Perturbative many-body expansion for electrostatic energy and field for system of polarizable charged spherical ions in a dielectric medium.

Abstract

An analytical solution for the electrostatic energy and potential for a system of charged, polarizable spheres in a dielectric medium is developed from a multiple scattering expansion that is equivalent to a formal solution to Poisson's equation for the system. The leading contributions emerge in the form of effective two-, three-, and four-body interactions that are explicit analytical functions of the sphere positions, charges, and internal dielectric constants and the external dielectric constant, thereby also enabling analytical computation of the electrostatic forces on the ions. Tests of successive terms demonstrate their rapid convergence. Similar methods can be used to evaluate higher order contributions and the expansion for the electrostatic field. The results will prove far more efficient for MD and MC simulations with spherical particles than current approximate methods that require the computation of surface polarization charge distributions but that apply also for systems with complex geometries.