One-Range Addition Theorems in Terms of -ETOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials of Integer and Noninteger Indices

TL;DR

This paper develops one-range addition theorems using -exponential type orbitals for Slater type orbitals and Coulomb-Yukawa potentials, aiding multicenter integral calculations in quantum chemistry.

Contribution

It introduces new one-center expansion formulas in terms of -ETOs for STOs and Coulomb-Yukawa potentials, applicable to integer and noninteger indices.

Findings

Derived one-range addition theorems for STOs and CIPs.

Formulas facilitate multicenter multielectron integral calculations.

Applicable to Hartree-Fock-Roothaan and explicitly correlated methods.

Abstract

In this study, the one-center expansion formulas in terms of complete orthonormal sets of -exponential type orbitals (-ETOs,) are established for the Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) of integer and noninteger indices. These relations are used in obtaining the unsymmetrical and symmetrical one-range addition theorems for STOs and Coulomb-Yukawa like CIPs. The final results are especially useful in the calculations of multicenter multielectron integrals of STOs and CIPs occurring when Hartree-Fock-Roothaan (HFR) and explicitly correlated method are employed.