Analytic Evaluation of two-electron Atomic Integrals involving Extended Hylleraas-CI functions with STO basis

TL;DR

This paper analytically evaluates key two-electron atomic integrals involving extended Hylleraas-CI functions with STO basis, simplifying calculations and providing closed-form expressions that match established results.

Contribution

It introduces analytical formulas for overlap, potential energy, and kinetic energy integrals involving extended Hylleraas-CI functions with STO basis, enhancing computational efficiency.

Findings

Analytical expressions agree with published results.

Simplified formulas for kinetic energy integrals.

Closed-form solutions for Hylleraas-CI related integrals.

Abstract

Some typical overlap/potential energy integrals which occur in the use of extended Hylleraas-configuration interaction (E-Hy-CI) functions with Slater-type orbital (STO) basis for two-electron atomic structure calculations, have been evaluated analytically. The corresponding kinetic energy integrals have been simplified first by using formulas derived from Gauss' divergence theorem in vector calculus, and then expressed in terms of overlap / potential energy matrix elements. Also closed-form expressions for such integrals which arise in the application of Hylleraas-CI functions, and CI functions have been obtained as special cases, and the calculated values are found to agree well with correct results published by other investigators.