Electronic Charge Density Distribution Research Articles

Electronic charge and momentum density distributions in ionic crystals: Li3N and Mg(OH)2

Electronic charge and momentum density distributions in ionic crystals: Li₃N and Mg(OH)₂

Models of electronic structure of hydrogen in metals: Pd-H

Local-density theory is used to study the electron charge-density distribution around hydrogen and host palladium metal atoms. Self-consistent calculations using a finite-size molecular-cluster model based on the discrete variational method are reported. Calculations are also done in a simple "pseudojellium" model to study the electron response to hydrogen within the framework of the density-functional formalism. Results of this simple approach agree very well with the molecular-cluster model. Partial densities of states obtained in the cluster model are compared with band-structure results and conclusions regarding the importance of the local environment on the electronic structure are drawn. Calculated core-level shifts and charge transfer from metal ions to hydrogen are compared with the results of x-ray---photoelectron spectroscopy experiments in metal hydrides and are discussed in terms of conventional anionic, covalent, and protonic models. The effect of zero-point vibration on the electron charge and spin-density distribution is studied by repeating the above calculations for several displaced configurations of hydrogen inside the cluster. The results are used to interpret the isotope effect on the electron distribution around proton and deuteron.

Effect of zero point motion on the hyperfine field at an interstitial positive muon site in ferromagnetic Ni

Abstract Using the inhomogeneous electron charge and spin density distribution around the octahedral site in ferromagnetic nickel from a self-consistent band structure scheme, and the abiabatic approximation, we have calculated the muon hyperfine field as a function of the muon displacement. By folding the electron spin density at the vibrating muon site obtained in a self-consistent Kohn-Sham scheme with the finite width of the muon wave function, we find a striking effect on the average muon hyperfine field. The result agrees better with the experiment than earlier calculations based on the jellium model.

Tight-binding study of the electronic states in GaSe polytypes

The electronic band structures of the beta , epsilon and gamma polytypes of GaSe are studied by the tight-binding method. The calculation takes into account interlayer interactions and the generally neglected lowest excited atomic states. The energy levels of the three polytypes differ from each other by 0.3 eV at most. Inclusion of excited atomic states strongly modifies the conduction bands but has little effect on all valence states. The calculated valence band structure compares well with both angular-resolved and integrated photoemission data. The electronic charge-density distribution resulting from tight-binding Block states confirms the chemical bonding picture proposed in recent pseudopotential investigations.

Analytic Expression for the Electronic Charge Density Distribution in Diamond‐Structure Crystals

AbstractThe explicit dependence of the valence band electronic charge density distribution on the pseudo‐potential form factors for the diamond structure crystals has been obtained using a weighted sum of the charge densities at the symmetry points Γ, X, and L of the Brillouin zone. The charge densities and energies for the bands at Γ X, and L, and their dependence on the lattice constant and pseudopotentials are also discussed.

Structure analysis of macromolecules by means of anomalous dispersion methods

The position coordinates of tile atoms in a single crystal are largely determined by diffraction methods. For small unit cells, a knowledge of the intensities of the waves measured in the various Bragg reflections often suffices to determine the atomic positions. However, for the very large unit cells, which are typical for macromolecules such as proteins, a knowledge of the phases of the various Bragg-scattered waves is required in addition. The paper examines the possibilities of measurements of such phases by means of resonant scattering of X-rays, neutrons and gamma-rays. In particular, the severe intensity problems affiliated with phase determinations by recoilless nuclear resonant scattering of gamma-radiation and possible remedies are dealt with in some detail. A. Introduction X-ray and neutron diffraction techniques have been widely used in determinations of the position coordinates of atoms or more generally of the electronic charge density distributions in single crystals. Such an analysis is based on measurements of the intensities of the scattered waves which are observed in the various Bragg reflections. The measured intensities are proportional to IF (h, k,/)[2, where F (h, k, l) is the structure amplitude of tile crystal unit cell which applies to a particular Bragg reflection characterized by reflection indices h, k, 1. This structure amplitude represents the addition--with proper phases--of the amplitudes of the waves which are scattered in a specific direction by the electrons within the unit cell. If we introduce the electronic density ~ (X, Y, Z) where X, Y, Z are fractional coordinates expressed in units of the basic lattice vectors, then we have

Semiempirical Approach to Density Distributions of Heavy Atoms

A method to determine radial electronic charge-density distributions of heavy elements has been indicated using the experimental coherent-scattering cross-section values of relativistic photons. In the absence of a generally valid relativistic theory of coherent scattering of $\ensuremath{\gamma}$ rays, relativistic effects have been taken into account semiempirically. In the present paper the radial electronic charge-density distributions have been determined for lead ($Z=82$) using this method. The results are then compared with the theoretical values obtained from nonrelativistic Hartree-Fock and relativistic Dirac-Fock self-consistent-field-model calculations.

Study of the Potential Surfaces of the Ground and First Excited Singlet States of H2O

The lowest 1A′ and 1B1 potential surfaces of the water molecule are calculated and are discussed together with the results of previous investigations concerning the reactions of O(1D) and O(3P) with H2(1Σ g+). It is found that the insertion of O(1D) into an H2 molecule to yield H2O and the abstraction of hydrogen to yield OH and H both occur preferentially for an acute angle approach of the oxygen atom with respect to the H–H bond. The activation energy of abstraction is found to be small enough to account for the formation of OH radicals which are also found as products during O(1D) insertion reactions. It is illustrated that the symmetry rules based on second-order perturbation theory may serve as a useful guide in the initial mapping of a potential energy surface. Finally, the electronic charge and spin density distributions of the lowest 1B1, 3B1, and 1A1 states are compared and discussed.

3dCharge Density Distribution and Crystal Field in FeCl2: A Mössbauer Study

Available M\ossbauer quadrupole-splitting (QS) data for Fe${\mathrm{Cl}}_{2}$ are analyzed in terms of crystal field and covalency parameters. It is shown that the temperature variation of QS in the paramagnetic phase is consistent with a large expansion of the $3d$ electronic charge density distribution (${\ensuremath{\alpha}}^{2}=\frac{〈{r}^{\ensuremath{-}3}〉}{{〈{r}^{\ensuremath{-}3}〉}_{0}}\ensuremath{\approx}0.4$) as was previously predicted from the systematics of QS and isomer shift in the halides. The analysis yields a large ratio of 8.4 between the trigonal field component and the spin-orbit coupling constant, which is consistent with the Ising model proposed by Kanamori for the low-temperature magnetic properties of Fe${\mathrm{Cl}}_{2}$.

Electron Charge Distribution about Zinc Ions in Aluminum

AbstractThe electron charge density distribution about a zinc solute ion in a dilute aluminum alloy is computed by three different methods. These are: a) an exact method where the solute ion potential is derived from the model potential difference between zinc and aluminum, b) a semiempirical method where the partial wave phase shifts are obtained from alloy specific electrical resistivity, and c) an approximate method where the solute ion potential is represented by a screened Coulomb potential. All three methods are in agreement with the experimentally observed solute ion clustering. Methods a and b also are in agreement with the observed decrease in lattice parameter with increase in zinc content.

Adiabatic Rate Processes at Electrodes. I. Energy-Charge Relationships

The distinction between adiabatic and nonadiabatic reaction mechanisms at an electrode/solution interface is emphasized; in general, only adiabatic or near-adiabatic paths are important in thermally activated reactions. The role of the dielectric in determining the course of such reactions is discussed. A general interpretation of the transfer coefficient and an account of the activation process in simple systems are given in terms of the distribution of electron charge density in the transition state; these are shown to be in good accord with experiment. The conventional approach to these problems, in which an approximate potential-energy path for the reaction is calculated from intersecting potential-energy curves for the initial and final states of the system, is criticized, and an alternative representation in terms of charge variation is proposed.