Numerical Hartree–Fock–Slater calculations on diatomic molecules

A completely numerical method is presented for the calculation of Hartree–Fock–Slater wave functions in diatomic systems. The method is numerical in the sense that no LCAO basis sets are employed. Muffin tin or other cellular approximations are also avoided. All molecular functions are defined on a two-dimensional discrete mesh in prolate spheroidal coordinate space. The method is mathematically very simple, and numerical accuracy is easily controlled by changing the number of mesh points. Calculations on the molecules B2, C2, N2, CO, O2, and F2 are reported, and we compare dissociation energies, bond lengths, vibrational frequencies, and charge moments with recent LCAO results and with experiment. These calculations indicate that the method works very nicely for the molecules considered, and also that the Hartree–Fock–Slater theory describes molecular systems remarkably well.