Highly accurate potential energy surface and dipole moment surface for nitrous oxide and 296K infrared line lists for ¹⁴N₂¹⁶O and minor isotopologues

Abstract

To facilitate the data analysis of current and future high-resolution space telescope missions, we adopt ‘Best Theory + Reliable High-resolution Experiment’ (BTRHE) strategy to develop highly accurate infrared line lists for nitrous oxide (N₂O). The ‘Ames-1’ potential energy surface (PES) is a CCSD(T)/aug-cc-pVQZ PES refined using selected HITRAN experimental data, with σ_rms = 0.02–0.03 cm^-1 for five isotopologues. The ‘Ames-1’ dipole moment surface (DMS) is fitted from CCSD(T)/aug-cc-pV(T,Q,5)Z dipoles extrapolated to one electron basis set limit. Using the Ames-1 PES and DMS, Ames-296K line lists are computed in the full range of 0–15,000 cm^-1 for 12 N₂O isotopologues, with S_296K ≥ 10⁻³¹ cm^-1/molecule.cm^-2. The reliability and consistency of Ames-296K intensity predictions (S_Ames) are demonstrated through comparisons with HITRAN (S_HITRAN), NOSL-296 (S_NOSL), recent observed intensities (S_obs) and Effective Dipole Model (EDM) intensities (S_EDM). Agreements and discrepancies are discussed, along with preliminary uncertainty estimate for S_Ames. The S_Ames provides a good constraint to prevent substantial errors in intensity predictions (e.g. for weak bands and minor isotopologues) and can be further improved. Ames-296K and NOSL-296 may complement each other to provide improved input for future database updates, combining the strengths of EH/EDM and BTRHE approaches. Data available at https://doi.org/10.5281/zenodo.7888194 and https://doi.org/10.48667/9kmk-0334.

GRAPHICAL ABSTRACT

KEYWORDS:

• Nitrous Oxide
• dipole moment surface
• rovibrational IR line list
• potential energy surface refinement
• IR intensity prediction

1. Introduction

There is an increasing need for highly accurate rovibrational line lists, including infrared intensities, of small molecules that are common in various solar system planet and moon environments, brown dwarfs, the interstellar medium (ISM) and exoplanet atmospheres. [1,2] This is being driven by the availability of ever increasingly high-resolution telescopes and instruments, including space-based such as JWST, TESS and NGRST, and ground based such as ALMA, several planned extremely large telescopes, as well as unassigned archived spectra from high-resolution instruments such as HiFi on Herschel and EXES on plane-based SOFIA mission. To maximise the scientific return for these missions, the line lists need to provide both accurate line positions and line strengths as well as being complete enough to be able to describe the large temperature extremes of the different environments.

Nitrous oxide, N₂O, was the third N–O bond molecule detected in the ISM, after NO and HNO. In 1994, Ziurys et al. [3] reported the P3–P6 transitions observed in the dense, higher temperature regions in the cold molecular cloud Sgr B2 (M) by the NRAO 12 m telescope. The N₂O distribution in Sgr B2 is different from that of NO and HNO, suggesting a hot chemistry pathway [4]. Nitrous oxide is a valuable tracer molecule for the nitrogen abundance and nitrogen chemistry in the ISM [5], although the role of related nitrogen chemistry in the whole ISM chemistry network is not fully understood yet. Experiments show it should exist on dust grains and icy mantles exposed to UV, solar wind and cosmic ray radiations [6–10]. In addition, N₂O is one of the 10 gases significantly contributing to Earth’s transit spectrum [11], with several strong bands in the mid-infrared (MIR) region, e.g. at 7.8, 8.5 and 17 $\mu$m. It is relatively stable up to a temperature of 1100 K. As one of the main greenhouse gases in the Earth’s atmosphere, it has a life time of 114 years with its main destruction mechanisms being absorption by bacteria, photodissociation by UV and other chemical reactions [12]. It is an important link of the nitrogen cycle on Earth and as well as in the ISM. It is related to organics breakdown by bacteria, agriculture and industrial activities. It also contributes to ozone depletion and acid rain formation, etc. Recent studies even suggest that in the early stage of life evolution some aquatic microbes may have breathed N₂O as the molecular oxygen level was very low [13]. Although the list of gases appropriate for other planets maybe different, recent modelling on exo-Earths and exo-Venuses usually include N₂O as a biosignature tracer molecule [14]. Its rovibrational spectroscopic signature can be used to deduce the conditions of the interstellar environment and exoplanetary atmospheres.

The N₂O data in existing high-resolution IR line list databases, e.g. HITRAN [15] and GEISA [16], is far from suitable for accurate modelling over the full IR range, at high temperatures, or for mixed isotopologues. HITRAN2004 [17] combined the microwave data from HITRAN2000 [18] with Toth's ‘SISAM.N2O’ line list [19] in the range of 500–7500 cm^-1 with intensity cut-off at 2×10⁻²⁵ cm/molecule. After that, there were very limited changes or updates for the main isotopologue. From HITRAN2016 [20] to HITRAN2020, only two ¹⁴N₂¹⁶O bands had intensities revised based upon the high accurate measurements from NIST [21]. In HITRAN2020, many bands are missing above 5000 cm^-1, or wavelengths shorter than 2 $\mu$m, and no ¹⁴N₂¹⁶O data beyond 1.28 $\mu$m or 7800 cm^-1 is included. Most data in GEISA [16] were also from Toth's list. Obviously, the databases are already insufficient at 296 K. They will be woefully inadequate at higher temperatures, where the weak lines missing at 296 K will become more dominant.

To fill in the data gap, numerous high-resolution IR studies have been reported in last 20 years by scientists in France, US, China, Russia and other countries, including measurements and modelling for both the main isotopologue ¹⁴N₂¹⁶O, e.g. Refs. [22–31] and [32–40], and several minor isotopologues including ¹⁴N¹⁴N¹⁸O [34], ¹⁴N¹⁵N¹⁶O [41–43], ¹⁵N¹⁴N¹⁶O [42], ¹⁵N¹⁵N¹⁶O [42,44–46] and ¹⁵N¹⁴N¹⁸O [47]. A summary of ¹⁴N₂¹⁶O IR intensity data sources can be found in Tashkun and Campargue's NOSL-296 paper [48]. Experimental data accumulated from these studies helped to improve the corresponding N₂O Effective Hamiltonian (EH) models (e.g. [39,40,46,49]) and Effective Dipole Models (EDM). Those models were developed to construct several EH/EDM line lists from NOSD-1000 [50], NOSD+ for HITEMP [51], to the latest NOSL-296 [48], with different wavenumber and intensity coverage. These experiments and EH/EDM line lists have significantly enhanced the completeness and quality of N₂O line lists. The EH-based line positions have excellent accuracy comparable to experiments in the interpolation region, while the EDM model accuracy for measured bands is more dependent on the systematic uncertainties in the intensity data, which is usually 1–20%. The bottleneck of EH/EDM based line lists mainly lies in the incompleteness of coverage caused by the difficulties in the measurements for thousands of weak bands and high energy bands, and bands of minor isotopologues. The reliability of EDM model extrapolations usually degrades quickly and predictions are much less accurate.

Our semi-empirical N₂O study answers the call for highly accurate IR line lists for the key molecules in astrophysical environments and atmospheric studies. The goal is to provide the most inclusive and accurate spectroscopic information for N₂O for astronomical Far/Mid/Near IR data analysis, with accuracy good enough to fill data gaps, identify bad data or model defects and provide high-quality simulations up to 1000 K or higher (if necessary). The strategy of ‘Best Theory + Reliable High-resolution Experimental data’ (BTRHE) combines the advantages of experiment and theory. It has been successfully extended at Ames from H₂O [52,53] to NH₃ [54–57], CO₂ [58–63] and SO₂ [64–67]. The semi-empirical rovibrational energy levels and/or IR line lists of these molecules were computed using highly accurate ab initio potential energy surface (PES) refined with selected experiment data and high-quality ab initio dipole moment surface (DMS). ExoMol [68] and TheoRets [69] colleagues adopt strategies with similar ideas. In addition to reproducing most existing measured transitions with σ_RMS = 0.01–0.02 cm^-1 and 1–10% intensity deviations, the core value of this strategy is to ensure most of our predictions have similar or good enough accuracy for those bands missing from observation or databases, i.e. higher energy bands, weak bands and minor isotopologue bands, etc. Consequently, the strengths of those reliable line lists mainly lie in the completeness and consistency across vibrational bands and isotopologues. For example, recent hot CO₂ line lists [60,63,70,71] have been expanded from 8310 to 20,000 cm^-1, and the IR and microwave (MW) line list consistencies among all CO₂ [61] and SO₂ [66,67,72,73] isotopologues have been qualitatively or semi-quantitatively explored [74,75]. Furthermore, these line lists can be enhanced with experimental or EH-based line positions and measured accurate intensities, to retain the advantages of both experiment and theory but avoid their potential deficits. Examples include the recent CO₂ line lists from the UCL-IAO list [76,77] in HITRAN2016 update [20] to UCL-4000 [71], and AI-3000 K [63].

The goals we have set out for ourselves take several upgrades or even cycles to fulfil. This paper is the initial one in a series, reporting the first generation of isotopologue independent Ames PES, DMS for nitrous oxide, and 296 K line lists for ¹⁴N₂¹⁶O and minor isotopologues. Additional papers are in preparation for new DMS and high temperature line list at 1000 K. Future upgrades of DMS, intensity predictions, next cycle of PES refinement and line lists are under investigation, and will be reported in due course. This paper is structured as follows. Section 2 simply introduces the BTRHE algorithm, basics of ab initio PES, DMS constructions and quantum rovibrational calculations. Section 3 presents the data products of Ames-1 PES, DMS and 296 K line lists. In Section 4, the Ames-296 K line list predictions are compared to HITRAN, NOSL-296 and recent experiments, with focus on intensity agreements and disagreements. Section 5 summarises the status of work, presents our perspectives on intensity comparisons and prospects for the next stage of future improvements.

Recently, Tashkun and Campargue [48] have reported NOSL-296 room temperature line list for ¹⁴N₂¹⁶O using non-polyad EH models and EDM models. It includes nearly 900,000 lines in the range of 0.02–13,378 cm^-1 with intensity ≥10⁻³⁰ cm/molecule at 296 K. The NOSL-296 list was compared to a preliminary Ames 296K line list [78] we released in Nov. 2021 at https://huang.seti.org/N2O/n2o.html. Their nice and detailed comparisons with that line list simplify the present discussion, for some of the discussion and figures of the general agreement on line position and intensity, and the comparison details on a few bands, are unchanged with the present line list. We will acknowledge the discrepancies, address some concerns and focus on other aspects, e.g. additional comparisons with historical experimental data and EDM models, and our perspective from semi-empirical calculations.

At the potential energy minimum of its electronic ground state, N₂O has a linear structure with experimentally determined r_NN =1.12729 Å, r_NO =1.18509 Å [79] and B₀ = 0.41901cm^-1, or 12,561.633 MHz [19]. The three vibrational fundamentals are ν₁ for r_NN+r_NO stretches at 1285 cm^-1, ν₂ for linear bending at 590 cm^-1 and ν₃ for r_NN–r_NO stretches at 2220 cm^-1. The polyad number P = 2ν₁+n₂+4n₃ has also been adopted in published studies, e.g. [39]. Both polyad and non-polyad vibrational band names are used in this paper for convenience when compared to experiments.

Please note that we use S for line intensity, and Fig.Sx for additional figures in supplementary file. We follow HITRAN to use the ones unit of N–N–O atomic mass numbers to label the isotopologue, e.g. the main isotopologue ¹⁴N₂¹⁶O: 446; ¹⁴N¹⁵N¹⁶O: 456; ¹⁵N¹⁴N¹⁶O: 546; ¹⁴N¹⁴N¹⁸O: 448; ¹⁵N¹⁵N¹⁶O: 556, etc. The terrestrial abundances HITRAN [15] adopted for the five most abundant isotopologues are: ¹⁴N₂¹⁶O (99.03%), ¹⁴N¹⁵N¹⁶O (0.36%), ¹⁵N¹⁴N¹⁶O (0.36%), ¹⁴N₂¹⁸O (0.20%) and ¹⁴N₂¹⁷O(0.04%). The ¹⁴N₂¹⁸O (448) line list in HITRAN (from SISAM.n2o [19]) was improved during HITRAN2016 [20] update by >110,000 new lines computed using a global EH polyad model and an EDM model for ¹⁴N₂¹⁸O [34]. Consequently, this minor isotopologue has the best coverage in all N₂O isotopologues: from 0 to 10,364 cm^-1 and intensity at 296 K as weak as 10⁻²⁹ cm/molecule after scaled by terrestrial abundances. In contrast, the main isotopologue (446) has 33,265 lines in HITRAN2020, with intensity stronger than 2 × 10⁻²⁵ cm/molecule at 296 K. This further indicates the necessity of a major upgrade for ¹⁴N₂¹⁶O line list.

2. Theory and methods

The procedure of BTRHE algorithm has been summarised in Ref. [80] for interested readers. Generally, a series of ab initio PES is fitted with σ_rms ∼0.1 cm^-1 or better to retain as much information as possible from electronic structure calculations. One PES is selected for refinement using hundreds of reliable rovibrational energy levels determined from experiments. When satisfactory accuracy is achieved for both refinement and overall energy level reproduction or prediction, the wave functions computed on the refined PES are utilised to compute the transition dipole elements and IR intensities of rovibrational transitions on one or more high quality ab initio DMS. The compilation of line position, lower state energy E'’, IR intensity and Einstein A₂₁ coefficients and line profile parameters (if available) of each transitions forms the final IR line lists. The line profile modelling is a very active research field, but out of the scope of this work. Note that because each molecule is different, there are always unique concerns and challenges requiring different treatments.

Before Toth’s N₂O line list collection [19,81] and HITRAN updates, several sextic force fields were determined experimentally in 1980s [82,83]. In the 90s, several experimental studies were carried out beyond 10,000 cm^-1, e.g. Campargue [84–87], Weirauch [88], Daumont [89], Milloud [29] and their co-workers.

High quality ab initio quartic force fields (QFF) (e.g. [90] and [91]) and refinements using experiment data are not new practices for N₂O either, e.g. Yan [92] and Zuniga [93] reported two QFF refinements giving σ_rms = 0.34 cm^-1 for 60 vibrational states and σ_rms = 0.52 cm^-1 for 71 vibrational states, respectively. Such accuracy is insufficient for the highly accurate astronomical applications. As far as we know, there were no theoretical rovibrational IR line lists reported for N₂O prior to our work.

2.1. Ab initio calculations

Electron structure energy calculations for both PES and DMS are carried out by MOLPRO 2015.1 [94–96]. Thousands of geometries were first randomly generated near the linear potential energy minimum of N₂O. Coupled Cluster singles and doubles calculations are carried out at all geometries, with perturbation of triples included (CCSD(T) [97]) and using Dunning’s correlation-consistent basis sets aug-cc-pVXZ (X = T, Q and 5) [98]. The energies are extrapolated to one-electron basis set limit using a three-point formula [99]. Core–valence interaction effects are investigated by extrapolating the differences between the energies computed with and without inner core electron correlations, using aug-cc-pCVXZ (X = T and Q) bases [100] and a two-point formula [101].

For the DMS, finite field CCSD(T)/aug-cc-pVXZ (X = T, Q and 5) dipoles are computed on a denser geometry grid, with external electric field strength 0.0005 a.u., then extrapolated to one-electron basis set limit using the same three-point formula [99]. The numbers of geometries in each 1000 cm^-1 range cannot have big changes or oscillations or else a distorted DMS is produced.

2.2. PES fit

Every set of electronic state energies, including single basis or extrapolated or enhanced by core correlation and relativistic corrections, are fitted to a potential representation which may facilitate following refinements. The potential energy V is divided into a long-range part V_Long, and a short-range expansion V_Short, both in cm^-1. (1) $V=V_{\mathrm{Long}}+V_{\mathrm{Short}}$(1) The long-range part includes Morse-function terms and bending simulation terms: (2) $\begin{array}{rl}{V}_{\mathrm{Long}}^{\mathrm{Morse}}& =62000\cdot (1-e^{-2.8\mathrm{\Delta }{r}_{NN}}{)}^2\\ & +35000\cdot (1-e^{-2.9\mathrm{\Delta }{r}_{NO}}{)}^2\end{array}$(2) (3) $\begin{array}{rl}{V}_{\mathrm{Long}}^{\mathrm{bend}}& =\left[70000\cdot {\left(\text{cos}\frac{\theta }{2}\right)}^2+28000\cdot {\left(\text{cos}\frac{\theta }{2}\right)}^4\right]\cdot \\ & e^{-0.1\sum {(\mathrm{\Delta }r)}^2}\end{array}$(3) where Δr_NN and Δr_NO are the bond displacements (in Å)with respect to reference bond lengths, i.e. Δr_NN = r_NN – r_NN (ref), Δr_NO = r_NO – r_NO (ref), and θ is the ∠NNO angle. Please note these reference bond lengths are manually adjusted to ensure the least-squares fitting procedure will generate non-zero and large enough gradients for refinement purpose, thus they are not equal to the minimum geometries determined by experiments or found on a specific PES. The alpha values (2.8 and 2.9), dissociation and bending energies are selected after trials to minimise the fitting deviations. Obviously, their optimal values will depend on the basis set adopted in the ab initio calculation, geometry set, energy cut off, fitting basis and the separation between V_Long and V_Short terms. Although stable value ranges could be found for the majority of data sets we investigated in this work, it is not suitable to claim any of these values have accurate physical meanings. (4) $\begin{array}{rl}{V}_{\mathrm{Short}}& =f_{\mathrm{damp}}\cdot \sum C_{ijk}^n\mathrm{\Delta }{r_{NN}}^i\mathrm{\Delta }{r_{NO}}^j(si{n}^2\theta {)}^k\end{array}$(4) (5) $\begin{array}{rl}{f}_{\mathrm{damp}}& =e^{-2\sum {(\mathrm{\Delta }r)}^2-4\sum {(\mathrm{\Delta }r)}^4-0.25{(\pi -\theta )}^2-0.5{(\pi -\theta )}^4}\end{array}$(5) The short-range function is a damped polynomial expansion in terms of bond length and sin²θ changes. Using sin²θ is numerically equivalent to using (1-cos2θ)/2 if the bond angle θ is restricted in the range of 90–180°.

The damping function, f_damp, is defined to reduce short range terms at large nuclei distances and strongly bent geometries. The coefficients in the exponential terms are also determined from least-squares fits, to find a balance between σ_rms error reduction and effective damping. It is effectively a single minimum PES fit without N … N permutation, and the bending part of V_Long helps to minimise the impact of N … O … N isomerisation.

The PES geometry sets have 2774 points with energies up to 100,000 cm^-1, plus 33 boundary points to ensure the fitted PES is globally positive above the linear N–N–O minimum, as required physically. To maintain satisfactory fitting accuracy and minimise the loss of information from ab initio calculations, heavier weights are applied on the 2017 geometries with energy in the range from 0 to 28,000 cm^-1. The weighting function is similar to that used in previous studies [58,64]. (6) $w_i=\left[\frac{\begin{array}{c}\tanh (-0.0035\cdot (E_i-28000))\\ +1.002002002\end{array}}{2.002002002}\right]/\text{max}(28000,E_i)$(6) The remainder of the points are necessary to restrict the PES behaviour at higher energy range, i.e. to follow the basic shape of pure ab initio PES.

2.3. PES refinement

The coefficients of V_Short expansion terms up to quartic order are refined with respect to nearly 1000 rovibrational energy levels derived from HITRAN2016 [20], and selected band origins for high lying vibrational states near or above 10,000 cm^-1. Cycles of weighted non-linear squares fitting are carried out on the energy levels of four isotopologues: 446, 456, 546, and 448 (with J = 0, 1, 5, 10, 25, 35, 50, 65 and 80) to minimise the deviations. This is different from other studies where the reference datasets for the first PES refinement are usually started with main isotopologue levels only. However, we found that if we followed that procedure, the minor N₂O isotopologue levels computed have noticeable isotope dependent deviations. This could be related to the specific PES representation (e.g. parameters), but may require further investigation. The weights are both isotopologue and J dependent, and adjusted between cycles.

It should be noted that using HITRAN2016 based levels is not an optimal choice, since we concluded from earlier studies [58] that only pure experimentally measured energy levels should be incorporated in such PES refinements. However, the ierr number in HITRAN [17] is a valuable reference indicating the estimated uncertainty of line positions. Following the practice in SO₂ work [64], the reference HITRAN levels for refinement are restricted to ierr≥4 lines, i.e. line position uncertainty ≤ 10⁻⁴ cm^-1. Please note that all HITRAN energy levels mentioned in this paper and related discussions belong to ierr≥4 category, unless specified otherwise.

Even so, the Ames-1 refinement still ran into difficulties, or larger uncertainties, in the range of 7000–8000 cm^-1. We have decided to leave the energy range and the rotational structure of higher energy states for future PES refinements. Ames-2 probably will try to utilise either the experimental dataset behind NOSL-296 [48] or the MARVEL [102,103] dataset (for 446 only). The current Ames-1 PES refinement will serve as a good start.

At the end of each cycle, refined coefficients and other coefficients are used to generate energies on the same set of grid points included in the PES fits. The ‘refined’ energies are then fitted to get a new set of V_Short terms. In this way, the refinement impact is better balanced and represented by the whole set of hundreds of coefficients. The references r_NN and r_NO in the refit are manually adjusted by 0.0003 Å from the true minimum found on the refined PES, to make sure the gradients have magnitude large enough to allow further optimisation on the minimum geometry. Then the new PES becomes the basis of the next cycle of refinement. This procedure continues until the energy level deviations associated with the refined and refitted PES meet certain criteria, which usually is σ_rms ∼0.02 cm^-1.

A new practice introduced in the present work is to allow fitting basis or coordinates to vary from one cycle to next. The benefit is to explore better choices in either accuracy or simplicity, while it is important to track both the advantage and disadvantage of those choices.

Another issue to investigate in future refinements is the large relative variation of certain V_short coefficients from one cycle to the next. Potential explanations include, but not limited to, (1) the choice of V_Long terms has significantly reduced the magnitude of those coefficients; (2) the reference energy level set does not have enough information to reliably determine certain coefficients; (3) the damping functions over reduced the impact of coefficient changes.

2.4. DMS fit

The N₂O molecular dipoles are expressed as geometry dependent pseudo nuclear charges at the nuclei positions, $\begin{array}{rl}\overrightarrow{\mu }& =q_{N1}\cdot \overrightarrow{r_{N1}}+q_{N2}\cdot \overrightarrow{r_{N2}}+q_O\cdot \overrightarrow{r_O}\\ & =q_{N1}\cdot \overrightarrow{r_{N1}}+q_O\cdot \overrightarrow{r_O},\end{array}$because the centre N atom (N2) is fixed at the origin of Cartesian system. The pseudo-charges on the ending N and O atoms are separately fitted to two 10^th-order polynomials, each with 286 expansion coefficients $C_{ijk}^n$ (for q_N1) and $X_{ijk}^n$ (for q_O). The sin² basis is also selected for the bending part of Ames-1 DMS, because it gives one of the smallest σ_rms errors. $\begin{array}{rl}{q}_{N1}& =\sum _{n=1}^{286}{C}_{ijk}^n\mathrm{\Delta }{r_{NN}}^i\mathrm{\Delta }{r_{NO}}^j(si{n}^2{\mathrm{\angle }}_{NNO}{)}^k,\\ q_O& =\sum _{n=1}^{286}{X}_{ijk}^n\mathrm{\Delta }{r_{NO}}^i\mathrm{\Delta }{r_{NN}}^j(si{n}^2{\mathrm{\angle }}_{NNO}{)}^k,\\ \mathrm{\Delta }{r}_{NN}& =r_{NN}-1.1282,\\ \mathrm{\Delta }{r}_{NO}& =r_{NO}-1.1842\end{array}$Further investigation is underway for Ames-2 DMS upgrade, which may or may not continue using sin² basis. The references r_NN and r_NO are fixed at approximate values, because small changes do not affect the fitting accuracy. Uniform weights are applied on all ab initio dipoles components.

2.5. Rovibrational and intensity calculation

All the rovibrational calculations for energy levels, wave functions, and transition IR intensities are computed using the procedure described in Ref. [52] implemented in a parallel version of the VTET program [104]. We used hyper-spherical Radau coordinates, with the central N atom as the ‘heavy’ atom, and llk coupling scheme with maximum bending quantum number of 240. The angular matrix elements of PES were analytically determined after making a 241-term Legendre expansion of the PES, with average deviation between re-expansion and original values of less than 10⁻¹² a.u. The contracted basis functions are optimised for each JPS block. The cut-off for solving the one-dimension stretching Schrödinger equations were 0.30 hartree, i.e. 65,842 cm^-1 (1 hartree = 219474.6 cm^-1) with error criterion 10⁻⁸ for determining the number of optimised quadrature points [105]. For each J_z, we keep all bending functions with energies up to 0.5 hartree, and coupled contracted functions with energies below 0.25 a.u. The bending and stretching functions are coupled to form the final CI matrices, including all functions whose sum of energies was less than 0.3 a.u. The matrix size is limited to 90,000. All roots with energies up to 0.1 hartree (or 21,947 cm^–1) are extracted using a parallel direct diagonalisation algorithm. Corresponding wave functions are saved for the following intensity calculations. Please note that these calculations use nuclei masses, specifically 25519.04228557 a.u. for ¹⁴N, 27336.52570632 a.u. for ¹⁵N, 29148.94559967 a.u. for ¹⁶O, 30979.52097760 a.u. for ¹⁷O and 32802.46213885 a.u. for ¹⁸O.

For intensity calculations, we use 24-point optimised quadrature for stretches, and do angular integrals analytically using a 60-term associated Legendre expansion of the DMS. The expansion coefficients were determined from 72-point Gauss–Legendre quadrature. In the line list generation, we use E’_max cut-off of 20,000 cm^-1 above zero-point energy for upper state and intensity cut-off of 10⁻³¹ cm/molecule (no isotopologue factors are used in the intensity computation at this step). No restriction is applied on lower state energy E’’. The reference temperature is 296 K, to be consistent with HITRAN, HITEMP databases and NOSL-296 list.

A stretching basis related defect inside VTET program was corrected in early 2022. The defect was the root cause of the ∼0.6% intensity gap between P and R branches of the old Ames ¹²C¹⁶O₂ IR line lists [61]. The intensity gaps have been fixed in the latest Ames CO₂ line lists [62,63]. The early release of Ames-1 PES and DMS-based 296 K line list for ¹⁴N₂¹⁶O was also affected. For example, it caused the intensity oscillations between the even J and odd J in the Q branch of 0110–0000 band, as reported in NOSL-296 comparison [48]. The current Ames-296 K line lists have been re-computed and updated using the corrected version of VTET.

3. Data products: PES, DMS and 296K line list

3.1 Ames-0 PES

J = 0 vibrational band origins are computed using each of the ab initio PES series, then compared to 26 vibrational band origins below 6600 cm^-1 in HITRAN. The CCSD(T)/aug-cc-pVQZ fit gives the best overall agreement and uncertainty, i.e. mean ± σ_rms = 5.6 ± 3.4 cm^-1. Therefore, it is chosen as the Ames-0 PES to refine. Other good candidates include fits on CCSD(T)/aug-cc-pCVTZ (with core) and CCSD(T)/aug-cc-pCVQZ (no core) energies, with mean ± σ_rms deviations of –2.7 ± 7.2 cm^-1 and 6.5 ± 3.8 cm^-1, respectively. This is similar to what we saw in our CO₂ and SO₂ studies, where a QZ level PES exhibited the best error cancellation, while the PES including one-electron basis set extrapolation yields larger errors.

Figure 1(a) and Figure 1(b) show the distribution of the number of geometries and fitting deviations of Ames-0 PES as a function of energy. The accumulated mean of |δ| is 0.09, 0.11 and 0.13 cm^–1 for 1082, 1718 and 2017 points up to 10,000, 20,000 and 28,000 cm^–1, respectively. Corresponding σ_rms values are 0.17, 0.20 and 0.22 cm^–1. Relative fitting deviations are 0.0017% (mean absolute) and 0.0031% (σ_rms) at 20,000 cm^-1.

Figure 1. (a) Number of N₂O geometries along potential energy, each point represents a 1000 cm^-1 interval; (b) averaged absolute fitting residual (squares) and σ_rms (circles) for each 1000 cm^-1 (solid) and accumulated from zero (open).

The minimum geometry on Ames-0 is r_NN =1.12910 Å, r_NO =1.18786 Å. Harmonic frequencies are 1299.1, 597.1 and 2281.7 cm^-1. Vibrational fundamentals are 1286.3, 605.5 and 2224.1 cm^–1, and ZPE at 2367.5 cm^–1.

3.2. Ames-1 PES refinement and statistics

The reference energy level set for Ames-1 PES refinement contains 524 levels for the main isotopologue (446), and 153/170/166 levels for isotopologues 456/546/448, respectively. The fitting deviations are shown in Figure 2(a) using isotopologue-dependent colours. The largest deviations are mainly from 446 levels beyond 7000 cm^-1. In the final step of the refinement, those levels are included with weights of 0.01, or even less: during the course of the refinement, our algorithm looks for outliers that preclude satisfactory fitting of the vast majority of data. As given in the inset of Figure 2(a), the mean deviations of four isotopologues are all within ±0.007 cm^–1, while their σ_rms are 0.058 cm^–1 (446), 0.018 cm^–1 (456), 0.026 cm^–1 (546) and 0.026 cm^–1 (448), respectively. Unweighted total σ_rms is 0.045 cm^–1 for all 1013 levels, or 0.024 cm^-1 for 955 levels below 7450 cm^-1.

Figure 2. Accuracy of Ames-1 PES refinement. (a) remain deviations of energy levels in reference data set; (b) J = 0 energy level differences between Ames-1 PES, NOSD-1000 and experimental values.

Figure 2(b) displays the differences of J = 0 vibrational band origins between Ames-1 PES, experiment and EH model (NOSD-1000 [50]). Clearly, the EH model behind NOSD-1000 gives better agreement with experiment, especially between 6000 and 11,000 cm^–1, than our results using Ames-1 PES. For the whole range of 0–15,000 cm^–1, the 1σ uncertainty range is 0.032 cm^–1 (NOSD) versus 0.095 cm^–1 (Ames-1). It will be the focus of next Ames-2 refinement to reduce σ_Ames up to 11,000 cm^–1 down to 0.05 cm^–1 or less.

In the final form of Ames-1 PES, r_NN(ref) =1.129753 Å, r_NO (ref) =1.183664 Å. At the potential energy minimum, r_NN is 1.12820 Å and r_NO is 1.18454 Å. Compared to experiment values [79] 1.12729 and 1.18509 Å, Ames-1 has r_NN longer by ∼0.001 Å, and r_NO shorter by ∼0.0005 Å. We note that the bond lengths reported in a high level ab initio study with empirical correction are closer to experimental values, 1.12695(10) Å and 1.18539(5) Å [106]. It should be noted that the experimental values are obtained from modelling part of the measured N₂O spectrum, thus the only meaningful comparison is if this same modelling procedure is used to determine the equivalent parameters from the theoretical spectrum.

Compared to Ames-0, the differences of harmonic frequencies are all less than 1 cm^–1: 596.3 cm^–1 (Ames-1) versus 597.1 cm^–1 (Ames-0), 1298.5 cm^–1 (Ames-1) versus 1299.1 cm^–1 (Ames-0), 2281.9 cm^-1 (Ames-1) versus 2281.7 cm^–1 (Ames-0). The zero point energy increases slightly from 2367.5 to 2370.5 cm^–1. The three vibrational fundamentals are 1284.9, 588.8, 2223.8 cm^–1.

3.3. Ames-1 PES-based energy levels

J = 0–150 rovibrational energy levels of ¹⁴N₂¹⁶O are computed up to 20,000 cm^-1 above potential energy minimum on Ames-1 PES. Figure 3(a) gives comparison on 6908 ¹⁴N₂¹⁶O levels in HITRAN2020 (J = 0–98), with mean ± σ = 0.000 ± 0.021 cm^–1. This is an important check for both accuracy and consistency, because the accuracy for the full HITRAN level set should be very similar to what we acquired for the reference data set used in refinement, otherwise the reference dataset is not representative enough. Now the σ_rms 0.021 cm^–1 is close to the σ_rms= 0.024 cm^–1 from refinement. The mean deviation of 0.000 cm^–1 indicates there is no systematic deviation with respect to HITRAN level set. Note all HITRAN levels for 446 are included in Figure 3(a) and the statistics, with the exception of the 0440 and 0441 levels. The later levels are excluded because Tashkun et al. [40] concluded that the data used for these levels in HITRAN was from an over-extrapolation of the EH model. Our predictions are consistent with that conclusion. The δ deviations of pure rotational levels follow a nearly linear function of energy, with |δ| < 0.0001 cm^-1 at J = 0, to δ = −0.0503 cm^-1 at J = 81 and δ = -0.0742 cm^-1 at J = 98. This is mainly resulted from the deviations on B rotational constant. The vibrationally averaged zero-point geometry and the minimum geometry on the refined PES probably could thus be further improved. However, it should be noted that our rotational transitions agree well with experimental EH model on their line positions. The Ames-NOSL differences of the pure rotational band are 10⁻⁵, 0.0008 and 0.0017 cm^-1 at J = 0, 60 and 110, respectively. Maximum differences are similar on other bands, e.g. 0.0004 cm^–1 for ν₁←ν₁ R94e, 0.0017 cm^–1 for ν₂←ν₂ R103e, 0.0009 cm^–1 for 2ν₂←2ν₂ R96e.

Figure 3. N₂O rovibrational energy level differences (in cm^-1). (a) 446 levels, Ames-1 versus HITRAN; (b) 456, 546, 448 and 447 levels, Ames-1 versus HITRAN; (c) 448 (blue) and 556 (orange), Ames-1 versus EH/EDM-based IR line lists [34,46].

Figure 3(b) provides support for the Ames-1 PES refinement consistency across isotopologues. The statistics over HITRAN levels gives σ ≈ 0.02 cm^–1 across minor isotopologues, very similar to those reported in Figure 2(a). Except for isotopologue 448, most HITRAN transitions for minor isotopologues have ierr ≥ 4, so the level sets being compared in Figure 3(b) are close to full sets. For 448, in total there are 17,165 levels in HITRAN with J up to 106, the EH/EDM based 448 line list reported in Tashkun et al. [34] contains 27,189 levels with J up to 112. But only ∼1900 levels meet the ierr ≥ 4 criteria for comparison, with J up to 77.

Beyond HITRAN, an EH/EDM based line list of 556 isotopologue was reported at room temperature in 2016 [46]. It includes 51,391 lines and 9720 levels with J up to 97. Comparisons between Ames and EH model levels are given in Figure 3(c) for 448 and 556 isotopologues, as the 446 levels were already reported in the NOSL-296 paper [48]. Taking each EH level as reference, the differences are computed using the closest level located in the same JPS block of Ames-1 level list. The results presented in Figure 3(c) are qualitatively correct and numerically accurate for >95% data, but not 100% ‘exact’, because the accurate match between EH and semi-empirically calculated energy levels has never been an easy task due to differences in quantum number assignments [61,63,107]. In making Figure 3(c), sometimes one Ames level may have multiple matches, e.g. the 27th root in J = 21 A” block of 448, thus the real δ could be larger. Overall, the δ₅₅₆ differences below 6000 cm^-1 still fall within or on the edge of our expectation for such comparisons. The δ beyond 6000 cm^–1 is larger and will be monitored in future refinements.

But δ₄₄₈ shows a series of deviations of –0.33 cm^–1 at such a low energy under 1800 cm^–1, for the 0330 state. This is the largest ‘abnormal’ discrepancies we noticed in N₂O isotopologues, because its δ₄₄₈(0310) value of –0.0237 cm^–1 is consistent with the value for main isotopologue 446: δ₄₄₆(0310) = −0.0048 cm^-1 and δ₄₄₆(0330) = 0.0064 cm^-1. In other words, at J = 3, the δ₄₄₈ change is way too large for l₂ increment from 1 to 3. We are inclined to believe this has essentially broken the isotopologue consistency between ¹⁶O and ¹⁸O isotopologues. We estimate the real |δ₄₄₈|(0330) is less than 0.05 cm^–1 or close to 0.10 cm^–1 at worst. However, it will require new high-resolution experimental studies to elucidate the δ₄₄₈ discrepancies. More dramatic l₂ related d increases are also found for states with higher quanta in bending mode. For example, the δ₄₄₈ of 6ν₂ states are –0.62, –1.16, –2.93 to –6.18 cm^–1 for l₂ = 0, 2, 4 and 6, respectively.

3.4 Partition function

For the principal isotopologue, the partition function Q_Ames is 4984.9900 at 296 K. It is in almost exact agreement with the Effective Hamiltonian (EH) model value of 4984.8964 reported in 2016 for NOSD-1000 [50]. The data in that paper was adopted by HITRAN2016 [108] and HITRAN2020 [109] for ¹⁴N₂¹⁶O partition functions. Therefore, both Q_NOSD and Q_HITRAN are based on same set of EH model levels.

Using our J = 0–150 level set computed on the Ames-1 PES, Q_Ames increases to 56912.18 at 1000 K, compared to Q_NOSD-1000 = 56,912 and Q_HITRAN = 56,910.45. They are still in excellent agreement. At 2000K, the difference rises to 3%, 534,428.2 (Ames) versus 519,661.3 (HITRAN). At 3000 K, Q_Ames = 2,522,551, which is 25% larger than the Q_HITRAN value, 2,083,489 [15]. Such large differences indicate the HITRAN partition model or data is not sufficient for 3000 K simulations. In Figure 5 of the NOSL-296 paper [48], it is clearly demonstrated that the NOSL-296 line positions are systematically lower than Ames-296 K line positions by 0–3 cm^–1. This means E_Ames are higher than the EH model energies. Given the same set of rovibrational levels (with two sets of energies), Q_HITRAN or Q_NOSL should be slightly larger than Q_Ames at high temperatures, not lower. Since the Q_NOSD-1000 was computed with polyad number P_max = 24 and J_max = 300 [50], it is reasonable to expect that including higher P_max, e.g., P_max ≥ 30, will bring better agreement with Q_Ames at 3000 K.

The partition functions of other minor N₂O isotopologues are also calculated consistently, using their J = 0–150 levels computed on the same Ames-1 PES, with energy cut-off 0.1 hartree for the six most abundant isotopologues and 0.08 hartree for the remaining six minor isotopologues. It is confirmed in ¹⁴N₂¹⁶O test that the Q(296 K) changes caused by this 0.10 a.u. → 0.08 a.u. reduction of E_max is less than 0.001, or less than 0.0001 for Q(296 K)/g. The corresponding change on Q(1000 K) is less than 0.03, or 0.00004% of 56,912. Therefore, the Q(296 K) and Q(1000 K) values on Ames-1 PES have been converged consistently across all 12 isotopologues. The convergence of all Q(296 K)/g values from the Ames-1 PES is better than 0.0005. At higher temperatures, the relative difference rises to 0.55% at 2000K and 6.6% at 3000 K.

The zero-point energy, degeneracy g, Q(296 K)/g, and Q(1000 K)/g are reported for all 12 N₂O isotopologues in Table 1. The degeneracy g is computed as the product of 2I+1, with nuclei spin quantum number I(¹⁴N) =1, I(¹⁵N) =  $\frac{1}{2}$, I(^16/18O)  = 0 and I(¹⁷O) = 5/2. For minor isotopologues in HITRAN (546, 456, 447 and 448), their Q_HITRAN at 296 K are 0.3% higher than the converged Q_Ames values. Their Q_HITRAN values were computed from simple model approximations. Note Q_Ames and Q_EH also have nearly prefect agreement for the 556 isotopologue (not available in HITRAN), with difference less than 0.01%.

Table 1. Zero-point energy, degeneracy g, and partition function Q/g at 296 K and 1000 K, computed from J = 0–150 levels on Ames-1 PES with E_max = 0.08 or 0.10 hartree, and compared to EH model based Q values.

				QAmes/g	QAmes/g	QHITRAN/g	QHITRAN/g	δ %HITRAN	δ %HITRAN
#	Iso	ZPE	g	296 K	1000 K	296 K	1000 K	296 K	1000 K
1	446	2370.496	9	553.8878	6323.5756	553.8774	6323.3835	−0.002%	−0.003%
2	456	2331.907	6	558.4468	6534.2659	560.2656	6576.9983	+0.326%	+0.654%
3	546	2347.339	6	574.5331	6633.4991	576.3402	6668.4865	+0.314%	+0.527%
4	448	2341.226	9	588.5450	6849.5808	590.3855	6879.1214	+0.313%	+0.431%
5	447	2355.084	54	571.6307	6591.7999	573.4410	6625.5291	+0.317%	+0.512%
6	556	2308.498	4	579.3312	6857.3297	579.3 ^$
7	548*	2317.917	6	611.0181	7194.1227
8	458*	2302.315	6	593.6758	7084.9530
9	547*	2331.849	36	593.2025	6919.2141
10	457*	2316.327	36	576.4738	6814.9243
11	558*	2278.757	4	616.3865	7443.9754
12	557*	2292.841	24	598.2837	7156.1535

* E_max = 0.08 hartree, 17558 cm^-1 above potential zero, so E'_max = 17558 – ZPE. No impact on Q(296 K)/g. ^$ Ref. [46].

The energy level list also contains vibrational quantum numbers for each level. They are based on the leading CI basis function of the corresponding wave function, mainly for VTET internal reference. They are not expected to match the vibrational quanta labels given by either polyad or non-polyad EH models, except for some vibrational states at low energy. The difference between Ames PES-based levels and EH models needs to be further reduced before meaningful 1-to-1 matches can be carried out up to 15,000 cm^–1.

3.5. Ames-1 DMS

The Ames-1 DMS is fitted from CCSD(T) dipoles computed on 5184 geometries with energies up to 20,000 cm^–1 above the potential energy minimum of Ames-1 PES. Figure 4(a) shows that distribution of geometries is nearly flat along energies, i.e. 110–120 geometries per 1000 cm^–1. Figure 4(b) plots the original fitting deviation δ (black) and relative deviation δ% (red). Figure 4(c) uses eight symbols to present the statistics in each 1000 cm^-1 (solid) or accumulated from lowest energy (open), including squares for averaged |δ| and |δ%|, circles for σ_rms(δ) and σ_rms(δ%), and black symbols for δ/|δ|, red symbols for δ% and |δ%|.

Figure 4. Ames-1 N₂O DMS statistics. (a) energy distribution of data set, with respect to potential energy minimum; (b) original fitting residual (black, ×10⁻⁴ a.u.) and relative fitting residual (red, %); (c) residual statistics in each 1000 cm^–1 (solid symbols) or accumulated from zero energy (open symbols), including squares for averaged |δ| and |δ%|, circles for σ_rms(δ) and σ_rms(δ%), and black symbols for δ and |δ|, red symbols for δ% and |δ%|.

From 0 to 20,000 cm^–1, the magnitude of dipole components (x or y) varies in the range of –0.78 to 0.64 a.u. Averaged absolute fitting deviation |δ| is 1.37 × 10⁻⁵ a.u. Overall fitting σ_rms is 2.73 × 10⁻⁵ a.u. and δ_max is 0.00046 a.u. The mean ± σ of relative fitting deviation δ% is 0.003 ± 0.33%, with 92% of them below 0.1%. The centre 50% of fitting δ is from –7.3 × 10⁻⁶ to 7.2 × 10⁻⁶ a.u. The centre 50% of relative fitting δ% is from – 0.0071% to 0.0074%.

The Ames-1 DMS fitting accuracy up to 20,000 cm^-1 is not as good as those acquired before on other triatomic dipole surfaces, but it is already the best we were able to get after many basis trials and dataset purifications. It has been a real concern that this σ_rms of 10⁻⁵ a.u. level may hurt the accuracy and the reliability of intensity predictions. However, the uniformly weighted DMS fit has better accuracy in the range of 0–10,000 cm^-1, where the fitting σ_rms is reduced by 2/3, from 2.73 × 10⁻⁵ a.u to 0.92 × 10⁻⁵ a.u., and the average |δ| is also reduced by half, from 1.37 × 10⁻⁵ to 0.68 × 10⁻⁵ a.u.

On the other hand, our investigations suggest the difficulties in our N₂O dipole fits could be related to intrinsic complexity of this molecule. The σ_rms can be reduced to as small as 5 × 10⁻⁷ a.u for the range of 0–10,000 cm^-1. But total fitting σ_rms rises by a factor of 2–3 when the ab initio dataset expands every 2000–3000 cm^-1. This is probably related to the bending part of the dipole surface. One possibility is that a more physically meaningful basis is needed to describe the dipole behaviour around a shallow well near 19,000 cm^-1 on PES. We are still working toward a more accurate least-squares dipole fit for N₂O DMS, and using high quality experimental intensity data to clarify ambiguities and identify better candidates.

3.6. Ames-1 line list for ¹⁴N₂¹⁶O (446)

The Ames-296 K line list for pure 446 contains 1,390,110 lines covering the full range of 0.005–15,000 cm^–1. Every line has E’ ≤ 20,000 cm^–1 and intensity ≥ 10⁻³¹ cm/molecule at 296 K. The highest wavenumber associated with a transition intensity stronger than 1×10⁻²⁵ cm/molecule is 8989 cm^–1, i.e. the last line with 10⁻²⁵ cm/molecule intensity is found at 8989 cm^–1. Lines with intensity ≥ 10⁻²⁶ cm/molecule reach 11,973 cm^–1, and lines with intensity ≥ 10⁻²⁷ cm/molecule appear at energies as high as 14,017 cm^-1. Some transitions beyond 15,000 cm^-1 are still stronger than 10⁻²⁸ cm/molecule. Obviously, more lines with intensity stronger than 10⁻²⁹ cm/molecule can be found in the range of 15,000–17,000 cm^–1. Current Ames-296 K line list stops at 15,000 cm^–1 for two reasons: (1) upgrades are expected soon for both Ames-1 PES and DMS and (2) no high-resolution rovibrational lines were measured beyond 15,000 cm^-1. In contrast, the latest NOSL-296 list covers up to 13,378 cm^-1, while many bands are missing above 11,000 cm^-1. See figures and more discussions in Section 4.4.

Each transition in the list starts with isotopologue ID# ‘41’, in which ‘4’ means N₂O is the fourth molecule in HITRAN database, ‘1’ refers to ¹⁴N₂¹⁶O (446) being the most abundant isotopologue of N₂O. Transition wavenumber, intensity in cm/molecule, Einstein A₂₁ coefficient in s^-1 and lower state energy E” in cm^-1 are given in order, followed by three sections: vibrational quantum numbers from leading CI coefficient in VTET calculation; JPS block index and root number diagonalised from that block; and Wang’s symmetry (e/f). Every section puts upper level information in front of lower level information.

The vibrational quantum numbers are based on the leading CI basis of corresponding wave function. They are mainly for VTET internal reference so should not be expected to match either polyad or non-polyad EH models. The difference between Ames PES based levels and EH models need to be further reduced before meaningful 1-to-1 matches can be carried out up to 15,000 cm^-1.

Figure 5(a and b) present the general comparison of line position and line intensity between the Ames-296 K line list and HITRAN2020. For the 33,169 lines in HITRAN, most line position differences are within ±0.05 cm^-1, with statistical mean ± σ of –0.007 ± 0.024 cm^-1, consistent with those from refinement and full energy level set. Relatively larger deviations are found 34⁰0 and 5000 bands near 6200 cm^–1.

Figure 5. The ¹⁴N₂¹⁶O line list comparison, Ames-296 K vs. HITRAN2020: (a) line position difference Δ (in cm^–1); (b) line intensity difference, δ% = (S_HITRAN/S_Ames – S_Ames/S_HITRAN) × 50%, abundance included.

Unless specified, all intensity comparison in this paper uses relative differences defined as δ% = (S₁/S₂ – S₂/S₁) × 50%. Figure 5(b) shows that the δS% for 33,169 matched HITRAN lines has statistical mean ± σ = −0.5 ± 19.7%. The 20% uncertainty matches our expectation for such a comparison between one set of semi-empirical rovibrational intensity calculations and a collection of various experimental data sources and EH/EDM model predictions. Larger than 50% discrepancies are mainly associated with some hot bands, e.g. ν₁ hot bands at 1300 cm^–1; some 0441 state-related bands, e.g. 0441–0440 and 0441–0330; and some 0201 related hot bands near 3500 cm^–1.

More figures with detailed comparison are reported in the supplementary file. In the following section, we will focus on intensity comparisons with experimental measurement, EDM models, and recent NOSL-296 K line list [48].

3.7. Ames-1 ‘natural’ line list

Rovibrational intensity and line list calculations have been carried out for each of the 11 minor isotopologues of stable N and O isotopes, using the Ames-1 DMS and the rovibrational energy levels and wave functions computed on the Ames-1 PES. Same or similar parameters and cut-offs are adopted to ensure the intensity consistency across isotopologues. Each line list contains 1.3–1.6 million lines using same data format of ¹⁴N₂¹⁶O line list, except isotopologue number changed from ‘41’ to ‘42’–’52’. A ‘natural’ IR line list for nitrous oxide is constructed to include IR transitions of all the 12 isotopologues under terrestrial natural environment, with intensities scaled by terrestrial abundances given in Table 2.

Table 2. Abundances and number of IR lines of 12 N₂O isotopologues in the Ames-296 K natural IR line list for N₂O up to 15,000 cm^-1 and intensity down to 10⁻³¹ cm/molecule. Their wavenumber range f_max (in cm^–1), intensity max S_296K^max, and intensity sum are also included for each isotopologue. Intensities are scaled by corresponding abundances, in cm^–1/molecule.cm^–2.

#	Iso	Abundance	#lines	fmax (cm^-1)	S296K^max	Intensity Sum
1	446	0.990333	1387178	15000	1.0217E-18	7.2848E-17
2	456	3.64093E-3	375607	14896	3.5696E-21	2.5816E-19
3	546	3.64093E-3	411253	14970	3.7098E-21	2.6639E-19
4	448	1.98582E-3	377008	14875	1.8990E-21	1.4206E-19
5	447	3.69280E-4	238697	13964	3.6668E-22	2.6767E-20
6	556	1.33858E-5	93754	11640	1.2867E-23	9.3609E-22
7	548	7.30080E-6	93609	10681	6.8881E-24	5.1939E-22
8	458	7.30080E-6	86397	10578	6.5998E-24	4.9864E-22
9	547	1.35765E-6	55324	9065	1.3299E-24	9.7874E-23
10	457	1.35765E-6	50539	8804	1.2718E-24	9.4017E-23
11	558	2.68412E-8	15761	6373	2.3969E-26	1.8219E-24
12	557	4.99134E-9	8498	4964	4.6171E-27	3.4327E-25

The natural line list and its 12 isotopologue components are presented in Figure 6, to illustrate the similarity and consistency between isotopologue line lists. In other words, the Ames-1 PES/DMS-based calculations are stable, both components and the composite ‘natural’ list are free of noticeable noise or crazy intensities. Obviously, the 446 IR features dominates the whole range from 0 to 15,000 cm^-1. The choice of E_max of 0.08 a.u. for the 6 least abundant isotopologues does not affect the quality of this line list, either, because their intensities above 12,000 cm^-1 are near or below the 10⁻³¹ cm/molecule cut-off due to their low abundances.

Figure 6. Ames-296 K natural IR line list (brown line on the top), and IR contributions from 12 isotopologues, with Gaussian convolution (FWHM =1 cm^–1).

4. Comparison of Ames-296K IR intensity predictions and experiments

The line position accuracy of Ames-296 K line list has been discussed in both previous section and NOSL-296 paper [48]. This section focuses on the intensity predictions comparing with experiments and databases. The band-specific discussions are sorted by their chronicle order in this study, not by their importance or the magnitude of intensity discrepancies. Preliminary results of sensitivity checks for Ames-296 K intensity predictions will be presented at the end of this section.

4.1 1000 ← 0110 band

The most significant difference between Ames-296 K and EH/EDM models under 1000 cm^-1 is the ν₁ ← ν₂ hot band, especially its Q branch. In figure 1 of Hargreaves et al. [51], the absorption cross sections of the Q branch at 695 cm^-1 computed using HITRAN and NOSD+ line lists are 20–30% lower than that computed using PNNL experimental data [110], while the NOSD-1000 absorptions were overestimated by at least 100%. Compared to these published line lists, Ames-296 K intensity will have the best agreement with PNNL data, because S_Ames is 25% stronger than EH/EDM model intensities, as shown in Figure 7(a). Differences between S_HITRAN and S_NOSL are small because they both were based on Toth’s line list [19]. The Q branch discrepancy between Toth’s list and PNNL data needs further experiment study.

Figure 7. ¹⁴N₂¹⁶O ν₁←ν₂ band intensity in HITRAN (black), NOSL-296 (blue), and Ames-296 K (magenta): (a) overall comparison; (b) relative differences δ% with respect to Ames-296 K.

A second discrepancy is the intensity order of P and R branches. HITRAN and NOSL-296 predict the peak intensity in the P branch is slightly larger than that in the R branch, i.e. P15 is 2.6% stronger than R16. But our calculation has found the opposite: R16 is stronger than P14 by 15%. Using S_Ames as reference, relative intensity differences, δ%_HITRAN and δ%_NOSL are plotted in Figure 7(b) along P, Q and R branches. The δ% for P and R branches have strong linear dependence with m, m = –J” for P branch and J” for Q/R lines, and they are off by – 20% ∼ – 25% around J = 0. From experiences [61,74], this usually suggests that certain linear term(s) in effective dipole model need improvement. We have checked all other bands mentioned in this paper with noticeable intensity deviations (or differences) from Ames-296 K, but none of them have such strong linear dependence along m. Quadratic dependence on m is common. Being essentially independent from m is also common. The linear part of the δ%_Ames changes is usually 10% or less.

For now, we have no evidence that suggests defects in S_Ames are the main source behind the discrepancies, especially since S_HITRAN/EDM(448) has excellent agreement with S_Ames(448) on all three branches, e.g. δ% =1–2% at J" = 16. Because S_Ames are highly consistent across isotopologues, it can be safely concluded that the correspondingly EDM model for S_HITRAN (446) and S_NOSL-296 needs to be revisited.

4.2 nν₃ related bands

Before NOSL-296 [48], the NOSD+ (2019) list [51] was the most comprehensive EH/EDM line list for N₂O. Comparing Ames-296 K to HITRAN and NOSD+, the most obvious δ% are found upon nν₃ and related hot bands because ν₃ is the major intensity contributor for N₂O system. For pure nν₃ overtones of 446 isotopologue, δ% changes from 3% to –28%, –22%, 6% and 14% for n increasing from 1 to 2, 3, 4 and 6, respectively. We acknowledge it is difficult to explain such variations from our side, especially to describe both the δ% drop from ν₃ to 2ν₃ and the δ% increments from 2ν₃ to 6ν₃. When compared to high quality intensity measured in lab, the Ames-1 PES and DMS should be able to have small and monotonic δ% for vibrational fundamental and lowest overtones, except those bands heavily impacted by resonances.

Similar variations can be found in the ν₃ overtones of 448 isotopologue, where the δ% goes from –2% to –23%, –21%, and 51% for n = 1–4. It is also shared by the 011n-0110 hot bands. From n =1 to n = 4, the δ% of 011n-0110 bands are 4%, –24%, –25%, and 10% for 446, and –8%, –20%, –14% and 51% for 448. Exceptions are found on 1003 and 1004 band of 448, where the EH/EDM models underestimated the 1003 band intensity, 3.0 × 10⁻²⁸ (NOSD+) versus 5.0 × 10⁻²⁷ (Ames), and overestimated the 1004 band intensity, 9.4 × 10⁻²⁹ (NOSD+) versus 3.6 × 10⁻²⁹ (Ames), with |δ%| as large as 836% and 110%, respectively.

4.3 50⁰0, 42⁰0, and nν₁

In 2021, Adkins et al. [21] reported the highly accurate intensity measurements from NIST group on 50⁰0 and 42⁰0 bands at 1.6 micron, with combined standard relative uncertainties near 1%. Related intensity data has been updated accordingly in HITRAN2020, which are roughly 5% larger than those in HITRAN2016 [20]. Figure 8 shows the differences of HITRAN, NOSL-296 (NOSL) and Ames-296 K (Ames) with respect to experimental intensities, i.e. (S/S_NIST–1) × 100%. For the 50⁰0 band, S_HITRAN2016 is 4.68% lower than S_NIST, S_Ames is 4.60% higher than S_NIST, while S_NOSL is 0.37% higher than S_NIST. In the range of J” ≤ 30, S_Ames is 4.19% higher and S_HITRAN2016 is 5.53% lower. For the 42⁰0 band, S_HITRAN2016 is 4.88% lower than S_NIST, S_Ames is 2.16% higher than S_NIST, while S_NOSL-296 is 0.78% higher than S_NIST. All these ratios are based on NIST modelled intensities and weighted by corresponding uncertainties given in their Tables 1 and 2 [21]. The deviations of Ames-296 K and old HITRAN intensities show quadratic pattern for 50⁰0 in Figure 8(a). For 42⁰0 band in Figure 8(b), both Ames and NOSL deviations have a quadratic drop at high J of R branch.

Figure 8. HITRAN2016 (grey), HITRAN2020 (black), NOSL-296 (blue) and Ames-296 K (magenta) intensity are compared against NIST experiment modelled intensity: (a) 50⁰0 band; (b) 42⁰0 band. The mean differences are computed in the range of J"≤30. Note that NOSL-296 labels them as 3400 and 5000 band, respectively.

A 2% difference is reasonable for the Ames-1 PES and DMS, but a 4.6% difference on 50⁰0 band is slightly larger than our expectation for a CCSD(T) dipole surface extrapolated to one-electron basis set limit. Taking the R16e transition as example, we checked its line intensity variations on more than 20 dipole surface candidates which we prepared toward future Ames-2 DMS upgrades. The S_Ames value, 1.4576 × 10⁻²⁴ cm/molecule, is only reduced by ∼1% at most, and very stable in the range of 1.441–1.451 × 10⁻²⁴ cm/molecule. This is still 3–4% higher than the 1.395 × 10⁻²⁴ cm/molecule from NIST experimental model [21] and adopted by HITRAN2020 [15], also higher than S_NOSL-296, 1.404 × 10⁻²⁴ cm/molecule [48]. Note all intensity values in this paragraph use 100% abundance. In addition, it is interesting to observe both δ%_Ames and δ%_HITRAN2016 show clear quadratic changes along m coordinate, where m = –J” for P branch or J” for R branch. No such quadratic behaviour appears in Figure 8(b) for 42⁰0 band, a neighbour band in the same vibrational polyad but all three groups of differences drop by a few percent beyond R30. These may be related to the rotational deficiencies in the experimental determination.

The intensity deviation found on 50⁰0 band may be attributed to two factors: the ab initio dipole surface is not sufficient for this band/energy range and upgrades are needed, and/or the intensity is very sensitive to the inaccuracy of the Ames-1 PES. We are inclined to believe the latter, because the line position of Ames-296 K is off by 0.075–0.090 cm^–1, e.g. 6385.523 cm^–1 (EH) versus 6385.601 cm^–1 (Ames) for R16e transition. The future Ames-2 PES is expected to bring more insight to the source of the current differences. But the convergence of ab initio dipole calculations should be further checked as well.

On the other hand, the Ames-296 K intensity predictions provide the smoothest data lines in both panels of Figure 8. This is because our calculations are highly consistent across J’s, and we keep more than five significant figures for the intensity. In recent Ames-2021 CO₂ PES studies, it has been demonstrated that the four significant figures given in HITRAN and other line lists are not enough to remove noticeable cut-off errors from comparisons at 1‰ (permille) level. In contrast, both HITRAN and NOSL used only three significant figures for the two bands shown in Figure 8.

If we step back from the accuracy level of |δ%| ∼ 1%, the 4.6% deviation on 50⁰0 band is compatible well with what we have for other nν₁ bands. For pure nν₁ overtones (n =1–6), relative intensity differences δ% of Ames vs Experiment are consistently small, e.g. 1.4 ± 3.9% for 19 intensities measured on their R16e transitions. For minor isotopologues, the Ames-296 K intensity comparisons to the EDM model intensities in HITRAN yields differences as small as 1.1 ± 2.9% for 13 overtone bands with n =1–3 (or 4). Such consistent agreements across isotopologues are in sharp contrast with several |δ%| as large as 100–201% found on the higher overtones of 448 isotopologue.

4.4. 10,000 cm^–1 and above

An overall spectra simulation is given in Figure 9, using Gaussian convolution for 4 line lists with full width half magnitude (FWHM) set to 1 cm^–1. HITRAN (black) covers the smallest range of spectrum, with peaks missing at 1400, 4000, and 5200 cm^–1_­, etc. At 296 K, NOSL-296 (blue) is more complete than CDSD+/HITEMP (orange), but Ames-296 K has continuous coverage up to 15,000 cm^–1.

Figure 9. Simple IR Simulation at 296 K using 4 N₂O IR line lists: HITRAN (black), HITEMP (orange), NOSL-296 (blue) and Ames-296 K natural (magenta). Gaussian convolution uses FWHM =1 cm^–1.

Between Ames-296 K (magenta) and NOSL-296 (blue) lines, a major discrepancy can be found for 03132–00001 band at 8000 cm^-1. S_NOSL-296 is more than two orders of magnitude stronger than S_Ames, e.g. 9.94 × 10⁻²⁷ cm/molecule versus 2.14 × 10⁻²⁹ cm/molecule for the peak transition Q15e at 8203.3 cm^–1. The corresponding δ% would be >20,000%. All other 0313n (n = 1,2) P and R transitions have much more reasonable related |δ%|. About 2/3 of them are 20–40% and the other 1/3 are 300–500%, indicating the rovibrational wave functions and dipoles for this band are not far from reality. This Q band is probably an outlier in NOSL-296 intensity predictions.

More discrepancies are found between magenta (Ames) and blue (NOSL-296) lines above 9000 cm^–1, such as 52011 band at 9410 cm^–1, 36011 band at 9700 cm^–1 and 06031 band at 9967 cm^–1. Starting from 10,350 cm^–1, overall S_Ames absorption is stronger in certain ranges, e.g. 50021 band near 10438 cm^–1. The NOSL-296 intensities for these bands are not based on observations, but from EDM models using parameters determined from bands with lower vibrational quanta or at lower energies. They reflect the methodological difference between EDM models extrapolated into unmeasured region versus ab initio calculations refined using experimental data. Future experimental studies will determine more EDM parameters helping to constrain intensity extrapolations and provide guidance for our DMS upgrades.

In 2007, Daumont et al. [89] reported their spectra measurement and analysis for the 14031 band at 10,080 cm^–1 and the 30031 band at 10,164 cm^–1. In 2011, the 00061 band, or 6ν₃ band, was reported at 12,892 cm^-1 by Milloud et al. [29] with 20% uncertainty estimated for intensity. Figure 10 compares the Ames-296 K line list to these three vibrational bands measured beyond 10,000 cm^-1, including experimental uncertainty and our line position deviations. The NOSL-296 list data is also shown for comparison. For the 14031 band (Figure 10a) and 30031 band (Figure 10b), weighted S_NOSL-296 intensity agreement with experimental data is nearly perfect, probably because the data have been incorporated into NOSL-296′s EDM modelling. In contrast, S_Ames predictions are lower by 20–30%. For the 00061 band in Figure 10(c and d), both S_Ames and S_NOSL-296 have good agreements on P branch lines, while S_Ames is higher than S_NOSL-296 by 13%. The observed intensity values are irregular on R11–R24, for which both NOSL-296 and Ames-296 K are more reliable. See the following section for more discussion on 6ν₃ band.

Figure 10. ¹⁴N₂¹⁶O (446) experimental IR intensity compared with NOSL-296 (blue) [48] and Ames-296 K (magenta). (a). 14031 band; (b). 30031 band; (c). 00061 band; (d). 00061 band along m coordinate, m = -J” (P branch) or J” (R branch). Line position deviations of Ames-296 K are represented by orange dots with respect to right – y axis.

The line position deviations of the Ames-296 K line list for the three bands are shown as solid blue dots. Compared to the R0 position in NOSL-296, our Ames-1 PES-based line positions are off by +0.034 cm^–1, –0.031 cm^–1 and +0.036 cm^–1 for the 14031, 30031 and 00061 bands, respectively. This is because their band origins were included in the reference dataset for the Ames-1 PES refinement, with weight 1.0, 0.3 and 1.0, respectively. In Figure 10(a) and Figure 10(b), the J or energy dependence of line position deviations for 14031 and 30031 bands is not significant, changing by 0.04–0.06 cm^–1 when J increases from 0 to 30. Without J > 0 levels incorporated during refinement, Ames-1 PES performs close to or better than our expectations. For the 00061 band in Figure 10(d), Ames-296 K line position deviations increase by 0.095–0.120 cm^-1 when J rises from 0 to 30. Obviously, its rotational structure could be polished in a future PES refinement.

4.5 Comparison to recent experiments, versus S_obs and S_EDM

We now compare the Ames-296 K natural line list to recent high-resolution IR experiments for N₂O isotopologues. The most helpful advantage of BTRHE based IR line lists is the prediction power, including both the reliability and the associated consistency across isotopologues, band series and J’s. These predictions are more valuable when EDM models need more accurate dipole parameters for certain high energy bands, weak bands and isotopologue bands, which were not observed before. A few examples are given here, as well as in Figs. S1–S14 of the supplementary file published along this paper.

One quantitative example for isotopologue consistency is the still the 6ν₃ band. Song et al. [42] measured its line intensities beyond 12,500 cm^–1 for 456, 546 and 556 isotopologue samples, and fit data to models. For three isotopologues, the experimental set up was the same and conditions were nearly identical. The formula and analysis were also the same. Therefore, the intensities derived from their fitted models should be highly self-consistent between isotopologues, and more suitable for comparison. Since S_Ames is also isotopologue consistent, their relative differences δ%_Ames should be consistent as well. In the range of J” ≤ 30, the δ%_Ames distributions are –6.8±1.5% (456), –7.6±0.4% (546) and –6.3±6.5% (556). See Fig. S12 in the supplementary file. The consistency within Song et al. models is probably near 1% or better. In contrast, the S_Ames (446) are +10% stronger than those P2–P30 intensity reported for the same band in Milloud et al. [29] and 13±1% higher than S_NOSL. Given the S_Ames consistency between 446 and the other three isotopologues, it can be concluded that the systematic difference between the two sets of experimental intensities could be as large as 15–20%, although not enough information is available to determine which set is more accurate.

Bertin et al. [35] measured 47 new bands of 5 N₂O isotopologues (446, 456, 546, 448 and 447) around 5800 cm^–1, focusing on the refinement of ΔP = 10 dipole parameters in EDM model. Those bands were beyond HITRAN cut-offs. In Fig. S1, observed transitions are easily matched to their counterpart in Ames-296 K with δ% ≤10–15%. In Fig. S2, the 2201 and 3001–0110 bands are compared across 5 isotopologues, where S_Ames are consistently greater than S_obs by about 10%. Such agreement and consistency level are what predictions normally look like, especially for bands carrying middle to strong intensities.

Karlovets et al. [33] reported 51 new bands of 5 N₂O isotopologues around 1.22 $\mu$m, or 8200 cm^–1, which is higher than HITRAN spectral range. In Fig. S3, S_Ames(446) predictions have overall agreement better than that in Fig. S1, with deviations <10%. In Fig. S4, the agreement of S_Ames on minor isotopologues are similar to those in Fig. S2, but with larger uncertainties in experimental data. The EDM model at that time used an incomplete ΔP = 14 parameter set determined from the main isotopologue 446. With some important dipole parameters missing, it has caused significant intensity overestimation on most major bands of 446 and 546, and intensity underestimations as large as half to one order of magnitude on 456, 448 and 447.

In 2021, Karlovets et al. [36] extended their study to the next 300 cm^–1 near 1.18 $\mu$m, or from 8325 to 8622 cm^–1. In Fig. S5, the EDM models and the S_Ames predictions both have good agreements with S_obs on the strongest 446 bands. This is probably because the principal dipole parameters in EDM have been improved, as two new ΔP = 15 parameters were determined from observed intensities. But S_EDM still runs into significant deviations on several secondary bands, e.g. 0(10)⁰0, 6200, 3112, 0712, 7110–0110, 1004–1000, 0204–1000, 6310–0110, etc. In contrast, S_Ames predictions have reasonable to good agreements as in Fig. S3 for most 446 bands, e.g. 6200 and 0(10)⁰0. But there is an outlier, the 1113e/f band near 8340 cm^-1. For this band, S_Ames is 60%+ stronger than S_obs. This is the first band we identified from recent experiments that the S_Ames prediction has such a noticeable overestimation. For minor isotopologues in Fig. S6, the ΔP = 14 and ΔP = 16 EDM models of main isotopologue 446 still lead to unsatisfactory deviations: |δ%| = 15–50% for 456 and 546, and δ% (448) < – 100%. In contrast, S_Ames predictions are still consistently reliable across isotopologues, and match well with observations.

An improved analysis was reported in 2022 [38] for natural N₂O in the same spectral range at 1.18 $\mu$m, but the spectra was measured at higher pressure of 10 Torr versus 1 Torr in the 2021 study. It successfully assigned more transitions to more bands of more isotopologues and significantly reduced the δ%_EDM on those secondary bands using the ΔP = 14–16 parameters refined or newly determined in 2021. See new comparison for the 446 isotopologue in Fig. S6b. But the S_EDM for 0(10)⁰1 band at 8319 cm^-1 were not updated, still about 40–50% weaker than S_obs. In NOSL-296, this band is labelled as 0(14)⁰0 with peak intensities increased by 2/3, so now S_NOSL are in very good agreement with S_obs. The S_EDM for 62⁰0 band at 8475 cm^-1 was over corrected to more than 30% greater than S_obs. Please note this band is also labelled as 0(14)⁰0 in NOSL-296, with peak intensities reduced by 17–18%, i.e. the latest EDM model intensity is only ∼10% higher than S_obs. The ΔP = 16 dipole parameters have also been further improved in NOSL-296 for some weaker bands at the bottom of Fig. S6b, e.g. 0(14)²0 at 8490 cm^-1 and 0(16)²0–02²0 at 8430 cm^-1. Comparisons of isotopologues 456, 546, 448 and 556 are collected in Fig. S6c. For 456 and 546, both S_Ames and new S_EDM fitted from observation have very similar agreements with S_obs. For 448, new S_EDM is 25–30% stronger than S_Ames. For 556, the S_EDM computed using main isotopologue ΔP = 16 parameters is 15% lower than S_Ames. These differences may need further investigations.

During the comparison, the 3112–0000 band near 8560 cm^–1 caught our attention. After the 1113 band, this is the second band we identified that having noticeable intensity overestimation in the Ames-296 K line list. The δ%_Ames deviations are 20–50% for Q and R transitions, and rise sharply along with J increasing in the P branch, to near +300% at P38. Such unusual δ%_Ames will prompt us to monitor its variations in future studies, along with other bands carrying unusual deviations. See Fig. S14 in the supplementary file and an update in the following section.

In 2022, Karlovtets et al. [37] also revisited weak bands between 7647 and 7918 cm^–1, using a non-polyad EDM model. In Fig. S7, S_EDM and S_Ames have similar agreements with S_obs on many bands, but with exceptions. S_EDM overestimated the 2003–1000 band at 7691 cm^–1, and underestimated a few weak bands between 7700 and 7850 cm^–1, e.g. 3311 band at 7818 cm^–1. At the meantime, the 0602 band at 7723 cm^–1 is the first new band that we identified with clear underestimation in the Ames-296 K line list, i.e. S_Ames ≈ 0.4 S_obs. Note in the range of 7680–7725 cm^–1, observed intensities appear doubled for some 1113–0110 and 1223–0220 transitions, so noticeably greater than both S_EDM and S_Ames. That is the result of e and f line mixing and their intensities are combined in S_obs. For minor isotopologues in Fig. S8, the ΔP = 14 EDM models fitted from Karlovets et al. [32] seems working well for a 447 band. For 456, 546 and 448, their EDM models have intensity deviations about 10–40%, except that S_EDM for the 3002 band of 448 is only 5% of S_obs, which means its relative δ% is close to –1000%. The S_Ames predictions work reliably and consistently as usual.

4.6 Quality test at 1.34 $\mu$m: Ames-296K versus NOSL-296

Given the comparisons above, we know there has been a clear history of diligent upgrades for N₂O EDM models when new experimental results become available. Those S_EDM deviations found in newer experiments provide basis and motivation for further EDM model improvements. Most published high-resolution experimental data have been incorporated into the global EDM fitting of NOSL-296 list [48]. The latest experimental study in Karlovets et al. [111] revisited the spectral range of 7250–7653 cm^–1 (or 1.34 $\mu$m), refined EH/EDM parameters, and compared to NOSL-296 and a preliminary release of Ames-296 K. It should be noted again that a full match between EH/EDM line lists and BTRHE based IR line lists is usually not a trivial task, and the difficulties would rise rapidly along with increased PES inaccuracy and extrapolations into the higher E’ range. However, for most N₂O transitions that can be measured at room temperature, a three-way match between observation, NOSL-296, and Ames-296 K surely can be successfully completed. This is because the density of rovibrational levels is still relatively low, so the resonances among states are not too complicated to track.

By enforcing strict agreements on J’, J”, and Wang symmetry (e/f), plus ±0.1 cm^-1 range for E” deviations, and ±1.5 cm^–1 range for E’ and line position deviations, we are able to find matches in Ames-296 K natural list for all 3326/359/325/174 transitions observed for 446/456/546/448 isotopologues, except 2 doubly assigned 446 lines at 7651.1739 cm^–1 (2003–1000 P33) and 7500.5314 cm^–1 (1602–1000 P25). About 300 transitions have two Ames-296 K lines meeting the criteria, and a few of them have three candidates. In such cases, most mismatches can be easily identified and rejected by taking advantage of intra-band consistencies of δE’, δ%, and leading CI basis coefficients. In related band(s), these properties would vary along J, but those variations are usually smooth or have trackable patterns. Sometimes root number (dis)agreement between NOSL-296 and Ames-296 K may also help. In the current work, we use the updated Ames-296 K line list and adopt slightly different matching criteria, e.g. putting higher priority on the intra-band consistency and keeping tight E” restrictions for ambiguous scenarios. This gives some different associations than that reported in Ref. [48]. Based on δE’ patterns, we are inclined to re-assign the R23e transition at 7541.4030 cm^–1 from the 1602–01100 band to the 6200–0100 band. The original NOSL-296 line matches are kept for the following comparison.

After the ¹⁴N₂¹⁶O lines are matched, corresponding relative deviations δ%_Ames and δ%_NOSL are computed against S_obs and plotted in Figure 11(a). Compared to NOSL-296 (blue), Ames-296 K (red) have much fewer lines with |δ%| beyond 150%, indicating lower risk for new band predictions. This is consistent with previous comparisons in Figs. S1–S8. The δ%_Ames between –300 ∼ –200% are mainly from the Q branch of 2112 band at 7440 cm^–1. But in the ±150% range (orange dashed lines), δ%_NOSL is better balanced around zero, compared to more δ%_Ames appear between –50% and –20%. The numbers of transitions with δ%_Ames and δ%_NOSL in each 10% bin are counted and plotted in Figure 11(b). According to these simple statistics, |δ%|_NOSL > 10% also has more lines in the lower side than in the higher side, but the number of lines with δ%_Ames between –50% and –20% are nearly doubled as those with δ%_NOSL in the same bins. Those sporadic extreme outliers of |δ%|_Ames and |δ%|_NOSL are not our concern yet, e.g. beyond 1000%, because in most cases they are affected by strong perturbation and band crossings. Note the δ%_Ames for 12 transitions of 4620–0110 band have no patterns, which warrant further investigation and/or matches.

Figure 11. Relative intensity deviations of NOSL-296 (blue) and Ames-296 K (red), compared to the measured ¹⁴N₂¹⁶O line intensities reported in Karlovets et al. (2023) [111], with δ% = (S_List/S_obs–S_obs/S_List) × 50%. (a) Overview in experimental spectral range. Dashed lines (orange) mark ±150%. 12 S_NOSL and 6 S_Ames points are out of range (|δ%| > 1000%); (b) numbers of ¹⁴N₂¹⁶O transitions with relative δ% in each 10% bins. In total, there are 2991 (NOSL-296) and 3259 (Ames-296 K) lines in the range of |δ%| ≤ 150%.

Karlovets et al. (2023) found S_Ames lower than S_obs by 20–25% on the 0203e band, which we identified as a potential ‘sensitive’ band with intensity variations up to 15% in tests. See the next section for details. Given the δ% in ν₃ series discussed earlier, and the overall agreement –0.5 ± 19.7% with HITRAN, the 20–25% underestimation on this band is not very surprising, but still needs further investigation and improvement. Our top priorities are to carry out Ames-2 PES refinement from scratch, and to rebuild Ames-2 DMS to get best ab initio intensities. Hopefully that will remove the discrepancy or at least ease a large part of the δ% deviations, especially those extra larger deviations, e.g. the 1113 band at 8335 cm^–1 or the 0602 band at 7725 cm^–1.

Overview comparison for 446 bands in observed spectral range is given in Fig. S9, including only those lines assigned in the Karlovets et al. [111]. The P branch peaks of 0203 band series that are underestimated by 20–30% by Ames-296K can be found at 7650, 7600 and 7550 cm^–1. As Karlovets et al. (2023) pointed out, the significant underestimation or overestimations of NOSL-296 in Figure 11(a) are mainly associated with ΔP = 14 bands missing the EDM parameter M⁰_–1,0,4g, e.g. the 0114–1110 band at 7360 cm^–1 and the 0004e-1000e band at 7430 cm^–1. In addition, it is noted that the 3401e-0200e band (ΔP = 12) at 7285 cm^–1 has a δ% distribution of –58 ± 24% (NOSL-296) versus 1 ± 21% (Ames-296K) in the range of J” ≤ 30. One of the ΔP = 14 bands, 1203e-1000e at 7590 cm^–1 is overestimated by four to five times in NOSL-296 with δ% = 223 ± 100%, but also underestimated by more than half in Ames-296K with δ% = −108 ± 90%. In other words, S_NOSL-296 is 1 order of magnitude stronger than S_Ames-296K. Note that our R13–R27 and R29–R35 line matches are different from those in Karlovets et al. [111].

In Fig. S10, we show that the EDM based intensities for minor isotopologues are overestimated by two to five times. According to Karlovets et al. [111], principal dipole parameters in their EDM models were fixed at values from the 446 EDM model. The overestimation is probably caused by some other dipole parameters that have not been reliably determined due to the lack of intensity information because of experimental difficulty with minor isotopologues. On the other hand, the S_Ames predictions on 0203 and 0313–0110 band series are noticeably lower than S_obs, which is consistent with the underestimation we found in the 446 comparison (shown in Fig. S9). Other than that, the S_Ames-296K agreements on isotopologues 456, 546 and 448 are similar to those in Figs. S2, S4, S6 and S8. Therefore, our isotopologue consistency still remains. Once S_obs (446) is improved for those bands, the large deviations on minor isotopologues will be also corrected. We noted that all four isotopologue datasets have intensities for (12,0,14) and (12,0,15) bands, i.e. 6000 and 5200. The δ%_Ames distributions for the eight bands are presented in Fig. S13, along with statistics in the range of J" ≤ 30.

For interested readers, statistics are given below for a subset of the lines matched between NOSL-296 and Ames-296K. The 889,509 lines in NOSL-296 are divided into three groups by their line intensity: 89,833 lines with S_NOSL ≥ 10⁻²⁶ cm/molecule, 215,509 lines with S_NOSL between 10⁻²⁸ and 10⁻²⁶ cm/molecule, and 584,167 lines with S_NOSL ≤ 10⁻²⁸ cm/molecule. Using the matching criteria of 0.5 cm^–1/0.5 cm^–1/0.2 cm^–1 for wavenumber/E’/E’’, and relative intensity difference |δ%| ≤ 100%, 96.5%/81.2%/65.6% of the three groups of NOSL-296 lines are matched to Ames-296K. In the 86,717 matched lines with S_NOSL > 10⁻²⁶ cm/molecule, 92.8%/79.4%/43.8% of them have |δ%| < 25%/10%/3%, respectively. In the 175,021 matched lines with S_NOSL between 10⁻²⁸ and 10⁻²⁶ cm/molecule, the corresponding percentages are reduced to 82.2%/58.2%/25.2% for |δ%| < 25%/10%/3%, respectively. In the 383,002 matched lines with S_NOSL below 10⁻²⁸ cm/molecule, the corresponding percentages further drop to 72.8%/45.2%/19.2%, respectively. Note the intensity values in this paragraph use 100% abundance.

4.7. R16e comparison and sensitivity/uncertainty estimate

Dr. Tashkun of the Tomsk team kindly shared with us an experimental intensity data collection for ¹⁴N₂¹⁶O R16 transitions measured in laboratory, in which one transition may have multiple intensity records. The 475 intensity records for R16e transitions are extracted to compare with Ames-296 K predictions and latest EDM model intensities in the NOSL-296 list. Results are shown in Figure 12. For convenience, the experiment data uncertainty, u_expt, is attached to δ%_NOSL as blue error bars. The magenta bars for S_Ames variation will be explained next.

Figure 12. ¹⁴N₂¹⁶O R16e intensity comparison, NOSL-296 (blue) and Ames-296 K (red) with respect to experimental observation. Relative difference δ% = (S_List/S_obs–S_obs/S_List) × 50%. Experimental uncertainty is attached to δ%_NOSL-296. Preliminary upper bound estimate of δ%_Ames variation range is shown as magenta error bars centred at mean S_Ames. In total there are 387 S_obs in panel (a) and 111 S_obs in panel (b). See text for more details.

For transitions with S_Expt > 3×10⁻²⁶ cm/molecule, S_Ames and S_NOSL have similar agreements for majority of the data. This includes majority of relatively larger deviations, such as 3000–2000 band, or 3ν₁←2ν₁. As we have discussed, S_Ames of ν₁←ν₂ band is higher than S_expt and S_NOSL by +29%, while more than 10 green dots of S_Ames come out noticeably lower than S_expt by 20–30%, such as the nν₃ series including 2ν₃ (−30%), 3ν₃ (−20%), hot band 0112–0110 (−24%), and 0113–0110 (about –30%). More band examples are 1002 (−46%), 0202 (∼−30%), 0203 (∼−25%), 0600 (−40%) and 1112–0110 (−40%). These underestimations are consistent with what we learned from other comparisons. They are probably systematic deviations hence are fixable. There are also cases where δ%_NOSL is significantly greater than δ%_Ames, e.g. 1110–0200 band (−58% vs –30%), 0002–1000 band (−43% vs 10%) and 0201–1000 band (72% vs 2%). The numbers in parentheses are δ%_NOSL and δ%_Ames, respectively. It is interesting to note S_Ames and S_NOSL have large but opposite δ% on few bands, e.g. –42% (Ames) and +65% (NOSL) for 3202 band. This is similar to the 1203–1000 band discussed in the previous section.

Between 1 × 10⁻³⁰ cm/molecule and 3 × 10⁻²⁶ cm/molecule, experimental uncertainties increase as shown in Figure 12(b). Both δ%_Ames and δ%_NOSL have wider distributions, but they still fall within the ±150% range. In general, the trends we observed in stronger region are still valid. There are clear similarities between δ%_Ames and δ%_NOSL. Exceptions can be found in both sides. Overall speaking, more S_Ames appear weaker than S_Expt, again.

Another important question is the stability, or sensitivity, of Ames-296 K intensity predictions. In other words, what are the error bars for those red dots in Figure 12? Assuming the Born-Oppenheimer approximation is sufficient and the rovibrational CI calculations are converged, the IR intensity we computed for N₂O would depend on the accuracy of both PES and DMS. Before much more accurate PES/DMS or extremely accurate S_expt become available, we can only basis the analysis on using different potential energy and dipole surfaces. We are trying to get a reasonable estimate of the upper bound of the uncertainty of S_Ames at current level of theory, assuming the differences between the Ames-1 PES/DMS and ideal (or perfect) PES/DMS are probably smaller than those between the Ames-1 PES/DMS and the less accurate PES/DMS included in comparison. In CO₂ studies, UCL colleagues also used three PES and 2 DMS to run a ‘scatter factor’ estimate in Zak et al. [112]. For N₂O, the DMS fitting error at 10⁻⁵ level is a concern. It seems more appropriate to generate a series of DMS candidates using various coordinates, coefficient sets, fitting basis, energy cut-offs, geometry subsets, as well as ab initio method and one electron basis. We have noted some band intensities between 12,000 and 15,000 cm^-1 may be sensitive to DMS fits. When DMS series are ready, we use every DMS to compute one or a few representative intensity dataset(s), e.g. R16e, P15e, R30e, etc. Then check and follow how a transition intensity changes with DMS features and fitting conditions. The fitting accuracy in associated energy range of upper and lower levels should also be included as a filter for sensitivity statistics. This is a long-term effort we started very recently. Many details have not been finalised, e.g. what is the most appropriate way to quantitatively define a ‘sensitivity’ from 10–50 pieces of data, how to identify outliers and convergence defects, and how to separate data contaminations and minimise their impact on uncertainty estimate.

We carried out an initial estimate on the PES/DMS sensitivity of Ames-296 K intensity for certain bands and transitions, by re-computing the line lists with less accurately fitted DMSs and a less accurate PES refinement. Range of intensity variation is divided by the mean of computed intensity values, then the quotient is plotted as magenta error bars in Figure 12. It may act as a rough estimate for S_Ames uncertainty or sensitivity, denoted as u_Ames = 50% × (S_max – S_min)/S_mean. Caution, this u_Ames definition is more qualitative than quantitative. It could be incomplete, or impacted by bad PES or DMS outliers that should not be included, so it is essentially different from experimental uncertainty. A general observation is that transitions associated with higher energy and/or lower intensity will have higher chances to experience larger variation ranges. This is similar to the trend of experimental uncertainties u_Expt shown as blue bars. In Figure 12(a), most u_Ames estimates are smaller or much smaller than u_Expt, especially for those strongest lines. There are 21, 68, 119, 213, 349 and 418 u_Ames estimates less than 0.1%, 0.3%, 0.6%, 1.0%, 5.0% and 10% respectively (with multiple duplicates included). Compared to u_expt, there are 106, 235, 320, and 387 u_Ames estimates less than 10%, 25%, 50% and 100% of corresponding u_expt values, respectively (with multiple duplicates included). For 225 S_expt values greater than 10⁻²⁴ cm/molecule, the u_Expt have a distribution of 4.5±2.0%, compared to 1.0±1.3% of u_Ames estimates. The range of centre quartiles of δ%_Ames is – 2.5 ∼ 4.4%, vs. –1.3 ∼ 2.6% for δ%_NOSL. There are 154 measured intensities in the range of 10⁻²⁶ ∼ 10⁻²⁴ cm/molecule, with statistical distribution of 8.5±9.9% for u_Expt, compared to 4.3±6.3% of u_Ames estimate. The range of centre quartiles of δ%_Ames is – 5.7 ∼ 8.3%, versus –1.4 ∼ 6.3% for δ%_NOSL. For 96 intensities below 10⁻²⁶ cm/molecule in Figure 12(b), less accurate PES and DMSs have raised u_Ames significantly to 22.5±30.6%, compared to 11.0±5.8% of u_Expt. The range of centre quartiles of δ%_Ames is – 14.9 ∼ 13.4%, vs. – 3.9 ∼ 15.7% for δ%_NOSL. For 378 intensity values greater than 10⁻²⁶ cm/molecule, the ratio of relative deviation to experimental uncertainty, δ%_Ames/u_expt, has a distribution of 0.0±7.1, vs. – 0.1±5.2 for δ%_NOSL/u_expt.

In Table 3, we give the list of R16e-based u_Ames for some bands discussed in this paper. Please remember these preliminary results are closer to the upper limits of u_Ames, which are subject to future improvements. The variation range equals to 2u_Ames, so 0203 band intensity range is 15.6%.

Table 3. Preliminary upper bound estimate for S_Ames-296K uncertainty using R16e transition intensities computed using Ames-1 PES/DMS, 4 additional DMS and one less accurate PES.

Band	uAmes (%)	Band	uAmes (%)
10^00–01^10	0.9	14031-GS	12.5
0002–0000	1.1	30031-GS	6.6
0003–0000	2.4	00061-GS	21.6
5000–0000	1.8	3112–0000	24.0
4200–0000	0.3	0602–0000	20.0
0203–0000	7.8	1113–0000	31.6

The u_Ames estimation above should include systematic errors originated from PES inaccuracy, ab initio method, one electron basis adopted in DMS calculation, numerical criteria in the rovibrational and intensity calculations as well as random errors introduced from DMS least-squares fitting. The random errors associated with DMS can be estimated by using additional dipole surfaces. If all those dipole surfaces have better fitting accuracy in the energy range associated with upper and lower energy levels, the random errors can be partially reduced or minimised. This can guide the further improvement of the DMS.

For now, a wholistic upgrade is not immediately available, but we have been able to conclude that the wild intensity deviations in P branch of 3112–0000 band are caused by Ames-1 DMS inaccuracy. Using a testing DMS fitted at same level of theory but with σ_rms = 5 × 10⁻⁷ a.u. in 0–10,000 cm^-1, our ‘new DMS test’ line list has found excellent agreements with many S_obs data points reported for the band in Karlovets et al. [38]. See Fig. S14 in the supplementary file. The |δ%|_Ames (J ≤ 30) with respect to S_obs (2022) are reduced to 0±24% for 25 R lines, – 4±23% for 21 Q lines, and – 11±27% for 19 P lines. On the other hand, the latest EDM model in NOSL-296 gives S_NOSL values substantially higher in R branch, not only higher than S_obs and our ‘new DMS test’, but also higher than the published S_EDM (2022). In the P branch, S_NOSL diverges beyond J = 10, and end up being significantly lower than other three sets of intensities. This is a good example demonstrating that the difficulties in weak intensity determination have different manifestations for theoretical calculations and EH/EDM models.

Using the same testing DMS, the δ%_Ames for the 1113 band is reduced from 50%+ to –10%. The –200%+ deviations found on the 2112 band are replaced by excellent matches on Q branch, and less than 10–20% on R branch. For this band, NOSL-296 has good agreement with S_obs on R branch, but its Q branch intensity is only 15–20% of that of S_obs, and its P branch intensity is nearly 1 order of magnitude overestimated. The δ%_Ames for the 0602 band at 7720 cm^–1 is also reduced by half. See Fig. S14b in supplementary file. However, the testing DMS does not lead to obvious intensity improvement for other bands with medium or less δ%, such as 50⁰0, 02⁰3, 12⁰3–10⁰0, or nν₃ series. This suggests different factors are playing leading roles for different bands, thus future work is required to resolve these issues.

5. Summary and future work

In this paper, we report a first-generation data product and IR line lists for N₂O, including an isotopologue-independent ab initio PES of nitrous oxide refined with selected HITRAN energy levels below 7000 cm^–1 and experimental G_V at higher energies, an ab initio DMS fitted with CCSD(T)/aug-cc-pV(T,Q,5)Z dipoles computed up to 20,000 cm^–1 above potential energy minimum and extrapolated to one-electron basis set limit, room temperature IR line lists for 12 N₂O isotopologues of ^14/15N and ^16/17/18O, and a combination ‘natural’ list with terrestrial abundances. The Ames-296 K line lists provide continuous coverage up to 15,000 cm^–1 with intensity cut off at 10⁻³¹ cm/molecule. Energy levels, partition functions, IR line lists are compared to the HITRAN database, recent experiments, EDM models, NOSL-296 line list and the R16e data collection of experimental intensity.

Most intensity comparisons in this paper are focused on the main isotopologue 446, except for the isotopologue consistency example of 6ν₃ in Sec.4.5, and the reliable predictions of S_Ames intensity in supplementary Figs. S2, S4, S6, S8, S10 and S12, for 456, 546, 448, 447 and 556. In addition, we compare Ames-296 K line lists of individual minor isotopologues to 456, 546, 448 and 556 data in HITRAN2020 and published line lists. See Figs. S15–S18 in supplementary file. For 456 and 546, our agreements are good for those strong lines collected in HITRAN, but many bands are missing in HITRAN above the threshold of 10⁻²⁵ cm/molecule. For 556 in Fig. S16, all bands below 5000 cm^-1 are present in 2016 EH/EDM line list [46]. Only a few weak bands are missing between 4500 and 9000 cm^–1. The agreements between EH/EDM line list and Ames-296 K are from fair to good above 10⁻²⁵ cm/molecule (abundance included) or below 2200 cm^-1. For other bands, the EH/EDM line list has intensity overestimation on more than ten of those strongest bands, by 50–250%. There are also underestimations on a few bands. For 448 in Fig. S15, 2016 EH/EDM line list [34] has only a few significant under – or over-estimations below 7000 cm^–1, and a strong band was missing at 1630 cm^–1. The agreement rapidly deteriorates beyond 7000 cm^–1. The 448 energy level differences shown in Figure 3(c) probably cannot explain the magnitude of intensity deviations δ%. Note only the differences of strongest bands can be easily identified in Figs. S15–S18 comparisons. The isotopologue consistency of EH/EDM intensity may require more experiments and EDM updates, especially for weak bands. More studies on the isotopologue consistency of S_Ames intensities will be reported in a separate paper, along with next generation of Ames-296 K line lists with PES or DMS upgrades.

The EH-based line positions in NOSD-296 have accuracy near 10⁻⁴∼10⁻³ cm^–1, i.e. 3–4 orders of magnitude better than Ames-296 K list. To find out exactly how much intensity deviations are caused by the Ames-1 PES inaccuracy, the Ames-1 PES needs a urgent upgrade using recent experimental data beyond HITRAN to improve the line position accuracy. An upgrade for Ames-1 DMS is already in progress. However, this first generation of Ames-296 K line lists and the ‘natural’ line list can still provide valuable references and alternative data for database upgrades.

The major advantage of Ames-296 K line lists is to provide reliable intensity prediction for most weak (hot) bands, higher energy bands, and isotopologue bands. Those bands are still beyond, or not fully described by the power of the EH/EDM models, including those in NOSL-296. In general, NOSL-296 may have more accurate intensities for measured bands, e.g. the δ%_EDM is better balanced than δ%_Ames in Figure 11(b). But from our experience on CO₂, the EDM models fitted from various experimental data sources usually do not have cross-band or cross-isotopologue consistencies comparable to those in semi-empirically refined line lists, unless experimental uncertainty of percent or sub percent level is available. Look at those blue circle series isolated from S_obs and S_Ames in Figs. S3, S5 (or S_6b), S7 and S9, they mainly reflect the flaws in ΔP = 14–16 EDM models of 446 isotopologue. Although the models keep improving with every piece of new experimental data, the construction and refinement of EDM models at each level may take years of efforts to achieve completeness and accuracy. To pursue less than 10–20% δ% deviations, the EDM models need to be mass dependent, too. Compared to S_Ames, the uncertainty of EDM intensities is higher on weak bands at room temperature, see Figure 11(a). The impact of those deficits on intensity and opacities might become greater at high temperature, e.g. 1000 K. In contrast, Ames-296 K predictions have a much lower chance to yield such significant deviations. After comparisons with several recent experimental studies in the range of 5700–8620 cm^–1, only a few bands are identified as ‘problematic’ with |δ%|_Ames = 40–75% (1113, 0602 and 3112 bands) or larger than 200% (2112 band). But it is confirmed the δ%_Ames for 1113, 2112 and 3112 bands can be satisfactorily fixed through DMS update, and the δ%_Ames for 0602 band can be reduced by half. Therefore, we conclude the Ames-296K predictions can provide realistic estimates for IR intensities.

At the meantime, the current Ames-296 K line lists can provide an independent check and verifications for discrepancies between S_EDM and S_obs. As shown in Figure 12, there are many cases where δ%_Ames and δ%_NOSL agree well with each other, but not so well with S_obs. There are also cases where S_Ames have much smaller δ% than S_NOSL, just like those in supplementary figures. If both S_NOSL/EDM and S_Ames are available, one can make a better-informed estimate over the potential existence of unknown EDM defects, systematic deviations or uncertainty underestimated in experimental measurement. One example is the 2003–1000 band at 7692 cm^–1 (see Fig. S7). Its R15e peak intensity (×10²⁶) are 1.38 (S_NOSL), 1.296 (S_EDM2022 in [37]), 0.7485 (S_obs in [37]) and 0.6351 (S_Ames). The u_Ames estimate for this line is 2.3%, i.e. S_Ames is stable. With S_Ames supporting S_obs, we hope the S_EDM/NOSL deviation for this ΔP = 14 band can motivate more EDM improvements. In our preliminary studies, the uncertainty or sensitivity of S_Ames can be much smaller than that of S_obs on many bands with middle to strong intensities.

Based on the investigations presented in this paper, we believe S_NOSL or other S_EDM intensities are the best choice for any bands or band series for which better agreements have been established between S_EDM and reliable experimental intensities. This surely includes those bands of minor isotopologues where S_EDM are found with agreements better than S_Ames, while S_Ames should be checked to make sure there is no breaking of isotopologue consistency. For discrepancies, it is more appropriate to solve them case by case. Reasons include: (1) both S_EDM and S_Ames may have relatively larger deviations with respect to experiments; (2) part of current S_Ames predictions are systematically underestimated, as shown in Figure 11 of Sec.4.6; (3) S_Ames analysis may help identify other flaws hidden in EDM models or associated experiment data, such as 3401–0200 band and 1000–0100 band. In cases like 3401–0200 band where S_Ames has a better agreement with S_obs, S_Ames can be scaled to minimise the mean of δ%. In rare cases like 1000–0110 band, S_Ames values can be directly adopted before new accurate S_obs data series become available for multiple isotopologues.

In most cases of extra-large discrepancies between S_EDM and S_Ames, e.g. |δ%| > 100–200%, S_Ames is probably the safer choice. For those 446 bands with peak intensity below 10⁻²⁸ cm/molecule, using S_Ames probably can effectively prevent orders of magnitude deviations. For minor isotopologue predictions, S_Ames will be the better choice in most cases, except those bands with better agreement from S_EDM. However, if we have a reliable estimate on the δ%_Ames (446) for a specific band, the S_Ames prediction for the same band of minor isotopologues may be scaled accordingly. Examples include the 1113 band in Fig. S5, 0602 band in Fig. S7, and 0203 band series in Fig. S10. Note that in many cases Ames-296K could be the only choice for pure predictions on minor isotopologues, as using the secondary dipole parameters of main isotopologue has high probability to introduce 20–50% or orders of magnitude deviations. This is in contrast with the reliability and isotopologue consistency of S_Ames discussed earlier and demonstrated in supplementary figures. For higher energy range, S_Ames can provide the most complete and overall reasonable coverage up to 15,000 cm^–1, but we will need more experimental studies between 11,000 cm^–1 and 14,000 cm^–1 to elucidate potential DMS sensitivity in S_Ames.

Nowadays it is agreed that the future of all BTRHE (or similar strategy) based line lists lies on the integration with EH/EDM line lists and high accurate experiments and preserving their strengths. High-quality BTRHE intensity predictions may combine with the EH-based line positions and confirmed EDM intensities in NOSL-296, especially for those undocumented higher energy or weak bands, to prepare a more inclusive and reliable line list for databases and various science applications. Currently, the first step would be to replace Ames-296 K line positions with accurate line positions in NOSL-296, and to combine S_Ames with EH models for 456, 546, 556 and 448. A more accurate PES refinement and DMS upgrade will improve the quality of such a hybrid line list.

At the current stage, an over-simplified advisory for interested readers is to use NOSL-296 line positions whenever available, to use S_NOSL intensity if available for 446 bands stronger than 10⁻²⁷–10⁻²⁸ cm/molecule but cross-check with S_Ames to avoid substantial deviations, and to use Ames-296K for higher energy, weaker intensity, and minor isotopologues but use EH model line positions whenever available. Caution must be used however, for there exist exceptions to this rule of thumb, such as 1000–0110, nν₃ related hot bands, or certain 448 band origins.

Acknowledgements

We gratefully acknowledge support from the NASA Grants 18-APRA18–0013 and 18-XRP18_2–0029. X.H. acknowledges the support by NASA/SETI Institute Co-operative Agreements 80NSSC19M0121 and 80NSSC20K1358. We thank Dr. Tashkun (IAO) and Dr. Campargue (Grenoble) for kindly sharing data and helpful discussions. We thank Dr. Gordon (Harvard CfA, HITRAN) for comments and discussions. Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center.

Dr. Timothy J. Lee tragically passed away during this work. As a senior scientist fascinated with the significance of highly accurate molecular IR line lists in exoplanetary research, Tim served as the technical officer for our project, helping it running smoothly to study the function and role of biosignature molecules like N₂O in atmospheres. We devote this paper to this memorial issue honouring Tim's contribution and continuous passion.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by NASA ROSES grants: [Grant Numbers 18-APRA18-0013 and 18-XRP18_2-0029].