Nonadiabatic dynamics near metal surface with periodic drivings: A Floquet surface hopping algorithm.

We develop a Floquet surface hopping approach to deal with nonadiabatic dynamics of molecules near metal surfaces subjected to time-periodic drivings from strong light-matter interactions. The method is based on a Floquet classical master equation (FCME) derived from a Floquet quantum master equation (FQME), followed by a Wigner transformation to treat nuclear motion classically. We then propose different trajectory surface hopping algorithms to solve the FCME. We find that a Floquet averaged surface hopping with electron density (FaSH-density) algorithm works the best as benchmarked with the FQME, capturing both the fast oscillations due to the driving and the correct steady-state observables. This method will be very useful to study strong light-matter interactions with a manifold of electronic states.