Nonadiabatic semiclassical scattering. II. Solution of two-dimensional models and comparison with quantum results

Abstract

The generalized surface-hopping procedure for semiclassical nonadiabatic scattering is applied to a two dimensional model for comparison with quantum results. The model consists of two adiabatic electronic potential energy surfaces with a radial nonadiabatic coupling between the electronic states. Both adiabatic potential surfaces are taken to be constant. The coupling is assumed to be weak. This model is sufficient to explore many of the important features of the generalized surface-hopping procedure. Comparison of the semiclasssical and quantum results demonstrates good agreement, and the first order quantum scattering amplitude is analytically found to be the ℏ→0 limit of the first order semiclassical scattering amplitude. The behavior of the wave function near singularities in the transition amplitudes is explored in a general context, independent of these simplified models. These singularities are found to be necessary to produce the correct behavior in the wave function.