  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

Computational Physics