Expansion formulae for one- and two-center charge densities over complete orthonormal sets of exponential type orbitals and their use in evaluation of multicenter-multielectron integrals

TL;DR

This paper develops expansion formulae for charge densities over exponential type orbitals and applies them to evaluate multicenter-multielectron integrals in quantum chemistry, enhancing computational methods.

Contribution

It introduces general formulae for charge densities over exponential orbitals and demonstrates their use in calculating complex multicenter integrals in electronic structure methods.

Findings

Derived series expansion formulae for charge densities.

Expressed three-center overlap integrals via two-center integrals.

Validated formulas for arbitrary quantum numbers and orbital parameters.

Abstract

The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations are expressed through the two-center overlap integrals between -orbitals. The general formulae obtained for the charge densities are utilized for the evaluation of arbitrary multicenter-multielectron integrals occurring when the complete orthonormal sets of exponential type orbitals are used as basis functions in the Hartree-Fock-Roothaan and explicitly correlated methods. The relationships for charge densities and multicenter-multielectron integrals obtained are valid for the arbitrary quantum numbers, screening constants and location of orbitals.