A new expansion of the Coulomb potential and linear $r_{ij}$ terms

TL;DR

This paper introduces new convergent expansions for the Coulomb potential and interparticle distance that are valid throughout the entire coordinate space, including near singularities, despite resulting in complex functional forms.

Contribution

The work presents novel expansions for Coulomb potential and $r_{12}$ that converge everywhere, improving accuracy near singularities compared to traditional methods.

Findings

Expansions converge to the exact value across all space.

The expansions include complex goniometric functions.

Simplification methods for these expansions are discussed.

Abstract

In this work a new expansions of Coulomb potential and interparticle distance, linear term $r_{12}$ are proposed. Except the singularities, the expansions converge to the exact value in the whole coordinate space including the vicinity of the singularities or correlation cusps points. The disadvantage of the expansion is, that it leads to complicated goniometric functional forms. Anyway, for their simplification, we used the method of their expansion developed by the author in the past.