  A recently developed statistical mechanical Quasi-Chemical 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 solute and solvent
are eliminated by spatial conditioning in this free energy piece, leading to
near-Gaussian distributions of solute-solvent interactions 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 the 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.
