Accuracy of free-energy perturbation calculations in molecular simulation. II. Heuristics

Abstract

We examine issues involved in applying and interpreting free-energy perturbation (FEP) calculations in molecular simulation, with the aim to develop simple heuristics that can guide their use and warn when a result is likely to be inaccurate. We build on the accuracy model developed in the first paper of this series [N. Lu and D. A. Kofke, J. Chem. Phys. 114, 7303 (2001)], which emphasized the sign of the entropy difference (ΔS) between the target and reference systems as an essential indicator for the correct implementation of FEP calculations: such calculations must be performed in the “insertion” direction, for which ΔS<0, or else they are very likely to be systematically incorrect (i.e., inaccurate). We describe here an extended analysis for insertion FEP calculations, and identify the group M exp(ΔS/k), where M is the number of independent FEP samples taken and k is Boltzmann’s constant, as a relevant quantity for characterizing the accuracy of FEP result. We find that if M exp(ΔS/k) is of order 100 or larger, then one can expect the FEP calculation to yield a result of minimally acceptable accuracy; for a margin of safety a value of 1000 or greater is preferable for this group. Although the FEP-measured ΔS is required to apply this heuristic, it is “safe” in that any inaccuracy in this ΔS will be such that the group M exp(ΔS/k) is even smaller than it is for the true ΔS, and will therefore still warn of an inaccurate result. The analysis is demonstrated for a very wide range of ΔS values, considering a model FEP calculation, a hard-sphere insertion calculation, and a diameter-change FEP in the Lennard-Jones model. We apply the results of this analysis, and earlier work, to consider the question of the optimal number of intermediate stages to use in a staged FEP calculation. The analysis shows that, for optimal accuracy, stages should be selected such that the entropy difference per stage satisfies ΔS/k=−1; however, consideration of the precision instead prescribes that ΔS/k=−2. Inasmuch as the precision is the larger concern once accuracy reaches an acceptable level, the latter criterion forms our recommendation for selecting the number of intermediate stages.