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

All-electron self-consistent determination of spin-polarization and knight shift of A Pt(001)film

The optical and electronic properties of Tl-chalcogenide, wide gap semiconductors, TlGaSe 2 , Tl 6 I 4 Se, and Tl 2 Au 4 S 3 for x-ray and γ ray detection were characterized. The semiconductor crystals are grown by the modified Bridgman method. The optical absorption and band gap energy of the materials were determined from UV-Vis-near
IR transmission and reflection spectra. The mobility-lifetime products were measured. For Tl 6 I 4 Se the values were comparable to those of CdZnTe. We measured room temperature detector response to x-ray and γ ray radiations.
Under 57 Co radiation, Tl 6 I 4 Se has a well-resolved spectral response and peak FWHM comparable to those of
Cd 0.9 Zn 0.1 Te.

Tl-based wide gap semiconductor materials for x-ray and gamma ray detection

Defect state model for localized excitations in LiF

The structural, electronic, and magnetic properties of mono and bilayer Rh and Ru transition metals deposited on a Fe(001) substrate or sandwiched by an additional Fe layer have been determined by using the highly precise local density full-potential linearized augmented plane-wave method. Significantly, the atomic force determinations demonstrate that a large interfacial relaxation plays an important role in their electronic and magnetic properties. Both mono and bilayer Ru and Rh in the systems considered are found to be able to retain large spin magnetic moments. The ground state of bilayer Rh is found to have its moments coupled antiferromagnetically. In good agreement with x-ray magnetic circular dichroism (MCD) measurements, the deposition of Rh layers on Fe(001) is found to enhance the Fe spin magnetic moments in the interface. Calculated values of the spin and orbital parts of the magnetic moments and the MCD spectra are presented, and the role of overlayer-substrate hybridization is discussed.

Arthur J Freeman

Papers

All-electron self-consistent determination of spin-polarization and knight shift of A Pt(001)film

Tl-based wide gap semiconductor materials for x-ray and gamma ray detection

Defect state model for localized excitations in LiF

Induced magnetism of 4d transition metals: Rh and Ru/Fe(001) overlayers and sandwiches

Electronic densities of states of semi-infinite disordered chains: Comparisons of exact and analytic calculations.