Derivation of Unified Analytic Electron Interaction Integrals over Slater Orbitals for Diatomic Molecules

TL;DR

This paper derives an analytic formula for electron interaction integrals over Slater orbitals in diatomic molecules, improving the efficiency of quantum chemical calculations involving correlated wavefunctions.

Contribution

It introduces a new analytic approach for evaluating complex electron interaction integrals, advancing computational methods in quantum chemistry.

Findings

Derived an explicit analytic formula for $r_{12}$ and $1/r_{12}$ integrals.

Discussed combinatorial aspects of multi-electron integrals.

Enhanced the computational efficiency for correlated wavefunction evaluations.

Abstract

In previous work, the necessary integrals arising from correlated wavefunctions were expressed in forms suitable for numerical integration. For the evaluation of $r_{12}$ and $1/r_{12}$ integrals an analytic formula is derived. Combinatorial aspects of more than two electron integrals are discussed.