Bipolar expansions and overlap corrections to the electrostatic interaction energy

TL;DR

This paper derives multiple bipolar expansion formulas for the inverse distance and applies perturbation theory to compute overlap corrections to electrostatic energy between hydrogen atoms and protons.

Contribution

It introduces four equivalent bipolar expansion expressions and calculates overlap corrections to electrostatic interactions using perturbation theory.

Findings

Derived four bipolar expansion formulas valid everywhere.

Calculated overlap corrections for hydrogen interactions.

Enhanced understanding of electrostatic energy corrections.

Abstract

We use the multipole technique to derive four equivalent expressions for the bipolar expansion of the inverse distance, valid in all the regions of configuration space. Using the first-order perturbation theory, we calculate the overlap correction to the long-range electrostatic energy between two hydrogen atoms and between a hydrogen atom and a proton.