Reducing the Statistical Error of Free Energy Calculations Through Functional Optimization of Pair Potential Pathways

Improving the efficiency of free energy calculations is important for many chemcial engineering and materials design applications.  We show that for any pair potential, moderately accurate estimation of the radial distribution function for a solute molecule is sufficient to accurately estimate the statistical variance along a free energy pathway. This allows inexpensive analytical identification of low statistical error free energy pathways. We find that the computationally cheap two-body approximation for g(r) performs as well or better than 3D–RISM theory to identify low variance free energy pathways.  We use this method to minimize the variance of solvation free energy over the entire parameter space of a generalized "soft core" potential.  The free energy pathway arising from this optimization procedure reduces the total variance by at least 50% compared to thetraditional pathways.  This free energy variance optimizationtechnique is generalizable to solvation in any homogeneous fluid and for any type of pairwise potential.  We also compare this minimum pairwise statistical error to the theoretically lowest statistical error possible using less computationally tractable nonpairwise potentials.