Classical path surface-hopping dynamics. I. General theory and illustrative trajectories

Abstract

A formulation of a trajectory surface-hopping method is presented which starts with some of the basic ideas of the standard method, extends these to include more than two states, and enlists the classical-path equations not only to propagate through the nonadiabatic region but also to effect the transitions, or surface hops, themselves. The latter is accomplished by letting the Hamiltonian matrix elements in the time-dependent Schrödinger equation become complex, allowing manipulation of the fluctuation in the various adiabatic state populations. The procedure automatically conserves total energy and angular momentum as well as probability, and ensures that energetically inaccessible states are not significantly populated. In regions of extended degeneracy, the method resembles the standard classical-path approach with no surface hopping. In fact, the evolution of the wave function can be controlled to behave either as in the surface-hopping extreme or in the pure semiclassical extreme, allowing the method to be tailored to suit individual systems. The procedure is illustrated by application to a well-studied collision induced predissociation, Ne+He+2→Ne++He+He, where vibration in the entrance channel, Ne+He+2, leads to the strong nonadiabatic behavior responsible for the large observed cross sections. A few preliminary calculations for singly charged argon trimer ions produced in the ionization process Arn→Ar+n→Ar+2+(n−2)Ar, demonstrate that the formulation can be easily extended to include many degrees of freedom.