Analytic evaluation of some three- and four- electron atomic integrals involving s STO's and exponential correlation with unlinked $r_{ij}$'s

TL;DR

This paper develops new analytical methods to evaluate complex three- and four-electron atomic integrals involving Slater-type orbitals and exponential correlations, providing explicit formulas and limiting expressions.

Contribution

It introduces novel closed-form and limiting expressions for specific multi-electron atomic integrals involving unlinked inter-electronic distances, extending previous evaluation techniques.

Findings

Derived closed-form expressions for multiple multi-electron integrals.

Established limiting expressions for these integrals.

Enhanced analytical tools for atomic structure calculations.

Abstract

The method of evaluation outlined in a previous work has been utilized here to evaluate certain other three- electron and four- electron atomic integrals involving s Slater-type orbitals and exponential correlation with unlinked $r_{ij}$'s. Limiting expressions for various such integrals have been derived, which has not been done earlier. Closed-form expressions for $<r_{12} r_{13} / r_{14}>$, $<r_{12}r_{34}/r_{23}>$, $<r_{12}r_{23}/r_{34}>$, $<r_{12}r_{13}/r_{34}>$ and $<r_{12}r_{34}/r_{13}>$ have been obtained.