Unsymmetrical and symmetrical one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials of integer and noninteger indices

TL;DR

This paper develops new one-range addition theorems for Slater type orbitals and Coulomb-Yukawa potentials with integer and noninteger indices, facilitating more efficient calculations in quantum chemistry.

Contribution

It derives general formulas for unsymmetrical and symmetrical addition theorems for STOs and CIPs involving noninteger principal quantum numbers, enhancing computational methods.

Findings

Formulas for one-center expansion relations of noninteger STOs in terms of integer STOs.

Derived addition theorems applicable to multicenter multielectron integrals.

Potential to improve accuracy and efficiency in quantum chemical calculations.

Abstract

Using one-center expansion relations for the Slater type orbitals (STOs) of noninteger principal quantum numbers in terms of integer n STOs derived in this study with the help of - exponential type orbitals (-ETOs, the general formulas are established for the unsymmetrical and symmetrical one-range addition theorems of STOs and Coulomb-Yukawa like correlated interaction potentials (CIPs) with integer and noninteger indices. The final results are especially useful for computations of arbitrary multicenter multielectron integrals over STOs that arise in the Hartree-Fock-Roothaan (HFR) approximation and also in the correlated methods which play a significant role in theory and application to quantum mechanics of atoms, molecules, and solids.