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Following the full realization of the importance of noncovalent interactions, finding and characterizing stationary points (SP), of various order, for weakly bound oligomers have become important tasks for computational chemists. An efficient algorithm and an associated computer code, called oligoCGO, are described, facilitating constrained geometry optimization of oligomers of arbitrary structure and complexity and normal-mode vibrational analysis at nonstationary geometries. To minimize the adverse effects of nonzero forces on harmonic vibrational analyses at constrained stationary points (cSP), two residual gradient correction (RGC) schemes are proposed. RGC

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.

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.

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 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 ).

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.

Cycle bases of graph theory are introduced for the analysis of transition data deposited in line-by-line rovibronic spectroscopic databases. The principal advantage of using cycle bases is that outlier transitions –almost always present in spectroscopic databases built from experimental data originating from many different sources– can be detected and identified straightforwardly and automatically. The data available for six water isotopologues, H 2 16 O, H 2 17 O, H 2 18 O, HD 16 O, HD 17 O, and HD 18 O, in the HITRAN2012 and GEISA2015 databases are used to demonstrate the utility of cycle-basis-based outlier-detection approaches. The spectroscopic databases appear to be sufficiently complete so that the great majority of the entries of the minimum cycle basis have the minimum possible length of four. More than 2000 transition conflicts have been identified for the isotopologue H 2 16 O in the HITRAN2012 database, the seven common conflict types are discussed. It is recommended to employ cycle bases, and especially a minimum cycle basis, for the analysis of transitions deposited in high-resolution spectroscopic databases.

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.

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.

Our former study Tobias and Tasi (J Math Chem 54:85, 2016) is continued, where a simple algebraic solution was given to the kinetic problem of triangle, quadrangle and pentangle reactions. In the present work, after defining chemical reaction networks and their connectedness, first-order chemical reaction networks (FCRNs) are studied on the basis of the results achieved by Chellaboina et al. (Control Syst 29:60, 2009). First, it is proved that an FCRN is disconnected iff its coefficient matrix is block diagonalizable. Furthermore, mass incompatibility is used to interpret the reducibility of subconservative networks. For conservative FCRNs, the so-called marker network is introduced, which is linearly conjugate to the original one, to describe the zero eigenvalue associated to the coefficient matrix of an FCRN. Instead of using graph-theoretical concepts, simple algebraic tools are applied to present and solve these problems. As an illustration, an industrially important ten-component (formal) FCRN is presented which has algebraically exact solution.

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.

In this paper, ignoring graph-theoretic tools, simple algebraic solutions are presented for the kinetic problems of the triangle, quadrangle and pentangle reactions with the help of Krylov and Vandermonde matrices. As far as we know at the time of writing, this is the first time for the cases of the quadrangle and pentangle reactions. Our solutions do not require diagonalizability and non-degenerate eigenvalues concerning the coefficient matrix of the first-order reaction network.

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.

Vector algebra, as developed by Josiah Willard Gibbs, is much simpler than matrix or tensor algebra, therefore, it is more suitable to introduce the students of chemistry into the wonderful world of molecular symmetry. A program based on elementary vector algebra has been written to determine all symmetry elements and symmetry operations of rigid molecular structures. The program also contains data for 57 point groups common in chemistry. Therefore, it automatically supplies the particular point group to which the structure belongs. Since the locations of the nuclei related to the symmetry elements are also revealed by the program, even the detailed notation of the framework group of the molecular structure can be deduced. The program can be a great help in determining the symmetries of the normal modes of vibration, too.