Single-stage direct Langevin dynamic simulations of transitions over arbitrary high energy barriers: Concept of the energy-dependent temperature

TL;DR

This paper introduces a novel single-stage Langevin dynamics algorithm using an energy-dependent temperature to efficiently simulate transitions over high energy barriers, achieving significant speedups and avoiding stability issues of multi-stage methods.

Contribution

The paper presents a new algorithm employing energy-dependent temperature for direct Langevin simulations, enabling barrier-independent computation time and improved stability over existing methods.

Findings

Simulation time does not increase with energy barrier height.

Results agree well with forward flux sampling (FFS) method.

Method achieves large speedup compared to FFS.

Abstract

In this paper we present an algorithm which allows single-stage direct Langevin dynamics simulations of transitions over arbitrary high energy barriers employing the concept of the energy-dependent temperature (EDT). In our algorithm, simulation time required for the computation of the corresponding switching rate does not increase with energy barrier. This is achieved by using in simulations an effective temperature which depends on the system energy: around the energy minima this temperature is high and tends towards the room temperature when the energy approaches the saddle point value. Switching times computed via our EDT algorithm show an excellent agreement with results obtained with the established forward flux sampling (FFS) method. As the simulation time required by our method does not increase with the energy barrier, we achieve a very large speedup when compared even to the highly optimized FFS version. In addition, our method does not suffer from stability problems occurring in multi-stage algorithms (like FFS and 'energy bounce' methods) due to the multiplication of a large number of transition probabilities between the interfaces.