Bond valences electron density

In an effort to emphasize the valence structure of chemical bonds, valence electron density maps have been constructed.9 In these studies the core electron density (the spin restricted Hartree-Fock Is orbital product for a first row atom) is assumed invariant to chemical bonding and is the basis of the scattering factor that is incorporated in Eq. (11). 

Figure 6. Contours of constant bonding valence electron density (calculated by adding the contributions from energy levels between -4 and 0 eV) for the most stable structure of the Li4Pb solid in a plane containing Pb atoms.

The simplest molecular orbital method to use, and the one involving the most drastic approximations and assumptions, is the Huckel method. One str ength of the Huckel method is that it provides a semiquantitative theoretical treatment of ground-state energies, bond orders, electron densities, and free valences that appeals to the pictorial sense of molecular structure and reactive affinity that most chemists use in their everyday work. Although one rarely sees Huckel calculations in the resear ch literature anymore, they introduce the reader to many of the concepts and much of the nomenclature used in more rigorous molecular orbital calculations. 

KT1 does not have the NaTl structure because the K+ ions are too large to fit into the interstices of the diamond-like Tl- framework. It is a cluster compound K6T16 with distorted octahedral Tig- ions. A Tig- ion could be formulated as an electron precise octahedral cluster, with 24 skeleton electrons and four 2c2e bonds per octahedron vertex. The thallium atoms then would have no lone electron pairs, the outside of the octahedron would have nearly no valence electron density, and there would be no reason for the distortion of the octahedron. Taken as a closo cluster with one lone electron pair per T1 atom, it should have two more electrons. If we assume bonding as in the B6Hg- ion (Fig. 13.11), but occupy the t2g orbitals with only four instead of six electrons, we can understand the observed compression of the octahedra as a Jahn-Teller distortion. Clusters of this kind, that have less electrons than expected according to the Wade rules, are known with gallium, indium and thallium. They are called hypoelectronic clusters their skeleton electron numbers often are 2n or 2n — 4. 

Since hardness and the shear modulus are usually proportional, the factors that determine the shear moduli need to be understood. The shear moduli are functions of the local polarizability and this depends on the valence electron density, as well as the energy needed to promote a valence electron to its first excited state. The latter depends on the strength of the chemical bond between two atoms. This will be discussed in more detail in Chapter 3. 

Figure 6.1 Bulk Modulus vs. Valence Electron Density (sp—bonded metals).

The carbides with the NaCl structure may be considered to consist of alternating layers of metal atoms and layers of semiconductor atoms where the planes are octahedral ones of the cubic symmetry system. (Figure 10.1). In TiC, for example, the carbon atoms lie 3.06A apart which is about twice the covalent bond length of 1.54 A, so the carbon atoms are not covalently bonded, but they may transfer some charge to the metal layers, and they do increase the valence electron density. 

Three of these compounds have cubic symmetry, while T1B2 has hexagonal symmetry. Since they are metallic, bond moduli cannot be defined for them, but valence electron densities can be. The hardnesses of the cubic titanium compounds depend linearly on their VEDs the numbers of valence electrons are (4 + 4 = 8)TiC, (4 + 3 = 7)TiN, and (4 + 2 = 6)TiO. The linear dependence is shown in Figure 11.10. A similar linear dependence on their C44s is also found (Figure 11.12). 

The redistribution of the valence electron density due to chemical bonding may be obtained from summing the multipole populations or Fourier transforming appropriately calculated structure factors, having removed the contribution from neutral spherical atoms, to produce a so-called deformation density map [2], This function was introduced by Roux et al. [23] and has been widely used since then. The deformation electron density represents the difference between the electron density of the system, p(r), and the electron... 

Although X-ray crystallography has mainly been used for structure determination in the past, the diffraction data, especially if measured carefully and to high orders, contain information about the total electron density distribution in the crystal. This may be analyzed to provide essential information about the chemical properties of molecules, in particular the characterization of covalent and hydrogen bonds, both from the point of view of the valence electron density, the Laplacian of the density and derived energy density distribution. In addition, calculation of the molecular electrostatic potential indicates direction of chemical attack as well as how molecules can interact with their environment. 

The probability of C-O bond scission within CO or CH, 0 is probably related to the adsorption geometry of these species. Whereas CO adsorbs perpendicularly on Pd(l 1 1), the C-O bond in CHO (and CH2O) species is tilted with respect to the palladium substrate (378). The tilted arrangement may allow for a better overlap between the CH O orbitals and the metal valence electron density, thus weakening the C-O bond. 

Equation (10) shows that the isomer shift IS is a direct measure of the total electronic density at the probe nucleus. This density derives almost exclusively from 5-type orbitals, which have non-zero electron densities at the nucleus. Band electrons, which have non-zero occurrence probabilities at the nucleus and 5-type conduction electrons in metals may also contribute, but to a lesser extent. Figure 3 shows the linear correlation that is observed between the experimental values of Sb Mossbauer isomer shift and the calculated values of the valence electron density at the nucleus p (0). The total electron density at the nucleus p C ) (Eq. 10) is the sum of the valence electron density p (0) and the core electron density p (0), which is assumed to be constant. This density is not only determined by the 5-electrons themselves but also by the screening by other outer electrons p-, d-, or /-electrons) and consequently by the ionicity or covalency and length of the chemical bonds. IS is thus a probe of the formal oxidation state of the isotope under investigation and of the crystal field around it (high- and low-spin Fe may be differentiated). The variation of IS with temperature can be used to determine the Debye temperature of a compound (see Eq. (13)). 

The reaction of 1,3-diboroles 4, LiMe and [ (C5Me5)RuCl 4] leads to the violet, highly air-sensitive Ru sandwich complexes 1810. The compounds 17 and 18 are derived from ferrocene and ruthenocene by formal replacement of two CH groups for B-R units. Therefore the complexes should have only 16 valence electrons (VE). However, the electronic structure of the iron compound 17, studied by EH-MO theory, exhibits a unique bonding The electron density of two B-C c orbitals participates in the bonding by... 

Figure 5. Shapes of the XeF ions based on steric activity of the nonbonding xenon valence-electron pairs. (Arrows indicate directions of maximum polarizing effect.) [These models represent the nonbonding xenon electrons in a formalistic way. In the Xe-F case the model cannot be realistic since such a cation has cylindrical symmetry. The postulated axial polarizing behavior can also be seen to be a consequence of Xe-F bond formation. Thus we can synthesize XeF by bringing F ( D) up to the spherical Xe atom. If we use a p-orbital pair of electrons of the Xe atom to form the Xe-F bond, the electron density will be diminished trans to the bond.]...

A general equation can be derived that describes the variation in direction of the valence electron density about the nucleus. The distortion from sphericity caused by valence electrons and lone-pair electrons is approximated by this equation, which includes a population parameter, a radial size function, and a spherical harmonic function, equivalent to various lobes (multipoles). In the analysis the core electron density of each atom is assigned a fixed quantity. For example, carbon has 2 core electrons and 4 valence electrons. Hydrogen has no core electrons but 1 valence electron. Experimental X-ray diffraction data are used to deri e the parameters that correspond to this function. The model is now more complicated, but gives a better representation of the true electron density (or so we would like to think). This method is useful for showing lone pair directionalities, and bent bonds in strained molecules. Since a larger number of diffraction data are included, the geometry of the molecular structure is probably better determined. 

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