Charge-density distribution

Its charge density distribution is like that of the cation (with sign reversal) because the added electron goes into the nonbonded orbital with a node at the central carbon atom. The probability of finding that electron precisely at the central carbon atom is zero. 

Au-Ni and Cu-Ni-Au alloys Magnetic hyperfine spitting at Au, // and isomer shift as function of composition, model to describe charge density distribution... 

Another observation should be made with respect to the term elastic in describing interfacial capacitors. It was originally introduced by Crowley [1] for membranes and reflects the compressibility of lipid layers which behave in some respects like an elastic film. Its relation to electrochemical interfaces is less obvious. Consider an interface between a metal electrode and an electrolyte. As we will see in Section III, the effective gap of the interfacial capacitor is the distance between the centers of mass of the electronic, e, and ionic, i, charge density distributions... 

Most of the relevant features of the charge density distribution can be elegantly elucidated by means of the topological analysis of the total electron density [43] nevertheless, electron density deformation maps are still a very effective tool in charge density studies. This is especially true for all densities that are not specified via a multipole model and whose topological analysis has to be performed from numerical values on a grid. 

Iversen, B.B., Jensen, J.L. and Danielsen, J. (1997) Errors in maximum-entropy charge-density distributions obtained from diffraction data, Acta Cryst., A53, 376-387. 

Reliability of charge density distributions derived by the maximum entropy method... 

At a certain stage in the refinement, the electron density map is interpreted using a model representation of the charge density distribution to extract the atomic coordinates. A commonly used scattering formalism is the independent-atom model (IAM), in which the total charge density in the crystal is approximated by the superposition... 

Gatti, C., R. Bianchi, R. Destro, and F. Merati. 1992. Experimental v. Theoretical Topological Properties of Charge Density Distributions. An Application to the L-alanine Molecule Studied by X-ray Diffraction at 23 K. J. Mol. Struct. (Theochem) 255, 409—433. 

What experimental evidence is available to clarify the resulting mode of spin-density and charge-density distribution If one characterizes the reduction of (i) a single annulene, (ii) a doubly layered and (iii) a triply layered analogue by cyclic voltammetry, one derives a first criterion (Alexander et al., 1989 Bohnen et al., 1992 Fry et a/., 1985). The potential... 

As Fig. 12 shows, the inner shell electrons of the alkaline ions behave classically like a polarizable spherical charge-density distribution. Therefore it seemed promising to apply a "frozen-core approximation in this case 194>. In this formalism all those orbitals which are not assumed to undergo larger changes in shape are not involved in the variational procedure. The orthogonality requirement is... 

Finally, it should be mentioned that Raman and infrared absorption spectra (i.e., absorption spectra among vibrational levels) are very often complementary methods with which to investigate the energy-level structure associated with vibrations. If a vibration (phonon) causes a change in the dipolar moment of the system, which occurs when the symmetry of the charge density distribution is changed, then the vibration... 

The various reactions of cyclopropane radical cations discussed in the preceding section have elucidated several facets of their reactivity. The results raise questions concerning the factors that determine the products observed. More significantly, we will consider whether the structures, the stereochemistry, and the chirality of the products can be related unambiguously to the structures of the radical cationic intermediates, particularly to their spin- and charge-density distributions. 

However, electron transfer-induced photoreactions in the presence of nucleophiles have attracted by far the greatest attention a rich variety of cyclopropane systems have been subjected to these reaction conditions. We will consider several factors that may affect the structure of the radical cations as well as the stereo- and regiochemistry of their nucleophilic capture. Factors to be considCTcd include (1) the spin and charge density distribution in the cyclopropane radical cation (the educt) (2) the spin density distribution in the free-radical product (3) the extent of... 

Figure 5.57 RNiInHi 333 structure and charge density distribution.

The X-N deformation densities are important for the study of the charge density distribution in and around hydrogen atoms. Without the extra effort required for a neutron experiment, assumptions on the hydrogen atom location and vibrations must be made which introduce a considerable uncertainty in the results. 

In this expression, the dipole dipole interactions are included in the electrostatic term rather than in the van der Waals interactions as in Eq. (9.43). Of the four contributions, the electrostatic energy can be derived directly from the charge distribution. As discussed in section 9.2, information on the nonelectrostatic terms can be deduced indirectly from the charge density. The polarizability a, which occurs in the expressions for the Debye and dispersion terms of Eqs. (9.41) and (9.42), can be expressed as a functional of the density (Matsuzawa and Dixon 1994), and also obtained from the quadrupole moments of the experimental charge density distribution (see section 12.3.2). However, most frequently, empirical atom-atom pair potential functions like Eqs. (9.45) and (9.46) are used in the calculation of the nonelectrostatic contributions to the intermolecular interactions. 

Fig. 4 (a) Charge density distribution and (b) coordination spheres of the star-like E4 units in Ba5MgigE]3 (E = Si, Ge). ([84] Copyright Wiley-VCH Verlag GmbH Co KGaA. Reproduced with permission)... 

The electron density distribution of a known surface structure can be calculated from first-principles. Thus, the He diffraction data can be compared with theoretical results, in particular, to verify different structural models. Hamann (1981) performed first-principles calculations of the charge-density distributions of the GaAs(llO) surface, for both relaxed and unrelaxed configurations. The He diffraction data are in excellent agreement with the calculated charge-density distributions of the relaxed GaAs(llO) surface, and are clearly distinguished from the unrelaxed ones (Hamann, 1981). 

A crude estimation of the charge-density distribution on simple metal surfaces can be made by assuming that the electron charge for each atom is spherical. Especially, as shown by Cabrera and Goodman (1972), by representing the atomic charge distribution with a Yukawa function. 

Fig. 5.1. A metal surface with one-dimensional periodicity. The lowest Fourier components of the charge-density distribution are determined by the Bloch functions at the r and the K points in reciprocal space.

The problem of the electron charge-density distribution of a surface with hexagonal symmetry has been treated by Liebsch, Harris, and Weinert (1984). Similar to previous cases, the oo(z) term in Eq. (5.41) comes mainly from the Bloch functions near E, whose lowest Fourier component is ... 

Since the application of pressure may modify strongly the charge density distribution in a solid, and therefore affects the orbital more than the spin moment, magnetic form factors and magnetic anisotropy may become much more pressure-dependent than usually assumed. 

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