Phase-space surface hopping: Nonadiabatic dynamics in a superadiabatic basis

In this paper, we construct a phase-space surface hopping algorithm for use in systems that exhibit strong nonadiabatic coupling. The algorithm is derived from a representation of the electronic basis which is a function of the nuclear phase-space coordinates rather than the nuclear position coordinates. This phase-space adiabatic basis can be understood in the context of Berry's superadiabatic basis formalism as the first-order superadiabatic correction to the conventional position-space adiabatic basis. This superadiabatic representation leads to nuclear dynamics described not by Newton's equations of motion but by generalized Hamilton's equations of motion. The phase-space surface hopping algorithm captures physical effects that cannot be described by traditional algorithms. For a simple model problem, we show that phase-space surface hopping is more accurate than position-space surface hopping, especially when the nonadiabatic coupling is strong.