  A statistical thermodynamic development is given of a new implicit solvent
model that avoids the traditional system size limitations of computer
simulation of macromolecular solutions with periodic boundary conditions. This
implicit solvent model is based upon the quasi-chemical approach, distinct from
the common integral equation trunk of the theory of liquid solutions. The
physical content of this theory is the hypothesis that a small set of solvent
molecules are decisive for these solvation problems. A detailed derivation of
the quasi-chemical theory escorts the development of this proposal. The
numerical application of the quasi-chemical treatment to Li$^+$ ion hydration
in liquid water is used to motivate and exemplify the quasi-chemical theory.
Those results underscore the fact that the quasi-chemical approach refines the
path for utilization of ion-water cluster results for the statistical
thermodynamics of solutions.
