Discrete Image Approximations of Ionic Solvent Induced Reaction Field to Charges

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.