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.

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

We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

To use solar irradiation or interior lighting efficiently, we sought a photocatalyst with high reactivity under visible light. Films and powders of TiO 2- x N x have revealed an improvement over titanium dioxide (TiO 2 ) under visible light (wavelength 2 has proven to be indispensable for band-gap narrowing and photocatalytic activity, as assessed by first-principles calculations and x-ray photoemission spectroscopy.

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Visible-Light Photocatalysis in Nitrogen-Doped Titanium Oxides

Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications

A method for accurate and efficient local density functional calculations (LDF) on molecules is described and presented with results The method, Dmol for short, uses fast convergent three‐dimensional numerical integrations to calculate the matrix elements occurring in the Ritz variation method The flexibility of the integration technique opens the way to use the most efficient variational basis sets A practical choice of numerical basis sets is shown with a built‐in capability to reach the LDF dissociation limit exactly Dmol includes also an efficient, exact approach for calculating the electrostatic potential Results on small molecules illustrate present accuracy and error properties of the method Computational effort for this method grows to leading order with the cube of the molecule size Except for the solution of an algebraic eigenvalue problem the method can be refined to quadratic growth for large molecules

An all‐electron numerical method for solving the local density functional for polyatomic molecules

As a possible means of alleviating the severe brittleness in the B2 compounds FeAl and NiAl, the all-electron self-consistent total energy linear muffin-tin orbital (LMTO) method was employed to investigate the possibility of lowering the ⟨111⟩ anti-phase boundary (APB) energies by changing compositions in FeAl and NiAl. For APB’s created in the regions with excess Fe (or Ni) atoms, APB energies for the model systems, Fe0.6Al0.4 and Ni0.6Al0.4, were found to be one order of magnitude smaller than those for stoichiometric B2 FeAl and NiAl, respectively. Apparently, the activation of ⟨111⟩ slip became possible in these cases. On the other hand, the APB energies remained at about the same as those in stoichiometric FeAl and NiAl for APB’s occurring in regions with equal numbers of Fe (Ni) and Al atoms, implying that the activation of ⟨111⟩ slip in these regions was not eased.

Effect of stoichiometry on the structural properties and the electronic structure of intermetallics: anti-phase boundary energies in FeAl and NiAl

The method of Nesbet is applied to the model investigated by Freeman and Watson to describe the Heisenberg exchange interaction between neighboring transition metal atoms. Pairs of atomic Hartree-Fock $d$ orbitals obtained from calculations on ${\mathrm{Co}}^{++}$ and Co are used; the nuclei and the remaining electrons are represented by two point charges at the nearest neighbor internuclear separation of Co atoms in the metal. Nuclear charges, $Z$, of one and ten are used to examine the effect of changing the assumed potential. The effective Heisenberg exchange parameter is large and negative for all values of the parameters used here. The present results agree in sign with the earlier results of Freeman and Watson, who used the Heitler-London method without the ionic configuration, but differ by an order of magnitude for $Z=1$, and are somewhat closer for $Z=10$. The discrepancy is probably due to this omission, since the present formalism takes all configurations into account for a system described by two basis orbitals. Since the observed exchange parameter for metallic cobalt is positive (ferromagnetic), and since previous investigations suggest that additional effects (due to including the remaining electrons of the ions) will not substantially alter the computed value, it appears that the ferromagnetic coupling must be explained by some mechanism other than the two-atom Heisenberg exchange interaction between localized $d$ orbitals.

Two-Electron Heisenberg Exchange Interaction between Neighboring Atoms

Bi-induced reconstructions on Si(100)

Proximity effects of a Cu(001) substrate on the ferromagnetism of Co mono- and bilayers

The electronic structure of the high-temperature rutile phase of Nb${\mathrm{O}}_{2}$ is studied by the linearized-augmented-plane-wave method Potentials constructed by superposition of neutral-atom and ionic-charge densities are used to explore variability of the electronic band structure A rigid-band scheme is shown to accurately describe optical absorption of the rutile phase of Nb${\mathrm{O}}_{2}$ stabilized by the addition of 20 at% Ti as measured by Raccah et al Differences between the band results for rutile Nb${\mathrm{O}}_{2}$ and the optical absorption measurements on the low-temperature body-centered tetragonal phase of Nb${\mathrm{O}}_{2}$ are attributed to band splittings induced by lattice distortion which occur at the phase transition The static-electron response function $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ is calculated in the constant-matrix-elements approximation In contrast to the case of isoelectronic V${\mathrm{O}}_{2}$, no Fermi-surface nesting features are observed, and $\ensuremath{\chi}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ is found to be structureless in the vicinity of the point $P=(\frac{1}{4}, \frac{1}{4}, \frac{1}{2})$ which has been associated with a possible soft-mode phonon instability responsible for the lattice transformation

Arthur J Freeman

Papers

Effect of stoichiometry on the structural properties and the electronic structure of intermetallics: anti-phase boundary energies in FeAl and NiAl

Two-Electron Heisenberg Exchange Interaction between Neighboring Atoms

Bi-induced reconstructions on Si(100)

Proximity effects of a Cu(001) substrate on the ferromagnetism of Co mono- and bilayers

Electronic band structure, optical properties, and generalized susceptibility of NbO2