Electron Gas Calculations Research Articles

Defect energies for magnesium oxide and lithium oxide

A new crystal potential has been developed for magnesium oxide. This is based on electron-gas calculations of the interaction energy for like and unlike pairs of ions, in the presence of a model crystal field. The calculated potentials are checked by calculating perfect lattice properties: cohesive energy, elastic constants, dielectric constants and some phonon frequencies; adjustments of potential parameters are made to ensure the best fit to these properties. Damping of the long-range dispersion energy is introduced during fitting of the potential and in the calculation of perfect lattice and defect properties.Similar methods have been used to develop a potential for lithium oxide. The calculated phonon dispersion in Li2O is in good agreement with experimental results from neutron scattering. The calculated defect energies are compared with experimental values from ionic conductivity and NMR measurements. Mg2+ substitutionals and Li+ vacancies exhibit a high degree of association, which is responsible for the curvature in the extrinsic region of the conductivity plot.

An improvedN-body semi-empirical model for body-centred cubic transition metals

Abstract The recently published semi-empirical potentials of Finnis and Sinclair for the metals V, Nb, Ta, Mo and W appear to give unphysical results for properties involving small interatomic separation. This is remedied by adding to the potentials cores fitted to electron gas calculations on dimers. The adjusted potentials are shown to predict a more realistic pressure-volume relationship. Interstitial formation energies are calculated for various configurations, using quenched molecular dynamics and static relaxation. Some preliminary results on interstitial migration are presented.

Electron correlation effects on the N2–N2 interaction

A b initio self-consistent field, configuration interaction, and many-body perturbation theory methods are used to calculate the intermolecular potential between two nitrogen molecules. The emphasis is placed on the repulsive region important at the temperatures and pressures encountered in detonations. In addition, electron gas calculations are employed to fit and extend the ab initio data. We also generate effective spherical potentials which fit dilute gas virial, viscosity, and differential scattering data while being constrained by Hugoniot or ab initio data in the repulsive region. Finally, we discuss the roles of electron correlation and of many-body effects on the N2–N2 interaction. Comparisons are also made to the Ar2 potential where similar ab initio calculations are compared to an accurate empirical potential.

Interatomic potentials for ionic materials from first principles calculations

Interatomic potentials for F -…F - and O 2-…O 2- from first principles calculations are presented and compared with previous estimates. The present non-coulombic non-polarised potential for F 2- 2 is close to that reported by Catlow and Hayns, while that for O 4- 2 is very similar to that obtained from electron-gas calculations. Electron correlation effects are found to make only a minor contribution to the short-range potentials of these systems.

The calculated defect structure of bulk and {001} surface cation dopants in MgO

Lattice defect calculations are presented for the cation doping of the bulk and {001} surface of MgO by Li+, Na+, Be2+, Ca2+, Fe2+, Al3+, Sc3+, Fe3+, Ti4+ and Si4+. Interionic potentials are derived from electron-gas calculations while the lattice relaxation methods are essentially those introduced by Lidiard and Norgett. An emphasis is placed on the differences between the bulk and surface, and, where possible, a comparison is made with the available experimental data.

Electron-gas theory of ionic crystals, including many-body effects

The electron-gas theory of ionic crystals is extended to include nonadditive (many-body) interactions arising from the simultaneous overlap of the densities of several ions. The theory is used to predict equilibrium geometries, lattice energies, and pressure-induced phase transitions for the fluorides and oxides of the alkali and alkaline earth metals. The results are in good agreement with electron-gas calculations assuming additive, two-body interactions between pairs of ions. This comparison shows that the simultaneous overlap of three or more ions has only a small effect on these crystals, and that for many purposes the simpler two-body approximation is adequate. The predictions of lattice distances and energies agree with experiment to a typical accuracy of 1 or 2%. In order to obtain this accuracy, it is necessary to calculate the electron densities for the anions in a stabilizing potential well whose size is determined self-consistently by the electrostatic potential of the crystal at the anion site. This shrinkage of the anion by the crystal is also a kind of many-body interaction, but it can be handled within the framework of an effective two-body interaction involving the stabilized anions. The corresponding cation expansion effect is also calculated, and shown to be negligible for the alkali and alkaline earth metal ions.

Density functional approximation for the quasiparticle properties of simple metals. I. Theory and electron gas calculations

Calculations of the self-energy of the electron gas for energies near the Fermi energy are presented. The results of these calculations are required to quantify a previously suggested approximation for the self-energy of real metals. Two separate types of improvement on the random-phase approximation (RPA) for the self-energy are considered. The first type is similar to the Hubbard approximation while the second type explicitly evaluates terms of second and third order in the renormalised interaction expansion for the self-energy. Local exchange-correlation potentials from these and other recent calculations and parameterised in a form that will be useful in bandstructure calculations. Results for the correlation contribution to the ground-state energy are also obtained and inciate that RPA gives results that are about 25% too large at the lowest metallic densities.

Ground-state potential curves forAl2andAl26+in the repulsive region

Self-consistent-field (SCF) calculations have been performed for the short-range interaction between two aluminum atoms. The ground-state potential curve (/sup 3/..sigma../sup -//sub g/..-->../sup 5/..sigma../sup -//sub u/..-->../sup 3/..sigma../sup +//sub u/..-->../sup 1/..sigma../sup +//sub g/ ..-->../sup 3/Pi/sub g/) is presented for internuclear separations between R/sub e/ and 0.1 a.u. (repulsive energies up to approx.10/sup 3/ a.u.). Basis sets consist of scaled even-tempered Slater orbitals of double-zeta quality, augmented by diffuse functions, with the addition of united or semiunited atom-basis sets centered on the bond. The SCF potentials are compared with Thomas-Fermi theory and with the electron-gas calculations of Wilson, Haggmark, and Biersack. A kink in the SCF screening function is found near R=2 a.u. This feature is believed related to changes in the ground-state configuration that occur in this region. Additional calculations (SCF and linear combination of atomic orbitals were performed on Al/sub 2//ts/sup 6 +// to determine individually the core overlap and the valence-electron contributions to the interatomic potential. The core-overlap interaction is compared with Gordon-Kim electron-gas calculations. Schematic calculations were also performed on the Al-Al/sup 3 +/ system to estimate the interaction between an atom and an energetic ion.

Monte Carlo trajectory study of Ar+H2 collisions. I. Potential energy surface and cross sections for dissociation, recombination, and inelastic scattering

Modified statistical electron–gas calculations using the methods of Gordon, Kim, Rae, Cohen, and Pack are carried out to obtain the interaction energy of Ar with H2 as a function of geometry. The results are combined with the accurate pairwise interactions, the long-range nonpairwise interaction, and the potential LeRoy and van Kranendonk fit to spectral data on the van der Waals’ complex to obtain a potential energy surface which is as accurate as possible at all geometries. This surface and the pairwise additive surface are then used in a Monte Carlo quasiclassical trajectory study of the cross sections (under shock-tube high-energy collision conditions) for complete dissociation, for production of quasibound states of H2, and for V–T, R–T, and V–R–T energy transfer. Except for R–T energy transfer, the accurate surface yields smaller cross sections than the pairwise additive surface does. The cross sections for dissociation are much smaller than predicted by the available-energy hard-sphere model but are larger than the inelastic cross sections for excitation to the highest bound vibrational energy levels. Initial vibrational excitation energy is more effective than rotational energy or relative translational energy in causing dissociation. Using the full potential surface the recombination cross section of the v=13, j=8 quasibound state of H2 is calculated at Erel=0.026 eV and is in good agreement with the result previously calculated by Whitlock, Muckerman, and Roberts using a less accurate, pairwise additive potential surface.

Calculation of molecule-molecule intermolecular potentials using electron gas methods

A procedure for extending electron gas calculations to molecule-molecule interactions is presented which allows rapid determination of the dependence of intermolecular potentials on all vibration and rotation coordinates. Results for HF-HF agree well with accurate SCF calculations.

Aspects on diagrammatic expansion for models related to a homogeneous electron gas

In a previous paper (see abstr. A76748 of 1974) the expansion of the irreducible self-energy of an electron gas was studied and found to give unreliable results for the satellites of the one-electron spectra function. This was due to the incorrect analytic properties of the corresponding green function. These results are confirmed and extended by studying a simple model (s-model) which allows the nature of different approximation schemes to be demonstrated clearly. A consistent iterative expansion method for the green function is also developed, which, in addition to giving a one-electron green function with correct analyticity and a spectral function fulfilling the sum rule, is computationally simple enough to be used for an electron gas and possibly for simple metals. The method gives quite reasonable results for the s-model when developed to second order in the screened interaction. From comparison with other electron gas calculations it is concluded that the method should also give reasonable results for an electron gas.

Light absorption of dye aggregates. Coupled oscillator and electron gas model for aggregates formed from polyene type monomers

A modified coupled oscillator model using extended dipoles in place of each double bond is found to be superior to the point dipole model and gives absorption shifts for polyenic dye aggregates in agreement with electron gas calculations and with experimental evi

Chemically Motivated Pseudopotential for Sodium

A local pseudopotential of the form $V={V}_{0}coskr+C$, $r<{r}_{c}$, $V=\ensuremath{-}\frac{1}{r}$, $r>{r}_{c}$, is used to fit the experimental ground-state energy of atomic sodium. This form is chosen so as to mirror as closely as possible the actual valence charge distribution of Na. This is important in the calculation of chemical properties such as bonding and cohesion. Electrostatic calculations of the cohesive energy of the bcc metal from the virial theorem and from the electrostatic self-energy of the lattice are performed and the results compared. The results bear on the accuracy of electron-gas calculations in metals and the techniques of pseudopotential calculations. The phonon spectrum is calculated and all results are compared to those obtained with a Shaw-type flat-bottom pseudopotential.

Local Exchange-Correlation Potentials and the Fermi Surface of Copper

Recent publications by Slater and, particularly, by Hedin and Lundqvist suggest that Hohenberg-Kohn-Sham theory used in conjunction with the local-density approximation and accurate atomic or electron-gas calculations at last make it possible to evaluate the ground-state properties of real solids without appeal to experimental data. Self-consistent Korringa-Kohn-Rostoker calculations of the Fermi surface of copper show that these two local assumptions lead to neck areas about 20% too large. However, a local exchange-correlation potential can be found which gives a copper Fermi surface in excellent agreement with experiment. We suspect that the 20% error in the ab initio methods is due mainly to nonlocal exchange-correlation effects.