Variationally Derived Intermediates for Correlated Free Energy Estimates between Intermediate States

TL;DR

This paper introduces a variational method to optimize intermediate states in free energy calculations, accounting for correlations to improve accuracy and efficiency in atomistic simulations.

Contribution

It develops a novel variational framework that derives optimal intermediate states and estimators considering correlations, enhancing free energy difference estimates.

Findings

Derives a sequence of intermediates minimizing mean squared error.

Proposes an estimator that accounts for correlations between samples.

Demonstrates improved accuracy over traditional methods.

Abstract

Free energy difference calculations based on atomistic simulations generally improve in accuracy when sampling from a sequence of intermediate equilibrium thermodynamic states that bridge the configuration space between two states of interest. For reasons of efficiency, usually the same samples are used to calculate the step-wise difference of such an intermediate to both adjacent intermediates. However, this procedure violates the assumption of uncorrelated estimates that is necessary to derive both the optimal sequence of intermediate states and the widely used Bennett acceptance ratio (BAR) estimator. In this work, via a variational approach, we derive the sequence of intermediate states and the corresponding estimator with minimal mean squared error that account for these correlations and assess its accuracy.