Boundary integral methods for the Poisson equation of continuum dielectric solvation models

Abstract

This article tests a dielectric model for the variation of hydration free energy with the geometry of complex solutes in water. It reexpresses the Poisson equation of the model to examine the basic aspects of boundary integral methods for these problems. It compares eight examples of dielectric model potentials of mean force in water with numerical results obtained from molecular scale models by simulation. Instructive and physical results are obtained but the model overstabilizes attractive, ion-pairing configurations. The article describes the algorithms, alternative to those in the literature, used here for high-precision solutions of that Poisson equation. Anticipating multigrid boundary integral approaches for similarly accurate treatment of larger solution complexes, the adaptation of spatial resolution is discussed. Finally, the statistical mechanical theory of the model is discussed together with a new proposal for describing the molecular detail of the solvation properties: integrating-out a probe solvent molecule using the dielectric model. The appendices give formal results relevant to periodic boundary conditions and infinite area surfaces such as solution interfaces and membranes. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 64: 121–141, 1997