Accurate Estimation of Solvation Free Energy Using Polynomial Fitting   Techniques
  This report details an approach to improve the accuracy and precision of free energy difference estimates using thermodynamic integration data (slope of the free energy with respect to the switching variable lambda) and its application to calculating solvation free energy. The central idea is to utilize polynomial fitting schemes to approximate the thermodynamic integration data to improve the accuracy and precision of the free energy difference estimates. In this report we introduce polynomial and spline interpolation techniques. Two systems with analytically solvable relative free energies are used to test the accuracy and precision of the interpolation approach (Shyu and Ytreberg, J Comput Chem 30: 2297-2304, 2009). We also use both interpolation and extrapolation methods to determine a small molecule salvation free energy. Our simulations show that, using such polynomial techniques and non-equidistant lambda values, the solvation free energy can be estimated with high accuracy without using soft-core scaling and separate simulations for Lennard-Jones and partial charges. The results from our study suggest these polynomial techniques, especially with use of non-equidistant lambda values, improve the accuracy and precision for dF estimates without demanding additional simulations. To allow researchers to immediately utilize these methods, free software and documentation is provided via http://www.phys.uidaho.edu/ytreberg/software 
Conrad Shyu and F. Marty Ytreberg