Interconfigurational Energy Research Articles

Exact-exchange extension of the local-spin-density approximation in atoms. II. The iron series

s-d interconfigurational energies, s-spin flip energies, and ionization potentials for atoms in the first transition series are calculated within a local-spin-density scheme, where the exchange is treated exactly. The results so obtained are in better agreement with experiments than those obtained by the Hartree–Fock (HF) or local-spin-density approximations (LSDA), while they are of the same quality as those obtained by the self-interaction-corrected (SIC) version of the LSDA. The merits of the proposed scheme with respect to the other mentioned approximations are discussed in detail.

Density functional calculations for atoms in the first transition series

s-d interconfigurational energies and spin-flip energies for atoms in the first transition series are examined in the self-interaction-corrected local spin density approximation (SIC-LSDA). The results are substantially improved over previous LSDA calculations and SIC-LSDA calculations employing sphericalized orbital densities. The implications for accurate cohesive energy calculations and molecular bonding in iron-series dimers are discussed.

Energy differences using an accurate local density functional

The accurate local spin density (LSD) functional of Vosko, Wilk, and Nusair, based on electron gas correlation energies of Ceperley and Alder, has been used to calculate interconfigurational energies for atoms and binding energies for first row diatomic molecules. The description of ionization and sp-transfer energies in first row atoms and of low-lying states in B2 and C2 are better than those obtained with earlier parametrizations. Interconfigurational energies in iron series atoms are essentially unchanged from values obtained using previous electron gas parametrizations. Spin–flip energies using the Xα approximation are uniformly inferior to those given by LSD.

Calculated electron affinities of the elements

The extra-electron binding energies of the ground-state monatomic negative ions with $Zl86$ are calculated using the self-interaction correction (SIC) to the local spin-density approximation (LSD) for exchange and correlation. The results agree reasonably with experiment, and the errors reflect the familiar interconfigurational energy error common to LSD and SIC. Some of the rare earths, e.g., Ce and possibly Gd, are predicted to form stable negative ions. In addition we have the following: (1) Relativistic (other than spin-orbit) contributions to the electron affinities are included and discussed. In Au the relativistic effects boost the calculated affinity from 1.5 to 2.5 eV. (2) The doubly negative ions ${\mathrm{O}}^{2\ensuremath{-}}$ and ${\mathrm{Te}}^{2\ensuremath{-}}$ are predicted to have no stable ground state. (3) Electron affinities are calculated for a few excited atomic states. (4) The calculated ground-state densities $n(r)$ of all the neutral atoms and negative ions are monotonically decreasing functions of $r$. (5) Corrections to the random-phase-approximation electron-gas correlation energy are shown to cancel out of SIC calculations for atoms.

Self-interaction correction to density-functional approximations for many-electron systems

The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.