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A detailed investigation of the electronic structure in the neighborhood of Cd impurities in ${\mathrm{CeO}}_{2}$ has been performed by ab initio calculations to elucidate the interplay between the oxygen vacancies and electric quadrupole interactions. The quadrupole frequency related to the major component of the electric-field gradient (EFG) at impurities sites from its neighboring charge density as well as its symmetry were calculated by simulating oxygen vacancies at oxygen nearest neighbor of Cd. Results show a very good agreement with experimental hyperfine interactions measurements at the $^{111}\mathrm{Cd}$ nucleus replacing Ce at ${\mathrm{CeO}}_{2}$. A systematic mapping of oxygen vacancies in ${\mathrm{CeO}}_{2}$ supercells was proposed within the framework of density-functional theory using the wien2k code focusing on the electronic distribution in the vicinity of Cd impurities. Results show that the calculated values of EFG crucially depend on impurity-vacancy complex position and the striking axial symmetry observed when an oxygen monovancy is at the nearest neighborhood of Cd is explained by a rearrangement of its $p$ orbitals.

We propose a hybrid approach which employs the dynamical mean-field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent DFT+DMFT scheme in a basis of maximally localized Wannier orbitals using Wien2K, wien2wannier, and the DMFT impurity solver w2dynamics. As a testbed material we apply the method to SrVO$_3$ and report a significant improvement as compared to previous $d$+$p$ calculations. In particular the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle with unwelcome consequences for the $d$-$p$ hybridization and correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation renders the so-called "double-counting" problem obsolete., Comment: 2nd version as submitted, taking into account the k-dependence of the double counting on the DMFT side. 10 pages, 4 figures

A detailed analysis of the theoretical x-ray absorption near-edge structures (XANES) for the boron and nitrogen $K$ edge in hexagonal boron nitride ($h$-BN) employing density-functional theory calculations is presented. The supercell core-hole method and the Bethe-Salpeter equation are used for the description of electron-hole interactions. The calculations are carried out with two different codes, the vasp and the wien2k codes, employing the projector augmented-wave and the full-potential linear augmented-plane-wave methods, respectively. We find close agreement between spectra obtained from the two codes and between calculations using the supercell core-hole method and the Bethe-Salpeter approach. All our calculations, as well as previous calculations using the ground-state structure, yield a single $2{p}_{{\ensuremath{\sigma}}^{*}}$ peak in the boron $K$-edge spectrum and hence fail to describe the experimental double-peak structure. We find that the inclusion of electron-phonon interactions is crucial to obtain the experimentally observed double-peak structure. We include these effects fully parameter free and ab initio using a one-shot sampling method and obtain excellent agreement with experiment.

We quantify the accuracy of different non-self-consistent and self-consistent spin-orbit coupling (SOC) treatments in Kohn-Sham and hybrid density functional theory by providing a band-structure benchmark set for the valence and low-lying conduction energy bands of 103 inorganic compounds, covering chemical elements up to polonium. Reference energy band structures for the PBE density functional are obtained using the full-potential (linearized) augmented plane wave code wien2k, employing its self-consistent treatment of SOC including Dirac-type ${p}^{1/2}$ orbitals in the basis set. We use this benchmark set to benchmark a computationally simpler, non-self-consistent all-electron treatment of SOC based on scalar-relativistic orbitals and numeric atom-centered orbital basis functions. For elements up to $Z\ensuremath{\approx}50$, both treatments agree virtually exactly. For the heaviest elements considered (Tl, Pb, Bi, Po), the band-structure changes due to SOC are captured with a relative deviation of 11% or less. For different density functionals (PBE versus the hybrid HSE06), we show that the effect of spin-orbit coupling is usually similar but can be dissimilar if the qualitative features of the predicted underlying scalar-relativistic band structures do not agree. All band structures considered in this work are available online via the NOMAD repository to aid in future benchmark studies and methods development.

In this work, we use density functional theory to predict the optical properties of TixSi1-xO2 solid solutions. The special quasirandom structure method and the simulated annealing procedure were applied to produce models of crystalline and amorphous TixSi1-xO2. These were fully structurally optimized by using the VASP package, while their electronic structure and optical properties were subsequently calculated by using the WIEN2k package employing the TB-mBJ potential. The calculated band gaps for a-TixSi1-xO2 evaluated by using the Tauc-like fitting approach are 8.53 eV for SiO2, quickly decreasing to 4.0 eV at x = 0.19, 3.52 eV at x = 0.34, and 3.24 eV for TiO2. Experimental samples were prepared by means of plasma-enhanced chemical vapor deposition to support the calculations. Ellipsometry and spectrophotometry yield a compositional trend for the experimental optical band gap comparable with our predictions: a quick decrease from 7.94 eV for pure SiO2 to 3.91 eV at x = 0.15, followed by a much slower decrease over the rest of the composition range ending at 3.26 eV for pure TiO2. A detailed analysis of anatase and rutile-based solid solutions reveals the introduction of silicon-induced oxygen states into the band gap in the TiO2-rich composition region, which results in the predicted reduction of the band gap. However, we show that the optical absorption of those states is negligible. We have obtained good agreement between the calculated and measured imaginary part of the dielectric function epsilon(i), especially for the TiO2-rich compositions. Finally, we predict an almost-linear refractive index change at 632.8 nm between a-SiO2 (1.36) and a-TiO2 (2.34), which was experimentally confirmed.

We study the effects of charge self-consistency within the combination of density functional theory (DFT; wien2k) with dynamical mean field theory (DMFT; w2dynamics) in a basis of maximally localized Wannier orbitals. Using the example of two cuprates, we demonstrate that even if there is only a single Wannier orbital with fixed filling, a noteworthy charge redistribution can occur. This effect stems from a reoccupation of the Wannier orbital in k-space when going from the single, metallic DFT band to the split, insulating Hubbard bands of DMFT. We analyze another charge self-consistency effect beyond moving charge from one site to another: the correlation-enhanced orbital polarization in a freestanding layer of ${\mathrm{SrVO}}_{3}$.

In this work, we propose a systematic way of computing a low-rank globally adapted localized Tucker-tensor basis for solving the Kohn-Sham density functional theory (DFT) problem. In every iteration of the self-consistent field procedure of the Kohn-Sham DFT problem, we construct an additive separable approximation of the Kohn-Sham Hamiltonian. The Tucker-tensor basis is chosen such as to span the tensor product of the one-dimensional eigenspaces corresponding to each of the spatially separable Hamiltonians, and the localized Tucker-tensor basis is constructed from localized representations of these one-dimensional eigenspaces. This Tucker-tensor basis forms a complete basis, and is naturally adapted to the Kohn-Sham Hamiltonian. Further, the locality of this basis in real-space allows us to exploit reduced-order scaling algorithms for the solution of the discrete Kohn-Sham eigenvalue problem. In particular, we use Chebyshev filtering to compute the eigenspace of the Kohn-Sham Hamiltonian, and evaluate nonorthogonal localized wave functions spanning the Chebyshev filtered space, all represented in the Tucker-tensor basis. We thereby compute the electron-density and other quantities of interest, using a Fermi-operator expansion of the Hamiltonian projected onto the subspace spanned by the nonorthogonal localized wave functions. Numerical results on benchmark examples involving pseudopotential calculations suggest an exponential convergence of the ground-state energy with the Tucker rank. Interestingly, the rank of the Tucker-tensor basis required to obtain chemical accuracy is found to be only weakly dependent on the system size, which results in close to linear-scaling complexity for Kohn-Sham DFT calculations for both insulating and metallic systems. A comparative study has revealed significant computational efficiencies afforded by the proposed Tucker-tensor approach in comparison to a plane-wave basis.

The structural, electronic, and optical properties of InAs, InSb, and their ternary alloys ${\mathrm{InAs}}_{x}{\mathrm{Sb}}_{1\ensuremath{-}x}$ ($x=0.25$, 0.5, 0.75) are investigated within density functional theory utilizing the wien2k package. We find that the lattice constants and bulk moduli as a function of $x$ are in best agreement with Vegard's linear rule. When computing the electronic band structures with the modified Becke-Johnson exchange-correlation functional (mBJLDA), our results for the band gaps of InAs, InSb, and their ternary alloys are in good agreement with the available experimental results while the conventional Wu-Cohen generalized gradient approximation (GGA) functional leads to zero or close to zero band gaps. In particular, our mBJLDA results confirm experimental evidence that the minimum band gap occurs for As concentrations around $x\ensuremath{\approx}0.3$. Furthermore, we investigate the dielectric function of these compounds within the random phase approximation using both the Wu-Cohen GGA and the mBJLDA functionals. While the mBJLDA results of our fully first-principles calculations show good agreement of the peak positions in ${\ensuremath{\epsilon}}_{2}(\ensuremath{\omega})$ with experiments, the peaks in the optical spectra based on the Wu-Cohen GGA band structure appear redshifted compared to experiment. We further identify the interband transitions responsible for the structures in the spectra. Looking at the optical matrix element, we note that the major peaks are dominated by transition from the Sb $5p$ (As $4p$) states to In $s$ states for InSb and ${\mathrm{InAs}}_{0.25}{\mathrm{Sb}}_{0.75}$ (InAs, ${\mathrm{InAs}}_{0.75}{\mathrm{Sb}}_{0.25}$, and ${\mathrm{InAs}}_{0.5}{\mathrm{Sb}}_{0.5}$).

We investigate the anisotropy of the optical properties of thin Fe films on GaAs(001) from first-principles calculations. Both intrinsic and magnetization-induced anisotropy are covered by studying the system in the presence of spin-orbit coupling and external magnetic fields. We use the linearized augmented plane wave method, as implemented in the WIEN2k density functional theory code, to show that the $C_{2v}$ symmetric anisotropy of the spin-orbit coupling fields at the Fe/GaAs(001) interface manifests itself in the corresponding anisotropy of the optical conductivity and the polar magneto-optical Kerr effect. While their magnetization-induced anisotropy is negligible, the intrinsic anisotropy of the optical properties is significant and reflects the underlying $C_{2v}$ symmetry of the Fe/GaAs(001) interface. This suggests that the effects of anisotropic spin-orbit coupling fields in experimentally relevant Fe/GaAs(001) slabs can be studied by purely optical means., Comment: 8 pages, 11 figures

Very recently, in the 2011 version of the Wien2K code, the long standing short come of the codes based on Density Functional Theory, namely, its impossibility to account for the experimental band gap value of semiconductors, was overcome. The novelty is the introduction of a new exchange and correlation potential, the modified Becke-Johnson potential (mBJLDA). In this letter, we report our detailed analysis of this recent work. We calculated using this code, the band structure of forty one semiconductors and found an important improvement in the overall agreement with experiment as Tran and Blaha [{\it Phys. Rev. Lett.} 102, 226401 (2009)] did before for a more reduced set of semiconductors. We found that by using the average of the two lattice parameters (LDA and GGA) a better agreement with the band gap experimental value is systematically obtained. On the other hand, the band structure calculated with the mBJLDA potential seems, at first sight, a simple rigid displacement of the conduction bands towards higher energies. We conclude that, in spite of the very important improvement in the band gap agreement with experiment using the new mBJLDA potential, there are issues that point to the fact that this problem is not yet totally closed.

We develop a computational approach for calculating the optical conductivity in the augmented plane wave basis set of Wien2K and apply it for thoroughly comparing the full dipole matrix element calculation and the Peierls approximation. The results for SrVO3 and V2O3 show that the Peierls approximation, which is commonly used in model calculations, works well for optical transitions between the d orbitals. In a typical transition metal oxide, these transitions are solely responsible for the optical conductivity at low frequencies. The Peierls approximation does not work, on the other hand, for optical transitions between p- and d-orbitals which usually became important at frequencies of a few eVs, Comment: 11 pages, 4 figures

The electronic properties of the layered transition metal dichalcogenide ZrS${}_{x}$Se${}_{2\ensuremath{-}x}$ semiconductors for $x$ $=$ 0 and 2 as well as for the ternary compound with $x$ $=$ 1 have been calculated by density functional theory for six different exchange-correlation energy approximations by the wien2k code. The results show that, among the functions we tested, a new semilocal potential that combines the modified Becke--Johnson potential and the local spin density approximation correlation potential as proposed by Tran and Blaha [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] (TB-MBJ) remains superior for estimating the band gap. Thus, the calculations have been performed within the TB-MBJ method both with and without spin-orbit interaction. Calculations by all methods reveal that the valence band maximum and conduction band minimum are located at the \ensuremath{\Gamma} and $M$ points, respectively, which are in agreement with experimental data. Moreover, in the three compounds the band gap decreases linearly from ZrS${}_{2}$ to ZrSe${}_{2}$. When considering spin-orbit (SO) coupling, the degeneracy of the valance bands is removed. The size of the SO splitting increases by the atomic number of chalcogenide from ZrS${}_{2}$ to ZrSe${}_{2}$.

The strength of the core-hole effect in simulations of electron energy-loss near edge structures or x-ray absorption near edge structures is investigated using ab initio calculations based on the density functional theory. Calculations were performed using the WIEN2K and FEFF codes at different edges for the following model compounds: rutile ${\text{TiO}}_{2}$, MgO, and for some transition metals (Ti, Fe, Co, Cu, and Zn). We demonstrate that although a core hole is always present in any core-level spectroscopy experiment, its effect is not always observable. To observe or not a core-hole effect in any experimental situation can, however, be predicted from the examination of the material's ground-state electronic structure, especially of the states just above the Fermi level. Indeed, it is shown that the two important criteria governing the core-hole strength at a given edge depend first on the localization and on the character of the first empty states of the material under investigation, and second on the nature of the compensating charge necessary to maintain the crystal neutrality. These criteria are expected to give a good description of the core-hole effect in the one-particle approximation. However, nothing can be inferred as for the good/bad agreement between calculations and experiments for more complex cases such as excitations of delocalized semicore states or of atomiclike multiplet structures.

Density functional theory (DFT)-based calculations for both the charge-ordered and the valence-mixed phases of ${\text{YBaFe}}_{2}{\text{O}}_{5}$ have been performed using the WIEN2K package and the generalized gradient approximation $(\text{GGA})+U$ method. ${\text{YBaFe}}_{2}{\text{O}}_{5}$ crystallizes in an oxygen-deficient perovskitelike structure featuring corner-sharing distorted square ${\text{FeO}}_{5}$ pyramids separated by a layer of yttrium atoms in the $c$ direction. It shows antiferromagnetic ordering below the N\'eel temperature of 430 K, below which it can be characterized as a Robin-Day class-III mixed-valence (MV) compound in which all iron atoms have the same noninteger oxidation state of 2.5. This compound is of particular interest since it undergoes a Verwey transition at approximately 309 K. Below the Verwey temperature the existence of two independent iron sites are found experimentally, which are occupied by fully localized divalent and trivalent iron atoms. This charge-ordered modification can thus be classified as a class-I MV compound. The Verwey transition of ${\text{YBaFe}}_{2}{\text{O}}_{5}$ is a first-order phase transition between low-temperature charge-ordered and high-temperature valence-mixed modifications which is accompanied with a dramatic change in the electronic configuration of the iron ions. For both phases the electronic and magnetic structures as well as electric field gradients, isomer shifts, and hyperfine fields have been calculated and compared to the experimental data. The value of ${U}_{\text{eff}}$ (needed for the $\text{GGA}+U$ calculation) has been estimated using a constrained DFT method. Different magnetic arrangements have been calculated in order to investigate the magnetic interactions and exchange parameters $J$, from which it was possible to verify the experimentally observed magnetic structures for both modifications.

First-principles calculations using the $\text{APW}+\text{lo}$ method, as implemented in the WIEN2K code, have been used to investigate the structural, electronic, and magnetic properties of the perovskite ${\text{CaCu}}_{3}{\text{Fe}}_{4}{\text{O}}_{12}$, including the high-temperature $Im\text{\ensuremath{-}}3$ and low-temperature $Pn\text{\ensuremath{-}}3$ phase. The high-temperature phase presents a homogeneous valence and an orbital degenerate half-metallic behavior, which is consistent with the previous theoretical result. Instead orbital ordering, charge ordering, or disproportionation on Fe sites occur in the low-temperature phase, leading to the insulating character. More importantly, the charge disproportionation is of $2{d}^{5}L\ensuremath{\rightarrow}{d}^{5}{L}^{2}+{d}^{5}$ type (where $L$ denotes an oxygen hole or a ligand hole), and the origin for the phenomenon is discussed in detail.

Changes in the dielectric properties during the ferroelectric transition of commercial $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_{3}$ powders were determined in situ, by analyzing the low-energy-loss region of electron energy loss spectroscopy (EELS) spectra in a transmission electron microscope, at room temperature (ferroelectric phase) and $150\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ (paraelectric phase). A comparison of experimental EELS spectra and ab initio density-functional theory calculations (WIEN2K code) within the generalized gradient approximation (GGA) is presented. A characteristic peak around $11\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ appears in the imaginary part of the dielectric function in paraelectric phase, which is absent in ferroelectric phase. The origin of the characteristic peak is analyzed by means of energy band structure calculations.

First-principles calculations using the augmented plane wave plus local orbital method, as implemented in the WIEN2K code, have been used to investigate the structural, electronic, and magnetic properties of the layered perovskite ${\mathrm{Cs}}_{2}\mathrm{Ag}{\mathrm{F}}_{4}$. Our calculations indicate that an orthorhombic ground state for ${\mathrm{Cs}}_{2}\mathrm{Ag}{\mathrm{F}}_{4}$ is energetically favored over tetragonal. We also find that ${\mathrm{Cs}}_{2}\mathrm{Ag}{\mathrm{F}}_{4}$ should be a strong two-dimensional ferromagnet, with very weak antiferromagnetic coupling between the layers, in agreement with the experiment. More importantly, an antiferrodistortive ordering of ${z}^{2}\text{\ensuremath{-}}{x}^{2}$ and ${z}^{2}\text{\ensuremath{-}}{y}^{2}$ orbitals is inferred from the density of states and from a spin density isosurface analysis.

The complex density-functional theory calculations of structural, electronic, and optical properties for two principal representatives of the filled skutterudites $\mathrm{Ce}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ have been reported using the full-potential linearized augmented plane-wave method plus local orbitals, as implemented in the WIEN2K code. In this approach, the local-density approximation is used for the exchange-correlation potential. We performed these calculations with and without spin-orbit interactions. Results are given for lattice constant, bulk modulus, and its pressure derivative. Band structure, density of states, pressure coefficients of energy gaps, and refractive indices are also given. We note that both $\mathrm{Ce}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ and $\mathrm{Th}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ are semiconductors with indirect and direct energy gaps, respectively. The valence-band maximum is located at $\ensuremath{\Gamma}$ for both compounds, whereas the conduction-band minimum is located at $\ensuremath{\Gamma}$ for $\mathrm{Th}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$ and at $N$ for $\mathrm{Ce}{\mathrm{Fe}}_{4}{\mathrm{P}}_{12}$. Our results are compared with previous theoretical calculations and experimental data.

The electronic and geometric properties of bulk fcc $\ensuremath{\delta}$-plutonium and the quantum size effects in the surface energies and the work functions of the (001) ultrathin films (UTF) up to seven layers have been investigated with periodic density-functional theory calculations within the full-potential--linearized-augmented-plane-wave (FP-LAPW) approach as implemented in the WIEN2k package. The effects of several approximations have been examined: (i) nonspin polarization (NSP) versus spin polarization (SP); (ii) scalar-relativity [no spin-orbit coupling (NSO)] versus full-relativity [i.e., with spin-orbit (SO) coupling included]. Our calculations show that both spin-polarization and spin-orbit coupling play important roles in determining the equilibrium atomic volume and bulk modulus for $\ensuremath{\delta}$-plutonium. Our calculated equilibrium atomic volume of $178.3\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}{.}^{3}$ and bulk modulus of 24.9 GPa at the fully relativistic level of theory, i.e., spin-polarization and spin-orbit coupling included, are in good agreement with the experimental values of $168.2\phantom{\rule{0.3em}{0ex}}\mathrm{a}.\mathrm{u}{.}^{3}$ and 25 GPa (593 K), respectively. In particular, the energy difference brought by spin-orbit coupling, $\ensuremath{\sim}7\text{--}8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, is dominant, but the energy difference brought by spin-polarization, from a few tenths to 2 eV, has a stronger dependence on the atomic volume. Features of the density of states show that $5f$ electrons are more itinerant when the volume of $\ensuremath{\delta}$-plutonium is compressed and they are more localized when the volume is expanded, which provides evidence to explain the origin of the volume expansion between the $\ensuremath{\alpha}$ and $\ensuremath{\delta}$ phases. The calculated equilibrium lattice constants at different levels of approximation are used in the surface property calculations for the thin films. The surface energy is found to be rapidly converged at all four level approximations, NSP-NSO, NSP-SO, SP-NSO, and SP-SO. The semi-infinite surface energy is predicted to be 0.692 eV at the full relativistic level with spin-polarization and spin-orbit coupling. Quantum size effect for the work function is not pronounced for the (001) surface at the LAPW level of theory.

Ab initio calculations using the APW+Io method as implemented in the WIEN2k code have been used to describe the electronic structure of the quasi-one-dimensional system BaCoO3. Both, GGA and LDA+U approximations were employed to study different orbital and magnetic orderings. GGA predicts a metallic ground state whereas LDA+U calculations yield an insulating and ferromagnetic ground state (in a low-spin state) with an alternating orbital ordering along the Co-Co chains, consistent with the available experimental data.

A method is given for generating sets of special points in the Brillouin zone which provides an efficient means of integrating periodic functions of the wave vector. The integration can be over the entire Brillouin zone or over specified portions thereof. This method also has applications in spectral and density-of-state calculations. The relationships to the Chadi-Cohen and Gilat-Raubenheimer methods are indicated.