VIBRATIONAL-ENERGY RELAXATION IN THE CONDENSED PHASES - QUANTUM VS CLASSICAL BATH FOR MULTIPHONON PROCESSES

We develop a theory for relating quantum and classical time correlatio n functions in the context of vibrational energy relaxation. The treat ment is based on the assumption that both the quantum and the classica l systems are characterized by effective harmonic Hamiltonians with id entical normal modes; and the solute-solvent interaction is taken to b e linear in the solute vibrational coordinate, but nonlinear in the ba th coordinates. We propose an approximate ''quantum correction'' which allows the determination of the quantum energy relaxation rates from the classical force-force time correlation functions in the limit of l arge solute's vibrational frequency. We test the accuracy of this appr oximate correction against exact numerical results for two forms of th e solute-solvent interaction (exponential and power law), and find it to be accurate for a wide range of solute vibrational frequencies and for different solvent thermodynamic states. A simple form of the ''qua ntum correction'' is proposed for the models based on Lennard-Jones in teractions. In all cases it is found that the vibrational relaxation t ime in a fully quantum system is better approximated by a fully classi cal theory (classical oscillator in classical bath) than by a mixed qu antum-classical theory (quantum oscillator in classical bath). (C) 199 7 American Institute of Physics.