| Part I. Vibrational dynamics of molecules in condensed phases is investigated. A theory for the effects of repulsive and spatially slowly varying attractive forces on the vibrational frequency and dephasing of polyatomic molecular liquids is developed. Proper separation of the rapidly and slowly varying branches of the intermolecular potentials lead to a separation of timescales that allows the dephasing relaxation to be computed using a combination of binary collision and mean field ideas. In all applications studied, the slowly varying attractive forces are found to play a significant role in determining the Raman linewidth. Resonance transfer processes and corrections to the weak coupling formulation are also investigated. An analogous theory for the dephasing of impurity molecules dissolved in rare gas solids is constructed. The role of acoustic phonons, local modes, and librational motions is studied. Finally, vibrational energy relaxation of simple molecules in solid and liquid media is considered, with emphasis on the multiphonon relaxation mechanism for impurities in rare gas solids. Model calculations are presented, and relationships between the spectral features and energy relaxation are derived.; Part II. In the path integral representation of quantum theory, a few body quantum problem becomes a classical many body problem. To exploit this isomorphism, a general methodology is developed by which degrees of freedom are explicitly removed from consideration. The methods are shown to provide rigorous upper and lower bounds to the free energy, and the upper bounds are optimized with variational theories. Several illustrative examples are provided including treatments of a tunneling system strongly coupled to a nonadiabatic bath. The classical isomorphism is then used to develop a quantum theory of polarization in liquids. The mean spherical approximation and related integral equations are solved for a fluid composed of atoms or spherical molecules with fluctuating quantum mechanical Drude internal dipoles. Quantum effects are found to play a dominant role for many experimentally relevant properties. Calculations of the solvation energy of an impurity molecule are presented. Generalizations of the theory to include features such as charge overlap and hyperpolarizabilities are also discussed. |
