Evaluation of potential energy of interaction between molecules using one-range addition theorems for Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials

TL;DR

This paper develops new mathematical formulas using one-range addition theorems for Slater type orbitals and Coulomb-Yukawa potentials, enabling detailed analysis of molecular interactions especially in complex atomic-molecular systems.

Contribution

It introduces series expansion formulas for molecular potential and interaction energy using noninteger orbital indices, applicable to systems with various electron shell configurations.

Findings

Formulas valid for arbitrary indices and screening constants.

Applicable to systems with multiple open and closed shells.

Enhances methods for Hartree-Fock-Roothaan and correlated calculations.

Abstract

Using one-range addition theorems for noninteger n Slater type orbitals and Coulomb-Yukawa like correlated interaction potentials with noninteger indices obtained by the author with the help of complete orthonormal sets of exponential type orbitals, the series of expansion formulas are established for the potential produced by molecule, and the potential energy of interaction between molecules through the radius vectors of nuclei of molecules, and the linear combination coefficients of molecular orbitals. The formulae obtained are useful especially for the study of interaction between atomic-molecular systems containing any number of closed and open shells when the Hartree-Fock-Roothaan and explicitly correlated methods are employed. The relationships obtained are valid for the arbitrary values of indices and screening constants of orbitals and correlated interaction potentials.