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

Origin of surface resonance states in nearly-free-electron metals: Al(001)

Structural, electronic, and magnetic properties of Au/Cr/Au(001) sandwiches: Theoretical total-energy studies.

Transport properties of ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_{3}$ and ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ are calculated by solving the Boltzmann equation using the electronic energy-band structures obtained with the local-density full-potential linearized augmented-plane-wave method. For ${\mathrm{Ba}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{K}}_{\mathit{x}}$${\mathrm{BiO}}_{3}$ the calculated Hall coefficient ${\mathit{R}}_{\mathit{H}}$ is (two times) larger than experiment and has the correct (negative) sign. For ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ a positive Hall coefficient is obtained for the magnetic field oriented perpendicular to the Cu-O planes. This is to be compared with a negative experimental value found for x0.18 and recent experiments that show a change of sign of this Hall coefficient (from negative to positive with increasing x) for x=0.18. These results indicate a trend (previously found for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$) towards a regime in which the conventional band-theoretical description comes into better agreement with experiment. The highly anisotropic nature of the resistivity of ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ is discussed.

Arthur J Freeman

Papers

Origin of surface resonance states in nearly-free-electron metals: Al(001)

Structural, electronic, and magnetic properties of Au/Cr/Au(001) sandwiches: Theoretical total-energy studies.

Transport properties of high-Tc superconductors: Fermi-liquid local-density electronic-structure predictions.

Advanced tetrahedrally-bonded magnetic semiconductors for spintronic applications

Hybridization, electronic structure and properties of uranium intermetallics: URu3, URh3, UPd3, UIr3 and UPt3