Ames-2016 line lists for 13 isotopologues of CO2: Updates, consistency, and remaining issues

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Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues Xinchuan Huang () a,b,∗, David W. Schwenke c, Richard S. Freedman a,b, Timothy J. Lee d,∗ a

MS 245-6, Astrophysics Branch, Space Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA 94035, USA SETI Institute, 189 Bernardo Avenue, Suite 200, Mountain View, CA 94043, USA MS 258-2, NAS Facility, NASA Ames Research Center, Moffett Field, CA 94035, USA d MS 245-3, Planetary Sciences Branch, Space Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA 94035, USA b c

a r t i c l e

i n f o

Article history: Received 14 January 2017 Revised 21 April 2017 Accepted 21 April 2017 Available online xxx Keywords: Carbon dioxide Infrared intensity Line list Isotopologues Semi-empirical refinement Spectroscopic database Potential energy surface Dipole moment surface Rovibrational

a b s t r a c t A new 626-based Ames-2 PES refinement and Ames-2016 line lists for 13 CO2 isotopologues are reported. A consistent σ RMS = ±0.02 cm−1 is established for hundreds of isotopologue band origins using the Ames2 PES. Ames-2016 line lists are computed at 296 K, 10 0 0 K and 40 0 0 K using the Ames-2 PES and the same DMS-N2 dipole surface used previously, with J up to 150, E up to 24,0 0 0 cm−1 or 18,0 0 0 cm−1 and appropriate intensity cutoffs. The lists are compared to the CDSD-296, CDSD-40 0 0 databases, UCL line lists, and a few recent highly accurate CO2 intensity measurements. Both agreements and discrepancies are discussed. Compared to the old Ames CO2 lists, the Ames-2016 line lists have line position deviations reduced by 50% or more, which consequently leads to more reliable intensities. The line shape parameters in the Ames-2016 line lists are predicted using the newly assigned conventional vibrational polyad quantum numbers for rovibrational levels below 12,0 0 0 cm−1 so the quality of the line shape parameters is similar to that of CDSD or HITRAN. This study further proves that a semi-empirically refined PES (Ames-1 and Ames-2) coupled with a high quality ab initio DMS (DMS-N2 and UCL) may generate IR predictions with consistent accuracy and is thus helpful in the analysis of laboratory spectra and simulations of various isotopologues. The Ames-2016 lists based on DMS-N2 have reached the ∼1% intensity prediction accuracy level for the recent 626 30 013-0 0 0 01 and 20 013-0 0 0 01 bands, but further quantification and improvements require sub-percent or sub-half-percent accurate experimental intensities. The inter-isotopologue consistency of the intensity prediction accuracies should have reached better than 1– 3% for regular bands not affected by resonances. Since the Effective Dipole Models (EDM) in CDSD and HITRAN have 1–20% or even larger uncertainties, we show that the Ames lists can provide better alternative IR data for many hard-to-determine isotopologue bands. Comparison at 40 0 0 K suggests that the Ames-40 0 0 K 12 C16 O2 line list is reliable and consistent within the current cutoffs of J ≤ 150 and E ≤ 24,0 0 0 cm−1 , but intensity contributions involving higher energy levels should not be omitted and future computations need to be converged up to at least 32,0 0 0 cm−1 or higher. The remaining issues are discussed regarding the source of energy level discrepancies, intensity underestimations by ∼50% for some weak bands, etc. and also future work. © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

1. Introduction

∗ Corresponding authors at: MS 245-6, Astrophysics Branch, and MS 245-3, Planetary Sciences Branch, Space Science and Astrobiology Division, NASA Ames Research Center, Moffett Field, CA 94035, USA. E-mail addresses: [email protected] (X. Huang ()), [email protected] (D.W. Schwenke), [email protected] (R.S. Freedman), [email protected] (T.J. Lee).

From 2012 to 2014, we reported the Ames-296 K and Ames10 0 0 K line lists for 13 CO2 isotopologues with line shape parameters [1–3]. The 13 isotopologues include twelve 12/13 C and 17/18 O isotopologues, and the radioactive 14 C16 O 2 isotopologue. The CO2 line lists were computed with a pure ab initio dipole moment surface (DMS) and a semi-empirically refined potential energy surface (PES), denoted Ames-1. The PES was refined using a few hundreds of the reliable experimentally measured

http://dx.doi.org/10.1016/j.jqsrt.2017.04.026 0022-4073/© 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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rovibrational energy levels. More details of these energy levels can be found in Ref. 1. The main merit of the published Ames line lists is the predictive accuracy for different CO2 isotopologues. The overall agreement with recent experimental measurements is better than 0.10 cm−1 (line positions) and 80–90% (intensities) or better for moderate to strong bands in the 40 0 0–12,0 0 0 cm−1 region [4–9]. Mean and root-mean-square (RMS) residuals of relative intensity deviations S are consistent among the isotopologues, usually ∼5–10% [10,11]. For the main isotopologue 626, Ames intensities of the 30 013-0 0 0 01 and 20 013-0 0 0 01 bands match high accuracy intensity measurements to the ∼1% level [12,13]. In short, reliable predictions from the Ames CO2 lists provide a more complete and consistent alternative and valuable reference data for missing bands or isotopologue spectral analysis, as well as for higher temperature IR simulations. On the other hand, the published Ames-1 PES and Ames line lists were affected by limitations and defects. For example, the stretching basis convergence defect [14] has led to unphysical “Jjumps” and 0.10–0.15 cm−1 band origin deviations of 17/18 O related isotopologues [1]. The variationally computed [15,16] energy levels were assigned using the leading configuration-interaction (CI) bases which are strongly dependent on the coordinate and basis utilized in the variational CI calculations. Such assignments are hard to match or compare with the conventional vibrational polyad assignments that experimental analyses and databases usually use. For some high-lying weak bands, the Ames intensity predictions are ∼20–50% away from reported intensity measurements, e.g. Refs. 8,9. In recent studies, the S(Ames) /S(Expt) or S(Ames) /S(H_eff) ratio curve is found to be not continuous at J = 0, with a ∼0.6% difference between the P branch and the R branch of strong 626 bands [12,13]. Also minor oscillations are found for even/odd J intensities of some ν 2 -related bands or asymmetric isotopologues. Recently we have re-run the PES refinement procedure to remove the basis defect and determine a new PES, denoted Ames-2. Isotopologue band origins computed on this Ames-2 PES are consistently within ±0.02 cm−1 . Details of the new refinement and the quality of the Ames-2 PES will be discussed in the next section. Rovibrational, intensity and line list calculations are carried out accordingly using the Ames-2 PES. Conventional vibrational polyad quantum numbers are assigned to most variationally computed rovibrational energy levels below 12,0 0 0 cm−1 . These vibrational quantum numbers are the necessary input for line shape parameter programs [17,3]. Therefore, the new Ames CO2 lists have more accurate or reasonable values for line positions, lower state energies, intensities, and line shape parameters. For the intensity break at J = 0, the source has also been identified and fixes will be made available in future updates. Compared to the Ames-1 PES and line lists, the new PES and lists focus on better line positions, and more consistent intensity predictions, especially among isotopologues. In addition to those spectral measurements mentioned above, more high resolution IR spectra have been recorded and analyzed in the last a few years for CO2 isotopologues, e.g. see Refs. [18,19,20,21,22]. A lot of new bands were reported for isotopologue data missing from HITRAN2012 [23]. Part of these new measurements and their Effective Hamiltonian (EH, or H_eff) models has been incorporated in the latest CDSD-296 database [24]. It has the best collection of CO2 EH models across isotopologues, so our Ames CO2 lists are first compared to CDSD-296 . A high quality MRCI/aug-cc-pwCVQZ DMS [5] was reported by Tennyson’s group at University College London (UCL). It has been adopted in the recent UCL line list computations for both the main 626 and minor isotopologues in the 0–80 0 0 cm−1 range [25–27]. The Ames-1 PES was used in the UCL line lists calculations. When compared to CDSD-296 K intensity data, the agreement for the UCL data on several of the strongest CO2 bands is 1–3% better than the

earlier Ames lists. For the rest of the CDSD band intensities, very similar performance was reported, but with exceptions (e.g. the 0 0 031-0 0 0 01 band) [25,26]. Compared to 2015–2016 experimental measurements of the 626 30,013-0 0 0 01 [5,12] and 20,013-0 0 0 01 bands [13], the UCL 626 list demonstrated that a high-quality ab initio dipole surface can help reach sub-percent accuracy for certain strong CO2 IR bands. If theoretical IR spectroscopy could seriously claim systematic sub-percent intensity accuracy for most CO2 bands, it indicates a new era for our CO2 spectral knowledge and simulations. However, experimental intensities rarely exist for subhalf-percent or sub-percent accuracy. Additional experimental and theoretical efforts are required for confirmation or additional evidence for a wide range of spectra and isotopologues. Thus it is of interest to report what we have found from the latest Ames lists and our analysis, including the PES dependence and DMS dependence of the band intensities. Note that Ames individual isotopologue line lists always use 100% abundances, while both Refs. 12 and 13 assumed that terrestrial abundances had been used in the Ames-296K 626 intensities. This caused a 1.6% shift in all related line intensity comparison figures. Here we report corrected comparisons, with proper abundances. Many aspects discussed in this paper deserve deeper or more thorough investigations. In other words, several topics may easily extend to full-length, independent papers. As the concluding summary of our Ames CO2 project, this paper will be more inclusive and up to date, touching the core facts as much as possible, but limited to simple examples and/or short discussions. Pointing out future directions and providing prompt updates online are more important for the next phase of our CO2 line list project. The paper is organized as follows: Section 2 describes the Ames-2 PES refinement and the quality of the PES. Section 3 compares the new Ames-296K lists to recent 30 013-0 0 0 01 and 20 013-0 0 0 01 experiments [12,13], UCL line lists [25,26], and the CDSD-296 database [24]. The various discussions in this section reflect our latest understanding of the advantages, limitations and sensitivities of the “Best Theory + Reliable High-Resolution Experimental Data” strategy. It also discusses the potential source of discrepancies reported in recent experiments (e.g. Ref. 8), what we can do, and the subjects worth investigating in the future. Section 4 focuses on the Ames vs. CDSD-296 intensity comparisons. It confirms the predictive power and isotopologues intensity consistency and that the Ames CO2 line lists can provide a reliable alternative for missing data or help to identify unreliable intensity data or models. Section 5 presents a comparison between the new Ames-40 0 0K lists and the CDSD-40 0 0 database (2014 version) [28], and discusses advantages, limitations, and future improvements. Finally, an example is given in Section 6 to show the accuracy and reliability of the Ames list predictions for a 17 O12 C18 O band. Similar to previous Ames-1 based lists reported in Ref. 3, the new Ames-2016 lists have complete coverage for J up to 150 and E up to 18,0 0 0 cm−1 (asymmetric isotopologues) or 24,0 0 0 cm−1 (symmetric isotopologues). The actual spectroscopic range depends on the intensity cutoffs adopted. Currently, the size-reduced version of the latest Ames-2 PES and DMS-N2 [2] based CO2 296 K line lists with Vogit profile line shape parameters are available at http://huang.seti.org/CO2/. The website may have future updates from time to time to reflect the latest improvements and fixes, e.g. more complete vibrational polyad quantum numbering at higher energies. For the reader’s convenience, Table 1 gives a short summary on several line lists and databases compared in this paper. Most values of the earlier Ames CO2 lists (2012–2014) are similar to those of the Ames-2016 lists, so they are not separately listed. Note the Ames and UCL lists are complete with respect to the specified intensity cutoff, frequency and J ranges, while CDSD lists have gaps or incomplete band coverage.

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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Table 1 Four sets of CO2 IR line lists compared in this study. The No. of lines refers to 626 list, except CDSD-296 K. EH and EDM refer to “Effective Hamiltonian” and “Effective Dipole Moment” models. CDSD-296K

CDSD-40 0 0 (626)

UCL (626)

Ames-2016 (626)

#Iso PES or EH DMS or EDM S Cutoff

12 EH EDM 1E-30

4 EH EDM 7.3E-109 (296 K)

12 Ames-1 PES MRCI/aug-cc-pwCVQZ 1E-30 (296 K)

Freq. range

6–14,075 cm−1

226–8310 cm−1

0–80 0 0 cm−1

J range

0–129

0–300

0–129

E /E range

15,562/6533 cm−1

<43,522 cm−1

11,400/6550 cm−1

No. of lines

534,227

573,881,316

152,260

13 Ames-2 PES CCSD(T)/aug-cc-pVQZ 1E-42 (296 K and 296 K reduced) 1E-29 or 1E-30 (40 0 0 K) 1–23,800 cm−1 (296 K) 8–14,884 cm−1 (40 0 0 K) 0–150 (296 K), 0–133 (296 K, reduced) 0–220 (40 0 0 K) 24,0 0 0 cm−1 /8257 cm−1 (296 K, reduced) <24,0 0 0 cm−1 (296 K, 40 0 0 K) 813,119 (296 K, reduced) 20,789,926 (296 K) 471,916,316 (40 0 0 K)

Many vibrational bands are discussed in this paper. They are selected because their intensity data carries very high accuracy, or the comparison demonstrates the deficits of existing databases, and the accuracy or potential deficiency of current Ames lists. 2. Ames-2 PES refinement and band origins At Ames, the “Best Theory + Reliable High-Resolution Experimental Data” strategy has been applied to H2 O [15], NH3 [29,30], SO2 [31] and CO2 [1]. Details of the CO2 Ames-1 PES refinement are not repeated here. It used 471 purely experimental 12 C16 O2 rovibrational levels as reference [1]. On the refined Ames-1 PES, 6873 purely experimentally determined 626 rovibrational levels were reproduced with the root-mean-square (RMS) error σ RMS consistently less than 0.02 cm−1 in J = 0–117. The overextrapolations in the old HITRAN databases prevented us from getting σ RMS better than 0.08 cm−1 in the high J region [1]. Later we found an internal parameter was not tightly converged for the C-O stretching basis [14]. This defect was automatically compensated during the 626based Ames-1 refinement. Consequently, 626 and 636 band origin accuracies were not significantly affected, but it caused damages to the accuracy for the 17/18 O isotopologues, where deviations for band origins could be as large as 0.10–0.15 cm−1 [1]. Even for 626 and 636, the defect has led to minor breaks on the J-ladder of energy levels [1] and intensity comparison to the measurement from Ref. 13. In order to fix the defect, the Ames-1 PES was used as a new “initial” surface on which we compute integral matrix elements over the to-be-refined short-range potential expansion coefficients up to quartic level using the VTET [32] diagonalized Hamiltonian matrices [15]. These integral matrix elements are multiplied by the minor changes of respective coefficients to simulate the changes of the final Hamiltonian matrix. In this 1st refinement, more than 300 band origins and 1101 J = 5/10/25/40/55 levels of 12 isotopologues were included. The final σ RMS for the ∼1400 levels was 0.0146 cm−1 . However, the refined PES is not the best replacement for the Ames-1 PES, which was 100% 626-based. This is because the massdependent corrections cannot be ignored if one prefers uniform accuracy for ALL isotopologues. It is especially true for those high J energy levels of 828 and 838 where the mass-dependent corrections are more significant than the other minor isotopologues, when compared to the main isotopologue 626. Therefore, this refined PES was “refined” again using exactly the same energy level set as used in the Ames-1 PES refinement. In this way, the 2nd refined PES is still 626-based, with a final σ RMS = 0.019 cm−1 for the energy level set. The refined PES is denoted Ames-2 and used in all the line list calculations discussed in this paper (unless specified otherwise).

During the Ames-1 PES refinement, we reported three highlying Gv above 22,0 0 0 cm−1 could not be matched down to an accuracy of ∼0.1 cm−1 . Now in the latest refinement procedure, we found that they can be reproduced with deviations less than 0.10 cm−1 . This may suggest the auto-fixing function of our procedure (when exactly same parameters are used, see the Note of Ref. 3) has its own accuracy limits at higher wavenumbers. Here the “auto-fixing function” refers to the fact that, although the old Ames-1 PES refinement was carried out with not strictly converged C-O stretch potential matrix parameter, the refined Ames-1 PES still works for 626 and 636 band origins, as long as we use the exactly same set of parameters before, during and after the refinements. The high lying overtone states may still lie within the range that does not require nonadiabatic corrections. To be consistent with Ames-1, the three high-lying Gv  s were not included in the Ames-2 refinement. For any mass-independent CO2 PES, it is essentially impossible to maintain consistent σ RMS = 0.01–0.02 cm−1 accuracy for all isotopologues in a wide range of J. Actually, a single number of a final σ RMS is not sufficient to describe the quality of the refinement that includes thousands of rovibrational energy levels of various isotopologues. It is necessary to look at the accuracy for each individual isotopologue and to balance the weights of higher J levels vs. lower J levels and the weights between heavier vs. lighter isotopologues. Fig. 1 shows how the accuracy of 626 and 828 rovibrational levels would vary from a 626-focused PES (top) to a more 828-focused PES (bottom). On the 626-based PES refinement similar to Ames-1 and Ames-2, the 626 level deviations are consistent in the J range while the 828 level deviations increase linearly along with J. The PES refinement shown at Fig. 1 bottom adopted higher weights on the 828 and 838 energy levels, although the 838 levels are not included in Fig. 1. Consequently, the 828 J dependence is significantly reduced (if not completely removed), while the 626 energy level deviations on that PES already show clear positive J dependence. As we know, Diagonal Born-Oppenheimer Corrections (DBOC) terms and nonadiabatic corrections are necessary to achieve such accuracy for all isotopologues [33–35]. It is very important to distinguish the measured (or refined) band origins and those predicted from EH models (or computed on the refined PES). All the band origin Gv values adopted in the refinement should be experimentally measured, or carrying uncertainties less than 0.01 cm−1 . As one can see from Fig. 2a, the Ames-2 PES performs very well for these band origins, where most deviations are within ±0.02 cm−1 . However, if we compare the 626 levels computed on the Ames-2 PES to those Gv predictions from CDSD-296 [24] and CDSD-40 0 0 [28] EH models, significant differences are found. See Fig. 2b. From 7400 cm−1 to 18,0 0 0 cm−1 , the largest Gv difference E increases from 0.2 cm−1 to ±5 cm−1 .

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els included in the PES refinement is usually consistently as good as or similar to that of reference data reproduction [30,31,36]. Here we found >0.05 cm−1 discrepancy in Ames vs. CDSD comparison. It starts from the 50 0 06 state at 6240 cm−1 : Band

40005 50006 60007 70008

CDSD

5022.3413 6240.0116 7447.4843 8646.0582

Ames

Ames-CDSD

5022.3602 6240.0951 7447.7048 8646.5208

0.02 0.08 0.22 0.46

Vib. States(l2 = 0)

8ν 2 10ν 2 12ν 2 14ν 2

The E discrepancies get larger for higher order overtones, e.g. 60 0 07 and 70 0 08. These ν 2 high-order overtones are predicted by an EH model. In CDSD-296, two very weak hot-bands are associated with 50 0 06. We believe all CDSD and HITRAN transitions of these two bands are EH-based predictions, i.e. no experimental data were ever recorded. In the two bands, the strongest transitions at 296 K are:

Fig. 1. Two PES refinement examples: (top) 626-based, similar to Ames-1 and Ames-2; (bottom) 828-oriented. 626 and 828 J = 0–90 levels are computed and compared to available CDSD data. The J-dependence of energy level deviations indicates the 626 and 828 need different mass-dependent corrections.

Note the E is computed as the difference between a E(CDSD) and the closest E(Ames) . Beyond 13,0 0 0 cm−1 , most Ames and CDSD levels are extrapolations. We acknowledge some CDSD predictions are more reliable than our ab initio values. This is a reasonable estimate based on the Ames vs. CDSD J = 0 prediction discrepancies shown in Fig. 2b. In the range of −5 ∼ + 5 cm−1 , there must exist some levels where CDSD predictions are more accurate than Ames, because the prediction accuracy of effective Hamiltonian models are band dependent and/or vibrational quanta dependent. However, for high lying levels without any experimental data, CDSD predictions would deteriorate quickly along with increasing vibrational quanta. The fraction or percentage of such “more reliable” extrapolations is simply unavailable. But for regions below 10,0 0 0 - 13,0 0 0 cm−1 , the differences revealed in Fig. 2b are somewhat strange. Previous experience suggests that the interpolation accuracy under the highest energy lev-

a

50 0 06 ← 11102 R27e at 4331.14 cm−1 , 5.462E-30 cm/molecule 50 0 06 ← 01101 Q16f at 5573.11 cm−1 , 3.767E-29 cm/molecule The empirical refinement procedure can provide tests on some Ames-2 band origins (but not all) or CDSD EH model extrapolated band origins to determine if they are unreliable. Previous studies [29–31] confirmed that, if a regular band origin or a normal rovibrational energy level cannot be reproduced to better than ±0.05 cm−1 no matter how hard we try to adjust the PES, the Gv or the level is probably unreliable. This does not apply to very high energy Gv  s. But if a band origin or a rovibrational level is successfully reproduced with tiny or negligible PES adjustments, it does not necessarily mean “reliable”. Instead, we could only claim it seems “consistent enough” with other rovibrational data which are reproduced with the expected accuracy. In other words, the checks can determine whether a Gv lies beyond the normal range of PES variations. When we included the CDSD 50 0 06/60 0 07/70 0 08 Gv  s into refining tests, the tests successfully run through and end up with similar deviations and σ RMS = 0.015 cm−1 . Then we manually change the three CDSD Gv  s to opposite direction, i.e. from smaller to larger than Ames Gv  s by same magnitude. New Gv  s are 6240.17 cm−1 , 7447.92 cm−1 , and 8646.95 cm−1 , respectively. The refining test using these new Gv  s still ended up with similar σ RMS . This basically means the series of states are less impacted by other states in their polyad, and/or current reference data set is insufficient for

b

Fig. 2. (a) Measured vibrational band origin reproduction accuracy for 12 CO2 isotopologues on Ames-2 PES refinement; (b) the J = 0 energy level differences between Ames-2 PES and CDSD EH modes.

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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those prediction. All other energy levels in these refinement tests are kept the same as those in the Ames-2 refinement. These test findings are important for both our CO2 project and future studies following the “Best Theory + Reliable HighResolution Experimental Data” strategy. Firstly, if a series of vibrational bands do not have strong interaction or couplings with other bands in the neighboring energy range, the extrapolations into higher vibrational quanta might be harder to maintain the same level of accuracy as we usually have for other interpolations and extrapolations. This apparently counter-intuitive statement reflects the difference between prediction and modeling. More couplings mean more terms for modeling which makes it less straightforward. At the same time, more couplings mean less energy levels required by our empirical refinements to reach same prediction accuracy, because each energy level would contain richer information of other energy levels. On the other hand, if a series of states are isolated without much couplings, the quality of both modeling extrapolation and empirical refinement extrapolation would depend on the anharmonicity of the states and the inputs we have. Right on-target data will be necessary – unless we already have enough extra information covering the range of even higher quanta. For example, if nν 1 levels are isolated, easy modeling of n = 1–5 levels does not automatically guarantee the n = 7–9 level prediction, while empirical refinement does need at least n = 7 or n = 8 level to ensure n = 6 level is accurately predicted. Secondly, some EH based Gv  s may have accuracy suitable for PES refinements, but it will take dedicated time and effort to: 1) identify obvious outliers; 2) double confirm consistencies; and 3) find the patterns of consistencies and inconsistencies with respect to vibrational quanta, J, and energies (if there are any). In the case of CO2 626, our primitive refinements using the CDSD Gv  s shows that most of the EH-model predicted J = 0 band origins below 10,0 0 0 cm−1 seem self-consistent, but a couple of states between 11,0 0 0 cm−1 and 12,0 0 0 cm−1 possibly carry uncertainties as large as ∼1 cm−1 . A future goal may be to identify all unreliable Gv levels in the CDSD EH models and use the remaining, more “consistent” levels to enhance the Ames PES refinement. It would help to generate IR line lists with better line positions, especially hot-band line positions. This step obviously needs extra highresolution CO2 experimental IR data to justify the data selection procedure. For example, the next cycle of PES improvement will benefit from new band origins determined around 15,0 0 0 cm−1 above the zero-point energy. Future DMSs should aim to have uniform 1–5% accuracy for measured IR intensities of weak bands (below 1E-28 cm/molecule) and those bands >11,0 0 0 cm−1 . Before more experimental data become available, we can do methodological tests. For example, randomly pick 60%−70% of bands for PES refinement, then use the remaining 30%−40% bands to check the predictive accuracy. Such a study would be an interesting contribution to the field. There still exist other factors contributing to the issue about predictive accuracy and consistency. Here is one example. From H2 O [15], NH3 [29,30], to CO2 [1] and SO2 [31], short-range potential coefficients up to the quartic level were refined. The assumption was taken for granted that this is good enough. But since all the PES expansions and refinements are molecule specific, it is reasonable to believe the predictive accuracy is not uniform from one molecule to another. In our NH3 project, we tried to refine up-tosextic coefficients and it did help reduce the σ RMS by ∼20%. But it is fairly expensive and the improvements were not as significant as nonadiabatic corrections [30 and unpublished work]. Now for CO2 , the >0.05 cm−1 Ames vs. CDSD Gv prediction discrepancies are first found on the 10ν 2 and higher ν 2 overtones. If their experimental Gv  s can be reliably measured, it would be worthwhile to investigate if including higher order PES coefficients in the refinement step lead to any new clues or suggestions. Cur-

5

rently, we are inclined to think this higher-order coefficient effect is not a major factor (for the 10ν 2 issue), but we are open to all possibilities. 3. 2016 Ames-296K lists vs. CDSD-296, and PES/DMS sensitivity of intensity This section first discusses the sensitivity of intensities with respect to the PES, DMS and variational programs. Then it compares Ames-296K lists with CDSD-296. 3.1. PES, DMS and variational calculations The latest Ames-2016 CO2 line lists are computed with the Ames-2 PES refined in this work and the existing DMS-N2 used for Ames-1 lists, including 296 K, 10 0 0 K and 40 0 0 K lists. The DMS-N2 dipole surface was fitted from ∼2500 CCSD(T)/aug-ccpVQZ dipoles with higher weights below 30,0 0 0 cm−1 . Although the recent UCL DMS and line lists [5,25] show subpercent agreement with highly accurate intensities measured on a few of the strongest bands [5,12,13], the DMS-N2 and UCL DMS have similar predictive accuracy for many transitions, especially those strong ones. For the 162,260 transitions reported in the UCL list file 626CO2_recommended_linelist_296.dat, 39.7% / 55.2% / 77.7% / 87.8% UCL intensities match Ames intensities with relative deviations S less than 1% / 2% / 5% / 10%, respectively. For the 37,769 transitions with UCL intensities > 1E-27 cm/molecule, the percentages are 47.6%, 62.6%, 86.3% and 91.9%, respectively. Recently, two vibrational bands 20 013-0 0 0 01 [13] and 300130 0 0 01 [5,12] have been re-measured and their intensities were accurately determined. The agreement for the 20 013-0 0 0 01 band is nearly the same. Around J = 0, the S% = (Scalc −Sexpt )/Sexpt are ∼0.4–0.5% (UCL) and ∼0.4–0.7% (Ames). See Fig. 3a. Note the m quantum number is defined as the rotational quantum number J of the lower level, times +1 for Q/R transitions, or times −1 for P transitions. For the 30 013–0 0 0 01 band, the UCL intensity agrees with the 2015 PRL measurement reported in Polyansky et al [5] to ∼−0.3%, but intensities reported in 2016 Devi et al. [12] are lower than 2015 values by more than 1%. Accordingly, the UCL intensity exhibit +1.0% deviation [25] vs. 2016 Devi et al. [12] The HITRAN2012 intensity deviations are ∼−1.0% vs. Polyansky et al. [5] and ∼+0.5% vs. Devi et al. [12]. Since the Ames-1 PES was used together with the UCL DMS in the DVR3D [37] calculations to get the UCL list [25], a natural choice is to use the UCL DMS in our VTET [32] intensity calculations and compare. However, there is a major difference between the two dipole surfaces. The Ames DMS-N2 was fitted to pseudo charges on atom nuclei and it fully satisfies the permutation properties of dipole vectors [1,2], while the UCL DMS fits to the x- and y- dipole components separately [5]. When the original UCL DMS was used with VTET, weird intensities appeared in certain bands (not all). For example, Ames-2 PES +original UCL DMS intensities for the 20 013-0 0 0 01 band are less than 10% of the expected magnitude, and cannot be shown in Fig. 3a. An extreme example is the R1 transition at 669.3 cm−1 of the 2ν 2 ← ν 2 band. R1(2ν 2 ← ν 2 )

Intensity (100% abundance)

Ames-1 +original UCL DMS (UCL) Ames-2 + DMS-N2 Ames-2 + UCL DMS (refitted) Ames-2 + UCL DMS (original)

3.551E-21 (DVR3D) 3.507E-21 (VTET) 3.497E-21 (VTET) 1.115E-23 (VTET)

Here the Ames-2 (VTET) + UCL DMS (original) intensity is more than two order of magnitude smaller. We believe the polynomial expansion basis of the UCL DMS is not fully compatible with the

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Fig. 3. The S% curves of variationally computed line intensities vs. 2016 Experimental data reported in Ref. [13] (left, 3a, 20 013-0 0 0 01) and Ref. [12] (right, 3b, 300130 0 0 01). Note the Ames + UCL DMS (original) intensities are too small (not in 3a scale, see text). The m is defined as J for Q/R transitions, or –J for P transitions. Note the m = J (R) definition in this paper is different from the m = J + 1 (R) defined by spectroscopists.

dipole surface re-expansion procedure required by the VTET program. Fig. 3b shows the comparison of 30 013-0 0 0 01 band intensities, where Ames-2 + original UCL DMS intensities (green open triangles) are reasonable (only off by 3.5%) but there is a very suspicious slope along the P→R direction. Because of such unpredictable intensities, it is impossible to reproduce the UCL list intensities from using VTET. Instead, an alternative approach is taken: the original UCL DMS was used to generate a new set of dipole moments on the exact same dipole grid of 2539 geometries [2], then the dipole moments are fitted with same set of polynomial basis as used in DMS-N2. The newly generated DMS is denoted “UCL DMS (refitted)” and it does work properly with VTET. The UCL DMS (refitted) intensities are found reasonable and close to DMSN2 based intensities, but with small differences. See examples in Fig. 3a and 3b. The limited J ranges in Fig. 3 are good enough to show the intensity differences. Note that the m = J (R) definition in this paper is different from the m = J + 1 (R) defined by spectroscopists. Examining the black open squares in Fig. 3a and 3b, which represent the Ames-2016 line lists reported in this paper, we can notice a ∼0.6% gap at J = 0. Actually such kind of S% gaps exist at J = 0 for most bands of symmetric CO2 isotopologues. It is usually about 0.5∼0.6%. For asymmetric CO2 isotopologues, Ames lists do not have such P→R gaps, thus it is probably a symmetry related issue. Such gaps simply disappear if we re-run symmetric isotopologue calculations with asymmetric isotopologue coordinate and basis. See those “asym” data in Fig. 3a and 3b. Without those gaps, the fixed “asym” data curve of red solid circles lies just between the old P and R branches (black open squares). Note the current Ames-2016 lists on http://huang.set.org/CO2/ and in the supplementary files attached to this paper still have these gaps for symmetric isotopologues. But these small breaks at J = 0 should not have any significant impact on most IR predictions, analysis or intensity comparisons. And we know that very limited experimental intensities have better than 0.5–1.0% accuracy, even for the strong bands. To prepare for the more accurate intensity data analysis and comparisons coming in the future, new CO2 line lists are being computed and will be made public once finished. The future lists expect to fix another symmetry related issue we found in Q branches, i.e. the S_calc/S_expt ratio bifurcates between even J and odd J , or e and f. The gaps between even and odd J branches vary from less than 0.5% to a few percent.

The data in Fig. 3b for the 30 013-0 0 01 band use Ref. 12 intensities as reference. Take the P4 transition at 6224.75 cm−1 as an example, and multiply all intensity values by 1024 , we have the following intensities: 6.6246

2015 Expt [5]

6.5830 UCL List [25]

6.518

2016 Expt [12]

6.459 Ames-1+DMS-N2

6.782

Ames-2+UCL DMS (original)

6.533 Ames-2 (asym) +DMS-N2 6.506 Ames-2+DMS-N2 6.641 Ames-2+UCL DMS (refitted)

Note that 100% abundance is assumed here. The published Ames-296K list had −2.4% vs. 2015 Expt [5] and −0.9% vs. 2016 Expt [12]. The new 2016 Ames-296K list see −1.8% vs. 2015 Expt [5] and −0.2% vs. 2016 Expt [12], or −1.4% vs. 2015 Expt [5] and +0.2% vs. 2016 Expt [12]. Compared to the old Ames-296K intensity, the improvement is obvious. For the 30 013-0 0 0 01 band, the measured line intensities at the NIST for 27 transitions have shown an excellent sub-precent agreement with the UCL calculations [5]. Interestingly, however, we have found that our calculations agree better (< 0.5%) with the Devi et al. [12]. We note that Ref. [5] adopted quadratic speed-dependent Nelkin-Ghatak profile for their analysis, while Ref. [12] analyzed the whole band spectra by adopting a speed-dependent parameter with full line mixing taken into account. Further laboratory study would be needed to resolve the disagreement. In Fig. 20a and Fig. 20b of Ref. [13] for the 20 013-0 0 0 01 band, there exist intensity breaks at J∼30 and J∼60, in addition to the gap at J = 0. Those breaks are similar to the energy level “J-jumps” we reported in Ref. 1. Both were caused by the C-O stretching basis convergence defect. Because the Ames-2 PES refinement has fixed the defect, the “J-jumps” in rovibrational levels and intensity ratio breaks disappeared. The current Ames CO2 lists on huang.seti.org are free of such breaks. In the future we will update the lists after the intensity ratio gap at J = 0 and the Q-branch even/odd J oscillation are fixed. Fig. 3 demonstrates mainly the DMS effects on intensities, while the intensity “gaps” at J = 0 reflect the variational calculation dependence. Now we examine the PES sensitivity for the 300130 0 0 01 band with DMS-N2 and three very similar PESs: Ames-1, Ames-2 and the 828-oriented refinement mentioned in Fig. 1. The line position deviations on all three PESs are compared in Fig. 4a. The Ames-2 deviations are about 50% of the Ames-1 deviations, i.e. within ± 0.01 cm−1 . Ames-2 data points are also continuous,

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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b

Fig. 4. The PES dependence of 30 013-0 0 0 01 band line positions and intensities of Ames CO2 626 lists. “Old Ames-1” refers to previous Ames-296K line list. CDSD-296 line position and intensities are used as reference.

while the other two PES data suffering from the C-O stretching basis convergence defects. Fig. 4b compares the corresponding intensities, using the CDSD-296 intensity as unity reference. The intensity changes are caused by the PES differences and rovibrational wavefunction changes on the three PESs. Taking the Ames-2 intensity (red circles) as reference, we can see that variationally computed intensities may have ±0.5–1.0% intensity variations. Even if we discard the 828-oriented PES (blue triangles), the intensity difference between Ames-1 (black squares) and Ames-2 (red circles) is still larger than 0.5%. Note the J = 0 gaps exist in all 3 data sets, but do not affect our discussion. Frankly speaking, such magnitude of PES sensitivities for intensities was beyond our expectation. We had thought the changes would be as small as up to 0.1–0.3%. But after verifying that the larger-than-expected PES sensitivity is real, it immediately poses a very serious concern on the predictive accuracy of theoretically computed intensities if very high accuracy is desired. In other words, it is clear that not only must extra care be taken in constructing the DMS in order to reach 1% accuracy, but the Ames-2 PES might also require additional work, especially when theoreticians have started working diligently and ambitiously towards subpercent or even sub-half-percent accuracy for intensity predictions. If the PES and rovibrational wavefunctions cannot guarantee less than 0.5% deviations, it is difficult to justify the related claims or argue with confidence. On the other hand, it should be noted that the PES sensitivity of intensity predictions is definitely molecule dependent and vibrational band dependent. Therefore, for some strong bands, it is still possible to maintain high confidence in the predictive accuracy claims. However, this also means the uncertainty could be potentially larger on some other bands. For now, more high accuracy intensity measurements are needed to confirm the sub-percent accuracy claim for the UCL lists. Another interesting observation in Fig. 4a and 4b is that, line position deviations (or differences) are not always a good indication of intensity deviations (or differences). Compared to the Ames-1 results, the line positions on the 828-oriented PES deviates more from Ames-2, but its intensity is closer to Ames-2. If we take Ames-2 line positions as “reference”, the better Ames-1 positions do not lead to better Ames-1 intensities. In other words, it would be very difficult for someone who saw Fig. 4b to imagine how Fig. 4a would look like, or vice versa. In short, the PES sensitivity may be larger than we had estimated for variationally computed intensities. More investigations are needed for both PES and DMS aspects. For example, the 0 0 0310 0 0 01 bands in the UCL lists have relatively larger deviations, 10% (UCL) vs. 4% (Ames) for 626. To fix the outlier(s), possible improvements may include extra grid points or a better optimized fitting

basis. It would also incur much more expensive ab initio dipole computations if scientists plan to extend the similar “sub-percent” accuracy to high lying IR bands beyond 80 0 0 cm−1 , which is the current limit of the published UCL lists [25–27]. Weaker bands call for more accurate higher order dipole terms as well. 3.2. Intensity agreement with latest experiments and uncertainty limit When compared to CDSD intensities, the relative differences of 80% transitions are less than 20% [3]. For the strong bands of various CO2 isotopologues, published Ames-1 PES based CO2 lists have showed ∼±5–10% (or better) relative deviations vs. new intensity measurements, e.g. Refs. 4,10 and 11. This is the reasonable deviation range we expect to see. The expectation is based on the method/basis of ab initio calculations, the PES and DMS fits, the PES reliability, as well as the uncertainties associated with experimental measurements and effective dipole models. In a few cases, deviations as large as ∼20–30% have been reported on a few weak bands, e.g. the 626 20 03n←0 0 0 01 (n = 1,2,3) [4] and 627 31101←01101 bands [11]. In 2014 Bierret et al. [38] reported the 636 20 05n←0 0 0 01 (n = 1,2,3) band at 734 nm where the ∼20–30% deviations are fully satisfactory because the experimental intensities have an uncertainty of 25%. These Ames vs. Effective Dipole Model (EDM) deviations can be partially attributed to the defects in higher order derivatives and experimental difficulties. A general trend is that larger intensity deviations are associated with weaker bands, due to the difficulties in both experiment and theory. Experimental determination of weak transition intensities has never been an easy task, just as theoretical calculations are not a black box, either. The difficulty increases if one wants to achieve 1% or better accuracy. See Section 4 for more details of comparison to the CDSD database. The comparison confirms the statistically averaged 5–15% uncertainty of experimental data based EDM models. Since the beginning [1], we have the following estimations and they have not changed: for regular > 1E-30 cm/molecule transitions at 296 K, the maximum S% of Ames intensity predictions (vs. Expt.) should always fall within ±75–133%, and the majority S% falls within ±5–20%. Exceptions are those transitions strongly affected by resonances. In some extreme cases, Ames intensities could only capture partial resonance effects and the relative S% could be still off by one order of magnitude. In 2015, Tan et al. [8] measured the intensity of the 626 40 03i←0 0 0 01 (i = 2,3,4) band near 830 nm. They reported that on average, the published Ames CO2 intensities are at least 50% lower than the experimental values [8,39]. See Fig. 5 for directly measured and Ames intensities of the 40 033-0 0 0 01 and 40 034-0 0 0 01

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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Fig. 5. Measured and computed intensities of the CO2 626 40 033-0 0 0 01 and 40 034-0 0 0 01 bands. Relative S% are computed as 50%∗ (SAmes /SExpt − SExpt /SAmes ). Experiment values are taken from Ref. [8].

bands. The transitions are very weak at room temperature, 2∼68E30 cm/molecule, and the experimental uncertainties are 20–50%. Even so, most S% still fall within ±100%. This is still fully within our expectations, but we take it seriously as a warning signal. It is worthwhile to figure out the source of discrepancy and reduce the overall S%. If the Ames intensities are found to underestimate certain bands >11,0 0 0 cm−1 systematically, the DMS fitting and choices may need a re-visit. In our 2013 JQSRT paper [2], the DMS-N2 was selected because it gave the lowest intensities for those weakest “gap” regions around 13,0 0 0 cm−1 . The rationale behind that choice is, most noise on a dipole surfaces is introduced during the least-squares fit and this probably will cause intensity artifacts. Therefore, smaller intensities could suggest smaller DMS noise. However, the DMS-N2 was fitted with 2539 ab initio points with E ≤ 30,0 0 0 cm−1 above equilibrium. There was another DMS, denoted DMS-N3 [2], which was fitted from points in the 0–60,0 0 0 cm−1 energy range. It showed slightly higher intensities than DMSN2 in the ∼13,0 0 0 cm−1 region [2]. The possibility cannot be totally ruled out that some higher order derivative terms are not sufficiently determined in DMS-N2. In other words, some non-zero derivatives came out closer to zero than what they should be. We plan to examine DMS-N3 further and determine if it contains some critical higher-order terms more reliable than those in DMS-N2. If the answer is “Yes”, probably we need to try combining the advantages of DMS-N2 and DMS-N3 to get a better DMS for future lists. On the other hand, it should be noted that some intensity discrepancy between the Ames list and databases could be tracked to the missing or inappropriate terms in EDM. For example, the 50 013(4)←0 0 0 01 band intensities in the old HITRAN2008 [40] were underestimated by two order of magnitude [2,4]. Recently, Bierret et al. [38] predicted that the 12 C16 O2 intensity sum of the 2ν 1 + 5ν 3 triad is very close to that of 13 C16 O2 , while Ames lists predicted that the 12 C16 O2 intensity is 30% stronger. To determine if the discrepancy between the two predictions was caused by some EDM terms, it requires further clarifications from the experimental side first, and then possible a new PES and DMS as a second option. In general, we hope future experiments can focus on both the shorter wavelength range and weaker bands. See more details about the inter-isotopologue consistency in Sec. 4.

3.3. New line shape parameters and conventional vibrational polyad quantum numbers In previous Ames CO2 line list releases, the vibrational quantum numbers were labeled using the leading variational Configuration Interaction (CI) basis of the corresponding eigenvectors. They are often different from the conventional quantum numbers used for vibrational polyads, where the polyad number P = 2ν 1 + ν 2 + 3ν 3 . For line shape parameter prediction as implemented in Gamache’s program [3,17], it is necessary to transform VTET quantum numbers into applicable vibrational polyad labels. Such transformation was not trivial, especially at high energies or high J’s. We have accomplished the labeling for more than 90–95% levels of 13 isotopologues below 11,0 0 0 cm−1 . Here is a short summary of our procedure. The J = 0 Gν band origins and lowest states of each l2 = 1–20 (J = 1–20) are first labeled from zero point to 15,0 0 0 cm−1 and above. The quantum numbers from the VTET basis usually have correct quanta for the asymmetric stretch, ν 3 , but can be ambiguous for ν 1 or ν 2 . Since ν 3 is available, a short program easily identifies all l2 = J > 0 levels and labels the rest of the J > l2 levels. Note the 20th overtone of the linear bending will be higher than 13,0 0 0 cm−1 . To extend the vibrational quanta assignments from J < 20 levels to higher J levels, the standard EH formula for a vibrationrotational energy level is adopted in our iterative search-and-assign procedure J→J + 2. The formula is:

Ev (J ) = Gv + J (J + 1 )BV − J 2 (J + 1 )2 DV + J 3 (J + 1 )3 HV where GV is the band origin, J is the rotational quantum number, B is the rotational constant, while D and H are centrifugal distortion constants. Instead of using a fixed B and explicit D and H, we use a series of B(J) to incorporate D and H effects. Since all J < 20 levels have been “found” and labeled, the energies of three “found” levels at J−4, J−2 and J are used to derive B(J−4), B(J−2), B(J) and predict B(J + 2) and E(J + 2) as

B(J + 2 ) = B(J − 4 ) + 3[B(J ) − B(J − 2 )]; E (J + 2 ) = E (J ) + (2J + 2 ) × B(J + 2 ). The predicted E(J + 2) is used to match the J + 2 level of the same band in the corresponding J + 2 symmetry block. An “actual” B(J + 2) is re-computed from E(J−2), E(J) and E(J + 2). The difference between the ‘predicted’ and ‘actual’ B values is also saved for each

Please cite this article as: X. Huang () et al., Ames-2016 line lists for 13 isotopologues of CO2 : Updates, consistency, and remaining issues, Journal of Quantitative Spectroscopy & Radiative Transfer (2017), http://dx.doi.org/10.1016/j.jqsrt.2017.04.026

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Fig. 6. Line position deviations (a) and relative intensity deviations (b) of 626 31113←01110 band, Ames 626 list vs. CDSD-296. The e and f splits become larger at higher J’s. Table 2 Number of “matched” and “mismatched” CDSD-296 levels, compared to new Ames assignments. #Iso

Matched

#Missed

#Iso

Matched

#Missed

#Iso

Matched

#Missed

626 636 628 627

18,123 10,179 16,400 12,294

515 255 371 118

638 637 828 728

8101 5698 2558 4134

147 11 251 76

727 838 738 737

2417 1061 1548 816

29 88 1 0

J. It helps to obtain a more reliable prediction of J + 2 level and corresponding B’s. Using J step of 2 is necessary, because the e and f components should be treated separately. An example is given in Fig. 6 for the 626 band 31113-01101, Ames vs. CDSD. Fig. 6a shows how the e/f line position differences diverge at higher J’s. Fig. 6b shows that most |m| < 20 intensity deviations are less than 1%, but the intensity agreement for the e and f branches follows different patterns. The intensity breaks at J = 0 are close to 1% for both e and f, but the directions are opposite. Using J step of 1 probably would fail in such cases. This kind of stepwise “search and labeling” will run into difficulty in the region of higher density of states, or at much higher J’s. The energy levels affected by significant resonances may also have minor deviations off the regular track, but their energy changes are usually less than 0.1 cm−1 . If a level affected by accidental degeneracy is mis-labeled, all higher J levels will inherit the wrong or reversed vibrational quanta. Several checks are put into place to handle such a scenario or circumvent it. Up to now, the issues are only partially solved. All J = 0–150 states up to 15,0 0 0 cm−1 are assigned by our autoassign code. For 626, this means 117,680 levels, and 146,174 levels for 838. For 628, this means 252,176 levels. The 738 has 281,861 levels, more than any of the other 12 isotopologues. But above 11,0 0 0 cm−1 , the number of duplicated (or triplicated) assignments starts rising quickly. This is due to imperfections in our assignment strategy. In such cases, only one of those assignments could be correct, and it is even possible that all could be wrong. The new Ames assignments are compared to the vibrational quanta assignments in CDSD-296 levels [24], which we assume are mostly reliable. Table 2 is a summary of the mismatched assignments for 12 isotopologues. Except for 828 and 838, the ratio of mismatches is less than 3%. Examining the remaining “mismatched” levels, we find that most are caused by an accidental degeneracy which our auto-assign program fails to handle properly. Using these new quantum numbers, we have re-generated our Ames-296K line lists with important line shape parameters. The parameters are predicted by Dr. Gamache’s program which was also applied in CDSD and HITRAN. After comparing our new pa-

rameters to those in CDSD and HITRAN, we believe that this time the majority of the line shape parameters are consistent with those databases. Note the co2.f90 program on http://huang.seti.org/CO2 provides output options for self-broadened half-width and T dependence exponent for 4 different temperature ranges associated with Mars, Earth, Venus, and HOT exoplanet conditions. Recently we found that the new Ames 838 assignments lose track on some bands after J = 28 or 38. This work will continue and the online data files will be updated accordingly. One possibility is to transfer all the quantum numbers of CDSD-296 or CDSD40 0 0 levels to carefully matched Ames levels, and fix the quantum number assignments. 3.4. Comparison to CDSD-296: overall comparison Using 1E-31 cm/molecule intensity cutoff and the commonly used terrestrial abundances [23], a “natural” Ames-296K line list was created from the combination of various isotopologue IR lists. It has 927,329 transitions up to 19,552 cm−1 . When compared with the latest CDSD-296 for atmospheric applications [24], the vibrational polyad quantum numbers are straightforward and easy to assign. One can simply match all CDSD-296 lines to the Ames-296K list, then transfer all the EH model quantum numbers. Most of the 534,227 transitions in CDSD-296 can be matched without knowing EH or VTET vibrational quanta, except for ∼400 lines. These lines have CDSD intensity from 1E-30 to 2.0E-28 cm/molecule, but their corresponding intensities in the Ames “natural” list are below 1E-31 cm/molecule. For example, the first transition that failed to match is the R17e of the 626 band 01111← 03301. Frequency (cm−1 ) Intensity

1013.25248 1013.27139

E (cm−1 )

(0.9842 abundance)

1.159E-30 2123.3006 (CDSD-296) 8.064E-32 2123.2805 (Ames)

If we check other stronger transitions associated with the exact same upper level of 626, 01111 18e at 3136.55 cm−1 , the S% are as small as ±1–3% for the P19e, Q18f and R17e transitions of the 01111←11101(2) and 01111←01101 bands. The S% are 68% and 26% for two other transitions in the 01111←03301

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band, Q18f and P19e. If we check stronger transitions involving the 626, 03301 17e level at 2123.28 cm−1 as the upper state, there are 9 transitions in CDSD-296. The S% are −2∼0% for the 03301←10 0 01(2) and 03301←02201 transitions, plus −13% and −65% for the 03301←0 0 0 01 P18 and R16, respectively. These agreements confirm the rovibrational wavefunctions we computed for both upper and lower states of the R17e transition. Therefore, the predicted transition intensity between them should be reliable, too. As stated, the Ames DMS-N2 should not have any errors of one order of magnitude or larger for such regular transitions. The next transition which failed to match is the 636 band 21103←10 0 01 P22e Frequency (cm−1 ) Intensity

1740.86739 1740.86391

E (cm−1 )

(0.01106 abundance)

1.089E-30 1567.2285 (CDSD-296) 7.403E-33 1567.2399 (Ames)

None of the 626 or 636 transitions can be found in the published UCL line lists [25,26], either. The cutoff in the UCL lists is 1E-30 cm/molecule. The first failed-to-match 628 transition is 20 0 03←01101 R1e Frequency (cm−1 ) Intensity

1839.86054 1839.86361

E (cm−1 )

(0.003947 abundance)

2.565E-30 663.1107 (CDSD-296) 1.019E-33 663.1003 (Ames)

And the strongest transition in our fail-to-match list is: 628 31104←01101 R27f: Frequency(cm−1 ) Intensity

3698.98350 3698.97533

[m5G;May 13, 2017;18:59]

E (cm−1 )

(0.003947 abundance)

2.063E-28 941.3846 (CDSD-296) 8.072E-32 941.3706 (Ames)

Both probably will not appear in the upcoming UCL lists for asymmetric isotopologues [27], either. For the matched CDSD-296 transitions, Fig. 7 shows the line position deviations for each isotopologues. Compared to the old Ames-1 based lists (as shown in Fig. 5 of Ref. 24), the deviations are significantly reduced by ∼50% or more. Most deviations are within ±0.1 cm−1 or even less than ±0.05 cm−1 . For every isotopologue, average |E| ≤ 0.015 cm−1 , and σ RMS (E) ≤ 0.025 cm−1 . For intensities, the relative deviation is defined as S = (SAmes /SCDSD – SCDSD /SAmes )∗ 50%. S are less than ±50% for most transitions with intensity > 1E-28 cm/molecule. Larger discrepancies are found for lower intensity transitions. Those larger S mainly occur on weaker transitions below 1E-28 cm/molecule. Fig. 8 gives the statistical distribution of E (left) and S% (right) on individual transitions (top) and bands (bottom). CDSD296 contains 534,227 transitions and nearly 20 0 0 vibrational bands. In Fig. 8a, approximately 50% of the transitions have line positions with E ≤ 0.01 cm−1 . This value even reaches 71% and 74% for 626 and 636, respectively. More than 95% (510,439) of the transitions have line position E ≤ 0.03 cm−1 . In the 1931 bands included in Fig. 8, ∼40% (774) of the bands have σ rms ≤ 0.01 cm−1 and ∼85% (1634) of the bands have σ rms ≤ 0.03 cm−1 . Only 6.6% (127) of the bands have σ rms > 0.05 cm−1 . The “avg |E|” and the “rms E” have similar distribution, which suggests the E of the majority of the bands are essentially systematic so that their “avg E” are very close to their “rms E”. Future E improvements may still focus on band origins. In Fig. 8b, more than 28% (151,713) transitions have relative S ≤ 2%, 61% (326,121) transitions have S ≤ 5%, and 89% (477,204) transitions have S ≤ 20%. Of the total 1931 bands, 442 (or 23%), 808 (or 42%) and 1218 (or 63%) bands have σ rms (S) less than 3%, 5%, or 10%, respectively. The “avg |S|” and “rms S” distri-

butions have relatively larger differences between 1–5%. Future investigations can decide if we need to work on both the systematic deviations of the Ames lists and the deficiencies of the CDSD EDM models. More detailed E and S statistics for each isotopologue are available upon request. No obvious outliers were found. The overall agreement between the Ames-296K and CDSD-296 lists is satisfactory, especially when we consider that most CDSD models of minor isotopologues were fitted from lab data measured with 5–20% uncertainties. The following section focuses on the internal consistency of the theoretical line lists vs. EH-EDM based databases. 4. Comparison to CDSD-296: isotopologue consistency and pure rotation bands of 628/627 4.1. Ames vs. Expt. or Ames vs. CDSD? This section is based on PES & DMS accuracy and reliable convergence of the variational calculations. The agreement between the UCL DMS and Ames DMS-N2 DMS has provided further supporting evidences [25,26]. Due to difficulties associated with the experimental determination of isotopologue IR band intensities, it has been a long-time pursuit to make reliable predictions for less abundant or harder to measure isotopologue bands, using existing intensities of the most (or more) abundant isotopologues. With the full set of Ames-296 K lists for 13 CO2 isotopologues, it is possible to carry out a systematic investigation about what we can provide now for isotopologue intensity predictions, and how we can further improve the prediction accuracies. We believe this type of analysis will benefit both the theoretical and experimental fields. The first question we ask is, should we use the experimentally measured intensities OR the effective dipole model (EDM) intensities in CDSD? The prediction formula adopted in this paper is simple and mainly for guidance purpose: S2_Predict = S1_Expt/CDSD × S2_Ames /S1_Ames . ‘1’ and ‘2’ refer to two different isotopologues. The predicted S2_Predict is compared to available S2 _Data , either measured or from CDSD. The 40 013-0 0 0 01 band is randomly chosen for this probing test. The test is to predict S(636) using measured or CDSD S(626) and Ames intensities computed for S(626) and S(636). All the measured intensity data were kindly shared by S.A. Tashkun back in 2013 [41]. The results in Fig. 9 firmly prove that only CDSD intensities can be used for systematic comparison and predictions. Predictions in Fig. 9a and b are based on experimental S(626), while those in Fig. 9c and 9d are based on CDSD S(626). Comparing 9a and 9c, the Ames 626 intensity has better agreement with the CDSD intensity than with the measured intensity, especially in the R branch. This is due to the uncertainties in the measured data. Although Fig. 9b shows that most Ames vs. Expt. S% are less than 5%, the agreements between the prediction and 636 experimental intensity have oscillations as large as ±10%. Examining the red balls and blue triangles in Fig. 9b, we see a clear correlation between the S636_Expt data uncertainty and the quality of the prediction. Using the CDSD intensity essentially removes all the noises and now we can see the Ames intensity jump at J = 0 in Fig. 9d. The predicted intensity (blue triangles) has an overall quality very similar to that of Ames 636 intensity, with very consistent S = 2–3%. Interestingly, the predicted intensity does not have a jump at J = 0, because the ab initio S(636)/S(626) ratio and experimental S(626) are both continuous at J = 0. The tests have been made using the 4 most abundant isotopologues, 626/636/628/627. The dataset kindly shared by Dr. Tashkun in 2013 [41] contains 120 bands comparable. All possible predictions are included. For example, one can use 628/626 Ames intensity and expt. (or CDSD) S(628) data to predict S(626).

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Fig. 7. Line position deviations of 12 CO2 isotopologues, Ames-2 PES based lists vs. CDSD-296 K. The x axis covers the wavenumber range of 0–16,0 0 0 cm−1 , while the y axis of E is from −0.35 cm−1 to +0.35 cm−1 .

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a

b

b

Fig. 8. Distribution of line position deviations E (left, 8a) and relative intensity deviations S% (right, 8b), Ames-2016 lists vs. CDSD. Top figures show statistics on transitions, bottom figures show statistics on bands. The ‘avg’ is for “Averaged” deviations, || is for absolute values, and the ‘rms’ is for the root-mean-square deviations.

For each band, the mean S% and σ rms (S%) are computed and plotted in Fig. 10a. It is clear that CDSD based predictions can lead to much smaller mean S% and σ RMS (S%). The mean S% and σ RMS (S%) are plotted in an amplified scale, see Fig. 10b. Most Ames + CDSD predictions match CDSD intensities with a σ RMS (S%) ≤ 5%. The distribution of the averaged Ames vs. CDSD relative S% is 0.9 ± 4.3% for all 120 bands, or 0.8 ± 2.2% for 90% of

c

d

Fig. 9. The accuracy of S(636) predicted with the Ames S(636)/S(626) ratio and S(CDSD) or S(Expt) 626 intensities. Top: Expt. S(636) values are used; Bottom: CDSD S(636) values are used; Left: absolute S; Right: relative S%.

the bands. It falls within ±1% for 30% of the bands. The distribution of the σ RMS (S%) is 4.0 ± 4.2% for all 120 bands, or 2.9 ± 1.9% for 90% of the bands, and less than 2% for ∼30% of the bands. The nice agreement for the mean S% suggests that the systematic deviations are usually small. The σ RMS (S%) agreements may contain more information about higher order terms in the EDM fits and experimental uncertainties.

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Fig. 10. Mean S% and σ RMS (S%) for 120 bands of 626,636,628 and 627. (a) Left panel used SExpt to predict, while the right panel used SCDSD to predict; (b) shows the mean S% and σ RMS (S%) separately.

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Fig. 11. Isotopologue consistency of Ames vs. CDSD intensity data, 10 0 01(2)←0 0 0 01 band of 628,627,638,637,728.

For weaker bands (with mean S ≤ 1E-25 cm/molecule), the agreement between Ames and CDSD intensities are far better than those of Ames vs. Expt. This verifies the validity of both dipole surface DMS-N2 and the CDSD effective dipole models. For many regular bands, both Ames and CDSD exhibit an agreement within ±5– 10%. This provides a solid basis for the following inter-isotopologue consistency check. The prediction consistency for regular, not-tooweak bands should be at least 1–3% for all isotopologues, and might be better for strong bands. This consistency claim does not hold for the bands affected by resonances. 4.2. Three fundamentals All CDSD intensity data for the ν 1 polyad (10 0 01 and 10 0 02 ← 0 0 0 01) are pure predictions. It is easy to understand that symmetric stretches of symmetric isotopologues would not cause dipole changes, i.e. be IR inactive. But the IR intensity of asymmetric isotopologues is not weak at all. For 10 0 01←0 0 0 01, the strongest 628 ν 1 transition at 296 K is R16e at 1378.46 cm−1 , S = 1.698E22 cm/molecule. The corresponding 627 R16e at 1388.95 cm−1 is 5.591E-23 cm/molecule, i.e. only 30% of the 628 intensity. The intensity ratio is clearly related to the O isotope mass difference. Similarly, the R16e intensity ratio of the 10 0 02←0 0 0 01 band is 4.009E-23 (627): 1.554E-22 (628) ≈ 36%. As 13 C substitution does not have a significant impact, we would expect a similar intensity ratio between the 638 and 637 ν 1 transition. The Ames intensities are 8.476E-23 (637): 2.646E-22 (638) ≈ 32% for 10 0 01 R16e, and 2.805E-23 (637): 1.172E-22 (638) ≈ 24% for 10 0 02 R16e. It is consistent with what we found for 628/627. Now examining the CDSD intensity data for strong bands at very low energy, the discrepancies we find for 637 and 728 are

beyond the reasonable range (see Fig. 11a). The CDSD intensities (with terrestrial abundances included) of 10 0 01-0 0 0 01 R16e are 6.724E-25 (628): 4.092E-26 (627), and 1.113E-26 (638): 2.082E-27 (637). Converted to 100% abundances, the true ratios are 5.575E23 (627): 1.703E-22 (628) ≈ 33%, and 2.525E-22 (637): 2.510E-22 (638) ≈ 101%. The 627/628 intensity ratio agrees well with the Ames ratios ∼30%, but the 637/638 ratio of 101% just cannot be right. The CDSD 637 intensity for the band is too strong, ∼280% of the Ames intensity. Similar problems are found for the 10 0 020 0 0 01 band, see Fig. 11b. Further, 728 intensities for both bands are nearly as much as 4.6 times what it should be. Note the intensity values are taken from the CDSD-296 file on ftp.iao.ru, and good agreement has been established between Ames and CDSD isotopologue abundances and partition functions. Since the ν 1 fundamental polyad intensities in Fig. 11 are pure predictions, we switch to the hot band ν 1 ←ν 2 , i.e. 10 0 01(2)←01101 for comparison. The CDSD intensities are based on real experimental data. The results are interesting. Figs. 12a and 12b show the Ames vs. CDSD intensity agreement for the 10 0 0101101 and 10 0 02-01101 bands, respectively. The ∼0.6% J = 0 breaks on the curves of the symmetric isotopologues have no effects on our discussions below. The perpendicular color bars at J = 0 refer to the Q branch data which are not discussed here. In Fig. 12a, all 12 isotopologues show agreement to within ±8%. This is the appropriate range we expect to see for regular bands of moderate to strong intensities. Assuming the CDSD models have overall correct intensities with small uncertainties on isotopologues, we estimate the Ames DMS-N2 based intensities are probably as accurate as −2 ± 2% for this band. The gradual changes from 0 to higher J usually indicates the higher order term differences between Ames and CDSD model. The P and R branches are

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Fig. 12. Intensity consistency of Ames vs. CDSD data of 12 CO2 Isotopologues. (a) 10 0 01←01101; (b) 10 0 02←01101.

a

b

Fig. 13. Intensity consistency of Ames vs. CDSD data of 12 CO2 Isotopologues. (a) 01101←0 0 0 01; (b) 02201←01101. Open circles in (b) are symmetric isotopologues, solid circles are asymmetric isotopologues.

roughly symmetric with respect to the m = 0. However, 628 and 627 stand as outliers. For example, the 627 S% goes from −6% (P90) to ∼+ 6% (R90). The reason behind such monotonic increases is not clear to us. Since the 637 and 638 curves look fine, a check on the EDM may give some hint. In Fig. 12b, similar S% curves are found for 628 and 627. The magnitude changes from P90 to R90 are approximately the same as in Fig. 12a. But their whole curves are now downshifted by ∼16%. This makes them outliers again, because all other isotopologue curves remain in the same range of Fig. 12a, i.e. ±8% The 628 and 627 intensity inconsistencies can be traced to the ν 2 band itself. The 01101←0 0 0 01 curves in Fig. 13a look similar to those in Fig. 12a. Most S% curves fall within −8% ∼ 1%, while the 628 and 627 curves are obvious outliers: monotonically increasing in contrast to all other isotopologues. In Fig. 13b, the hot-band 02201←01101 is shown with open (solid) dots for (a)symmetric isotopologues. The P→R slopes of S(628) and S(627) are nearly as monotonic as those in a). The rest of the isotopologue curves are roughly symmetric with respect to m = 0. But S(627) moves up by 2%, and S(636) downshifts by 4%. It suggests the CDSD S(636) and S(627) for the two bands are less consistent than for other isotopologues. The ν 3 -related S% curves are in Fig. 14, a) ν 3 , b) 2ν 3 ←ν 3 , and c) ν 2 +ν 3 ←ν 2 . The a) and b) are very similar, just less EH model extrapolation in b). Contrary to ν 1 and ν 2 , here the J dependence of ν 3 S% is mostly linear. This could indicate the higher order terms in the dipole models are either much smaller in magnitude or have excellent agreement between Ames and CDSD. In all three figures, all S% fall within ±10%. The 638 S% (bottom cyan lines)

might have a ∼7–10% systematic error, and the 627 S% (top orange lines) may have 1–3% shifts. Another “outlier” is 838. From P to R, the 838 S% rises linearly with a slope steeper than any other regular bands we checked. It suggests a first-order term in the 838 EDM may need improvement. The 627 slope suggests the need for a smaller fix. Note that the S% curves in Fig. 14c are nearly doubled due to the e/f split and the even/odd J intensity oscillation issue we mentioned earlier, but the S% e/f splits are very small for the P branches of asymmetric isotopologues. These double lines (e.g. 838) do not affect the overall discussion here. 4.3. Pure rotational bands of 628 and 627 The O isotope mass differences in asymmetric CO2 isotopologues leads to an effective dipole moment and accordingly, pure rotational microwave spectra (R branch only). The magnitude of these vibrationally introduced dipoles are very small and the intensities are on the order of 1E-27 cm/molecule. See Fig. 15a for the Ames microwave intensities. These are highly reliable and consistent, because we trust the quality of the PES, the DMS and the variational rovibrational computations. Obviously, the 628 and 638 intensities are the strongest. The 627/637 and 728/738 intensities are only 25–30% of the 628/638 intensity. This is because the pure rotational spectra intensity is proportional to the effective dipole moment, and the larger relative O isotope mass differences yield larger effective dipoles. The 728/738 intensities are lowest because their total reduced masses are larger than those of 627/637, so the relative % mass differences

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a

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Fig. 14. Intensity consistency of Ames vs. CDSD data of 12 CO2 Isotopologues. (a) 0 0 011←0 0 0 01; (b) 0 0 021←0 0 011; (c) 01111←01101.

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Fig. 15. CO2 628 and 627 pure rotational transition intensities. (a). Ames intensities in normal scale; (b) Ames, CDSD, HITRAN, JPL intensities in log scale and E is (Ames – CDSD); (c) relative S% vs. the three databases.

are smaller. The 13 C substitution does not have a significant effect on the intensities. Fig. 15b and c compare three databases, CDSD, JPL, and HITRAN to Ames. All data in these plots have been adjusted to 100% abundances. As shown in Fig. 15b, the Ames line positions are as good as −0.0 0 05 ∼ 0 cm−1 . Also in Fig. 15b, the Ames data have a 2nd intensity peak in the J = 75–100 region. We believe this is probably real but too weak to be measured at room temperature. Note that HITRAN2012 has hyperfine splitting structure for 627 R0 to R25 transitions, so Fig. 15(b) and (c) used the sums of the split intensities for comparison. Fig. 15c shows the relative intensity differences between Ames and the three databases. It should be acknowledged the 628 and 627 EDM intensities do have large uncertainties as labeled. The CDSD file specifies their 1σ uncertainty as 50% [24]. The HITRAN ierr index for these transition intensities is ‘2’, which means “Average or estimate” [42]. But the magnitude of the discrepancies and 628/627 inconsistencies are still surprisingly large. Comparing Ames consistent intensities to the three databases, all S% are negative which simply means the Ames intensities are weaker. For J = 0–10, the EDMs in the three databases significantly overestimate the intensities, with S = −60% ∼ −300%. The baselines are different from one database to another, and from 628 to 627. This suggests that the experimental data sources might be different. Going to higher J, all S% curves dive further negative but their J dependences are similar. This may indicate a systematic deficiency in the EDMs for higher J. The 628 vs. 627 comparisons reveal that of the three databases, the HITRAN2012 has the best consistency and the largest overestimations, and the CDSD has the worst 628/627 consistency. In Fig. 15c, the HITRAN 628 and 627 S% curves almost completely overlap with each other. In contrast, the JPL 628 and 627 S% curves

differ by ∼40% at J = 0. CDSD 628 and 627 S% curves are separated by more than 250% at J = 15, i.e. −70% on 628 and −320% on 627. Meanwhile, the CDSD intensities of 628 and 627 seem very similar, which cannot be right, as we already know 628 intensities should be as much as 2–3 times stronger than the 627 values. For example, R25e of pure rotation is the strongest transition at 296 K. Its intensity values are:

Ames CDSD HITRAN UCL

S(628)

S(627)

S(628)/S(627)

1.588E-27 3.463E-27 1.248E-26 1.486E-27

0.459E-27 3.642E-27 2.970E-27 0.429E-27

3.46 0.95 4.20 3.46

HITRAN intensities are approximately 7 times the Ames intensity, but its S(628)/S(627) ratio is reasonable. The CDSD S(627) is actually larger than S(628) by nearly 5%, which is contradictory to the mass analysis. Randomly selecting another transition, R15e, we perform the same analysis:

Ames CDSD HITRAN UCL

S(628)

S(627)

S(628)/S(627)

0.9126E-27 1.7112E-27 6.167E-27 0.8563E-27

0.271E-27 1.838E-27 1.834E-27 0.254E-27

3.37 0.93 3.36 3.36

This time Ames and HITRAN have nearly perfect agreement on the S(628)/S(627) ratio. But again the CDSD has S(627) stronger than S(628) by 6%. Probably the 628 and 627 EDM models are

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Fig. 16. CO2 626 IR simulation at 40 0 0 K. Ames vs. CDSD. (a). 0–4500 cm−1 ; (b) 4000–8000 cm−1 ; (c) 8000–14,000 cm−1 . Two Ames lists are included, plus 4 different subsets of CDSD 626 data.

based on data acquired from quite different experimental setups. On the other hand, the S(627) of HITRAN does match well with the corresponding CDSD value. This confirms the HITRAN online notes [23] that its 627 hyperfine intensities from Ref. 43 were scaled by 1.34 to make the sums matching the corresponding CDSD intensity values. In short, the HITRAN dipole model is more physically selfconsistent than CDSD and JPL, while the HITRAN intensities are still too strong. Reducing the effective dipole terms by ∼60% might help. At the meantime, the latest UCL line list [27] reported essentially identical S(628)/S(627) ratios, which intensities are to be adopted in HITRAN2016. But the Ames vs. UCL absolute intensity differences are ∼7%, surprisingly larger than we had expected. More investigations are underway. 5. 40 0 0 K comparison The CDSD-40 0 0 database [28] is taken from ftp.iao.ru. It has 628,324,454 transitions with J up to 300 and E ≤ 44,000 cm−1 . Only the 626 data is considered in this work. The original Ames40 0 0 K list has 298,232,789 transitions of J up to 150, E ≤ 24,0 0 0 cm−1 and intensity ≥ 1E-29 cm/molecule at 40 0 0 K. To make an apple to apple comparison, CDSD-40 0 0 is filtered with J ≤ 150 and E ≤ 24,0 0 0 cm−1 to get a 626 subset. The subset has 123,005,146 transitions. The simulations are carried out at 1 torr and 40 0 0 K. Voigt profile and self-broadening line shape parameters are adopted. Note the published UCL lists are cut off at 1E30 cm/molecule at 296 K which is not sufficient for high temperature simulations. Differences between the Ames and CDSD lists are clear. To better understand the source of differences, a new Ames line list is computed with J extended to 220 and intensity extended to 1E30 cm/molecule. In this new list, J = 126–150 rovibrational wavefunctions and intensities also have been re-calculated for consistency. In total the new Ames 12 C16 O2 40 0 0 K list has 471,916,316 transitions. As shown in Fig. 16a, the two Ames lists are almost the same from 0 to 80 0 0 cm−1 , except at 140 0 cm−1 . Beyond 80 0 0 cm−1 , the new list has much more complete coverage and stronger intensity. This suggests the higher J effects are mainly important for the higher energy region. As CDSD-40 0 0 is cut off at 8300 cm−1 , we may use either Ames list in a comparison with CDSD. The IR feature below 300 cm−1 is missing from CDSD-40 0 0, which is not a surprise since similar comparisons at 296 K indicate that a similar feature is missing from CDSD-296. The bands below 300 cm−1 are mostly hot bands, which are very weak at 296 K. A few randomly picked examples include 20 0 03←0 0 011

band in 175–241 cm−1 , 20 0 02←0 0 011 band in 294–361 cm−1 , and 21112←→41105 bands under 50 cm−1 . The strongest single transition intensity at 296 K are always under 8E-28 cm/molecule in 0– 345 cm−1 , or below 1E-31 cm/molecule in 0–147 cm−1 . Note the UCL 296 K list adopts intensity threshold of 1E-30 cm/molecule, so it starts at 158 cm−1 . Both CDSD and HITRAN2012 data of CO2 626 start from 345 cm−1 . Either the CDSD EDM models have not been extrapolated into this spectral region, or certain critical effective dipole terms are still missing for part of these hot bands which rise from highly excited vibrational states and are extremely weak at 296 K. From 300 cm−1 to 5500 cm−1 , CDSD-4000 has more intensity in several regions, e.g. 110 0–20 0 0 cm−1 , and 2200 cm−1 – 3500 cm−1 . These intensity differences require detailed analysis. In Fig. 16, the solid blue (CDSD.E 24K) and dotted green (CDSD.E 24K.J150) curves are completely overlapped with each other, indicating that when E ≤ 24,0 0 0 cm−1 , the J ≤ 150 or J ≤ 300 cutoff does not exhibit much difference for CDSD-40 0 0. This is also true for the original CDSD-40 0 0 dataset where E ≤ 44,0 0 0 cm−1 . The dotted black curve of CDSD. J = 0–150 is also very similar to the full original CDSD-40 0 0 with J up to 300 (not shown). Therefore, the first observation is, for this spectral range, only the E cutoff really matters for the CDSD-40 0 0 intensity. At least this is true for J ≥ 150. This roughly agrees with what we can see for the Ames J ≤ 150 vs. J ≤ 220 comparison. The minor difference at 1400 cm−1 we found between the two Ames lists does not show up in CDSD40 0 0 data analysis. The black curve can be taken safely as “full CDSD 626” in the following comparisons. The E cutoff effects on the CDSD-40 0 0 intensity are better manifested in Fig. 16c, from black (original.J = 150), grey (E 32K) to blue (E 24K). Although, it is also clear that the difference between E 32K and E 44K (original) is noticeable but not very significant. It becomes even smaller at higher wavenumbers, i.e. no discernible difference beyond 4200 cm−1 . However, the difference between the E 24K and E 32K lists is still large even at 7500 cm−1 , see Fig. 16b. Because the CDSD.E 24K (blue) and CDSD.E 24K.J0-150 (green) overlap with each other, the Ames.1E-29.J ≤ 150 (cyan) vs. CDSD.E 24K.(blue) can be taken as the apple-to-apple comparison. In the rest of this section, the solid blue curve is denoted C (for CDSD-40 0 0), the solid cyan curve is denoted A (for Ames). In Fig. 16, we can see the C and A curves have good agreement for strong peaks below 50 0 0 cm−1 . Their main differences are clearly noted in all the weakest IR regions between strong peaks. For example, A is stronger than C in 1100–1250 cm−1 , ∼2700 cm−1 , and ∼4100 cm−1 . Then C is stronger than A in 1250–1700 cm−1 , and 510 0–550 0 cm−1 . This suggests that the higher E cutoff effects play a more important role. Beyond 5800 cm−1 , the A

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intensity is always larger than C and all other subsets of CDSD40 0 0, especially between 70 0 0–80 0 0 cm−1 . We believe the intensity contribution from the Ames-40 0 0K’s COMPLETE coverage up to E = 24,0 0 0 cm−1 dominates the higher wavenumber region. In other words, there are two factors contributing simultaneously: CDSD-40 0 0 has higher E and accordingly more intensities from high lying bands that still follow the similar delta P (polyad number) intensity models, Ames-40 0 0 has complete transitions up to 24,0 0 0 cm−1 and accordingly more intensities for those bands not covered by CDSD intensity models. In current comparison, if C is stronger than A, first factor prevails; if A is stronger than C, the 2nd factor dominates, this is especially true for the higher wavenumber range >5800 cm−1 . Based on these observations, our summary and suggestions about the reliability of the Ames and CDSD 626 lists at 40 0 0 K are: (1) 0–300 cm−1 or >5800 cm−1 , the Ames list is better than the full CDSD-40 0 0, but the Ames lists need E extended to 44,0 0 0 cm−1 for intensity compensation. (2) 30 0–110 0 cm−1 , 20 0 0–250 0 cm−1 , 350 0–390 0 cm−1 differences are small in peak regions. (3) for the remaining regions, if C roughly agrees with A, full CDSD is considered more reliable. Where the E cutoff effect is large, the CDSD list is more complete than the current A list, e.g. 1750–20 0 0 cm−1 , 290 0–340 0 cm−1 , and 410 0–510 0 cm−1 . (4) if C is significantly higher than A, e.g. 1250–1750 cm−1 , the real intensity could lie somewhere between full CDSD and A. For the 5150–5500 cm−1 range, the E cutoff effect on the CDSD intensity is small, so the real intensity curve could be closer to A. (5) if C is lower than A, we expect the real intensity to be even higher than the full CDSD, e.g. 110 0–1250 cm−1 , 250 0 −2900 cm−1 , and 3900–4200 cm−1 . The two basic assumptions behind these claims are: our confidence in the DMS-N2 performance for E up to 24,0 0 0 cm−1 ; and the effective coverage completeness of the EDM model extrapolation from measured bands to higher energy bands. However, it should be noted that this discussion is based on a log scale, and conclusions may be different if one only focuses on the strongest peak regions and uses a linear scale. 6. Prediction example: identifying a missing band In last a few years, the completeness and reliability of the Ames line lists have been verified in various CO2 isotopologue IR experiments. Using 17 O or 18 O enriched gas samples, currently experimentalists focus on either weak bands of relatively abundant isotopologues, or strong bands of less abundant isotopologues. These studies can improve the completeness of CO2 line list databases. Fig. 17 gives an unpublished example we studied in Feb. 2015. The blue sticks (top and bottom panels) and circles (middle panel) are the residuals determined in a spectrum of 17 O-enriched (> 45%) CO2 mixture sample obtained at JPL [44,45]. The spectra was recorded at 299.4 K with a total mixture pressure of 44.97 Torr and an optical path length of 20.94 m. The residuals did not match any bands in HITRAN2012 or CDSD, so it probably represents a missing band. Note the experimental temperature at 299.4 K is close enough to make direct comparison with Ames-296 K lists. With all 13 Ames-296 K lists plotted in the range of 4580–4650 cm−1 , these residual transitions have been confidently identified as the 2ν 3 band of 728, 0 0 021 ← 0 0 0 01. The Ames 728 2ν 3 transitions are shown by red sticks in the three panels. In the top panel, the overall comparison confirms the assignment. The JPL residual data includes transitions from P38e at 4585.336 cm−1 to R43e at 4640.587 cm−1 . The experimental line positions and peak heights

Fig. 17. Ames-296K 728 2ν 3 list (red) vs. JPL Expt. IR analysis residuals (blue). The 728 2ν 3 band is missing in CDSD or HITRAN2012. Top: overall comparison; middle: intensity pattern matches; bottom: line position matches. The S(Ames) intensities are given in cm/molecule, and with 100% abundance. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

were determined using a peak find algorithm. Note that the experimental line positions of P24e, P1e, R0e, R1e are not available, because they are either overshadowed by other strong transitions, or too weak to be determined here. See top and middle panels. In general, the intensity patterns match very well. The only outlier at 4630.745 cm−1 is P16e. Since it was manually separated from a doublet feature, the associated uncertainty is relatively larger. In the middle panel, we can see the residual peak heights (blue circles) can roughly match the line intensities. But the ‘measured’ line positions do carry very high precision, i.e. better than 0.002 cm−1 . The bottom panel indicates that the E(Ames – Expt) deviations are systematically negative. The red shifts from J = 0 to J ∼40 vary from −0.043 cm−1 to −0.049 cm−1 . For the 17 O/18 O mixed isotopologue, the deviations on the band origins can be minimized in future PES refinements and lists. 7. Summary and future work In addition to many checks on the predictive accuracy and completeness using the latest experimental high-resolution IR data, we have made progress in several aspects of the Ames CO2 IR line list project. (1) A new 626-based PES refinement was carried out, denoted Ames-2. It is utilized in the latest IR list computations. The C-O stretching basis defect is fixed. Now it can reproduce most experimental Gv with σ RMS = 0.012 cm−1 . The Ames2 PES also fixes the energy level and intensity breaks at J∼30–40 and J∼60. Future PES refinements can wait until more high-resolution experimental data become available for higher energy bands and/or very weak bands. Isotopespecific PES correction terms are necessary for isotopologues to reach uniform accuracy at high J’s. (2) Conventional vibrational polyad quantum numbers are assigned for the J = 0–150 levels with E < 15,0 0 0 cm−1 . This means 117,0 0 0 to 282,0 0 0 levels for every isotopologue. Although our assignments >10,0 0 0 cm−1 require more effort, the new line shape parameters generated with these vibrational quanta are very similar in quality to those in HITRAN2012. The new parameters in the Ames-2016 lists are expected to be realistic and helpful. These will be updated when more robust assignments become available for higher energies.

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(3) ∼1% agreement is found with the latest experimental IR intensities of the 626 30 013-0 0 0 01 and 20 013-0 0 0 01 bands. Though the variationally computed intensities do have PES or DMS dependence as large as 0.5–1%. This analysis indicates that certifying the quality of the DMS and line list intensities to 1% or sub-percent accuracy will require further work. It also casts doubt on the validity of any ∼1% accuracy claim, and other sub-percent accuracy claims. More highly accurate intensity measurements are desperately needed to properly estimate and improve the quality of Ames (and UCL) line lists and PES/DMS; (4) Ames CO2 intensities are considered highly consistent among isotopologues. The consistency for regular vibrational bands should be at least 1–3% (or better). It can provide reliable checks on measured intensity data and effective dipole models. By checking the S% (Ames vs. CDSD), we have demonstrated that, starting from vibrational fundamental bands and pure rotational bands, there exist many inter-isotopologue inconsistencies and systematic deviations in the CDSD intensity data. For example, the pure rotational band intensity of 628 and 627 are greatly overestimated. The inter-isotopologue inconsistency is usually band dependent, e.g. ν 3 is different from ν 2 . But sometimes there patterns exist. For example, the ν 2 related bands have 628 and 627 as common outliers. This could be a result from using the same EDM dataset in several related studies. (5) Compared with the CDSD-40 0 0 database (E < 44,0 0 0 cm−1 ), the Ames-40 0 0 list (E < 24,0 0 0 cm−1 ) already has more intensity below 300 cm−1 or above 5800 cm−1 . But the CDSD40 0 0 database still exhibits more complete intensities in several wavenumber ranges from 300 cm−1 to 5800 cm−1 . We believe this will be the case until the Ames lists can recover all “gap” intensities by running more robust calculations to include all levels up to E = 32,0 0 0 cm−1 - 44,0 0 0 cm−1 , (6) The ∼0.6% intensity gaps found at J = 0 between the P and R branches of symmetric CO2 isotopologue line lists can be fixed by reducing the symmetry of VTET calculations. Future line list updates will fix these gaps, and hopefully fix the e/f oscillations (∼1% or less) of asymmetric isotopologue for Q branches, too. Currently these gaps do not impact any qualitative, semi-quantitative IR comparisons, or most quantitative IR comparison. However, the situation may change if more highly accurate measured intensities become available. (7) To address other issues about the CO2 line lists and our strategy, more experimental data and systematic tests are required before we can make any reliable comments or suggestions, especially the issue of how the extrapolation accuracy degrades. Note that the choices of the vibrational bands compared in this paper really depend on their data quality and how it compares to Ames results. For example, the 20 013-0 0 0 01 and 30 013-0 0 0 01 bands are the first sets of intensity data carrying such high accuracy. Such comparison is a must-do and sure-to-include when new data become available. The 40 033(4)-0 0 0 01 bands are the first such weak bands (1E-29 magnitude) of CO2 626 which were reliably measured and reported that Ames lists could have intensity underestimation by half. It is worthwhile to discuss why and how to check and improve in future. The “missing band” example of 728 2ν 3 band is the only one we knew about its existence, compared, assigned, however not really experimentally “measured” or “published”. In other words, these bands were experimentalists’ choice, actually. The bands chosen to check the inter-isotopologue consistency are the three vibrational fundamental bands (and corresponding lowest hot bands, if not experimentally available), plus

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the pure rotational band of 628 and 627. We show that the consistency of these basic, fundamental bands are not good, not to mention bands with higher vibrational quanta. In addition, we did carry out the consistency check on EVERY vibrational bands in CDSD and interested readers can do the comparisons, too. The 50 0 06/60 0 07/70 0 08 bands in Ames prediction vs. CDSD extrapolation are reported because they are the lowest Gv series where Ames and CDSD numbers start to diverge. Scientists have asked about the possibility of rovibrational line position prediction as accurate as 0.002 cm−1 , e.g. for remotesensing applications. The request is well justified, but the core value of our line lists is to provide high quality predictions which we hope useful for the communities including lab spectra analysis. Based on our experience, the PES refinements are possible to reach 0.005 cm−1 for certain wavenumber range, but we seriously worry that the potential over-refinements could cause unexpected PES behavior in both lower and higher wavenumber regions. In short, it is possible (though very hard) to reach 0.002 cm−1 for a few bands, but it is probably not realistic (yet) for all IR bands on a global PES. There might exist exceptions where the molecular PES is relatively more harmonic. But generally, the empirical refinement based theoretical line lists cannot guarantee 0.002 cm−1 accuracy for rovibrational IR lines. It cannot be directly applied on remote-sensing, although we can manage to reach 3– 6 MHz (0.0 0 01–0.0 0 02 cm−1 ) for microwave spectra at low temperature, and 30–60 MHz at higher temperature. One temporary solution for now is to combine Ames or UCL rovibrational lists with the experimentally determined band origins or the effective Hamiltonian model based line positions, which in principle should result in 0.002 cm−1 or better accuracy for majority lines. For example, a “combined” list of CDSD-296 line position + Ames-2016 intensity is included in the Supplementary file. The 296 K size-reduced lists for all 13 CO2 isotopologues and a combined “natural” CO2 list are open to public access at http: //huang.seti.org. Full lists are available upon request, and will be made available on the NASA data portal http://data.nasa.gov soon. The “natural” CO2 list and the “combined” CDSD + Ames list are available in the Supplementary file. Note the Ames list files use the data format specified in the Table 2 of Ref. 3.

Acknowledgments DWS, TJL, and XH gratefully acknowledge financial support from the NASA Venus Express Supporting Investigator Program and from the NASA 13-PATM13-0012 grant. Huang acknowledges the NASA/SETI Co-operative Agreement NNX15AF45A. R.S Freedman acknowledges the NASA/SETI Co-operative Agreement NNX12AJ19A. We sincerely thank Dr. Keeyoon Sung (JPL) for kindly sharing unpublished CO2 spectra data and Professor Jonathan Tennyson (UCL) for kindly sharing the UCL DMS. We also thank Dr. Keeyoon Sung (JPL), Professor Jonathan Tennyson (UCL), and Dr. Iouli Gordon (Harvard CfA) for many helpful suggestions. References [1] Huang X, Schwenke DW, Tashkun SA, Lee TJ. An isotopic-independent highly accurate potential energy surface for CO2 and an initial 12 C16 O2 infrared line list. J Chem Phys 2012;136:124311. [2] Huang X, Freedman RS, Tashkun SA, Schwenke DW, Lee TJ. Semi-empirical 12 16 C O2 IR line lists for simulations up to 1500 K and 20,000 cm−1 . J Quant Spectrosc Radiat Transf 2013;130:134. [3] Huang X, Gamache RR, Freedman RS, Schwenke DW, Lee TJ. Reliable infrared line lists for 13 CO2 isotoplogues up to E’=18,0 0 0 cm−1 and 1500 K, with line shape parameters. J Quant Spectrosc Radiat Transf 2014;147:134. [4] Petrova TM, Solodov AM, Solodov AA, Lyulin OM, Tashkun SA, Perevalov VI. Measurements of 12 C16 O2 line parameters in the 8790-8860, 9340-9650 and 11430-11505 cm−1 wavenumber regions by means of Fourier transform spectroscopy. J Quant Spectrosc Radiat Transf 2013;124:21.

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[5] Polyansky OL, Bielska K, Ghysels M, Lodi L, Zobov NF, Hodges JT, et al. High-accuacy CO2 line intensities determined from theory and experiment. Phys Rev Lett 2015;114:243001. [6] Jacquemart D, Borkov YG, Lyulin OM, Tashkun SA, Perevalov VI. Fourier transform spectroscopy of CO2 isotopologues at 1.6 μm: line positions and intensities. J Quant Spectrosc Radiat Transf 2015;160:1. [7] Petrova TM, Solodov AM, Solodov AA, Lyulim OM, Borkov YG, Tashkun SA, et al. Measurements of CO2 line parameters in the 9250-9500 cm−1 and 10,700-10,860 cm−1 regions. J Quant Spectrosc Radiat Transf 2015;164:109. [8] Tan Y, Zhao XQ, Liu AW, Hu SM, Lyulin OM, Tashkun SA, et al. Cavity ring– down spectroscopy of CO2 overtone bands near 830 nm. J Quant Spectrosc Radiat Transf 2015;165:22. [9] Serdyukov VI, Sinitsa LN, Loguovskoi AA, Borkov YG, Tashkun SA, Perevalov VI. LED-based Fourier transform spectroscopy of 16 O12 C18 O and 12 C18 O2 in the 11,260-11430 cm−1 range. J Quant Spectrosc Radiat Transf 2016;177:145. [10] Karlovets EV, Kassi S, Tashkun SA, Perevalov VI, Campargue A. High sensitivity cavity ring down spectroscopy of carbon dioxide in the 1.19-1.26 μm region. J Quant Spectrosc Radiat Transf 2014;144:137. [11] Vasilchenko S, Konefal M, Mondelain D, Kassi S, Cermak P, Tashkun SA, et al. The CO2 absorption spectrum in the 2.3 μm transparency window by high sensitivity CRDS: (I) Rovibrational lines. J Quant Spectrosc Radiat Transf 2016;184:233. [12] Devi VM, Benner DC, Sung K, Brown LR, Crawford TJ, Miller CE, et al. Line parameters including temperature dependences of self- and air-broadened line shapes of 12 C16 O2 : 1.6-μm region. J Quant Spectrosc Radiat Transf 2016;177:117. [13] Benner DC, Devi VM, Sung K, Brown LR, Miller CE, Payne VH, et al. Line parameters including temperature dependences of air- and self-broadened line shapes of 12 C16 O2 : 2.06-μm region. J Mol Spectrosc 2016;326:21. [14] Huang X, Schwenke DW, Lee TJ. Empirical infrared line lists for five SO2 isotopologues: 32/33/34/36 S16 O2 and 32 S18 O2 . J Mol Spectrosc 2015;311:19 Similar issue as in CO2 . [15] Patridge H, Schwenke DW. The determination of an accurate isotope-dependent potential energy surface for water from extensive ab initio calculations and experimental data. J Chem Phys 1997;106:4618. [16] Schwenke DW. Variational calculations of rovibrational energy levels and transition intensities for tetratomic molecules. J Phys Chem 1996;100:2867. [17] Gamache RR, Lamouroux J. The vibrational dependence of half-widths of CO2 transitions broadened by N2 , O2 , air, and CO2 . J Quant Spectrosc Radiat Transf 2013;117:93–103. [18] Karlovets EV, Campargue A, Mondelain D, Beguier S, Kassi S, Tashkun SA, et al. High sensitivity Cavity Ring Down spectroscopy of 18 O enriched carbon dioxide between 5850 and 70 0 0 cm−1 : I. Analysis and theoretical modeling of the 16 O12 C18 O spectrum. J Quant Spectrosc Radiat Transf 2013;130:116 – Not really compared here. [19] Borkov YG, Jacquemart D, Lyulin OM, Tashkun SA, Perevalov VI. Infrared spectroscopy of 17 O- and 18 O-enriched carbon dioxide: Line positions and intensities in the 320 0-470 0 cm−1 region. Global modeling of the line positions of 16 12 17 O C O and 17 O12 C17 O. J Quant Spectrosc Radiat Transf 2014;137:57. [20] Elliott BM, Sung K, Miller CE. FIT-IR spectra of 17 O-enriched CO2 in the ν 3 region: high accuracy frequency calibration and spectroscopic constants for 16 12 17 17 12 17 O C O, O C O, and 17 O12 C18 O. J Mol Spectrosc 2014;304:1. [21] Elliott BM, Sung K, Miller CE. FIT-IR spectra of 18 O- and 13 C-enriched CO2 in the ν 3 region: High accuracy frequency calibration and spectroscopic constants for 16 O12 C18 O,18 O12 C18 O, and 16 O13 C16 O. J Mol Spectrosc 2015;312:78. [22] Borkov YG, Jacquemart D, Lyulin OM, Tashkun SA, Perevalov VI. Infrared spectroscopy of 17 O- and 18 O-enriched carbon dioxide: line positions and intensities in the 4681-5337 cm−1 region. J Quant Spectrosc Radiat Transf 2015;159:1. [23] 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.

[24] Tashkun SA, Perevalov VI, Gamache RR, Lamouroux J. CDSD-296 high resolution carbon dioxide spectroscopic databank: Version for atmospheric applications. J Quant Spectrosc Radiat Transf 2015;152:45. [25] Zak E, Tennyson J, Polyansky OL, Lodi L, Zobov NF, Tashkun SA, et al. A room temperature CO2 line list with ab initio computed intensities. J Quant Spectrosc Radiat Transf 2016;177:31. [26] Zak E, Tennyson J, Polyansky OL, Lodi L, Zobov NF, Tashkun SA, et al. Room temperature line lists for CO2 symmetric isotopologues with ab initio computed intensities. J Quant Spectrosc Radiat Transf 2017;189:267–80. [27] Zak E, Tennyson J, Polyansky OL, Lodi L, Zobov NF, Tashkun SA, et al. Room temperature line lists for CO2 asymmetric isotopologues with ab initio computed intensities. J Quant Spectrosc Radiat Transf 2017 (in press). doi:10.1016/ j.jqsrt.2017.01.037. [28] Tashkun SA, Perevalov VI. CDSD-40 0 0: high-resolution, high-temperature carbon dioxide spectroscopic databank. J Quant Spectrosc Radiat Transf 2011;112:1403–10. [29] Huang X, Schwenke DW, Lee TJ. An accurate global potential energy surface, dipole moment surface, and rovibrational frequencies for NH3 . J Chem Phys 2008;129:214304. [30] Huang X, Schwenke DW, Lee TJ. Rovibrational spectra of ammonia. I. Unprecedented accuracy of a potential energy surface used with nonadiabatic corrections. J Chem Phys 2011;134:044320. [31] Huang X, Schwenke DW, Lee TJ. Highly accurate potential energy surface,dipole moment surface, rovibrational energy levels, and infrared line list for 32 S16 O2 up to 80 0 0 cm−1 . J Chem Phys 2014;140:114311. [32] Schwenke DW. Variational calculations of rovibrational energy levels and transition intensities for tetratomic molecules. J Phys Chem 1996;100:2867–84. [33] Schwenke DW. Beyond the potential energy surface: ab initio corrections to the Born-Oppenheimer approximation for H2 O. J Phys Chem A 2001;105:2352–60. [34] Polyansky OL, Csaszar AG, Shirin SV, Zobov NF, Barletta P, Tennyson J, et al. High-accuracy ab initio rotation-vibration transitions for water. Science 2003;299:539–42. [35] Schwenke DW. First principles prediction of isotopic shifts of H2 O. J Chem Phys 2003;118:6898. [36] Sung K, Brown LR, Huang X, Schwenke DW, Lee TJ, Coy SL, et al. Extended line positions, intensities, empirical lower state energies and quantum assignments of NH3 from 6300 to 70 0 0 cm−1 . J Quant Spectrosc Radiat Transf 2012;113:1066–83. [37] Tennyson J, Henderson JR, Fulton NG. DVR3D: programs for fully pointwise calculation of rovibrational spectra of tri-atomic molecules. Comput Phys Commun 1995;86:175–98. [38] Bierret A, Desbois Q, Martin J-L, Kassi S, Tashkun SA, Perevalov VI, et al. Intracavity laser absorption spectroscopy of 13 C16 O2 near 734 nm. J Mol Spectrosc 2014;298:38. [39] Tan Y. private communications (Aug. 2016) [40] Rothman LS, Gordon IE, Barbe A, et al. The HITRAN2008 molecular spectroscopic database. J Quant Spectrosc Radiat Transf 2009;110:533–72. [41] Tashkun SA, private communications (2013). [42] Rothman LS, Jacquemart D, Barbe A, et al. The HITRAN 2004 molcular spectroscopic database. J Quant Spectrosc Radiat Transf 2005;96:139–204. [43] Pickett HM, Poynter RL, Cohen EA, Delitsky ML, Pearson JC, Muller HSP. Submillimeter, millimeter, and microwave spectral line catalog. J Quant Spectrosc Radiat Transf 1998;60:883–90. [44] Sung K, private communications (2015, 2016). [45] Jacquemart D, Sung K, Coleman M, Crawford T, Brown LR, Mantz AW, et al. Measurements and modeling of 16 O12 C17 O spectroscopic parameters at 2 μm. J Quant Spectrosc Radiat Transf 2017 Special issue for HITRAN, in press. doi:10. 1016/j.jqsrt.2017.03.002.

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