Self-interaction Correction Research Articles

Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory

The Perdew–Zunger self-interaction correction (SIC) was implemented self-consistently within a molecular density functional theory (DFT) program, using the Krieger–Li–Iafrate approximation to the optimized effective potential, and the Vosko–Wilk–Nusair (VWN) functional. The computationally efficient implementation relies on the fitting of orbital densities for the evaluation of orbital Coulomb potentials, and allows for routine applications to large molecules. Due to the use of the effective potential approach, the evaluation of the energy derivatives can be handled by standard Kohn–Sham DFT techniques in a straightforward way. The SIC-VWN technique is applied to the calculation of nuclear magnetic resonance (NMR) parameters in representative small molecules, containing C, H, N, O, and F. Removal of self-interaction leads to a substantial improvement in the calculated isotropic chemical shifts for N, O, and F, where SIC-VWN holds an advantage over both local (VWN), and gradient-corrected functionals (Becke 88-Perdew 86, BP86). For C and H isotropic chemical shifts, which are well described by the gradient-corrected functionals, SIC-VWN performs as well as BP86. SIC-VWN also improves the description of the absolute chemical shielding, and of the principal components of the NMR shielding tensors. The changes arise mainly from adjustments in the Kohn–Sham orbital energies, leading to a better description of the paramagnetic contribution to the shielding tensor. For spin–spin coupling constants, SIC-VWN improves the description of the paramagnetic contribution. At the same time, the magnitude of the Fermi contact term is underestimated, yielding mixed overall results. Slow convergence of the spin-spin coupling results with the basis set size prevents a conclusive statistical evaluation for this property. The clear physical origin of the SIC-VWN effect in the prediction of magnetic properties opens the tantalizing possibility that this technique may be effective in solving problems often encountered in the calculations of NMR parameters of heavier nuclei.

Multiphoton ionization and high-order harmonic generation of He, Ne, and Ar atoms in intense pulsed laser fields: Self-interaction-free time-dependent density-functional theoretical approach

We present a detailed study of the multiphoton ionization and high-order harmonic generation (HHG) processes of rare-gas atoms (He, Ne, and Ar) in intense pulsed laser fields by means of a self-interaction-free time-dependent density-functional theory (TDDFT) recently developed. The time-dependent exchange-correlation potential with proper short- and long- range potential is constructed by means of the time-dependent optimized effective potential (TDOEP) method and the incorporation of an explicit self-interaction-correction (SIC) term. The TDOEP-SIC equations are solved accurately and efficiently by the time-dependent generalized pseudospectral technique. In this study, all the valence electrons are treated explicitly and nonperturbatively and their partial contributions to the ionization and HHG are analyzed. The results reveal instructive and qualitatively different behavior from each subshell orbital. Moreover, we found that the HHG yields from Ne and Ar atoms are considerably larger than that of the He atom in strong fields. Three main factors are identified for accounting the observed phenomena: (a) the binding energy of the subshell valence electron, (b) the orientation of the valence electron orbital (with respect to the electric-field polarization), and (c) the effect of multiphoton resonant excitation. In particular, we found that the ${\mathrm{np}}_{0}$ valence electrons (in Ne and Ar) with lowest binding energies and electron orbital orientation parallel to the electric-field direction, make the dominant contributions to both ionization and HHG processes in sufficiently strong fields.

Self-interaction correction with an explicitly density-dependent functional

A new method for self-interaction correction in the density functional theory is given using an explicit energy functional of the density. The SI correction is locally carried out. The theory includes effects of strong correlations in form of Hubbard-like terms which create atomic plateaus in the potential.

Energy structure of hollow atoms or ions in the bulk of metallic materials

The local-spin-density functional method, with an optimized effective potential and self-interaction correction, is used to study the energy structure of hollow atoms and ions in the bulk of metallic materials. The energy structure of conduction electrons in the bulk of metallic material is treated by the jellium model. Based on this method, we have studied the x-ray spectra and Auger spectra of ${\mathrm{N}}^{q+}$ hollow atoms and ions in the bulk of Al, as well as in the vacuum. The experimental Auger spectra in the collision of ${\mathrm{N}}^{6+}$ with an insulating surface and conducting surface can be well understood based on our studies. Our calculated x-ray and Auger spectra of hollow atoms or ions in the vacuum and in the bulk of material suggest the need for further systematic experimental investigation.

Cu valency change induced by O doping in YBCPO.

An ab initio local spin density study of YBa2Cu3O6, YBa2Cu3O6.5, and YBa2Cu3O7 is presented. The method includes self-interaction corrections for the Cu d states, which enables a description of various valency configurations of both planar and chain Cu atoms. For YBa2Cu3O6 the antiferromagnetic and insulating state is described with planar (chain) Cu occurring in a divalent (trivalent) state. The evolution in the CuO2 plane from insulating to metallic behavior upon oxygenation is accomplished by the delocalization of the majority Cu d(x2-y2)-O2 p(x)-O3 p(y) band.

Vertically coupled quantum dots in the local spin-density functional theory

We have investigated the structure of double quantum dots vertically coupled at zero magnetic field within local spin-density functional theory. The dots are identical and have a finite width, and the whole system is axially symmetric. We first discuss the effect of thickness on the addition spectrum of one single dot. Next, we describe the structure of coupled dots as a function of the interdot distance for different electron numbers. Addition spectra, Hund's rule and molecular-type configurations are discussed. It is shown that self-interaction corrections to the density functional results do not play a very important role in the calculated addition spectra.

Self-interaction-free time-dependent density-functional theory for molecular processes in strong fields: High-order harmonic generation ofH2in intense laser fields

We present a self-interaction-free time-dependent density-functional theory (TDDFT) for nonperturbative treatment of multiphoton processes of many-electron molecular systems in intense laser fields. The time-dependent exchange-correlation (xc) energy potential with proper short- and long-range potential is constructed by means of the time-dependent optimized effective potential (OEP) method and the incorporation of an explicit self-interaction-correction (SIC) term. The resulting time-dependent OEP/SIC equations are structurally similar to the time-dependent Hartree-Fock equations, but include the many-body effects through an orbital-independent single-particle local time-dependent xc potential. A numerical time-propagation technique is introduced for accurate and efficient solution of the TDDFT/OEP-SIC equations for two-center diatomic molecular systems. This procedure involves the use of a generalized pseudospectral method for nonuniform optimal grid discretization of the Hamiltonian in prolate spheroidal coordinates and a split-operator scheme in the energy representation for the time development of the electron orbital wave functions. High-precision time-dependent wave functions can be obtained by this procedure with the use of only a modest number of spatial grid points. The theory is applied to a detailed study of high-order harmonic generation (HHG) processes of ${\mathrm{H}}_{2}$ molecules in intense pulsed laser fields. Particular attention is paid to the exploration of the spectral and temporal structures of HHG by means of the wavelet time-frequency analysis. The results reveal striking details of the spectral and temporal fine structures of HHG, providing new insights regarding the detailed HHG mechanisms in different energy regimes.

Orbital energy analysis with respect to LDA and self-interaction corrected exchange-only potentials

The self-interaction correction of Perdew and Zunger with the optimized effective potential using the Krieger–Li–Iafrate approximation is analyzed for atomic and molecular systems in the exchange-only context. Including the self-interaction correction (SIC) orbital by orbital shows that the appropriate asymptotic behavior of the exchange potential can be achieved if just the contribution of the highest occupied molecular orbital (HOMO) is considered. However, if a good description of the exchange potential in the valence region is required, and consequently a good description of the HOMO energy, then all electrons of the valence shell must be taken into account. In contrast, the lowest unoccupied molecular orbital (LUMO) is described adequately if just the HOMO SIC contribution is employed. In addition, if the lowest occupied orbital is also considered in the SIC approximation, there is an improvement in the description of the exchange potential in inner regions of an atom. When all electrons in an atom or in a molecule are considered in the SIC approximation, there exists a linear relationship between their occupied orbital energies and those obtained with the local density approximation (LDA). This indicates that the SIC and LDA occupied orbital energies are related by a shift. Furthermore, for a set of atoms or molecules there is a linear relationship between HOMO energies obtained with LDA and those obtained with the SIC approximation. Using both observations, the shift between the occupied orbital energies LDA and SIC is reported. We found that this shift (obtained for the occupied orbitals) cannot be applied to the virtual orbitals, in particular to the LUMO. However, we do find an additional linear relationship between LUMO energies obtained with LDA and those obtained with the SIC approximation. The difference between the LUMO and HOMO energy (GAP) obtained with the LDA and SIC approximations is compared with that obtained with an exact local-multiplicative exchange potential and all are compared with experimental vertical excitation energies. Whereas the LDA GAP underestimates the excitation energies, the GAP obtained with the SIC approximation and with an exact local-multiplicative exchange potential overestimates this quantity. From an analysis of the exchange energy for simple molecules, and with a similar approach to the modified Xα method, we found a linear relationship between the SIC and Hartree–Fock (HF) methods. We show numerically that the nondiagonal terms of the exact orbital representation of the exchange energy can be approximated by the SIC approach.

Generalized spin density functional theory for noncollinear molecular magnetism II—Influence of gradient correction and self‐interaction correction

AbstractWe have implemented generalized spin orbital (GSO) based localized spin density approximation (LSDA) and general gradient approximation (GGA) calculations for noncollinear magnetic systems. Further self‐interaction correction (SIC) within a perturbational scheme is applied for the GSO solutions of LSDA and GGA. The Boys localization is employed to obtain appropriate SIC orbitals. The calculational results are compared with those of generalized Hartree–Fock (GHF) methods and full configuration interaction (FCI). From our calculations of equilateral and isosceles triangular H3 molecule, it was found that SIC improves significantly the feature of potential surface as well as the total energy values. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self-interaction correction (SIC) used in density functional theory does not remove all self-interaction. We present as an alternative a novel method that, by construction, is totally free from self-interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001

Novel method of self-interaction corrections in density functional calculations

It is demonstrated that the commonly applied self-interaction correction (SIC) used in density functional theory does not remove all self-interaction. We present as an alternative a novel method that, by construction, is totally free from self-interaction

Simplified implementation of self-interaction correction in sodium clusters

In density-functional theory, the standard Perdew-Zunger method of self-interaction correction leads to exchange-correlation (xc) potentials that are orbital-dependent. We study various simplified implementations of self-interaction correction\char22{}derived in the framework of the so-called optimized effective potential method\char22{}that lead to a single, orbital-independent xc potential. The performance of the various self-interaction corrected functionals is tested for sodium clusters: we first consider a variety of ground-state properties (total energies, Kohn-Sham orbital eigenvalues, and ionic potential curves) and then study the dynamical regime of weak and strong electronic excitations. It turns out that for sodium clusters the simplest, global-averaging scheme gives a good description of static and dynamic properties, even in the regime of strong excitations.

Self-interaction-corrected local density approximationpseudopotential calculations of the structural phase transformationsof ZnO and ZnS under high pressure

The structural phase transformations under high pressure of ZnO and ZnS have been investigated by using theVogel-Krüger-Pollmann (VKP) scheme, in which theelectronic self-interaction correction to the local densityapproximation (LDA) is introduced in a non-self-consistentmanner within the pseudopotential approach. In these calculations, I have used highly optimized pseudopotentials and a plane-waveexpansion of the wavefunctions. Moreover, the electronic structuresof the zinc-blende (ZB) and rock-salt (RS) phases ofboth compounds have been similarly calculated. It has been foundthat the VKP scheme provides a highly improved description, relative to the LDA results, for the structural and electronicstructure properties of the considered systems. However, theso-calculated transition pressures of the ZB-to-RStransition for both ZnO and ZnS are found to besignificantly larger than the experimental data. RS-ZnO ispredicted to be an indirect-gap semiconductor, with a wide band gap of 4.2 eV.

The optimized effective potential and the self-interaction correction in density functional theory: Application to molecules

The Krieger, Li, and Iafrate approximation to the optimized effective potential including the self-interaction correction for density functional theory has been implemented in a molecular code, NWChem, that uses Gaussian functions to represent the Kohn and Sham spin–orbitals. The differences between the implementation of the self-interaction correction in codes where planewaves are used with an optimized effective potential are discussed. The importance of the localization of the spin–orbitals to maximize the exchange-correlation of the self-interaction correction is discussed. We carried out exchange-only calculations to compare the results obtained with these approximations, and those obtained with the local spin density approximation, the generalized gradient approximation and Hartree–Fock theory. Interesting results for the energy difference (GAP) between the highest occupied molecular orbital, HOMO, and the lowest unoccupied molecular orbital, LUMO, (spin–orbital energies of closed shell atoms and molecules) using the optimized effective potential and the self-interaction correction have been obtained. The effect of the diffuse character of the basis set on the HOMO and LUMO eigenvalues at the various levels is discussed. Total energies obtained with the optimized effective potential and the self-interaction correction show that the exchange energy with these approximations is overestimated and this will be an important topic for future work.

Criteria of parameter selection for quantum chemical simulation of the electronic structure of rare-earth ions by the scattered wave cluster method

Electronic structure calculations of the Ce3+ ion in terms of a molecular cluster model in a quasirelativistic approximation are reported. The influence of the self-interaction correction and variations of muffintin parameters on the calculation results is discussed. A method is proposed for estimating the 4f→5d transition energy in the cerium ion using the SCF-SW formalism.

Shell structure in free and confined atoms using the density functional theory

The average local electrostatic potential function, defined as the electrostatic potential divided by the electron density, is used to study the shell structure in free and confined atoms within Kohn–Sham density functional theory. Several exchange-correlation functionals have been used to calculate the average potential function. It was observed that the self-interaction correction significantly alters the shell structure along the large radial distances. Many electron atoms confined in a sphere exhibit a gradual loss of the shell structure as the confinement is increased. The loss of structure can be characterized by the sphere radius rc and in the limit rc→0, the electron gas behavior is obtained.

Mechanisms of giant resonance in 4d photoionization of Eu

We have studied the mechanisms of giant resonance in 4d photoionization of Eu atoms by density functional theory with the optimized effective potential and self-interaction correction method. The dynamic electron correlation is taken into account by the linear density response method. Our calculated photoionization cross sections in the giant resonance region are in good agreement with experimental measurements. Since Eu is a highly spin polarized system, by decomposing the contribution of 4d electrons in spin-up and spin-down states, we clearly identified that the strong asymmetry line profile of the giant resonance is due to a broad resonance of 4d spin-down electrons interaction with a sharp resonance of 4d spin-up electrons.

The Hartree product and the description of local and global quantities in atomic systems: A study within Kohn–Sham theory

The Hartree product is analyzed in the context of Kohn–Sham theory. The differential equations that emerge from this theory are solved with the optimized effective potential using the Krieger, Li, and Iafrate approximation, in order to get a local potential as required by the ordinary Kohn–Sham procedure. Because the diagonal terms of the exact exchange energy are included in Hartree theory, it is self-interaction free and the exchange potential has the proper asymptotic behavior. We have examined the impact of this correct asymptotic behavior on local and global properties using this simple model to approximate the exchange energy. Local quantities, such as the exchange potential and the average local electrostatic potential are used to examine whether the shell structure in an atom is revealed by this theory. Global quantities, such as the highest occupied orbital energy (related to the ionization potential) and the exchange energy are also calculated. These quantities are contrasted with those obtained from calculations with the local density approximation, the generalized gradient approximation, and the self-interaction correction approach proposed by Perdew and Zunger. We conclude that the main characteristics in an atomic system are preserved with the Hartree theory. In particular, the behavior of the exchange potential obtained in this theory is similar to those obtained within other Kohn–Sham approximations.

Self-interaction-corrected local-spin-density calculations for rare earth materials

The ab initio self-interaction-corrected (SIC) local-spin-density (LSD) approximation is discussed with emphasis on the ability to describe localized f -electron states in rare earth solids. Two methods for minimizing the SIC-LSD total energy functional are discussed, one using a unified Hamiltonian for all electron states, thus having the advantages of Bloch's theorem, the other one employing an iterative scheme in real space. Results for cerium and cerium compounds as well as other rare earths are presented. For the cerium compounds the onset of f -electron delocalization can be accurately described, including the intricate isostructural phase transitions in elemental cerium and CeP. In Pr and Sm the equilibrium lattice constant and zero temperature equation of state is greatly improved in comparison with the LSD results. c 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 799-813, 2000

Many-body effects and autoionization resonances in the photoionization of simple metal clusters

Within the framework of the time-dependent local-density approximation (TDLDA) and the spherical background jellium model, we have estimated the photoionization cross sections for a medium-size closed-shell sodium cluster, Na20. We have also introduced a self-interaction correction to ensure the correct asymptotic behaviour of the potential seen by the ejected electron. Our results show that in contrast to the photoexcitation process, the photoionization cross sections are very sensitive to the approximation used to describe the cluster electrons. Futhermore, many-electron correlations are found to be very large. Similarly to the atomic case, when correct asymptotic conditions are taken properly into account, cross sections exhibit many one-electron autoionization resonances.