Transition paths in molecules at finite temperature

Abstract

In the zero temperature limit, it is well known that in systems evolving via Brownian dynamics, the most likely transition path between reactant and product may be found as a minimizer of the Freidlin–Wentzell action functional. An analog for finite temperature transitions is given by the Onsager–Machlup functional. The purpose of this work is to investigate properties of Onsager–Machlup minimizers. We study transition paths for thermally activated molecules governed by the Langevin equation in the overdamped limit of Brownian dynamics. Using gradient descent in pathspace, we minimize the Onsager–Machlup functional for a range of model problems in one and two dimensions and then for some simple atomic models including Lennard-Jones seven-atom and 38-atom clusters, as well as for a model of vacancy diffusion in a planar crystal. Our results demonstrate interesting effects, which can occur at nonzero temperature, showing transition paths that could not be predicted on the basis of the zero temperature limit. However the results also demonstrate unphysical features associated with such Onsager–Machlup minimizers. As there is a growing literature that addresses transition path sampling by related techniques, these insights add a potentially useful perspective into the interpretation of this body of work.