Self-interaction Correction Research Articles

Theoretical study on the electronic structure of (Si)m/(Ge)n superlattices.

The electronic structures of (Si${)}_{\mathrm{m}}$/(Ge${)}_{\mathrm{n}}$ superlattices with (001) stacking were studied by using the linear-muffin-tin-orbital method. A simple scheme of a self-interaction correction was implemented in order to predict the semiconductor band gap quantitatively. As the ten-layer periodicity is particularly suitable for realizing direct-band-gap superlattices, we studied several modulated superlattices (Si${)}_{\mathrm{m}\ensuremath{'}}$/(Ge${)}_{\mathrm{n}\ensuremath{'}}$/(Si${)}_{\mathrm{m}\mathrm{\ensuremath{''}}}$/(Ge${)}_{\mathrm{n}\mathrm{\ensuremath{''}}}$$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{ct}}$ with m\ensuremath{'}+n\ensuremath{'}+m\ensuremath{''}+n\ensuremath{''}+$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{ct}}$=10. We found interesting variations in the symmetry of the conduction-band bottom state and also in the wave-function confinement in the Si layer with regard to the variation in the set of (m\ensuremath{'},n\ensuremath{'},m\ensuremath{''},n\ensuremath{''},...). These results were analyzed with simple models. The dipole transition probability was also estimated. Some calculations were also performed to discuss the alloying effects at the interface for the (Si${)}_{4}$/(Ge${)}_{4}$ superlattice on the Si substrate.

Multiply charged anionic metal clusters

The stability and decay channels of multiply charged anionic metal clusters are studied using the uniform jellium background model and the local density approximation, with self-interaction corrections when necessary. Shell effects are introduced using an adaptation of the nuclear Strutinsky method. Singly charged anions are stable for all sizes, but multiply charged negative ions are stable against spontaneous electron decay only above certain critical sizes. Below the border of stability, the anions are metastable against electron tunneling through a Coulombic barrier. Lifetimes for such decay processes are estimated. Fission channels may compete with the electron autodetachment and are studied for the case of doubly charged anions.

Self-interaction-corrected electronic structure of La2CuO4.

We have applied the self-interaction-corrected (SIC) local-spin-density-approximation (LSDA) formalism to ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$. In contrast to the local-spin-density result the self-interaction-corrected formalism yields correctly an antiferromagnetic semiconducting ground state as found experimentally. The band gap of 2.1 eV and spin magnetic moment of 0.66${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$ compare favorably with experimental values. The bonding properties are correctly described proving that the SIC LSDA is also capable of describing the properties that have been correctly predicted within LSDA.

A band structure treatment of 4f electrons in DHCP Pr metal

We implement the self-interaction correction to the local density approximation for elemental DHCP Pr metal. We find that the occupied f-bands are split by ∼ 10 eV from the unoccupied ones. The occupied f-bands occur well below the bottom of the conduction band, whilst the unoccupied f-bands strongly hybrize with the conduction s, p, d bands, creating flat d-bands at the Fermi level. The Fermi surface consists of four sheets of predominantly d-character, in agreement with de Haas-van Alphen experiment. We estimate mass enhancement λ to be 1.6, in contrast to frozen core LDA value of 4.5.

4f energy levels in band theory and the Fermi surface structure of La and Ce compounds

We calculate 4f energy levels by a non-empirical band theory including the self-interaction correction and the unoccupied states potential correction. The 4f levels of La compounds appear at about 6 eV above the Fermi energy consistently with Bremsstrahlung isochromat spectroscopy experiments, but further improvements are necessary for the Fermi surface structure calculation.

Self-interaction corrected density functionals and the structure of metal clusters

An approach, based upon the Car–Parrinello method, for finding the electronic ground state for a self-interaction corrected density functional theory is described. The influence of the self-interaction correction for the ground-state properties and for predicted equilibrium molecular structures is illustrated with reference to calculations on small clusters of sodium.

ELECTRONIC STRUCTURE OF SOLIDS IN THE SELF-INTERACTION CORRECTED LOCAL-SPIN-DENSITY APPROXIMATION

An ab-initio implementation of self-interaction corrections (SIC) within local spin density (LSD) electronic structure calculations of solids is presented. The linear-muffin-tin orbital method is used in the tight-binding representation and with the atomic spheres approximation. The variational minimum of the SIC-LSD energy functional is found by the steepest descent method, i.e., no matrix diagonalizations are involved. Special care is taken to secure stability with respect to unitarian mixing of electron states. Applied to the transition metal monoxides and La 2 CuO 4 the SIC-LSD significantly improves the desription in comparison to LSD.

Towards an understanding of the electronic structure of mott-insulating transition metal oxides

Due to suggestions that Self Interaction Corrections (SIC), gradient corrections, and short-range electron–electron interactions in the Local (Spin) Density Approximation (L(S)DA) scheme may significantly influence the computed electronic structure for the Mott-insulating (MI) transition metal oxides (TMOS), a comparative study has been made of Hartree Fock (HF) and L(S)DA computations for NiO. Since HF lacks electronic correlation, it overestimates band width (in conductors) and/or band gaps (in insulators). It gives the band gap for NiO two times larger than that in experiment, while LSDA gives the gap one order of magnitude smaller than the experimental value. We demonstrate that the HF results are consistent with some previously believed to be well-understood experiments, while the L(S)DA results are not. It is suggested that HF may offer a better reference state for the development of a LSDA scheme. © 1993 John Wiley & Sons, Inc.

Application of the self-interaction correction to transition-metal oxides.

We have implemented the self-interaction-corrected local-spin-density approximation within the standard linear-muffin-tin-orbital--atomic-sphere-approximation band-structure method making use of a unified Hamiltonian concept. We have used this ab initio band-structure scheme to study the electronic structure of MnO, FeO, CoO, NiO, and CuO. We find them to be wide-gap insulators, where the top of the valence band, of predominantly oxygen p character, shows a substantial hybridization with the metal d states.

Band-structure method for 4f electrons in elemental Pr metal.

We implement the self-interaction correction to the local-density approximation (LDA) for elemental double hexagonal-close-packed (dhcp) Pr metal. We find that the occupied f bands are split by \ensuremath{\sim}10 eV from the unoccupied ones. The occupied f bands occur well below the bottom of the conduction band, while the unoccupied f bands strongly hybridize with the conduction s, p, and d bands, creating flat d bands at the Fermi level. The on-site Coulomb energy for the localized electrons, ${\mathit{U}}_{\mathit{f}\mathit{f}}$, is about 12 eV, and the Fermi surface consists of four sheets of predominantly d character, in agreement with de Haas--van Alphen experiment. We estimate mass enhancement \ensuremath{\lambda} to be 1.6, in contrast to a frozen-core LDA value of 4.5.

Spin-density functionals for the electron correlation energy with automatic freedom from orbital self-interaction

Using two different interpretations of the concept of the Fermi hole curvature, the author derives a class of correlation energy expressions for the inhomogeneous interacting electron gas. Their properties include freedom from spurious orbital self-interaction, invariance under unitary transformations among occupied orbitals, correct values in the homogeneous limit, correctly normalized correlation hole, inclusion of kinetic energy (KE) as well as potential energy of correlation, and non-vanishing values for fully spin-polarized systems (in contrast with some similar schemes developed for chemical applications). Minimization of the energy with respect to the orbitals leads to a Euler-Lagrange equation resembling the Hartree-Fock one-electron effective Schrodinger equation, with the addition of a term resembling the KE operator for an inhomogeneous effective mass. For current-carrying states there is a further term involving an effective dynamically induced vector potential. Despite these complications the effective one-electron Hamiltonian is Hermitian, so that the canonical orbitals are orthogonal, in contrast with those of the commonest self-interaction correction scheme.

A density functional study of the aluminium dimer

The ground state of the aluminium dimer was investigated using the density functional method within the self-interaction correction to local spin density. The results confirm that the lowest states are triplets according to the most recent ab initio quantum chemistry calculations, even if the ordering of the symmetries is reversed. The lowest state is interpreted in terms of two spin-parallel one-electron banana bonds. Spin-coupled results are also presented in order to complete the scenario of different computational schemes.

Spectroscopic constants of diatomic molecules computed correcting Hartree-Fock or general-valence-bond potential-energy curves with correlation-energy functionals.

The Kohn-Sham energy with exact exchange [using the exact Hartree-Fock (HF) exchange but an approximate correlation-energy functional] may be computed very accurately by adding the correlation obtained from the HF density to the total HF energy. Three density functionals are used: local spin density (LSD), LSD with self-interaction correction, and LSD with generalized gradient correction. This scheme has been extended (Lie-Clementi, Colle-Salvetti, and Moscardo--San-Fabian) to be used with general-valence-bond (GVB) energies and wave functions, so that the extra correlation included in the GVB energy is not counted again. The effect of all these approximate correlations on HF or GVB spectroscopic constants (${\mathit{R}}_{\mathit{e}}$,${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$, and ${\mathit{D}}_{\mathit{e}}$) is studied. Approximate relations showing how correlation affects them are derived, and may be summarized as follows: (1) the effect on ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$ depends only on the correlation derivative at ${\mathit{R}}_{\mathit{e}}$, and (2) the effect on ${\mathit{D}}_{\mathit{e}}$ depends mainly on the correlation difference between quasidissociated and equilibrium geometries. A consequence is that all the correlation corrections tested here give larger ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$ and ${\mathit{D}}_{\mathit{e}}$ and shorter ${\mathit{R}}_{\mathit{e}}$ than the uncorrected HF or GVB values. This trend is correct for ${\mathit{D}}_{\mathit{e}}$ for both HF and GVB. For ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$, it is correct in most cases for GVB, but it often fails for the HF cases. A comparison is made with Kohn-Sham calculations with both exchange and correlation approximated. As a final conclusion, it is found that, within the present scheme, a qualitatively correct HF or GVB potential-energy curve, together with a correlation-energy approximation with correct dissociation behavior, is crucial for obtaining good estimates of spectroscopic constants.

Electronic structure of La2CuO4 in the self-interaction-corrected density-functional formalism.

The electronic structure of tetragonal ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ is calculated in the self-interaction-corrected (SIC) local-spin-density (LSD) approximation. In contrast to LSD, the SIC-LSD approach reveals the experimentally observed antiferromagnetic and semiconducting ground state. The energy gap is 1.04 eV and of indirect charge-transfer character, and the Cu moment is 0.47${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$. The valence-band top states have about equal weight on the in-plane and out-of-plane O atoms. This region is dominated by O states not coupling to the Cu d states, but with a significant component of O states having Cu d-like symmetry.

A new formulation of the dynamical response of many-electron systems and the photoabsorption cross section of small metal clusters

Static polarizabilities and photoabsorption cross sections of clusters Na7−, Na8, Na19− Na20 are calculated, based on the spherical jellium model including the self-interaction correction (SIC) of Perdew and Zunger. To this end, a new formulation of the theory of the linear response is presented, which is suitable for general, self-interaction corrected, many-electron systems. The results obtained display an overall agreement with available experimental data, offering a systematic improvement with respect to the standard TDLDA. Furthermore, the cross sections of the negatively charged clusters are found to be dominated by a broad peak in the visible region, whose line width can be related to the lifetime of the surface plasmon against electron detachment.

First-order perturbation calculations for transition-metal atoms and ions.

We have calculated the total energy and s-d promotion energies of 3d-transition-metal atoms using a common set of orbitals but various expressions for the energy. These include Hartree-Fock (HF), local-spin-density-approximation (LSDA), and self-interaction-corrected (SIC) LSDA expressions. The orbitals were generated from a self-consistent, spherically averaged, local-density calculation. The results using the HF expression are in remarkably good agreement with self-consistent Hartree-Fock calculations both for the total energy and for the HF eigenvalues. Further, the LSDA underestimates the total correlation energy by roughly 30 eV, while the SIC calculation overestimates the correlation energy in calcium by \ensuremath{\sim}15 eV.

Electron density of metal surfaces: Cu(113), Cu(115), Cu(117) and Ag(110)

By superposing the electron density of the Ag and Cu free atoms, as evaluated by local density calculations with self-interaction corrections, the laterally averaged electron densities of the Ag(110), Cu(113), Cu(115) and Cu(117) surfaces are determined. The superposition of atomic densities is shown to be consistent with the He-surface bound state resonance measurements.

Response of finite many‐electron systems beyond the time‐dependent local density approximation: Application to small metal clusters

AbstractA linear response formalism is developed which is based on density functional theory within the local density approximation, but which is now corrected for its spurious self‐interaction errors, in the way originally proposed by Perdew and Zunger for ground state calculations. The original formulation is extended to incorporate self‐interaction corrections in the scrrening terms. The general formalism is then applied to the calculation of the static and dynamic response of the metal clusters {Na8, Na9+}, {Na20, Na} and {Na40 Na} within the jellium model. Comparison with experimental data and with other theoretical calculations indicates that the present formalism accounts for the overall (and most of the fine) features of the photoabsorption spectrum of these systems, providing a systematic improvement with respect to previous approaches. The remaining discrepancies are rationalized in terms of the effects to be expected by correctly accounting for the discrete structure of the ionic cores.

Band-structure calculations of noble-gas and alkali halide solids using accurate Kohn-Sham potentials with self-interaction correction.

The optimized-effective-potential (OEP) method and a method developed recently by Krieger, Li, and Iafrate (KLI) are applied to the band-structure calculations of noble-gas and alkali halide solids employing the self-interaction-corrected (SIC) local-spin-density (LSD) approximation for the exchange-correlation energy functional. The resulting band gaps from both calculations are found to be in fair agreement with the experimental values. The discrepancies are typically within a few percent with results that are nearly the same as those of previously published orbital-dependent multipotential SIC calculations, whereas the LSD results underestimate the band gaps by as much as 40%. As in the LSD---and it is believed to be the case even for the exact Kohn-Sham potential---both the OEP and KLI predict valence-band widths which are narrower than those of experiment. In all cases, the KLI method yields essentially the same results as the OEP.

Simplified Green-function approximations: Further assessment of a polarization model for second-order calculation of outer-valence ionization potentials in molecules.

Ab initio methods for calculating the binding-energy spectra of large molecules have traditionally been restricted to primarily either Koopmans's theorem or the density-functional transition-orbital method. The limitations of the former are well known, and the density-functional ``band-gap problem'' has led to a further realization of intrinsic difficulties with the latter. An increasingly popular alternative to these two methods is to seek a simple approximation for the Green-function self-energy. The Green-function self-energy is the optical potential seen by a scattering particle (hole). As such, the dominant many-body effects contributing to the self-energy result from polarization of the charge density at energies below the first excitation energy of the target molecule (quasiparticle regime), as well as excitations of the target at higher energies. The physical importance of polarization effects is apparent in Hedin's GW approximation, which treats the self-energy as a product of the Green function (G) and a screened interaction (W) that can be calculated (essentially) from the time-dependent linear response of the charge density. In the present paper, we examine the contribution of polarization to the usual second-order Green-function (GF2) approximation with respect to the calculation of outer-valence ionization potentials in small molecules. A simplified version (GW2) of the GW approximation is found to be an acceptable substitute for the GF2 approximation, provided a self-interaction correction is included to prevent an electron from polarizing itself.Polarization effects are further analyzed using the Coulomb-hole and screened-exchange (COHSEX) and modified-COHSEX (M-COHSEX) approximations. A second-order version (M-COHSEX2) of the M-COHSEX approximation is used to examine the origin of the incorrect ordering by Koopmans's theorem of the first three ionization potentials of the nitrogen molecule in terms of static polarization and retardation effects. Finite-basis-set errors are also explored. Although higher-order Green-function approximations must be examined before drawing final conclusions, we believe that the present work provides preliminary evidence that suitably modified versions of time-dependent density-functional, dielectric-function-based self-energy approximations can be useful for molecules.