Improved treatment of momentum at classically forbidden electronic transitions in trajectory surface hopping calculations

We present a new prescription (called the ∇V prescription) for treating classically forbidden surface hops in semiclassical trajectory surface hopping simulations. The new method uses gradient information about the target electronic surface to determine the nuclear dynamics at a frustrated hopping event. We have tested this prescription, along with previously suggested prescriptions, against accurate quantum dynamics for 21 cases. We find that the fewest switches with time uncertainty (FSTU) algorithm with the ∇V prescription for momentum changes at frustrated hops is the most accurate of the six variants of the surface hopping approach that we tested.