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

A semiclassical surface hopping formalism is developed for the time-dependent probability of transitions between vibrational states for a molecule in a solvent. An adiabatic separation of time scales is made between the fast vibrational motions and the comparatively slow solvent motions. The vibrational transition probability is evaluated by propagating the density for the system with the molecule in the initial vibrational state forward in time, and then projecting this propagated density onto the final vibrational state. Semiclassical non-adiabatic propagators are employed for the time propagation. The transitions take place in the form of discrete hops between the vibrational states, and integrations are performed over all possible hopping points. The method is quite general and allows for the interaction of any number of vibrational states and any number of hops.