Quantum-Mechanical Integrals over Gaussian Atomic Orbitals

Formulas for the one-, two-, three-, and four-center energy integrals are derived using the general class of single-particle Gaussian atomic orbitals χ=xiyjzk exp[−(α1x2+α2y2+α3z2)].The overlap, kinetic energy, and dipole moment integrals are given in closed form. The potential energy integrals require a one-dimensional numerical quadrature. A technique due to Singer was used in obtaining these latter formulas.