Fewest-switches with time uncertainty: A modified trajectory surface-hopping algorithm with better accuracy for classically forbidden electronic transitions

We present a modification of Tully’s fewest-switches (TFS) trajectory surface-hopping algorithm (also called molecular dynamics with quantum transitions) that is called the fewest-switches with time uncertainty (FSTU) method. The FSTU method improves the self-consistency of the fewest-switches algorithm by incorporating quantum uncertainty into the hopping times of classically forbidden hops. This uncertainty allows an electronic transition that is classically forbidden at some geometry to occur by hopping at a nearby classically allowed geometry if an allowed hopping point is reachable within the Heisenberg interval of time uncertainty. The increased accuracy of the FSTU method is verified using a challenging set of three-body, two-state test cases for which accurate quantum-mechanical results are available. The FSTU method is shown to be more accurate than the TFS method in predicting total nonadiabatic quenching probabilities and product branching ratios.