Analytic Evaluation of Three Different Five-Electron Atomic Integrals Involving Exponentially Correlated Functions of $r_{ij}$ With $r_{ij}$'s Not Forming A Closed Loop

TL;DR

This paper presents an analytic method to evaluate three specific five-electron atomic integrals involving exponential correlations, expanding the computational tools for multi-electron atomic systems.

Contribution

It introduces a simple analytic approach for five-electron integrals with non-looping exponential correlations, extending previous methods for multi-electron atomic calculations.

Findings

Successfully evaluated three five-electron integrals analytically.

Method applicable to integrals with non-looping exponential correlations.

Enhances computational techniques for complex atomic systems.

Abstract

The simple method outlined in our earlier paper [B.Padhy, Orissa Journal of Physics, vol.19, No.1, p.1, February 2012] has been utilized here for analytic evaluation of three different five-electron atomic integrals with integrands involving products of s Slater-type orbitals and exponentially correlated functions of the form $r_{ij} exp(-\lambda_{ij} r_{ij})$. Only products of those $r_{ij}$'s which do not form a closed loop by themselves, are considered.