Non-adiabatic molecular dynamics: Split-operator multiple spawning with applications to photodissociation

Abstract

A classically motivated quantal method, designed to allow for molecular dynamics occurring on more than one potential-energy surface, is extended in two directions. The extensions are shown to be accurate while retaining the classical flavour which is useful for both interpretation and computation. The first extension allows for the evaluation of the required inter-state coupling matrix elements for potential-energy surfaces even when these are given numerically rather than fitted to some analytical form. Moreover, the procedure is a local one, requiring only the values of the two potentials and their gradients. It is thus particularly suitable for applications where the electronic and nuclear problems are solved simultaneously. The second extension strengthens the connections to classical mechanics while avoiding ambiguities in the choice of the classical trajectories which will represent the dynamics. The accuracy and limitations of the proposed procedures are tested for several model problems.