Electron Density Correlation Research Articles

Correlation of electron density and spin-exchange interaction in dimeric copper(II) formates, acetates and silanecarboxylates

L'etude structurale des complexes du cuivre montre qu'il n'y a pas de difference geometrique importante dans les cages Cu 2 (COO) 4 entre les cuivre acetate et cuivre formiate. Les populations electroniques des groupes carboxylate des coordinats pontants sont correlees avec les valeurs −25 des carboxylate des complexes de Cu(II). le point-cle de la force de l'interaction d'echange de spins reside dans la population de l'orbitale 2p x de l'atome C du carboxylate

Electron correlation in doubly excited S states: large-Z limit

The intrashell states of two-electron atoms are studied using the diagonalisation of the electron interaction r12-1. The relationship between the spatial structure of the electron density and electron correlation is established. (r12-1) is obtained as an asymptotic function of the principal quantum number n for the lower (r12-1)0=(1-2/ pi )n-2/5+(8 pi )n-3 and the higher (r12-1)n-1=0.5 ln 4n+0.6 states. It is shown that the screening approximation can be used for reliable non-relativistic estimation of lower state energies along the whole isoelectric series. It is predicted that for any positive ion there exists an n0, at which intrashell multiplets start to overlap.

Density correlation function of a superlattice with wave function overlap

We have studied the electron density correlation function of a tunneling superlattice using a tight-binding envelope function and taking account of the nearest-neighbor overlap. A matrix density correlation function Π is introduced, which can be expressed explicitly in terms of a matrix density correlation bubble Π 0 and a matrix effective Coulomb potential V in RPA. The plasmon dispersion relation of a superlattice with electron wave function overlap, given by the equation det(1 − VΠ 0)=0, is determined.

Electron density correlation of a superlattice with wave function overlaps

A calculation of RPA electron-electron density correlation function of a type I superlattice is presented. The electron tunneling between adjacent quantum wells is taken into consideration. A formal expression of density correlation function is explicitly given within single band tight binding approximation.

Small-Angle X-Ray Scattering of Carbon-Supported Metal Catalysts

AbstractThe slit-smeared intensity of X-radiation scattered from carbon-supported metal catalysts behaves as clh−1 + c2h−3 for higher h-values in the small-angle region (h+4πλ−1 sinθ, λ + X-ray wavelength,θ + half of scattering angle, c1, c2 are constants). For three-phase systems with sharp phase boundaries, uniform electron-densities in the metal and void phases, and lamellar electrondensity fluctuations in the carbon phase, the small-angle X-ray scattering (SAXS) can be described in terms of inter- and intraphase electron-density correlation functions, and can be shown to yield the observed behavior. Further assumptions are required to separate these contributions and calculate interfacial specific surfaces. SAXS measurements on Pt, Ru, Pd, and Rh/C are presented.

Pseudoclassical approach to electron and ion density correlations in simple liquid metals

Electron-electron and electron-ion structural correlations in simple liquid metals are treated by using effective pair potentials to incorporate quantal effects into a pseudoclassical description of the electron fluid. An effective pair potential between simultaneous electron density fluctuations is first constructed from known properties of the degenerate jellium model, which are the plasmon sum rule, the Kimball-Niklasson relation and Yasuhara’s values of the electron pair distribution function at contact. An analytic expression is theraby obtained in the Debye-Huckel approximation for the electronic structure factor in jellium over a range of density appropriate to metals, with results which compare favourably with those of fully quantal evaluations. A simple pseudoclassical model is then set up for a liquid metal: this involves a model of charged hard spheres for the ion-ion potential and an empty-core model for the electron-ion potential, the Coulombic tails being scaled as required by the relation between the long-wave-length partial structure factors and the isothermal compressibility of the metal. The model is solved analytically by a pseudoclassical linear response treatment of the electron-ion coupling and numerical results are reported for partial structure factors in liquid sodium and liquid beryllium. Contact is made for the latter system with data on the electron-electron structure factor in the crystal from inelastic X-ray scattering experiments of Eisenberger Marra and Brown.

Investigations on linear segmented polyurethane elastomers, 1. Temperature dependence of microphase segregated structure

AbstractThe temperature dependence of microphase segregation in polyester and polyether segmented urethane elastomers has been studied by small‐angle X‐ray scattering, viscoelasticity, and infrared spectroscopy. The mean‐square electron density fluctuations distincitly decrease with increasing temperature above about 60°C. Their value estimated from the location of the first peak of the electron density correlation function increases with increasing temperature; at the same time the peak becomes flat and finally disappears. The infrared absorbance for the NH vibration decreases above about 80°C. These results correspond to an increase of the mean distance between the centers of the nearest neighbouring microdomains, mainly composed of the hard segments, and to intermixing of hard and soft segments in the boundaries of the domains by heat treatment. This fact suggests that a domain structure is formed by casting in these polyurethane elastomers. The dynamic storage moduli G′ for both samples investigated decrease in the two temperature ranges, −70 to −20°C and 60 to 120°C, the former corresponds to the dispersion of soft segments and the latter to the dissociation of hydrogen bonds.

Elimination and addition reactions. Part 37. A comparative study of electronic, steric, and solvent effects upon reactivity in additions of benzenesulphenyl chloride to alkenes

Rates of additions of benzenesulphenyl chloride to 35 alkenes in several solvents have been measured, and the products of the reactions have in most cases been identified. Results for arylalkenes broadly confirm previous work, but the responses to solvent change are not uniform throughout. The reactivity of bridged cycloalkenes is substantially greater than that of cycloalkenes, but that of cyclo-pentadiene dimer is anomalously small. For allylic substrates, the correlation of electron density at the double bond with reactivity is shown by a rectilinear relationship between log k and σI. Allyl iodide and allyl alcohol are anomalously more reactive than this correlation would predict; this is accounted for by solvation and by internal solvation effects respectively.

High-temperature nuclear spin relaxation in51V metal: self-diffusion and interstitial-impurity diffusion effects

Zeeman and dipolar reservoir nuclear spin relaxation times T1Z, T1D and T2 in 51V metal have been measured in samples with different purities, over temperatures within the 300-1700K range. T1Z and T1D have been analysed into electronic, quadrupolar and diffusion contributions, whose temperature dependences have been determined. For the electronic contributions it has been shown that T1eZ=(2+ epsilon )T1eD with epsilon <0.05 which means that electron-density correlation effects are negligible. From the quadrupolar contribution to T1Z an activation energy value of (0.8+or-0.1) eV has been determined for interstitial oxygen migration around 1000K. From the diffusion contributions to T2 and T1D the authors have deduced a self-diffusion activation energy of (3.2+or-0.1) eV on the purest sample and values of the diffusion coefficients in the 1200-1600K temperature range which are in agreement with measurements made by radioactive tracers. This 3.2 eV value is attributed to a single-vacancy mechanism and it has been shown that interstitial oxygen increases the self-diffusion through extrinsic vacancies with lower activation energy values.

Direct evaluation of the electron density correlation function of partially crystalline polymers

AbstractA discussion of the general properties of the one‐dimensional electron density correlation function K(z) of a partially crystalline polymer with lamellar structure shows that application of a graphical extrapolation procedure permits direct determination of the crystallinity, the specific inner surface, and the electron density difference ηc − ηa. The procedure is based upon the occurrence of a straight section in the “self‐correlation” range of K(z). Curved and nonparallel lamellae do not invalidate the concept. In the case of heterogeneous samples composed of partially crystalline and totally amorphous regions, some of the parameters of the experimentally obtained correlation function, as for example the invariant K(0), are affected and may lose their definiteness. Use of the method is demonstrated in a detailed discussion of the correlation functions measured for a sample of lowdensity polyethylene at 25 and 100°C.

Interaction between two ground-state helium atoms

This paper presents the calculations of the energy and interaction potential of two ground-state helium atoms for a wide range of internuclear distances 0.1 Å⩽R⩽1.75 Å, using the one-electron wave functions obtained by numerical solution of the Schrödinger equation for an electron moving in the field of two fixed arbitrary charged nuclei, and assuming compensation of errors made in calculating atomic and molecular energies. The agreement between the calculations and experimental values is within ∼2.2%, this value being by order of magnitude better than the accuracy of any quantum-mechanical method available so far. Both the kinetic and potential energies of the He–He system are calculated. The effects of correlation and polarization of electron density which occurs when atoms come closer are taken into account by means of introducing of variable constants of nuclear screening directly into Schrödinger equations thus providing the high efficiency of the method.

Berechnung der streuspektren schwach ionisierter plasmen mit hilfe zweizeitiger wahrscheinlichkeitsdichten

Zusammenfassung In the present paper we report a calculation of scattering spectra from weakly ionized plasmas, using two-time probability densities. Williams and Chappell, and Klingenberg and Richter assumed identical BGK collision integrals for the self-and distinct parts of the electron density correlation function. There, BGK terms with different “collision frequencies” are used. Finally, the spectral density is given for modified initial correlations.

Pseudosymmetry in the structure of myohemerythrin.

The three-dimensional structure of the protein myohemerythrin from retractor muscles of the sipunculan worn Themiste zostericola has been explored for the existance of approximately symmetry operators that locally interrelate portions of the molecule. First, the electron denisty distribution at 5.5 A resolution was examined. A local 2-fold axis that transposes the C-D helix pair into the A-B helix pair was found and refined by the method of least squares. The match in electron densities for a pure 2-fold rotation had a correlation coefficient of 0.56. Next, a comprehensive search was made for rotational symmetry in the Patterson function of an isolated molecule. The rotation function based on data to 6 A spacings showed a major peak, 72% of the self-peak height, that confirmed the result from electron density correlations. In addition, a pattern of lower level peaks revealed approximate point group symmetry as high as D4. Finally, the amino acid sequence has been inspected for evidence of a repeated structure. The level of amino acid identities between positions in the A-B and C-D helix pairs is 28%. Several factors are discussed to suggest that this homology, although low, is nonetheless significant.

Correlation of effective atomic number and electron density with attenuation coefficients measured with polychromatic x rays.

Attenuation coefficients of nine different plastics and water were measured with EMI computed transaxial tomography (CT) and radioisotopic sources with photons of 14 to 136 keV. The EMI values were correlated with physical density, electron density, and atomic number cubed (Z3). The best correlation was obtained with electron density, the exception being the value for water. This descrepancy was explained on the basis of X-dependent photoelectric absorption with verification from monoenergetic measurements.

Single-particle excitations in narrow energy bands

The Hubbard hamiltonian is analysed by means of Gutzwiller's variational scheme for both the nondegenerate and the degenerate band models. The single-particle excitations in the correlated ground state, which is determined by a balance between the electron hopping energy and the intra-atomic interaction energy, are investigated for arbitrary electron density and arbitrary correlation strength. It is found that the single-particle excitation energies forming a quasi-energy band. The centre of gravity of the quasi band is shifted from that of the bare band, and the bulk part of the density of states function for the quasi particles is narrowed by the correlation effect. Both the shift and the narrowing are spin-dependent. In the limit of strong correlation, our results agree with those obtained by Harris and Lange (1967) and Roth (1969).

Ultrastructural age changes in hippocampal neurons, synapses and neuroglia

Ultrastructural studies of age changes in hippocampal neurons, synapses and neuroglial elements of 24 wistar rats (12 ‘young’, ages 4–12 months and 12 ‘old’, ages 24–40 months) were carried out with the electron microscope after perfusion-fixation. The neurons showed increasing accumulation of lipofuscin in the perikaryon, disorganization of the normally well-developed laminated pattern of the rough-surfaced endoplasmic reticulum and multiple invaginations of the nuclear membranes with the increase in age. Increasing accumulation of neurofibrils and neurotubules and higher electron density of the axons was apparent with age. A possible significance of the correlation of altered electron density with the zinc content of hippocampus has been discussed. Also, the increase with age in the incidence of dendritic profiles and dendro-dendritic contacts without intervening glial fibres has been correlated with aging. Axo-somatic synapses are less frequently encountered in the senile rats. The age-changes observed in the oligodendrocytes are: (1) increased neuronal satellitosis (2) appearance of binucleated forms or fusion of oligodendrocytes. (3) Invagination of the nuclear membranes and characteristics marginal condensation of nuclear chromatin. The microglia showed numerous “lipid” vacuoles in the perikaryon. Obvious changes in the astrocytes were not observed. Attention has been drawn to the significance of further ultrastructural investigations related to age changes particularly in the hippocampus. On aétudiéau microscopeélectronique et après fixation et perfusion des altérations ultrastructurales associéesàl'âge des neurones, synapses etéléments névrogliques de l'hippocampe chez 24 rats Wistar, en l'occurrence 12 animaux “jeunes” (4–12 mois) et 12 animaux “âgés” (24–40 mois). Les neurones ont présenté, selon l'aˆge du sujet, une accumulation croissante de lipofuscine dans le péricaryon, une désorganisation du pattern laminéet normalement bien développédu réticulum endoplasmique et des invaginations multiples des membranes nucléaires. On a aussi observé, avec l'aˆge, une accumulation plus forte de neurofibrilles et de neurotubules et une plus grande densitéd'électrons des axones. On s'est interrogésur la signification possible de la corrélation entre l'altération de la densitéd'électrons et la teneur en zinc de l'hippocampe. L'augmentation avec l'aˆge de la fréquence de profils dendritiques et de contacts dendro-dendritiques sans intervention de fibres gliales a aussiétémise en corrélation avec l'aˆge. On rencontre moins fréquemment des synapses axo-somatiques chez les rats séniles. Les changements associésàl'âge et observés sur les oligodendrocytes sont: 1° une augmentation de la staellitose neuronique, 2° l'apparition de formes binucléès ou une fusion d'oligodendrocytes, 3° l'invagination des membranes nucléaries et une condensation marginale caractéristique de chromatine nucléaire. Les microglies ont présentéde nombreuses vacuoles “lipides” dans le péricaryon. Aucune altérationévidente des astrocytes n'aétéobservée. On attire l'attention sur la signification de recherches ultérieures sur le plan ultrastructural quant aux altérations associées avec le vieillissement, plus particulièrement en ce qui concerne l'hippocampe. Untersuchungen der Altersveränderungen der Ultrastruktur in Neuronen, Synapsen und neuroglialen Elementen des Hippocampus wurden mit dem Elektronenmikroskop nach Perfusionsfixation bei 24 Wistarraten (12 ‘jung’, 4–12 Monate alt, und 12 ‘alt’, 24–40 Monate alt). Die Neuronen zeigten zunehmende Akkumulation von Lipofuszin im Perikaryon, Desorganisation des normalerweise gutentwickelten laminierten Musters des rauhen endoplasmatischen Retikulums, und multiple Invaginationen der Kernmembranen mit zunehmendem Alter. Mit dem Alter nahm die Akkumulation von Neurofibrillen und Neurotubuli zu, ebenso die Elektronendichte der Axone. Ein mögliche Bedeutung der Korrelation der veränderten Elektronendichte mit dem Zinkgehalt des Hippocampus wurde diskutiert. Die Zunahme mit dem Alter des Auftretens von dendritischen Profilen und dendrodendritischer Kontakte ohne vermittelende Gliafasern wurde ebenfalls mit dem Altersprozeβ korreliert. Axo-somatische Synapsen werden bei senilen Ratten weniger häufig beobachtet. Die bei Oligodendrozyten beobachteten Altersveränderungen sind: (1) erhöhte neuronale Satellitose. (2) Auftreten von zweikernigen Formen oder Fusionen von Oligodendrozyten. (3) Invagination der Kernmembranen und charakteristische Randkondensation des Kernchromatins. Die Mikroglia zeigte zahlreiche ‘Lipid’—vakuolen im Perikaryon. Offensichtliche Veränderungen der Astrozyten wurden nicht beobachtet. Die Aufmerksamkeit wurde auf die Bedeutung weiterer ultrastruktureller Untersuchungen in Beziehung zu Altersveränderungen gelenkt, besonders im Hippocampus.

Analysis of reduced density matrices in the co‐ordinate representation. III. Electron density and correlation in the ground states of H2 and the H6 ring system within some approximations of the simple LCAO type

AbstractThe electron density and spatial correlation as given by the MO, VB and AMO methods for H2 and H6 are studied by means of diagrams. For comparison, diagrams representing accurate wave functions for H2 are also given. The study of model functions representing localized bonds leads to results concerning the nature of localized electron pairs in agreement with those of Lennard‐Jones.

A study of superconductivity in interstitial compounds

A large number of interstitial compounds with the NaCl crystal structure have been prepared with particular emphasis laid on pseudo-binary alloys based on niobium nitride and vanadium nitride in combination with other nitrides and carbides. In addition several pseudo-ternary systems and a pseudo-quaternary system based on niobium carbonitride have been investigated. The results of X-ray and chemical analyses, and measurements of critical temperature T c , are presented. It is concluded that values of T c > 18°K should be attainable in the pseudo-ternary system NbNNbCTiN. Several empirical correlations between transition temperatures and other simple physical quantities have been evaluated in terms of the new experimental data and shown to be only partially successful in systematizing interstitial compounds. The T c -electron density correlation is shown, however, to be the most successful empirical method of systematizing both β- W and NaCl structure compounds.

Microscopic Fluctuations and Diffusion Coefficients of a Nonequilibrium Plasma in a Magnetic Field

A relationship is deduced between the electron density correlation function and the ``parallel'' and ``perpendicular'' diffusion coefficient of a partially ionized nonequilibrium (but homogeneous) plasma in an external magnetic field. This relationship is derived in a particularly simple and direct way from within the rigorous framework of microscopic theory by expanding the Fourier transform of the microscopic electron density in terms of semi-invariants. The previous result derived by Ichimaru—by means of hydrodynamic arguments—is seen to be a special case of the present result.

Scattering of Light by Light in Plasmas

A quantum-mechanical calculation of the scattering rate of light by light in the polarizable medium of a plasma is carried out. It is shown that if the frequency ${\ensuremath{\omega}}_{0}$ of the incident light is much greater than the electron plasma frequency ${\ensuremath{\omega}}_{p}$, the $\ensuremath{\rho}{A}^{2}$ term in the nonrelativistic Hamiltonian coupling the radiation to matter dominates the j.A interaction, provided the frequency shifts $\ensuremath{\Delta}\ensuremath{\omega}$ satisfy $\ensuremath{\Delta}\ensuremath{\omega}\ensuremath{\ll}{\ensuremath{\omega}}_{0}$. In this approximation, the scattering amplitude is proportional to the Green's function for electron-density fluctuations (which reduces to the electron-density correlation function in the classical limit). This leads to an expression for the differential scattering rate which is formally exact to all orders in the interparticle interactions. The spectrum of the scattered light in this approximation has resonances at the collective modes of the plasma if $\frac{{\ensuremath{\omega}}_{0}}{c}\ensuremath{\ll}{k}_{D}$, the Debye wave number. The total scattering rate is estimated in the collisionless (random-phase) approximation. Under the conditions of this calculation, rather high plasma densities and temperatures are required to obtain a detectable rate.