A SEMICLASSICAL SURFACE HOPPING PROPAGATOR FOR NONADIABATIC PROBLEMS

A semiclassical propagator is developed for general multisurface, mult idimensional nonadiabatic problems. It is demonstrated that this propa gator satisfies the time-dependent Schrodinger Equation through order HBAR. This is the same order satisfied by the usual semiclassical prop agator in single surface problems. The zeroth-order term (in the nonad iabatic coupling) for the propagator is just the well-known single sur face adiabatic propagator. The first-order terms involve single hops f rom the initial adiabatic state to other states. Energy is conserved i n these hops and the momentum change accompanying each hop occurs in t he direction parallel to the nonadiabatic coupling for the transition. Both transmitted and reflected contributions are included after a hop . The propagator expression has the zeroth-order (single surface) semi classical form before and after the hop. The complete propagator inclu des terms with any number of hops and all possible hopping points. The se multihop terms are defined analogously to the first-order (single h op) terms. An alternative formulation of the semiclassical propagator, which includes contributions from a broader range of hopping trajecto ries, is also developed. (C) 1995 American Institute of Physics.