Wave Functions and Energy Levels for Fe as Found by the Unrestricted Hartree-Fock Method

Results of a self-consistent field calculation using Slater's average exchange potential are given for atomic iron. The usual restriction of doubly filled orbitals in closed shells is dropped and orbitals, with the same $n$ and $l$ quantum numbers but different $m_s$ are varied separately. This results in a separate set of radial wave functions for the two one-electron spin directions. The differences in these functions arise from an exchange polarization effect produced by the net spin of the Fe atom. Wave functions, one-electron energy parameters, net spin charge density, and electrostatic potential functions for each spin are given. A comparison is made between these results and those obtained by the Hartree method. The magnetic form factor found with these new Fe orbitals is shown to be in good agreement with experiment. The fine-structure splittings are also evaluated and found not to be in as good agreement as those calculated by the Hartree method. The hyperfine splitting of the ${\mathrm{Mn}}^{++}$ ion is estimated using the new orbitals and found to be in much better agreement than estimates based on a limited configuration interaction.