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

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Abstract
A Hartree–Fock single-determinant wavefunction is calculated numerically for the normal state Σg+1 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.

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