Discrete Image Approximations of Ionic Solvent Induced Reaction Field to Charges

Abstract

Two methods of discrete images are proposed to approximate the reaction field from ionic solvent for a point charge inside a dielectric spherical cavity. Fast and accurate calculation of such a reaction field is needed in hybrid explicit/implicit solvation models of biomolecules. A first- and a second-order image approximation methods, in the order of u=λa (λ – the inverse Debye screening length of the ionic solvent, a – the radius of the spherical cavity), are derived. Each method involves a point image at the conventional Kelvin image point and a line image along the ray from the Kelvin image point to infinity. Based on these results, discrete point images are obtained by using Jacobi-Gauss quadratures. Numerical results demonstrate that two to three point images are sufficient to achieve a 10−3 accuracy in the reaction field with the second-order image approximation.