Yukawa-Field Approximation of Electrostatic Free Energy and Dielectric Boundary Force

Abstract

A Yukawa-field approximation of the electrostatic free energy of a molecular solvation system with an implicit or continuum solvent is constructed. It is argued through the analysis of model molecular systems with spherically symmetric geometries that such an approximation is rational. The construction extends non-trivially that of the Coulomb-field approximation which serves as a basis of the widely used generalized Born model of molecular electrostatics. The electrostatic free energy determines the dielectric boundary force that in turn influences crucially the molecular conformation, stability, and dynamics. An explicit formula of such forces with the Yukawa-field approximation is obtained using local coordinates and shape differentiation.

Keywords: Molecular solvation; Yukawa-field approximation; electrostatic free energy; shape derivative.

Figure 1

The geometry of a solvation system with an implicit solvent.

Figure 2

Definition of the function f_i(·, κ, Γ).

Figure 3

A spherically symmetric model system. The grey region is the solute molecular region Ω₋ defined by (4.1). The white region is the solvent region Ω₊ defined by (4.2).

Figure 4

Local perturbation of the boundary Γ near z ∈ Γ.