Efficient dynamical correction of the transition state theory rate estimate for a flat energy barrier

TL;DR

This paper introduces an efficient hyperplane-based method to accurately compute recrossing corrections in transition state theory for flat energy barriers, significantly reducing computational effort especially at low temperatures.

Contribution

The authors develop a novel hyperplane sequence approach for calculating recrossing corrections, improving efficiency over traditional methods in flat barrier scenarios.

Findings

Method agrees well with Langevin dynamics and forward flux sampling.

Speeds up recrossing correction calculations by an order of magnitude.

Effective for polymers with up to 64 beads at various temperatures.

Abstract

The recrossing correction to the transition state theory estimate of a thermal rate can be difficult to calculate when the energy barrier is flat. This problem arises, for example, in polymer escape if the polymer is long enough to stretch between the initial and final state energy wells while the polymer beads undergo diffusive motion back and forth over the barrier. We present an efficient method for evaluating the correction factor by constructing a sequence of hyperplanes starting at the transition state and calculating the probability that the system advances from one hyperplane to another towards the product. This is analogous to what is done in forward flux sampling except that there the hyperplane sequence starts at the initial state. The method is applied to the escape of polymers with up to 64 beads from a potential well. For high temperature, the results are compared with direct Langevin dynamics simulations as well as forward flux sampling and excellent agreement between the three rate estimates is found. The use of a sequence of hyperplanes in the evaluation of the recrossing correction speeds up the calculation by an order of magnitude as compared with the traditional approach. As the temperature is lowered, the direct Langevin dynamics simulations as well as the forward flux simulations become computationally too demanding, while the harmonic transition state theory estimate corrected for recrossings can be calculated without significant increase in the computational effort.