Self-interaction Correction Research Articles

Avoiding singularity problems associated with meta-GGA (generalized gradient approximation) exchange and correlation functionals containing the kinetic energy density

Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy is suggested that cures meta-XC functionals such as VSXC, TPSS, M05, M06, and their derivatives without extra cost.

Self-Interaction Corrected Density Functional Theory for the Study of Intramolecular Electron Transfer Dynamics in Radical Carbocations

We derived an orbital dependent Kohn-Sham based scheme for the correction of the self-interaction error in DFT, which is particularly suited for the study of open shell molecular systems. Our approach is based on a weighted form of the Perdew and Zunger (PZ) self-interaction correction scheme, in which an empirical coefficient is introduced in front of the SIC term to remove overcorrections. The method is used to investigate the first principle molecular dynamics of the intramolecular electron transfer (IET) in bis(methylene) adamanthyl radical cation and allows the analysis of the free energy surface that governs the IET process at room temperature (300 K). Indeed, the thermal activation of all molecular degrees of freedom provides important additional information about the mechanisms involved in the IET process. Our study confirms and extends previous results obtained with CASSCF and shows that there is no predominant degeneracy-lifting mode even at room temperature. However, we also identified regions in the phase space for which there is a significant probability for a productive IET event. In addition, we performed thermodynamic integrations along selected reaction coordinates to determine an estimate of the activation free energy barrier for the IET process.

Migration of positively charged defects inα-quartz

We apply a quantum-mechanics/molecular-mechanics (QM/MM) scheme to simulate the migration of charged defects in $\ensuremath{\alpha}$-quartz. A QM/MM framework together with a self-interaction correction (SIC) scheme was used to investigate the stability of the charged dimer defect and the ${E}_{1}^{\ensuremath{'}}$ center in $\ensuremath{\alpha}$-quartz. The use of a SIC scheme makes the charged dimer center unstable in $\ensuremath{\alpha}$-quartz, in agreement with the experimental failure of identifying this defect, while the effects of the correction of the self-interaction error on the ${E}_{1}^{\ensuremath{'}}$ center are negligible. Moreover, we conjecture that by overcoming a low energy barrier, the puckering mechanism (ideally heading from the charged dimer defect to the ${E}_{1}^{\ensuremath{'}}$ center in SIC-free calculations) can be reiterated allowing the drift of the positive charge localized on an overcoordinated oxygen atom. This process can be regarded as an important channel of structural reorganization of oxygen deficient silica in the presence of strong polarizing electric fields.

Core ionization potentials from self-interaction corrected Kohn-Sham orbital energies

We propose a simple self-interaction correction to Kohn-Sham orbital energies in order to apply ground state Kohn-Sham density functional theory to accurate predictions of core electron binding energies and chemical shifts. The proposition is explored through a series of calculations of organic compounds of different sizes and types. Comparison is made versus experiment and the "DeltaKohn-Sham" method employing separate state optimizations of the ground and core hole states, with the use of the B3LYP functional and different basis sets. A parameter alpha is introduced for a best fitting of computed and experimental ionization potentials. It is found that internal parametrizations in terms of basis set expansions can be well controlled. With a unique alpha=0.72 and basis set larger than 6-31G, the core ionization energies (IPs) of the self-interaction corrected Kohn-Sham calculations fit quite well to the experimental values. Hence, self-interaction corrected Kohn-Sham calculations seem to provide a promising tool for core IPs that combines accuracy and efficiency.

Quasiparticle self-consistentGWmethod: A basis for the independent-particle approximation

We have developed a type of self-consistent scheme within the $GW$ approximation, which we call quasiparticle self-consistent $GW$ (QS$GW$). We have shown that QS$GW$ describes energy bands for a wide range of materials rather well, including many where the local-density approximation fails. QS$GW$ contains physical effects found in other theories such as $\mathrm{LDA}+U$, self-interaction correction, and $GW$ in a satisfactory manner without many of their drawbacks (partitioning of itinerant and localized electrons, adjustable parameters, ambiguities in double counting, etc.). We present some theoretical discussion concerning the formulation of QS$GW$, including a prescription for calculating the total energy. We also address several key methodological points needed for implementation. We then show convergence checks and some representative results in a variety of materials.

Structure Stability and Electronic Structure of Semiconducting Rhenium Silicide with Doping

Full-potential linearized augmented plane-wave (FP-LAPW) method within the local density approximation plus self-interaction correction (LDA+USIC) has been applied to study the structure stability and electronic structure of ReSi1.75 and its doped systems with Al and Mo. Structural relaxation results show that the vacancy prefers to occupy the Si3 and Si4 site in the lattice with little ordering. For doping systems, Al prefers to substitute for Si at the Si3 site and Mo prefers to substitute for Re at the Re1 site. ReSi1.75 shows narrow gap semiconductor behavior with an indirect gap of 0.12 eV and a direct gap of 0.36 eV. Al doping compound remains semiconductor while Mo doping compound has a tendency to change into semimetals or metals. The Fermi level of doped systems moves into the valence band resulting in an increase of density of state at the Fermi level. It will enhance the thermoelectric properties and agrees well with the experiment results.

Excess Electron in Water at Different Thermodynamic Conditions

A hydrated electron in water at different densities and temperatures is studied via a set of density functional based molecular dynamics simulations, showing that a localization of an excess electron is still present even at very low densities. Space variations of the molecular dipole moments are analyzed, proposing a simple algorithm to identify the region of localization of the wavefunction relative to the solvated electron in terms of orientation of the H2O molecular dipole moments. Finally, the effects of the self-interaction corrections on the optical absorption spectra are analyzed and compared with both available experimental data and path integral molecular dynamics calculations, showing that a weighted subtraction of the self-interaction yields a systematic improvement in the position of the absorption peak.

Variational QMC study of a hydrogen atom in jellium with comparison to LSDA and self-interaction corrected LSDA solutions

A Hydrogen atom immersed in a finite jellium sphere is solved using variational quantum Monte Carlo (VQMC). The same system is also solved using density functional theory (DFT), in both the local spin density (LSDA) and self-interaction correction (SIC) approximations. The immersion energies calculated using these methods, as functions of the background density of the jellium, are found to lie within 1eV of each other with minima in approximately the same positions. The DFT results show overbinding relative to the VQMC result. The immersion energies also suggest an improved performance of the SIC over the LSDA relative to the VQMC results. The atom-induced density is also calculated and shows a difference between the methods, with a more extended Friedel oscillation in the case of the VQMC result.

Efficient Atomic Self-Interaction Correction Scheme for Nonequilibrium Quantum Transport

Density-functional theory calculations of electronic transport based on local exchange and correlation functionals contain self-interaction errors. As a consequence, insulating molecules in weak contact with metallic electrodes erroneously form highly conducting junctions. Here we present a fully self-consistent and still computationally undemanding self-interaction correction scheme that overcomes these limitations. The method is implemented in the transport code SMEAGOL and applied to the prototypical case of benzene molecules and gold electrodes. The Kohn-Sham highest occupied molecular orbital now reproduces closely the negative of the molecular ionization potential and is moved away from the gold Fermi energy. This leads to a drastic reduction of the low-bias current in much better agreement with experiments.

Exchange parameters from approximate self-interaction correction scheme

The approximate atomic self-interaction correction (ASIC) method to density functional theory is put to the test by calculating the exchange interaction for a number of prototypical materials, critical to local exchange and correlation functionals. ASIC total energy calculations are mapped onto a Heisenberg pairwise interaction and the exchange constants J are compared to those obtained with other methods. In general the ASIC scheme drastically improves the band structure, which for almost all the cases investigated resemble closely available photoemission data. In contrast the results for the exchange parameters are less satisfactory. Although ASIC performs reasonably well for systems where the magnetism originates from half-filled bands, it suffers from similar problems than those of local density approximation for other situations. In particular, the exchange constants are still overestimated. This reflects a subtle interplay between exchange and correlation energy, not captured by the ASIC.

Self-interaction correction in theLDA+Umethod

We present one inherent shortcoming of the LDA+U method in respect of its self-interaction correction of the LDA. By reexamining the mean-field approximation on the Hubbard energy in the Hartree-Fock form, we have derived a new expression for the ``double-counting'' energy which led to a more reasonable self-interaction correction in an alternative LDA+U scheme. For the bulk Gd metal, the new scheme resulted in electronic properties more consistent with experiments in comparison to the LDA and the existing LDA+U schemes.

Diminished gradient dependence of density functionals: Constraint satisfaction and self-interaction correction

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.

Self-Interaction and Strong Correlation in DFTB

The density functional based tight-binding (DFTB) method can benefit substantially from a number of developments in density functional theory (DFT) while also providing a simple analytical proving ground for new extensions. This contribution begins by demonstrating the variational nature of charge-self-consistent DFTB (SCC-DFTB), proving the presence of a defined ground-state in this class of methods. Because the ground state of the SCC-DFTB method itself can be qualitatively incorrect for some systems, suitable forms of the recent LDA+U functionals for SCC-DFTB are also presented. This leads to both a new semilocal self-interaction correction scheme and a new physical argument for the choice of parameters in the LDA+U method. The locality of these corrections can only partly repair the HOMO-LUMO gap and chemical potential discontinuity, hence a novel method for introducing this further physics into the method is also presented, leading to exact derivative discontinuities in this theory at low computational cost. The prototypical system NiO is used as an illustration for these developments.

Ab initio materials design for transparent-conducting-oxide-based new-functional materials

Based upon ab initio electronic structure calculations for delafossite CuAlO2 and ZnO, we report on the design of new-functional materials for transparent conducting oxides (TCO), such as (i) low-resistive p-type ZnO and CuAlO2 by co-doping, (ii) high-efficiency thermoelectric power in CuAlO2 (ZT>3) by p-type doping, (iii) half-metallic ferromagnetism in transition-metal-impurity doped CuAlO2 and ZnO-based diluted magnetic semiconductors, and (iv) CaO, MgO, SrO and BaO based DMS without transition metal impurities. We also discuss the implementation of the self-interaction correction to our materials design method.

Tests of functionals for systems with fractional electron number

In the exact theory, the ground state energy of an open system varies linearly when the electron number is changed between two adjacent integers. This linear dependence is not reproduced by common approximate density functionals. Deviation from linearity in this dependence has been suggested as a basis for the concept of many-electron self-interaction error (SIE). In this paper, we quantify many-electron SIE of a number of approximations by performing calculations on fractionally charged atoms. We demonstrate the direct relevance of these studies to such problems of common approximate functionals as instabilities of anions, spurious fractional charges on dissociated atoms, and poor description of charge transfer. Semilocal approximations have the largest many-electron SIE, which is only slightly reduced in typical global hybrids. In these approximations the energy versus fractional electron number curves upward, while in Hartree-Fock theory the energy curves downward. Perdew-Zunger self-interaction correction [Phys. Rev. B 23, 5048 (1981)] significantly reduces the many-electron SIE of semilocal functionals but impairs their accuracy for equilibrium properties. In contrast, a long-range corrected hybrid functional can be nearly many-electron SIE-free in many cases (for reasons we discuss) and at the same time performs remarkably well for many molecular properties.

Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+

The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1<N<or=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.

Investigation of n-type donor defects in Co-doped ZnO

We investigate using density functional theory (DFT) the electronic structure of (∼3%) Co-doped ZnO in the presence of native n-type donor defects such as V O and Zn I. In particular, we apply a pseudopotential-based self-interaction correction (pseudo-SIC) scheme as an improvement to the local spin-density approximation (LSDA). This overcomes major short comings of the LSDA in describing Co-doped ZnO. Donor+dopant pair complexes such as Co–V O and Co–Zn I are studied as relevant magnetic centres for long-range magnetic interactions at low-dopant concentrations. We find that complex formation is energetically favourable but the inter-complex magnetic coupling is too weak to account for room temperature ferromagnetism in ZnO:Co

Electron, hole and exciton self-trapping in germanium doped silica glass from DFT calculations with self-interaction correction

Density functional theory (DFT) calculations were employed to understand the refractive index change in germanium doped silica glasses for the trapped states of electronic excitations induced by UV irradiation. Local structure relaxation and excess electron density distribution were calculated upon self-trapping of an excess electron, hole, and exciton in germanium doped silica glass. The results show that both the trapped exciton and excess electron are highly localized on germanium ion and, to some extent, on its oxygen neighbors. Exciton self-trapping is found to lead to the formation of a Ge E′ center and a non-bridging hole center. Electron trapping changes the GeO 4 tetrahedron structure into trigonal bi-pyramid with the majority of the excess electron density located along the equatorial line. The self-trapped hole is localized on bridging oxygen ions that are not coordinated to germanium atoms that lead to elongation of the Si–O bonds and change of the Si–O–Si bond angles. We carried out a comparative study of standard DFT versus DFT with a hybrid PBE0 exchange and correlation functional. The results show that the two methods give qualitatively similar relaxed structure and charge distribution for electron and exciton trapping in germanium doped silica glass; however, only the PBE0 functional produces the self-trapped hole.

Atomic and electronic structure ofBeOand theBeO(101¯0)surface: Anab initioinvestigation

We report the atomic and electronic structure of bulk $\mathrm{BeO}$ and the nonpolar $\mathrm{BeO}(10\overline{1}0)$ surface as resulting from density functional theory (DFT). Employing norm-conserving pseudopotentials which incorporate self-interaction corrections (SICs) we arrive at structural and electronic properties of bulk $\mathrm{BeO}$ which are not subject to the usual shortcomings of the standard local density approximation (LDA), most noticeably the underestimate of the band gap. The latter is particularly large for $\mathrm{BeO}$ amounting to more than $3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. It turns out that the LDA problems can largely be overcome by employing SIC pseudopotentials in DFT calculations. They cause no additional computational effort, as compared to standard LDA calculations. Our SIC approach yields a bulk band gap of $10.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ in excellent agreement with the measured gap of $10.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and calculated structural bulk properties are found to be in very good accord with experiment, as well. Also the surface electronic structure of $\mathrm{BeO}\phantom{\rule{0.3em}{0ex}}(10\overline{1}0)$ shows very significant SIC-induced changes, as compared to the respective standard LDA surface band structure. For the relaxed surface, showing a bond lengths contracting rotation relaxation, we find three salient bands of surface states. Two of these occur within the fundamental gap fairly close to the projected bulk bands from which they are derived. The surface band gap resulting in SIC is $9.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, as opposed to the LDA surface band gap of $6.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$.

Theoretical Study on the Structure, Stability, and Electronic Properties of the Guanine−Zn−Cytosine Base Pair in M-DNA

M-DNA is a type of metalated DNA that forms at high pH and in the presence of Zn, Ni, and Co, with the metals placed in between each base pair, as in G-Zn-C. Experiments have found that M-DNA could be a promising candidate for a variety of nanotechnological applications, as it is speculated that the metal d-states enhance the conductivity, but controversy still clouds these findings. In this paper, we carry out a comprehensive ab initio study of eight G-Zn-C models in the gas phase to help discern the structure and electronic properties of Zn-DNA. Specifically, we study whether a model prefers to be planar and has electronic properties that correlate with Zn-DNA having a metallic-like conductivity. Out of all the studied models, there is only one which preserves its planarity upon full geometry optimization. Nevertheless, starting from this model, one can deduce a parallel Zn-DNA architecture only. This duplex would contain the imino proton, in contrast to what has been proposed experimentally. Among the nonplanar models, there is one that requires less than 8 kcal/mol to flatten (both in gas and solvent conditions), and we propose that it is a plausible model for building an antiparallel duplex. In this duplex, the imino proton would be replaced by Zn, in accordance with experimental models. Neither planar nor nonplanar models have electronic properties that correlate with Zn-DNA having a metallic-like conductivity due to Zn d-states. To understand whether density functional theory (DFT) can describe appropriately the electronic properties of M-DNAs, we have investigated the electronic properties of G-Co-C base pairs. We have found that when self-interaction corrections (SIC) are not included the HOMO state contains Co d-levels, whereas these levels are moved below the HOMO state when SIC are considered. This result indicates that caution should be exercised when studying the electronic properties of M-DNAs with functionals that do not account for strong electronic correlations.