Computing Transition Rates for Rare Event: When Kramers Theory meets Free Energy Landscape

TL;DR

This paper develops a novel approach combining Kramers' Theory and metadynamics to accurately compute transition rates for rare events in complex systems, accounting for free energy barriers and configurational entropy.

Contribution

It introduces a new formalism that integrates FE barrier height and entropy measures to improve rate calculations beyond standard Kramers' Theory.

Findings

Good agreement with simulations and experiments

Significant improvement over standard KT

Applicable to complex systems with competing entropy and energy

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.