Dielectric Screening in a Spherical Cavity

TL;DR

This paper derives approximate electrostatic screening potentials for a point charge in a spherical dielectric cavity, providing analytical expressions useful for molecular dynamics simulations involving charged molecules.

Contribution

It introduces new analytical expressions for the screening potential expanded to third order in dielectric constant, with error bounds, for off-center charges in spherical cavities.

Findings

Closed-form expressions up to third order in ε

Error bounds for the approximations

Potential applications in molecular dynamics simulations

Abstract

In this work we examine the electrostatic screening potential due to a point charge located off-centre in a spherical dielectric cavity. This potential is expanded for the case in which the dielectric constant $\epsilon$ is large, several methods of finding the terms in the expansion are investigated, and closed-form expressions are found through third order in $\epsilon$ along with error bounds. Finally, possible uses of these expressions in molecular dynamics simulations of isolated charged molecules is discussed.