Local Density Approximation Exchange Research Articles

Improved electronic structure and optical properties of sp-hybridized semiconductors using LDA+U SIC

We propose the local density approximation (LDA) plus an on-site Coulomb self-interaction-like correction (SIC) potential for describing sp-hybridized bonds in semiconductors and insulators. We motivate the present LDA+U SIC scheme by comparing the exact exchange (EXX) hole with the LDA exchange hole. The LDA+U SIC method yields good band-gap energies Eg and dielectric constants epsilon(omega ~ 0) of Si, Ge, GaAs, and ZnSe. We also show that LDA consistently underestimates the gamma-point effective electron m c and light-hole m lh masses, and the underlying reason for this is a too strong light-hole-electron coupling within LDA. The advantages of the LDA+U SIC approach are a computational time of the same order as the ordinary LDA, the orbital dependent LDA+U SIC exchange-correlation interaction is asymmetric analogously to the EXX potential, and the method can be used for materials and compounds involving localized d- and f-orbitals.

Semiempirical van der Waals correction to the density functional description of solids and molecular structures

The influence of a simple semiempirical van der Waals (vdW) correction on the description of dispersive, covalent, and ionic bonds within density functional theory is studied. The correction is based on the asymptotic London form of dispersive forces and a damping function for each pair of atoms. It thus depends solely on the properties of the two atoms irrespective of their environment and is numerically very efficient. The correction is tested in comparison with results obtained using the generalized gradient approximation or the local density approximation for exchange and correlation. The results are also compared with reference values from experiment or quantum chemistry methods. In order to probe the universality and transferability of the semiempirical vdW correction, a range of solids and molecular systems with covalent, heteropolar, and vdW bonds are studied.

Electronic structure of zinc-blendeAlxGa1−xN: Screened-exchange study

We present a first principle investigation of the electronic structure and the band gap bowing parameter of zinc-blende using both local density approximation and screened-exchange density functional method. The calculated screened exchange local density approximation (sX-LDA) band gaps for GaN and AlN are 95% and 90% of the experimentally observed values, respectively, while LDA underestimates the gaps to 62% and 70%. In contrast to the gap itself, the band gap bowing parameter is found to be very similar in sX-LDA and LDA. Because of the difference in the conduction band structure, the direct to indirect band gap crossover is predicted to occur at different Al concentration.

Electron correlation effects on SiC(111) and SiC(0001) surfaces

The possibility is discussed that, independent of the polytype, large electronic correlationeffects give rise to semiconducting SiC surfaces with [111] or [0001] orientations. The mostimportant surface translational symmetries and 3 × 3 are considered. The discussion is based on the detailed knowledge of the surfaceatomic geometries and the electronic structures derived for these geometries usinga local density approximation for exchange and correlation. It is argued thatthe resulting half-filled, weakly dispersive dangling-bond bands within thefundamental gaps are split according to a Hubbard interaction parameterU, and that the surface systems undergo a Mott–Hubbard transition. Such a physical pictureprovides a qualitatively correct account of the single-particle excitation spectra eitherinferred from angle-resolved photoemission and inverse photoemission experiments orobtained from scanning tunnelling spectroscopy. The gap opening and hence the HubbardU parameter are discussed in terms of their dependence on the surface reconstruction as wellas the SiC polytype.

Meta-generalized gradient approximation: explanation of a realistic nonempirical density functional.

Tao, Perdew, Staroverov, and Scuseria (TPSS) have constructed a nonempirical meta-generalized gradient approximation (meta-GGA) [Phys. Rev. Lett. 91, 146401 (2003)] for the exchange-correlation energy, imposing exact constraints relevant to the paradigm densities of condensed matter physics and quantum chemistry. Results of their extensive tests on molecules, solids, and solid surfaces are encouraging, suggesting that this density functional achieves uniform accuracy for diverse properties and systems. In the present work, this functional is explained and details of its construction are presented. In particular, the functional is constructed to yield accurate energies under uniform coordinate scaling to the low-density or strong-interaction limit. Its nonlocality is displayed by plotting the factor F(xc) that gives the enhancement relative to the local density approximation for exchange. We also discuss an apparently harmless order-of-limits problem in the meta-GGA. The performance of this functional is investigated for exchange and correlation energies and shell-removal energies of atoms and ions. Non-self-consistent molecular atomization energies and bond lengths of the TPSS meta-GGA, calculated with GGA orbitals and densities, agree well with those calculated self-consistently. We suggest that satisfaction of additional exact constraints on higher rungs of a ladder of density functional approximations can lead to further progress.

Electronic and crystallographic structure of apatites

An ab initio study of four different stoichiometric apatites (oxyapatite, hydroxyapatite, fluorapatite, and chlorapatite) is presented. The calculations were performed using density-functional theory with the local-density approximation for exchange and correlation, and a full relaxation of the electronic structure, the atomic arrangement, and the unit cell. Hexagonal unit cells were obtained for all four apatites, and the calculated atomic arrangements are in close agreement with observation in those cases for which the structure is firmly established. A zero-temperature structure is predicted for oxyapatite, and two possible configurations were found for the ${\mathrm{Cl}}^{\ensuremath{-}}$ ions in chlorapatite. The possibility of the monoclinic structure in hydroxyapatite and chlorapatite was also studied but no indication of greater stability with respect to the hexagonal structure was found. A relationship between the structure of the apatites and that of pure calcium is discussed.

Effect of Fock exchange on the electronic structure and magnetic coupling in NiO

The effect of Fock exchange on the periodic description of the geometrical structure, elastic constants, and electronic and magnetic properties of NiO is analyzed. Hybrid density functionals which combine a portion of ``exact'' Fock exchange with conventional local density approximation (LDA) or generalized gradient approximation (GGA) functionals remedy a number of serious inconsistencies with the traditional LDA or GGA descriptions of this prototypical ``Mott'' insulator. For example, the hybrid B3LYP functional (which mixes \ensuremath{\sim}20% Fock exchange with GGA functionals) introduces a significant insulating gap and yields antiferromagnetic Heisenberg coupling constants between Ni sites ${(J}_{2})$ in semiquantitative agreement with experiment. Closer inspection shows that while the B3LYP orbital band gap is in excellent agreement with experiment, the magnitude of the antiferromagnetic coupling is overestimated by slightly more than 50%. This has led us to examine a simplified model which combines Fock exchange with the LDA exchange and correlation functionals. This combination allows us to study the magnitude and nature of the band gap, the magnitude of the unpaired spin densities in the different magnetic phases, and the two most important magnetic coupling constants as a function of the fraction of Fock exchange included. It is concluded that \ensuremath{\sim}35% Fock exchange gives a reasonably balanced description of all properties, including structural parameters, magnetic form factors, the antiferromagnetic Ni-Ni exchange constant, and the character and magnitude of the band gap.

Localized non-orthogonal orbitals in silicon

A comparison of orthogonal and non-orthogonal localized wavefunctions for Si in the diamond structure is carried out. We have used a real-space grid formulation of density functional theory in combination with the local density approximation for exchange and correlation to describe the energetics. Maximally localized wavefunctions, obtained from the extended Kohn-Sham states with and without an orthogonality constraint, are calculated and it is found that the wavefunctions calculated without any orthogonality constraint are the most localized. When solving directly for localized states, by applying a localization constraint to each electronic state, we find that there is a large difference between orthogonal and non-orthogonal states: when the localization region is a sphere with a radius of 3.0 Å, we get an error in the total energy due to the localization constraint of 0.2 and 2.7 eV/atom for non-orthogonal and orthogonal wavefunctions respectively.

COMPARISON OF DENSITY FUNCTIONAL APPROXIMATIONS IN THE JELLIUM MODEL FOR METAL CLUSTERS

We calculated the exchange, correlation and total energies of clusters of alkali metals with N=1-150 atoms in the spherical jellium model. The calculations were made using the Kohn-Sham method with exchange and correlation energies evaluated in the meta-generalized gradient approximation (MGGA), proposed by J. P. Perdew, S. Kurth, A. Zupan and P. Blaha, in the generalized gradient approximation (GGA) of J. P. Perdew, K. Burke and M. Ernzerhof, and in the Local Density Approximation (LDA). We evaluated the relative deviations of MGGA and GGA energies with respect to LDA. Exchange energies of MGGA and GGA are more negative than the LDA exchange energy and become closer to this as the cluster size increases. On the other hand, the GGA and MGGA correlation energies, which are almost identical, are less negative than LDA. The deviations of GGA and MGGA exchange-correlation energies with respect to LDA are smaller than those of the exchange and correlation energies separately. For clusters with 18 and 20 atoms we have compared our jellium results with Variational and Diffusion Monte-Carlo results. Errors of LDA for exchange and correlation tend to cancel so that the total exchange-correlation energy is close to the Monte-Carlo results. Similar cancellations occur with GGA and MGGA. We also examined the validity of the liquid drop model.

Dynamic Image Potential at an Al(111) Surface

We evaluate the electronic self-energy $\ensuremath{\Sigma}(E)$ at an Al(111) surface using the $\mathrm{GW}$ space-time method. This self-energy automatically includes the image potential ${V}_{\mathrm{im}}$ not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure.

Relativistic models for nuclear structure calculations: Comparative study of mean-field and Hartree-Fock approximation for superheavy nuclei

The relevance of exchange effects for the stability of superheavy nuclei is examined within a linear QHD-II model by comparing Hartree-Fock with meanfield results. To allow a scan of the complete superheavy regime the recently developed local density approximation (LDA) for the exchange potential is employed for the Hartree-Fock level calculations. It turns out that, while many nuclear properties obtained with the LDA approach differ significantly from the corresponding mean-field results, the predictions of the two methods for shell closures are very similar. Furthermore, a comparison with a nonlinear variant of QHD-II shows that many nuclear properties obtained with the LDA in the framework of linear QHD-II are somewhere in-between the corresponding linear and nonlinear mean-field results. This indicates that the LDA exchange partially includes nonlinear contributions, which supports the interpretation of the meson self-coupling as a parametrization of many-body effects.

Gradient-corrected correlation with nearly exact Kohn-Sham exchange: Calculations for Si and Ge

We have constructed a pseudopotential that reduces the errors inherent in ordinary pseudopotentials when used together with nonlocal exchange potentials. Using the very accurate approximation of Krieger, Li, and Iafrate to the exact Kohn-Sham exchange potential together with correlation in the local-density approximation (LDA) both with and without the generalized gradient correction of Perdew and Wang, we calculated the electronic and physical properties of Si and Ge. The gradient corrections result in a large reduction of the indirect energy gaps, worsening agreement with experiment. They also reduce the total energy of both of the atoms and both of the crystals, resulting in increases of the Si and Ge cohesive energies which improve their agreement with experiment. In addition we have studied the effect of adding gradient corrections when the valence electrons see a Hartree-Fock potential from the core electrons and LDA exchange and correlation among themselves.

Transferable model for the atomistic simulation of Al2O3.

We calculate the energies of different solid phases of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ using a shell model, a compressible ion model, and a compressible ion model which includes both dipole and quadrupolar polarizability of the ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions. Compressible oxygen ions are found to stabilize the corundum structure with respect to the \ensuremath{\theta} form of alumina. The observed corundum structure is nevertheless unstable with respect to the bixbyite structure until quadrupolar polarizability of the oxygen is also included. Entropy differences are estimated with a lattice dynamics calculation and are found to make an insignificant contribution to stabilizing the corundum. We also calculate the relative energies of the corundum and bixbyite structures using the ab initio pseudopotential method, within the local-density approximation for exchange and correlation. The resulting self-consistent electron density shows graphically how the quadrupolar distortions around the oxygen develop as the basis is made more complete (the plane-wave cutoff is increased from 500 to 700 eV), which at the same time brings the energy of the corundum structure below that of the bixbyite structure. \textcopyright{} 1996 The American Physical Society.

Ensuring the constancy of the chemical potential within the local-density approximation for exchange and correlation: Implications for near-edge x-ray-absorption fine structure.

We investigate the correct implementation of the exchange-correlation potential for the excited core electron in near-edge x-ray-absorption fine structure (NEXAFS). We examine the effects on NEXAFS spectra of the ground-state Slater and excited-state Dirac-Hara exchange potentials and current implementations of the Hedin-Lundqvist exchange-correlation potential on the muffin-tin model. For a test case of gas-phase acetylene, we find good agreement with prior experimental spectra only with the Hedin-Lundqvist potential implemented on the local-density approximation with a Thomas-Fermi-like requirement of constancy of the chemical potential.

Exchange and correlation in density functional theory

The accurate description of exchange and correlation effects is a key issue in density functional theory (DFT). In spite of its widespread use, the local density approximation (LDA) has well-known deficiencies. In atoms, the empirical correlation energies are of the same magnitude as the errors of the LDA for exchange. This means that an accurate description of exchange in atoms or molecules is a prerequisite for the introduction of Coulomb correlation. One of the methods that today achieve such an accuracy is the weighted density approximation (WDA). Calculations of the exchange and total energies are presented to substantiate this statement. An optimized local-like approximation (OLA) to Coulomb correlation, based on an explicit modeling of the Coulomb hole, is then combined with the WDA for exchange. The results for total energies and other atomic properties look very promising. A combination of the OLA with several generalized gradient approximations (GGAS) for exchange is explored for molecules. © 1995 John Wiley & Sons, Inc.

Interpretation of electron correlation in the local-density approximation for exchange.

We provide a new interpretation of how electron correlations are represented within the local-density approximation for exchange by deducing via Harbola-Sahni theory the corresponding pair-correlation density. The expression differs from that in the literature and contains, in addition to the uniform electron-gas result, a term proportional to the gradient of the density. Thus, the nonuniformity of the electronic density is explicitly incorporated in the approximation, and constitutes thereby the reason underlying its success.

Rigorous and unifying physical interpretation of the exchange potential and energy in the local-density approximation.

In this paper we explain that the exchange potential and energy in the local-density approximation (LDA) of density-functional theory has a IrigorousP and IunifiedP physical interpretation founded in the work of Harbola and Sahni. Accordingly, the IsourceP charge distribution that gives rise to both the LDA exchange (path-independent) potential IandP energy is the Fermi hole as derived in the gradient-expansion approximation (GEA) to O(\ensuremath{\nabla}). Thus, the LDA exchange potential, or equivalently the functional derivative of the LDA exchange-energy functional of the density, is the work required to bring an electron from infinity to its position at r against the force field of this charge distribution. The LDA exchange energy in turn is the energy of interaction between the electronic density and this charge. However, it is the non-spherically-symmetric component of the source charge that gives rise to the potential but its spherically symmetric component that contributes to the energy. Since the underlying physics of the LDA for exchange lies in its source charge, we next determine the structure of the GEA Fermi hole to O(\ensuremath{\nabla}) for the nonuniform electronic system in atoms and at metallic surfaces. A study of this structure as a function of electron position shows that the errors in the LDA arise because the source charge does not in general reproduce accurately the structure of the exact Fermi hole, that it violates the quantum-mechanical requirement of positivity, and further that it oscillates, albeit with decaying amplitude, far into the classically forbidden region.

R-T and R-R exchange interactions in the rare-earth (R)-transition-metal (T) intermetallics: an evaluation from relativistic atomic calculations

Intra-atomic exchange integrals J4f-5d, J4f-6s and J4f-6p for rare-earth trivalent ions were obtained from relativistic self-consistent field atomic calculations, using the local-density approximation for exchange and correlation potential. The effective (molecular-field) exchange coefficients nRT between rare-earth and transition-metal ions and nRR between rare-earth ions were obtained based on a simplified three-sublattice (4f, 3d and conduction electron) mean-field model. Quantitative results show a decrease in magnitude of nRT across the rare-earth series, which agrees well with values observed in many rare-earth-transition-metal intermetallic series. It is shown that the 4f-5d exchange interaction is far more important than the 4f-6s and 4f-p interactions, as expected from the Campbell model for the exchange interactions occurring in rare-earth-transition-metal intermetallics.

Pseudo-atom calculation of energetics in metals

A mixed-basis approach for calculating first-principles electronic structure and total energies in metals is presented. The technique uses the local-density approximation for exchange and correlation in the pseudopotential framework and a minimal basis of localised pseudo-atomic orbitals which may be supplemented with a few low-energy plane waves. Aside from being accurate, the method is faster and the results are more easily interpretable than conventional plane-wave methods. The method is used to calculate bulk properties of Al and Nb and the vacancy and high-symmetry octahedral-site self-interstitial formation energies in Al.

Simple formula for the atomic forces in the augmented-plane-wave method.

We present a simple and explicit method for the computation of atomic forces in ab initio total-energy calculations using a basis of augmented plane waves (APW) and the local-density approximation for exchange and correlation. The force on an atom is given by integrals over its muffin-tin sphere only, which can be obtained easily in existing implementations of the linear APW method, for example. The extra computational cost of calculating the forces on all the atoms is negligible compared with that of performing one single self-consistency iteration step.