Nonadiabatic transition state theory and multiple potential energy surface molecular dynamics of infrequent events

Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of "surface-hopping" MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the "molecular dynamics with quantum transitions" (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem.