Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds

A recently developed statistical mechanical quasichemical theory (QCT) has led to significant insights into solvation phenomena for both hydrophilic and hydrophobic solutes. The QCT exactly partitions solvation free energies into three components: (1) Inner-shell chemical, (2) outer-shell packing, and (3) outer-shell long-ranged contributions. In this paper, we discuss efficient methods for computing each of the three parts of the free energy. A Bayesian estimation approach is developed to compute the inner-shell chemical and outer-shell packing contributions. We derive upper and lower bounds on the outer-shell long-ranged portion of the free energy by expressing this component in two equivalent ways. Local, high-energy contacts between the solute and solvent are eliminated by spatial conditioning in this free energy piece, leading to near-Gaussian distributions of solute-solvent interaction energies. Thus, the average of the two mean-field bounds yields an accurate and efficient free energy estimate. Aqueous solvation free energy results are presented for several solutes, including methane, perfluoromethane, water, and sodium and chloride ions. The results demonstrate the accuracy and efficiency of the methods. The approach should prove useful in computing solvation free energies in inhomogeneous, restricted environments.