Self-consistent Electron Densities Research Articles

Revealing non-covalent interactions in solids: NCI plots revisited

In this article, the NCI method [Johnson et al., J. Am. Chem. Soc., 2010, 132, 6498] for plotting and analysing non-covalent interactions (NCI) is extended to periodic (solid-state) electron densities and implemented in the critic program. The new code uses self-consistent electron densities from a variety of electronic structure methods (pseudopotentials/plane-wave, FP-LAPW, local orbitals, etc.), and it can also build the promolecular density from the crystal geometry alone. As an example of the new code, intermolecular interactions in several molecular crystals are presented and analyzed. The connection with QTAIM studies is established and a reinterpretation of the NCI domains is given regarding the current knowledge of the field. The connection between NCI domains and intermolecular vibrations is made apparent, as well as the ability of the method to reveal the locality of bonding.

RISM-SCF-SEDD Study on the Symmetry Breaking of Carbonate and Nitrate Anions in Aqueous Solution

The planarity of carbonate and nitrate anions was investigated in the gas and solution phases by means of the reference interaction site model self-consistent field spatial electron density distribution (RISM-SCF-SEDD) method. The computed optimized geometries and solvation structures are compared with the diffraction data. In the solution phase, the symmetry of carbonate anion is changed from D3h to C3v, whereas the planarity of nitrate anion is still retained. These are fully consistent with experimental knowledge. The classical electrostatic model was also utilized to elucidate the mechanism of the symmetry breaking. It should be emphasized that the symmetry breaking occurs not only by a specific solvent molecule attaching to the ion but by an overall electrostatic interaction between the infinite number of solvent molecules and the ion.

Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing a large number of atoms

The recent fabrication of graphene nanoribbon (GNR) field-effect transistors poses a challenge for first-principles modeling of carbon nanoelectronics due to many thousand atoms present in the device. The state of the art quantum transport algorithms, based on the nonequilibrium Green function formalism combined with the density functional theory (NEGF-DFT), were originally developed to calculate self-consistent electron density in equilibrium and at finite bias voltage (as a prerequisite to obtain conductance or current-voltage characteristics, respectively) for small molecules attached to metallic electrodes where only a few hundred atoms are typically simulated. Here we introduce combination of two numerically efficient algorithms which make it possible to extend the NEGF-DFT framework to device simulations involving large number of atoms. We illustrate fusion of these two algorithms into the NEGF-DFT-type code by computing charge transfer, charge redistribution and conductance in zigzag-GNR/variable-width-armchair-GNR/zigzag-GNR two-terminal device covered with a gate electrode made of graphene layer as well. The total number of carbon and edge-passivating hydrogen atoms within the simulated central region of this device is ~7000. Our self-consistent modeling of the gate voltage effect suggests that rather large gate voltage might be required to shift the band gap of the proposed AGNR interconnect and switch the transport from insulating into the regime of a single open conducting channel.

Self-consistent Wigner distribution function study of gate-voltage controlled triple-barrier resonant tunnelling diode

The electron transport through the triple-barrier resonant tunnelling diode (TBRTD) has been studied by the self-consistent numerical method for the Wigner–Poisson problem. The electron flow through the TBRTD can be controlled by the gate voltage applied to one of the potential well regions. For different gate voltage values we have determined the current–voltage characteristics, potential energy profiles and electron density distribution. We have found the enhancement of the peak-to-valley ratio (up to ∼10), the appearance of the linear current versus bias voltage behaviour within the negative-differential resistance region and the bistability of the current–voltage characteristics. We provide a physical interpretation of these results based on the analysis of the self-consistent potential profiles and electron density distribution.

The effect of inelastic absorption on the elastic scattering of electrons and positrons in amorphous solids

The effect of inelastic absorption on the elastic scattering of electrons and positrons in amorphous solids is studied by means of an optical-potential model. Atomic electron densities and electrostatic potentials for atoms in solids are obtained from Dirac–Fock self-consistent electron densities for free atoms using Raith’s muffin-tin model. In the case of electron projectiles, the exchange interaction is described by means of the local approximation of Furness and McCarthy. Correlation effects are modeled using a local-density approximation. The absorption potential, i.e., the imaginary part of the optical potential, is obtained from the local-density approximation, using the Born–Ochkur approximation and the Lindhard dielectric function to describe the interactions with a free-electron gas, and multiplied by an energy-independent empirical strength factor A abs . With an appropriate selection of A abs , the absorption cross section σ abs , obtained from the partial-wave calculation with the aid of the optical theorem, practically equals the inelastic cross section for projectiles with energies from about 100 eV up to 1 MeV. The effects of inelastic absorption and aggregation are analyzed by comparison of differential cross sections, calculated with and without allowance of those effects, and by Monte Carlo simulations of electron elastic backscattering from solids. It is found that the effect of inelastic absorption on the scattering by atoms in solids is much weaker than for free atoms.

Structure and Positron Characteristics of Basic Open Volume Defects in Zirconia

In this contribution we report on the theoretical study of basic vacancy-like defects in cubic zirconia and yttria stabilized zirconia. In particular, we concentrate on oxygen vacancy, zirconium vacancy and oxygen vacancy – yttrium complex. Relaxed atomic configurations of studied defects are obtained by means of an ab initio pseudopotential method within the supercell approach. Positron characteristics, like positron lifetime and binding energy to defects, are calculated using self-consistent electron densities and potentials taken from ab initio calculations.

Current collection by a cylindrical probe in a partly ionized, collisional plasma

A numerical calculation of ion and electron current collection by a cylindrical Langmuir probe in a partly ionized plasma has been done. The effect of electron and ion collisions with neutrals on the current collected by the probe has been investigated. The validity of the collisionless theory of Laframboise [J. G. Laframboise, University of Toronto, Institute for Aerospace Studies, UTIAS Report No. 100 (1966)] has been studied. The iterative scheme of Laframboise has been combined with Monte Carlo solution of the Boltzmann equation to provide self-consistent steady-state electron and ion density and electric potential distributions as functions of radius. Our model includes elastic ion-neutral and electron-neutral collisions, ionization of neutrals by electron impact, energy loss of electrons due to excitation and ionization of neutrals, and charge-exchange collisions. Our model has been demonstrated by calculating the current collection by a probe in a nitrogen plasma, but it can be applied in other cases because we avoided adjustable parameters. Our results confirm published experimental data which indicate that Laframboise’s theory can be applied when the attracted particles are electrons and ionization processes do not play an important part. When the attracted particles are ions, it is found that charge-exchange collisions in the sheath produce by far the largest contribution to the increase in their collection current. For this situation, collisionless theory can be applied only when the mean distance traveled by ions inside the sheath is much less than the mean free path. The condition that the sheath size is much smaller than the mean free path does not guarantee a collisionless sheath near a cylindrical probe. This condition is in good agreement with experimental results in the literature.

Optical-model potential for electron and positron elastic scattering by atoms

An optical-model potential for systematic calculations of elastic scattering of electrons and positrons by atoms and positive ions is proposed. The electrostatic interaction is determined from the Dirac-Hartree-Fock self-consistent atomic electron density. In the case of electron projectiles, the exchange interaction is described by means of the local-approximation of Furness and McCarthy. The correlation-polarization potential is obtained by combining the correlation potential derived from the local density approximation with a long-range polarization interaction, which is represented by means of a Buckingham potential with an empirical energy-dependent cutoff parameter. The absorption potential is obtained from the local-density approximation, using the Born-Ochkur approximation and the Lindhard dielectric function to describe the binary collisions with a free-electron gas. The strength of the absorption potential is adjusted by means of an empirical parameter, which has been determined by fitting available absolute elastic differential cross-section data for noble gases and mercury. The Dirac partial-wave analysis with this optical-model potential provides a realistic description of elastic scattering of electrons and positrons with energies in the range from $\ensuremath{\sim}100\mathrm{eV}$ up to $\ensuremath{\sim}5\mathrm{keV}.$ At higher energies, correlation-polarization and absorption corrections are small and the usual static-exchange approximation is sufficiently accurate for most practical purposes.

The distribution of the valence electron density in predominantly ionic crystals with different Bravais sublattices

Based on the theory of the local-density functional, self-consistent valence electron densities are calculated for CaO with a rock-salt lattice, CaF2 with a fluorite lattice, K2O with an antifluorite lattice, and for their constituent sublattices. It is shown that in the crystals with different Bravais sublattices, the anionic sublattice is a framework with covalent bonds containing a metal sublattice inside of them. The coupling between the sublattices is characterized by the density difference, which is deflned as the difference between the total electron density and the densities of the individual sublattices. The density difference is found to be an order of magnitude smaller than the crystal and sublattice densities, which is evidence of weak hybridization of the sublattices and of the predominately ionic character of the bonding between them.

Role of sublattices in the formation of electron density in metal nitrites

The self-consistent valence electron densities of NaNO2, AgNO2, and their constituent sublattices are calculated on the basis of the theory of the local-density functional. The quantity characterizing the relation between different sublattices is introduced as the difference density resulting from the subtraction of the densities of the individual sublattices from the total electron density. The role of metal in the formation of electron density is established, and, in particular, it is shown that, in AgNO2, anionic bonds have the covalent component formed at the expense of the electron density of the cation. It is also shown that, qualitatively, the difference density in NaNO2 corresponds to the experimental deformation density.

Electron density calculations for MgCO3 using the sublattice technique

Self-consistent valence electron densities of a MgCO3 crystal and of its constituent sublattices are calculated on the basis of the local-density functional theory. The coupling between the sublattices is characterized by the density difference, introduced as the difference between the total electron density and the densities of individual sublattices. Intra-and interlattice hybridization effects are considered. It is shown that the density difference is in qualitative agreement with the experimental deformational density.

The quasibound state model for self-consistent characteristics of semiconductor intersubband devices

The quasibound state model (QBSM) for determining the self-consistent conduction band profile and space charge density of semiconductor intersubband devices is presented. This new method is based on the quasibound (QB) state resonances of quantum structures. For heterostructures, the traditional self-consistent energy continuum model (ECM) calculates space charge by integration over the entire energy continuum, weighted by Fermi–Dirac statistics. In the present approach, the continuum of energy states of the heterostructure is accurately represented by a small number of QB states, and the space charge calculations are performed only at these eigen-energies. This approach significantly reduces the computational burden associated with all self-consistent algorithms. Theoretical formulation of QBSM is compared with the traditional ECM approach. The bound (B) and QB eigenenergies of the structure are obtained by solving the single-band effective-mass Schrödinger equation using the argument principle method. The performance and the accuracy of the QBSM are evaluated for a double-barrier resonant structure and an asymmetric Fabry–Perot electron-wave interference filter. The self-consistent electron density and potential profiles calculated by the present method are shown to be in excellent agreement with the results obtained from the traditional ECM model. In addition to requiring less computational time, the present method is easily implemented and may be applied equally well to biased/unbiased, symmetric/asymmetric heterostructures.

The Role of Sublattices in Chemical Bonding in Essentially Ionic Crystals

A technique for calculating the self-consistent electron density of sublattice and crystal as a whole has been developed based on the local electron density functional theory (DFT). Difference density, obtained by subtraction of the densities of the individual sublattices from the total electron density, is introduced as a quantity defining the relationship between the sublattices. Self-consistent calculations have been performed for series of compounds with a NaCl lattice: alkali and noble metal halides and alkali metal oxides and sulfides with an antifluorite lattice. As a result of these calculations, we formulated the key principle of chemical bonding based on sublattices. In the anion sublattice, alike atoms form a covalent type of bond with each other by transferring some portion of the charge to the interstice. The same mechanism of bonding is realized in sublattices of metal atoms containing the levels of the d-states in the valence region. In sublattices of simple metals, the valence density behaves as “metallic,” changing slightly within the unit cell, with electrons again moving from the metal sites into the interstice. Addition of the valence densities of sublattices leads to two essentially different situations: in one case, the metal sites coincide with the density maxima at the interstice of the anion sublattice, and in the other, they do not. In the first case, the superposition of the sublattice densities at the lattice sites leads to anion-cation hybridization, forming an essentially ionic chemical bond with a possible admixture of the covalent bond. In the second case, the anion sublattice is a covalently bonded framework incorporating the metal sublattice. This takes place in alkali metal oxides and sulfides.

Jellium surface energy beyond the local-density approximation: Self-consistent-field calculations

We report extensive self-consistent calculations of jellium surface energies, by going beyond the local-density approximation. The density-response function of a bounded free-electron gas is evaluated within the random-phase approximation, with use of self-consistent electron density profiles. The exchange-correlation energy is then obtained from an exact adiabatic fluctuation-dissipation formula. We also investigate quantum-size effects and the extrapolation of finite-slab calculations to the infinite-width limit.

Homogeneities in density of various LDA energy functionals

Expanding on the work of March (Phys. Rev. A 56 (1997) 1025), partial differential equations are obtained for self-consistent atomic electron densities in the local density approximation. Local models treated include the Thomas–Fermi model, the Thomas–Fermi–Dirac model, and the Thomas–Fermi–Dirac model plus correlation. It is shown that within these models, the Thomas–Fermi kinetic energy functional can be expressed as a functional homogeneous of degree one with respect to the self-consistent-density scaling. In addition, the Dirac exchange functional and the Liu–Parr correlation functional each also can be rewritten as a functional homogeneous of degree one in the density scaling.

THE ATTRACTIVE HUBBARD MODEL IN 2-D : IS IT CAPABLE OF DESCRIBING A PSEUDOGAP AND PREFORMED PAIRS?

Deviations from Fermi liquid behavior are well documented in the normal state ofthe cuprate superconductors, and some of these differences seem to be related topretransitional features appearing at temperatures above T c. The observationof a pseudogap, e.g., in ARPES experiments, is a familiar example of this physics. Onepotential explanation for this behavior involves preformed pairs with finite lifetimesexisting in the normal state above T c. In this way, two characteristictemperatures can be established. A higher one T* at which pairs begin toform and the actual T c at which a phase-coherent superconducting phaseis established. In order to test these ideas we have investigated the negative UHubbard model in two dimensions in the fully self-consistent ladder approximation atlow electron densities. In the non-self-consistent version of this theory the systemalways shows an instability toward Bose-condensation of infinite lifetime pairs. In contrastto this, pairs obtain a finite lifetime due to pair–pair interaction and thesharp two-particle bound state is strongly lifetime broadened when self-consistency isapplied. A quasiparticle scattering rate which varies linearly with temperature is alsofound. The fully self-consistent calculation we were able to perform employed ak →-averaged approximation in which the self-energyloses its k →-dispersion due to ak →-average. This approximation is found to preservethe essential physics.

Surface plasmons at MOCVD-grown GaN

We report on the first observation of surface plasmons at a GaN surface by high-resolution electron energy loss (HREEL) spectroscopy. Dipole scattering theory using self-consistent electron density profiles is employed to calculate the surface energy loss function and hence the expected energy loss spectra. The characteristic features of both the surface plasmons and the Fuchs-Kliewer (FK) surface optical phonons are well reproduced in the framework of this model. Fitting measured HREEL spectra allows us to give estimates of important semiconductor parameters such as electron density, electron mobility and band bending. Moreover, it is found that the plasmon damping strongly depends on primary beam energy. Similarly, the FK phonon damping and frequency are also affected by the variation of primary beam energy.

Density-functional study of the magnetic and metal-insulator transition of bcc hydrogen

A model body-centered cubic (bcc) hydrogen solid is studied using density functional theory in the local spin density approximation (LSDA) and in the generalized gradient approximation (GGA). In GGA, the paramagnetic to antiferromagnetic phase transition occurs at a higher density, and is in much better agreement with previous variational quantum Monte Carlo (VQMC) calculations than LSDA. The metal-insulator transition in GGA is observed at a higher density and is also closer to the VQMC result than LSDA. In the limit of isolated hydrogen atoms, we find that in GGA the self-consistent electron density is greatly improved over LSDA due to a better cancellation of the electronic self-interaction.

Density functional pseudopotential study of the endohedral complex Li 2@C 60

The spherically averaged pseudopotential (SAPS) model for treating the electronic structure and the energetics of a cluster of atoms is extended to allow use of first principles norm-conserving pseudopotentials including some nonlocality. The main theoretical development is the spherical average about the chosen cluster centre of an s-wave projection operator associated with an off-centre ion which results in an additional radially nonlocal term in the radial Schrödinger equation. However, much of the simplicity of the SAPS model is preserved. The approach is used to study the electronic structure and the energetics of Li 2@C 60. Self-consistent electron densities are obtained for the spherically averaged pseudopotentials corresponding to this endohedral complex and its component Li 2 and C 60 parts. The atoms are then allowed to relax their positions to minimize the total energy. In the cases of Li 2 and C 60 considerable improvement is achieved over calculations using the SAPS model with local pseudopotentials. Two minimum energy configurations are found for the Li 2 encapsulated inside a C 60 molecule. That with the longer LiLi bond length is the higher in energy by 0.88 eV and is marked by almost complete charge transfer from the Li 2 to the C 60 cage. The other more stable isomer shows little charge transfer but there is a noticeable build up of charge between the Li 2 and the C 60.

Transferable model for the atomistic simulation of Al2O3.

We calculate the energies of different solid phases of ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ using a shell model, a compressible ion model, and a compressible ion model which includes both dipole and quadrupolar polarizability of the ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ ions. Compressible oxygen ions are found to stabilize the corundum structure with respect to the \ensuremath{\theta} form of alumina. The observed corundum structure is nevertheless unstable with respect to the bixbyite structure until quadrupolar polarizability of the oxygen is also included. Entropy differences are estimated with a lattice dynamics calculation and are found to make an insignificant contribution to stabilizing the corundum. We also calculate the relative energies of the corundum and bixbyite structures using the ab initio pseudopotential method, within the local-density approximation for exchange and correlation. The resulting self-consistent electron density shows graphically how the quadrupolar distortions around the oxygen develop as the basis is made more complete (the plane-wave cutoff is increased from 500 to 700 eV), which at the same time brings the energy of the corundum structure below that of the bixbyite structure. \textcopyright{} 1996 The American Physical Society.