Electrostatic interaction between two point charges in spherical cavities embedded in dielectric continuum revisited: role of high-order multipole interactions

Abstract Electrostatic interactions between charged species in polar solvents are universally important in a wide area of chemistry. Being complementary to sophisticated, quantitative modelling, it is useful to simplify the problem as much as possible to offer clear interpretation of the underlying physics. In the present study, we investigate, from both analytical and numerical points of view, the electrostatic interaction between two ions in separate cavities in a dielectric continuum. Truncating the multipolar interactions up to the quadrupolar level, an analytical expression for the interaction energy is derived; to the best of our knowledge, the formally exact formula up to the R−6 terms, with R being the distance between ion centers, is first presented. Numerical results are presented for two example cases, i.e., Na+/Cl− interaction in water and methanol, and protein–protein (barnase–barstar) interactions in water. The interaction energies are separately evaluated for R−1, R−4, and R−6 terms and their role is discussed.