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Understanding the energy-levels and 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.

The linear molecular ions H2He+, HHe+2, and He+3 are the central units (chromophores) of certain He-solvated complexes of the H2He+n, HHe+n, and He+n families, respectively.

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.

The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy levels is investigated, employing triatomic AB$${}_{2}$$ 2 molecules as models. In particular, calculations are performed for H$${}_{2}$$ 2 $${}^{16}$$ 16 O, across a range of vibrational and rotational excitations, both with and without the Coriolis contribution. A variety of different embedding choices are considered, together with a hierarchy of increasingly severe approximations culminating in a generalized version of the so-called “centrifugal sudden” method. Several surprising and remarkable conclusions are found, including that the Eckart embedding is not the best embedding choice.

The technique of Noise-Immune Cavity Enhanced Optical Heterodyne Molecular Spectroscopy (NICE-OHMS) is employed to detect rovibrational transitions of (Formula presented.) at wavelengths of 1.4 (Formula presented.) m. This intracavity-saturation approach narrows down the typical Doppler-broadened linewidths of about 600 MHz to the sub-MHz domain. The locking of the spectroscopy laser to a frequency-comb laser and the assessment of collisional and further line broadening effects result in transition frequencies with an absolute uncertainty below 10 kHz. The lines targeted for measurement are selected by the spectroscopic-network-assisted precision spectroscopy (SNAPS) approach. The principal aim is to derive precise and accurate relative energies from a limited set of Doppler-free transitions (Formula presented.). The 71 newly observed lines, combined with further highly accurate literature transitions, allow the determination of the relative energies for all of the 59 rovibrational states up to J = 6 within the (Formula presented.) vibrational parent of (Formula presented.), where J is the overall rotational quantum number and (Formula presented.), (Formula presented.), and (Formula presented.) are quantum numbers associated with the symmetric stretch, bend, and antisymmetric stretch normal modes, respectively. An experimental curiosity of this study is that for strong transitions an apparent signal inversion in the Lamb-dip spectra is observed; a novelty reserved to the NICE-OHMS technique.

A non-linear spectroscopic study of the HDO molecule is performed in the wavelength range of 1.36–1.42 μ m using noise-immune cavity-enhanced optical-heterodyne molecular spectroscopy (NICE-OHMS). More than 100 rovibrational Lamb dips are recorded, with an experimental precision of 2–20 kHz, related to the first overtone of the O–H stretch fundamental of HD16O and HD18O. Significant perturbations, including distortions, shifts, and splittings, have been observed for a number of Lamb dips. These spectral perturbations are traced back to an AC-Stark effect, arising due to the strong laser field applied in all saturation-spectroscopy experiments. The AC-Stark effect mixes parity pairs, that is pairs of rovibrational states whose assignment differs solely in the K c quantum number, where K c is part of the standard J K a , K c asymmetric-top rotational label. Parity-pair mixing seems to be especially large for parity pairs with K a ≥ 3, whereby their energy splittings become as small as a few MHz, resulting in multi-component asymmetric Lamb-dip profiles of gradually increasing complexity. These complex profiles often include crossover resonances. This effect is well known in saturation spectroscopy, but has not been reported in combination with parity-pair mixing. Parity-pair mixing is not seen in H 2 16 O and H 2 18 O, because their parity pairs correspond to ortho and para nuclear-spin isomers, whose interaction is prohibited. Despite the frequency shifts observed for HD16O and HD18O, the absolute accuracy of the detected transitions still exceeds that achievable by Doppler-limited techniques.

Another manifestation of the Aharonov-Bohm effect is introduced to chemistry, in fact to nuclear quantum dynamics and high-resolution molecular spectroscopy. As demonstrated, the overall rotation of a symmetric-top molecule influences the dynamics of an internal vibrational motion in a way that is analogous to the presence of a solenoid carrying magnetic flux. To a good approximation, the low-energy rovibrational energy-level structure of the quasistructural molecular ion H+5can be understood entirely in terms of this effect.

Rovibronic energy levels are determined for four low-lying electronic states (\X, \A, \Sa, and \Sc) of the imidogen free radical ($^{14}$NH) using the \Marvel\ (Measured Active Rotational-Vibrational Energy Levels) technique. Compilation of transitions from both laboratory measurements and solar spectra, found in 18 publications, yields a dataset of 3002 rovibronic transitions forming elements of a measured spectroscopic network (SN). At the end of the MARVEL procedure, the majority of the transitions form a single, self-consistent SN component of 2954 rovibronic transitions and 1058 energy levels, \NoX, \NoA, and \Noc\ for the \X, \A, and \Sc\ electronic states, respectively. The \Sa\ electronic state is characterized by \Noa\ $\Lambda$-doublet levels, counting each level only once. Electronic structure computations show that unusually the CCSD(T) method does not accurately predict the \Sa\ excitation energy even at the complete basis set limit.

The structures and the vibrational dynamics of the complexes HHe are investigated experimentally (via mass spectrometry (MS)) and at high levels of electronic-structure theory. The MS measurements reveal interesting trends about the stability of the starting members of the HHe family. The computations establish that the basically linear, strongly bound, symmetric triatomic molecular ion He(H)He, with an equilibrium H-He distance of 0.925 angstrom and about 2/3 but at least 1/2 of the positive charge on H, is the molecular core of all of the complexes. Definitive quantum-chemical results are obtained for HHe and HHe, including the proton affinity of He (computed to be cm(-1) via the focal-point analysis (FPA) scheme), the FPA isomerisation energy between the two linear isomers of HHe ( cm(-1)), and the dissociation energy of the HHe HHe + He reaction, with an FPA estimate of cm(-1). The structural isomers of the He-solvated complexes are discussed up to n=18. A useful notation, [k-l-m]-HHe, is introduced to characterise qualitatively the three possible belts around the He-H-He core in HHe (), where l denotes the number of He atoms in the central belt and denote the number of He atoms in the top and bottom belts. Capping He atoms attached to the belts can be indicated by sub- and superscripts. Several possible indicators of microscopic superfluidity are investigated: He evaporation energies, rotational constants, and vibrational fundamentals. [GRAPHICS] .

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.

© 2021 Author(s).Taking advantage of the extreme absolute accuracy, sensitivity, and resolution of noise-immune-cavity-enhanced optical-heterodyne-molecular spectroscopy (NICE-OHMS), a variant of frequency-comb-assisted Lamb-dip saturation-spectroscopy techniques, the rotational quantum-level structure of both nuclear-spin isomers of H218O is established with an average accuracy of 2.5 kHz. Altogether, 195 carefully selected rovibrational transitions are probed. The ultrahigh sensitivity of NICE-OHMS permits the observation of lines with room-temperature absorption intensities as low as 10−27 cm molecule−1, while the superb resolution enables the detection of a doublet with a separation of only 286(17) kHz. While the NICE-OHMS experiments are performed in the near-infrared window of 7000-7350 cm−1, the lines observed allow the determination of all the pure rotational energies of H218O corresponding to J values up to 8, where J is the total rotational quantum number. Both network and quantum theory have been employed to facilitate the measurement campaign and the full exploitation of the lines resolved. For example, to minimize the experimental effort, the transitions targeted for observation were selected via the spectroscopic-network-assisted precision spectroscopy (SNAPS) scheme built upon the extended Ritz principle, the theory of spectroscopic networks, and an underlying dataset of quantum chemical origin. To ensure the overall connection of the ultraprecise rovibrational lines for both nuclear-spin isomers of H218O, the NICE-OHMS transitions are augmented with six accurate microwave lines taken from the literature. To produce absolute ortho-H218O energies, the lowest ortho energy is determined to be 23.754 904 61(19) cm−1. A reference, benchmark-quality line list of 1546 transitions, deduced from the ultrahigh-accuracy energy values determined in this study, provides calibration standards for future high-resolution spectroscopic experiments between 0-1250 and 5900-8380 cm−1

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH 5 +based on the motion of an effective particle confined to a 60-vertex graphΓ 60with a single edge length parameter. Within this model, the quantum states of CH 5 +are obtained in analytic form and are related to combinatorial properties ofΓ 60. The bipartite structure ofΓ 60gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH 5 +

Improving the accuracy of absolute energies associated with rovibronic quantum states of molecules requires accurate high-resolution spectroscopy measurements. Such experiments yield transition wavenumbers from which the energies can be deduced via inversion procedures. To address the problem that not all transitions contribute equally to the goal of improving the accuracy of the energies, the method of Connecting Spectroscopic Components (CSC) is introduced. Using spectroscopic networks and tools of graph theory, CSC helps to find the most useful target transitions and target wavenumber regions for (re)measurement. The sets of transitions suggested by CSC should be investigated by experimental research groups in order to select those target lines which they can actually measure based on the apparatus available to them. The worked-out examples, utilizing extensive experimental spectroscopic data on the molecules H$$_2^{~16}$$ 2 16 O, $$^{32}$$ 32 S$$^{16}$$ 16 O$$_2$$ 2 , H$$_2^{~12}$$ 2 12 C$$^{16}$$ 16 O, and $$^{14}$$ 14 NH$$_{3}$$ 3 , clearly prove the overall usefulness of the CSC method and provide suggestions how CSC can be used for various tasks and under different practical circumstances.

The fourth age of quantum chemistry offers fully flexible, black-box-type protocols for the accurate and detailed study of nuclear motions, applicable equally well to semirigid, floppy, flexible, polytopic, fluxional, and quasistructural polyatomic molecular systems, including complexes and clusters. Several codes, based on advanced fourth-age protocols, have been developed for the variational (or variational-like) solution of the time-independent nuclear-motion (rotational-vibrational) Schrodinger equation. These codes yield accurate rovibrational energy levels, wavefunctions, and to some extent quantum-number assignments for bound, resonance, and scattering states, revealing important spectroscopic and dynamical characteristics about the systems studied. When no approximations are introduced to the kinetic energy part of the rovibrational Hamiltonian, the accuracy of the computed results, assuming the validity of the Born–Oppenheimer approximation, depends solely on the accuracy of the representation of the potential energy surface utilized during these computations. From the point of view of potential applications it is important to emphasize that the most general codes can be employed both in full and any number of reduced dimensions. Several a posteriori analysis tools are available to improve the understanding of the extreme amount of numerical results produced by the stationary-state nuclear-motion computations. As shown through a few examples, these stationary-state solutions can straightforwardly be utilized for detailed quantum-dynamics studies. The applications briefly detailed at the end of this chapter help appreciate the power of the fourth-age quantum-chemical techniques developed and available to the spectroscopic and dynamics communities.

The laser-induced alignment-and-orientation (A&O) dynamics of the prolate symmetric top CH$_3$X (X = F, Cl, Br, I) molecules is investigated, with particular emphasis on the effect of halogen substitution on the rotational constants, dipole moments, and polarizabilities of these species, as these quantities determine the A&O dynamics. Insight into possible control schemes for preferred A&O dynamics of halogenated molecules and best practices for A&O simulations are provided, as well. It is shown that for accurate A&O-dynamics simulations it is necessary to employ large basis sets and high levels of electron correlation when computing the rotational constants, dipole moments, and polarizabilities. The benchmark-quality values of these molecular parameters, corresponding to the equilibrium, as well as the vibrationally averaged structures are obtained with the help of the focal-point analysis (FPA) technique and explicit electronic-structure computations utilizing the gold-standard CCSD(T) approach, basis sets up to quintuple-zeta quality, core-correlation contributions and, in particular, relativistic effects for CH$_3$Br and CH$_3$I. It is shown that the different A&O behavior of the CH$_3$X molecules in the optical regime is mostly caused by the differences in their polarizability anisotropy, in other terms, the size of the halogen atom. In contrast, the A&O dynamics of the CH$_3$X series induced by an intense few-cycle THz pulse is mostly governed by changes in the rotational constants, due to the similar dipole moments of the CH$_3$X molecules. The A&O dynamics is most sensitive to the $B$ rotational constant: even the difference between its equilibrium and vibrationally-averaged values results in noticeably different A&O dynamics. The contribution of rotational states having different symmetry, weighted by nuclear-spin statistics, to the A&O dynamics is also studied.

Internal vibrational and rotational partition functions are calculated for nine molecules that are abundant in the terrestrial atmosphere and some are also observed in planetary and exoplanet atmospheres. These molecules are often observed in non-local thermodynamic equilibrium (NLTE) conditions. Calculations are made for all isotopologues of these molecules for which data are available, generally for the temperature range T = 1–5000 K. The methods of calculation of the vibrational and rotational partition functions, Qv and Qr, respectively, the convergence, and the uncertainties for each isotopologue are discussed. Finally, a FORTRAN program, NLTE_TIPS_2021.FOR, to recall the NLTE partition sums is discussed.

Spectroscopic networks provide a particularly useful representation of observed rovibronic transitions of molecules, as well as of related quantum states, whereby the states form a set of vertices connected by the measured transitions forming a set of edges. Among their several uses, SNs offer a practical framework to assess data in line-by-line spectroscopic databases. They can be utilized to help detect flawed transition entries. Methods which achieve this validation work for transitions taking part in at least one cycle in a measured spectroscopic network but they do not work for bridges. The concept of two-edge-connectivity of graph theory, introduced here to high-resolution spectroscopy, offers an elegant approach that facilitates putting the maximum number of bridges, if not all, into at least one cycle. An algorithmic solution is shown how to augment an existing spectroscopic network with a minimum number of new spectroscopic measurements selected according to well-defined guidelines. In relation to this, two metrics are introduced, ranking measurements based on their utility toward achieving the goal of two-edge-connectivity. Utility of the new concepts are demonstrated on spectroscopic data of $$^{14} {\text {NH}}_3$$ 14 NH 3 .

Resonance states are characterized by an energy that is above the lowest dissociation threshold of the potential energy hypersurface of the system and thus resonances have finite lifetimes. All molecules possess a large number of long- and short-lived resonance (quasibound) states. A considerable number of rotational–vibrational resonance states are accessible not only via quantum-chemical computations but also by spectroscopic and scattering experiments. In a number of chemical applications, most prominently in spectroscopy and reaction dynamics, consideration of rotational–vibrational resonance states is becoming more and more common. There are different first-principles techniques to compute and rationalize rotational–vibrational resonance states: one can perform scattering calculations or one can arrive at rovibrational resonances using variational or variational-like techniques based on methods developed for determining bound eigenstates. The latter approaches can be based either on the Hermitian (L2, square integrable) or non-Hermitian (non-L2) formalisms of quantum mechanics. This Perspective reviews the basic concepts related to and the relevance of shape and Feshbach-type rotational–vibrational resonance states, discusses theoretical methods and computational tools allowing their efficient determination, and shows numerical examples from the authors' previous studies on the identification and characterization of rotational–vibrational resonances of polyatomic molecular systems.

The first application of quantum graphs to the vibrational quantum dynamics of molecules is reported. The quantum-graph model is applied to the quasistructural molecular ion CH5+, whose nuclear dynamics challenges the traditional understanding of chemical structures and molecular spectra. The vertices of the quantum graph represent versions of the equilibrium structure with distinct atom numbering, while the edges refer to collective nuclear motions transforming the versions of the equilibrium structure into one another. These definitions allow the mapping of the complex vibrational quantum dynamics of CH5+ onto the motion of a particle confined in a quantum graph. The quantum-graph model provides a simple understanding of the low-energy vibrational quantum dynamics of CH5+ and is able to reproduce the low-lying vibrational energy levels of CH5+ (and CD5+) with remarkable accuracy.

Despite decades of diligent work on their development, line-by-line (LBL) spectroscopic information systems, widely employed by scientists and engineers, may still contain a number of incorrect rovibronic lines. A novel heuristic protocol, relying on cycle bases of spectroscopic networks (SN) and a system of linear constraints, is proposed to unravel incorrect transitions present in the database. The algorithm is named autoECART, standing for automatic Energy Conservation Analysis of Rovibronic Transitions. The autoECART method is tested on synthetic SNs constructed from spectroscopic databases of nine water isotopologues. The systematic numerical tests demonstrate the outstanding capability of the autoECART procedure to identify almost all of the outliers generated randomly in these synthetic SNs. As a ‘real-life’ example, the GEISA-2019-H 2 18 O database is scrutinized, revealing 17 rough outlier lines. Developers of spectroscopic information systems are encouraged to utilize autoECART for cleansing the huge number of transitions deposited in LBL databases.

Total internal partition sums (TIPS) are reported for 166 isotopologues of 51 molecules important in planetary atmospheres. Molecules 1 to 50 are taken from the HITRAN2016 list, and, in some cases, additional isotopologues are considered for some of the molecules. Molecules 51–53 are C3H4, CH3, and CS2, respectively. TIPS are not reported for the O atom and CF4; thus, while there are 53 species in the list, data are reported for 51 molecules. The TIPS are determined by various methods from 1 K to a Tmax that ensures the TIPS reported have converged. These data are provided with HITRAN2016 and a new version of the TIPS code is available in both FORTRAN and python languages.

The ground-state rotational spectrum of propene-3-d1, CH2═CHCH2D, was measured by Fourier transform microwave spectroscopy. Transitions were assigned for the two conformers, one with the D atom in the symmetry plane (S) and the other with the D atom out of the plane (A). The energy difference between the two conformers was calculated to be 6.5 cm–1, the S conformer having lower energy. The quadrupole hyperfine structure due to deuterium was resolved and analyzed for both conformers. The experimental quadrupole coupling and the centrifugal distortion constants compared favorably to their ab initio counterparts. Ground-state rotational constants for the S conformer are 40582.157(9), 9067.024(1), and 7766.0165(12) MHz. Ground-state rotational constants for the A conformer are 43403.75(3), 8658.961(2), and 7718.247(2) MHz. For the A conformer, a small tunneling splitting (19 MHz) due to internal rotation was observed and analyzed. Using the new rotational constants of this work as well as those previously det...

Rovibrational states of the four dimers formed by the light and the heavy isotopologues of the methane and the water molecules are computed using a potential energy surface taken from the literature. The general rovibrational energy-level pattern characteristic to all systems studied is analyzed employing two models of a dimer: the rigidly rotating complex and the coupled system of two rigidly rotating monomers. The rigid-rotor model highlights the presence of rovibrational sequences corresponding to formally negative rotational excitation energies, which is explained in terms of the coupled-rotors picture.

The theory of rovibronic spectroscopy of light-dressed molecules is presented within the framework of quantum mechanically treated molecules interacting with classical light fields. Numerical applications are demonstrated for the homonuclear diatomic molecule Na$_2$, for which the general formulae can be simplified considerably and the physical processes leading to the light-dressed spectra can be understood straightforwardly. The physical origin of different peaks in the light-dressed spectrum of Na$_2$ is given and the light-dressed spectrum is investigated in terms of its dependence on the dressing field's intensity and wavelength, the turn-on time of the dressing field, and the temperature. The important implications of light-dressed spectroscopy on deriving field-free spectroscopic quantities are also discussed.

A general and semi-automatic technique, based on the complex absorbing potential (CAP) method, is developed for the variational computation and identification of rotational-vibrational resonance states. This technique is an extension of a method introduced by Tremblay and Carrington ( J. Chem. Phys. 2005, 122, 244107 ), and it employs the damped eigenvectors of a CAP-modified Hamiltonian as a basis to describe resonance wave functions. The low-lying resonances of the weakly bound Ar·NO+ complex are computed with the new and the traditional CAP techniques to test the new algorithm. As an additional, more challenging test case, the bound and resonance rovibrational states of the H2 dimer, the latter with both negative and positive binding energies, are determined, corresponding to different rotational excitations of the H2 monomers. Resonances above the first few dissociation channels of (H2)2 are computed with the new and the traditional CAP methods, revealing some new, assigned resonance quantum states not reported in the literature.

The use of one- and two-mode reduced-density matrices (RDM), and , respectively, and in particular the use of their diagonal elements, and , is suggested for the assignment of normal-mode-like quantum numbers to variationally computed vibrational wave functions of semirigid molecules when the computation is based on a nuclear-motion Hamiltonian expressed in curvilinear internal coordinates . The use of RDMs for the semi-automatic assignment of vibrational states is tested on the HO molecule, whereby about the first 250 states, in the energy range of 0-25,000cm(-1), are assigned. The proposed semi-automatic assignment procedure takes advantage of the fact that (a) for semirigid molecules it is often possible to define internal coordinates which mimick normal coordinates defined by the harmonic counterparts of the anharmonic vibrations, (b) overlaps between already assigned and yet unassigned RDMs provide outstanding and often unambiguous suggestions for the quantum numbers, and (c) an energy-decomposition scheme helps to decide among possible assignment possibilities suggested by the computed density overlaps. [GRAPHICS] .

For centuries, it has been known that vibrational and rotational degrees of freedom are in general not separable. Nevertheless, surprisingly little is known about the best strategies for approximately separating these degrees of freedom in practice—even in the case of semirigid molecules, where the separation is most meaningful. There is also some confusion in the literature about the proper way to quantify the magnitude of the Coriolis (i.e., rotation-vibration) coupling in rovibrational Hamiltonians or its effect on the rovibrational eigenenergies. In this study, a vibrational-coordinate-independent metric is proposed to quantify the magnitude of the Coriolis contribution to the rovibrational Hamiltonian. The impact of Coriolis coupling on the rovibrational eigenenergies is computed numerically exactly, using both full and various truncated Hamiltonians. The role played by the choice of the vibrational coordinate system—and especially by the choice of “embedding” or body-fixed frame—is examined extensively, both numerically and analytically. This investigation targets several molecular prototypes, all of which serve as important benchmarks for the high-resolution spectroscopic community. Most of these are triatomic molecules, including water (H2 16 O), its deuterated isotopologues ( D 2 16 O and HD 16 O), H 3 + , and ozone ( 16 O3), but the tetratomic ammonia molecule ( 14 NH3) is also investigated. These studies provide important insight into the nature of Coriolis coupling under various circumstances. The findings of this study also have significant practical ramifications, vis-a-vis the use of simplifying numerical approximation techniques in nuclear-motion computations.

An alternative combinatorial expression is presented for the Wigner numbers Wm,nJ that leads to a generating function and to several new identities. An extended class of Wigner numbers, Wigner numbers of the lth order, Wm,nJ,l, is also introduced.

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.

A detailed understanding of the complex rotation–vibration spectrum of the water molecule is vital for many areas of scientific and human activity, and thus, it is well studied in a number of spectral regions. To enhance our perception of the spectrum of the parent water isotopologue, H216O, a dataset of 270 745 non-redundant measured transitions is assembled, analyzed, and validated, yielding 19 204 rovibrational energy levels with statistically reliable uncertainties. The present study extends considerably an analysis of the rovibrational spectrum of H216O, published in 2013, by employing an improved methodology, considering about one-third more new observations (often with greatly decreased uncertainties), and using a highly accurate first-principles energy list for validation purposes. The database of experimental rovibrational transitions and empirical energy levels of H216O created during this study is called W2020. Some of the new transitions in W2020 allow the improved treatment of many parts of the dataset, especially considering the uncertainties of the experimental line positions and the empirical energy values. The W2020 dataset is examined to assess where measurements are still lacking even for this most thoroughly studied isotopologue of water, and to provide definitive energies for the lower and upper states of many yet-to-be-measured transitions. The W2020 dataset allows the evaluation of several previous compilations of spectroscopic data of water and the accuracy of previous effective Hamiltonian fits.

Frequency combs and cavity-enhanced optical techniques have revolutionized molecular spectroscopy: their combination allows recording saturated Doppler-free lines with ultrahigh precision. Network theory, based on the generalized Ritz principle, offers a powerful tool for the intelligent design and validation of such precision-spectroscopy experiments and the subsequent derivation of accurate energy differences. As a proof of concept, 156 carefully-selected near-infrared transitions are detected for H216O, a benchmark system of molecular spectroscopy, at kHz accuracy. These measurements, augmented with 28 extremely-accurate literature lines to ensure overall connectivity, allow the precise determination of the lowest ortho-H216O energy, now set at 23.794 361 22(25) cm−1, and 160 energy levels with similarly high accuracy. Based on the limited number of observed transitions, 1219 calibration-quality lines are obtained in a wide wavenumber interval, which can be used to improve spectroscopic databases and applied to frequency metrology, astrophysics, atmospheric sensing, and combustion chemistry., Precision-spectroscopy techniques can accurately measure lines in constrained frequency and intensity ranges. The authors propose a spectroscopic-network-assisted precision spectroscopy method by which transitions measured in a narrow range provide information in other, extended regions of the spectrum.

Rovibronic spectra of the field-dressed homonuclear diatomic Na2 molecule is in- vestigated to identify direct signatures of the light-induced conical intersection (LICI) on the spectrum. The theoretical framework formulated allows the computation of the (1) field-dressed rovibronic states induced by a medium intensity continuous-wave laser light and the (2) transition amplitudes between these field-dressed states with respect to an additional weak probe pulse. The field-dressed spectrum features ab- sorption peaks resembling the field-free spectrum as well as stimulated emission peaks corresponding to transitions not visible in the field-free case. By investigating the dependence of the field-dressed spectra on the dressing-field wavelength, both in full- and reduced dimensional simulations, direct signatures of the LICI can be identified. These signatures include (1) the appearance of new peaks and the splitting of peaks for both absorption and stimulated emission, and (2) the manifestation of an intensity borrowing effect in the field-dressed spectrum.

A fundamental theoretical framework is formulated for the investigation of rovibronic spectra resulting from the coupling of molecules to one mode of the radiation field in an optical cavity. The approach involves the computation of (1) cavity-field-dressed rovibronic states, which are hybrid light-matter eigenstates of the `molecule + cavity radiation field' system, and (2) the transition amplitudes between these field-dressed states with respect to a weak probe pulse. The predictions of the theory are shown for the homonuclear Na$_2$ molecule. The field-dressed rovibronic spectrum demonstrates undoubtedly that the Born--Oppenheimer approximation breaks down in the presence of the cavity radiation field. A clear fingerprint of the strong nonadiabaticity is found, which can only emerge in the close vicinity of conical intersections. In this work, the conical intersection is induced by the quantized radiation field, and it is thus called a "light-induced conical intersection" (LICI). Dependence of the cavity-field-dressed spectrum on the cavity-mode wavelength as well as on the light-matter coupling strength is investigated. Essential changes are identified in the spectra from the weak to the ultrastrong coupling regimes.

An additive, linear, atom-type-based (ATB) scheme is developed allowing no-cost estimation of zero-point vibrational energies (ZPVE) of neutral, closed-shell molecules in their ground electronic states. The atom types employed correspond to those defined within the MM2 molecular mechanics force field approach. The reference training set of 156 molecules cover chained and branched alkanes, alkenes, cycloalkanes and cycloalkenes, alkynes, alcohols, aldehydes, carboxylic acids, amines, amides, ethers, esters, ketones, benzene derivatives, heterocycles, nucleobases, all the natural amino acids, some dipeptides and sugars, as well as further simple molecules and ones containing several structural units, including several vitamins. A weighted linear least-squares fit of atom-type-based ZPVE increments results in recommended values for the following atoms, with the number of atom types defined in parentheses: H(8), D(1), B(1), C(6), N(7), O(3), F(1), Si(1), P(2), S(3), and Cl(1). The average accuracy of the ATB ZPVEs is considerably better than 1 kcal mol(-1), that is, better than chemical accuracy. The proposed ATB scheme could be extended to many more atoms and atom types, following a careful validation procedure; deviation from the MM2 atom types seems to be necessary, especially for third-row elements.

Rovibronic energy levels are determined for four low-lying electronic states (X 3 Σ - , A 3Π, a 1 Δ , and c 1 Π ) of the imidogen free radical ( 14 NH) using the M arvel (Measured Active Rotational-Vibrational Energy Levels) technique. Compilation of transitions from both laboratory measurements and solar spectra, found in 18 publications, yields a dataset of 3002 rovibronic transitions forming elements of a measured spectroscopic network (SN). At the end of the MARVEL procedure, the majority of the transitions form a single, self-consistent SN component of 2954 rovibronic transitions and 1058 energy levels, 542, 403, and 58 for the X 3 Σ - , A 3Π, and c 1 Π electronic states, respectively. The a 1 Δ electronic state is characterized by 55 Λ -doublet levels, counting each level only once. Electronic structure computations show that unusually the CCSD(T) method does not accurately predict the a 1 Δ excitation energy even at the complete basis set limit.