Measured Active Rotational-Vibrational Energy Levels Research Articles

The W2024 database of the water isotopologue H216O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\rm{H}}}_{2}^{\\,16}{\\rm{O}}$$\\end{document}

The rovibrational spectrum of the water molecule is the crown jewel of high-resolution molecular spectroscopy. While its significance in numerous scientific and engineering applications and the challenges behind its interpretation have been well known, the extensive experimental analysis performed for this molecule, from the microwave to the ultraviolet, is admirable. To determine empirical energy levels for H216O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\bf{H}}}_{{\\bf{2}}}^{\\,{\\bf{16}}}{\\bf{O}}$$\\end{document}, this study utilizes an improved version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) scheme, which now takes into account multiplet constraints and first-principles energy-level splittings. This analysis delivers 19027 empirical energy values, with individual uncertainties and confidence intervals, utilizing 309 290 transition wavenumbers collected from 189 (mostly experimental) data sources. Relying on these empirical, as well as some computed, energies and first-principles intensities, an extensive composite line list, named CW2024, has been assembled. The CW2024 dataset is compared to lines in the canonical HITRAN 2020 spectroscopic database, providing guidance for future experimental investigations.

MARVEL analysis of high-resolution rovibrational spectra of 16O12C18O.

Empirical rovibrational energy levels are presented for the third most abundant, asymmetric carbon dioxide isotopologue, 16O12C18O, based on a compiled dataset of experimental rovibrational transitions collected from the literature. The 52 literature sources utilized provide 19,438 measured lines with unique assignments in the wavenumber range of 2-12,676 cm-1. The MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol, which is built upon the theory of spectroscopic networks, validates the great majority of these transitions and outputs 8786 empirical rovibrational energy levels with an uncertainty estimation based on the experimental uncertainties of the transitions. Issues found in the literature data, such as misassignment of quantum numbers, typographical errors, and misidentifications, are fixed before including them in the final MARVEL dataset and analysis. Comparison of the empirical energy-level data of this study with those in the line lists CDSD-2019 and Ames-2021 shows good overall agreement, significantly better for CDSD-2019; some issues raised by these comparisons are discussed.

MARVEL analysis of high-resolution rovibrational spectra of C O .

A set of empirical rovibrational energy levels, obtained through the MARVEL (measured active rotational-vibrational energy levels) procedure, is presented for the C O 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 C O , which is also presented. A total of 60sources out of more than 750 checked provided 14,101uniquely measured and assigned rovibrational transitions in the wavenumber range of 579-13,735 cm . This is followed by a weighted least-squares refinement yielding the energy levels of the states involved in the measured transitions. Altogether 6318empirical rovibrational energies have been determined for C O . 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 analysis.

ExoMol line lists – LII. Line lists for the methylidyne cation (CH+)

ABSTRACT Comprehensive and accurate rovibronic line lists for the X 1Σ+ and A 1Π states of 12C1H+ and 13C1H+ which should be applicable up to temperatures of 5000 K are presented. Available empirical potential energy curves and high-level ab initio dipole and transition dipole moment curves are used with the program level to compute rovibronic energy levels and Einstein A coefficients. Λ-doubling is incorporated into the energy levels and A-coefficients involving the A 1Π state using an empirical method. For 12C1H+, line positions are improved by using both laboratory and astronomical observational spectra as input to the MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure. The 12C1H+ line list contains 1505 states and 34 194 transitions over the frequency range of 0–33 010 cm−1 (λ > 300 nm). Comparisons with observed astronomical and laboratory spectra give very good agreement. The PYT CH+ line lists and partition functions are available from the ExoMol database at www.exomol.com.

Empirical rovibrational energy levels for carbonyl sulphide

ABSTRACT An exhaustive review of the measured rovibrational transitions of the 16 O 12 C 32 S isotopologue of carbonyl sulphide is undertaken. A comprehensive analysis of data from 100 papers is carried out using a consistent set of harmonic oscillator quantum numbers which are recommended for future studies. A corrected compilation of 14,071 OCS transitions is then subjected to a Measured Active Rotational-Vibrational Energy Levels (MARVEL) analysis, resulting in 5729 empirical energy levels. The uncertainties corresponding to these levels are analysed using different procedures; the newly implemented bootstrap method is used to provide final uncertainties.

Empirical rovibronic energy levels of C3

ABSTRACT The carbon trimer, C 3 also known as propadienediylidene, is a quasi-linear molecule with an unusual electronic structure and a very flat bending potential in its ground electronic state. C 3 is an important species in astrophysics and carbon plasmas. Observed transition wavenumbers within and between the X ~ 1 Σ g + and A ~ 1 Π u states of C 3 are extracted from 21 papers and then subjected to a Measured Active Rotational-Vibrational Energy Levels (MARVEL) analysis: a corrected list of 4940 transitions are inverted to yield 1887 empirical energy levels. Uncertainties for these levels are determined using a newly implemented bootstrap method. These levels will provide input for developing a full spectroscopic model for C 3 which can used to generate a line list for the X ~ 1 Σ g + and A ~ 1 Π u states.

MARVEL analysis of high-resolution spectra of thioformaldehyde (H[formula omitted]CS)

We present a comprehensive analysis of the published spectroscopic literature on the main isotopologue of thioformaldehyde (1H212C32S). All reliable experimental transitions from publications over the last 42 years have been extracted and compiled into a consistent dataset with unique quantum number labelling and measurement uncertainties. The dataset covers the ground, ν1, ν2, ν3, ν4, ν5, ν6, and 2ν2 vibrational bands of H2CS. The ν4 and ν6 modes have very close band centres and consequently different data sources had incompatible vibrational assignments. Variational calculations are used as a basis to assign vibrational states of the associated transitions consistently. The transitions could then be processed using the robust MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure to produce a highly accurate set of 4254 rotation-vibration energy levels up to J=54 and 3729cm−1. The resulting set of labelled empirical-quality energies will be of significant use in the production of a hot molecular line list of H2CS, as well as other spectroscopic and radiative applications given the astrophysical importance of thioformaldehyde.

Fine and hyperfine resolved empirical energy levels of VO

A MARVEL (measured active rotational-vibrational energy levels) analysis of the spectra of vanadium oxide (VO) is performed, involving thirteen electronic states (6 quartets and 7 doublets). 51V16O data from 14 sources are used to form three networks: hyperfine-resolved quartets, hyperfine-unresolved quartets and hyperfine-unresolved doublets. A single quartet network is formed by deperturbing the hyperfine lines and 190 lines are assigned to an intercombination 2 2Π–X 4Σ− band system in the visible region previously recorded by Hopkins et al. (J. Chem. Phys. 130 (2009) 144308), allowing the doublet and quartet networks to be merged. As a result 6 603/4 402 validated transitions/final energies were obtained from analysis of the hyperfine-resolved network and 9 087/4 712 from the unresolved. Tv energy values and other molecular constants are determined for all doublet states within the networks.

ExoMol line lists – XLIV. Infrared and ultraviolet line list for silicon monoxide (28Si16O)

ABSTRACT A new silicon monoxide (28Si16O) line list covering infrared, visible, and ultraviolet regions called SiOUVenIR is presented. This line list extends the infrared EBJT ExoMol line list by including vibronic transitions to the $A\, {}^{1}\Pi$ and $E\, {}^{1}\Sigma ^{+}$ electronic states. Strong perturbations to the $A\, {}^{1}\Pi$ band system are accurately modelled through the treatment of six dark electronic states: $C\, {}^{1}\Sigma ^{-}$, $D\, {}^{1}\Delta$, $a\, {}^{3}\Sigma ^{+}$, $b\, {}^{3}\Pi$, $e\, {}^{3}\Sigma ^{-}$, and $d\, {}^{3}\Delta$. Along with the $X\, {}^{1}\Sigma ^{+}$ ground state, these nine electronic states were used to build a comprehensive spectroscopic model of SiO using a combination of empirical and ab initio curves, including the potential energy (PE), spin–orbit, electronic angular momentum, and (transition) dipole moment curves. The ab initio PE and coupling curves, computed at the multireference configuration interaction level of theory, were refined by fitting their analytical representations to 2617 experimentally derived SiO energy levels determined from 97 vibronic bands belonging to the X–X, E–X, and A–X electronic systems through the MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure. 112 observed forbidden transitions from the C–X, D–X, e–X, and d–X bands were assigned using our predictions, and these could be fed back into the MARVEL procedure. The SiOUVenIR line list was computed using published ab initio transition dipole moments for the E–X and A–X bands; the line list is suitable for temperatures up to 10 000 K and for wavelengths longer than 140 nm. SiOUVenIR is available from www.exomol.com and the CDS data base.

The W2020 Database of Validated Rovibrational Experimental Transitions and Empirical Energy Levels of Water Isotopologues. II. H217O and H218O with an Update to H216O

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 for H216O and newly populated with data for H217O and H218O. The H217O/H218O 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 H216O, H217O, and H218O 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 H217O and H218O form a complete set through 3204 cm−1 and 4031 cm−1, respectively. Vibrational band origins are reported for 37 and 52 states of H217O and H218O, respectively. The spectroscopic data of this study extend and improve the data collated by an International Union of Pure and Applied Chemistry Task 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 a minor but significant update to the W2020-H216O dataset, the joint analysis of the rovibrational levels for the series H216O, H217O, and H218O facilitated development of a consistent set of labels among these three water 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, 9925/8409 pseudo-experimental levels have been derived for H217O/H218O, significantly improving the coverage of accurate lines for these two minor 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

ABSTRACT The spectrum of dicarbon (C2) is important in astrophysics and for spectroscopic studies of plasmas and flames. The C2 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 12C2, 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 3Πg 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 1Πg state, the upper state of the insufficiently characterized Deslandres–d’Azambuja (C 1Πg–A 1Πu) 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 C2 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.

Empirical rovibrational energy levels of ammonia up to 7500 cm[formula omitted

The most recent version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) protocol and code is used to update and extend the list of accurately known empirical rovibrational energy levels of 14NH3 falling in the range of 0−7500 cm−1. Compared to an earlier similar study covering all the measured transitions of 14NH3 [22], the present investigation is limited to transitions with an upper energy level below 7500 cm−1, considers 82 sources (28 new) of transitions data, corrects several older assignments, and utilizes an improved validation procedure based partially on high-quality first-principles rovibrational energies. This study yields 4936 uniquely labelled empirical rovibrational energy levels, the set is complete up to 2413 cm−1. We confirm the overall high accuracy of the most recent “spectroscopic” (fitted) 14NH3 potential energy surface, C2018, up to 7500 cm−1. Investigation of energy values resulting from previous effective-Hamiltonian fits forms an important part of this study. It is established that previous effective-Hamiltonian fits, using high expansion orders in the Hamiltonian, are inaccurate for certain high rotational excitations of all vibrational parents considered. Employing the ground vibrational state as a test case, it is shown that the origin of the problem is that the observed 14NH3 spectroscopic network formed by rotational transitions and used for the effective-Hamiltonian fit contains floating components. A much improved effective-Hamiltonian fit is presented whereby the floating components are connected to the principal components of the spectroscopic network by carefully selected first-principles links. It is recommended that for all molecules the experimental set of transitions employed for an effective Hamiltonian fit should be checked for floating components and extra care be exercised if they exist, as in these cases the adequate reproduction of the transitions does not automatically mean that the energies derived from the effective-Hamiltonian parameters are correct as well. The connectivity problem of measured spectroscopic networks becomes more and more pronounced as the order of the Hamiltonian is increased.

MARVEL Analysis of the Measured High-Resolution Rovibronic Spectra and Definitive Ideal-Gas Thermochemistry of the 16O2 Molecule

Accurate, empirical rovibronic energy levels, with associated uncertainties, are determined for the lowest seven electronic states of the 16O2 molecule using the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm. After careful analysis and validation of 30 671 rovibronic transitions (including 24 376 measured and 6295 artificial transitions), collected from 91 publications, 4279 empirical rovibronic energy levels are determined. The highly accurate empirical (MARVEL) energy database is then augmented with rovibronic energies obtained from accurate effective Hamiltonians for the lowest six electronic states, establishing a hybrid database containing 15 946 rovibronic energy levels. Based on this hybrid database, complete up to the first dissociation limit, 41 260 cm−1, an accurate temperature-dependent ideal-gas partition function, Qint(T), and some related thermochemical functions [isobaric heat capacity, Cpo(T), entropy, So(T), and (absolute) enthalpy, Ho(T)] are derived for 16O2 employing the direct-summation technique. All thermochemical functions are reported, in 1 K increments up to 5000 K, in the supplementary material to this paper.

Accurate empirical rovibrational energies and transitions of H216O.

Several significant improvements are proposed to the computational molecular spectroscopy protocol MARVEL (Measured Active Rotational-Vibrational Energy Levels) facilitating the inversion of a large set of measured rovibrational transitions to energy levels. The most important algorithmic changes include the use of groups of transitions, blocked by their estimated experimental (source segment) uncertainties, an inversion and weighted least-squares refinement procedure based on sequential addition of blocks of decreasing accuracy, the introduction of spectroscopic cycles into the refinement process, automated recalibration, synchronization of the combination difference relations to reduce residual uncertainties in the resulting dataset of empirical (MARVEL) energy levels, and improved classification of the lines and energy levels based on their accuracy and dependability. The resulting protocol, through handling a large number of measurements of similar accuracy, retains, or even improves upon, the best reported uncertainties of the spectroscopic transitions employed. To show its advantages, the extended MARVEL protocol is applied for the analysis of the complete set of highly accurate H216O transition measurements. As a result, almost 300 highly accurate energy levels of H216O are reported in the energy range of 0-6000 cm-1. Out of the 15 vibrational bands involved in accurately measured rovibrational transitions, the following three have definitely highly accurate empirical rovibrational energies of 8-10 digits of accuracy: (v1v2v3) = (0 0 0), (0 1 0), and (0 2 0), where v1, v2, and v3 stand for the symmetric stretch, bend, and antisymmetric stretch vibrational quantum numbers. The dataset of experimental rovibrational transitions and empirical rovibrational energy levels assembled during this study, both with improved uncertainties, is considerably larger and more accurate than the best previous datasets.

Critical evaluation of measured rotational–vibrational transitions of four sulphur isotopologues of S16O2

A critical evaluation and validation of the complete set of previously published experimental rotational–vibrational line positions is reported for the four stable sulphur isotopologues of the semirigid SO2 molecule – i.e., 32S16O2, 33S16O2, 34S16O2, and 36S16O2. The experimentally measured, assigned, and labeled transitions are collated from 43 sources. The 32S16O2, 33S16O2, 34S16O2, and 36S16O2 datasets contain 40,269, 15,628, 31,080, and 31 lines, respectively. Of the datasets collated, only the extremely limited 36S16O2 dataset is not subjected to a detailed analysis. As part of a detailed analysis of the experimental spectroscopic networks corresponding to the ground electronic states of the 32S16O2, 33S16O2, and 34S16O2 isotopologues, the MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the rovibrational energy levels. The rovibrational levels and their vibrational parent and asymmetric-top quantum numbers are compared to ones obtained from accurate variational nuclear-motion computations as well as to results of carefully designed effective Hamiltonian models. The rovibrational energy levels of the three isotopologues having the same labels are also compared against each other to ensure self-consistency. This careful, multifaceted analysis gives rise to 15,130, 5852, and 10,893 validated rovibrational energy levels, with a typical accuracy of a few 0.0001 cm−1, for 32S16O2, 33S16O2, and 34S16O2, respectively. The extensive list of validated experimental lines and empirical (MARVEL) energy levels of the S16O2 isotopologues studied are deposited in the Supplementary Material of this article, as well as in the distributed information system ReSpecTh (http://respecth.hu).

The 1943 K emission spectrum of H216O between 6600 and 7050 cm[formula omitted

An emission spectrum of H216O has been recorded, with Doppler-limited resolution, at 1943 K using Hot Gas Molecular Emission (HOTGAME) spectroscopy. The wavenumber range covered is 6600 to 7050 cm−1. This work reports the analysis and subsequent assignment of close to 3700 H216O transitions out of a total of more than 6700 measured peaks. The analysis is based on the Measured Active Rotational-Vibrational Energy Levels (MARVEL) energy levels of H216O determined in 2013 and emission line intensities obtained from accurate variational nuclear-motion computations. The analysis of the spectrum yields about 1300 transitions not measured previously and 23 experimentally previously unidentified rovibrational energy levels. The accuracy of the line positions and intensities used in the analysis was improved with the spectrum deconvolution software SyMath via creating a peak list corresponding to the dense emission spectrum. The extensive list of labeled transitions and the new experimental energy levels obtained are deposited in the Supplementary Material of this article as well as in the ReSpecTh (http://www.respecth.hu) information system.

Small Molecules-Big Data.

Quantum mechanics builds large-scale graphs (networks): the vertices are the discrete energy levels the quantum system possesses, and the edges are the (quantum-mechanically allowed) transitions. Parts of the complete quantum mechanical networks can be probed experimentally via high-resolution, energy-resolved spectroscopic techniques. The complete rovibronic line list information for a given molecule can only be obtained through sophisticated quantum-chemical computations. Experiments as well as computations yield what we call spectroscopic networks (SN). First-principles SNs of even small, three to five atomic molecules can be huge, qualifying for the big data description. Besides helping to interpret high-resolution spectra, the network-theoretical view offers several ideas for improving the accuracy and robustness of the increasingly important information systems containing line-by-line spectroscopic data. For example, the smallest number of measurements necessary to perform to obtain the complete list of energy levels is given by the minimum-weight spanning tree of the SN and network clustering studies may call attention to "weakest links" of a spectroscopic database. A present-day application of spectroscopic networks is within the MARVEL (Measured Active Rotational-Vibrational Energy Levels) approach, whereby the transitions information on a measured SN is turned into experimental energy levels via a weighted linear least-squares refinement. MARVEL has been used successfully for 15 molecules and allowed to validate most of the transitions measured and come up with energy levels with well-defined and realistic uncertainties. Accurate knowledge of the energy levels with computed transition intensities allows the realistic prediction of spectra under many different circumstances, e.g., for widely different temperatures. Detailed knowledge of the energy level structure of a molecule coming from a MARVEL analysis is important for a considerable number of modeling efforts in chemistry, physics, and engineering.

EXPERIMENTAL ENERGY LEVELS AND PARTITION FUNCTION OF THE 12C2 MOLECULE

ABSTRACT The carbon dimer, the 12C2 molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for 12C2, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5699 rovibronic energy levels, 1325, 4309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the state, corresponding to the J = 2 total angular momentum quantum number and the F 1 spin-multiplet component, is 603.817(5) cm−1. This well-determined energy difference should facilitate observations of singlet–triplet intercombination lines, which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with ab initio variational ones based on empirically adjusted and spin–orbit coupled potential energy curves obtained using the Duo code, are used to obtain a highly accurate partition function, and related thermodynamic data, for 12C2 up to 4000 K.

On spectra of spectra

Spectroscopic networks (SNs), where the vertices are discrete, rovibronic energy levels and the edges are transitions among the levels allowed by quantum mechanics, serve as useful models helping to understand high-resolution spectra of molecular systems. The experimental SNs of the $$^{12}\hbox {C}_{2}, \hbox {H}_{3}^{+}$$ , $$\hbox {H}_{2}\hbox {D}^{+}$$ , $$\hbox {HD}_{2}^{+}$$ , $$^{14}\hbox {NH}_{3}$$ , and $$\hbox {H}_{2}{}^{16}\hbox {O}$$ molecules, containing a single copy of the known measured and assigned transitions, are investigated via the corresponding network representation matrices, including the Ritz matrix $${\varvec{X}}$$ , the adjacency matrix $${\varvec{A}}$$ , the combinatorial Laplacian matrix $${\varvec{L}}^{\mathrm{C}}$$ , and the normalized Laplacian matrix $${\varvec{L}}^{\mathrm{N}}$$ . Using elements of graph (network) theory and the eigenvalue spectra of the matrices mentioned, several interesting results relevant for high-resolution molecular spectroscopy are revealed about the structure of the investigated SNs. For example, as long as the parity selection rule of molecular rovibrational transitions is not violated, the experimental SNs investigated not only contain, with the exception of $$^{12}\hbox {C}_{2}$$ , two principal components but they are all bipartite networks, as proven by the symmetry of the eigenvalue spectrum of $${\varvec{A}}$$ about the origin. Furthermore, the PageRank ordering system is introduced to molecular spectroscopy to identify the most important vertices of SNs. The rankings provided by the degree of the levels and by PageRank may differ significantly; it appears that PageRank provides the more useful ranking. The connectors of relatively dense clusters of the SNs are identified and analysed via spectral clustering techniques based on $${\varvec{L}}^{\mathrm{C}}$$ and $${\varvec{L}}^{\mathrm{N}}$$ . The identification of connectors becomes especially important when judging the true accuracy of the experimental rovibrational energy levels obtained through the Measured Active Rotational-Vibrational Energy Levels (MARVEL) approach, built with the help of the Ritz matrix $${\varvec{X}}$$ .

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 0.7–17000cm−1 region, with a large gap between 7000 and 15000cm−1. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) algorithm is used to determine the energy levels. Out of the 29450 measured transitions 10041 and 18947 belong to ortho- and para-14NH3, respectively. A careful analysis of the related experimental spectroscopic network (SN) allows 28530 of the measured transitions to be validated, 18178 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.