Search

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 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.

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.

Generalization of an earlier reduced-density-matrix-based vibrational assignment algorithm is given, applicable for systems exhibiting both large-amplitude motions, including tunneling, and degenerate vibrational modes. The algorithm developed is used to study the structure of the excited vibrational wave functions of the ammonia molecule, 14NH3. Characterization of the complex dynamics of systems with several degenerate vibrations requires reconsidering the traditional degenerate-mode description given by vibrational angular momentum quantum numbers and switching to a symmetry-based approach that directly predicts state degeneracy and uncovers relations between degenerate modes. Out of the 600 distinct vibrational eigenstates of ammonia obtained by a full-dimensional variational computation, the developed methodology allows for the assignment of about 500 with meaningful labels. This study confirms that vibrationally excited states truly have modal character recognizable up to very high energies even for the non-trivial case of ammonia, a molecule which exhibits a tunneling motion and has two two-dimensional normal modes. The modal characteristics of the excited states and the interplay of the vibrational modes can be easily visualized by the reduced-density matrices, giving an insight into the complex modal behavior directed by symmetry.

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.

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.

We present a theoretical approach for simulating rovibronic spectra of molecules dressed by medium-intensity laser fields. Numerical results, obtained through the formalism described, are presented for the homonuclear diatomic molecule Na\(_2\), a system suitable for demonstrating and understanding various aspects of light-dressed spectroscopy. We discuss the physical origin of the peaks in the light-dressed spectrum of Na\(_2\) and investigate the light-dressed spectrum in terms of its dependence on the dressing field’s intensity and wavelength, temperature, and the turn-on time of the dressing field. The possibility of using light-dressed spectroscopy to derive field-free spectroscopic quantities is also addressed.

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 nuclear dynamics of the metastable H2He+ complex is explored by symmetry considerations and angular momentum addition rules as well as by accurate quantum chemical computations with the complex coordinate scaling, the complex absorbing potential, and the stabilization techniques. About 200 long-lived rovibrational resonance states of the complex are characterized, among which selected long-lived states are analyzed in detail. The stabilization mechanism of these long-lived resonance states is discussed on the basis of probability density plots of the wave functions. Overlaps of wave functions derived by a reduced-dimensional model with the full-dimensional wave functions reveal dissociation pathways for the long-lived resonance states and allow the calculation of their branching ratios.

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.

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.

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.

Motivated by the energetic and environmental relevance of methane clathrates, highly accurate ab initio potential energy surfaces (PESs) have been developed for the three possible dimers of the methane and water molecules: (H2O)2, CH4·H2O, and (CH4)2. While only a single monomer geometry was used for each monomer in the ab initio calculations, the PES parameterization makes it possible to produce distinct surfaces for all isotopologues within the rigid-monomer approximation. The PESs were fitted to computations at the frozen-core coupled-cluster level with single, double, and non-iterative triple excitations, employing basis sets of augmented triple- and quadruple-zeta quality plus bond functions, followed by extrapolations to the complete basis set limit. The long-range parts of the PESs are computed using the asymptotic version of symmetry-adapted perturbation theory based on a density-functional description of the monomers. All PESs are polarizable, i.e., in cluster or condensed-phase applications they approximate many-body effects by the induced dipole polarization model. The PESs were developed in a fully automated procedure applying the autoPES method, which is used for the first time to generate near-spectroscopic quality surfaces. The stationary points (SPs) on the PESs have been determined and compared with literature data. For CH4·H2O, previously unknown SPs have been identified and the first detailed study of the (CH4)2 potential energy landscape has been carried out. The PESs were used in variational quantum nuclear motion computations. For the water dimer, the resulting vibrational transitions are in excellent agreement with available high-resolution spectroscopic data. For (CH4)2, the intermonomer vibrational states are reported for the first time.

We report results of full-dimensional variational rovibrational quantum-dynamical computations for several ammonia isotopomers, based on selected potential energy and electric dipole moment hypersurfaces. The variational rovibrational eigenstates have been used as a basis for the solution of the time-dependent Schrodinger equation for nuclear motion including coherent infrared multiphoton excitation. The theoretical and computational framework developed during this study enables the investigation of the coherent inhibition or enhancement of tunneling in ammonia isotopomers by appropriately chosen laser fields. Our quantum-dynamical computations include all vibrational and rotational degrees of freedom and assume neither the alignment nor the orientation of the molecules under investigation. Specific results include accurate rotational-vibrational levels for NH2D, NHD2, NHDMu, and NHDT, probability densities for structural parameters as a function of time from the full-dimensional wavepacket results, time-dependent chirality for the isotopically chiral molecule NHDT, and detailed analyses of the enhancement and inhibition of stereomutation dynamics.

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.

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.

Rotational-vibrational states up to 3200 cm-1, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H2Cβ[double bond, length as m-dash]CαH, and the following deuterated isotopologues of VR: CH2[double bond, length as m-dash]CD, CHD[double bond, length as m-dash]CH, and CD2[double bond, length as m-dash]CD. The height of the CαH tunneling rocking barrier of VR, partially responsible for the complex nuclear dynamics of VR and its isotopologues, is determined to be 1641 ± 25 cm-1 by the focal-point analysis approach. The definitive nuclear-motion computations performed utilize two previously published potential energy hypersurfaces and reveal interesting energy-level and tunneling patterns characterizing the internal motions of the four isotopologues. A full assignment, including symmetry labels, of the vibrational states computed for CH2[double bond, length as m-dash]CH is provided, whenever feasible, based on the analysis of wave functions and the related one- and two-mode reduced density matrices. The computed vibrational states of CH2[double bond, length as m-dash]CD and CD2[double bond, length as m-dash]CD are characterized up to slightly above the top of the barrier. Interestingly, it is the interplay of the ν6 (formally CH2 rock) and ν7 (formally CH rock) modes that determines the tunneling dynamics; thus, the description of tunneling in VR needs, as a minimum, the consideration of two in-plane bending motions at the two ends of the molecule. When feasible, the computed results are compared to their experimental counterparts as well as to previous computational results. Corrections to the placement of the ν4 and ν6 fundamentals of VR are proposed. Tunneling switching, a unique phenomenon characterizing tunneling in slightly asymmetric effective double-well potentials, is observed and discussed for CHD[double bond, length as m-dash]CH. Despite the extensive tunneling dynamics, the rotational energy-level structure of VR exhibits rigid-rotor-type behavior.

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.

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.

The focal-point analysis (FPA) technique is used for the definitive characterization of conformational interconversion parameters, including activation energy barriers, activation free energies, and kinetic rate coefficients at 298 K, of two n-alkanes, n-butane, and n-pentane, yielding the first complete analysis of their interconversion kinetics. The FPA implementation developed in this study is based on geometry optimizations and harmonic frequency computations carried out with density functional theory methods and single-point energy computations up to the CCSD(T) level of electronic structure theory using atom-centered Gaussian basis sets as large as cc-pV5Z. The anharmonic vibrational computations are carried out, at the MP2/6-31G* level of theory. Reflecting the convergence behavior of the Gibbs free-energy terms and the interconversion parameters, well-defined uncertainties, mostly neglected in previous theoretical studies, are provided. Finally, the effect of these uncertainties on the concentrations of the conformers of n-butane and n-pentane is examined via a global Monte-Carlo uncertainty analysis. © 2017 Wiley Periodicals, Inc.

Accurate, experimental rovibronic energy levels, with associated labels and uncertainties, are reported for 11 low-lying electronic states of the diatomic \TiO\ 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{} 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 \TiO\, 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 \TiO\ rovibrational energy levels is 8682 and 1882, respectively. The lists of validated lines and levels for \TiO\ are deposited in the Supporting Information to this paper.

A hybrid variational–perturbational nuclear motion algorithm based on the perturbative treatment of the Coriolis coupling terms of the Eckart–Watson kinetic energy operator following a variational treatment of the rest of the operator is described. The algorithm has been implemented in the quantum chemical code DEWE. Performance of the hybrid treatment is assessed by comparing selected numerically exact variational vibration-only and rovibrational energy levels of the C2H4, C2D4, and CH4 molecules with their perturbatively corrected counterparts. For many of the rotational–vibrational states examined, numerical tests reveal excellent agreement between the variational and even the first-order perturbative energy levels, whilst the perturbative approach is able to reduce the computational cost of the matrix-vector product evaluations, needed by the iterative Lanczos eigensolver, by almost an order of magnitude.

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.

The rovibrational eigenenergy set of molecular systems is a key feature needed to understand and model elementary chemical reactions. A unique class of molecular systems, represented by an ${}^{4}{A}^{\ensuremath{'}\ensuremath{'}}$ excited electronic state of the ${[\mathrm{H},\mathrm{S},\mathrm{N}]}^{\ensuremath{-}}$ system comprising several distinct dipole-bound isomers, is found to contain both bent and linear minima separated by relatively small barriers. Full-dimensional nuclear-motion computations performed in Jacobi coordinates using three-dimensional potential energy surfaces describing the stable isomers and the related transition states yield rovibrational eigenstates located both below and above the barriers. The rovibrational wave functions are well localized, regardless of whether the state's energy is below or above the barriers. We also show that the states preserve the memory of the isomeric forms they ``originate from,'' which is signature of a strong vibrational memory effect above isomerization barriers.

The molecular ion is the simplest polyatomic and poly-electronic molecular system, and its spectrum constitutes an important benchmark for which precise answers can be obtained ab initio from the equations of quantum mechanics. Significant progress in the computation of the ro–vibrational spectrum of is discussed. A new, global potential energy surface (PES) based on ab initio points computed with an average accuracy of 0.01 cm −1 relative to the non-relativistic limit has recently been constructed. An analytical representation of these points is provided, exhibiting a standard deviation of 0.097 cm −1 . Problems with earlier fits are discussed. The new PES is used for the computation of transition frequencies. Recently measured lines at visible wavelengths combined with previously determined infrared ro–vibrational data show that an accuracy of the order of 0.1 cm −1 is achieved by these computations. In order to achieve this degree of accuracy, relativistic, adiabatic and non-adiabatic effects must be properly accounted for. The accuracy of these calculations facilitates the reassignment of some measured lines, further reducing the standard deviation between experiment and theory.

When determining energy levels from several, in cases many, measured and assigned high-resolution molecular spectra according to the Ritz principle, it is advantageous to investigate the spectra via the concept of spectroscopic networks (SNs). Experimental SNs are finite, weighted, undirected, multiedge, rooted graphs, whereby the vertices are the energy levels, the edges are the transitions, and the weights are provided by transition intensities. A considerable practical problem arises from the fact that SNs can be very large for isotopologues of molecules widely studied; for example, the experimental dataset for the H2 16O molecule contains some 160,000 measured transitions and 20,000 energy levels. In order to treat such large SNs and extract the maximum amount of information from them, sophisticated algorithms are needed when inverting the transition data. To achieve numerical effectiveness, we found the following efficient algorithms applicable to very large SNs: reading the input data employs hash codes, building the components of the SN utilizes a recursive depth-first search algorithm, solving the linear least-squares problem is via the conjugate gradient method, and determination of the uncertainties of the energy levels takes advantage of the robust reweighting algorithm.

Given the large energy required for its electronic excitation, the most important properties of the water molecule are governed by its ground potential energy surface (PES). Novel experiments are now able to probe this surface over a very extended energy range, requiring new theoretical procedures for their interpretation. As part of this study, a new, accurate, global spectroscopic-quality PES and a new, accurate, global dipole moment surface are developed. They are used for the computation of the high-resolution spectrum of water up to the first dissociation limit and beyond as well as for the determination of Stark coefficients for high-lying states. The water PES has been determined by combined ab initio and semi-empirical studies. As a first step, a very accurate, global, ab initio PES was determined using the all-electron, internally contracted multi-reference configuration interaction technique together with a large Gaussian basis set. Scalar relativistic energy corrections are also determined in order to move the energy determinations close to the relativistic complete basis set full configuration interaction limit. The electronic energies were computed for a set of about 2500 geometries, covering carefully selected configurations from equilibrium up to dissociation. Nuclear motion computations using this PES reproduce the observed energy levels up to 39 000 cm −1 with an accuracy of better than 10 cm −1 . Line positions and widths of resonant states above dissociation show an agreement with experiment of about 50 cm −1 . An improved semi-empirical PES is produced by fitting the ab initio PES to accurate experimental data, resulting in greatly improved accuracy, with a maximum deviation of about 1 cm −1 for all vibrational band origins. Theoretical results based on this semi-empirical surface are compared with experimental data for energies starting at 27 000 cm −1 , going all the way up to dissociation at about 41 000 cm −1 and a few hundred wavenumbers beyond it.

Due to its crucial importance, numerous studies have been conducted to determine the enthalpy difference between the conformers of butane. However, it is shown here that the most reliable experimental values are biased due to the statistical model utilized during the evaluation of the raw experimental data. In this study, using the appropriate statistical model, both the experimental expectation values and the associated uncertainties are revised. For the 133-196 and 223-297 K temperature ranges, 668 ± 20 and 653 ± 125 cal mol(-1), respectively, are recommended as reference values. Furthermore, to show that present-day quantum chemistry is a favorable alternative to experimental techniques in the determination of enthalpy differences of conformers, a focal-point analysis, based on coupled-cluster electronic structure computations, has been performed that included contributions of up to perturbative quadruple excitations as well as small correction terms beyond the Born-Oppenheimer and nonrelativistic approximations. For the 133-196 and 223-297 K temperature ranges, in exceptional agreement with the corresponding revised experimental data, our computations yielded 668 ± 3 and 650 ± 6 cal mol(-1), respectively. The most reliable enthalpy difference values for 0 and 298.15 K are also provided by the computational approach, 680.9 ± 2.5 and 647.4 ± 7.0 cal mol(-1), respectively.

This is the second of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This article presents Preprint submitted to Journal of Quantitative Spectroscopy & Radiative Transfer10th June 2010 energy levels and line positions of the following singly deuterated isotopologues of water: HD16O, HD17O, and HD18O. The MARVEL (Measured Active Rotational-Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–22 708, 0–1 674, and 0–12 105 cm−1 for HD16O, HD17O, and HD18O, respectively. For HD16O, 54 740 transitions were analyzed from 76 sources, the lines come from spectra recorded both at room temperature and from hot samples. These lines correspond to 36 690 distinct assignments and 8 818 energy levels. For HD17O, only 485 transitions could be analyzed from 3 sources; the lines correspond to 162 MARVEL energy levels. For HD18O, 8 729 transitions were analyzed from 11 sources and these lines correspond to 1 860 energy levels. The energy levels are checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators. This comparison shows that the measured transitions account for about 86 % of the anticipated absorbance of HD16O at 296 K and that the transitions predicted by the MARVEL energy levels account for essentially all the remaining absorbance. The extensive list of MARVEL lines and levels obtained are given in the Supplementary Material of this article, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved. In addition, the transition and energy level information for H2 17O and H2 18O, given in the first paper of this series [J. Quant. Spectr. Rad. Transfer 110 (2009) 573-596], has been updated. Key words: Water vapor, transition wavenumbers, atmospheric physics, energy levels, MARVEL, information system, database, W@DIS, infrared spectra, microwave spectra, HD16O, HD17O, HD18O

The Born–Oppenheimer (BO) equilibrium molecular structure (r BO e )o fcis-methyl formate has been determined at the CCSD(T) level of electronic structure theory using Gaussian basis sets of at least quadruple-f quality and a core correlation correction. The quadratic, cubic and semi-diagonal quartic force field in normal coordinates has also been computed at the MP2 level employing a basis set of triple-f quality. A semi-experimental equilibrium structure (r SE e ) has been derived from experimental ground-state rotational constants and the lowest-order rovibrational interaction parameters calculated from the ab initio cubic force field. To determine r SE e structures, it is important to start from accurate ground-state rotational constants. Different spectroscopic methods, applicable in the presence of internal rotation and used in the literature to obtain ‘‘unperturbed” rotational constants from the analysis and fitting of the spectrum, are reviewed and compared. They are shown to be compatible though their precision may be different. The r BO e and r SE e structures are in good agreement showing that, in the particular case of cis-methyl formate, the methyl torsion can still be treated as a small-amplitude vibration. The best equilibrium structure obtained for cis-methyl formate is: r(Cm–O) = 1.434 A, r(O–Cc) = 1.335 A, r(Cm–Hs) = 1.083 A, r(Cm– Ha) = 1.087 A, r(Cc–H) = 1.093 A, r(C@O) = 1.201 A, \(COC) = 114.4, \(CCHs) = 105.6, \(CCHa) = 110.2, \(OCH) = 109.6, \(OCO) = 125.5, and s(HaCOC) = 60.3. The accuracy is believed to be about 0.001 A for the bond lengths and 0.1 for the angles.

The protocol MARVEL, standing for measured active rotational–vibrational energy levels, is used to study high-accuracy measurements of rotational lines of four isotopologues of water, H 2 16 O , H 2 17 O , H 2 18 O , and D 2 16 O , obtained by spectroscopy in the far-infrared (FIR) region of 15–170 cm−1 by Matsushima et al. [Matsushima F, Odashima H, Iwasaki T, Tsunekawa S, Takagi K. Frequency measurement of pure rotational transitions of H2O from 0.5 to 5 THz. J Mol Struct 1995; 352/353, 371–8; Matsushima F, Nagase H, Nakauchi T, Odashima H, Takagi K. Frequency measurement of pure rotational transitions of H 2 17 O and H 2 18 O from 0.5 to 5 THz. J Mol Spectrosc 1999;193: 217–23; Matsushima F, Matsunaga M, Qian GY, Ohtaki Y, Wang RL, Takagi K. Frequency measurement of pure rotational transitions of D2O from 0.5 to 5 THz. J Mol Spectrosc 2001;206: 41–6; Matsushima F, Tomatsu N, Nagai T, Moriwaki Y, Takagi K. Frequency measurement of pure rotational transitions in the v2=1 state of H2O. J Mol Spectrosc 2006;235: 190–5]. MARVEL validates the high accuracy of most of the measured line positions. It results in a considerable number of energy levels with an average internal uncertainty of only 40 kHz (2σ). It also supports serious inaccuracy problems when Watson-type A-reduced Hamiltonians are used for predicting the highly accurate rotational measurements for water. Finally, MARVEL suggests a large number of para-water levels, for example 41 for H 2 16 O , which are candidates for becoming frequency standards in the FIR region of 15–170 cm−1 (the 0.5–5 THz window) when an accuracy of about 0.1 MHz is deemed to be sufficient.

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 H2 17 O isotopologue of water and a list of 2736 depend

Fully variational energies and structures are obtained for the few-electron prototypical atomic and molecular systems H þ ,H 2, HHe + , H þ , Be, and LiH at the Hartree–Fock basis-set limit (HFL). The HFL computations are made possible by a global optimization technique employing analytic derivatives of the energy with respect to nuclear centers as well as to positions and exponents of Gaussian-type basis functions (GTF). The efficiency of the procedure presented means that the HFL structure and energy of few-electron systems can be obtained even with a few-dozen distributed s-type GTFs. � 2007 Elsevier B.V. All rights reserved.

Accurate, experimental rotational-vibrational energy levels determined via the MARVEL (Measured Active Rotational-Vibrational Energy Levels) algorithm and published recently for the symmetric-top (14)NH3 molecule in J. Quant. Spectrosc. Radiat. Transfer, 2015, 116, 117-130 are analyzed to unravel the promoting and inhibiting effects of vibrations and rotations on the tunneling splittings of the corresponding symmetric (s) and antisymmetric (a) rovibrational energy level pairs. The experimental transition data useful from the point of view of the present analysis cover the range 0.7-7000 cm(-1), sufficiently detailed rovibrational energy sets worth analyzing are available for 20 vibrational bands. The highest J value, where J stands for the rotational quantum number, within the experimental dataset employed is 30. Coupling of the "umbrella" motion of (14)NH3 with other vibrational degrees of freedom has only a minor effect on the a-s tunneling splitting characterizing the ground vibrational state, 0.79436(70) cm(-1). In the majority of the cases rotation around the C3 axis increases, while rotation around the two perpendicular axes decreases the tunneling splittings. For example, for the pair of vibrational ground states, 0(+) and 0(-), the tunneling splitting basically disappears at around J = 25 for the (J,K) = (J,1) states, where K = |k| is the usual quantum number characterizing the projection of the rotational angular momentum on the principal axis. The tunneling splittings, defined as energy differences E(a) - E(s) of corresponding energy level pairs, as a function of J and K show a very regular behavior for the ground state (GS) and the nν2 bands. For the other bands investigated exceptions from a regular behavior do occur, especially for bands characterized by degenerate vibrations, and occasionally the data available are not sufficient to arrive at definitive conclusions. The most irregular behavior is observed for rotational states characterized by the k - l = 3n rule (l is the vibrational angular momentum quantum number), with n = 0, 1, 2,… High-quality, variationally computed rovibrational data support all the conclusions of this study based on experimental energy levels.

A simple variational procedure, termed DOPI for discrete variable representation—Hamiltonian in orthogonal coordinates—direct product basis–iterative diagonalization, is described and applied to compute low-lying vibrational band origins (VBOs) of the triatomic systems H2O, CO2, and N2O, employing published empirical and theoretical sextic force fields. While in these cases no difficulties arise when quartic potentials are used, the limited range of applicability of 6th-order potentials presents difficulties for the variational determination of VBOs, in particular for the higher-lying bending states. For H2O, transformation of quadratic and quartic force fields from simple bond stretching to Simons–Parr–Finlan (SPF) coordinates results in computed VBOs deviating less from experiment. This, however, does not hold for the VBOs computed from the transformed sextic force fields where the two representations provide highly similar results. While use of empirical quartic and sextic force fields result in a much...

The rho-axis system and the rho-axis-system Hamiltonian were devised and formulated to describe the rotational–internal–rotational motion of molecules possessing certain local geometrical symmetries. Nevertheless, they were employed to molecules without the required symmetries and apparently lying outside the range of their applicability. To justify such applications and to facilitate first-principles calculation of the corresponding spectroscopic parameters, the rho-axis-system and the rho-axis system Hamiltonian must be derived without assuming or imposing symmetry constraints. A derivation satisfying this requirement is described, and the rho-axis method is extended to molecules having a large amplitude internal motion of any kind.

The standard enthalpy of formation, Δ f H°, of 2 Π CH has been determined at converged levels of ab initio electronic structure theory, including high order coupled cluster and full configuration interaction benchmarks. The atomic Gaussian basis sets employed include the (aug)-cc-p(C)VXZ family with X = 3, 4, 5 and 6. Extrapolations to the complete one-particle basis set and the full configuration interaction limits, where appropriate, have been performed to reduce remaining computational errors. Additional improvements in the enthalpy of formation of 2 Π CH were achieved by appending the valence-only treatment with core-valence correlation, relativistic effects including spin-orbit correlation, and the diagonal Born-Oppenheimer correction. The recommended values for Δ f H° 0 and Δ f H° 2 9 8 of 2 Π CH are 592.48 + 0 . 4 7 - 0 . 5 6 kJ mol - 1 and 595.93 + 0 . 4 7 - 0 . 5 6 kJ mol - 1 , respectively.

Calculation of the rotation-vibration spectrum of H3+, as well as of its deuterated isotopologues, with near-spectroscopic accuracy requires the development of sophisticated theoretical models, methods, and codes. The present paper reviews the state-of-the-art in these fields. Computation of rovibrational states on a given potential energy surface (PES) has now become standard for triatomic molecules, at least up to intermediate energies, due to developments achieved by the present authors and others. However, highly accurate Born--Oppenheimer energies leading to highly accurate PESs are not accessible even for this two-electron system using conventional electronic structure procedures e.g., configuration-interaction or coupled-cluster techniques with extrapolation to the complete basis set limit). For this purpose highly specialized techniques must be used, e.g., those employing explicitly correlated Gaussians and nonlinear parameter optimizations. It has also become evident that a very dense grid of \ai\ points is required to obtain reliable representations of the computed points extending from the minimum to the asymptotic limits. Furthermore, adiabatic, relativistic, and QED correction terms need to be considered to achieve near-spectroscopic accuracy during calculation of the rotation-vibration spectrum of H3+. The remaining and most intractable problem is then the treatment of the effects of non-adiabatic coupling on the rovibrational energies, which, in the worst cases, may lead to corrections on the order of several \cm. A promising way of handling this difficulty is the further development of effective, motion- or even coordinate-dependent, masses and mass surfaces. Finally, the unresolved challenge of how to describe and elucidate the experimental pre-dissociation spectra of H$_3^+$ and its isotopologues is discussed., Topical review to be published in J Phys B: At Mol Opt Phys

This paper is the fourth of a series of papers reporting critically evaluated rotational–vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This paper presents energy level and transition data for the following doubly and triply substituted isotopologues of water: D216O, D217O, and D218O. The MARVEL (Measured Active Rotational–Vibrational Energy Levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0–14 016, 0–7969, and 0–9108 cm−1 for D216O, D217O, and D218O, respectively. For D216O, D217O, and D218O, 53 534, 600, and 12 167 lines are considered, respectively, from spectra recorded in absorption at room temperature and in emission at elevated temperatures. The number of validated energy levels is 12 269, 338, and 3351 for D216O, D217O, and D218O, respectively. The energy levels have been checked against the ones determined, with an average accuracy of about 0.03 cm−1, from variational rovibrational computations employing exact kinetic energy operators and an accurate potential energy surface. Furthermore, the rovibrational labels of the energy levels have been validated by an analysis of the computed wavefunctions using the rigid-rotor decomposition (RRD) scheme. The extensive list of MARVEL lines and levels obtained is deposited in the Supplementary Material of this paper, in a distributed information system applied to water, W@DIS, and on the official MARVEL website, where they can easily be retrieved.

The report of an IUPAC Task Group, formed in 2011 on "Intensities and line shapes in high-resolution spectra of water isotopologues from experiment and theory" (Project No. 2011-022-2-100), on line profiles of isolated high-resolution rotational-vibrational transitions perturbed by neutral gas-phase molecules is presented. The well-documented inadequacies of the Voigt profile (VP), used almost universally by databases and radiative-transfer codes, to represent pressure effects and Doppler broadening in isolated vibrational-rotational and pure rotational transitions of the water molecule have resulted in the development of a variety of alternative line-profile models. These models capture more of the physics of the influence of pressure on line shapes but, in general, at the price of greater complexity. The Task Group recommends that the partially Correlated quadratic-Speed-Dependent Hard-Collision profile should be adopted as the appropriate model for high-resolution spectroscopy. For simplicity this should be called the Hartmann--Tran profile (HTP). The HTP is sophisticated enough to capture the various collisional contributions to the isolated line shape, can be computed in a straightforward and rapid manner, and reduces to simpler profiles, including the Voigt profile, under certain simplifying assumptions., Comment: Accepted for publication in Pure and Applied Chemistry

Two-electron relativistic corrections to the ground-state electronic energy of water are determined as a function of geometry at over 300 points. The corrections include the two-electron Darwin term (D2) of the Coulomb–Pauli Hamiltonian, obtained at the cc-pVQZ CCSD(T) level of theory, as well as the Gaunt and Breit corrections, calculated perturbationally using four-component fully variational Dirac–Hartree–Fock (DHF) wavefunctions and two different basis sets. Based on the calculated energy points, fitted relativistic correction surfaces are constructed. These surfaces are used with a high-accuracy ab initio nonrelativistic Born–Oppenheimer (BO) potential energy hypersurface to calculate vibrational band origins and rotational term values for H 2 16 O . The calculations suggest that these two-electron relativistic corrections, which go beyond the usual kinetic relativistic effects and which have so far been neglected in rovibrational calculations on light many-electron molecular systems, have a substantial influence on the rotation–vibration levels of water. The three effects considered have markedly different characteristics for the stretching and bending levels, which often leads to fortuitous cancellation of errors. The effect of the Breit interaction on the rovibrational levels is intermediate between the effect of the kinetic relativistic correction and that of the one-electron Lamb-shift effect.

International audience; This is the third of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, and energy levels, with associated critically reviewed labels and uncertainties, for all the main isotopologues of water. This paper presents experimental line positions, experimental-quality energy levels, and validated labels for rotational-vibrational transitions of the most abundant isotopologue of water, H216O. The latest version of the MARVEL (Measured Active Rotational-Vibrational Energy Levels) line-inversion procedure is used to determine the rovibrational energy levels of the electronic ground state of H216O from experimentally measured lines, together with their self-consistent uncertainties, for the spectral region up to the first dissociation limit. The spectroscopic network of H216O containstwo components, an ortho (o) and a para (p) one. For o-H216O and p-H216O, experimentally measured, assigned, and labeled transitions were analyzed from more than 100 sources. The measured lines come from one-photon spectra recorded at room temperature in absorption, from hot samples with temperatures up to 3000 K recorded in emission, and from multiresonance excitation spectra which sample levels up to dissociation. The total number of transitions considered is 184 667 of which 182 156 are validated: 68 027 between para states and 114 129 ortho ones. These transitions give rise to 18 486 validated energy levels, of which 10 446 and 8040 belong to o-H216O and p-H216O, respectively. The energy levels, including their labeling with approximate normal-mode and rigid-rotor quantum numbers, have been checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators as well as against previous compilations of energy levels. The extensive list of MARVEL lines and levels obtained are deposited in the supplementary data of this paper, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved.

Forms for the exact non-relativistic quantum mechanical vibrational (J = 0) kinetic energy operators for sequentially bonded (A-B-C-D-E) and (A,B)-C-D-E-type penta-atomic molecules, expressed in valence internal coordinates, are presented. As advocated earlier (Handy, N. C., 1987, Molec. Phys., 61, 207), computer algebra has been employed during the derivation. The suggested use of these operators in calculations for vibrational energy levels of interesting penta-atomic molecules (e.g., C3O2, and H2CCO) is outlined.