A SEMICLASSICAL SURFACE HOPPING FORMALISM FOR SOLVENT-INDUCED VIBRATIONAL-RELAXATION

A semiclassical surface hopping formalism is developed for the time-de pendent probability of transitions between vibrational states for a mo lecule in a solvent. An adiabatic separation of time scales is made be tween the fast vibrational motions and the comparatively slow solvent motions. The vibrational transition probability is evaluated by propag ating the density for the system with the molecule in the initial vibr ational state forward in time, and then projecting this propagated den sity onto the final vibrational state. Semiclassical non-adiabatic pro pagators are employed for the time propagation. The transitions take p lace in the form of discrete hops between the vibrational states, and integrations are performed over all possible hopping points. The metho d is quite general and allows for the interaction of any number of vib rational states and any number of hops.