Dynamic reaction paths and rates through importance-sampled stochastic dynamics

We extend a previously developed method, based on Wagner’s stochastic formulation of importance sampling, to the calculation of reaction rates and to a simple quantitative description of finite-temperature, average dynamic paths. Only the initial and final states are required as input—no information on transition state(s) is necessary. We demonstrate the method for a single particle moving on the two-dimensional Müller–Brown potential surface. Beyond computing the forward and reverse rates for this surface, we determine the average path, which exhibits “saddle point avoidance.” The method may be generalized to arbitrary numbers of degrees of freedom and to arbitrary types of stochastic dynamics.