Abstract
We report a number of new exact expressions, within the realm of classical statistical mechanics, for the solvation contribution ΔA to the free energy change of a solute that undergoes a transformation between two states that differ in the way they interact with the solvent. Our basic result is a coupling-parameter expression that is equivalent to the usual cumulant expansion of ΔA. In our formula, which is derived from a linear coupling-parameter scheme, all the cumulant terms beyond the first one are collected into an integral over the coupling parameter. From this formula, with the help of the mean-value theorems of calculus, we derive exact one- and two-reference-point mean-energy expressions for the solvation free energy change, neither of which is limited to the linear response regime. Both the one- and the two-reference point formulae are given in terms of one distinguished value of the coupling parameter (
Acknowledgement
We dedicate this work to Ben Widom, whose many exact results have been crucial in shaping modern liquid-state thermodynamics. Support for this work from the National Science Foundation, award numbers 0029963 (for FOR) and CHE-0455968 (for DB-A) and the Department of Energy (for GS) is gratefully acknowledged.