MARVEL analysis of high-resolution rovibrational spectra of 13 C 16 O 2

A set of empirical rovibrational energy levels, obtained through the MARVEL (measured active rotational-vibrational energy levels) procedure, is presented for the  13 C  16 O  2 isotopologue of carbon dioxide. This procedure begins with the collection and analysis of experimental rovibrational transitions from the literature, allowing for a comprehensive review of the literature on the high-resolution spectroscopy of  13 C  16 O  2 , which is also presented. A total of 60 sources out of more than 750 checked provided 14,101 uniquely measured and assigned rovibrational transitions in the wavenumber range of 579-13,735 cm  - 1 . This is followed by a weighted least-squares refinement yielding the energy levels of the states involved in the measured transitions. Altogether 6318 empirical rovibrational energies have been determined for  13 C  16 O  2 . Finally, estimates have been given for the uncertainties of the empirical energies, based on the experimental uncertainties of the transitions. The detailed analysis of the lines and the spectroscopic network built from them, as well as the uncertainty estimates, all serve to pinpoint possible errors in the experimental data, such as typos, misassignment of quantum numbers, and misidentifications. Errors found in the literature data were corrected before including them in the final MARVEL dataset and analysis.

All paths lead to hubs in the spectroscopic networks of water isotopologues H216O and H218O

Network theory has fundamentally transformed our comprehension of complex systems, catalyzing significant advances across various domains of science and technology. In spectroscopic networks, hubs are the quantum states involved in the largest number of transitions. Here, utilizing network paths probed via precision metrology, absolute energies have been deduced, with at least 10-digit accuracy, for almost 200 hubs in the experimental spectroscopic networks of H216O and H218O. These hubs, lying on the ground vibrational states of both species and the bending fundamental of H216O, are involved in tens of thousands of observed transitions. Relying on the same hubs and other states, benchmark-quality line lists have been assembled, which supersede and improve, by three orders of magnitude, the accuracy of the massive amount of data reported in hundreds of papers dealing with Doppler-limited spectroscopy. Due to the omnipresence of water, these ultraprecise line lists could be applied to calibrate high-resolution spectra and serve ongoing and upcoming space missions.

Verification labels for rovibronic quantum-state energy uncertainties

Transition wavenumbers contained in line-by-line rovibronic databases can be compromised by errors of various nature. When left undetected, these errors may result in incorrect quantum-state energies, potentially compromising a large number of derived spectroscopic data. Spectroscopic networks treat the complete set of line-by-line spectroscopic data as a large graph, and through a least-squares refinement the measured line positions are converted into empirical quantum-state energies. Spectroscopic networks also offer a highly useful framework to develop mathematical tools helping to identify possible errors and conflicts within the dataset. For example, wavenumber errors can be detected by checking for violations of the law of energy conservation. This paper describes a new graph-theory tool, which results in so-called verification labels for the quantum states. Verification labels help to express the vulnerability of a calculated empirical energy value and its uncertainty against possible wavenumber errors, providing complementary information to simple statistical uncertainties.

Temperature-Dependent Line-Broadening Effects in CO2 Caused by Ar

This computational study of line-broadening effects is based on an accurate, analytical representation of the intermonomer potential energy surface (PES) of the CO2  ⋅ Ar van der Waals (vdW) complex. The PES is employed to compute collisional broadening coefficients for rovibrational lines of CO2 perturbed by Ar. The semiclassical computations are performed using the modified Robert-Bonamy approach, including real and imaginary terms, and the exact trajectory model. The lines investigated are in the 10001←00011, 01101←00001, 00011←00001, and 00031←00001 vibrational bands and the computations are repeated at multiple temperatures. The computed results are in good agreement with the available experimental values, validating both the intermonomer PES developed and the methodology used. For lines in the 01101←00001 band of CO2 , temperature-dependent Ar-broadening coefficients are reported for the first time. The parameters presented should prove useful, among other applications, for the accurate experimental determination of CO2 and Ar abundances in planetary atmospheres.

Unusual Dynamics and Vibrational Fingerprints of van der Waals Dimers Formed by Linear Molecules and Rare-Gas Atoms

Detailed structural, dynamical, and vibrational analyses have been performed for systems composed of linear triatomic molecules solvated by a single rare-gas atom, He, Ne, or Ar. Among the chromophores of these van der Waals (vdW) dimers, there are four neutral molecules (CO2, CS2, N2O, and OCS) and six molecular cations (HHe2+, HNe2+, HAr2+, HHeNe+, HHeAr+, and HNeAr+), both of apolar and polar nature. Following the exploration of bonding preferences, high-level four-dimensional (4D) potential energy surfaces (PESs) have been developed for 24 vdW dimers, keeping the two intramonomer bond lengths fixed. For these 24 complexes, over 1500 bound vibrational states have been obtained via quasi-variational nuclear-motion computations, employing exact kinetic-energy operators together with the accurate 4D PESs and their 2D/3D cuts. The reduced-dimensional (2D to 4D) dimer models have been compared with full-dimensional (6D) ones in the cases of the neutral CO2·Ar and charged HHe2+·He dimers, corroborating the high accuracy of the 2D to 4D vibrational energies. The reduced-dimensional models suggest that (a) while the equilibrium structures are T-shaped and planar, the effective ground-state structures are nonplanar, (b) certain bound states belong to collinear molecular structures, even when they are not minima, (c) the vdW vibrations are heavily mixed and many states have amplitudes corresponding to both the T-shaped and collinear structures, (d) there are a few dimers, for which even some of the vdW fundamentals lie above the first dissociation limit, and (e) the vdW vibrations are almost fully decoupled from the intramonomer bending motion.

Quantum Chemical Investigation of the Cold Water Dimer Spectrum in the First OH-Stretching Overtone Region Provides a New Interpretation

Intramolecular vibrational transition wavenumbers and intensities were calculated in the fundamental HOH-bending, fundamental OH-stretching, first OH-stretching-HOH-bending combination, and first OH-stretching overtone (ΔvOH = 2) regions of the water dimer's spectrum. Furthermore, the rotational-vibrational spectrum was calculated in the ΔvOH = 2 region at 10 K, corresponding to the temperature of the existing jet-expansion experiments. The calculated spectrum was obtained by combining results from a full-dimensional (12D) vibrational and a reduced-dimensional vibrational-rotational-tunneling model. The ΔvOH = 2 spectral region is rich in features due to contributions from multiple vibrational-rotational-tunneling sub-bands. Origins of the experimental vibrational bands depend on the assignment of the observed sub-bands. Based on our calculations, we assign the observed sub-bands, and our reassignment leads to new values for the vibrational band origins of the free donor and antisymmetric acceptor OH-stretching first overtones of ∼7227 and ∼7238 cm-1, respectively. The observed bands with origins at 7192.34 and ∼7366 cm-1 are assigned to the symmetric acceptor OH-stretching first overtone and the OH-stretching combination of the donor, respectively.

Quantum Nuclear Delocalization and its Rovibrational Fingerprints

Quantum mechanics dictates that nuclei must undergo some delocalization. In this work, emergence of quantum nuclear delocalization and its rovibrational fingerprints are discussed for the case of the van der Waals complexHHe 3 + ${{\rm{HHe}}_3^ + }$ . The equilibrium structure ofHHe 3 + ${{\rm{HHe}}_3^ + }$ is planar and T-shaped, one He atom solvating the quasi-linear He-H+ -He core. The dynamical structure ofHHe 3 + ${{\rm{HHe}}_3^ + }$ , in all of its bound states, is fundamentally different. As revealed by spatial distribution functions and nuclear densities, during the vibrations of the molecule the solvating He is not restricted to be in the plane defined by the instantaneously bentHHe 2 + ${{\rm{HHe}}_2^ + }$ chomophore, but freely orbits the central proton, forming a three-dimensional torus around theHHe 2 + ${{\rm{HHe}}_2^ + }$ chromophore. This quantum delocalization is observed for all vibrational states, the type of vibrational excitation being reflected in the topology of the nodal surfaces in the nuclear densities, showing, for example, that intramolecular bending involves excitation along the circumference of the torus.

On the 12C2H2 near-infrared spectrum: absolute transition frequencies and an improved spectroscopic network at the kHz accuracy level

Lamb dips of twenty lines in the P, Q, and R branches of the ν1 + ν3 + ν41 vibrational band of 12C2H2, in the spectral window of 7125-7230 cm-1, have been measured using an upgraded comb-calibrated frequency-stabilized cavity ring-down spectrometer, designed for extensive sub-Doppler measurements. Due to the large number of carefully executed Lamb-dip experiments, and to the extrapolation of absolute frequencies to zero pressure in each case, the combined average uncertainty of the measured line-center positions is 15 kHz (5 × 10-7 cm-1) with a 2-σ confidence level. Selection of the twenty lines was based on the theory of spectroscopic networks (SN), ensuring that a large number of transitions, measured previously by precision-spectroscopy investigations, could be connected to the para and ortho principal components of the SN of 12C2H2. The assembled SN contains 331 highly precise transitions, 119 and 121 of which are in the ortho and para principal components, respectively, while the rest remain in floating components. The para- and ortho-12C2H2 energy-level lists, determined during the present study, contain 82 and 80 entries, respectively, with an accuracy similar to that of the lines. Based on the newly assembled lists of para- and ortho-12C2H2 empirical energy levels, a line list, called TenkHz, has been generated. The TenkHz line list contains 282 entries in the spectral range of 5898.97-7258.87 cm-1; thus far, only 149 of them have been measured directly via precision spectroscopy. The TenkHz line list includes 35 intense lines that are missing in the HITRAN2020 database.

Quantum-Chemical and Quantum-Graph Models of the Dynamical Structure of CH5. J Chem Theory Comput 2023;19:42-50. [PMID: 36534596 DOI: 10.1021/acs.jctc.2c00991] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Experimental and computational results about the structure, dynamics, and rovibrational spectra of protonated methane have challenged a considerable number of traditional chemical concepts. Hereby theoretical and computational results are provided about the dynamical structure of CH₅⁺. It is shown that the ground vibrational state investigated thus far by computations, forbidden by nuclear-spin statistics, has a structure similar to the first allowed vibrational state and, in fact, the structures of all vibrational states significantly below 200 cm^-1 are highly similar. Spatial delocalization of the nuclei, determined by nuclear densities computed from accurate variational vibrational wave functions, turns out to be limited when viewed in the body-fixed frame, confirming that the effective structure of CH₅⁺ is well described as a CH₃⁺ tripod with a H₂ unit on top of it. The interesting and unusual qualitative aspects of the sophisticated state-dependent variational results receive full explanation via simple quantum-graph models.

Parity-pair-mixing effects in nonlinear spectroscopy of HDO

A non-linear spectroscopic study of the HDO molecule is performed in the wavelength range of 1.36-1.42 μm 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 H2 16O and H2 18O, 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.

Structure, energetics, and spectroscopy of the chromophores of HHe+n, H2He+n, and He+n clusters and their deuterated isotopologues

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. These are complexes which do exist, according to mass-spectrometry studies, up to very high n values. Apparently, for some of the H₂He+n and He+n complexes, the linear symmetric tetratomic H₂He+2 and the diatomic He+2 cations, respectively, may also be the central units. In this study, definitive structures, relative energies, zero-point vibrational energies, and (an)harmonic vibrational fundamentals, and, in some cases, overtones and combination bands, are established mostly for the triatomic chromophores. The study is also extended to the deuterated isotopologues D₂He⁺, DHe+2, and D₂He+2. To facilitate and improve the electronic-structure computations performed, new atom-centered, fixed-exponent, Gaussian-type basis sets called MAX, with X = T(3), Q(4), P(5), and H(6), are designed for the H and He atoms. The focal-point-analysis (FPA) technique is employed to determine definitive relative energies with tight uncertainties for reactions involving the molecular ions. The FPA results determined include the 0 K proton and deuteron affinities of the ⁴He atom, 14 875(9) cm^-1 [177.95(11) kJ mol^-1] and 15 229(8) cm^-1 [182.18(10) kJ mol^-1], respectively, the dissociation energies of the He+2 → He⁺ + He, HHe+2 → HHe⁺ + He, and He+3 → He+2 + He reactions, 19 099(13) cm^-1 [228.48(16) kJ mol^-1], 3948(7) cm^-1 [47.23(8) kJ mol^-1], and 1401(12) cm^-1 [16.76(14) kJ mol^-1], respectively, the dissociation energy of the DHe+2 → DHe⁺ + He reaction, 4033(6) cm^-1 [48.25(7) kJ mol^-1], the isomerization energy between the two linear isomers of the [H, He, He]⁺ system, 3828(40) cm^-1 [45.79(48) kJ mol^-1], and the dissociation energies of the H₂He⁺ → H+2 + He and the H₂He+2 → H₂He⁺ + He reactions, 1789(4) cm^-1 [21.40(5) kJ mol^-1] and 435(6) cm^-1 [5.20(7) kJ mol^-1], respectively. The FPA estimates of the first dissociation energy of D₂He⁺ and D₂He+2 are 1986(4) cm^-1 [23.76(5) kJ mol^-1] and 474(5) cm^-1 [5.67(6) kJ mol^-1], respectively. Determining the vibrational fundamentals of the triatomic chromophores with second-order vibrational perturbation theory (VPT2) and vibrational configuration interaction (VCI) techniques, both built around the Eckart-Watson Hamiltonian, proved unusually challenging. For the species studied, VPT2 has difficulties yielding dependable results, in some cases even for the fundamentals of the H-containing molecular cations, while carefully executed VCI computations yield considerably improved spectroscopic results. In a few cases unusually large anharmonic corrections to the fundamentals, on the order of 15% of the harmonic value, have been observed.

Reduced-dimensional vibrational models of the water dimer

A model based on the finite-basis representation of a vibrational Hamiltonian expressed in internal coordinates is developed. The model relies on a many-mode, low-order expansion of both the kinetic energy operator and the potential energy surface (PES). Polyad truncations and energy ceilings are used to control the size of the vibrational basis to facilitate accurate computations of the OH stretch and HOH bend intramolecular transitions of the water dimer (H₂ ¹⁶O)₂. Advantages and potential pitfalls of the applied approximations are highlighted. The importance of choices related to the treatment of the kinetic energy operator in reduced-dimensional calculations and the accuracy of different water dimer PESs are discussed. A range of different reduced-dimensional computations are performed to investigate the wavenumber shifts in the intramolecular transitions caused by the coupling between the intra- and intermolecular modes. With the use of symmetry, full 12-dimensional vibrational energy levels of the water dimer are calculated, predicting accurately the experimentally observed intramolecular fundamentals. It is found that one can also predict accurate intramolecular transition wavenumbers for the water dimer by combining a set of computationally inexpensive reduced-dimensional calculations, thereby guiding future effective-Hamiltonian treatments.

Normal-Mode Vibrational Analysis of Weakly Bound Oligomers at Constrained Stationary Points of Arbitrary Order

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. RGC₁, for which a rigorous justification is given, is based on ignoring the remaining forces in internal-coordinate space. RGC₂ modifies the geometry of the cSP in a single Newton step and recalculates the Cartesian Hessian at this updated geometry. As demonstrated by 10 examples related to the water-water, water-methane, and methane-methane dimers as well as the methane trimer, without RGC the harmonic analysis of cSPs may result in even qualitatively incorrect results when compared to reference values obtained at the nearby unconstrained SPs (uSP). Both RGC protocols work exceedingly well, and the corrected harmonic wavenumbers of the cSPs are very close to their uSP counterparts.

A quantum-chemical perspective on the laser-induced alignment and orientation dynamics of the CH3 X (X = F, Cl, Br, I) molecules

Motivated by recent experiments, the laser-induced alignment-and-orientation (A&O) dynamics of the prolate symmetric top CH₃ 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 CH₃ Br and CH₃ I. It is shown that the different A&O behavior of the CH₃ 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 CH₃ 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 CH₃ 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.

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

Detailed understanding of the energy-level structure of the quantum states as well as of the rovibronic spectra of the ethylidyne (CH) and the hydroxyl (OH) radicals is mandatory for a...

The rovibrational Aharonov-Bohm effect

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+5 can be understood entirely in terms of this effect.

Selecting lines for spectroscopic (re)measurements to improve the accuracy of absolute energies of rovibronic quantum states

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2^{~16}$$\end{document}216O, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{32}$$\end{document}32S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{16}$$\end{document}16O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}2, H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2^{~12}$$\end{document}212C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{16}$$\end{document}16O, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{14}$$\end{document}14NH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}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.

Exactly solvable 1D model explains the low-energy vibrational level structure of protonated methane

A new one-dimensional model is proposed for the low-energy vibrational quantum dynamics of CH5+ based on the motion of an effective particle confined to a 60-vertex graph Γ60 with a single edge length parameter. Within this model, the quantum states of CH5+ are obtained in analytic form and are related to combinatorial properties of Γ60. The bipartite structure of Γ60 gives a simple explanation for curious symmetries observed in numerically exact variational calculations on CH5+.

Understanding the structure of complex multidimensional wave functions. A case study of excited vibrational states of ammonia

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.

On neglecting Coriolis and related couplings in first-principles rovibrational spectroscopy: Considerations of symmetry, accuracy, and simplicity. II. Case studies for H2O isotopologues, H3+, O3, and NH3

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 (H₂¹⁶O), its deuterated isotopologues (D₂¹⁶O and HD¹⁶O), H₃⁺, and ozone (¹⁶O₃), but the tetratomic ammonia molecule (¹⁴NH₃) 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-à-vis the use of simplifying numerical approximation techniques in nuclear-motion computations.

Comment on "Wigner numbers" [J. Chem. Phys. 151, 244122 (2019)]

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

From bridges to cycles in spectroscopic networks

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{14} {\text {NH}}_3$$\end{document}14NH3.

Rotational-vibrational resonance states

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.

On neglecting Coriolis and related couplings in first-principles rovibrational spectroscopy: considerations of symmetry, accuracy, and simplicity

The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy levels is investigated, employing triatomic AB[Formula: see text] molecules as models. In particular, calculations are performed for H[Formula: see text][Formula: see text]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.

Spectroscopic signatures of HHe2+ and HHe3. Phys Chem Chem Phys 2020;22:22885-22888. [PMID: 33034329 DOI: 10.1039/d0cp04649c]

Using two different action spectroscopic techniques, a high-resolution quantum cascade laser operating around 1300 cm-1 and a cryogenic ion trap machine, the proton shuttle motion of the cations HHe2+ and HHe3+ has been probed at a nominal temperature of 4 K. For HHe3+, the loosely bound character of this complex allowed predissociation spectroscopy to be used, and the observed broad features point to a lifetime of a few ps in the vibrationally excited state. For He-H+-He, a fundamental linear molecule consisting of only three nuclei and four electrons, the method of laser-induced inhibition of complex growth (LIICG) enabled the measurement of three accurate rovibrational transitions, pinning down its molecular parameters for the first time.

Heterocumulenic carbene nitric oxide radical OCCNO˙

The elusive heterocumulenic radical OCCNO˙ and its isotopologues OC13CNO˙ and OCC15NO˙ have been prepared by reacting photolytically generated unsaturated carbene OCC/OC13C with ˙NO/15˙NO in cryogenic N2-, Ar-, and Ne-matrices. Upon UV-light (365 nm) irradiation, the C-C bond in OCCNO˙ breaks and yields a long-sought ground-state radical CNO˙ (X2Π), which has also been identified with matrix-isolation infrared spectroscopy.

Infrared Signatures of the HHen+ and DHen+ (n = 3-6) Complexes

Combination of a cryogenic ion-trap machine, operated at 4.7 K, with the free-electron-laser FELIX allows the first experimental characterization of the unusually bright antisymmetric stretch (ν₃) and π-bending (ν₂) fundamentals of the He-X⁺-He (X = H, D) chromophore of the in situ prepared HHe_n⁺ and DHe_n⁺ (n = 3-6) complexes. The band origins obtained are fully supported by first-principles quantum-chemical computations, performed at the MP2, the CCSD(T), and occasionally the CCSDTQ levels employing extended basis sets. Both the experiments and the computations are consistent with structures for the species with n = 3 and 6 being of T-shaped C_2v and of D_4h symmetry, respectively, while the species with n = 4 are suggested to exhibit interesting dynamical phenomena related to large-amplitude motions.

Toward Automated Variational Computation of Rovibrational Resonances, Including a Case Study of the H2 Dimer

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.

Accurate empirical rovibrational energies and transitions of H216O

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

Molecular dimers of methane clathrates: ab initio potential energy surfaces and variational vibrational states

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.

Rovibrational quantum dynamics of the vinyl radical and its deuterated isotopologues

Rotational–vibrational states up to 3200 cm⁻¹, beyond the highest-lying stretching fundamental, are computed variationally for the vinyl radical (VR), H₂C_βC_αH, and the following deuterated isotopologues of VR: CH₂CD, CHDCH, and CD₂CD.

Conical Intersections Induced by Quantum Light: Field-Dressed Spectra from the Weak to the Ultrastrong Coupling Regimes

In classical laser fields with frequencies resonant with the electronic excitation in molecules, it is by now known that conical intersections are induced by the field and are called light-induced conical intersections (LICIs). As optical cavities have become accessible, the question arises whether their quantized modes could also lead to the appearance of LICIs. A theoretical framework is formulated for the investigation of LICIs of diatomics in such quantum light. The eigenvalue spectrum of the dressed states in the cavity is studied, putting particular emphasis on the investigation of absorption spectra of the Na₂ molecule, that is, on the transitions between dressed states, measured by employing a weak probe pulse. The dependence of the spectra on the light-matter coupling strength in the cavity and on the frequency of the cavity mode is studied in detail. The computations demonstrate strong nonadiabatic effects caused by the appearing LICI.

A general variational approach for computing rovibrational resonances of polyatomic molecules. Application to the weakly bound H2He+ and H2⋅CO systems

The quasi-variational quantum chemical protocol and code GENIUSH [E. Mátyus et al., J. Chem. Phys. 130, 134112 (2009) and C. Fábri et al., J. Chem. Phys. 134, 074105 (2011)] has been augmented with the complex absorbing potential (CAP) technique, yielding a method for the determination of rovibrational resonance states. Due to the effective implementation of the CAP technique within GENIUSH, the GENIUSH-CAP code is a powerful tool for the study of important dynamical features of arbitrary-sized molecular systems with arbitrary composition above their first dissociation limit. The GENIUSH-CAP code has been tested and validated on the H₂He⁺ cation: the computed resonance energies and lifetimes are compared to those obtained with a previously developed triatomic rovibrational resonance-computing code, D²FOPI-CCS [T. Szidarovszky and A. G. Császár Mol. Phys. 111, 2131 (2013)], utilizing the complex coordinate scaling method. A unique feature of the GENIUSH-CAP protocol is that it allows the simple implementation of reduced-dimensional dynamical models. To prove this, resonance energies and lifetimes of the H₂⋅CO van der Waals complex have been computed utilizing a four-dimensional model (freezing the two monomer stretches), and a related potential energy surface, of the complex.

Direct Signatures of Light-Induced Conical Intersections on the Field-Dressed Spectrum of Na2

Rovibronic spectra of the field-dressed homonuclear diatomic Na₂ molecule are investigated 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 absorption 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, in both 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.

Definitive thermochemistry and kinetics of the interconversions among conformers of n-butane and n-pentane

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.

Rovibrational Resonances in H2He. J Chem Theory Comput 2018;14:1523-1533. [PMID: 29390185 DOI: 10.1021/acs.jctc.7b01136]

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 complex coordinate scaling, complex absorbing potential, and stabilization techniques. About 200 long-lived rovibrational resonance states of the complex are characterized and 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.

Vibrational quantum graphs and their application to the quantum dynamics of CH5+

The first application of quantum-graph theory to molecular vibrations helps understand the low-energy vibrational quantum dynamics of CH₅⁺.

Fourier Transform Microwave Spectrum of Propene-3-d1 (CH2═CHCH2D), Quadrupole Coupling Constants of Deuterium, and a Semiexperimental Equilibrium Structure of Propene

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 determined for the ¹³C species and for some deuterium-substituted species from the literature, a new semiexperimental equilibrium structure was determined and its high accuracy was confirmed. The difficulty in obtaining accurate coordinates for the out-of-plane hydrogen atom is discussed.

Complex rovibrational dynamics of the Ar·NO+ complex

Rotational-vibrational states of the Ar·NO⁺ cationic complex are computed, below, above, and well above the complex's first dissociation energy, using variational nuclear motion and close-coupling scattering computations. The HSLH potential energy surface used in this study (J. Chem. Phys., 2011, 135, 044312) is characterized by a first dissociation energy of D₀ = 887.0 cm^-1 and supports 200 bound vibrational states. The bound-state vibrational energies and the corresponding wave functions allow the interpretation of the scarcely available experimental results about the intermonomer vibrational motion of the complex. A very large number of long-lived quasibound combination states of the three vibrational modes, exhibiting a very similar energy-level structure as that of the bound states, are found embedded in the continuum. Additional short-lived resonance states are also identified and their properties are analyzed.

Rovibrational quantum dynamical computations for deuterated isotopologues of the methane–water dimer

Rovibrational states of methane–water isotopologues are computed in a variational procedure and the wave functions are analyzed in terms of the rigid-rotor and coupled-rotors models.

Small Molecules-Big Data

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

Promoting and inhibiting tunneling via nuclear motions

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.