Contact electron density

The RKKY formalism allows also to relate the changes in Neel temperature with those of the contact electron density as measured by isomer shift. The combination of eqs. (45) and (46) leads to... 

The Fermi contact density is defined as the electron density at the nucleus of an atom. This is important due to its relationship to analysis methods dependent... 

Crystal can compute a number of properties, such as Mulliken population analysis, electron density, multipoles. X-ray structure factors, electrostatic potential, band structures, Fermi contact densities, hyperfine tensors, DOS, electron momentum distribution, and Compton profiles. 

A common interpretation of the interaction of chalcogens with nucleophiles considers donation of electron density from a lone pair on the donor atom into the o- (E-X) orbital (Figure 15.1). As the degree of covalency increases, a hypervalent three-centre four-electron bond is formed. Real systems fall somewhere between secondary interactions and hypervalent (three centre - four electron) bonds. The two extremes can be distinguished by the correlation of X-E and E D distances.In the hypervalent case both bond distances decrease simultaneously, whereas in the secondary bond the distances are anticorrelated. This concept has been applied in a study of selenoquinones 15.17 (R = Ph, Me) with short Se 0 contacts,for... 

The and operators determine the isotropic and anisotropic parts of the hyperfine coupling constant (eq. (10.11)), respectively. The latter contribution averages out for rapidly tumbling molecules (solution or gas phase), and the (isotropic) hyperfine coupling constant is therefore determined by the Fermi-Contact contribution, i.e. the electron density at the nucleus. 

Another issue that can be clarified with the aid of numerical simulations is that of the recombination profile. Mailiaras and Scott [145] have found that recombination takes place closer to the contact that injects the less mobile carrier, regardless of the injection characteristics. In Figure 13-12, the calculated recombination profiles arc shown for an OLED with an ohmic anode and an injection-limited cathode. When the two carriers have equal mobilities, despite the fact that the hole density is substantially larger than the electron density, electrons make it all the way to the anode and the recombination profile is uniform throughout the sample. 

A polymer layer al a contact can enhance current How by serving as a transport layer. The transport layer could have an increased carrier mobility or a reduced Schottky barrier. For example, consider an electron-only device made from the two-polymer-layer structure in the top panel of Figure 11-13 but using an electron contact on the left with a 0.5 eV injection barrier and a hole contact on the right with a 1.2 cV injection barrier. For this case the electron current is contact limited and thermionic emission is the dominant injection mechanism for a bias less than about 20 V. The electron density near the electron injecting contact is therefore given by... 

The isotropic Fermi contact field B, which arises from a net spin-up or spin-down -electron density at the nucleus as a consequence of spin-polarization of -electrons by unpaired valence electrons [63] ... 

In this chapter we make first contact with the electron density. We will discuss some of its properties and then extend our discussion to the closely related concept of the pair density. We will recognize that the latter contains all information needed to describe the exchange and correlation effects in atoms and molecules. An appealing avenue to visualize and understand these effects is provided by the concept of the exchange-correlation hole which emerges naturally from the pair density. This important concept, which will be of great use in later parts of this book, will finally be used to discuss from a different point of view why the restricted Hartree-Fock approach so badly fails to correctly describe the dissociation of the hydrogen molecule. 

The shortest cation-anion distance in an ionic compound corresponds to the sum of the ionic radii. This distance can be determined experimentally. However, there is no straightforward way to obtain values for the radii themselves. Data taken from carefully performed X-ray diffraction experiments allow the calculation of the electron density in the crystal the point having the minimum electron density along the connection line between a cation and an adjacent anion can be taken as the contact point of the ions. As shown in the example of sodium fluoride in Fig. 6.1, the ions in the crystal show certain deviations from spherical shape, i.e. the electron shell is polarized. This indicates the presence of some degree of covalent bonding, which can be interpreted as a partial backflow of electron density from the anion to the cation. The electron density minimum therefore does not necessarily represent the ideal place for the limit between cation and anion. 

Figure 5.2 (a) Electron density contour map of the CI2 molecule (see Chapter 6) showing that the chlorine atoms in a CI2 molecule are not portions of spheres rather, the atoms are slightly flattened at the ends of the molecule. So the molecule has two van der Waals radii a smaller van der Waals radius, r2 = 190 pm, in the direction of the bond axis and a larger radius, r =215 pm, in the perpendicular direction, (b) Portion of the crystal structure of solid chlorine showing the packing of CI2 molecules in the (100) plane. In the solid the two contact distances ry + ry and ry + r2 have the values 342 pm and 328 pm, so the two radii are r 1 = 171 pm and r2 = 157, pm which are appreciably smaller than the radii for the free CI2 molecule showing that the molecule is compressed by the intermolecular forces in the solid state. 

Unlike the other alkaline earth and transition metal ions, essentially on account of its small ionic radius and consequent high electron density, Mg2+ tends to bind the smaller water molecules rather than bulkier ligands in the inner coordination sphere. Many Mg2+-binding sites in proteins have only 3, 4 or even less direct binding contacts to the protein, leaving several sites in the inner coordination sphere occupied by water, or in the phosphoryl transferases, by nucleoside di- or triphosphates. 

When the solution is formed in the places of atom-components contact, the unified electron density has to be established. The dissolving process is accompanied by the redistribution of this density between valence areas of both particles and transition of some electrons from external spheres to the neighboring ones. 

During the formation of solution and other structural interactions the same electron density must be formed in the areas of contact of atoms-components. This process is accompanied by the redistribution of electron density between valence zones of both particles and transition of a part of electrons from some outer spheres into neighboring ones. Apparently, spanning electrons of atoms do not participate in such an exchange. 

As the donor and acceptor molecules approach each other closely so that their regions of electron density overlap, electrons can be exchanged between the two molecules. This mechanism is therefore called the exchange mechanism. The electron-exchange mechanism requires a close approach (1-1.5nm), though not necessarily actual contact,... 

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