Standard Local Density Approximation Research Articles

A LDA+U and LDA+DMFT study of uranium mononitride: from nonmagnetic to paramagnetic and ferromagnetic

ABSTRACTThe combination of density functional theory in local density approximation and dynamical mean field theory (LDA+DMFT) was employed in a preliminary study of the strong electron correlation effects in a promising nuclear fuel—uranium mononitride (UN). For the ferromagnetic phase, the effective impurity problem arising in the LDA+DMFT [1-3] cycle is solved with the spin-polarized T-matrix fluctuation exchange (SPTF) solver, which includes spin–orbit interactions. Concerning the paramagnetic phase, the disordered local moment (DLM) approach was used, based on both standard local density approximation (LDA) and LDA+U. Basic spectral properties and material properties, such as the spin, orbital and total magnetic moments on U atom were calculated for various values of the Hubbard parameter U with a fixed exchange parameter J. Our main focus was to compare the calculated spectral functions (density of states) for different magnetic phases and different methods to the experimental XPS data [4]. On top of that, the total moments of the paramagnetic and ferromagnetic phases are compared with the measured values by neutron spectroscopy [4, 5].

A first-principles study on the structural, elastic, electronic, and optical properties of CdRh2O4

The structural, elastic, electronic, and optical properties of CdRh2O4 with cubic \( (Fd\overline{ 3} m) \) and orthorhombic (Pnma) structures have been investigated using a pseudopotential plane wave (PP-PW) method within the local density approximation (LDA). The calculated lattice parameters agree reasonably with the experimental values. The single-crystal elastic stiffness constants Cijs of the cubic and orthorhombic phases are investigated using the stress–strain method. In addition, the polycrystalline elastic properties including bulk modulus, shear modulus, Young’s modulus, bulk modulus–shear modulus ratio, Poisson’s ratio, and elastic anisotropy ratio are determined based on Voigt–Reuss–Hill approach. The use of the hybrid functional sX-LDA leads to considerably improved electronic properties compared to standard LDA approach. On the other hand, the dielectric function, refraction index, reflectivity, conductivity function, and energy-loss spectra were obtained and analyzed on the basis of electronic band structures and density of states.

Structural, electronic and thermodynamic properties of SrxCd1−xO: A first-principles study

First principles calculations have been performed within the framework of density functional theory to investigate the structural, electronic and thermodynamic properties of SrxCd1−xO ternary alloys. The exchange-correlation potential for structural properties was calculated by the standard local density approximation (LDA) and GGA (PBE), a more accurate nonempirical density functional generalized gradient approximation (GGA), as proposed by Wu and Cohen [Physical Review B 73 (2006) 235116], while for electronic properties, the Engel and Vosko GGA (EVGGA) and the modified Becke–Johnson (MBJ) of the exchange-correlation energy and potential, respectively, are used. Deviation of the lattice constants from Vegard's law and bulk modulus from linear concentration dependence (LCD) were observed for the ternary alloys. The MBJ band gaps values agree well with the available experimental results. In addition the thermodynamic stability of the alloys was investigated by calculating the critical temperatures of alloys.

ChemInform Abstract: Structural, Elastic, Electronic and Optical Properties of Beryllium Chalcogenides BeX (X: S, Se, Te) with Zinc‐Blende Structure

Abstracttheoretical study

Structural, elastic, electronic and optical properties of beryllium chalcogenides BeX (X = S, Se, Te) with zinc-blende structure

The structural stability, elastic, electronic structures and optical properties of the BeX (X=S/Se/Te) cubic compounds in zinc-blende (B3) structure have been investigated using a pseudopotential plane wave (PP-PW) method within the generalized gradient approximation (GGA) and the local density approximation (LDA). The use of the hybrid functional sX-LDA leads to considerably improved electronic properties compared to standard GGA and LDA approaches. The calculated lattice parameters and bulk modulus agree reasonably with the previous results. The second-order elastic constants have been calculated and we also obtained phase transition pressure of BeX from B3 to NiAs (B8) structures. The enthalpy of formation, band structure, density of states and electric charge density is as well given. On the other hand, an accurate calculation of linear optical functions (the dielectric function, refraction index and reflectivity) is performed. The results obtained are compared with other calculations and experimental measurements.

Beyond standard local density approximation in the study of magnetoelectric effects in Fe/BaTiO3 and Co/BaTiO3 interfaces

First-principles density functional theory (DFT) simulations for Fe/BaTiO3 and Co/BaTiO3 junctions have been performed with different treatments of the exchange–correlation potential, ranging from standard semilocal density approximations to a Hubbard-like approach and to hybrid functionals. With the aim of elucidating the role of correlations in the microscopic interplay between ferroelectricity and magnetism in the interfacial region, we find that, compared to standard DFT approximations, Hubbard-like approaches and hybrid functionals do not qualitatively modify the physical origin behind magnetoelectric effects driven by interfacial orbital hybridization. Rather, more accurate treatments of correlations for both Fe/BaTiO3 and Co/BaTiO3 interfaces predict a stronger change of the interface magnetization upon switching the direction of polarization in the ferroelectric layer.

Correlation effects in magnetic materials: An ab initio investigation on electronic structure and spectroscopy

Various technical developments enlarged the potential of angle-resolved photoemission spectroscopy (ARPES) tremendously during the last two decades. In particular improved momentum and energy resolution in combination with spin-resolution as well as the use of photon energies from few eV up to several keV makes ARPES a rather unique tool to investigate the electronic properties of solids and surfaces. Obviously, this rises the need for a corresponding theoretical formalism that allows to accompany experimental ARPES studies in an adequate way. As will be demonstrated by several examples this goal could be achieved by various recent developments on the basis of density functional theory (DFT) in combination with dynamical mean field theory (DMFT) and with the one-step model of photoemission (1SM). A concrete realization of electronic structure calculations in the framework of multiple scattering theory further more provides direct access to the spectral function of the initial states via the one-electron Green function. Based on this bare spectral function matrix-element and final-state effects as well as surface related features may be calculated in addition using the one-step formalism that offers the possibility to analyse corresponding angle-resolved photoemission experiments in a quantitative sense. The impact of chemical disorder can be handled by means of the coherent potential approximation (CPA) alloy theory, in the electronic structure calculation as well as in the photoemission analyses. The same holds for the influence of electronic correlation effects. These are accounted for by means of the DMFT that removes the most serious short comings of calculations based on the standard local spin density approximation (LSDA). The self-consistent combination of this approach with the CPA allows, for example, the investigation of correlated transition metal alloys. Finally, accounting for the photon momentum and going beyond the single scatterer approximation for the final state allows to deal quantitatively with ARPES in the high-energy regime (HAXPES) that reduces the influence of the surface on the spectra and therefore probes primarily the bulk electronic structure this way.

Band structure calculations of CuAlO2, CuGaO2, CuInO2, and CuCrO2by screened exchange

We report density functional theory (DFT) band structure calculations on the transparent conducting oxides CuAlO2, CuGaO2, CuInO2 and CuCrO2. The use of the hybrid functional sX-LDA leads to considerably improved electronic properties compared to standard local density approximation (LDA) and generalized gradient approximation (GGA) approaches. We show that the resulting electronic band gaps compare well with experimental values and previous quasiparticle calculations and show the correct trends with respect to the atomic number of the cation (Al, Ga, In). The resulting energetic depths of Cu d and O p levels and the valence band widths are considerable improvements compared to LDA and GGA and in good agreement with available x-ray photoelectron spectroscopy (XPS) data. Lastly, we show the calculated imaginary part of the dielectric function for all four systems.

Energy calculations of quantum dot

We calculated the total energy of a semiconductor quantum dot formed in gate and etching defined devices. A 3D Poisson equation is solved self-consistently to obtain the electron density and potential profile. The total energies of electrons in the quantum dots with two different sizes are calculated with three different approximations by using the density and potential obtained from self-consistent procedure. In our calculation we used a recently developed energy functional called “orbital-free energy functional”, Thomas–Fermi approximation and standard local-density approximation within density functional theory. The comparison of these methods reveals the efficacy of the used newly developed orbital-free energy functional which facilitates the calculation of Hartree integral for treatment of electron–electron interaction.

Calculation of angle-resolved photo emission spectra within the one-step model of photo emission—Recent developments

Various technical developments enlarged the potential of angle-resolved photo emission spectroscopy (ARPES) tremendously during the last one or two decades. In particular improved momentum and energy resolution as well as the use of photon energies from few eV up to several keV makes ARPES a rather unique tool to investigate the electronic properties of solids and surfaces. Obviously, this rises the need for a corresponding theoretical formalism that allows to accompany experimental ARPES studies in an adequate way. As will be demonstrated by several examples this goal could be achieved by various recent developments on the basis of the one-step model of photo emission: the spin–orbit induced Rashba-splitting of Shockley-type surface states is discussed using a fully relativistic description. The impact of chemical disorder within surface layers can be handled by means of the coherent potential approximation (CPA) alloy theory. Calculating phonon properties together with the corresponding electron–phonon self-energy allows a direct comparison with features in the ARPES spectra caused by electron–phonon interaction. The same holds for the influence of electronic correlation effects. These are accounted for by means of the dynamical mean field theory (DMFT) that removes the most serious short comings of standard calculations based on the standard local density approximation (LDA). The combination of this approach with the CPA allows the investigation of correlated transition metal alloys. Finally, accounting for the photon momentum and going beyond the single scatter approximation for the final state allows to deal quantitatively with ARPES in the high-energy regime (HAXPES) that reduces the influence of the surface on the spectra and probing primarily the bulk electronic structure this way. Corresponding calculations of ARPES spectra, however, have to deal with thermal vibrations in an adequate way. For this, a new scheme is suggested that makes use of the CPA.

SEMICLASSICAL DESCRIPTION OF AVERAGE PAIRING PROPERTIES IN NUCLEI

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the ħ → 0, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvment of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

First-principles accurate total energy surfaces for polar structural distortions ofBaTiO3,PbTiO3, andSrTiO3: Consequences for structural transition temperatures

Specific forms of the exchange correlation energy functionals in first-principles density functional theory-based calculations, such as the local density approximation (LDA) and generalized-gradient approximations (GGA), give rise to structural lattice parameters with typical errors of -2% and 2%. Due to a strong coupling between structure and polarization, the order parameter of ferroelectric transitions, they result in large errors in estimation of temperature dependent ferroelectric structural transition properties. Here, we employ a recently developed GGA functional of Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] and determine total-energy surfaces for zone-center distortions of BaTiO3, PbTiO3, and SrTiO3, and compare them with the ones obtained with calculations based on standard LDA and GGA. Confirming that the Wu and Cohen functional allows better estimation of structural properties at 0 K, we determine a new set of parameters defining the effective Hamiltonian for ferroelectric transition in BaTiO3. Using the new set of parameters, we perform molecular-dynamics (MD) simulations under effective pressures p=0.0 GPa, p=-2.0 GPa, and p=-0.005T GPa. The simulations under p=-0.005T GPa, which is for simulating thermal expansion, show a clear improvement in the cubic to tetragonal transition temperature and c/a parameter of its ferroelectric tetragonal phase, while the description of transitions at lower temperatures to orthorhombic and rhombohedral phases is marginally improved. Our findings augur well for use of Wu-Cohen functional in studies of ferroelectrics at nano-scale, particularly in the form of epitaxial films where the properties depend crucially on the lattice mismatch.

Band structures of delafossite transparent conductive oxides from a self-consistentGWapproach

We present a comparative study of the electronic band structures of the compounds CuMO2 M=B,Al,In,Ga which belong to the family of delafossite transparent conductive oxides. The theoretical approaches we use are the standard local-density approximation LDA to density-functional theory, LDA + U, hybrid functionals, and perturbative GW on top of LDA or self-consistent Coulomb hole plus screened exchange calculations. The latter approach, state-of-the-art theoretical approach for quasiparticle band structures, predicts direct band gaps that are compatible with experimental optical gaps only after including the strong polaronic and excitonic effects present in these materials. For what concerns the so-called band-gap anomaly of delafossite compounds, we find that GW approaches yield the same qualitative trends with increasing anion atomic number as the LDA: accounting for the oscillator strength at the absorption edge is the key to explain the experimental trend. None of the methods that we applied beyond the simple LDA is in agreement with the small indirect gaps found by many early experiments. This supports the recent view that the absorption bands identified as a sign of the indirect experimental gaps are likely due to defect states in the gap and are not a property of the pristine material.

First-principles calculations of structural, electronic and optical properties of Cd xZn 1 −xS alloys

Structural, electronic and optical properties of ternary alloy system Cd x Zn 1 −x S have been studied using first-principles approach based on density functional theory. Electronic structure, density of states and energy band gap values for Cd x Zn 1 −x S are estimated in the range 0 ≤ x ≤ 1 using both the standard local density approximation (LDA) as well as the generalized gradient approximations (GGA) of Wu–Cohen (WC) for the exchange-correlation potential. It is observed that the direct band gap E g Γ − Γ of Cd x Zn 1 −x S decreases nonlinearly with the compositional parameter x, as observed experimentally. It is also found that Cd s and d, S p and Zn d states play a major role in determining the electronic properties of this alloy system. Furthermore, results for complex dielectric constant ɛ( ω), refractive index n( ω), normal-incidence reflectivity R( ω), absorption coefficient α( ω) and optical conductivity σ( ω) are also described in a wide range of the incident photon energy and compared with the existing experimental data.

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

First-principles modeling of systems with localized $d$ states is currently a great challenge in condensed-matter physics. Density-functional theory in the standard local-density approximation (LDA) proves to be problematic. This can be partly overcome by including local Hubbard $U$ corrections $(\text{LDA}+U)$ but itinerant states are still treated on the LDA level. Many-body perturbation theory in the $GW$ approach offers both a quasiparticle perspective (appropriate for itinerant states) and an exact treatment of exchange (appropriate for localized states), and is therefore promising for these systems. $\text{LDA}+U$ has previously been viewed as an approximate $GW$ scheme. We present here a derivation that is simpler and more general, starting from the static Coulomb-hole and screened exchange approximation to the $GW$ self-energy. Following our previous work for $f$-electron systems [H. Jiang, R. I. Gomez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. 102, 126403 (2009)] we conduct a systematic investigation of the $GW$ method based on $\text{LDA}+U(GW@\text{LDA}+U)$, as implemented in our recently developed all-electron $GW$ code FHI-gap (Green's function with augmented plane waves) for a series of prototypical $d$-electron systems: (1) ScN with empty $d$ states, (2) ZnS with semicore $d$ states, and (3) late transition-metal oxides (MnO, FeO, CoO, and NiO) with partially occupied $d$ states. We show that for ZnS and ScN, the $GW$ band gaps only weakly depend on $U$ but for the other transition-metal oxides the dependence on $U$ is as strong as in $\text{LDA}+U$. These different trends can be understood in terms of changes in the hybridization and screening. Our work demonstrates that $GW@\text{LDA}+U$ with ``physical'' values of $U$ provides a balanced and accurate description of both localized and itinerant states.

Antiadiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

We express the high-frequency (anti-adiabatic) limit of the exchange-correlation kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the kinetic stress tensor, the pair-correlation function, and the ground-state exchange-correlation potential. Of these quantities, the first three are amenable to exact evaluation by Quantum Monte Carlo methods, while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The anti-adiabatic xc kernels should be useful in calculations of excitation energies by time-dependent DFT in atoms, molecules, and solids, and provides a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

Orbital-free energy functional for electrons in two dimensions

We derive a nonempirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr for three-dimensional systems [R. G. Parr, J. Phys. Chem. 92, 3060 (1988)], and the Thomas-Fermi approximation for the kinetic energy. The freedom from orbitals and from the Hartree integral makes the proposed approximation numerically highly efficient. The total energies obtained for confined two-dimensional systems are in a good agreement with the standard local-density approximation within density-functional theory and considerably more accurate than the Thomas-Fermi approximation.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transition state) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schr\odinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self-interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self-energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

First principles calculations of structural, electronic and optical properties of various phases of CaS

First principles calculations have been performed within the framework of density functional theory to investigate the structural, electronic and optical properties of all four possible B1, B2, B3 and B4 phases of CaS. Apart from the standard local density approximation (LDA) and GGA (PBE), a more accurate nonempirical density functional generalized gradient approximation (GGA), as proposed by Wu and Cohen [Phys. Rev. B 73, 235116 (2006)] for the exchange-correlation energy, EXC, has been attempted in these calculations. Calculated electronic structure and the density of states are analyzed in terms of the contribution of Ca d states and S s and p states in determining the nature of the fundamental band gap in various phases. Reflectivity, R (ω), the real and imaginary part of the dielectric functions, e(ω), have been calculated for all the phases and the results have been discussed and compared with the existing experimental data.

Including nonlocality in the exchange-correlation kernel from time-dependent current density functional theory: Application to the stopping power of electron liquids

We develop a scheme for building the scalar exchange-correlation (XC) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent current density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical XC contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA.