Manifestations of spatially dependent friction in classical activated rate processes

Abstract

Classical activated rate processes are examined for systems which are influenced by a spatially dependent friction on the reaction coordinate motion. In these systems, the spatial dependence of the friction kernel arises from nonlinear couplings between the reaction coordinate and a many-dimensional harmonic oscillator representation of the bath fluctuations. This model is thought to provide a reasonable representation of many charge transfer reactions in polar solvents. One of the systems studied corresponds to the case where the friction along the reaction coordinate is weaker in the region of the barrier than in the reactant and product states, while the second system exhibits the opposite behavior. In the first system, significant effects due to the nonlinear dissipation are found over the entire range of the friction strength. In the second system, the nonlinear effects are largely confined to the weak to intermediate damping regime, but they can be quite large. Interestingly, for some values of the nonlinearity parameters, the second system does not exhibit a simple single exponential rate behavior for a long period of time. Mathematical analysis is provided to help explain the computer simulation results in both the weak and strong damping limits of each system.