Abstract
A variational approach is developed to generalize Kramers–Grote–Hynes theory into the regime of spatially-dependent friction. The theory is developed by identifying the probability function for a particle to retain its energy as it leaves the barrier region. This function provides the basis for a variational equation to determine the zero-time value of an effective linear friction. The latter quantity, which characterizes the effect of the spatially-dependent friction in the barrier region, leads to the formulation of an effective Grote–Hynes relationship for the classical correction to transition state theory. The predictions of the analytic theory are compared to computer simulation results for a model system and found to be in excellent agreement.
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