Continuous surface switching: An improved time-dependent self-consistent-field method for nonadiabatic dynamics

We present a new semiclassical method for electronically nonadiabatic collisions. The method is a variant of the time-dependent self-consistent-field method and is called continuous surface switching. The algorithm involves a self-consistent potential trajectory surface switching approach that is designed to combine the advantages of the trajectory surface hopping approach and the Ehrenfest classical path self-consistent potential approach without their relative disadvantages. Viewed from the self-consistent perspective, it corresponds to “on-the-fly histogramming” of the Ehrenfest method by a natural decay of mixing; viewed from the surface hopping perspective, it corresponds to replacing discontinuous surface hops by continuous surface switching. In this article we present the method and illustrate it for three multidimensional cases. Accurate quantum mechanical scattering calculations are carried out for these three cases by a linear algebraic variational method, and the accurate values of reactive probabilities, quenching probabilities, and moments of final vibrational and rotational distributions are compared to the results of continuous surface switching, the trajectory surface hopping method in two representations, the time-dependent self-consistent-field method, and the Miller–Meyer classical electron method to place the results of the semiclassical methods in perspective.