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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.

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

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.

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.

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 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.

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...

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

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.

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.

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.

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.

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.