NATPS: Nonadiabatic Transition Path Sampling Using the Time-Reversible Mapping Approach to Surface Hopping.

Rare nonadiabatic events play a central role in photochemistry but remain difficult to simulate because excited-state dynamics is computationally demanding and often stochastic. Here we introduce a deterministic and time-reversible implementation of nonadiabatic dynamics that enables the application of transition path sampling (TPS) to excited-state processes. Our approach builds on the mapping approach to surface hopping (MASH) and establishes the conditions required for path ensemble sampling, in particular, time reversibility and detailed balance. The combination of MASH with the TPS framework gives rise to a new method termed nonadiabatic transition path sampling (NATPS). We demonstrate its capabilities on a model system of electronically coupled potential energy surfaces, where it efficiently generates ensembles of reactive trajectories and provides mechanistic insight into nonadiabatic pathways. Compared with brute-force trajectory simulations and forward-flux sampling approaches, NATPS substantially reduces the computational effort required to obtain reactive trajectories.