The generalization of the Local Density Approximation (LDA) method for the systems with strong Coulomb correlations is presented which gives a correct description of the Mott insulators. The LDA+U method is based on the model hamiltonian approach and allows to take into account the non-sphericity of the Coulomb and exchange interactions. parameters. Orbital-dependent LDA+U potential gives correct orbital polarization and corresponding Jahn-Teller distortion. To calculate the spectra of the strongly correlated systems the impurity Anderson model should be solved with a many-electron trial wave function. All parameters of the many-electron hamiltonian are taken from LDA+U calculations. The method was applied to NiO and has shown good agreement with experimental photoemission spectra and with the oxygen Kα X-ray emission spectrum.

https://iopscience.iop.org/article/10.1088/0953-8984/9/4/002/pdf

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA+ U method

We have performed a comprehensive first-principles investigation of native point defects in ZnO based on density functional theory within the local density approximation (LDA) as well as the $\mathrm{LDA}+U$ approach for overcoming the band-gap problem. Oxygen deficiency, manifested in the form of oxygen vacancies and zinc interstitials, has long been invoked as the source of the commonly observed unintentional $n$-type conductivity in ZnO. However, contrary to the conventional wisdom, we find that native point defects are very unlikely to be the cause of unintentional $n$-type conductivity. Oxygen vacancies, which have most often been cited as the cause of unintentional doping, are deep rather than shallow donors and have high formation energies in $n$-type ZnO (and are therefore unlikely to form). Zinc interstitials are shallow donors, but they also have high formation energies in $n$-type ZnO and are fast diffusers with migration barriers as low as $0.57\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$; they are therefore unlikely to be stable. Zinc antisites are also shallow donors but their high formation energies (even in Zn-rich conditions) render them unlikely to be stable under equilibrium conditions. We have, however, identified a different low-energy atomic configuration for zinc antisites that may play a role under nonequilibrium conditions such as irradiation. Zinc vacancies are deep acceptors and probably related to the frequently observed green luminescence; they act as compensating centers in $n$-type ZnO. Oxygen interstitials have high formation energies; they can occur as electrically neutral split interstitials in semi-insulating and $p$-type materials or as deep acceptors at octahedral interstitial sites in $n$-type ZnO. Oxygen antisites have very high formation energies and are unlikely to exist in measurable concentrations under equilibrium conditions. Based on our results for migration energy barriers, we calculate activation energies for self-diffusion and estimate defect-annealing temperatures. Our results provide a guide to more refined experimental studies of point defects in ZnO and their influence on the control of $p$-type doping.

Native point defects in ZnO

http://nano-bio.ehu.es/files/articles/Gonze_CPC_2009_590.pdf

ABINIT: First-principles approach to material and nanosystem properties

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized "Wannier functions" was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or "Boys orbitals" as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices.

Maximally-localized Wannier Functions: Theory and Applications

The electronic properties of ZnO have traditionally been explained by invoking intrinsic defects In particular, the frequently observed unintentional n-type conductivity has often been attributed to oxygen vacancies We report first-principles calculations showing that the oxygen vacancy VO is not a shallow donor, but has a deep e(2+∕0) level at ∼10eV below the conduction band The negative-U behavior that causes the 1+charge state to be unstable is associated with large local lattice relaxations We present a detailed configuration coordinate diagram, which allows us to provide a detailed interpretation of recently reported ODEPR (optically detected electron paramagnetic resonance) measurements [L S Vlasenko and G D Watkins, Phys Rev B 71, 125210 (2005)]

Oxygen vacancies in ZnO

The generalization of the local-density-approximation method for the systems with strong Coulomb correlations is proposed, which restores the discontinuity in the one-electron potential as in the exact density functional. The method is based on the model-Hamiltonian approach and allows us to take into account the nonsphericity of the Coulomb and exchange interactions. The calculation scheme could be regarded as a first-principle method due to the absence of adjustable parameters. The method was applied to the calculation of the photoemission (x-ray photoemission spectroscopy) and bremsstrahlung isochromat spectra of NiO.

Density-functional theory and NiO photoemission spectra

State-of-the-art electronic-structure calculations based on the local-density approximation (LDA) to the density functional fail to reproduce the insulating antiferromagnetic ground state in the parent compounds of the high-temperature oxide superconductors. Similar problems have been observed earlier in classical transition-metal oxides such as FeO, CoO, and NiO. In this work we present the method which delivers the correct insulating antiferromagnetic ground state in the correlated oxides preserving other properties as well as the efficiency of the standard LDA. The method embeds the relevant (for a given system of electrons) part of the Hubbard Hamiltonian into the Kohn-Sham LDA equation. The resulting Hamiltonian attempts to fix two intrinsic problems of the LDA: the deficiency in forming localized (atomiclike) moments and the lack of discontinuity of the effective one-particle potential when going from occupied to unoccupied states. We present the detailed study of La2CuO4 and LaCuO3. In the case of La2CuO4 the energy gap and the value of the localized magnetic moment in the stable insulating antiferromagnetic solution are in good agreement with experiment. We compare our results with the standard local spin density approximation calculation and multiband Hubbard model calculations, as well as with results of spectroscopy: inverse photoemission, valence photoemission, and x-ray absorption at the K edge of oxygen. In the case of LaCuO3 such an extensive comparison is limited due to the limited data available for this compound. We discuss, however, the electric and magnetic properties and the insulator-metal-insulator transitions upon increase of oxygen deficiency.

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3

LiCoO2 can be viewed as the end member of the Li-doped LixCo1-xO2 system It was suggested that this system exhibits a transition from high-spin Co ions in CoO to low-spin Co ions in LiCoO2 We present a systematic study of the electronic properties of LiCoO2 based on a density-functional calculation From a good agreement between the theoretical results and the results of various spectroscopies (x-ray photoemission spectroscopy, bremsstrahlung isochromat spectroscopy, and x-ray absorption spectroscopy) we conclude that a one-particle band-structure approach is basically adequate for LiCoO2 while being still controversial for CoO) and we support the conclusion of low-spin Co ions in this compound

M. T. Czyżyk

Papers

Density-functional theory and NiO photoemission spectra

Local-density functional and on-site correlations: The electronic structure of La2CuO4 and LaCuO3

Band-theory description of high-energy spectroscopy and the electronic structure of LiCoO2