A one-centre S.C.F. wave function for the methane molecule

A Hartree-Fock single-determinant wave function is calculated for the ground state of the methane molecule. The one-electron molecular orbitals in this determinant are expanded up to third-order terms as a series of spherical harmonics about the central carbon nucleus. The potential field due to the nuclei is correspondingly expanded up to sixth-order terms and the complete Hartree-Fock S.C.F. equations are set up and solved numerically for the six radial functions occurring in the molecular orbitals. The numerical techniques employed differ in certain respects from those used in previous atomic calculations. The total molecular energy obtained from this approximation is -39·90 a.u. The spherically symmetric model, in which only the first term in each expansion is retained, is re-examined to settle an uncertainty in the associated energy value; this energy value is here found to be -39·53 a.u.