Unified Treatment of One- and Two-Electron Multicenter Integrals for Harmonic Oscillator Functions

Abstract

Compact formulas are derived for one‐ and two‐electron multicenter energy integrals between an orthogonal basis of isotropic harmonic oscillator (Gaussian) functions in Cartesian coordinates. Up to four centers are considered. Overlap and kinetic energy integrals are given in closed form, but the potential energy integrals require a one‐dimensional numerical quadrature. A technique due to Smirnov was used to obtain all formulas.