Coordination model

Chemical changes are not irreversible unless tliere is some fonn of dissipation in tire system. That is, tire reaction free energy must be dispersed to a number of degrees of freedom distinct from tire reaction coordinate. Models tliat include... 

The biradical model suggests a connection between the single coordinate model, emphasizing reactions on a single energy surface, and the two-coordinate model, in which the coupling between states is important. 

The Configuration Coordinate Model. To illustrate how the luminescent center in a phosphor works, a configurational coordinate diagram is used (2) in which the potential energy of the luminescent or activator center is plotted on the vertical axis and the value of a single parameter describing an effective displacement of the ions surrounding the activator, is plotted on the horizontal axis (Fig. 2). At low temperatures, near room... 

Every phase of internal coordinate modeling admits many methodological variations, and I do not attempt to review them all. I outline only the standard problems encountered in any particular domain of application and the common practical solutions. 

Wojcik, J. and Jones, A.G., 1998a. Dynamics and stability of continuous MSMPR agglomerative precipitation numerical analysis of the dual particle coordinate model. Computers and Chemical Engineering, 22, 535-545. 

The coordination model for non-aqueous solvent behaviour. R. S. Drago and K. F. Purcell, Prog. Inorg. Chem., 1964, 6, 271-322 (125). 

The X-ray structure of the dibromine complex with toluene (measured at 123 K) is more complicated, and shows multiple crystallographically independent donor/acceptor moieties [68]. Most important, however, is the fact that in all cases the acceptor shows an over-the-rim location that is similar to that in the benzene complex. In both systems, the acceptor is shifted by 1.4 A from the main symmetry axis, the shortest Br C distances of 3.1 A being significantly less than the sum of the van der Waals radii of 3.55 A [20]. Furthermore, the calculated hapticity in the benzene/Br2 complex (x] = 1.52) is midway between the over-atom (rj = 1.0) and over-bond (rj = 2.0) coordination. In the toluene complex, the latter varies from rj = 1.70 to 1.86 (in four non-equivalent coordination modes) and thus lies closer to the over-bond coordination model. Moreover, the over-bond bromine is remarkably shifted toward the ortho- and para-carbons that correspond to the positions of highest electron density (and lead to the transition states for electrophilic aromatic bromination [12]). Such an experimental location of bromine is in good agreement with the results of high level theoretical... 

There has been particular recent interest in zinc nitrate complexes as coordination models for bicarbonate binding in carbonic anhydrase. The mono- or bidentate coordination modes have been studied with tris-pyrazolyl borate complexes and can be rationalized in the context of the enzyme activity.433 Caution in this comparison is introduced by ab initio calculations on these model systems demonstrating both monodentate and bidentate coordination energy minima for nitrate binding to zinc 434... 

Single coordinate model, molecular photochemistry, 493-496 Single-surface nuclear dynamics geometric phase theory, 23-31... 

The coordination model provides a way to explain many reactions that occur in nonaqueous solvents without having to assume that autoionization takes place. As shown in Eq. (10.17), the fact that FeCl4 is produced can be explained by substitution rather than autoionization. However, as has been shown earlier in this chapter, it is sometimes useful to assume that the solvent concept is valid, and many reactions take place just as if the solvent has ionized to a slight degree into an acidic and a basic species. 

The chemistry of the specific solvents discussed in this chapter illustrates the scope and utility of nonaqueous solvents. However, as a side note, several other nonaqueous solvents should at least be mentioned. For example, oxyhalides such as OSeCl2 and OPCl3 (described in the discussion of the coordination model earlier in this chapter) also have received a great deal of use as nonaqueous solvents. Another solvent that has been extensively investigated is sulfuric acid, which undergoes autoionization,... 

Figure 56 Configuration coordinate model for higher-dimensionality polysilanes.360 Reprinted with permission from Watanabe, A. J. Organomet. Chem. 2003, 685, 122-133, 2003 Elsevier.

The dynamics of polysilane dendrimer excited states were also studied by Watanabe as mentioned above in a comparison with polysilynes,360,364 and suggested that a configuration coordinate model is applicable to the photophysics of branched silicon chains. Calculations showed a distorted geometry of the excited state localized at a branching point. 

Some emphasis is given in the first two chapters to show that complex formation equilibria permit to predict quantitatively the extent of adsorption of H+, OH , of metal ions and ligands as a function of pH, solution variables and of surface characteristics. Although the surface chemistry of hydrous oxides is somewhat similar to that of reversible electrodes the charge development and sorption mechanism for oxides and other mineral surfaces are different. Charge development on hydrous oxides often results from coordinative interactions at the oxide surface. The surface coordinative model describes quantitatively how surface charge develops, and permits to incorporate the central features of the Electric Double Layer theory, above all the Gouy-Chapman diffuse double layer model. 

Table I. Examples of Sub-Reactions Needed to Describe Overall Metal Adsorption Using Surface Coordination Models.

The four-coordinate model complex RuHCl(PH3)2 is not planar but has a saw-horse geometry withtrans phosphines and H-Ru-Cl = 101.3°. This angle illustrates that a d6 tetra coordinated complex prefers to be a piece of an octahedron with two empty coordination sites in order to keep the six electrons of the metal in nonbonding orbitals (essentially similar to the t2g set of an octahedron). 

Two configurational coordinate models, presented in Figure 11.13 and 11.14, are sufficient to allow the interpretation of the temperature dependences of the Cr3+ fluorescence in crystal materials qualitatively, even quantitatively to an extent of sufficient precision for thermometric applications, as shown in the cases of CnLiSAF, alexandrite, and ruby. In high-field-strength host crystals, two mechanisms, the thermal repopulation of the 473 and 2E states and the nonradiative process, dominate the... 

Figure 11.13. The single configurational coordinate model for Cr5 fluorescence in low-field crystals, r = configurational coordinate.

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