Computing transition rates for rare events: When Kramers theory meets the free-energy landscape

Abstract

Computing reactive trajectories and free energy (FE) landscapes associated to rare event kinetics is key to understanding the dynamics of complex systems. The analysis of the FE surface on which the underlying dynamics takes place has become central to compute transition rates. In the overdamped limit, most often encountered in biophysics and soft condensed matter, the Kramers' Theory (KT) has proved to be quite successful in recovering correct kinetics. However, the additional calculation to obtain rate constants in complex systems where configurational entropy is competing with energy is still challenging conceptually and computationally. Building on KT and the metadynamics framework, the rate is expressed in terms of the height of the FE barrier measured along the minimum FE path and an auxiliary measure of the configurational entropy. We apply the formalism to two different problems where our approach shows good agreement with simulations and experiments and can present significant improvement over the standard KT.