Including tunneling in non-born-oppenheimer simulations

For electronically nonadiabatic processes in all but the simplest systems, the most practical multidimensional simulation method is a semiclassical approximation in which a trajectory or the center of a wave packet follows a classical path governed by an effective potential energy function. Here, we show how such simulations can be made more realistic by including tunneling by the army ants tunneling method. We illustrate the theory by calculations with model potential energy surfaces; one model study is in the adiabatic limit, and the other one has nonadiabatic transitions between two electronic states during the tunneling event. The army ants tunneling algorithm is used to efficiently sample tunneling events in the trajectories in both cases. This work makes it possible to simulate complex nonadiabatic chemical processes by efficiently including the important quantum effect of tunneling.