Conditions for the equivalence of the “surface hopping” and complex-valued time methods to affect nonadiabatic transitions

In this paper we examine two semiclassical theories used to describe collision induced electronic transitions, namely the surface hopping method of Tully and Preston and the “exact” semiclassical method of Miller and George, and give conditions such that the two methods are equivalent. An example using a DIM potential energy for H⁺₃ is discussed.