Unified Treatment of Two-Center, Two-Electron Integrals. I. Electron-Repulsion, Spin-Spin, and Spin-Orbit Integrals Over Slater Functions

Abstract

Utilizing the Neumann expansions of the electron-repulsion operator, all two-electron two-center spin-spin, spin-orbit, and electron-repulsion, hybrid, Coulomb, and exchange integrals arising in computations of expectation values of the respective operators over wavefunctions written as linear combinations of Slater functions are expressed in terms of a simple formula requiring, effectively, a one-dimensional numerical integration. A general formula for one-center integrals is also derived by utilizing the Laplace expansion of the electron-repulsion operator.