Exchange-correlation Interaction Research Articles

A comparative study for structural and electronic properties of single-crystal ScN

A comparative study by FP-LAPW calculations based on DFT within LDA, PBE-GGA, EV$_{ex}$-PW$_{co}$-GGA, and EV$_{ex}$-GGA-LDA$_{co}$ schemes is introduced for the structural and electronic properties of ScN in RS, ZB, WZ, and CsCl phases. According to all approximations used in this work, the RS phase is the stable ground state structure and makes a transition to CsCl phase at high transition pressure. While PBE-GGA and EV$_{ex}$-PW$_{co}$-GGA's have provided better structural features such as equilibrium lattice constant and bulk modulus, only EV$_{ex}$-PW$_{co}$-GGA and EV$_{ex}$-GGA-LDA$_{co}$'s have given the non zero, positive indirect energy gap for RS-ScN, comparable with the experimental ones. The indirect band gap of ScN in RS phase is enlarged to the corresponding measured value by EV$_{ex}$-PW$_{co}$-GGA+U$^{SIC}$ calculations in which the Coulomb self and exchange-correlation interactions of the localized d-orbitals of Sc have been corrected by the potential parameter of U. The EV$_{ex}$-PW$_{co}$-GGA calculations have also provided good results for the structural and electronic features of ScN in ZB, WZ, and CsCl phases comparable with the theoretical data available in the literature. EV$_{ex}$-PW$_{co}$-GGA and EV$_{ex}$-PW$_{co}$-GGA+U$^{SIC}$ schemes are considered to be the best ones among the others when the structural and electronic features of ScN are aimed to be calculated by the same exchange-correlation energy approximations.

Self-Consistent Subband Calculations of Al<sub>x</sub>Ga<sub>1-x</sub>N/(AlN)/GaN-Based High Electron Mobility Transistor

In this paper, there is an attempt to present the two dimensional electron gas (2DEG) transport characteristics of AlxGa1-xN/(AlN)/GaN-based High Electron Mobility Transistor (HEMT) using a self-consistent numerical method for calculating the conduction-band profile and subband structure. The subband calculations take into account the piezoelectric and spontaneous polarization effects and the Hartree and exchange-correlation interaction. Here the dependency of conduction band profile, subband energies, 2DEG sheet concentration and sheet resistance on various Al mole fractions of AlxGa1-xN barrier layer are presented by incorporating simulation as well as available experimental data. Introduction of very thin binary AlN layer at the heterojunction of AlxGa1-xN/GaN resulting high mobility at high sheet charge densities by increasing the effective and decreasing alloy disorder scattering. Devices based on this structure exhibit good DC and RF performance as an increase of . Owing to high 2DEG density , the proposed device leads to operate in microwave and millimeter wave applications.

Study of the orbital hardness and the Kohn-Sham radius on single monoatomic anions

Within the Kohn-Sham framework and for a series of single charged monatomic anions, the orbital hardness is calculated as a change in the frontier eigenvalue, which is equivalent to integrate the local hardness function obtained through the derivative of the KS effective potential respect to the occupation number. The local hardness function is composed by the sum of two terms with opposite sign that describe the electrostatic and exchange-correlation interactions. Moreover, it is found that, at the KS radii, the last term vanishes with the result that the orbital hardness of the anion is a measure of the electrostatic potential exerted by the frontier density at the KS radii. A further derivation leads to establish a direct relationship between hardness and the inverse of the KS radii. The polarizability of the anion is also examined by computing it from the volume of a sphere having the KS radii. These results show that anions from the halide group are hard and little polarizable, whereas anions from the alkali group are soft and highly polarizable. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Origin of bulklike optical response in noble-metal Ag and Au nanoparticles

The origin of bulk-like optical response of noble (silver and gold) metal nanoparticles has been studied using classical (Mie) and time-dependent density functional theories. We find that the bulk-like optical response in the silver and gold nanoparticles is strongly correlated to the electronic d-character of the valence electrons, while the correlations with atomic coordination and particle size are weaker. The importance of Coulomb and exchange-correlation interactions to model optical responses is also discussed.

Steric, quantum, and electrostatic effects on S(N)2 reaction barriers in gas phase.

Biomolecular nucleophilic substitution reactions, S(N)2, are fundamental and commonplace in chemistry. It is the well-documented experimental finding in the literature that vicinal substitution with bulkier groups near the reaction center significantly slows the reaction due to steric hindrance, but theoretical understanding in the quantitative manner about factors dictating the S(N)2 reaction barrier height is still controversial. In this work, employing the new quantification approach that we recently proposed for the steric effect from the density functional theory framework, we investigate the relative contribution of three independent effects-steric, electrostatic, and quantum-to the S(N)2 barrier heights in gas phase for substituted methyl halide systems, R(1)R(2)R(3)CX, reacting with the fluorine anion, where R(1), R(2), and R(3) denote substituting groups and X = F or Cl. We found that in accordance with the experimental finding, for these systems, the steric effect dominates the transition state barrier, contributing positively to barrier heights, but this contribution is largely compensated by the negative, stabilizing contribution from the quantum effect due to the exchange-correlation interactions. Moreover, we find that it is the component from the electrostatic effect that is linearly correlated with the S(N)2 barrier height for the systems investigated in the present study. In addition, we compared our approach with the conventional method of energy decomposition in density functional theory as well as examined the steric effect from the wave function theory for these systems via natural bond orbital analysis.

First-principles and experimental analysis offn−fn−1d1absorption spectra and multiplet energy levels ofPr3+,Nd3+, andU3+inLiYF4

We performed experimental and theoretical investigation of the ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ transitions of ${\text{Pr}}^{3+}$, ${\text{Nd}}^{3+}$, and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra for ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$ and the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ were measured using a synchrotron radiation light source at several different temperatures while the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ absorption spectra for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ referred to report of Hubert et al. The multiplet energy levels and ${f}^{n}\text{\ensuremath{-}}{f}^{n\text{\ensuremath{-}}1}{d}^{1}$ absorption spectra were calculated by a first-principles four-component relativistic configuration-interaction method. For all calculations of ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$, we used the Dirac-Coulomb-Breit Hamiltonian and the molecular spinors obtained from the relativistic Vosko-Wilk-Nusair potential. The overall features of the theoretical absorption spectra of both ${\text{Nd}}^{3+}$ and ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$ reproduced the experimental features well. The origins of the experimental absorption spectra were clarified by performing a configuration analysis based on the many-electron wave functions. The splitting between peaks were affected by both spin-orbit interaction of $f$ orbitals and crystal-field splitting of $d$ orbitals. We found that the oscillator strengths of the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ transition for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ are slightly larger than those of the $5{f}^{3}\text{\ensuremath{-}}5{f}^{2}6{d}^{1}$ transition for ${\text{U}}^{3+}$ in ${\text{LiYF}}_{4}$. The experimental absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ measured at nine different temperatures indicated that the $4{f}^{3}\text{\ensuremath{-}}4{f}^{2}5{d}^{1}$ absorption spectra for ${\text{Nd}}^{3+}$ in ${\text{LiYF}}_{4}$ have no significant temperature dependence. For ${\text{Pr}}^{3+}$ in ${\text{LiYF}}_{4}$, we performed more detailed investigations. The lattice relaxation effects due to the substitution of ${\text{Y}}^{3+}$ by ${\text{Pr}}^{3+}$ were estimated using a first-principles density-functional calculation. Structural optimization calculations indicated that the local structure of the ${\text{Pr}}^{3+}$ site was slightly distorted. Overall, the theoretical $4{f}^{2}\text{\ensuremath{-}}4{f}^{1}5{d}^{1}$ absorption spectra reproduced the experimental spectra. The experimental absorption spectra were investigated by configuration analysis based on the many-electron wave functions. The theoretical calculations indicated that the temperature dependence of the experimental spectra was due to both thermal excitation and phonon effects. In addition, we also investigated the effects of the exchange-correlation interaction and the Breit term by comparing the results from six different Hamiltonians.

An atomistic approach to self-diffusion in uranium dioxide

Abstract The formation and mobility of point defects in UO 2 have been studied within the framework of the Density Functional Theory. The ab initio Projector Augmented Wave method is used to determine the formation and migration energies of defects. The results relative to intrinsic point defect formation energies using the Generalized Gradient Approximation (GGA) and GGA+U approximations for the exchange-correlation interactions are reported and compared to experimental data. The GGA and GGA+U approximations yield different formation energies for both Frenkel pairs and Schottky trios, showing that the 5 f electron correlations have a strong influence on the defect formation energies. Using GGA, various migration mechanisms were investigated for oxygen and uranium defects. For oxygen defects, the calculations show that both a vacancy and an indirect interstitial mechanism have the lowest associated migration energies, 1.2 and 1.1 eV respectively. As regards uranium defects, a vacancy mechanism appears energetically more favourable with a migration energy of 4.4 eV, confirming that oxygen atoms are much more mobile in UO 2 than uranium atoms. Those results are discussed in the light of experimentally determined activation energies for diffusion.

Singlet–triplet transitions in highly correlated nanowire quantum dots

We consider a quantum dot embedded in a three-dimensional nanowire with tunable aspect ratio a. A configuration interaction theory is developed to calculate the energy spectra of the finite 1D quantum dot systems charged with two electrons in the presence of magnetic fields B along the wire axis. Fruitful singlet–triplet transition behaviors are revealed and explained in terms of the competing exchange interaction, correlation interaction, and spin-Zeeman energy. In the high aspect ratio regime, the singlet–triplet transitions are shown designable by tuning the parameters a and B. The transition also manifest the highly correlated nature of long nanowire quantum dots.

First-principles calculations for electronic and optical properties of the zinc-blende structured BeS compound under pressure

The electronic and the optical properties of the cubic zinc-blende (ZB) BeS under high pressure have been investigated by using ab initio plane-wave pseudopotential density functional theory method in the generalised gradient approximation (GGA) for exchange-correlation interaction. The electronic band structure and the pressure dependence of the total and partial densities of state under pressure are successfully described. Our calculations show that the ZB BeS has large and indirect band gaps associated with (Γ → X) transitions in ambient conditions. The results obtained are consistent with the experimental data available and other calculations. The optical properties, including dielectric function, energy-loss function, complex refractive index, reflection and absorption spectra, are investigated and analysed at different external pressures. The results suggest that the optical absorption appears mostly in the ultra-violet region and the curve of refractive index shift toward high energies (blue shift) with pressure increasing.

Interaction of fast charged projectiles with two-dimensional electron gas: Interaction and collisional-damping effects

The results of a theoretical investigation on the stopping power of ions moving in a two-dimensional degenerate electron gas are presented. The stopping power for an ion is calculated employing linear-response theory using the dielectric function approach. The collisions, which lead to a damping of plasmons and quasiparticles in the electron gas, is taken into account through a relaxation-time approximation in the linear-response function. The stopping power for an ion is calculated in both the low- and high-velocity limits. In order to highlight the effects of damping, we present a comparison of our analytical and numerical results, in the case of pointlike ions, obtained for a nonzero damping with those for a vanishing damping. It is shown that the equipartition sum rule first formulated by Lindhard and Winther for three-dimensional degenerate electron gas does not necessarily hold in two dimensions. We have generalized this rule introducing an effective dielectric function. In addition, some results for two-dimensional interacting electron gas have been obtained. In this case, the exchange-correlation interactions of electrons are considered via local-field corrected dielectric function.

Self-consistent solution of Kohn-Sham equations for infinitely extended systems with inhomogeneous electron gas

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistence searching method involves iterations with alternate solving of the Poisson and Schr\"{o}dinger equations. One of problems of such an approach is that the charge distribution renewed by means of the Schr\"{o}dinger equation solution does not conform to boundary conditions of Poisson equation for Coulomb potential. The resulting instability or even divergence of iterations manifests itself most appreciably in the case of infinitely extended systems. The published attempts to deal with this problem are reduced in fact to abandoning the original iterative method and replacing it with some approximate calculation scheme, which is usually semi-empirical and does not permit to evaluate the extent of deviation from the exact solution. In this work, we realize the iterative scheme of solving the Kohn-Sham equations for extended systems with inhomogeneous electron gas, which is based on eliminating the long-range character of Coulomb interaction as the cause of tight coupling between charge distribution and boundary conditions. The suggested algorithm is employed to calculate energy spectrum, self-consistent potential, and electrostatic capacitance of the semi-infinite degenerate electron gas bounded by infinitely high barrier, as well as the work function and surface energy of simple metals in the jellium model. The difference between self-consistent Hartree solutions and those taking into account the exchange-correlation interaction is analyzed. The case study of the metal-semiconductor tunnel contact shows this method being applied to an infinitely extended system where the steady-state current can flow.

Dense electron–hole plasma in silicon light emitting diodes

Efficient electroluminescence of silicon light emitting p–n diodes of different sizes andshapes is investigated at room temperature. High quantum efficiency of the diodes, along linear dependence of the electroluminescence intensity on the diode currentand a low energy shift of the emission line in electroluminescence spectra withincreasing diode current are explained by the self-compression of the injectedelectron–hole plasma into dense electron–hole plasma drops. Experiments onspace scanning of the electroluminescence intensity of the diodes support thisconclusion. The plasma self-compression is explained by the existence of an attractionin electron–hole plasma compensating the plasma pressure. A decrease of thesemiconductor energy gap due to local lattice overheating, produced by the plasma,and the exchange–correlation interaction could contribute to this attraction. Theself-focusing of the injection current can accompany the plasma self-compression.

Field effects on the electronic and spin properties of undoped and doped graphene nanodots

We report a spin-polarized density-functional theory study of electric-field effects on the electronic and spin properties of graphene nanodots. Both undoped and graphene nanodots doped with nitrogen and boron are considered. In the presence of nonlocal exchange-correlation interactions, undoped graphene nanodots are found to be half-semiconductors when a weak electric field is applied across the zigzag edge. At high electric fields these graphene nanodots become nonmagnetic semiconductors. When the electric field is applied across the armchair edge, these graphene nanodots maintain an antiferromagnetic ground state with the energy gap strongly dependent on the magnitude of the electric field. For graphene nanodots doped with nitrogen or boron we find that energetically the most favorable state among all possible configurations is the one in which the dopant replaces the carbon atom at the center of the zigzag edge. The substitutional dopant atom at the zigzag edge leads to a spin-polarized half-semiconducting state in which the spin degeneracy is broken. The spin-dependent energy gaps can be tuned within a wide range by applying electric fields. In addition, we find the half-semiconducting state under doping occurs even when the electric field is very strong. This indicates that edge doping can significantly widen the operating range of applied electric fields for spintronic applications because undoped graphene nanodots become spinless semiconductors under certain applied electric fields.

Quantum chemical study and low-temperature calorimetry of phase transition in V 4S 9Br 4

The phase transition in a mixed-valence tetranuclear compound V 4S 9Br 4 was studied by DFT calculations and low-temperature high-precision calorimetry. According to DFT data, the phase transition of the low-temperature modification may be accompanied by C 4v→ C 2v symmetry lowering and electron spin pairing. A weak exchange-correlation interaction discovered between μ 4-S 2− and S 2− ions in V 4S 9Br 4 may play an important part in multicentered interactions. Experimental calorimetric data show that the phase transition is a displacive phase transformation.

Spin-density-functional theory for imbalanced interacting Fermi gases in highly elongated harmonic traps

We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with a Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikov-type phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.

Low-energy spin-polarized two-electron spectroscopy: a powerful tool for studying exchange correlation and spin-orbit interaction on surfaces

Spin-polarized two-electron spectroscopy-in-reflection has been proven to be a very efficient technique for studying the exchange correlation and spin-orbit interaction on magnetic and non-magnetic surfaces and thin ferromagnetic films. The essence of the technique is the detection of two time-correlated electrons emitted from the sample surface upon an impact of a single incident electron and measurements of their momenta. The coincidence technique has been combined with a time-of-flight electron energy analysis to measure momentum distributions of correlated electron pairs for various orientations of the electron beam polarization relative to the scattering plane and magnetization of the sample. This set of measurements allows to extract the information on exchange correlation and spin-orbit interaction from measured spectra. Energy- and momentum-conservation in the electron-electron scattering allows the valence electron involved into collision to be located in the energy-momentum space of the valence band of the sample. In this way the energy and momentum location of the exchange and SOI can be established. A few examples of the application of this technique for studying ferromagnetic and non-magnetic surfaces are presented.

Half-Metallicity in Undoped and Boron Doped Graphene Nanoribbons in the Presence of Semilocal Exchange-Correlation Interactions

We perform density functional calculations on one-dimensional zigzag edge graphene nanoribbons (ZGNRs) of different widths, with and without edge doping including semilocal exchange correlations. Our study reveals that, although the ground state of edge-passivated (with hydrogen) ZGNRs prefers to be anti-ferromagnetic, the doping of both of the edges with boron atoms stabilizes the system in a ferromagnetic ground state. Both the local and semilocal exchange correlations result in half-metallicity in edge-passivated ZGNRs at a finite cross-ribbon electric field. However, the ZGNR with boron edges shows half-metallic behavior irrespective of the ribbon width even in the absence of electric field and this property sustains for any field strength, opening a huge possibility of applications in spintronics.

Post-Hartree-Fock methods and dynamic correlation in atoms and molecules

The methods of calculation of the matrix of the exchange-correlation interaction are considered within the framework of one post-Hartree-Fock one-electron method of investigation of the properties of many-electron systems. Such post-Hartree-Fock methods are based on two-step variational self-consistent calculations of the spin orbitals and superposition coefficients of configurations in the multiconfiguration approximation. The post-Hartree-Fock method used involves an approach related to the extended Koopmans’ theorem, which, in turn, proves to be a high-energy approximation for quantum Green’s functions. Obvious application areas of the calculations of the exchange-correlation interaction within the framework of the method proposed are the multiparticle perturbation theory, the parameterization of the energy representation as a functional of the single-particle density matrix, and the theory of Green’s functions in the multiconfiguration approximation. A relativistic generalization of the method with the aim of calculating the radiative corrections for many-electron atoms and for problems of interaction with an external field in the nonstationary Floquet theory is possible.

Numerical self-consistent field calculation of a ferromagneticZnMnOquantum well

The magnetic properties of a $p$-type $\mathrm{ZnMnO}$ diluted magnetic semiconductor quantum well are investigated by a numerical self-consistent field calculation taking into account the spin-exchange interaction between free carriers and magnetic impurities and the carrier exchange-correlation interaction based on the mean field theory of carrier-induced ferromagnetism. The dependence of the carrier spin polarization on magnetic impurity density and the spin-exchange interaction energy is presented in comparison with well-known III-V-based diluted magnetic semiconductors. The results show that room temperature operation of $\mathrm{ZnMnO}$-based spin devices is probably easier than that of any other materials investigated with the same numerical method.

Exchange-correlation energy in molecules: A variational quantum Monte Carlo study

We have used the combination of the coupling-constant integration procedure and the variational quantum Monte Carlo method to study the exchange-correlation (XC) interaction in small molecules: ${\mathrm{Si}}_{2}$, ${\mathrm{C}}_{2}{\mathrm{H}}_{2}$, ${\mathrm{C}}_{2}{\mathrm{H}}_{4}$, and ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$. In this paper we report the calculated XC energy density, a central quantity in density functional theory, as deduced from the interaction between the electron and its XC hole integrated over the interaction strength. Comparing these ``exact'' XC energy densities with results using the local-density approximation (LDA), one can analyze the errors in this widely used approximation. Since the XC energy is an integrated quantity, error cancellation among the XC energy density in different regions is possible. Indeed we find a general error cancellation between the high-density and low-density regions. Moreover, the error distribution of the exchange contribution is out of phase with the error distribution of the correlation contribution. Similar to what is found for bulk silicon and an isolated silicon atom, the spatial variation of the errors of the LDA XC energy density in these molecules largely follows the sign and shape of the Laplacian of the electron density. Some noticeable deviations are found in ${\mathrm{Si}}_{2}$ in which the Laplacian peaks between the atoms, while the LDA error peaks in the regions ``behind'' atoms where a good portion of the charge density originates from an occupied $1{\ensuremath{\sigma}}_{u}$ antibonding orbital. Our results indicate that, although the functional form could be quite complex, an XC energy functional containing the Laplacian of the energy is a promising possibility for improving LDA.