Commun. Comput. Phys., 2 (2007), pp. 1007-1026.

Discrete Image Approximations of Ionic Solvent Induced Reaction Field to Charges

Shaozhong Deng 1*, Wei Cai 1

1 Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001, USA.

Received 18 January 2007; Accepted (in revised version) 17 February 2007
Available online 18 April 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 $u=\la$ ($\lambda$ -- 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.

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PACS: 41.20.Cv, 02.60.-x
Key words: Method of images, reaction field, ionic solvent, hybrid solvation model.

*Corresponding author.
Email: (S. Deng), (W. Cai)

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