Metal crystals, electron-density distributions

Intercalation of cations into a framework of titanium dioxide is a process of wide interest. This is due to the electrochromic properties associated with the process (a clear blue coloration results from the intercalation) and to the system s charge storage capabilities (facilitated by the reversibility of the process) and thus the potential application in rocking-chair batteries. We have studied alkali-metal intercalation and ion diffusion in the Ti02 anatase and spinel crystals by theoretical methods ranging from condensed-phase ab initio to semiempirical computations [65, 66]. Structure relaxation, electron-density distribution, electron transfer, diffusion paths and activation energies of the ion intercalation process were modeled. 

In 1973, Iwata and Saito determined the electron-density distribution in crystals of [Co(NH3)6]fCo(CN)6l (37). This was the first determination of electron density in transition metal complexes. In the past decade, electron-density distributions in crystals of more than 20 transition metal complexes have been examined. Some selected references are tabulated in Table I. In most of the observed electron densities, aspherical distributions of 3d electron densities have been clearly detected in the vicinities of the metal nuclei. First we shall discuss the distributions of 3d electron density in the transition metal complexes. Other features, such as effective charge on transition metal atoms and charge redistribution on chemical bond formation, will be discussed in the following sections. 

Some Selected Measurements of Electron-Density Distributions in Crystals of Transition Metal Complexes... 

Analyses of electron density distributions have enabled the positions of major elements of high atomic weights such as iron and other transition elements to be located relative to lighter elements such as magnesium and aluminium in mineral crystal structures. The widespread availability of automated X-ray dif-fractometry and least squares refinement programs have increased the availability of site occupancy data for transition metal ions in most contemporary crystal structure refinements. 

In order to describe the cohesion in the same terms as was done for metals and noble gas crystals, electron density is proposed to accumulate in the vacant interstitial octahedral sites and the remaining tetrahedral sites. This distribution is shown for two CC4 tetrahedral units in Figure 5.17. The central carbon in the outlined tetrahedron is surrounded by an octahedron (in stippled outline) of interstitials defined by the set of vacant tetrahedral sites. 

Of great importance is the nature of surface bonding of intermediates to the metal this depends very much on the geometry and orientation of the crystal plane on which the chemisorption takes place, and on the orientation and symmetry of emergent orbitals (especially dsp hybrid orbitals at transition metal surfaces) at the metal surface as emphasized and illustrated by Bond (24, 7) (Fig. 5 A). These factors determine the geometry of coordination of the adspecies at the catalyst or electrocatalyst surface. Since that work (41), a great many papers have appeared on molecular-orbital calculations for bonding at surfaces and on surface states and electron-density distributions. 

In its treatment of ferroelectricity, the OOA introduces inaccuracies and may bring to wrong conclusions. One example is shown in Fig. 11. Applied to layered perovskite Pro.eoCao.aoMnOs, the OOA gives a bond-centered electron density distribution. The bonds are directed along axes of the primitive crystal lattice, from one metal site to another, over the distance of about 4 A (Fig. 11a). As every chemist knows, there are no true metal-to-metal 3d — 3d bonds that extend over a distance of 4 A. 

To obtain the electron density distribution it is necessary to guess, calculate or indirectly estimate the phases. Various methods have been developed to tackle the phase problem. For proteins the most common strategy is multiple isomorphous replacement in which the protein crystals are soaked in solutions containing salts of heavy metals such as mercury. 

Whereas in gases or liquids the particles are disordered and cause random. scattering, atoms or molecules in the surface layer of solids (especially crystals and metals) are very highly ordered. Especially metals exhibit extremely polarizable electron density distributions. The many Hertz dipoles show constructive interference in certain directions. At solid surfaces this leads to directional reflection, which encloses the same angle with the optical normal to the surface as the incident radiation [11], [20] (Fig. 5). Reflectance R is given by the Fresnel equation, which, for the simplest case of normal incidence and a transparent medium. is [II], [13]... 

For simple monovalent metals, the pseudopotential interaction between ion cores and electrons is weak, leading to a uniform density for the conduction electrons in the interior, as would obtain if there were no point ions, but rather a uniform positive background. The arrangement of ions is determined by the ion-electron and interionic forces, but the former have no effect if the electrons are uniformly distributed. As the interionic forces are mainly coulombic, it is not surprising that the alkali metals crystallize in a body-centered cubic lattice, which is the lattice with the smallest Madelung energy for a given density.46 Diffraction measurements... 

Fig. 1-2. Energy distribution of electrons near the Fermi level, cf> in metal crystals c = electron energy f(.i) s distribution function (probability density) ZXe) = electron state density, = occupied...

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