Dynamics of Barrier Crossings for the Generalized Anderson-Holstein Model: Beyond Electronic Friction and Conventional Surface Hopping

We investigate barrier crossings within the context of the Anderson-Holstein model, as relevant to coupled nuclear-electronic dynamics near a metal surface. Beyond standard electronic friction or conventional surface-hopping dynamics, we show that a broadened classical master equation can recover both the correct nonadiabatic and the correct adiabatic dynamics for a general escape problem (even with possibly multiple escape channels). In the case of a large barrier with only a single escape channel, we also find a surprising conclusion: electronic friction can recover Marcus's nonadiabatic theory of electron transfer in the limit of small molecule-metal couplings. The latter conclusion establishes a hidden connection between Marcus's nonadiabatic theory and Kramer's adiabatic theory of rate constants.