Self-interaction Correction Research Articles

Electronic states of neutral and ionized alkali clusters calculated on one-particle models

We propose a one-electron potential, having a V-shaped valley at the surface, for an alkali cluster. The energy levels calculated by a perturbation method agree with those calculated by a density functional method. From those energy levels, we derive the sum of one-particle energies and clarify its correspondence to the total energy per atom. It is shown that 3/4 of the summed energy levels per atom agree with an oscillatory part of the total energy per atom. By adding another perturbation potential, we obtain the size dependence of ionization energy, which agrees with measured data and the data calculated by a density functional method including self-interaction correction.

Penning detachment from atomic clusters

Theoretical cross-sections are presented for Penning detachment of negatively-charged sodium clusters, receiving their detachment energy from Na*(3p0,2P). Two clusters are examined: Na7− and Na19−. Classical trajectories describe the relative motion of the colliding species. Kohn–Sham density functional theory in local approximation, with exchange, correlation, and self-interaction corrections, and a spherical jellium potential, describe the electrons involved in the transition. In the range of collision energies from 0.1 to 10 eV/amu, the cross-sections for Penning detachment are approximately 10−13 cm2. This implies that Penning detachment may be an effective means to prepare neutral clusters from size-selected negative-ion clusters in the laboratory.

Dipole polarization and charge transfer effects in the lattice dynamics and dielectric properties of ionic crystals

We extend our formalism of an ab initio description of electronic screening in solids with a strong ionic component of bonding by introducing electronic density polarization effects of dipole type in addition to charge transfer polarization processes. The latter have been found earlier to be very important for the lattice dynamics and the electron-phonon interaction in the high-temperature superconductors. The dipole deformations are calculated with the Sternheimer method and the influence on the polarizability induced by the crystalline environment and by self-interaction corrections is studied. We further derive detailed expressions for the various coupling coefficients appearing in the dynamical matrix in our formalism and apply this theory in a first step in view of the ultimate goal, namely, the high-temperature superconductors, to the calculation of complete dispersion curves for the alkali halide NaCl and the alkaline-earth oxide MgO taking into account for the first time dipole polarization and charge transfer effects together. The agreement of our calculated results with the experiments is good. As a main effect we find a renormalization of the LO modes and a reduction of the LO-TO splitting by both types of polarization processes. The dipole polarization, however, dominates the electronic screening by far. Finally, we investigate the macroscopic dielectric constant and the transverse effective charges and discuss the results in context with the Clausius-Mossotti relation.

Obtaining localized orbitals and band structure in self-interaction-corrected density-functional theory

An efficient minimization method is presented to find the optimal orthogonal localized orbitals within the self-interaction-corrected (SIC) local spin-density (LSD) approximation. By introducing a unified Hamiltonian, both the canonicalvalence bands and conduction bands are obtained by diagonalizing the same matrix. A general criterion for the existence of the self-consistent localized solutions of the SIC-LSD equations is proposed. As an application, we consider the phase diagram and the band structure of the half-filled two-dimensional extended Hubbard model with the next-nearest-neighbor hopping amplitude ${t}^{\ensuremath{'}}.$ The phase boundary between the charge-density wave (CDW) and the spin-density wave (SDW) is determined by comparing the ground-state energies. For nonzero ${t}^{\ensuremath{'}},$ the CDW and SDW states are unstable over a finite portion of the phase diagram at weak coupling.

Atomic Compton profiles within different exchange-only theories

The Impulse Compton Profiles (CP's) J(q) and the <p^n> - expectation values for some inert gas atoms (He-Kr) are computed and compared within the Harbola-Sahni (HS), Hartree-Fock(HF) theories and a Self Interaction Corrected (SIC) density functional model. The Compton profiles for excited states of Helium atom are also calculated. While the calculated CP's are found to generally agree, they differ slightly from one another for small values of the Compton parameter q and are in good agreement for large q values. The <p^n> expectation values within the three theories are also found to be comparable. The HS formalism seem to mimic HF reasonably well in the momentum space, establishing the logical consistency of the former.

Recent New Developments of Steady‐State and Time‐Dependent Density Functional Theories for the Treatment of Structure and Dynamics of Many‐Electron Atomic, Molecular, and Quantum Dot Systems

AbstractWe present a short account of recent new developments of density‐functional theory (DFT) for accurate and efficient treatments of the electronic structure and quantum dynamics of many‐electron systems. The conventional DFT calculations contain spurious self‐interaction energy and improper long‐range potential, preventing reliable description of the excited and resonance states. We present a new DFT with optimized effective potential (OEP) and self‐interaction‐correction (SIC) to overcome some of the major difficulties encountered in conventional DFT treatments using explicit energy functionals. The OEP‐SIC formalism uses only orbital‐independent single‐particle local potentials and is self‐interaction free, providing a theoretical framework for accurate description of the excited‐state properties and quantum dynamics. Several applications of the new procedure are presented, including: (a) the first successful DFT treatment of the atomic autoionizing resonances, (b) a relativistic extension of the OEP‐SIC formalism for the calculation of the atomic structure with results in good agreement with the experimental data across the periodic table (Z = 2–106), (c) electronic structure calculation of the ionization properties of molecules, and (d) the delicated “shell‐filling” electronic structure in quantum dots. Finally we present also new formulations of time‐dependent DFT for nonperturbative treatment of atomic and molecular multiphoton and nonlinear optical processes in intense and superintense laser fields. Both the time‐independent Floquet approach and the time‐dependent OEP‐SIC technique are introduced. Application of the time‐dependent DFT/OEP‐SIC procedure to the study of multiple high‐order harmonic generation processes in intense ultrashort pulsed laser fields is discussed in detail.

The importance of self-interaction and nonlocal exchange corrections to the density functional theory of intracavity electrons in Na-doped sodalites

Electrons that are confined to zeolite cavities are modeled using a simplified pseudopotential scheme to represent the interaction of the electrons with both the sodalite framework and the Na+ ions. By comparing theory with recent experimental studies of G centers in Na-doped NaBr-SOD it is demonstrated that restricted forms of density functional theory, where two electrons are forced to pair in the same Kohn–Sham orbital, fail to correctly predict the true nature of the singlet, (spin unpolarized), G center. Electron confinement leads to generalized gradient corrections to the exchange of 0.74 eV and self-interaction corrections (SIC) of 0.7 eV over calculations performed in the local spin density approximation (LSDA). Only the self-interaction corrected generalized gradient approximation and the unrestricted Hartree–Fock approximation are in accord with experiment for the relative stability of the triplet (spin polarized) state. The unrestricted Hartree–Fock method is used to show that G-center absorptions will be blueshifted with respect to absorptions due to the isolated F centers. Constructing a Hubbard Hamiltonian we show that the exchange coupling ranges in values from 2.3 meV(UHF) to 3.6 meV(SIC-LSDA) corresponding to Neel temperatures that range from 27 to 41 K in agreement with experiment.

Electron removal energies from density functional computations

We present a simple method for estimating electron removal energies from ground-state density functional computations. We discuss the relation of our method with previous schemes, like the self-interaction correction, the Slater transition state method, and a semi-empirical scheme. The comparison of our results with experimental data for atoms and molecules shows that the proposed method corrects most of the error present in the single electron eigenvalues of density functional theory.

Relativistic density functional approach to open shells

A full application of relativistic spin-density functional theory in noncollinear treatment of the exchange and correlation field is given to open-shell atoms and ions of the carbon group. It is shown that the influence of noncollinearity is small as compared with self-interaction corrections. Unfortunately, the defect of the local spin-density approximation not to yield a source-free exchange and correlation field increases in noncollinear treatment. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 23–30, 1999

Effects of self-interaction correction on momentum density in copper

The full-potential linearized APW (FLAPW) method is employed to find out effects of introducing the self-interaction correction (SIC) on the band structure, the Fermi surface geometry, electron wavefunctions and Compton profiles. Introduction of the SIC lowers and narrows the d bands. As the results, the theoretical Compton profiles are brought into a better agreement with the experimental profiles on one hand, and the area of the Fermi surface neck at the L point becomes too small to explain the dHvA result on the other hand.

Application of self-interaction-corrected density-functional formalism to the extended Hubbard model

The density-functional theory for the half-filled extended Hubbard model in one and two dimensions has been studied within the self-interaction-corrected (SIC) local-spin-density (LSD) approximation. The SIC to the total energy is expressed in terms of the Wannier functions which have the most optimal degree of localization. The system at ground state can have spin-density wave (SDW) or charge-density wave (CDW) ordering depending on the relative strength of the on-site repulsion and the nearest-neighbor repulsion. Like the Hartree-Fock approximation, the SIC-LSD scheme predicts a first-order transition between CDW and SDW. However, in the SDW, the nearest-neighbor repulsion V near the transition point tends to increase the band gap for small U and decrease the band gap for large U, with a crossover around $U\ensuremath{\approx}4$ in one dimension, which corresponds to the tricritical point predicted by other theories. The ground-state energies are better described in SIC-LSD than in the Hartree-Fock approximation.

Electronic structure ofLa1.85Sr0.15CuO4:Characterization of a Fermi-level band crossing

We present the results of a Hubbard model for optimally doped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}.$ This model uses parameters derived from Becke-Lee-Yang-Parr calculations on the cluster ${\mathrm{CuO}}_{6}.$ It explicitly includes the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals, the O ${p}_{\ensuremath{\sigma}}$ orbitals, and the apical O ${p}_{z}$ orbitals. We find that when the mean-field equation is appropriately modified to include a self-interaction correction, a crossing of two bands is observed in the vicinity of the Fermi level for the optimally doped superconductor. This crossing rigorously occurs along the $(0,0)\ensuremath{-}(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$ direction of the two-dimensional (2D) Brillouin zone. The crossing arises due to the overlap of a broad ``${B}_{1g}$'' band dominated by Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ character and a narrower ``${A}_{1g}$'' band dominated by Cu ${d}_{{z}^{2}}$ character. We conclude that optimal doping of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ and related materials is achieved when the Fermi level coincides with this crossing. At this point, formation of Cooper pairs between the two bands (i.e., interband pairing or IBP) leads to superconductivity. We further extend our conclusions to ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\mathrm{\ensuremath{\delta}}}$ and offer a simple explanation for the seemingly complex behavior of ${T}_{c}$ as a function of doping in this material. This behavior can be understood on the basis of multiple band crossings predicted from geometric considerations.

Generation of circularly polarized multiple high-order harmonic emission from two-color crossed laser beams

We present a scheme for the production of circularly polarized multiple high-order harmonic generation (HHG). The proposed experimental setup involves the use of two-color laser fields, consisting of a circularly polarized fundamental laser field and a linearly polarized second-harmonic laser field, in crossed-beam configuration. The feasibility of such a scheme is demonstrated by an ab initio quantal study of the HHG power spectrum of He atoms by means of the time-dependent density-functional theory with optimized effective potential and self-interaction correction recently developed. The theoretical study also provides insights regarding the different mechanisms responsible for the production of HHG in different energy regimes as well as the mechanism for the generation of continuous background radiation.

Why semilocal functionals work: Accuracy of the on-top pair density and importance of system averaging

Gradient-corrected density functionals provide a common tool for electronic structure calculations in quantum chemistry and condensed matter physics. This article explains why local and semilocal approximations work for the exchange-correlation energy. We demonstrate the high accuracy of the local spin-density (LSD) approximation for the on-top pair density, which provides the missing link between real atoms and molecules and the uniform electron gas. Special attention is devoted to the leading correction to exchange in the high-density (or weakly correlated) limit. We give an improved analytic expression for the on-top pair density in the uniform electron gas, calculating its spin-polarization dependence exactly in the high-density limit. We find the exact form of the gradient expansion for the on-top pair density, using Levy’s scaling of the interacting wave function. We also discuss the importance of system averaging, which unweights spatial regions where the density varies most rapidly. We show how the depth of the on-top hole correlates with the degree of locality of the exchange-correlation energy. Finally, we discuss how well fully nonlocal approximations (weighted-density, self-interaction correction, and hybrid-exchange) reproduce the on-top hole.

Electron capture and excitation in proton-Na20collisions at low velocities

We present a many-electron theoretical study of electron capture and excitation in collisions of ${\mathrm{H}}^{+}$ with ${\mathrm{Na}}_{20}$ clusters for impact energies 40--500 eV. The collision is treated semiclassically using the independent-electron model, and the cluster is described in the framework of the Kohn-Sham formalism with a local-density approximation which includes exchange, correlation, and a self-interaction correction. We have found that capture cross sections are $\ensuremath{\sim}(2\ensuremath{-}5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14} {\mathrm{cm}}^{2}$ and dominate in the above energy range. In contrast with ion-atom collisions, excitation cross sections are comparable to the former, and multiple processes such as capture excitation cannot be neglected at low velocities. From the analysis of the vacancies originated in the collision, we have evaluated the energy deposited in the cluster, which is an essential parameter in the study of cluster fragmentation.

Two electrons in an external oscillator potential: exact solution versus one-particle approximations

We use the two-electron oscillator (with Coulomb interaction between the electrons) as a test system for a selection of the most common one-particle approximations: Hartree-Fock (HF), local spin density approximation (LSDA), with self-interaction correction (SIC), generalized gradient correction (GGA) and corrections for excitation energies. Moreover we compared excitation energies from total energy differences with the concept of the Slater transition state (STS) and with the difference of approximate and exact Kohn-Sham energies. By tuning the external oscillator frequency, one can realize the strong, intermediate and weak correlation regime within one system. The results are compared with exact charge densities, Kohn-Sham potentials, ground-state energies and excitation energies. Unlike previous papers on this model, we used self-consistent (and not the exact) charge densities as input for the density functional theory, which makes it possible to check the accuracy of the approximated density itself. We found that the LSDA describes the charge density even in the Wigner crystal limit qualitatively correct, although only SIC provides quantitatively satisfactory results. For all oscillator frequencies, the spurious wiggles in the GGA exchange potential are located near the classical turning point suggesting that they are a consequence of the divergence of the underlying Kirshnitz expansion in this region. It is also observed that the well known large error in the LSDA and GGA exchange potential is not present in self-interaction free methods such as HF and SIC giving rise to the assumption that self-interaction is responsible for this defect. KS eigenvalue differences (as zeroth approximations for excitation energies) calculated from the exact and LSDA effective potential are very close. Therefore, their common large difference with the exact excitation energies cannot be fixed by nonlocal corrections to the LSDA.

A simple theory of angle-resolved photoemission spectroscopy cross sections with applications to and

We try to interpret angle-resolved photoemission spectroscopy (ARPES) cross sections directly in band-structure terms by approximating the one-particle propagator needed to evaluate the lowest-order Keldysh diagram using the bulk Green function. As applications to and demonstrate, this is a sensible approach, since it reproduces important features of experimental curves. Matrix element effects strongly enhancing the contributions of individual bands at certain energies and depressing them at others are well described. Self-energy corrections included in an average way improve the agreement and allow for a rough estimate of the magnitude of the band broadening. In the case of our investigations demonstrate the significance of correlations, since adding self-interaction corrections to the local density approximation leads to considerable improvement of the calculated ARPES cross sections.

Electron dynamics in strongly excited sodium clusters: a density-functional study with self-interaction correction

We study the linear and nonlinear electron dynamics of a cluster using time-dependent density functional theory. Exchange-correlation (xc) effects are treated in the adiabatic local density approximation with and without self-interaction correction (SIC). The latter is implemented within the time-dependent optimized effective potential method, leading to a self-interaction-free xc potential which is orbital independent. The method is applied to compare the electronic response of the cluster, calculated with and without SIC, in different dynamical regimes. We focus on the dipole response in the weakly excited regime, and on multiphoton ionization induced by strong femtosecond laser pulses. It is found that including SIC produces minor differences in the dipole power spectra and leaves the ionization mechanism essentially unchanged.

Inclusion of exact exchange for self-interaction corrected H 3 density functional potential energy surface

The effect of the inclusion of the exact exchange into self-interaction corrected generalized gradient approximation density functional theory (GGA-DFT) for the simplest hydrogen abstraction reaction, H + H2 → H3 → H2 + H, is presented using a triple-zeta augmented 6-311++G(d,3pd) basis set. The introduction of the self-interaction correction has a considerably larger effect on molecular geometry and vibrational frequencies than the inclusion of the exact exchange. We investigate the influence of the self-interaction error on the shape of the potential energy surface around the transition state of the hydrogen abstraction reaction. The decomposition of the self-interaction error into correlation and exchange parts shows that the exchange self-interaction error is the main component of the energy barrier error. The best agreements with the experimental barrier height were achieved by self-interaction corrected B3LYP, B-LYP and B3PW functionals with errors of 1.5, 2.9 and 3.0 kcal/mol, respectively.

Relativistic density-functional theory with the optimized effective potential and self-interaction correction: Application to atomic structure calculations(Z=2–106)

We present a self-interaction-free relativistic density-functional theory ~DFT!. The theory is based on the extension of our recent nonrelativistic DFT treatment with optimized effective potential ~OEP! and selfinteraction correction ~SIC !@ Phys. Rev. A 55, 3406 ~1997!# to the relativistic domain. Such a relativistic OEP-SIC procedure yields an orbital-independent single-particle local potential with proper long-range Coulombic (21/r) behavior. The method is applied to the ground-state energy calculations for atoms with Z52 ‐106. A comparison with the corresponding nonrelativistic OEP-SIC calculations and other relativistic calculations is made. It is shown that the ionization potentials ~obtained from the highest occupied orbital energies! and individual orbital binding energies determined by the present relativistic OEP-SIC method agree well with the experimental data across the Periodic Table. @S1050-2947~98!06201-5#