Self-interaction Correction Research Articles

Vacancies in GaN bulk and nanowires: effect of self-interaction corrections

We investigate gallium and nitrogen vacancies in gallium nitride (GaN) bulk and nanowires using self-interaction corrected pseudopotentials (SIC). In particular, we examine the band structures to compare and contrast differences between the SIC results and standard density functional theory (DFT) results using a generalized gradient approximation (GGA) (Perdew et al 1996 Phys. Rev. Lett. 77 3865) functional. For pure nanowires, we observed similar trends in the bandgap behaviour, with the gap decreasing for increasing nanowire diameters (with larger bandgaps using SIC pseudopotentials). For gallium vacancies in bulk GaN and GaN nanowires, SIC results are similar to DFT-GGA results, albeit with larger bandgaps. Nitrogen vacancies in bulk GaN show similar defect-induced states near the conduction band, whilst a lower lying defect state is observed below the valence band for the DFT-GGA calculations and above the valence band for the SIC results. For nitrogen vacancies in GaN nanowires, similar defect states are observed near the conduction band, however, while the SIC calculations also show a defect state/s above the valence band, we were unable to locate this state for the DFT-GGA calculations (possibly because it is hybridized with edge states and buried below the valence band).

Ab-initio Calculation of Half-Metal Ferrimagnetic Sn0.9Mn0.05Co0.05O2

Based on first-principles spin-density functional calculations, using the Korringa–Kohn–Rostoker (KKR) method combined with the coherent potential approximation (CPA), we investigated the half-metallic ferrimagnetic properties of SnO2 codoped with Mn and Co impurities (Sn0.90(Mn0.05, Co0.05)O2) within the self-interaction-corrected (SIC) local density approximation. Mechanism of hybridization and interaction between magnetic ions in Sn0.90(Mn0.05, Co0.05)O2 is investigated. The band structure model has been used to explain the strong ferrimagnetic interaction observed and the mechanism that stabilizes this state is proposed.

Quasiparticle band structure of alkali-metal fluorides, oxides, and nitrides

We present a comparative study of one-particle excitation energies of alkali-metal fluorides (MF), oxides (M${}_{2}$O), and nitrides (M${}_{3}$N) with M = Li, Na, and K. To this end, we have calculated quasiparticle band structures within the ${G}_{0}{W}_{0}$ approximation. We arrive at valence and conduction bands that are in good agreement with the scarcely available experimental data. In addition, the quasiparticle bands corroborate our earlier results of density functional calculations including self-interaction corrections for the fluorides and oxides and yield significant improvements for the nitrides. For example, the ${G}_{0}{W}_{0}$ quasiparticle gap of Na${}_{3}$N amounts to 1.5 eV in close agreement with the experimental gap of 1.6 eV. Finally, we consider the effects of iteratively updating the screening in the Coulomb interaction $W$.

Kohn-Sham Self-Interaction Correction in Real Time

We present a solution scheme for the time-dependent Kohn-Sham self-interaction correction. Based on the generalized optimized effective potential approach, the multiplicative Kohn-Sham potential is constructed in real time and real space for the self-interaction corrected local density approximation. Excitations of different character, including charge-transfer excitations that had been regarded as prime examples for the failure of standard time-dependent density functionals, are described correctly by this approach. We analyze the time-dependent exchange-correlation potential and density, revealing features that are decisive for the correct description of the response.

Importance of the correlation contribution for local hybrid functionals: Range separation and self-interaction corrections

Local hybrid functionals with their position-dependent exact-exchange admixture are a conceptually simple and promising extension of the concept of a hybrid functional. Local hybrids based on a simple mixing of the local spin density approximation (LSDA) with exact exchange have been shown to be successful for thermochemistry, reaction barriers, and a range of other properties. So far, the combination of this generation of local hybrids with an LSDA correlation functional has been found to give the most favorable results for atomization energies, for a range of local mixing functions (LMFs) governing the exact-exchange admixture. Here, we show that the choice of correlation functional to be used with local hybrid exchange crucially influences the parameterization also of the exchange part as well as the overall performance. A novel ansatz for the correlation part of local hybrids is suggested based on (i) range-separation of LSDA correlation into short-range (SR) and long-range (LR) parts, and (ii) partial or full elimination of the one-electron self-correlation from the SR part. It is shown that such modified correlation functionals allow overall larger exact exchange admixture in thermochemically competitive local hybrids than before. This results in improvements for reaction barriers and for other properties crucially influenced by self-interaction errors, as demonstrated by a number of examples. Based on the range-separation approach, a fresh view on the breakdown of the correlation energy into dynamical and non-dynamical parts is suggested.

Forces and atomic relaxation in density functional theory with the pseudopotential self-interaction correction

We present the scheme that allows for efficient calculations of forces in the framework of pseudopotential self-interaction corrected (pSIC) formulation of the density functional theory. The scheme works with norm conserving and also with ultrasoft pseudopotentials and has been implemented in the plane-wave basis code {\sc quantum espresso}. We have performed tests of the internal consistency of the derived expressions for forces considering ZnO and CeO$_2$ crystals. Further, we have performed calculations of equilibrium geometry for LaTiO$_3$, YTiO$_3$, and LaMnO$_3$ perovskites and also for Re and Mn pairs in silicon. Comparison with standard DFT and DFT+U approaches shows that in the cases where spurious self-interaction matters, the pSIC approach predicts different geometry, very often closer to the experimental data.

Variational pseudo-self-interaction-corrected density functional approach to theab initiodescription of correlated solids and molecules

We present a fully variational generalization of the pseudo self-interaction correction (VPSIC) approach previously presented in two implementations based on plane-waves and atomic orbital basis set, known as PSIC and ASIC, respectively. The new method is essentially equivalent to the previous version for what concern the electronic properties, but it can be exploited to calculate total-energy derived properties as well, such as forces and structural optimization. We apply the method to a variety of test cases including both non-magnetic and magnetic correlated oxides and molecules, showing a generally good accuracy in the description of both structural and electronic properties.

Room-temperaturep-induced surface ferromagnetism: First-principles study

We prove a spontaneous magnetization of the oxygen-terminated ZnO (0001) surface by utilizing a multicode, SIESTA and KKR, first-principles approach, involving both LSDA+$U$ and self-interaction corrections to treat electron correlation effects. Critical temperatures are estimated from Monte Carlo simulations, showing that at and above 300 K the surface is thermodynamically stable and ferromagnetic. The observed half-metallicity and long-range magnetic order originate from the presence of $p$ holes in the valence band of the oxide. The mechanism is universal in ionic oxides and points to a new route for the design of ferromagnetic low-dimensional systems.

Importance of complex orbitals in calculating the self-interaction-corrected ground state of atoms

The ground state of atoms from H to Ar was calculated using a self-interaction correction to local and gradient dependent density functionals. The correction can significantly improve the total energy and makes the orbital energies consistent with ionization energies. However, when the calculation is restricted to real orbitals, application of the self-interaction correction can give significantly higher total energy and worse results, as illustrated by the case of the Perdew-Burke-Ernzerhof gradient dependent functional. This illustrates the importance of using complex orbitals for systems described by orbital density dependent energy functionals.

Electronic levels and electrical response of periodic molecular structures from plane-wave orbital-dependent calculations

Plane-wave electronic-structure predictions based upon orbital-dependent density-functional theory (OD-DFT) approximations, such as hybrid density-functional methods and self-interaction density-functional corrections, are severely affected by computational inaccuracies in evaluating electron interactions in the plane-wave representation. These errors arise from divergence singularities in the plane-wave summation of electrostatic and exchange interaction contributions. Auxiliary-function corrections are reciprocal-space countercharge corrections that cancel plane-wave singularities through the addition of an auxiliary function to the point-charge electrostatic kernel that enters into the expression of interaction terms. At variance with real-space countercharge corrections that are employed in the context of density-functional theory (DFT), reciprocal-space corrections are computationally inexpensive, making them suited to more demanding OD-DFT calculations. Nevertheless, there exists much freedom in the choice of auxiliary functions and various definitions result in different levels of performance in eliminating plane-wave inaccuracies. In this work we derive exact point-charge auxiliary functions for the description of molecular structures of arbitrary translational symmetry, including the yet unaddressed one-dimensional case. In addition, we provide a critical assessment of different reciprocal-space countercharge corrections and demonstrate the improved accuracy of point-charge auxiliary functions in predicting the electronic levels and electrical response of conjugated polymers from plane-wave OD-DFT calculations.

Theoretical study of band gap in CuAlO2: Pressure dependence and self-interaction correction

By using first-principles calculations, we studied the energy gaps of delafossite CuAlO2: (1) pressure dependence and (2) self-interaction correction (SIC). Our simulation shows that CuAlO2 transforms from a delafossite structure to a leaning delafossite structure at 60GPa. The energy gap of CuAlO2 increases through the structural transition due to the enhanced covalency of Cu 3d and O 2p states. We implemented a self-interaction correction (SIC) into first-principles calculation code to go beyond local density approximation and applied it to CuAlO2. The energy gap calculated within the SIC is close to experimental data while one calculated without the SIC is about 1eV smaller than the experimental data.

Density functional theory study of stoichiometric and nonstoichiometric ZnO grain boundaries

We present a density functional theory analysis of stoichiometric and nonstoichiometric ZnO tilt grain boundaries (GBs) that reveals under which conditions such extrinsically undoped GBs may become electrically active. In the case of ZnO the self-interaction correction (SIC) scheme used allows a more accurate description of the formation energies as well as the electronic levels than the local density approximation (LDA). The results obtained with the SIC scheme deviate in some crucial ways from the LDA results of recent years. First, stoichiometric and nonstoichiometric ZnO GBs can show occupied deep levels whenever oxygen atoms are undercoordinated. Second, ZnO GBs with an oxygen excess at the boundary plane can exhibit unoccupieddeep levels which may account for an experimentally observed weak varistor effect found in undoped polycrystalline ZnO.

Density functional theory study of dopants in polycrystalline TiO2

We present a density functional theory (DFT) study of doped rutile and anatase TiO${}_{2}$ in which we investigate the impact of grain boundaries on the physics of atomic defects. The main goal is to obtain information about the positions of the defect levels generated by an oxygen vacancy, a titanium interstitial, cation dopants Nb, Al, and Ga, and an anion dopant N in the electronic band gap having in mind the application of TiO${}_{2}$ as a transparent conducting oxide (TCO) or its use in heterogeneous catalysis. Due to the known deficiency of the local density approximation (LDA) of DFT to yield accurate values for band gap energies for insulators such as TiO${}_{2}$, a self-interaction correction (SIC) to the LDA is employed. The main result of our study is that grain boundaries do affect the defect formation energies as well as the position and shape of the dopant-induced electronic energy levels significantly with respect to the single crystal. According to our study Nb doping may lead to $n$-conducting TiO${}_{2}$ whereas doping with N, Al, or Ga is not promising in order to achieve $p$-conducting TiO${}_{2}$. Furthermore an increase in the photoconductivity of TiO${}_{2}$:N and the colorlessness of TiO${}_{2}$:Al may be explained by our results.

Density functional theory study for polycrystalline ZnO doped with Si or Nb

We present a density functional theory analysis for polycrystalline ZnO doped with the potential multiple donors silicon and niobium. A self-interaction correction allows a more accurate description of the defect formation energies as well as the additional electronic doping levels, which enable us to evaluate the influence of Si and Nb doping on the optical transparency and electrical conductivity of ZnO. According to our study, Si and Nb point defects in the bulk crystal or at grain boundaries lead to electronic dopant levels that may explain the high electrical $n$-type conductivity combined with the high transparency achieved by several experimental groups.

Self-Interaction Corrected Electronic Structure and Energy Gap of CuAlO2 beyond Local Density Approximation

We implemented a self-interaction correction (SIC) into first-principles calculation code to go beyond local density approximation and applied it to CuAlO 2 . Our simulation shows that the valence band width calculated within the SIC is narrower than that calculated without the SIC because the SIC makes the d -band potential deeper. The energy gap calculated within the SIC expands and is close to experimental data.

Strong-field ionization of Li and Be: a time-dependent density functional theory with self-interaction correction

In the framework of the time-dependent density functional theory, we have performed 3D calculations of multiphoton ionization of Li and Be atoms by strong near-infrared laser fields. The results for the intensity-dependent probabilities of single and double ionization are presented. We make use of the time-dependent Krieger-Li-Iafrate exchange-correlation potential with self-interaction correction (TD-KLI-SIC). Such a potential possesses an integer discontinuity which improves description of the ionization process. However, we have found that the discontinuity of the TD-KLI-SIC potential is not sufficient to reproduce characteristic feature of double ionization.

Electronic hole localization in rutile and anatase TiO2 – Self-interaction correction in Δ-SCF DFT

We study electronic hole localization in rutile and anatase titanium dioxide by means of Δ-Self-Consistent Field Density Functional Theory. In order to compare stabilities of the localized and the delocalized hole states we introduce a simple correction to the wrong description of the localization processes within DFT. The correction removes the non-linearity of energy for fractional excitations. We show that the self-trapped and the delocalized hole states have comparable stability in rutile TiO2 whereas in anatase the former is favoured. The theoretical prediction of the adiabatic Potential Energy Surfaces for the hole localization compares well with published photoluminescence measurements.

Self-consistent GW calculations of electronic transport in thiol- and amine-linked molecular junctions

The electronic conductance of a benzene molecule connected to gold electrodes via thiol, thiolate, or amino anchoring groups is calculated using nonequilibrium Green functions in combination with the fully self-consistent GW approximation for exchange and correlation. The calculated conductance of benzenedithiol and benzenediamine is one-fifth that predicted by standard density functional theory (DFT), in very good agreement with experiments. In contrast, the widely studied benzenedithiolate structure is found to have a significantly higher conductance due to the unsaturated sulfur bonds. These findings suggest that more complex gold-thiolate structures where the thiolate anchors are chemically passivated by Au adatoms are responsible for the measured conductance. Analysis of the energy level alignment obtained with DFT, Hartree-Fock, and GW reveals the importance of self-interaction corrections (exchange) on the molecule and dynamical screening at the metal-molecule interface. The main effect of the GW self-energy is to renormalize the level positions; however, its influence on the shape of molecular resonances also affects the conductance. Non-self-consistent ${\text{G}}_{0}{\text{W}}_{0}$ calculations, starting from either DFT or Hartree-Fock, yield conductance values within 50% of the self-consistent GW results.

On the relation between orbital-localization and self-interaction errors in the density functional theory treatment of organic semiconductors

It is commonly argued that the self-interaction error (SIE) inherent in semilocal density functionals is related to the degree of the electronic localization. Yet at the same time there exists a latent ambiguity in the definitions of the terms "localization" and "self-interaction," which ultimately prevents a clear and readily accessible quantification of this relationship. This problem is particularly pressing for organic semiconductor molecules, in which delocalized molecular orbitals typically alternate with localized ones, thus leading to major distortions in the eigenvalue spectra. This paper discusses the relation between localization and SIEs in organic semiconductors in detail. Its findings provide further insights into the SIE in the orbital energies and yield a new perspective on the failure of self-interaction corrections that identify delocalized orbital densities with electrons.

The generalized SIC‐OEP formalism and the generalized SIC‐Slater approximation (stationary and time‐dependent cases)

AbstractWe present a generalized formulation of the Optimized Effective Potential (OEP) approach to the Self Interaction Correction (SIC) problem in Time Dependent (TD) Density Functional Theory (DFT). The formulation relies on the introduction of a double set of single electron orbitals. It allows the derivation of a generalized Slater approximation to the full OEP formulation, which extends the domain of validity of the standard Slater approximation. We discuss both formal aspects and practical applications of the new formalism and give illustrations in cluster and molecules. The new formalism provides a valuable ansatz to more elaborate (and computationally very demanding) full TD OEP and full TD SIC calculations especially in the linear domain.