Computational studies are presented which examine the accuracy of two approximate theories for activated rate processes in condensed matter classical systems. One theory is based on the generalized Langevin equation and the other on multidimensional transition state theory. The specific focus is on studies of effective Hamiltonians which contain nonlinear coupling terms between the reaction coordinate and bath coordinates. Two of these systems phenomenologically describe the activated dynamics of realistic physical problems. The reactive flux correlation function method is used to calculate the numerically exact rate constant and, in turn, compared to the value of the rate constant calculated from approximate analytic theories. In all cases, the value of the rate constant exhibits a dependence on the nonlinearities in the equations of motion. The results suggest that the generalized Langevin equation model and multidimensional harmonic transition state theory may give different predictions for the activated rate constant in nonlinear systems and that both theories should be applied with some care.

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