Sampling along reaction coordinates with the Wang-Landau method

TL;DR

This paper adapts the Wang-Landau algorithm to efficiently compute free energy profiles along reaction coordinates in molecular systems, avoiding complex constraints and biasing potentials.

Contribution

It introduces a generalized method for extracting partial averages in various ensembles using the Wang-Landau algorithm, demonstrated on multiple molecular models.

Findings

Accurate free energy profiles for a 10D potential energy surface.

Application to dihedral angle of butane in different environments.

Comparison of isomerization results with parallel tempering Monte Carlo.

Abstract

The multiple range random walk algorithm recently proposed by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)] is adapted to the computation of free energy profiles for molecular systems along reaction coordinates. More generally, we show how to extract partial averages in various statistical ensembles without invoking simulations with constraints, biasing potentials or unknown parameters. The method is illustrated on a model 10-dimensional potential energy surface, for which analytical results are obtained. It is then applied to the potential of mean force associated with the dihedral angle of the butane molecule in gas phase and in carbon tetrachloride solvent. Finally, isomerization in a small rocksalt cluster, Na4F4, is investigated in the microcanonical ensemble, and the results are compared to those of parallel tempering Monte Carlo.