Improved approximate representation of the Hartree-Fock potential in atoms

Abstract

A new method is proposed to approximate the exchange-correlation potential in the Hartree-Fock equations for a many-electron atom. The exchange-correlation potential is separated into a self-interaction term and a characteristic exchange term. The self-interaction term is evaluated exactly, while the exchange term is approximated in a manner similar to Slater's statistical average method using a previously obtained theoretical exchange parameter $\alpha$. In the present method different potentials are used for different spin orbitals instead of the average potential used in the Hartree-Fock-Slater (HFS) scheme. The separation of the exchange-correlation potential into a self-interaction plus exchange terms removes all the major defects of the HFS potential, such as the wrong asymptotic behavior at large $r$ values and the underestimation of the self-interaction. The accuracy of the present method is demonstrated by calculations on the first-row transitionmetal ions ${\mathrm{Cu}}^{+}$ and ${\mathrm{Mn}}^{+2\mathrm{}}$. The results for exchange potentials, one-electron eigenvalues, spin density distribution, and contact hyperfine interaction agree excellently with Hartree-Fock values. The relative importance of the self-interaction and exchange terms for various electron shells are discussed. Computationally, the method is as simple as the Hartree-Fock-Slater scheme.