Hydration Free Energies by Energetic Partitioning of the Potential Distribution Theorem

In the quasichemical theory of molecular solutions, the hydration free energy is spatially partitioned in a three-step thermodynamic process: cavity formation, solute insertion into the cavity, and relaxation of the cavity constraint. In the alternative local molecular field theory that focuses on the relationship of fluid structure and forces, the interaction energies are directly partitioned into local and far-field components; a restructured local potential incorporates information from the far-field interactions at the mean-field level. Here the quasichemical and local molecular field theories are related via energetic partitioning of the potential distribution theorem free energy. The resulting theory leads to a free energy division in which the local contribution requires direct evaluation, but the far-field component can be accurately estimated at the Gaussian level. A numerical approach for computing hydration free energies is developed that employs interaction energy distributions from several sampling states. Classical model problems of nonpolar, polar, and ionic hydration are presented to illustrate the theory. Extensions of the theory for estimating free energies at the quantum level are also discussed.