Ab Initio Dipole Moment Surfaces Research Articles

ExoMol line lists – LIX. High-temperature line list for N2O

Abstract New hot line lists for five isotopologues of N2O are presented, for the parent 14N216O and 4 singly substituted species 14N217O, 14N218O, 14N15N16O and 15N14N16O. The line lists have been computed with the variational program TROVE using a new empirical potential energy surface (PES) and an accurate ab initio dipole moment surface of N2O Ames-1. The PES was obtained by fitting to experimentally derived energies of N2O compiled using the well established MARVEL procedure. Here we also introduce an ‘artificial symmetry group’ Cns(AEM) for an efficient construction of rotation-vibrational basis set of a linear non-symmetric triatomic molecule of the XYZ type. The line lists cover the rotational excitations up to J = 160 and the wavenumber range up to 20000 cm−1. MARVEL energies are also used to improve predicted line positions resulting in excellent agreement with the available experimental spectra, as demonstrated. An extensive comparison with existing line lists for N2O HITRAN, HITEMP, NOSL-296, NOSD-1000 and Ames-296K is provided. The line lists are freely accessible from www.exomol.com.

First Ab Initio Line Lists for Triatomic Sulfur-Containing Molecules: S2O and S3.

We present in this paper the first room temperature rovibrational line lists for the main isotopologues of disulfur monoxide (S2O) and thiozone (S3) variationally computed from newly developed ab initio potential energy and dipole moment surfaces (PESs and DMSs). S2O and S3 are supposed to be potential candidates for astronomical detection, especially in the Venusian atmosphere where sulfur chemistry plays a major role. Contrary to other stable sulfur-containing species like SO2 or H2S, there is much less experimental data for the short-lived reactive S2O and S3 molecules. Indeed, the infrared spectra of S2O and S3 are quite complicated to analyze without consistent theoretical predictions because they contain both high J (∼100) and a lot of hot band transitions, even at T = 296 K. In this work, we have constructed PESs based on the single-reference coupled cluster approach [CCSD(T)] and including corrections due to the scalar relativistic effects, DBOC, and highly excited Slater determinants. The structure of the excited electronic states of S3 was also discussed. The nuclear-motion Eckart-Watson Hamiltonian expressed in terms of normal-mode irreducible tensor operators was used to compute the energy levels. For line intensity calculation, ab initio DMSs were computed at the CCSD(T)/aug-cc-pV5Z level of the theory. Rotation-vibration patterns in the fundamental bands of S2O and S3 have been simulated taking into account the recent Fourier-transform spectra of S2O recorded at the SOLEIL synchrotron. The present work aims at providing line intensities of S2O and S3 that are missing in the literature as well as new spectroscopic support for atmospheric applications.

New quantum assignments and analysis of high-resolution H212CO spectra in the range 3700–4450 cm-1

Four spectra of formaldehyde in natural isotopic abundance in the 3700–5200 cm-1 region were recorded at low temperature 160–166 K at Synchrotron SOLEIL for various pressures. Line positions and intensities were retrieved by non-linear least-squares curve-fitting procedures in the range 3700–4450 cm-1 and analyzed using ab initio based effective Hamiltonian and line intensities computed using new ab initio dipole moment surface. A new measured line list contains positions and intensities for 6177 features. Refined parameters of effective Hamiltonian were fitted to all assigned line positions with the RMS deviations of 0.001 cm-1. Updated line lists include intensity values based on ab initio variational calculations which were subsequently empirically optimized. Comparison of our theoretical simulation with previously available data as well as with high-resolution and low-resolution experimental spectra are reported.

The spectrum of radioactive water vapor: the H219O radio-isotopologue

The absorption spectrum of H219O, a radioactive isotopologue of the water molecule, is predicted using variational nuclear motion calculated based on a high precision potential energy function and ab initio dipole moment surface. Vibrational - rotational energy levels and wave functions, line centers and Einstein coefficients for dipole transitions are calculated. Predicted transition wavenumbers are improved by extrapolating known empirical energy levels of the stable H216O, H217O and H218O isotopologues to H219O. A line list for possible atmospheric application is presented which includes air line broadening coefficients. The calculations span a wide spectral range covering infrared and visible wavelengths, and are appropriate for temperatures up to 1000 K. Windows suitable for observing absorption by H219O are identified and comparisons made with the infrared spectra of water vapor in natural abundance, H215O and H214O.

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

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

ExoMol line lists – LVIII. High-temperature molecular line list of carbonyl sulphide (OCS)

ABSTRACT A new molecular line list covering wavelengths λ > 1 μm (the 0–10 000 cm−1 range) for the main isotopologue of carbonyl sulphide 16O12C32S is presented. The OCS line list, named OYT8, contains almost 2.5 billion transitions between 2.4 million rotation-vibration energy levels with the total angular momentum up to J = 223. It is suitable for high-temperature environments up to T = 2000 K. Line list calculations were performed with the variational nuclear motion code trove in conjunction with a highly accurate, empirically refined potential energy surface and a newly computed ab initio dipole moment surface of OCS. The OYT8 line list is adapted for high-resolution applications by replacing computed energy levels with empirically derived values of OCS where available. Comparisons of the OYT8 line list with other OCS line lists and spectra yields excellent agreement for both strong and weak spectroscopic bands. The increased coverage of the OYT8 line list and the many new spectral features that are available will greatly facilitate the future observation of OCS on exoplanets. Carbonyl sulphide joins a growing number of sulphur-bearing molecules available from the ExoMol database. The OYT8 line list along with the associated temperature- and pressure-dependent molecular opacities can be downloaded from www.exomol.com and the CDS astronomical database.

ExoMol line lists – LVII. High accuracy ro-vibrational line list for methane (CH4)

ABSTRACT The MM ro-vibrational line list for methane (12CH4) is presented; MM covers wavelengths λ > 0.83 μm (wavenumbers up to 12 000 cm−1) and contains over 50 billion transitions between 9155 208 states with total angular momentum J ≤ 60. MM was generated through solution of the nuclear motion Schrödinger equation using variational program trove for an empirically derived potential energy surface (PES) and a new high-level ab initio dipole moment surface. The PES was constructed by fitting the ro-vibrational energies of CH4 to a set of highly accurate, experimentally derived energies. Molecular states are classified using the Td(M) symmetry group and are fully assigned with rotation and vibration quantum numbers. The MM line list is adapted to high-resolution applications by replacing the calculated ro-vibrational energies with the experimentally derived values where available, namely for 23 208 states with J ≤ 27 below 9986 cm−1. Doing so leads to over 1000 000 experimentally derived CH4 lines compared to approximately $330\, 000$ lines of 12CH4 in the HITRAN data base. The MM line list is shown to be more complete than the recent HITEMP methane line list. Methane spectra computed using MM across a broad range of temperatures and wavenumbers show excellent agreement with experiment. The MM line list supersedes the previous ExoMol methane line lists 10to10 and 30to10 both in terms of accuracy and coverage. Together with the pre-computed ExoMolOP molecular atmospheric opacity tables, it is now the recommended CH4 data set in the ExoMol data base (www.exomol.com).

Analysis of experimental spectra of phosphine in the Tetradecad range near 2.3 μm using ab initio calculations

Due to its major interest for the chemistry of planetary atmospheres and exobiology, accurate spectroscopy data of phosphine are required for the search of signatures of this molecule in astronomical observations. In this work, high resolution infrared laboratory spectra of phosphine were analyzed for the first time in the full Tetradecad region (3769–4763 cm−1) involving 26 rotationally resolved bands. Overall, 3242 lines were assigned in spectra previously recorded by Fourier transform spectroscopy at temperatures 200 K and 296 K, using a combined theoretical model based on ab initio calculations. The total nuclear motion Hamiltonian of PH3 including ab initio potential energy surface, was reduced to an effective Hamiltonian using the high-order contact transformation method adapted to vibrational polyads of the AB3 symmetric top molecules, followed by empirical optimization of the parameters. At this step, the experimental line positions were reproduced with a standard deviation of 0.0026 cm−1 that provided unambiguous identification of observed transitions. The effective dipole transition moments of the bands were obtained by fitting to the intensities obtained from variational calculations using the ab initio dipole moment surface. The assigned lines were used to newly determine 1609 experimental vibration-rotational levels up to Jmax = 18 with energy in the range 3896–6037 cm−1 that represents significant extension towards higher energies compared to previous works. Transitions for all 26 sublevels of the Tetradecad were identified but with noticeably fewer transitions for fourfold excited bands because of their weaker intensity. At the final step, pressure-broadened half widths were attached to each transition and a composite line list adopting ab initio intensities and empirical line positions corrected to the accuracy of about 0.001 cm−1 for strong and medium transitions was validated against experimental spectra available in the literature.

ExoMol line lists – XLVIII. High-temperature line list of thioformaldehyde (H2CS)

ABSTRACT A comprehensive rotation–vibration (ro–vibrational) line list of thioformaldehyde (1H212C32S) that is applicable for elevated temperatures (${2000}{\, \mathrm{K}}$) is presented. The new MOTY line list covers the 0–8000 cm−1 range (wavelengths $\lambda \gt {1.3}{\, \mu \mathrm{m}})$ and contains around 43.5 billion transitions between 52.3 million states with rotational excitation up to J = 120. Line list calculations utilize a newly determined empirically refined potential energy surface (PES) – the most accurate H2CS PES to date – a previously published high-level ab initio dipole moment surface, and the use of an exact kinetic energy operator for solving the ro–vibrational Schrödinger equation. Post-processing of the MOTY line list is performed by replacing calculated energy levels with empirically derived values, vastly improving the accuracy of predicted line positions in certain spectral windows and making the line list suitable for high-resolution applications. The MOTY line list is available from the ExoMol data base at www.exomol.com and the CDS astronomical data base.

Direct frequency comb spectroscopy of HCN to evaluate line lists.

We report direct frequency comb spectroscopy of the 2ν1 band of H13CN in the short-wave infrared (λ = 1.56 μm) towards experimental validation of molecular line lists that support observatories like JWST. The laboratory measurements aim to test spectral reference data generated from an experimentally accurate potential energy surface (PES) and an ab initio dipole moment surface (DMS) calculated from quantum chemistry theory. Benchmarking theory with experiment will improve confidence in new astrophysics and astrochemistry inferred from spectroscopic observations of HCN and HNC. Here we describe our instrumentation and initial results using a cross-dispersed spectrometer with a virtually imaged phased array (VIPA).

New Theoretical Infrared Line List for the Methyl Radical with Accurate Vibrational Band Origins from High-Level Ab Initio Calculations.

In the present work, high-level ab initio calculations were carried out for the ground electronic state of the methyl radical (CH3). Dunning's augmented correlation-consistent orbital basis sets were employed up to the quintuple-ζ valence quality with the core-valence electron correlation [aug-cc-pCV5Z] combined with the single- and double-excitation unrestricted coupled-cluster approach with a perturbative treatment of triple excitations [RHF-UCCSD(T)]. The explicitly correlated version of the coupled-cluster approach [RHF-UCCSD(T)-F12x{x = a, b}] was additionally applied with the core-valence cc-pCVQZ-F12 basis set in order to study convergence with respect to the basis set size. The contributions beyond the coupled-cluster level of the theory like Douglas-Kroll-Hess scalar relativistic Hamiltonian, diabatic Born-Oppenheimer corrections, and high-order electronic correlations have been included into the ab initio potential energy surfaces (PESs). It is shown that the theoretical band origins of CH3 converge gradually to the experimental values when applying the ab initio PESs using the aug-cc-pCVXZ [X = T, Q, and 5] basis sets. For the first time, all available experimental band origins of the gaseous CH3 are reproduced within an accuracy of 0.2 cm-1 using a newly developed PES extrapolated to the complete basis set limit [CBS(TQ5Z)]. The reached accuracy is one order of magnitude better than that of the best available calculations. A new theoretical infrared line list was generated for astrophysical applications using an ab initio dipole moment surface computed at the RHF-UCCSD(T)/aug-cc-pCVQZ level of the theory. The manifestation of a large-amplitude motion in CH3 is also discussed.

ExoMol line lists – XLVII. Rovibronic molecular line list of the calcium monohydroxide radical (CaOH)

ABSTRACT Any future detection of the calcium monohydroxide radical (CaOH) in stellar and exoplanetary atmospheres will rely on accurate molecular opacity data. Here, we present the first comprehensive molecular line list of CaOH covering the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration-electronic and $\tilde{X}\, ^2\Sigma ^+$–$\tilde{X}\, ^2\Sigma ^+$ rotation-vibration bands. The newly computed OYT6 line list contains over 24.2 billion transitions between 3.2 million energy levels with rotational excitation up to J = 175.5. It is applicable to temperatures up to T = 3000 K and covers the 0–35 000 cm−1 range (wavelengths λ > 0.29 μm) for rotational, rotation-vibration and the $\tilde{A}\, ^2\Pi$–$\tilde{X}\, ^2\Sigma ^+$ electronic transitions. The strong band around 16 000 cm−1 (λ = 0.63 μm) is likely to be of interest in future astronomical observations, particularly in hot rocky exoplanets where temperatures can become extremely high. The OYT6 line list has been generated using empirically refined $\tilde{X}\, ^2\Sigma ^+$ and $\tilde{A}\, ^2\Pi$ state potential energy surfaces, high-level ab initio transition dipole moment surfaces, and a rigorous treatment of both Renner–Teller and spin-orbit coupling effects, which are necessary for correctly modelling the CaOH spectrum. Post-processing of the CaOH line list has been performed so as to tailor it to high-resolution applications, i.e. by replacing calculated energy levels with more accurate empirically derived values (where available), hence improving the accuracy of the predicted line positions in certain regions. The OYT6 line list is available from the ExoMol data base at www.exomol.com and the CDS astronomical data base.

Ames-2021 CO2 Dipole Moment Surface and IR Line Lists: Toward 0.1% Uncertainty for CO2 IR Intensities.

A highly accurate CO2 ab initio dipole moment surface (DMS), Ames-2021, is reported along with 12C16O2 infrared (IR) intensity comparisons approaching a 1-4‰ level of agreement and uncertainty. The Ames-2021 DMS was accurately fitted from CCSD(T) finite-field dipoles computed with the aug-cc-pVXZ (X = T, Q, 5) basis for C atom and the d-aug-cc-pVXZ (X = T, Q, 5) basis for O atoms, and extrapolated to the one particle basis set limit. Fitting σrms is 3.8 × 10-7 au for 4443 geometries below 15 000 cm-1. The corresponding IR intensity, SAmes-2021, are computed using the Ames-2 potential energy surface (PES), which is the best PES available for CO2. Compared to high accuracy IR studies for 2001i-00001 and 3001i-00001 bands, SAmes-2021 matches NIST experiment-based intensities [SNIST-HIT16 or SHIT20] to -1.0 ± 1.3‰, or matches DLR experiment-based intensities [SDLR-HIT16/UCL/Ames] to 1.9 ± 3.7‰. This indicates the systematic deviations and uncertainties have been significantly reduced in SAmes-2021. The SUCL2015 (or SHITRAN2016) have larger deviations (vs SDLR) and uncertainties (vs SDLR, SNIST) which are attributed to the less accurate Ames-1 PES adopted in UCL-296 line list calculation. The SAmes-2021 intensity of 12C16O2 and 13C16O2 is utilized to derive new absolute 13C/12C ratios for Vienna PeeDee Belemnite (VPDB) with uncertainty reduced by 1/3 or 2/3. Further evaluation of SAmes-2021 intensities are carried out on those CO2 bands discussed in the HITRAN2020 update paper. Consistent improvements and better accuracies are found in band-by-band analysis, except for those bands strongly affected by Coriolis couplings, or very weak bands measured with relatively larger experimental uncertainties. The Ames-2021 296 K IR line lists are generated for 13 CO2 isotopologues, with 18 000 cm-1 and S296K > 1 × 10-31 cm/molecule cutoff and then combined with CDSD line positions (except 14C16O2). The Ames-2021 DMS and 296 K IR line lists represent a major improvement over previous CO2 theoretical IR intensity studies, including Ames-2016, UCL-296, and recent UCL DMS 2021 update. A real 1 permille level of agreement and uncertainty will definitely require both more accurate PES and more accurate DMS.

A full-dimensional ab initio potential energy and dipole moment surfaces for (NH3)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) for the ammonia dimer (NH3)2 are reported. The database of the PES consists of 27 736 ab initio energy points and all of these points were calculated at the UCCSD(T)-F12a/AVTZ level. The PES was fitted by using the fundamental invariant neural network (FI-NN) method that satisfies the permutational symmetry of identical atoms, and the root mean square fitting error for the PES is very small as low as 0.562 meV. The geometries for the (NH3)2 DMS are the same as those used for the PES and are calculated at the XYG3/AVTZ level. This PES can describe a variety of internal floppy motions, including all kinds of vibrational modes no matter intermolecular or intramolecular. The CCSD(T)-PES can dissociate correctly to two NH3 monomers, with De = 1135.55 cm−1 (13.58 kJ/mol) which agrees accurately with the 13.5 ± 0.3 kJ/mol predicted by previous work.

An experimentally-accurate and complete room-temperature infrared HCN line-list for the HITRAN database

A hydrogen cyanide line list (MOMeNT-90) developed for the HITRAN spectroscopic database covering 0–7500 cm−1 range (λ>1330 nm) is presented. The line list is a combination of the variationally calculated line intensities with line centers obtained from experimentally derived energy levels. There are four features of this line list which distinguishes it from the previously calculated ones. First, the intensities are variationally calculated using a new, high-accuracy potential energy surface (PES) obtained via fitting the PES using experimental energy levels. Second, a new ab initio dipole moment surface was calculated at a high level of quantum chemical theory. Based on the wave functions calculated with the new PES and use of the new dipole moment surface, line intensities are reported which of similar accuracy to those obtained experimentally. Third, the calculated states are mapped to the existing complete set of experimental eigenenergies, resulting in an assigned and complete HCN line list down to the HITRAN intensity threshold of 10−34 cm/molecule. Fourth, extensive validation of the line list is provided through line-by-line comparisons of the results with measured HCN spectra which confirms the accuracy of the intensities used to construct the line list. The line list is augmented with parameters needed to calculate line widths for pressure-dependent simulations.

Synthesis of ab initio and effective Hamiltonian line lists for ozone

A synthetic line list for the ozone molecule is presented. Variational calculation using the semi-empirical potential energy surface (PES) and ab initio dipole moment surface (DMS) produce very accurate values of line intensities, but give line positions far away from their experimental values. Furthermore assignment of approximate rotational and vibrational quantum numbers are missing from variationally calculated line list. Effective Hamiltonian calculations are complimentary to ab initio line lists in these properties giving excellent value of line positions, close to experimental ones, and a full set of quantum numbers assignment. The synthesis of both these qualities in one line list is highly desirable. Here a synthetic line list for 16O3 is presented. The method of corrections of distorted intensities in variational linelist with ab initio DMS due to the artificial intensity stealing is developed and applied. Comparison of the synthetic line list with all major published line lists and available experimental data is given. The calculated line intensities agree to within experimental error for most bands for which accurate measurements are available.

ExoMol line lists – XL. Rovibrational molecular line list for the hydronium ion (H3O+)

ABSTRACT A new line list for hydronium (H316O+) is computed. The line list is based on a new ab initio dipole moment surface (CCSD(T)/aug-cc-pVQZ) and a new empirical potential energy surface (PES). The empirical PES of H3O+ was obtained by refining an ab initio surface through a global fit to the experimentally determined rovibrational energies collected from the literature covering the ground, $\nu _1^{\pm }$, $\nu _2^{\pm }$, $2\nu _2^{\pm }$, $\nu _3^{\pm }$, and $\nu _4^{\pm }$ vibrational states. The line list covers the wavenumber range up to 10 000 cm−1 (wavelengths $\gt 1 \, \mu$m) and should be complete for temperatures up to T = 1500 K. This is the first comprehensive line list for H3O+ with extensive wavenumber coverage and accurate transitional probabilities. Prospects of detection of hydronium in spectra of Solar system giant planets as well as exoplanets are discussed. The eXeL line list is publicly available from the ExoMol and CDS data bases.

ExoMol line lists – XXXIX. Ro-vibrational molecular line list for CO2

ABSTRACT A new hot line list for the main isotopologue of CO2, 12C16O2 is presented. The line list consists of almost 2.5 billion transitions between 3.5 million rotation-vibration states of CO2 in its ground electronic state, covering the wavenumber range 0–20 000 cm−1 (λ > 0.5 µm) with the upper and lower energy thresholds of 36 000 cm−1 and 16 000 cm−1, respectively. The ro-vibrational energies and wavefunctions are computed variationally using the accurate empirical potential energy surface Ames-2. The ro-vibrational transition probabilities in the form of Einstein coefficients are computed using an accurate ab initio dipole moment surface with variational program TROVE. A new implementation of TROVE which uses an exact nuclear-motion kinetic energy operator is employed. Comparisons with the existing hot line lists are presented. The line list should be useful for atmospheric retrievals of exoplanets and cool stars. The UCL-4000 line list is available from the CDS and ExoMol data bases.

Cavity ring-down spectroscopy of CO2 near λ = 2.06 µm: Accurate transition intensities for the Orbiting Carbon Observatory-2 (OCO-2) “strong band”

The λ = 2.06 µm absorption band of CO2 is widely used for the remote sensing of atmospheric carbon dioxide, making it relevant to many important top-down measurements of carbon flux. The forward models used in the retrieval algorithms employed in these measurements require increasingly accurate line intensity and line shape data from which absorption cross-sections can be computed. To overcome accuracy limitations of existing line lists, we used frequency-stabilized cavity ring-down spectroscopy to measure 39 transitions in the 12C16O2 absorption band. The line intensities were measured with an estimated relative combined standard uncertainty of ur = 0.08 %. We predicted the J-dependence of the measured intensities using two theoretical models: a one-dimensional spectroscopic model with Herman-Wallis rotation-vibration corrections, and a line-by-line ab initio dipole moment surface model [Zak et al. JQSRT 2016;177:31-42]. For the second approach, we fit only a single factor to rescale the theoretical integrated band intensity to be consistent with the measured intensities. We find that the latter approach yields an equally adequate representation of the fitted J-dependent intensity data and provides the most physically general representation of the results. Our recommended value for the integrated band intensity equal to 7.183 × 10−21 cm molecule−1 ± 6 × 10−24 cm molecule−1 is based on the rescaled ab initio model and corresponds to a fitted scale factor of 1.0069 ± 0.0002. Comparisons of literature intensity values to our results reveal systematic deviations ranging from −1.16 % to +0.33 %.

Coupled cluster spectroscopic properties of the coinage metal nitrosyls, M–NO (M = Cu, Ag, Au)

Ab initio near-equilibrium potential energy and dipole moment surfaces for the bent CuNO, AgNO, and AuNO molecules have been calculated under the Feller–Peterson–Dixon (FPD) composite framework at the coupled cluster level of theory including complete basis set extrapolation, outer-core correlation, scalar relativistic effects, and spin–orbit coupling. The Brueckner coupled cluster doubles with perturbative triples method, BCCD(T), was used to greatly improve upon CCSD(T), which was particularly problematic for CuNO. In the latter case, the BCCD(T) vibrational frequencies showed significant differences compared to CCSD(T), e.g., nearly 65 cm−1 for the NO stretching frequency, and BCCD(T) also resulted in much better agreement with the available experimental frequencies. A full range of ro-vibrational spectroscopic constants are given for all three molecules of this study using the accurate composite potential energy functions and employing second-order vibrational perturbation theory.