Showing papers on "Charge density published in 1977"

Bonded-atom fragments for describing molecular charge densities

Abstract: For quantitative description of a molecular charge distribution it is convenient to dissect the molecule into well-defined atomic fragments. A general and natural choice is to share the charge density at each point among the several atoms in proportion to their free-atom densities at the corresponding distances from the nuclei. This prescription yields well-localized bonded-atom distributions each of which closely resembles the molecular density in its vicinity. Integration of the atomic deformation densities — bonded minus free atoms — defines net atomic charges and multipole moments which concisely summarize the molecular charge reorganization. They permit calculation of the external electrostatic potential and of the interaction energy between molecules or between parts of the same molecule. Sample results for several molecules indicate a high transferability of net atomic charges and moments.

Self-consistent field model for condensed matter

Abstract: A model for condensed matter is described in which the ions surrounding a particular atom are replaced by a positive charge distribution which is constant outside of a sphere containing the atom and zero inside. The orbital functions, both bound and free, are obtained as solutions of the Dirac equation and are used to self-consistently determine the potential function. In order to obtain the desired equation-of-state data from the calculations, three different and somewhat arbitrary prescriptions are used to separate quantities pertaining to the atom from those of the electron gas in which it is imbedded. Results are shown for 14 elements, including the $5d$ transition metals, in the neighborhood of normal solid density. Equation-of-state data for nickel, copper, and zinc are also given and are compared with experiment.

Microscopic Model of Charge Density Waves in 2H-TaSe2

Abstract: The ultimate goal of the theoretician in studying a particular phenomenon is to produce a quantitative microscopic theory from which one can calculate anything That goal has been pretty well achieved in superconductivity We are still struggling with the theory of charge density waves The way that one progresses in solid state physics is to compute the properties of a theoretical model, compare the predictions with experiment, and modify the model when it fails I want to discuss one iteration of this process today

Electronic properties of TTF-TCNQ : an NMR approach

Abstract: This paper presents the frequency dependance of the proton spin-lattice relaxation time T1 at several temperatures and pressures in TTF-TCNQ(D4) and TTF(D4)-TCNQ. It is shown that only backward (q = 2 kF) and forward (q = 0) scatterings contribute to the nuclear relaxation induced by the modulation of the hyperfine field in these one-dimensional conductors. At medium fields, H 0 ~ 30 kOe, the frequency dependence of T1 originates from the diffuse character of the spin density wave excitations around q = 0, leading to T1-1 αH0- 1/2 . The enhancement of T1 -1, is at low fields, limited by the existence of a finite interchain coupling (tunnelling type). We find, within a RPA analysis, close correlations between the pressure and temperature dependences of the spin excitations diffusion constant and the collision time derived from the longitudinal conductivity. The interpretation of the NMR data in terms of a Hubbard model excludes both big U and small U pictures. However, we point out the importance of the electron-electron interactions on the relaxation rate of TTF-TCNQ. We derive a ratio U/4 t II ~ 0.9 for the TCNQ chain. We also assume that besides charge density waves fluctuations existing between 300 K and the phase transition at 53 K, electron-electron interactions make an important contribution to the temperature dependence of the spin susceptibility. Finally, we give a unified description of quasi one dimensional conductors in which the various systems are classified according to the transverse tunnelling coupling and the electron lifetime. It follows from this description that for TTF-TCNQ and its derivatives, transverse couplings (tunnelling and Coulomb) are large enough to justify the use of a mean-field theory.

Longueurs de liaison et transfert de charge dans les sels du tétracyanoquinodiméthane (TCNQ)

Abstract: An examination of most of the known crystal structures of TCNQ salts is made in connexion with deter mining the amount of charge transfer A method based on the bond lengths is shown to provide a sensitive test for determining this important quantity' The charge distribution between different TCNQ molecules of the same compound can also be deduced The results obtained are used to correlate the degree of charge with the occurrence of a hydrogen bond the rotation of C(CN)z groups and the experimental values of dipolar splittings D and E

High-Momentum-Transfer Electron Scattering from Pb 208

Abstract: $^{208}\mathrm{Pb}$ elastic electron scattering data have been extended to large momentum transfer ($q=3.7$ ${\mathrm{fm}}^{\ensuremath{-}1}$). The present data combined with previous electromagnetic data allow a precise determination of the charge density. It shows a small central depression and density fluctuations much less pronounced than theoretically predicted.

Ground- and excited-state properties of LiF in the local-density formalism

Abstract: The band structure, charge density, x-ray scattering factor (and their behavior under pressure), equilibrium lattice constant, and cohesive energy of the prototype ionic solid LiF were determined using our recently developed self-consistent numerical basis set (non-muffin-tin) linear-combination-of-atomic-orbitals method, within the local-density formalism (LDF). The details of the bonding and the effects of exchange and correlation on the electronic structure are discussed with reference to the conventional picture of ionic bonding. Remarkably good agreement is found with the observed data for the ground-state properties of the system. Contrary to the results of previous band studies, the conventional band-structure approach to excitation energies (i.e., identifying them with the band eigenvalue differences) is found to fail completely in accounting for the observed data in the entire x-ray and optical spectral region when fully self-consistent solutions of the LDF one-particle equation with no further approximation to the crystal potential are obtained. It is found that in the presence of some spatial localization of the initial or final crystal states, the spurious self-interaction terms, as well as the polarization and orbital relaxation self-energy effects are of a similar order of magnitude as the Koopmans'-like interband terms. In order to treat these effects within the LDF self-consistently, we describe the excitation processes as transitions involving point-defect-like states in the solid calculated by a supercell method in which the excitation energies are determined as total-energy differences between (separately calculated) excited- and ground-state configurations. The excited state is represented as a superlattice of locally excited sites using large (8-and 16-atom) unit cells, each containing a single excited site. We find, in the self-consistency limit, that a small but finite degree of spatial localization of the excited states exists even for valence excitations, inducing thereby self-interaction as well as self-energy relaxation and polarization effects. The LDF model is found to account very well for both interband and exciton transitions over the entire spectral region (12-695 eV) and to yield definite predictions regarding the exciton bandwidths and series limits.

Electrical stimulation with Pt electrodes: Trace analysis for dissolved platinum and other dissolved electrochemical products.

Abstract: A conservative requirement for 'safe' electrical stimulation is the absence of chemical changes adjacent to the stimulating electrodes. In electrochemical terms, this means that charge transfer processes producing dissolved species must be avoided. With this restriction, the aim of this study has been to establish the maximum charge density that can be passed during each half of a biphasic stimulation pulse. Possible dissolved species resulting from faradaic reactions at the Pt/saline interface include chloride oxidation products (ClO-, ClO3-, etc.) H+ or OH- ions and Pt ions. For balanced biphasic pulses, neither Cl- oxidation nor pH shifts appear likely to constitute significant problems and the most difficult problem to avoid appears to be metal dissolution. Pt dissolution has been monitored by UV spectrophotometric analysis and, because protein interferes with the analysis, the tests were run in inorganic saline solution. Results are presented in the form of nomographs which relate Pt dissolution to the charge density per pulse and the current density. Specific recommendations for minimizing Pt dissolution include the use of platinized electrodes, the restriction of charge densities per pulse to greater than or equal to 300 muC/geom cm2 of electrode surface, and preferably the use of cathodic-first biphasic pulses.

Accurate X-Ray Diffraction and Quantum Chemistry: The Study of Charge Density Distributions

Abstract: Publisher Summary This chapter discusses the theory of X-ray scattering and provides the derivation of electron densities from X-Ray scattering amplitudes. Even though X-ray diffraction is conventionally used for the determination of atomic positions, the X-ray scattering amplitudes depends directly on the electronic wavefunction, from which atomic positions can only be derived under the assumption of coincidence of the nuclear positions and the centroids of electronic charge. The comparison of theoretical and experimental densities is discussed, and the functions based on experimental densities are reviewed. In addition to Fourier methods, least-squares fitting of density functions may be accomplished directly in scattering space analogous to least-squares adjustment of atomic parameters in conventional crystallography. The chapter briefly mentions the valence shell deformation methods. The space-filling properties of formalisms, including atomic dipole, quadrupole, octopole, and hexadecapole terms may be judged from the molecular density maps based on the multipole expansion coefficient.

Charge density effects in ion exchange. Part 1.—Heterovalent exchange equilibria

Abstract: A thermodynamic study is made on the effect of surface charge density on the sodium–cesium equilibrium in three clay minerals, Otay montmorillonite, hectorite and a series of Camp Berteau montmorillonite samples with reduced layer charge.It is shown that the standard free energy, enthalpy and entropy changes for the reversible displacement of sodium by cesium ions increase linearly with surface charge density. The opposite effect of charge density on cesium selectivity in zeolites and clay minerals is discussed in terms of electrostatic and hydration effects and the swelling properties of clays.

Charge transfer and ionic bonding in organic solids with segregated stacks

Abstract: In ionic charge-transfer salts which have segregated stacks of organic donor ($D$) and acceptor ($A$) molecules, the major feature of the classical electrostatic interactions is the strong repulsion between like charges along the stacks. Two ways are described by which the magnitude of this repulsion may be decreased: (i) by the formation of a complex salt (i.e., one whose ratio $D:A\ensuremath{ e}1:1$); and (ii) by incomplete transfer of charge from $D$ to $A$. In both cases, some of the molecules in the stack are neutral, giving rise to a mixed-valence, partly ionic ground state. The first effect is quantitatively investigated by a Madelung energy calculation of tetrathiafulvalene-${\mathrm{Br}}_{0.79}$ as a function of (theoretical) bromine concentration. The results of this calculation show that the unusual composition of this salt occurs in order to reduce the Coulomb repulsion along the stacks. As an example of the second effect, a similar calculation is described for TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane), as a function of the amount of charge transferred from TTF to TCNQ. Although electrostatic interactions do not give a complete description in this case, they are clearly an important factor in determining the degree of charge transfer in such salts. In fact, in cases where the net electrostatic binding energy is small, incomplete charge transfer may be energetically favored. In this case, the charge distribution is shown to be modulated along the stack and charge density waves are formed, with wave vector "$4{k}_{F}$". These results are compared to the case of Rb-TCNQ, where the Madelung energy is shown to favor complete charge transfer.

Collective dynamical properties of molten salts: molecular dynamics calculations on sodium chloride

Abstract: We present the results of molecular dynamics calculations on a system simulating molten NaCl at a temperature of 1090 K. Attention has been focused on the study of the collective modes, as described by the auto-correlation functions of the longitudinal and transverse components of the currents of mass and charge. Explicit expressions are given for the coefficients in the small-time Taylor development of the autocorrelation functions and these, together with data on the static structure factors, are used in analysing the current fluctuations and their spectra in terms of memory functions. The memory function has the same basic structure in all cases, consisting of a short-lived initial decay and a long-lived quasi-exponential tail. Inclusion of the tail is essential in order to achieve quantitative agreement with the measured spectra, particularly at small wavenumbers. To that extent our results are consistent with calculations on simpler systems, suggesting that the dynamical events which contribute to the tail in the memory functions are a feature characteristic of liquids in general. The relation to neutron-scattering experiments is also discussed. It is shown, in particular, that a propagating charge density fluctuation of the type seen in the molecular dynamics results is likely to be undetectable in a neutron experiment, except in particularly favourable circumstances.

Ground-state electronic properties of diamond in the local-density formalism

Abstract: We use our previously reported method for solving self-consistently the local-density one-particle equations in a numerical-basis-set linear combination of atomic orbitals expansion to study the ground-state charge density, x-ray structure factors, directional Compton profile, total energy, cohesive energy, equilibrium lattice constant, and behavior of one-electron properties under pressure of diamond. Good agreement is obtained with available experiment data. The results are compared with those obtained by the restricted Hartree-Fock model: the role of electron exchange and correlation on the binding mechanism, the charge density, and the momentum density is discussed. I. INTRODU(.'TION The local density functional (LDF) formalism of Hohenberg, Kohn, and Sham, " and its recent extension as a local spin-density functional formalism, ' form the basis of a new approach to the study of electronic structure in that the effects of exchange and correlation are incorporated directly into a charge- density- dependent potential term that is determined self -consistently from the solution of an effective one-particle equation. Applications of the LDF formalism to atoms+' and molecules' have yielded encouraging results. Similar applications for solids are complicated by (i) the need to con sider both the short-range and the long- range multicenter crystal potential having nonspherical components, (ii) the difficulties in obtaining full self-consistency in a periodic system, and (iii) the need to provide a basis set with sufficient variational flexibility. Hence, theoretical. studies of ground- state electronic properties of solids in the LDF formalism have been mainly l.imited to muffin-tin models for the potential, " non-selfconsistent schemes, ' treatments of simplified jellium models'0 or spherical cellular schemes We have recently proposed"" a general selfconsistent method for solving the LDF formalism one-particle equation for realistic solids using a numerical-basis-set LCAO (linear combination of atomic orbitals) expansi. on and retaining all nonspherical parts of the crystal potential. We have demonstrated a rapid convergence of the selfconsistent (SC) cycle when the treatment of the full crystal charge density is suitably apportioned between real- space and Fourier- transformed reciprocal-space parts and have indicated the large degree of variational flexibility offered by a nonlinearly optimized (exact) numerical atomiclike basis set. We have shown that all multicenter interactions as well as the nonconstant parts of the crystal potential are efficiently treated by a three- dimensional Diophantine integration scheme.

The Nearly Commensurate Phase and Effect of Harmonics on the Successive Phase Transition in 1T-TaS2

Abstract: The phase transitions of the charge density wave (CDW) state in 1T-TaS 2 are studied both theoretically and experimentally. The positions and intensities of the fundamental and third-order harmonic...

V. One‐Electron Density Functions and Many‐Centered Finite Multipole Expansions

Abstract: The one-electron density function, ρ(r), (in principle deduced from elastically scattered X-ray intensities) is the probability distribution function of an electron, averaged over the positions of all other electrons. A partitioning of ρ(r) into constituent parts is an intellectual exercise that does not lend itself to unique measurement from elastic X-ray scattering experiments. It is shown that in the limit of perfect data and an infinite Ewald sphere, a least-squares fit with a many-centered finite multipole expansion of the charge density about the N nuclei will necessarily satisfy the q-centered multipoles of the molecule for q = 1, 2,…, N. This means that a large number of static-charge physical properties (averages over ρ(r)) are correctly given. Several expressions for averages of ρ(r) or over FH are given. It is shown that outer moments, such as atomic charges, dipole moments and quadrupole moments, always depend on a shape function. On the other hand, inner moments such as potentials, electric forces, and electric field gradients, may be represented by direct Fourier analysis of FH (obs) (suitably phased, of course). Nuclear vibrations have been neglected throughout the discussion.

The experimental charge density in sulfur‐containing molecules. A study of the deformation electron density in sulfamic acid at 78 K by X‐ray and neutron diffraction

Abstract: The deformation electron density in sulfamic acid (H3NSO3) has been determined by a combined X-ray and neutron diffraction study at 78 K. X-N maps show strong bond populations in all bonds. The nature of the S--N and S O bonds is found to be similar to bonds between first-row atoms. The O atoms show single, fairly broad lone-pair peaks and are shifted towards the lone pairs in comparison with the neutron parameters. This shift disappears when only X-ray reflections with sin 0//1, > 0.85 A -1 are considered. A population analysis shows a net charge of +0.7 to +1.0 e on the S atom, -0 .3 to -0 .5 e on the O atoms and + 0.12 e on the H atoms, while the N atom is close to neutral.

XVII. Spatial Partitioning of Charge Density

Abstract: Quantitative indices of a molecular charge distribution are provided by the values of volume integrals of the deformation density times a set of appropriate sampling functions. These integrals may, for example, represent the net charges in particular atomic or bond regions. A sharing function derived from the promolecule density defines a general partitioning of any molecule into bonded-atom fragments, whose net charges and multipole moments determine the electrostatic properties of the molecule. Expressions are available for estimating the experimental accuracy of such indices but they are not easy to evaluate nor very reliable.

Location of charge centroid in electron‐beam‐charged polymer films

Abstract: The centroid of the charge distribution of electron‐beam‐charged polymer films electroded on both sides is determined by measurements of the charges on, or currents into, the two electrodes during or after electron‐beam injection. Results obtained with 25‐μm Teflon FEP films charged with a diffuse monoenergetic beam of 5–40‐keV electrons show that the charge centroid is initially located between the average and maximum electron ranges regardless of whether the electrode of injection is floating or grounded (open or short circuit, respectively). During and after charging under open‐circuit conditions the centroid moves further into the material beyond the maximum range.

Experimental Electron Densities and Chemical Bonding

Abstract: Some recent results of charge density analysis by X-ray and neutron diffraction are discussed. Problems that have been studied in a number of laboratories include the nature of single, double, and triple bonds, lone-pair hybridization, bonding in some metals, alloys, and organometallic compounds, and the derivation of physical properties from X-ray diffraction densities. At the present stage of development of methods studies of series of related compounds are feasible and expected to find widespread application.

Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. II. Electrode Systems

Abstract: In certain electrode processes involving electron transfer mechanisms, a portion of the dielectric polarization is not in electrostatic equilibrium with the charge distribution. In the present paper expressions are deduced for the properties of such systems. These properties include the electrostatic free energy, entropy and energy, and the spatial dependence of the inner potential. The method of images provides a convenient means for determining the electrode charge distribution, due account being taken of its quantum limitations. These expressions have been used to formulate a quantitative theory of overvoltage for electron transfer electrode processes.

Nuclear magnetic resonance studies of diamagnetic metal-aminopolycarboxylate complexes

Abstract: Proton resonance spectra of EDTA, MEDTA, and HEDTA complexes of diamagnetic ions including alkali, alkaline earth, and rare earth metals are described. Quartet splittings of the methylenic protons of the acetate groups, indicative of long-lived metal--nitrogen bonds, are found for each ligand in the complexes of the cations of higher charge density. The ligand proton chemical shifts are shown to correlate with the effective charge density of the metal ion. Evidence is presented that this correlation is reflective of ordering in the solvation shell rather than a result of direct metal--ligand electrostatic or inductive effects.

Ab initio calculations on 4-substituted styrenes: a theoretical model for the separation and evaluation of field and resonance substituent parameters

Abstract: Ab initio (STO-3G minimal basis set) molecular orbital calculations on 4-substituted styrenes and CH3X–C2H4 pairs indicate that ΔqH (the charge density difference between β-vinyl protons) provides a direct theoretical measure of the field effect of a polar substituent. Σqcπ, the total substituent-induced π electron density change in styrene provides a theoretical measure of the resonance effect of the substituent. ΔqH and Σqcπ provide the basis of a theoretical dual substituent parameter scale, TF and TR0. This scale compares very closely with experimental DSP scales, indicating the latter scales are fundamentally valid. The calculations also indicate that field effects and σ inductive effects do not show parallel trends. It is concluded that field effects are more important than σ inductive effects except at very close range. Individual carbon π electron densities reflect both resonances effects and polar π inductive effects.