The highly excited vibrational states of polyatomic molecules are investigated using canonical Van Vleck perturbation theory, implemented in a superoperator framework. This approach is used to transform a vibrational Hamiltonian to a new representation which has a form ideally suited to the study of the dynamics of interest. The key advantage is that the solution to the full problem is obtained in the new representation using significantly smaller basis sets than are needed to obtain the solutions in the original representation. The transformations are applied to the Hamiltonian operator itself, not the Hamiltonian matrix; this superoperator approach obviates the need for large basis sets. The tedious and complex algebra, that is required to perform these transformations, is readily implemented with FORTRAN codes. Combining these two features has enabled the investigations of vibrational dynamics in energy regimes and densities of states, unattainable by standard methods. These methods are applied to two model problems and to the study of the highly excited overtones of CHD3 with up to five quanta of excitation in the CH bond.

Carboxylic acid dimers serve as prototypical systems for modeling the unusual spectral behavior of the hydride stretch fundamental. Large anharmonic effects associated with the pair of cooperatively strengthened OH¯OvC hydrogen bonds produces complicated infrared spectra in which the OH stretch oscillator strength is spread over hundreds of wave numbers, resulting in a complicated band sub-structure. In this work cubic anharmonic constants are computed along internal coordinates associated with the intramolecular OH stretch, intermolecular stretch, and OH bend internal coordinates for the formic acid and benzoic acid dimers. These are then projected onto the normal coordinates to produce mixed states that are used in computing the OH stretch infrared spectrum. For the benzoic acid dimer the calculations accurately reproduce for three deuterated isotopomers the overall breadth and much of the vibrational sub-structure in the observed spectra. For the formic acid dimer, the spectrum is calculated using a model employing a subset of the cubic force constants as well as using the full cubic force field. The spectra calculated for the formic acid dimer are sparser and somewhat more sensitive to the exact positions of the anharmonically coupled states than that of the benzoic acid dimer. Again semiquantitative agreement with experiment is obtained.

A theoretical model is presented for the vibrational dynamics of highly excited CH and CD overtones in benzene and perdeuterobenzene. The origin, path, and time scale for the overtone relaxation are described. The critical near resonant interaction responsible for the energy flow from an excited CH(D) oscillator to the ring is a Fermi resonance coupling, identified by Sibert, Reinhardt, and Hynes [Chem. Phys. Lett. 92, 455 (1982)]. Quantum overtone spectra are calculated both from time independent and time dependent perspectives and good qualitative agreement is found with the experimental overtone spectra of Reddy, Heller, and Berry [J. Chem. Phys. 76, 2814 (1982)]. Some expected consequences for future experiments on benzene and related systems are indicated.

Experimental and theoretical studies explore the reactivity of the symmetric and the antisymmetric stretching vibrations of monodeuterated methane (CH3D). Direct infrared absorption near 3000 cm−1 prepares CH3D molecules in three different vibrationally excited eigenstates that contain different amounts of symmetric C–H stretch (ν1), antisymmetric C–H stretch (ν4), and bending overtone (2ν5) excitation. The reaction of vibrationally excited CH3D with photolytic chlorine atoms (Cl, 2P3/2) yields CH2D products mostly in their vibrational ground state. Comparison of the vibrational action spectra with the simulated absorption spectra and further analysis using the calculated composition of the eigenstates show that the symmetric C–H stretching vibration (ν1) promotes the reaction seven times more efficiently than the antisymmetric C–H stretching vibration (ν4). Ab initio calculations of the vibrational energies and eigenvectors along the reaction coordinate demonstrate that this difference arises from changes in the initially excited stretching vibrations as the reactive Cl atom approaches. The ν1 vibration of CH3D becomes localized vibrational excitation of the C–H bond pointing toward the Cl atom, promoting the abstraction reaction, but the energy initially in the ν4 vibration flows into the C–H bonds pointing away from the approaching Cl atom and remains unperturbed during the reaction. A simple model using vibrational symmetries and vibrational adiabaticity predicts a general propensity for the greater efficiency of the symmetric stretch for accelerating the reaction in the vibrationally adiabatic limit.

Vibrational energy flow in liquid chloroform that follows the ultrafast excitation of the CH stretch fundamental is modeled using semiclassical methods. Relaxation rates are calculated using Landau-Teller theory and a time-dependent method both of which consider a quantum mechanical CHCl3 solute molecule coupled to a classical bath of CHCl3 solvent molecules. Probability flow is examined for several potentials to determine the sensitivity of calculated relaxation rates to the parameters that describe the model potentials. Three stages of relaxation are obtained. Probability is calculated to decay initially to a single acceptor state, a combination state of the solute molecule with two quanta of excitation in the CH bend and one in the CCl stretch, in 13–23 ps depending on the potential model employed. This is followed by rapid and complex intramolecular energy flow into the remaining vibrational degrees of freedom. During this second stage the lowest frequency Cl–C–Cl bend is found to serve as a conduit for energy loss to the solvent. The bottleneck for relaxation back to the ground state is predicted to be the slow 100–200 ps relaxation of the CH bend and CCl stretch fundamentals. Several aspects of the incoherent anti-Stokes scattering that follows strong infrared excitation of the CH fundamental as observed by Graener, Zürl, and Hoffman [J. Phys. Chem. B 101, 1745 (1997)] are elucidated in the present study.

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The vibrations of methane isotopomers with Td, C3v, and C2v symmetry are studied by means of high order Van Vleck perturbation theory. The vibrational states up to 9000 cm−1 are investigated by combining the ab initio force field of Lee, Martin and Taylor [J. Chem. Phys. 95, 254 (1995)] with a fourth order perturbative treatment based on curvilinear normal coordinates. Implementation of the perturbation theory using both analytical and numerical expression of the kinetic energy operator is considered. The quadratic and select cubic and quartic force constants are refined via a nonlinear least squares fit to experimental data The fit force constants reproduce 130 experimental band centers with a root mean squares deviation of 0.70 cm−1. The choice of polyad quantum number is discussed with respect to different molecules. The convergence of the energy levels is discussed by carrying out the perturbation calculation up to eighth order.

The observed IR spectra of the CH3NO2−⋅(H2O) and CH3CO2−⋅(H2O) complexes display sequences of up to seven transitions in the region of the OH stretch fundamentals. This is indicative of strong anharmonic coupling between the OH stretch modes and one or more low-frequency modes. Cubic force fields have been calculated for these two complexes using the MP2 method, and these have been used to calculate the vibrational spectra and to identify the key couplings responsible for the “extra” lines in the observed spectra. In addition, a simple adiabatic model involving the OH stretch and intermolecular rock vibrations is introduced and shown to account in an near quantitative manner for the structure in the OH stretch region of the spectra.