Numerical Single-Center Self-Consistent-Field Function for the Hydrogen Molecule

Abstract

A Hartree–Fock single‐determinant wavefunction is calculated numerically for the normal state ${}^1{\Sigma }_g^{+}$ of the hydrogen molecule. The one‐electron molecular orbitals in this determinant are expanded up to fourth‐order terms as a product of a series of spherical harmonics and radial wavefunctions about the molecular midpoint of the molecule. The potential field due to the nuclei is expanded in spherical harmonics up to eighth‐order terms and the complete Hartree–Fock equations are set up and solved numerically for the three radial functions occurring in one‐electron molecular orbitals. The numerical technique used to solve the three coupled second‐order differential–integral equations differs from that usually used in atomic calculations. The total numerical energy is −1.13236 a.u. The more accurate Kolos and Roothaan analytic total energy result is −1.13364 a.u.