Using non-Gaussian density functional fits to improve relative free energy calculations

The accurate and reliable computation of relative free energy differences remains an important long-term goal. Major stumbling blocks for achieving this goal reflect the difficulty of sampling in a known fashion along the reaction coordinate and of maximally combining information that has been collected from the simulation along the reaction coordinate. In this paper we examine the utility of a probability density functional type fit to the distribution of work events collected during a nonequilibrium sample along the reaction coordinate. This approach can readily be generalized to equilibrium sampling and has the potential to estimate the quality of a relative free energy estimate as data are being collected. The method may have the greatest utility for nonequilibrium sampling where non-Gaussian work distributions are generally present that are strongly dominated by rare event sampling in the tail region. We believe that the approach can be used to augment the design and the error analysis of relative free energy computations thus improving the ability to reliably and with known accuracy compute a relative free energy.