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

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 (DeltaS) 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 DeltaS <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(DeltaS/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(DeltaS/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 DeltaS is required to apply this heuristic, it is "safe" in that any inaccuracy in this DeltaS will be such that the group M exp(DeltaS/k) is even smaller than it is for the true DeltaS, and will therefore still warn of an inaccurate result. The analysis is demonstrated for a very wide range of DeltaS 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 DeltaS/k=-1; however, consideration of the precision instead prescribes that DeltaS/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. (C) 2001 American Institute of Physics.