Quasi-Chemical Theory and Implicit Solvent Models for Simulations

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 idea is geometrically to define molecular-scale regions attached to the solute macromolecule of interest. It is then shown that the quasi-chemical approach corresponds to calculation of a partition function for an ensemble analogous to, but not the same as, the grand canonical ensemble for the solvent in that proximal volume. The distinctions include: (a) the defined proximal volume — the volume of the system that is treated explicitly — resides on the solute; (b) the solute conformational fluctuations are prescribed by statistical thermodynamics and the proximal volume can fluctuate if the solute conformation fluctuates; and (c) the interactions of the system with more distant, extra-system solution species are treated by approximate physical theories such as dielectric continuum theories. The theory makes a definite connection to statistical thermodynamic properties of the solution and fully dictates volume fluctuations, which can be awkward in more ambitious approaches. It is argued that with the close solvent neighbors treated explicitly the thermodynamic results become less sensitive to the inevitable approximations in the implicit solvent theories of the more distant interactions. 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.