Free energy derivatives: A new method for probing the convergence problem in free energy calculations

Abstract

AbstractThe convergence behavior of free energy calculations has been explored in more detail than in any previously reported work, using a model system of two neon atoms in a periodic box of water. We find that for thermodynamic integration‐type free energy calculations as much as a nanosecond or more molecular dynamics sampling is required to obtain a fully converged value for a single λ point of the integrand. The concept of “free energy derivatives” with respect to the individual parameters of the force field is introduced. This formalism allows the total convergence of the simulation to be deconvoluted into components. A determination of the statistical “sampling ratio” from these simulations indicates that for window‐type free energy calculations carried out in a periodic waterbox of typical size at least 0.6 ps of sampling should be performed at each window (0.7 ps if constraint contributions to the free energy are being determined). General methods to estimate and reduce the error in thermodynamic integration and free energy perturbation calculations are discussed. We show that the difficulty in applying such methods is determining a reliable estimate of the correlation length from a short series of data. © 1994 by John Wiley & Sons, Inc.