from 0 cm −1 ("accu").

Figure 4 .
Figure 4. (Left) J dependence of energy-level difference δE = E Ames − E HITRAN for 12 C 32 S 2 .(Right) Line position difference between Ames-296K line list and HITRAN2020 for four CS 2 isotopologues.

Figure 6 .
Figure6.Overview of IR simulation of four CS 2 isotopologues: 222 (red), 224 (blue), 232 (magenta), and 234 (green).Intensities are scaled by their terrestrial abundances.The Gaussian convolution uses FWHM = 1 cm −1 .The "natural" CS 2 line list of 20 isotopologues is plotted as a black line in the top panel.At the bottom, the ratios of four isotopologue intensities to the total intensity in the "natural" list are presented, as examples for the significance of minor-isotopologue contributions.A complete overview of the 20 isotopologue line lists is available at https://huang.seti.org/CS2/cs2.html.

Figure 7 .
Figure7.Energy difference between Ames-1 PES based levels and H eff model levels.

Figure 8 .
Figure8.Left vertical axis: number of 12 C 32 S 2 (222) levels on Ames-1 PES in the range of 0-9000 cm −1 , J max = 200; right vertical axis: percentage of Ames-1 PES levels matched to the global effective Hamiltonian (H eff ) levels.

Figure 9 .
Figure 9.Comparison of cross sections generated from the line lists from this work and PNNL experimental cross sections in the region of the ν 3 band.The top panel shows weaker absorption primarily due to isotopologues, while the bottom panel shows the region underlying the ν 3 fundamental of the principal isotopologue.Note the different scales on the panels."HIT"-HITRAN, "TW"-this work.

Figure 10 .
Figure 10.Comparison of cross sections generated from the line lists from this work and PNNL experimental cross sections in different regions.The top panel shows the absorption region where multiple hot bands overlap including the strongest (in this region) ν 3 -ν 1 band, while the bottom panel shows the region underlying the ν 1 + ν 3 combination band.Note the different scales on the panels."HIT"-HITRAN, "TW"-this work.

Figure 11 .
Figure 11.Comparison of cross sections generated from the line lists from this work and PNNL experimental cross sections in different combination bands and their hot bands.The top panel shows the absorption region dominated by the 2ν 2 + ν 3 band, while the bottom panel shows the region underlying the 2ν 1 + ν 3 combination band.Note the different scales on the panels."HIT"-HITRAN, "TW"-this work.

Table 1
ZPE, Degeneracy g, and Partition Function Q/g at 296 K for 20 CS 2 Isotopologues The partition functions Q/g are computed from J = 0-200 levels on the Ames-1 PES with E max = 0.10 Hartree (222) or 0.07 Hartree (minor isotopologues).They are compared to the H eff model based Q values in HITRAN2016 and HITRAN2020.

Table 2
Abundance Values and Number of Transitions for 20 CS 2 Isotopologues in the Ames-296K "Natural" IR Line List