# Efficient estimation of free energy differences from Monte Carlo data

## Abstract

Near-optimal strategies are developed for estimating the free energy difference between two canonical ensembles, given a Metropolis-type Monte Carlo program for sampling each one. The estimation strategy depends on the extent of overlap between the two ensembles, on the smoothness of the density-of-states as a function of the difference potential, and on the relative Monte Carlo sampling costs, per statistically independent data point. The best estimate of the free energy difference is usually obtained by dividing the available computer time approximately equally between the two ensembles; its efficiency (variance x computer time)-1 is never less, and may be several orders of magnitude greater, than that obtained by sampling only one ensemble, as is done in perturbation theory. © 1976.