MARVEL: measured active rotational-vibrational energy levels

An algorithm is proposed, based principally on an earlier proposition of Flaud and co-workers [Mol. Phys. 32 (1976) 499], that inverts the information contained in uniquely assigned experimental rotational-vibrational transitions in order to obtain measured active rotational-vibrational energy levels (MARVEL). The procedure starts with collecting, critically evaluating, selecting, and compiling all available measured transitions, including assignments and uncertainties, into a single database. Then, spectroscopic networks (SN) are determined which contain all interconnecting rotational-vibrational energy levels supported by the grand database of the selected transitions. Adjustment of the uncertainties of the lines is performed next, with the help of a robust weighting strategy, until a self-consistent set of lines and uncertainties is achieved. Inversion of the transitions through a weighted least-squares-type procedure results in MARVEL energy levels and associated uncertainties. Local sensitivity coefficients could be computed for each energy level. The resulting set of MARVEL levels is called active as when new experimental measurements become available the same evaluation, adjustment, and inversion procedure should be repeated in order to obtain more dependable energy levels and uncertainties. MARVEL is tested on the example of the H-2 O-17 isotopologue of water and a list of 2736 dependable energy levels, based on 8369 transitions, has been obtained. (c) 2007 Elsevier Inc. All rights reserved

Analysis of measured high-resolution doublet rovibronic spectra and related line lists of 12CH and 16OH

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a multitude of modelling efforts within multiple chemical, combustion, astrophysical, and atmospheric environments. Accurate empirical rovibronic energy levels, with associated uncertainties, are reported for the low-lying doublet electronic states of 12CH and 16OH, using the Measured Active Rotational-Vibrational Energy Levels (Marvel) algorithm. For 12CH, a total of 1521 empirical energy levels are determined in the primary spectroscopic network (SN) of the radical, corresponding to the following seven electronic states: X 2Π, A 2Δ, B 2Σ−, C2 Σ+, D 2Π, E 2Σ+, and F 2Σ+. The energy levels are derived from 6348 experimentally measured and validated transitions, collected from 29 sources. For 16OH, the lowest four doublet electronic states, X 2Π, A 2Σ+, B 2Σ+, and C 2Σ+, are considered, and a careful analysis and validation of 15 938 rovibronic transitions, collected from 45 sources, results in 1624 empirical rovibronic energy levels. The large set of spectroscopic data presented should facilitate the refinement of line lists for the 12CH and 16OH radicals. For both molecules hyperfine-resolved experimental transitions have also been considered, forming SNs independent from the primary SNs

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3x10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e)(BO)=0.957 82 A and theta(e)(BO)=104.48(5)degrees, respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of (H2O)-O-16 is r(e)(ad)=0.957 85 A and theta(e)(ad)=104.50(0)degrees, respectively, while those of (D2O)-O-16 are r(e)(ad)=0.957 83 A and theta(e)(ad)=104.49(0)degrees. Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A(0) and B-0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of (H2O)-O-16, obtained from experimentally determined A(0)(') and B-0(') rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e)(sp)=0.957 77 A and theta(e)(sp)=104.48 degrees

MARVEL Analysis of the Measured High-resolution Rovibronic Spectra of 48 Ti 16 O

Accurate, experimental rovibronic energy levels, with associated labels and uncertainties, are reported for 11 low-lying electronic states of the diatomic ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ molecule, determined using the Marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. All levels are based on lines corresponding to critically reviewed and validated high-resolution experimental spectra taken from 24 literature sources. The transition data are in the 2–22,160 cm−1 region. Out of the 49,679 measured transitions, 43,885 are triplet–triplet, 5710 are singlet–singlet, and 84 are triplet–singlet transitions. A careful analysis of the resulting experimental spectroscopic network (SN) allows 48,590 transitions to be validated. The transitions determine 93 vibrational band origins of ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$, including 71 triplet and 22 singlet ones. There are 276 (73) triplet–triplet (singlet–singlet) band-heads derived from Marvel experimental energies, 123(38) of which have never been assigned in low- or high-resolution experiments. The highest J value, where J stands for the total angular momentum, for which an energy level is validated is 163. The number of experimentally derived triplet and singlet ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ rovibrational energy levels is 8682 and 1882, respectively. The lists of validated lines and levels for ${}^{48}{\mathrm{Ti}}^{16}{\rm{O}}$ are deposited in the supporting information to this paper

Recommended ideal-gas thermochemical functions for heavy water and its Substituent isotopologues

Accurate temperature-dependent ideal-gas internal partition functions, Qint(T), and several derived thermochemical functions are reported for heavy water, with an oxygen content corresponding to the isotopic composition of Vienna Standard Mean Ocean Water (VSMOW), and its constituent isotopologues, D216O, D217O, and D218O, for temperatures between 0 and 6000 K. The nuclear-spin-dependent partition functions are obtained by the direct summation technique, involving altogether about 16 000 measured and more than nine million computed bound rovibrational energy levels for the three molecules. Reliable standard uncertainties, as a function of temperature, are estimated for each thermochemical quantity determined, including the enthalpy, the entropy, and the isobaric heat capacity of the individual nuclear-spin-equilibrated isotopologues and of heavy water. The accuracy of the heavy-water ideal-gas Cp(T) is unprecedented, below 0.01% up to 1800 K. All the thermochemical functions are reported, in 1 K increments, in the supplementary material

MARVEL analysis of high-resolution rovibrational spectra of ¹³C¹⁶O₂

A set of empirical rovibrational energy levels, obtained through the MARVEL (measured active rotational-vibrational energy levels) procedure, is presented for the 13C16O2 isotopologue of carbon dioxide. This procedure begins with the collection and analysis of experimental rovibrational transitions from the literature, allowing for a comprehensive review of the literature on the high-resolution spectroscopy of 13C16O2, which is also presented. A total of 60 sources out of more than 750 checked provided 14,101 uniquely measured and assigned rovibrational transitions in the wavenumber range of 579–13,735 cm-1. This is followed by a weighted leastsquares refinement yielding the energy levels of the states involved in the measured transitions. Altogether 6318 empirical rovibrational energies have been determined for 13C16O2. Finally, estimates have been given for the uncertainties of the empirical energies, based on the experimental uncertainties of the transitions. The detailed analysis of the lines and the spectroscopic network built from them, as well as the uncertainty estimates, all serve to pinpoint possible errors in the experimental data, such as typos, misassignment of quantum numbers, and misidentifications. Errors found in the literature data were corrected before including them in the final MARVEL dataset and analysi

The W2020 Database of Validated Rovibrational Experimental Transitions and Empirical Energy Levels of Water Isotopologues. II. (H2O)-O-17 and (H2O)-O-18 with an Update to (H2O)-O-16

The W2020 database of validated experimental transitions and accurate empirical energy levels of water isotopologues, introduced in the work of Furtenbacher et al. [J. Phys. Chem.Ref.Data 49, 033101 (2020)], is updated forH2 16Oand newly populated with data forH2 17OandH2 18O. TheH2 17O/ H2 18O spectroscopic data utilized in this study are collected from 65/87 sources, with the sources arranged into 76/99 segments, and the data in these segments yield 27 045/66 166 (mostly measured) rovibrational transitions and 5278/6865 empirical energy levels with appropriate uncertainties. Treatment and validation of the collated transitions of H2 16O, H2 17O, and H2 18O utilized the latest, XML-based version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol and code, called xMARVEL. The empirical rovibrational energy levels of H2 17O and H2 18O form a complete set through 3204 cm−1 and 4031 cm−1, respectively. Vibrational band origins are reported for 37 and 52 states of H2 17O andH2 18O, respectively. The spectroscopic data of this study extend and improve the data collated by an InternationalUnion of Pure andApplied ChemistryTask Group in 2010 [J. Tennyson et al., J. Quant. Spectrosc. Radiat. Transfer 110, 2160 (2010)] as well as those reported in the HITRAN2016 information system. Following aminor but significant update to theW2020-H2 16Odataset, the joint analysis of the rovibrational levels for the seriesH2 16O,H2 17O, andH2 18Ofacilitated development of a consistent set of labels among these threewater isotopologues and the provision of accurate predictions of yet to be observed energy levels for the minor isotopologues using the combination of xMARVEL results and accurate variational nuclear-motion calculations. To this end, 9925/8409pseudo-experimental levels have been derived forH2 17O/H2 18O, significantly improving the coverage of accurate lines for these twominor water isotopologues up to the visible region. The W2020 database now contains almost all of the transitions, apart from those of HD16O, required for a successful spectroscopic modeling of atmospheric water vapor

An update to the MARVEL data set and ExoMol line list for ¹²C₂

The spectrum of dicarbon (C_{2}) is important in astrophysics and for spectroscopic studies of plasmas and flames. The C_{2} spectrum is characterized by many band systems with new ones still being actively identified; astronomical observations involve eight of these bands. Recently, Furtenbacher et al. presented a set of 5699 empirical energy levels for {12}^C_{2}, distributed among 11 electronic states and 98 vibronic bands, derived from 42 experimental studies and obtained using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. Here, we add data from 13 new sources and update data from 5 sources. Many of these data sources characterize high-lying electronic states, including the newly detected 3 {3}^Π_{g} state. Older studies have been included following improvements in the MARVEL procedure that allow their uncertainties to be estimated. These older works in particular determine levels in the C {1}^Π_{g} state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C {1}^Π_{g}–A {1}^Π_{u}) band. The new compilation considers a total of 31 323 transitions and derives 7047 empirical (MARVEL) energy levels spanning 20 electronic and 142 vibronic states. These new empirical energy levels are used here to update the 8states C_{2} ExoMol line list This updated line list is highly suitable for high-resolution cross-correlation studies in astronomical spectroscopy of, for example, exoplanets, as 99.4 per cent of the transitions with intensities over 10^{−18} cm molecule^{−1} at 1000 K have frequencies determined by empirical energy levels

An improved rovibrational linelist of formaldehyde, H₂¹²C¹⁶O

Published high-resolution rotation-vibration transitions of H₂¹²C¹⁶O the principal isotopologue of methanal, are analyzed using the MARVEL (Measured Active Rotation-Vibration Energy Levels) procedure. The literature results are augmented by new, high-accuracy measurements of pure rotational transitions within the ground, ν_{3}, ν_{4}, and ν_{6} vibrational states. Of the 16 596 non-redundant transitions processed, which come from 43 sources including the present work, 16 403 could be validated, providing 5029 empirical energy levels of H₂¹²C¹⁶O with statistically well-defined uncertainties. All the empirical rotational-vibrational energy levels determined are used to improve the accuracy of ExoMol’s AYTY line list for hot formaldehyde. The complete list of collated experimental transitions, the empirical energy levels determined, as well as the extended and improved line list are provided as Supplementary Material

MARVEL analysis of the measured high-resolution spectra of 14NH3

Accurate, experimental rotational–vibrational energy levels and line positions, with associated labels and uncertainties, are reported for the ground electronic state of the symmetric-top 14NH3 molecule. All levels and lines are based on critically reviewed and validated high-resolution experimental spectra taken from 56 literature sources. The transition data are in the 0.7–17 000 cm−1 region, with a large gap between 7000 and 15 000 cm−1. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) algorithm is used to determine the energy levels. Out of the 29 450 measured transitions 10 041 and 18 947 belong to ortho- and para-14NH3, respectively. A careful analysis of the related experimental spectroscopic network (SN) allows 28 530 of the measured transitions to be validated, 18 178 of these are unique, while 462 transitions belong to floating components. Despite the large number of spectroscopic measurements published over the last 80 years, the transitions determine only 30 vibrational band origins of 14NH3, 8 for ortho- and 22 for para-14NH3. The highest J value, where J stands for the rotational quantum number, for which an energy level is validated is 31. The number of experimental-quality ortho- and para-14NH3 rovibrational energy levels is 1724 and 3237, respectively. The MARVEL energy levels are checked against ones in the BYTe first-principles database, determined previously. The lists of validated lines and levels for 14NH3 are deposited in the Supporting Information to this paper. Combination of the MARVEL energy levels with first-principles absorption intensities yields a huge number of experimental-quality rovibrational lines, which should prove to be useful for the understanding of future complex high-resolution spectroscopy on 14NH3; these lines are also deposited in the Supporting Information to this paper