Optimal intermediates in staged free energy calculations

Abstract

We examine the precision of free energy perturbation (FEP) methods of molecular simulation. We develop a quantitative model of the calculation in terms of the so-called f and g distributions that characterize the energies sampled in a FEP calculation. The model is then re-expressed in terms of the entropy difference between the systems of interest, and the variance of the g distribution. We apply the model to analyze the optimization of multistage insertion free energy calculations, and reach a quantitative criterion for minimizing the overall variance. The analysis indicates that the appropriate heuristic for optimizing the choice of intermediates is to select them to equalize the entropy differences among all stages of the overall FEP calculation. A more accurate criterion is specified, but in practice it differs little from this simpler one. We illustrate our conclusions by conducting two-stage FEP calculations using Monte Carlo simulations on Lennard-Jones (LJ) systems at several temperatures and two densities. The LJ systems differ in the presence of a single LJ particle, and the intermediate is defined to have a single hard sphere of diameter that can be used to optimize the two-stage FEP calculation. The model provides an excellent description of the precision of the FEP calculations.