Discrete Charge Dielectric Model of Electrostatic Energy

Studies on nanoscale materials merit careful development of an electrostatics model concerning discrete point charges within dielectrics. The discrete charge dielectric model treats three unique interaction types derived from an external source: Coulomb repulsion among point charges, direct polarization between point charges and their associated surface charge elements, and indirect polarization between point charges and surface charge elements formed by other point charges. The model yields the potential energy, U(N), stored in a general $N$ point charge system differing from conventional integral formulations, $1\mathrm{/}2\int \mathit{E}\cdot \mathit{D}dV$ and $1\mathrm{/}2\int \rho \mathrm{\Phi }dV$, in a manner significant to the treatment of few electron systems.