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The interaction of a molecule with the quantized electromagnetic field of a nanocavity gives rise to light-induced conical intersections between polaritonic potential energy surfaces. We demonstrate for a realistic model of a polyatomic molecule that the time-resolved ultrafast radiative emission of the cavity enables following both nuclear wavepacket dynamics on, and nonadiabatic population transfer between, polaritonic surfaces without applying a probe pulse. The latter provides an unambiguous (and in principle experimentally accessible) dynamical fingerprint of light-induced conical intersections.

Polaritons - hybrid light-matter states formed in cavity - strongly change the properties of the underlying matter. In optical or plasmonic nanocavities, polaritons decay by radiative emission of the cavity, which is accessible experimentally. Due to the interaction of a molecule with the quantized radiation field, polaritons exhibit light-induced conical intersections (LICIs) which dramatically influence the nuclear dynamics of molecular polaritons. We show that ultrafast radiative emission from the lower polariton is controlled by the geometric phase imposed by the LICI. This finding provides insight into the process of emission and, furthermore, allows one to compute these signals by augmenting the Born-Oppenheimer approximation for polaritons with a geometric phase term.

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 CH

A discrepancy between theoretical and experimental values of the rotational barrier in benzaldehyde has been observed, which was attributed to inaccurate experimental results in part. Here, we report results on the -CHO torsion of benzaldehyde (C6H5CHO) based on a high resolution spectroscopic investigation in the far-infrared range in an effort to remove the experimental ambiguity. The rotationally-resolved vibrational spectra were measured with an unapodized resolution of 0.00064 cm-1 using synchrotron-based Fourier transform infrared (FTIR) spectroscopy at the Canadian Light Source. The torsional fundamental νt = 109.415429(20) cm-1 was unambiguously assigned via rovibrational analysis, followed by the tentative assignment of the first (2νt-νt) and second (3νt- 2νt) hot bands at 107.58 cm-1 and 105.61 cm-1, respectively, by comparison of the observed Q branch structures at high resolution with simulation based on a previous microwave study. This assignment is different from any previous low resolution infrared studies in which the intensity patterns were misleading. The key result of the assignment of the first three transitions allowed the determination of the barrier to internal rotation of (hc)1533.6 cm-1 (4.38 kcal mol-1). When compared with calculated results from vibrational second-order perturbation theory (VPT2) and the quasiadiabatic channel reaction path Hamiltonian (RPH) approach, the experimental value is still too low and this suggests that the discrepancy between theory and experiment remains despite the best experimental efforts.

The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated. For polyatomic molecules, reduced-dimensional models and the use of the Born–Oppenheimer approximation (BOA) may remedy the situation. It is demonstrated that contrary to expectation, BOA may even fail in a one-dimensional model and is generally expected to fail in two- or more-dimensional models due to the appearance of conical intersections induced by the cavity., The coupling of a molecule and a cavity induces nonadiabaticity in the molecule which makes the description of its dynamics complicated.

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.

International audience; Nonadiabaticity, i.e., the effect of mixing electronic states by nuclear motion, is a central phenomenon in molecular science. The strongest nonadiabatic effects arise due to the presence of conical intersections of electronic energy surfaces. These intersections are abundant in polyatomic molecules. Laser light can induce in a controlled manner new conical intersections, called light-induced conical intersections, which lead to strong nonadiabatic effects similar to those of the natural conical intersections. These effects are, however, controllable and may even compete with those of the natural intersections. In this work we show that the standard low-energy vibrational spectrum of the electronic ground state can change dramatically by inducing nonadiabaticity via a light-induced conical intersection. This generic effect is demonstrated for an explicit example by full-dimensional high-level quantum calculations using a pump-probe scheme with a moderate-intensity pump laser and a weak probe laser.

Quantum mechanical tunnelling provides an important avenue for chemical reactions unable to make an over-the-barrier passage from reactants to products. Tunnelling control of these chemical reactions means that it is neither the barrier height (part of kinetic control) nor the Gibbs energy gain (part of thermodynamic control) but basically the width of the reaction barrier that determines which way a chemical transformation, which could follow at least two distinct pathways, will proceed. Quantum mechanical tunnelling is also important for understanding observed (ro)vibrational spectra of a large number of molecular systems exhibiting the effect of “tunnelling splitting”. For both reaction kinetics and spectroscopy, quantum mechanical tunnelling can be influenced by internal and external means. Internal control of tunnelling means control either via excitations of internal motions (rotations and vibrations) or by isotopic substitutions. In particular, asymmetric isotopic substitution results in an interesting molecular phenomenon called tunnelling switching. External (coherent) control of tunnelling can be achieved by shaped laser pulses. Molecular examples are provided and discussed for each tunnelling case and control scenario.

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.

We report the first successful high-resolution analyses of the Fourier transform infrared (FTIR) spectrum of trisulfane. A band centered at 861.0292 cm−1 can be assigned unambiguously to the chiral trans conformer by means of ground state combination differences in comparison with known rotational spectra. A second band near 864.698 cm−1 is tentatively assigned to the cis conformer by comparison with theory. The results are discussed in relation to their importance for experimental attempts to measure the parity violating energy difference ΔpvE between the ground states of enantiomers of chiral molecules.

We report a comparison of the analysis of the low energy spectrum of 13CHF3 and 12CHF3 from the THz (FIR) range to the ν1 fundamental at high resolution (δ[small nu, Greek, tilde] < 0.001 cm-1 or otherwise Doppler limited) on the basis of FTIR spectra taken both with ordinary light sources and with the synchrotron radiation from the Swiss Light Source. Several vibrational levels are accurately determined including, in particular, the 2ν4 CH-bending overtone and the ν1 CH-stretching fundamental of 13CHF3. Comparison of experimental results with those from accurate full dimensional vibrational calculations allows for a study of the time-dependent quantum dynamics of intramolecular vibrational redistribution (IVR) in the CH chromophore both on short time scales (fs) and longer time scales (ps) when coupling to the lower frequency modes becomes important and where the 12C/13C isotope effects are very large.

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.

Nonadiabatic coupling is absent between the electronic ground X and first excited (singlet) A states of formaldehyde. As laser fields can induce conical intersections between these two electronic states, formaldehyde is particularly suitable for investigating light-induced nonadiabaticity in a polyatomic molecule. The present work reports on the spectrum induced by light-the so-called field-dressed spectrum-probed by a weak laser pulse. A full-dimensional ab initio approach in the framework of Floquet-state representation is applied. The low-energy spectrum, which without the dressing field would correspond to an infrared vibrational spectrum in the X-state, and the high-energy spectrum, which without the dressing field would correspond to the X → A spectrum, are computed and analyzed. The spectra are shown to be highly sensitive to the frequency of the dressing light allowing one to isolate different nonadiabatic phenomena.

We report results on the dynamics of tunnelling switching based on a high-resolution spectroscopic investigation of meta-D-phenol in GHz and THz ranges. The pure rotational spectra were recorded in the range of 72–117 GHz and assigned to the localized syn- and anti-structures in the ground and the first excited torsional states. Specific torsional states were unambiguously assigned by comparison of the experimental rotational constants with theoretical results from quasiadiabatic channel reaction path Hamiltonian (RPH) calculations. The torsional fundamental νT at ≈ 309 cm−1 and the first hot band (2νT – νT) at ≈ 277 cm−1 were subsequently assigned in synchrotron based high-resolution Fourier transform infrared (FTIR, THz) spectra. The analyses provided accurate spectroscopic constants of all six states involved. It was found that the 2νT states are interacting through anharmonic resonances, indicating tunnelling switching as predicted by theory. Furthermore, tunnelling–rotation–vibration transiti...

The chiral C2 symmetric molecule 1,2-dithiine (1,2-dithia-3,5-hexadiene, C4H4S2) has been identified as a possible candidate for measuring the parity violating energy difference between enantiomers. We report here the observation and analysis of the low-frequency fundamental ν24 using highest resolution synchrotron-based interferometric Fourier transform infrared (FTIR) spectroscopy in the terahertz range with a band center of ν0 = 6.95375559 THz (ν0 = 231.952319 (10) cm-1) and two related hot bands, the (ν13 + ν24) ← ν13 band at ν0 = 6.97256882 THz (ν0 = 232.579861 (33) cm-1) and the 2ν24 ← ν24 band at ν0 = 7.01400434 THz (ν0 = 233.962001 (14) cm-1). This success in the difficult analyses of the THz spectrum of a complex chiral molecule of importance for fundamental tests on molecular parity violation is enabled by the ideal setup of an FTIR experiment of currently unique resolution with the very stable and bright synchrotron radiation at the Swiss Light Source (SLS).

We report high resolution spectroscopic results of 1,2-dithiine-(1,2-dithia-3,5-cyclohexadiene, C4H4S2) in the gigahertz and terahertz spectroscopic ranges and exploratory theoretical calculations of parity violation and tunneling processes in view of a possible experimental determination of the parity violating energy difference ΔpvE in this chiral molecule. Theory predicts that the parity violating energy difference between the enantiomers in their ground state (ΔpvE ≃ 1.1 × 10−11(hc) cm−1) is in principle measurable as it is much larger than the calculated tunneling splitting for the symmetrical potential ΔE± < 10−24 (hc) cm−1. With a planar transition state for stereomutation at about 2500 cm−1 tunneling splitting becomes appreciable above 2300 cm−1. This makes levels of well-defined parity accessible to parity selection by the available powerful infrared lasers and thus useful for one of the existing experimental approaches towards molecular parity violation. The new GHz spectroscopy leads to greatly improved ground state rotational parameters for 1,2-dithiine. These are used as starting points for the first successful analyses of high resolution interferometric Fourier transform infrared (FTIR, THz) spectra of the fundamentals ν17 (1308.873 cm−1 or 39.23903 THz), ν22 (623.094 cm−1 or 18.67989 THz) and ν3 (1544.900 cm−1 or 46.314937 THz) for which highly accurate spectroscopic parameters are reported. The results are discussed in relation to current efforts to measure ΔpvE., Physical Chemistry Chemical Physics, 18 (31), ISSN:1463-9084, ISSN:1463-9076

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.

We introduce the concept of a molecular quantum switch and demonstrate it with the example of meta-d-phenol, based on recent theoretical and high-resolution spectroscopic results for this molecule. We show that in the regime of tunneling switching with localized low-energy states and delocalized high-energy states the molecular quantum switch can be operated in two different ways: (i) a quasiclassical switching by coherent infrared radiation between the two isomeric structures syn- and anti-m-d-phenol; and (ii) a highly nonclassical switching making use of bistructural quantum superposition states of the syn and anti structures, which can be observed by their time-dependent spectra after preparation.

Measuring the parity-violating energy difference Δpv E between the enantiomers of chiral molecules is a major challenge of current physical-chemical stereochemistry. An important step towards this goal is to identify suitable molecules for such experiments by means of theory. This step has been made by calculations for the complex dynamics of tunneling and electroweak quantum chemistry of parity violation in the "classic" molecule trisulfane, HSSSH, which satisfies the relevant conditions for experiments almost ideally, as the molecule is comparatively simple and parity violation clearly dominates over tunneling in the ground state. At the same time, the barrier for stereomutation is easily overcome by the S-H infrared chromophore.

One-dimensional (1D) and two-dimensional (2D) models are investigated, which help to understand the unusual rovibrational energy-level structure of the astronomically relevant and chemically interesting astructural molecular ion H+5. Due to the very low hindering barrier characterising the 1D torsion-only vibrational model of H+5, this model yields strongly divergent energy levels. The results obtained using a realistic model for the torsion potential, including the computed (near) degeneracies, can be rationalised in terms of the model with no barrier. Coupling of the torsional motion with a single rotational degree of freedom is also investigated in detail. It is shown how the embedding-dependent rovibrational models yield energy levels that can be rationalised via the 2D vibrational model containing two independent torsions. Insight into the complex rovibrational energy level structure of the models and of H+5 is gained via variational nuclear motion and diffusion Monte Carlo computations and by the an...

A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric CH

We report a comparison of the analysis of the low energy spectrum of

We report the first successful high-resolution analyses of the Fourier transform infrared (FTIR) spectrum of trisulfane. A band centered at 861.0292 cm−1 can be assigned unambiguously to the chiral trans conformer by means of ground state combination differences in comparison with known rotational spectra. A second band near 864.698 cm−1 is tentatively assigned to the cis conformer by comparison with theory. The results are discussed in relation to their importance for experimental attempts to measure the parity violating energy difference ΔpvE between the ground states of enantiomers of chiral molecules.

The liquid vapor interface is difficult to access experimentally but is of interest from a theoretical and applied point of view and has particular importance in atmospheric aerosol chemistry. Here we examine the liquid vapor interface for mixtures of water sodium chloride and formic acid an abundant chemical in the atmosphere. We compare the results of surface tension and X ray photoelectron spectroscopy (XPS) measurements over a wide range of formic acid concentrations. Surface tension measurements provide a macroscopic characterization of solutions ranging from 0 to 3 M sodium chloride and from 0 to over 0.5 mole fraction formic acid. Sodium chloride was found to be a weak salting out agent for formic acid with surface excess depending only slightly on salt concentration. In situ XPS provides a complementary molecular level description about the liquid vapor interface. XPS measurements over an experimental probe depth of 51 Å gave the C1s to O 1s ratio for both total oxygen and oxygen from water. XPS also provides detailed electronic structure information that is inaccessible by surface tension. Density functional theory calculations were performed in order to understand the observed shift in C 1s binding energies to lower values with increasing formic acid concentration. Part of the experimental -0.2 eV shift can be assigned to the solution composition changing from predominantly monomers of formic acid to a combination of monomers and dimers however the lack of appropriate reference to calibrate the absolute BE scale at high formic acid mole fraction complicates the interpretation. Our data are consistent with surface tension measurements yielding a significantly more surface sensitive measurement than XPS due to the relatively weak propensity of formic acid for the interface. A simple model allowed us to replicate the XPS results under the assumption that the surface excess was contained in the top four angstroms of solution.

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.

It is shown that the use of an Eckart-frame embedding with a kinetic energy operator expressed in curvilinear internal coordinates becomes feasible and straightforward to implement for arbitrary molecular compositions and internal coordinates if the operator is defined numerically over a (discrete variable representation) grid. The algorithm proposed utilizes the transformation method of Dymarsky and Kudin to maintain the rotational Eckart condition. In order to demonstrate the applicability and flexibility of our approach the non-rigid ammonia molecule is considered and the corresponding rotational–vibrational energy levels and wave functions are computed using kinetic energy operators with three different embeddings. Two of them fulfill the Eckart conditions corresponding to a trigonal pyramidal ( C 3v ) and a trigonal planar ( D 3h ) reference structure and the third one is a non-Eckart frame. The computed energy levels are, of course, identical, and the structure of the three different wave-function representations are analyzed in terms of the rigid rotor functions for a symmetric top. The possible advantages of one frame representation over another are discussed concerning the interpretation of the rovibrational states in terms of the traditional rigid rotor labels.

On the basis of both experiment and theory, accurate rotational–vibrational line positions and energy levels, with associated critically reviewed labels and uncertainties, are reported for the ground electronic state of the H3+ molecular ion. An improved MARVEL algorithm is used to determine the validated experimental levels and their self-consistent uncertainties from a set of 1610 measured transitions and associated uncertainties, coming from 26 sources. 1410 transitions have been validated for ortho-H3+ and para-H3+, 78 belong to floating components of the spectroscopic network (SN) investigated and thus left unvalidated, while 122 measured transitions had to be excluded from the MARVEL analysis for one reason or another. The spectral range covered by the experiments is 7–16 506 cm–1 . Altogether 13 vibrational band origins are reported, the highest J value, where J stands for the rotational quantum number, for which energy levels are validated is 12. The MARVEL energy levels are checked against ones d...

The chiral C

A discrete-variable-representation-based symmetry adaptation algorithm is presented and implemented in the fourth-age quantum-chemical rotational-vibrational code GENIUSH. The utility of the symmetry-adapted version of GENIUSH is demonstrated by the computation of seven-dimensional bend-only vibrational and rovibrational eigenstates of the highly fluxionally symmetric C H 5 + molecular ion, a prototypical astructural system. While the numerical results obtained and the symmetry labels of the computed rovibrational states of C H 5 + are of considerable utility by themselves, it must also be noted that the present study confirms that the nearly unconstrained motion of the five hydrogen atoms orbiting around the central carbon atom results in highly complex rotational-vibrational quantum dynamics and renders the understanding of the high-resolution spectra of C H 5 + extremely challenging.

The fourth-age quantum chemical code GENIUSH is used for the variational determination of rotational-vibrational energy levels corresponding to reduced- and full-dimensional models of H(+)(5), a molecular ion exhibiting several strongly coupled large-amplitude motions. The computations are supplemented with one- and two-dimensional analytic results which help to understand the peculiar rovibrational energy-level structure computed correctly for the first time. An unusual aspect of the results is that the canonical Eckart-embedding of molecule-fixed axes, a cornerstone of the computational spectroscopy of semirigid molecules, is found to be inadequate. Furthermore, it is shown that while the 1D "active torsion" model provides proper results when compared to the full, 9D treatment, models excluding the torsion have limited physical significance. The structure of the rovibrational energy levels of H(+)(5) proves that this is a prototypical astructural molecule: the rotational and vibrational level spacings are of the same order of magnitude and the level structure drastically deviates from that computed via perturbed rigid-rotor and harmonic-oscillator models.

Critically evaluated rotational-vibrational line positions and energy levels, with associated critically reviewed labels and uncertainties, are reported for two deuterated isotopologues of the H3(+) molecular ion: H2D(+) and D2H(+). The procedure MARVEL, standing for Measured Active Rotational-Vibrational Energy Levels, is used to determine the validated levels and lines and their self-consistent uncertainties based on the experimentally available information. The spectral ranges covered for the isotopologues H2D(+) and D2H(+) are 5.2-7105.5 and 23.0-6581.1 cm(-1), respectively. The MARVEL energy levels of the ortho and para forms of the ions are checked against ones determined from accurate variational nuclear motion computations employing the best available adiabatic ab initio potential energy surfaces of these isotopologues. The number of critically evaluated, validated and recommended experimental (levels, lines) are (109, 185) and (104, 136) for H2D(+) and D2H(+), respectively. The lists of assigned MARVEL lines and levels and variational levels obtained for H2D(+) and D2H(+) as part of this study are deposited in the ESI to this paper.

Variational rotational-vibrational quantum chemical computations are performed for the F(-)-CH4 and F(-)-CH2D2 anion complexes using several reduced-dimensional models in a curvilinear polyspherical coordinate system and utilizing an accurate ab initio potential energy surface (PES). The implementation of the models is made practical by using the general rovibrational code GENIUSH, which constructs the complicated form of the exact rovibrational kinetic energy operator in reduced and full dimensions in any user-specified coordinates and body-fixed frames. A one-dimensional CF stretch, 1D(RCF), a two-dimensional intermolecular bend, 2D(θ,φ), and a three-dimensional intermolecular, 3D(RCF,θ,φ), rigid methane model provide vibrational energies for the low-frequency, large-amplitude modes in good agreement with full-dimensional MCTDH results for F(-)-CH4. The 2D(θ,φ) and 3D(RCF,θ,φ) four-well computations, describing equally the four possible CH-F(-) bonds, show that the ground-state tunneling splitting is less than 0.01 cm(-1). For the hydrogen-bonded CH stretching fundamental a local-mode model is found to have almost spectroscopic accuracy, whereas a harmonic frequency analysis performs poorly. The 2D(θ,φ) and 3D(RCF,θ,φ) rotational-vibrational computations on the Td-symmetric four-well PES reveal that in most cases F(-)-CH4 behaves as a semirigid C3v symmetric top. For the degenerate intermolecular bending vibrational states substantial splittings of the rigid rotor levels are observed. For F(-)-CH2D2 the rotational levels guide the assignment of the vibrational states to either F(-)-H or F(-)-D connectivity.

Measurements result in effective, usually temperature-dependent structural parameters of molecules, and never directly in equilibrium structures, which are theoretical constructs. A recent high-accuracy semiglobal potential energy surface of the electronic ground state of the ammonia molecule, called NH3-Y2010 (J. Mol. Spectrosc. 2011, 268, 123), which exhibits mass-independent equilibrium NH bond length and a HNH bond angle of 1.0109 Å and 106.75°, respectively, is employed together with the variational nuclear motion code GENIUSH (J. Chem. Phys. 2009, 130, 134112; 2011, 134, 074105) to determine directly measurable, effective structural parameters of the (14)NH(3) and (14)ND(3) molecules. The effective r(g)- and r(a)-type NH(ND) distances determined at 300 K are 1.0307(1.0254) and 1.0256(1.0217) Å, respectively, with an estimated accuracy of 2 × 10(-4) Å. The effective θ(g) HNH and DND bond angles at 300 K are 106.91° and 106.85°, respectively. The root-mean-square amplitudes of vibration, l(g), for the NH(ND) distances at 300 K are 0.073(0.062) Å. These structural parameters confirm the less accurate results of a room-temperature gas-electron-diffraction study (J. Chem. Phys. 1968, 49, 2488, all data in Å): r(g)(NH) = 1.030(2), l(g)(NH) = 0.073(2), r(g)(ND) = 1.027(3), and l(g)(ND) = 0.061(2). The computed difference in the r(g,T)(NH) bond lengths of the two spin isomers (ortho and para forms) of (14)NH(3) is 3 × 10(-5) Å at 0 K, the difference diminishes at temperatures of about 30-50 K.

Developments during the last two decades in nuclear motion theory made it possible to obtain variational solutions to the time-independent, nuclear-motion Schrödinger equation of polyatomic systems as "exact" as the potential energy surface (PES) is. Nuclear motion theory thus reached a level whereby this branch of quantum chemistry started to catch up with the well developed and widely applied other branch, electronic structure theory. It seems to be fair to declare that we are now in the fourth age of quantum chemistry, where the first three ages are principally defined by developments in electronic structure techniques (G. Richards, Nature, 1979, 278, 507). In the fourth age we are able to incorporate into our quantum chemical treatment the motion of nuclei in an exact fashion and, for example, go beyond equilibrium molecular properties and compute accurate, temperature-dependent, effective properties, thus closing the gap between measurements and electronic structure computations. In this Perspective three fundamental algorithms for the variational solution of the time-independent nuclear-motion Schrödinger equation employing exact kinetic energy operators are presented: one based on tailor-made Hamiltonians, one on the Eckart-Watson Hamiltonian, and one on a general internal-coordinate Hamiltonian. It is argued that the most useful and most widely applicable procedure is the third one, based on a Hamiltonian containing a kinetic energy operator written in terms of internal coordinates and an arbitrary embedding of the body-fixed frame of the molecule. This Hamiltonian makes it feasible to treat the nuclear motions of arbitrary quantum systems, irrespective of whether they exhibit a single well-defined minimum or not, and of arbitrary reduced-dimensional models. As a result, molecular spectroscopy, an important field for the application of nuclear motion theory, has almost black-box-type tools at its disposal. Variational nuclear motion computations, based on an exact kinetic energy operator and an arbitrary PES, can now be performed for about 9 active vibrational degrees of freedom relatively straightforwardly. Simulations of high-resolution spectra allow the understanding of complete rotational-vibrational spectra up to and beyond the first dissociation limits. Variational results obtained for H(2)O, H, NH(3), CH(4), and H(2)CCO are used to demonstrate the power of the variational techniques for the description of vibrational and rotational excitations. Some qualitative features of the results are also discussed.

Scaling factors for Pulay’s scaled quantum mechanical (SQM) scheme have been determined for four different widely used DFT functionals (PBE, B3LYP, B3PW91, and M06-2X) and for two basis sets (6-31++G** and aug-cc-pVTZ) by fitting computed results to 347 fundamental experimental vibrational frequencies of 33 molecules. Measurements in the gas phase and in solid argon matrices were used independently in the fitting procedure in order to provide a simple method of estimating matrix shifts. The accuracy of the new scaling factors is demonstrated on test molecules including hydrogen-bonded systems and molecules containing chlorine and sulfur atoms.

A procedure is investigated for assigning physically transparent, approximate vibrational and rotational quantum labels to variationally computed eigenstates. Pure vibrational wave functions are analyzed by means of normal-mode decomposition (NMD) tables constructed from overlap integrals with respect to separable harmonic oscillator basis functions. Complementary rotational labels J(K(a)K(c)) are determined from rigid-rotor decomposition (RRD) tables formed by projecting rotational-vibrational wave functions (J not equal 0) onto products of symmetrized rigid-rotor basis functions and previously computed (J=0) vibrational eigenstates. Variational results for H(2)O, HNCO, trans-HCOD, NCCO, and H(2)CCO are presented to demonstrate the NMD and RRD schemes. The NMD analysis highlights several resonances at low energies that cause strong mixing and cloud the assignment of fundamental vibrations, even in such simple molecules. As the vibrational energy increases, the NMD scheme documents and quantifies the breakdown of the normal-mode model. The RRD procedure proves effective in providing unambiguous rotational assignments for the chosen test molecules up to moderate J values.

The effect of an adiabatic approximation, named adiabatic Jacobi correction (AJC) and introduced in J. Chem. Phys. 126, 024102 (2007), was investigated on the complete set of vibrational levels of H(2)(+) and its isotopologues, most importantly on the highest-lying vibrational states of HD(+). In order to perform clamped nuclei calculations employing finite nuclear masses a constrained Hamiltonian has been derived utilizing interparticle coordinates. The Born-Oppenheimer (BO) potential, the adiabatic potential obtained after taking into account the traditional diagonal Born-Oppenheimer correction (DBOC), as well as the AJC-corrected potential have been determined by an accurate fitting to computed energy values. These potentials were included in one-dimensional variational computations and yielded the complete set of energy levels for H(2)(+), D(2)(+), and HD(+). A detailed investigation of the potential and the complete set of vibrational energy levels show the merits and the deficiencies of the BO, DBOC, and AJC treatments. In particular, it is shown that the AJC corrections are systematically smaller and have a different distance dependence than the DBOC corrections. For a large part of the spectrum of H(2)(+) and its isotopologues the adiabatic correction to the vibrational energy levels is smaller than the nonadiabatic correction, the adiabatic DBOC correction has the highest overall accuracy for the prediction of vibrational energy levels, it is surpassed by the AJC correction only for the highest energy levels of HD(+), and thus the use of the AJC correction is clearly the best choice only for states close to the dissociation limit of nonsymmetric isotopologues.

Approximate rotational characterization of variational rovibrational wave functions via the rigid rotor decomposition (RRD) protocol is developed for Hamiltonians based on arbitrary sets of internal coordinates and axis embeddings. An efficient and general procedure is given that allows employing the Eckart embedding with arbitrary polyatomic Hamiltonians through a fully numerical approach. RRD tables formed by projecting rotational-vibrational wave functions into products of rigid-rotor basis functions and previously determined vibrational eigenstates yield rigid-rotor labels for rovibrational eigenstates by selecting the largest overlap. Embedding-dependent RRD analyses are performed, up to high energies and rotational excitations, for the H(2) (16)O isotopologue of the water molecule. Irrespective of the embedding chosen, the RRD procedure proves effective in providing unambiguous rotational assignments at low energies and J values. Rotational labeling of rovibrational states of H(2) (16)O proves to be increasingly difficult beyond about 10,000 cm(-1), close to the barrier to linearity of the water molecule. For medium energies and excitations the Eckart embedding yields the largest RRD coefficients, thus providing the largest number of unambiguous rotational labels.

A variational quantum mechanical protocol is presented for the computation of rovibrational energy levels of semirigid molecules using discrete variable representation of the Eckart-Watson Hamiltonian, a complete, "exact" inclusion of the potential energy surface, and selection of a vibrational subspace. Molecular symmetry is exploited via a symmetry-adapted Lanczos algorithm. Besides symmetry labels, zeroth-order rigid-rotor and harmonic-oscillator quantum numbers are employed to characterize the computed rovibrational states. Using the computational molecular spectroscopy algorithm presented, a large number of rovibrational states, up to J = 50, of the ground electronic state of the parent isotopologue of ketene, H(2) (12)C=(12)C=(16)O, were computed and characterized. Based on 12 references, altogether 3982 measured and assigned rovibrational transitions of H(2) (12)C=(12)C=(16)O have been collected, from which 3194 were validated. These transitions form two spectroscopic networks (SN). The ortho and the para SNs contain 2489 and 705 validated transitions and 1251 and 471 validated energy levels, respectively. The computed energy levels are compared with energy levels obtained, up to J = 41, via an inversion protocol based on this collection of validated measured rovibrational transitions. The accurate inverted energy levels allow new assignments to be proposed. Some regularities and irregularities in the rovibrational spectrum of ketene are elucidated.