Effect of Coordination Number on a and

Can one deduce reasonable values for the effective electronegativity of the p orbitals of C upon reduction of the coordination number from 3 to 2 (i.e., C2), as in alkynes, allenes, nitriles (R—CN), or carbenes, or even to 1, as in CO, isonitriles (R—NC), or acetylides A linear extrapolation from dicoordinated O (ao2 = oc — 2.09 j ) and dicoordinated N (aN2 = oc — 0.51 PI) to dicoordinated C yields an estimate of the energy of the 2p orbital as a + 0.86 j. This value is probably too high. It places the energy of the 2p orbital of a dicoordinated carbon above that of the 2p of a tricoordinated boron, but the same is not true in the case of a dicoordinated N and a tricoordinated C, and the 

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The effect of coordination number on the Madelung constant, A, and therefore on the lattice energy, is clearly demonstrated in Table 3.4 when same-formula types are compared the larger the coordination number, the larger the value of A. This is due, of course, to the larger number of attractive interactions that are possible. On the whole, though, this variation amounts to only a few per cent of the lattice energy. 

Factors that influence ionic size include the coordination number of the ion, the covalent character of the bonding, distortions of regular crystal geometries, and delocalization of electrons (metallic or semiconducting character, described in Chapter 7). The radius of the anion is also influenced by the size and charge of the cation (the anion exerts a smaller influence on the radius of the cation). The table in Appendix B-1 shows the effect of coordination number. 

It is expected that the rotation of an active ligand will be changed when coordination with a metal ion occurs. Thus, when coordinated, /-propylene-diamine (/pn) has quite a different specific rotation than when in the pure form. Even on dilution this ligand shows something of an anomaly. The effect of coordinating /-propylenediamine on its activity has been studied by a number of investigators. Toole and O Brien have reported that molar rotation of /pn increases almost three-fold as the concentration is raised from 5 to 95 %. In contrast, there is strict linearity (constant specific rotation) observed in the rotation of metal (as well as H ) ionic salts of BCS". 

Unfortunately, the number of mechanistic studies in this field stands in no proportion to its versatility" . Thermodynamic analysis revealed that the beneficial effect of Lewis-acids on the rate of the Diels-Alder reaction can be primarily ascribed to a reduction of the enthalpy of activation ( AAH = 30-50 kJ/mole) leaving the activation entropy essentially unchanged (TAAS = 0-10 kJ/mol)" . Solvent effects on Lewis-acid catalysed Diels-Alder reactions have received very little attention. A change in solvent affects mainly the coordination step rather than the actual Diels-Alder reaction. Donating solvents severely impede catalysis . This observation justifies the widespread use of inert solvents such as dichloromethane and chloroform for synthetic applications of Lewis-acid catalysed Diels-Alder reactions. 

The moment equations of the size distribution should be used to characterize bubble populations by evaluating such quantities as cumulative number density, cumulative interfacial area, cumulative volume, interrelationships among the various mean sizes of the population, and the effects of size distribution on the various transfer fluxes involved. If one now assumes that the particle-size distribution depends on only one internal coordinate a, the typical size of a population of spherical particles, the analytical solution is considerably simplified. One can define the th moment // of the particle-size distribution by... 

Bolis et al (43) reported volumetric data characterizing NH3 adsorption on TS-1 that demonstrate that the number of NH3 molecules adsorbed per Ti atom under saturation conditions was close to two, suggesting that virtually all Ti atoms are involved in the adsorption and have completed a 6-fold coordination Ti(NH3)204. The reduction of the tetrahedral symmetry of Ti4+ ions in the silicalite framework upon adsorption of NH3 or H20 is also documented by a blue shift of the Ti-sensitive stretching band at 960 cm-1 (43,45,134), by a decrease of the intensity of the XANES pre-edge peak at 4967 eV (41,43,134), and by the extinction of the resonance Raman enhancement of the 1125 cm-1 band in UV-Raman spectra (39,41). As an example, spectra in Figs. 15 and 16 show the effect of adsorbed water on the UV-visible (Fig. 15), XANES (Fig. 16a), and UV-Raman (Fig. 16b) spectra of TS-1. 

Table 1. Calculated Values of the Effect of Particle Size on the Fraction of Atoms on the Surface and First Shell Coordination Numbers (CN) for Cuboctahedron (A/ cuboct) and Icosahedron (Alices) Models for Pt Clusters ...

The effects of particle size on the EXAFS region of the XAS spectra are reflected in the coordination numbers obtained in the fits to the EXAFS data. Figure 15 shows the EXAFS or xi ) data and corresponding Fourier transforms for a Pt foil, a Pt02... 

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