Unified treatment of complex and real rotation-angular functions for two-center overlap integrals over arbitrary atomic orbitals

TL;DR

This paper develops unified formulas for complex and real rotation-angular functions to evaluate two-center overlap integrals over arbitrary atomic orbitals, aiding quantum mechanical calculations across various atomic and molecular systems.

Contribution

It introduces a unified approach for complex and real rotation-angular functions in overlap integral calculations, extending previous work to improve computational methods.

Findings

Formulas applicable to both complex and real atomic orbitals

Useful for calculations involving atoms, molecules, nuclei, and solids

Enhances accuracy and efficiency in quantum mechanical computations

Abstract

The new combined formulas have been established for the complex and real rotation-angular functions arising in the evaluation of two-center overlap integrals over arbitrary atomic orbitals in molecular coordinate system. These formulas can be useful in the study of different quantum mechanical problems in both the theory and practice of calculations dealing with atoms, molecules, nuclei and solids when the integer and noninteger n complex and real atomic orbitals basis sets are emploed. This work presented the development of our previous paper (I.I. Guseinov, Phys. Rev. A, 32 (1985) 1864).