Discrete Image Approximations of Ionic Solvent Induced Reaction Field to Charges (Communications in Computational Physics, 2007)
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.