Self-interaction Correction Research Articles

Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids

We present an atomic orbital based approximate scheme for self-interaction correction (SIC) to the local density approximation of density functional theory. The method, based on the idea of Filippetti and Spaldin [Phys. Rev. B 67, 125109 (2003)], is implemented in a code using localized numerical atomic orbital basis sets and is now suitable for both molecules and extended solids. After deriving the fundamental equations as a non-variational approximation of the self-consistent SIC theory, we present results for a wide range of molecules and insulators. In particular, we investigate the effect of re-scaling the self-interaction correction and we establish a link with the existing atomic-like corrective scheme LDA+U. We find that when no re-scaling is applied, i.e. when we consider the entire atomic correction, the Kohn-Sham HOMO eigenvalue is a rather good approximation to the experimental ionization potential for molecules. Similarly the HOMO eigenvalues of negatively charged molecules reproduce closely the molecular affinities. In contrast a re-scaling of about 50% is necessary to reproduce insulator bandgaps in solids, which otherwise are largely overestimated. The method therefore represents a Kohn-Sham based single-particle theory and offers good prospects for applications where the actual position of the Kohn-Sham eigenvalues is important, such as quantum transport.

Theoretical investigation of the optical and magneto-optical properties of EuX (X=S, Se, and Te)

The optical and magneto-optical (MO) properties of europium sulphide (EuS) have been studied by employing the full potential linearized augmented plane wave method as implemented in the WIEN2K code, with the Coulomb corrected local spin density approximation (LSDA+U) in the self-interaction correction (SIC). Our calculations give an energy gap of 1.58 eV for ferromagnetic semiconductor EuS in fair agreement with experiment. The calculated Faraday rotation spectrum of EuS is in better agreement with available experimental data, compared to a previous calculation. We have also performed calculations for EuSe and EuTe in the fictitious ferromagnetic phase with a view of exploring the effect of replacing S by Se and Te on the optical and magneto-optical properties.

Theory of ferromagnetic semiconductors

AbstractBased upon ab initio electronic structure calculations by the Korringa–Kohn–Rostoker coherent‐potential approximation (KKR‐CPA) method within the local‐density approximation (LDA), we propose a unified physical picture of magnetism and an accurate calculation method of Curie temperature (T C) in dilute magnetic semiconductors (DMSs) in II–VI and III–V compound semiconductors. We also propose the unified physical picture of magnetism in the DMS, where ferromagnetic Zener's double‐exchange mechanism (or Zener's p–d exchange mechanism) caused by the partially occupied impurity band and anti‐ferromagnetic super‐exchange mechanism (or ferromagnetic super‐exchange mechanism) is competing to determine the magnetic states in the DMS. We propose that the three‐dimensional 3D Dairiseki‐phase and one‐dimensional 1D Konbu‐phase caused by spinodal nano‐decomposition are responsible for high‐T C phase in the inhomogeneous system. We propose the new methodology to go beyond LDA to describe the highly correlated electron system by taking into account the self‐interaction correction (SIC) to the LDA. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

First-principles electronic-structure calculation on the spin distribution and the conductive properties of (n-C3H7)4N[FeIIFeIII(dto)3] (dto=C2O2S2)

The first principles within the full potential linearized augmented plane wave (FP-LAPW) method with the self-interaction corrected (SIC) GGA + U approach were applied to study the compound of ( n -C 3 H 7 ) 4 N[Fe II Fe III (dto) 3 ] (dto = C 2 O 2 S 2 ). The density of states, the electronic band structure and the spin magnetic moment are calculated. The calculations reveal that the compound has a ferromagnetic interaction between the Fe III ( S = 1 / 2 ) and Fe II ( S = 2 ) ions arising from the bridging dithiooxalato molecule. The spin magnetic moment mainly comes from the Fe III ( S = 1 / 2 ) and Fe II ( S = 2 ) ions with little contribution from O, S, and C anion. By analysis of the band structure, we find that the compound has metallic property.

Comparison of theoretical approaches for computing the bond length alternation of polymethineimine

Using electron-correlated wavefunction approaches and several pure and hybrid density functionals combined with three atomic basis sets, we have optimized the ground-state geometry of increasingly long polymethineimine oligomers presenting all- trans and gliding-plane symmetries. It turns out that MP2 bond length alternations (BLA) are in good agreement with higher-order electron-correlated wavefunction approaches, whereas, for both conformers, large qualitative and quantitative discrepancies between MP2 and DFT geometries have been found. Indeed, all the selected GGA, meta-GGA and hybrid functionals tend to overestimate bond length equalization in extended polymethineimine structures. On the other hand, self-interaction corrections included in the ADSIC framework provide, in this particular case, a more efficient approach to predict the BLA for medium-size oligomers.

Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals

Semilocal density functional approximations for the exchange-correlation energy can improperly dissociate a neutral molecule XY (Y not =X) to fractionally charged fragments X(+q)...Y(-q) with an energy significantly lower than X0...Y0. For example, NaCl can dissociate to Na(+0.4)...Cl(-0.4). Generally, q is positive when the lowest-unoccupied orbital energy of atom Y0 lies below the highest-occupied orbital energy of atom X0. The first 24 open sp-shell atoms of the Periodic Table can form 276 distinct unlike pairs XY, and in the local spin density approximation 174 of these display fractional-charge dissociation. Finding these lowest-energy solutions with standard quantum chemistry codes, however, requires special care. Self-interaction-corrected (SIC) semilocal approximations are exact for one-electron systems and also reduce the spurious fractional charge q. The original SIC of Perdew and Zunger typically reduces q to 0. A scaled-down SIC with better equilibrium properties sometimes fails to reduce q all the way to 0. The desideratum of "many-electron self-interaction freedom" is introduced as a generalization of the one-electron concept.

Mott transition of MnO under pressure: A comparison of correlated band theories

The electronic structure, magnetic moment, and volume collapse of MnO under pressure are obtained from four different correlated band theory methods; local density $\text{approximation}+\text{Hubbard}$ $U$ $(\mathrm{LDA}+U)$, pseudopotential self-interaction correction (pseudo-SIC), the hybrid functional (combined local exchange plus Hartree-Fock exchange), and the local spin density SIC (SIC-LSD) method. Each method treats correlation among the five Mn $3d$ orbitals (per spin), including their hybridization with three O $2p$ orbitals in the valence bands and their changes with pressure. The focus is on comparison of the methods for rocksalt MnO (neglecting the observed transition to the NiAs structure in the $90--100\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ range). Each method predicts a first-order volume collapse, but with variation in the predicted volume and critical pressure. Accompanying the volume collapse is a moment collapse, which for all methods is from high-spin to low-spin $(\frac{5}{2}\ensuremath{\rightarrow}\frac{1}{2})$, not to nonmagnetic as the simplest scenario would have. The specific manner in which the transition occurs varies considerably among the methods: pseudo-SIC and SIC-LSD give insulator-to-metal, while $\mathrm{LDA}+U$ gives insulator-to-insulator and the hybrid method gives an insulator-to-semimetal transition. Projected densities of states above and below the transition are presented for each of the methods and used to analyze the character of each transition. In some cases the rhombohedral symmetry of the antiferromagnetically ordered phase clearly influences the character of the transition.

A simple method to selectively scale down the self-interaction correction

The method of Perdew and Zunger is commonly used to correct the self-interaction error of approximate density functionals. However, it has been shown that this orbital-based self-interaction correction (SIC) tends to overcorrect and often impairs molecular properties. We have recently proposed a method to improve the performance of the SIC by scaling it down in many-electron regions. In this communication, we present a simplification of this scheme. For every occupied orbital, we introduce a scaling factor determined by the ratio of the orbital density to the total spin-density. Thus, the magnitude of the correction is adjusted depending on how much orbital densities overlap with one another. Such a modification of the Perdew-Zunger SIC does not add any appreciable time to the computation, but significantly improves the accuracy for a number of benchmark properties.

Self-interaction-corrected pseudopotentials for silicon carbide

We report electronic and structural properties of cubic and hexagonal $3\mathrm{C}\text{\ensuremath{-}},\phantom{\rule{0.3em}{0ex}}2\mathrm{H}\text{\ensuremath{-}},\phantom{\rule{0.3em}{0ex}}4\mathrm{H}\text{\ensuremath{-}}$, and $6\mathrm{H}\text{\ensuremath{-}}\mathrm{SiC}$ bulk crystals and of the C-terminated $\mathrm{SiC}(001)\text{\ensuremath{-}}c(2\ifmmode\times\else\texttimes\fi{}2)$ surface as resulting from density functional theory (DFT) within local density approximation (LDA). In particular, we employ newly constructed nonlocal, norm-conserving pseudopotentials which incorporate self-interaction corrections. Results obtained with usual pseudopotentials show the typical LDA shortcomings, most noticeably the systematic underestimate of the band gap. These problems are attributed to an unphysical self-interaction inherent in the common DFT-LDA. We describe the construction of appropriate self-interaction-corrected pseudopotentials for Si and C atoms and show how they can be transferred to the $\mathrm{SiC}$ solid by adequate modifications. It is in the very nature of our pseudopotentials that they cause no additional computational effort, as compared to usual pseudopotentials in standard LDA calculations. To test their transferability to different crystal structures we apply these pseudopotentials to both cubic and hexagonal polytypes of $\mathrm{SiC}$. The resulting energy gaps are in excellent agreement with experimental data and the bulk band structures are in most gratifying agreement with the results of considerably more elaborate quasiparticle calculations. Structural properties of the different polytypes are found in excellent agreement with experiment, as well, not showing the usual LDA underestimate of lattice constants and overestimate of bulk moduli. Also the electronic structure of $\mathrm{SiC}(001)\text{\ensuremath{-}}c(2\ifmmode\times\else\texttimes\fi{}2)$, calculated to exemplify the usefulness of the pseudopotentials for surfaces, shows improved agreement with experiment as compared to the respective surface band structure obtained within standard LDA.

First-principles study of intrinsic point defects in ZnO: Role of band structure, volume relaxation, and finite-size effects

Density-functional theory (DFT) calculations of intrinsic point defect properties in zinc oxide were performed in order to remedy the influence of finite-size effects and the improper description of the band structure. The generalized gradient approximation (GGA) with empirical self-interaction corrections $(\mathrm{GGA}+U)$ was applied to correct for the overestimation of covalency intrinsic to GGA-DFT calculations. Elastic as well as electrostatic image interactions were accounted for by application of extensive finite-size scaling and compensating charge corrections. Size-corrected formation enthalpies and volumes as well as their charge state dependence have been deduced. Our results partly confirm earlier calculations but reveal a larger number of transition levels: (1) For both the zinc interstitial as well as the oxygen vacancy, transition levels are close to the conduction band minimum. (2) The zinc vacancy shows a transition rather close to the valence band maximum and another one near the middle of the calculated band gap. (3) For the oxygen interstitials, transition levels occur both near the valence band maximum and the conduction band minimum.

Electron correlation of one-dimensionalH2in intense laser fields: Time-dependent extended Hartree-Fock and time-dependent density-functional-theory approaches

Ionization and high-order harmonic generation of the one-dimensional (1D) ${\mathrm{H}}_{2}$ molecule in intense ultrashort laser fields are investigated using several current approximations for electron dynamics. Single- and double-ionization probabilities are compared with exact results. It is found that for the ground state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$, time-dependent extended Hartree-Fock gives generally comparable results except in the plateau region. The adiabatic local density approximation and time-dependent optimized effective potential with self-interaction correction (TDKLI) methods underestimate the ionization probabilities with no plateau and knee for double ionization contrary to the exact results. For the triplet excited state $A\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}$, where exchange is important, the TDKLI results agree well with the exact results. The exact double-ionization probabilities suggest the need for accurate pair-correlation functions.

Scaling down the Perdew-Zunger self-interaction correction in many-electron regions

Semilocal density functional approximations (DFAs) for the exchange-correlation energy suffer from self-interaction error, which is believed to be the cause of many of the failures of common DFAs, such as poor description of charge transfer and transition states of chemical reactions. The standard self-interaction correction (SIC) of Perdew and Zunger mends some of these failures but spoils such essential properties as thermochemistry and equilibrium bond lengths. The Perdew-Zunger SIC seems to overcorrect many-electron systems. In this paper, we propose a modified SIC, which is scaled down in many-electron regions. The new SIC has an improved performance for many molecular properties, including total energies, atomization energies, barrier heights of chemical reactions, ionization potentials, electron affinities, and bond lengths. The local spin-density approximation (LSDA) benefits from SIC more than higher-level functionals do. The scaled-down SIC has only one adjustable parameter. Rationalization of the optimal value of this parameter enables us to construct an almost-nonempirical version of the scaled-down SIC-LSDA, which is significantly better than uncorrected LSDA and even better than the uncorrected generalized gradient approximation. We present an analysis of the formal properties of the scaled-down SIC and define possible directions for further improvements. In particular, we find that exactness for all one-electron densities does not guarantee correct asymptotics for the exchange-correlation potential of a many-electron system.

Confined helium atom low-lying S states analyzed through correlated Hylleraas wave functions and the Kohn-Sham model

Calculation including the electron correlation effects is reported for the ground 1 1S and lowest triplet 1 3S state energies of the confined helium atom placed at the center of an impenetrable spherical box. While the adopted wave-functional treatment involves optimization of three nonlinear parameters and 10, 20, and 40 linear coefficients contained in wave functions expressed in a generalized Hylleraas basis set that explicitly incorporates the interelectronic distance r12, via a Slater-type exponent and through polynomial terms entering the expansion, the Kohn-Sham model employed here uses the Perdew and Wang exchange-correlation functional in its spin-polarized version within the local-density approximation (LDA) with and without the self-interaction correction. All these calculations predict a systematic increase in the singlet-triplet energy splitting toward the high confinement regime, i.e., when the box radius is reduced. By using the variational results as benchmark, it is found that the LDA underestimates the singlet-triplet energy splitting, whereas the self-interaction correction overestimates such a quantity.

Valence-band structure of InN from x-ray photoemission spectroscopy

The valence-band structure of clean, high-quality, single-crystalline wurtzite InN thin films prepared with atomic hydrogen is investigated using x-ray photoemission spectroscopy. The $\mathrm{In}4{d}_{5∕2}$ semicore level due to the In-N bond is found to lie $16.0\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ above the valence band maximum. Experimental valence-band spectra are compared with theoretical calculations of the valence-band density of states (VB-DOS), employing density functional theory within the local density approximation with quasiparticle and self-interaction corrections. Agreement between the experimental valence band spectrum and the theoretical VB-DOS is obtained.

About the calculation of exchange coupling constants using density-functional theory: The role of the self-interaction error

The effect of the correction of the self-interaction error on the calculation of exchange coupling constants with methods based on density-functional theory has been tested in simple model systems. The inclusion of the self-interaction correction cancels the nondynamical correlation energy contributions simulated by the commonly used functionals. Hence, such correction should be important in the accurate determination of exchange coupling constants. We have also tested several recent functionals to calculate exchange coupling constants in transition-metal complexes, such as meta-GGA functionals or new formulations of hybrid functionals. The influence of the basis set and of the use of pseudopotentials on the calculated J values has also been evaluated for a Fe(III) dinuclear complex in which the paramagnetic centers bear several unpaired electrons.

Self-Interaction Errors in Density-Functional Calculations of Electronic Transport

All density-functional calculations of single-molecule transport to date have used continuous exchange-correlation approximations. The lack of derivative discontinuity in such calculations leads to the erroneous prediction of metallic transport for insulating molecules. A simple and computationally undemanding atomic self-interaction correction (SIC) opens conduction gaps in I-V characteristics that otherwise are predicted metallic, as in the case of the prototype Au/ditholated-benzene/Au junction.

Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the Møller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals.

Koopmans-like Approximation in the Kohn−Sham Method and the Impact of the Frozen Core Approximation on the Computation of the Reactivity Parameters of the Density Functional Theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.

Recent development of self-interaction-free time-dependent density-functional theory for nonperturbative treatment of atomic and molecular multiphoton processes in intense laser fields

In this paper, we present a short account of some recent developments of self-interaction-free density-functional theory (DFT) and time-dependent density-functional theory (TDDFT) for accurate and efficient treatment of the electronic structure, and time-dependent quantum dynamics of many-electron atomic and molecular systems. The conventional DFT calculations using approximate and explicit exchange-correlation energy functional contain spurious self-interaction energy and improper long-range asymptotic potential, preventing reliable treatment of the excited, resonance, and continuum states. We survey some recent developments of DFT/TDDFT with optimized effective potential (OEP) and self-interaction correction (SIC) for both atomic and molecular systems for overcoming some of the above mentioned difficulties. These DFT (TDDFT)/OEP-SIC approaches allow the use of orbital-independent single-particle local potential which is self-interaction free. In addition we discuss several numerical techniques recently developed for efficient and high-precision treatment of the self-interaction-free DFT/TDDFT equations. The usefulness of these procedures is illustrated by a few case studies of atomic, molecular, and condensed matter processes of current interests, including (a) autoionizing resonances, (b) relativistic OEP-SIC treatment of atomic structure (Z=2-106), (c) shell-filling electronic structure in quantum dots, (d) atomic and molecular processes in intense laser fields, including multiphoton ionization, and very-high-order harmonic generation, etc. For the time-dependent processes, an alternative Floquet formulation of TDDFT is introduced for time-independent treatment of multiphoton processes in intense periodic or quasiperiodic fields. We conclude this paper with some open questions and perspectives of TDDFT.

Coexistence of ionic and metallic bonding in noble-metal oxides

We investigate the nature of bonding in noble-metal oxides ${\mathrm{Cu}}_{2}\mathrm{O}$, ${\mathrm{Ag}}_{2}\mathrm{O}$, and ${\mathrm{Au}}_{2}\mathrm{O}$ using a combination of first-principles density-functional-based methodologies including self-interaction correction, polarization theory, and the electron localization function. A long-standing question concerns the type of bonding operating in these compounds. They are prevailingly ionic, but their observed cubic structure is stabilized by weak cation-cation interactions whose nature is not fully understood. A currently credited picture is that electron promotion out of the filled cation $d$ shells produces nonspherical charge distributions on the cations, which interact in a van der Waals fashion according to some or form covalent cation-cation bonds according to others. In this work we give a detailed and consistent picture of bonding in ${\mathrm{Cu}}_{2}\mathrm{O}$ (and related compounds) at some variance with that hitherto assumed. First, we show that no trace of interstitial covalency is to be found, which negates the covalent bonding hypothesis. Second, we show the cation on-site $s\text{\ensuremath{-}}d$ hybridization causes only a marginal deviation from the exact sphericity of the electron charge and contributes negligibly to the stabilization of the cubic phase. Third, we show that the cubic phase is stable because of incomplete ionic charge transfer, leaving on the cation an excess of delocalized charge which establishes weakly metallic cation-cation bonding.