An integral equation approach to calculate electrostatic interactions in many-body dielectric systems

Highlights: • Numerically efficient solution to the problem of calculating electrostatic interactions between many dielectric particles is presented. • The method is general as it treats systems containing an arbitrary number of particles of any size, charge, dielectric constant. • The algorithmic complexity is reduced to linear scaling with respect to the number of particles. • The effect of polarization at short separations on the electrostatic force is considered. • The method is tested by the accurate estimations of the Madelung energy and constant of halite lattice. In this article, a numerical method to compute the electrostatic interaction energy and forces between many dielectric particles is presented. The computational method is based on a Galerkin approximation of an integral equation formulation, which is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. The algorithmic complexity is linear scaling with respect to the number of particles for the computation of the energy which has been achieved through the use of a modified fast multipole method. The method scales with the third power of the degree of spherical harmonics used in the underlying expansions, for general three-dimensional particle configurations. Several simple numerical examples illustrate the capabilities of the model, and the influence of mutual polarization between particles in an electrostatic interaction is discussed.