Generalized Gradient Approximation Calculations Research Articles

Magnetic anisotropy in Gd, GdN, andGdFe2tuned by the energy of gadolinium4fstates

The tiny magnetocrystalline anisotropy energies (MAEs) of bulk Gd, GdN, and ${\text{GdFe}}_{2}$ have been calculated by means of the force theorem in conjunction with the full-potential linear augmented plane-wave (FLAPW) method. The generalized gradient correction including the Hubbard interaction $U$ $(\text{GGA}+U)$ produced the best possible agreement with the experimental MAE strength compared to either the generalized gradient approximation (GGA), where the $4f$ electrons are treated as valence states, or the GGA core, where they are treated as core electrons. Indeed, the magnetic anisotropy is three times that of the $\text{GGA}+U$ if the $4f$ orbitals are prevented to hybridize correctly with the other orbitals like in the GGA-core calculation and 1 order of magnitude if they hybridize too much, like in the GGA calculation. The $\text{GGA}+U$ results can be explained in terms of orbital moment anisotropy using Bruno's model showing that the MAE is due to the orbital magnetic-moment anisotropy. In addition, because the $4f$ states of Gd are half filled their orbital moment and spin-orbit coupling are zero; the Gd MAE is tuned by the spin-orbit coupling of $5d$ states rather than by that of the $4f$ states like in other rare-earth systems, such as Tb or Dy. Nevertheless, the strength of MAE is found to depend on the energy position of the $4f$ states. The MAE of Gd is therefore much similar to that of a transition metal rather than that of a typical rare-earth metal such as Tb or Dy. It is not surprising that Gd shows a calculated easy axis along the (0001) direction like hcp cobalt. All converged calculations within the GGA, the GGA core, or the $\text{GGA}+U$ methods show that the magnetization is along the $c$ axis, in disagreement with an experiment and a recent calculation which show that the easy axis makes an angle of $20\ifmmode^\circ\else\textdegree\fi{}$ with the hcp $c$ direction. Based on the present calculations, the disagreement with experiment might be due to possible presence of symmetry-breaking imperfections, such as defect states or impurities, and cannot be explained using bulk MAE calculations. As for the MAE of GdN and ${\text{GdFe}}_{2}$ compounds, crystallizing in, respectively, cubic rocksalt and Laves phase structures, despite the qualitative agreement with Bruno's model, their interpretation is much more complex. Indeed, their predicted magnetization easy axis is along one of the symmetry equivalent (100), (010), and (001) directions rather than the (111) direction of fcc nickel, and their MAEs are much smaller than that of Gd. The removal of N from the GdN structure without changing the lattice parameter re-established the easy axis along the (111) direction as expected, showing that the easy axis of GdN is a consequence of $\text{Gd}\text{ }5d$ and $\text{N}\text{ }2p$ hybridizations.

Density Functional Study of the Structural Properties of Copper Iodide: LDA vs GGA Calculations

We have performed first principles total energy calculations to investigate the structural properties of copper iodide (CuI) in its sodium chloride, cesium chloride, zincblende and wurtzite structures. Calculations are done using the density functional theory. We employ the full potential linearized augmented plane wave method as implemented in the wien2k code. The exchange and correlation potential energies are treated in the generalized gradient approximation (GGA), and the local density approximation (LDA). Optical absorption experiments and x-ray diffraction measurements have shown that zincblende is the ground state of CuI. Our calculations find that in the GGA formalism wurtzite and zincblende have similar total energies, while in the LDA formalism the lowest minimum corresponds to zincblende. Results show that the energy difference between the wurtzite and the zincblende structures, as calculated within the GGA formalism is 2 meV, and within the LDA formalism, is 31 meV. These results may suggest a coexistence of both wurtzite and zincblende structures in the ground state of CuI. Structural parameters are correctly reproduced by the GGA calculations. We obtain that under the application of external pressure the atomic configuration may transform into the NaCl structure. At higher pressures it is possible to have a phase transition to the CsCl geometry.

Excess electron states in reduced bulk anatase TiO2: Comparison of standard GGA, GGA+U, and hybrid DFT calculations

The removal of lattice O atoms, as well as the addition of interstitial H atoms, in TiO(2) is known to cause the reduction in the material and the formation of "Ti(3+)" ions. By means of electronic structure calculations we have studied the nature of such oxygen vacancy and hydrogen impurity states in the bulk of the anatase polymorph of TiO(2). The spin polarized nature of these centers, the localized or delocalized character of the extra electrons, the presence of defect-induced states in the gap, and the polaronic distortion around the defect have been investigated with different theoretical methods: standard density functional theory (DFT) in the generalized-gradient approximation (GGA), GGA+U methods as a function of the U parameter, and two hybrid functionals with different admixtures of Hartree-Fock exchange. The results are found to be strongly dependent on the method used. Only GGA+U or hybrid functionals are able to reproduce the presence of states at about 1 eV below the conduction band, which are experimentally observed in reduced titania. The corresponding electronic states are localized on Ti 3d levels, but partly delocalized solutions are very close in energy. These findings show the limited predictive power of these theoretical methods to describe the electronic structure of reduced titania in the absence of accurate experimental data.

Electronic structure and Fermi surface of the superconductors LaNiBiO and LaCuBiO from first principles

Based on first-principle full-potential linearized augmented plane wave generalized gradient approximation calculations, we have investigated electronic structure of synthesized superconductors LaMBiO, where $M=\text{Ni}$ or Cu as examples of bismuth-containing compounds in the family of superconducting quaternary oxypnictides. The band structure, density of states, and Fermi-surface features are discussed. Our results indicate that chemical bonding inside La-O and M-Bi layers is covalent while the interlayer binding is mostly ionic. The states of M-Bi layers are found to prevail at the Fermi level. The corresponding Fermi surfaces bear a two-dimensional character thus suggesting strongly anisotropic conduction mostly via M-Bi layers. On the whole, the oxybismuthides may be described as superconducting nonmagnetic ionic metals.

Many-body electronic structure of metallicα-uranium

We present results for the electronic structure of $\ensuremath{\alpha}$-uranium using a recently developed quasiparticle self-consistent GW (QSGW) method. This is the first time that the $f$-orbital electron-electron interactions in an actinide have been treated by a first-principles method beyond the level of the generalized gradient approximation (GGA) or the local-density approximation (LDA) to the density-functional theory (DFT). We show that the QSGW approximation predicts an $f$-level shift upward of about 0.5 eV with respect to the other metallic $s\ensuremath{-}d$ states and that there is a significant $f$-band narrowing when compared to LDA band-structure results. We predict a considerable QSGW enhancement of the linear coefficient of specific heat. Nonetheless, because of the overall low $f$-electron occupation number in uranium, ground-state properties and the occupied band structure around the Fermi energy are not significantly affected. The correlations predominate in the unoccupied part of the $f$ states. This provides the first formal justification for the success of LDA and GGA calculations in describing the ground-state properties of this material.

Jahn–Teller distortion and electronic structure of LiMn 2O 4

LiMn 2O 4 is one of the important cathode material for rechargeable lithium batteries. Standard ab initio studies within local density approximation (LDA) and generalized gradient approximation (GGA) are not able to reproduce the intrinsic insulating electronic structure and Jahn–Teller-type local atomic distortion of LiMn 2O 4. In the present work, GGA+U method is shown to be able to localize electrons to Mn 3 d z 2 orbits in the majority spin channel, and open a gap of about 0.5 eV between the Mn 3 d z 2 and Mn 3 d x 2 − y 2 . Results from GGA+U calculation showed that Mn ions are in the mixed valence state of Mn 3+ and Mn 4+. This is in good agreements with experimental observations and different to Mn 3.5+ obtained from standard GGA calculations. While Jahn–Teller distortion is not observed in Mn 4+O 6 octahedra, it is clearly seen in Mn 3+O 6 octahedra, in which Mn O bond lengths along the z-axis direction are obviously elongated.

X-ray spectra and electronic structure of Sc and Ti dihydrides

We measured x-ray resonant and nonresonant emission and absorption spectra ofSc2O3 and emissionspectra of ScH2, ScD2 and TiH2. Ab initio generalized gradient approximation calculations of the electronic structure areperformed using the experimental crystal structures as input. The dependence of the resonantx-ray spectra on the excitation energy is measured and the difference between that forSc2O3 and that forScH2 and betweenthat for ScH2 and that for TiH2 is shown. The difference is due to the dominance of ionization over excitation processes inhydrides and higher 3d filling in Ti with respect to Sc. Good agreement between calculatedand experimental spectra is found.

Atomistic study of magnetism effect on structural stability in Fe3Al and Fe3AlX (X = H, B, C, N, O) alloys

AbstractAtomistic modeling based on the density‐functional theory (DFT) within the generalized‐gradient approximation (GGA) is used to study the magnetic properties Fe3Al and Fe3AlX (X = H, B, C, N, O) compounds. The phase stability and the structural parameters are calculated for the selected iron‐aluminide alloys. The magnetic effects in Fe3AlX are shown and the predicted properties agree very well with the available experimental data. In the case of Fe3Al alloy, the DO3 structure is found to be more favorable than the L12 one. To the authors' knowledge, this is the first time that spin‐polarized GGA calculations have given the correct ground state of the Fe3Al alloys. In addition, the hypothetical phase of Fe3AlX′ (X′ = H, B, N, and O) structure is compared to the experimentally observed Fe3AlC structure. The unusual effect on magnetic properties of the C addition is shown. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Origin of the light green color and electronic ground state ofLaCrO3

The electronic structure and optical properties of LaCrO3 have been calculated and the origin of the light green color of LaCrO3 has been identified. An optical gap of 1=3.4 eV was reproduced in agreement with experiment, which is a charge transfer gap. Another optical gap, 0=2.15 eV, which is not present in experiments has also been found and explains the light green color of this compound. The energy band gap between the top of the valence band and the bottom of the conduction band is =1.40 eV and has Mott character. Our calculated x-ray photoemission spectra XPS and x-ray absorption spectra at the oxygen K edge O-K XAS are in very good agreement with experiments. In contrast to previous reports, these results have been obtained using standard generalized gradient approximation calculations, while additional correlation effects for Cr 3d states due to an effective Hubbard U would result in a colorless LaCrO3 and a disagreement with XPS and XAS experiments. Thus, LaCrO3 should not be considered as highly correlated transition metal oxide, a conclusion also valid for many Cr3+ compounds.

Ab initiocalculations of the phonon spectra and the thermal expansion coefficients of the4dmetals

We have performed first principles calculations of the phonon spectra of the $4d$ transition metals with the so-called supercell method and found good agreement with observations. Furthermore, the electron and phonon contributions to the free energy for the $4d$ metals have been calculated from a first principles method. From the free energy, the thermal expansion of the metals is calculated. The calculated thermal expansion coefficients for the cubic elements are in overall good agreement with the experiment when the local density approximation is employed, while the generalized gradient approximation calculations yield a discrepancy as big as $\ensuremath{\sim}30%$. For the hexagonal elements, reasonable agreement is found between calculations and experiment for the volume thermal expansion at temperatures $200\phantom{\rule{0.3em}{0ex}}\mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.

Density functional study of the structural properties of silver halides: LDA vs GGA calculations

We perform first principles total energy calculations to investigate the atomic structure of three silver halides: AgCl, AgBr, and AgI in sodium chloride, cesium chloride, zincblende and wurtzite structures. Calculations are done within the density functional theory. We employ the full potential linearized augmented plane wave method as implemented in the wien2k code. The exchange and correlation potential energies are treated in the generalized gradient approximation (GGA) within the Perdew, Burke, Ernzerhof (PBE) parameterization, and the local density approximation (LDA). Our results show that the LDA calculations correctly predict the ground state structure of all three binary compounds: rocksalt for AgCl and AgBr, and zincblende/wurtzite for AgI, while the PBE calculations always prefer the more covalent zincblende/wurtzite configurations (although the difference between rocksalt and wurtzite energies is very small). We observe that the distribution of electron densities for rocksalt is more homogeneous than that for zincblende. As a consequence, the energy difference between zincblende/wurtzite and rocksalt phases is enhanced in the PBE calculations, predicting the wrong ground state structure for AgCl and AgBr. Assuming the right experimental structure, the PBE parameterization gives lattice parameters, bulk moduli and cohesive energies closer to experimental values.

First-Principles Langevin Molecular Dynamics Studies of Metallic and Semiconductor Clusters: GGA versus LDA Results

The combination of Langevin molecular dynamics for simulated annealing with realistic quantum-mechanical interactions obtained from first principles supercell calculations within the pseudo potential plane-wave method are applied to examine the structural and electronic properties of the following systems i) pure and mixed GenTem (n, m = 0 - 2), Ge3, Te3 and Ge3Te3 semiconductor clusters, and ii) bimetallic PbNan (n ≤ 7) clusters. Results using the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange correlation functional are compared with available experimental data. It is found that the GGA leads to larger bond lengths and smaller binding energies than the LDA, but both approximations lead to the same group symmetry for the ground state of these clusters. Two isomeric configurations for PbNa6, having C3v and Oh symmetries, respectively, are found. The dipole moments of semiconductor clusters are compared with those estimated from recent experiments at room temperature. The dipole moments from GGA calculations are, on average, in better agreement with experiments than those calculated with the LDA.

Density-functional and Monte Carlo study ofO∕Mo(110): Structures and desorption

Structures of oxygen layers on the Mo(110) surface and desorption kinetics have been investigated by means of density-functional theory and generalized gradient approximation calculations and Monte Carlo simulations. It has been found that triply coordinated hollow sites are favorable for oxygen adatoms. All energies of lateral interactions, used in the Monte Carlo simulations of the formation of oxygen structures, are found to be positive, which means that neither trio interactions nor explicit attraction between oxygen adatoms is needed to explain the formation of the $p(2\ifmmode\times\else\texttimes\fi{}1)$ oxygen structure. Simulated scanning tunneling microscopy (STM) images reveal a strong dependence of the relative brightness of images of O adatoms on the sample bias voltage. In particular, protrusions in STM images of oxygen-covered Mo(110) surface, obtained with a negative sample bias, cannot be attributed to images of substrate Mo atoms, but correspond to increased electron density induced by the overlap of atomic densities of neighboring oxygen adatoms. The estimated binding energy between adsorbed O atoms and Mo surface substantially exceeds the binding energy between two oxygen atoms in a free molecule. This feature is suggested to be responsible for the atomic form of oxygen desorption from the Mo(110) surface.

Theoretical analysis on the structure and properties of thiourea dioxide crystal

The equilibrium geometry, electronic structure and optical properties of thiourea S, S-dioxide crystal have been studied using DFT within generalized gradient approximation (GGA) and the local density approximation (LDA), implemented using ultrasoft pseudo-potentials. The optimum bulk geometry is in good agreement with crystallographic data. An analysis of electronic structure, charge and bond order is presented. The energy gap of thiourea dioxide with GGA and LDA calculation is 3.217 or 3.210 eV, respectively, indicating that the compound is an insulator. The calculated absorption spectrum shows a number of absorption peaks, which are believed to be associated with different exciton states, in the fundamental absorption region.

Stability of the cubic phase in GaN doped with 3d-transition metal ions

We investigate the stability of the zinc-blende (ZB) phase in GaN doped with transition metal ions using generalized-gradient approximation (GGA) calculations. The GGA calculations show that the ZB phase can be stabilized when the concentrations of the Cr and Mn ions are greater than 21% and 27% in GaCrN and GaMnN alloys, respectively. In GaFeN alloys, the stabilization of the ZB phase occurs at a much higher concentration of the Fe ions. If strong on-site Coulomb repulsion ( U) is included, the ZB phase cannot be stabilized for all Fe concentrations. We also study the effects of electron and hole doping on the stability of the ZB phase in GaMnN alloys, and find that the critical concentration is reduced to 13% by doping one electron per Mn ion, while hole doping with a hole per Mn ion does not much affect the critical concentration.

Ab initio study on the structural and elastic properties of MAlSi (M=Ca, Sr, and Ba)

Using first-principles total energy calculations within the local density approximation (LDA) and the generalized gradient approximation (GGA), we have investigated the structural and elastic properties of MAlSi (M=Ca,Sr, and Ba) crystallized in hexagonal C32 structure. The lattice parameters and independent elastic constants of MAlSi have been obtained from LDA and GGA calculations. The bulk modulus along crystallographic axes of single crystal, shear modulus, Young’s modulus, and Poisson’s radio of MAlSi are also estimated. The calculated elastic moduli of MAlSi compare well with available experimental values. In addition, the mechanical anisotropy of MAlSi is also discussed.

Surface termination of hematite at environmental oxygen pressures: Experimental surface phase diagram

We provide an experimental surface phase diagram (surface termination versus chemical oxygen potential) of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Fe}}_{2}{\mathrm{O}}_{3}(0001)$ using a natural single crystal surface. In a partial reduction reoxidation cycle, we observe a sequence from oxygen-, to ferryl-, and again oxygen-terminated surfaces, in better agreement with recent density functional theory in the generalized gradient approximation calculations than with calculations taking into account on-site $\mathrm{Fe}\phantom{\rule{0.2em}{0ex}}3d$ Coulomb repulsion. The nonreversible change in surface termination is accompanied by the formation of basal twins, which act as a sink for the extra Fe ions during the surface transformation processes.

Structure of small silver clusters and static response to an external electric field

The static response properties and the structural stability of silver clusters in the size range $1\ensuremath{\le}n\ensuremath{\le}23$ have been studied using a linear combination of atomic Gaussian-type orbitals within the density functional theory in the finite field approach. The Kohn-Sham equations have been solved in conjunction with a generalized gradient approximation (GGA) exchange-correlation functional. A proof that the finite basis set GGA calculation satisfies the Hellmann-Feynman theorem is also included in the Appendix. The calculated polarizabilities of silver clusters are compared with the experimental measurements and the jellium model in the spillout approximation. Despite the fact that the calculated polarizabilities are in good agreement with both of them, we have found that the polarizability appears to be strongly correlated to the cluster shape and the highest occupied--lowest unoccupied molecular-orbital gap.

Realizing the semiconducting state of delafossite AgFeO 2 by GGA + U calculations

The electronic structures of delafossite-type oxide AgFeO 2 have been calculated by using the full potential linearlized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA) and GGA + U. It was found that the GGA calculations lead to a metallic state for AgFeO 2 which is in contradiction with the experiment that AgFeO 2 is a semiconductor. By taking into account the Hubbard interaction parameter U, the GGA + U calculations produce a semiconducting state for AgFeO 2 when U > 0.68 eV. An energy band gap which is the gap between the highest occupied valance band of Ag-3d and the lowest upper Hubbard band of Fe-3d was predicted to be 1.15 eV with an effective U eff = 7.86 eV.

Structural distortion and electronic properties of NiO under high pressure: an abinitio GGA+U study

The structural distortion and electronic properties of NiO under high pressureare investigated by means of first-principles calculations within the densityfunctional theory (DFT) in the generalized gradient approximation (GGA).The strong electronic correlations are also taken into account in the form ofGGA+U. Recent experiments implied that previous local density approximation (LDA) calculationsincorrectly predicted structural distortion under high pressure, especially above 60 GPa.The present results show that even GGA calculations do not give a proper description ofstructural distortion under high pressure, although much improved structural and bulkproperties are obtained. When strong correlations are included, overall agreement of thestructural distortions of NiO under high pressure is obtained. The lattice constantsa andc as well as theaxial ratio c/a are in good agreement with experiment over the entire experimentalpressure range. The successful prediction of the structural distortion ofGGA+U can be attributed to the reasonable description of nearest-neighbour magnetic exchangeinteractions. In addition, we also analyse the density of states under different pressures.Present results indicate that, with increasing pressure, the bandwidth increases and thebandgap transits from being a mixture of charge-transfer and Mott–Hubbard type towardssolely Mott–Hubbard type.