Geometrically nonplanar

Benzenoids and single coronoids represent two main classes of polyhexes (Sect. 2.1). The inclusion of multiple coronoids represents an extension in one direction. Classes of multiple coronoids are defined and discussed in the next chapter. Here we shall concentrate upon polyhexes without holes (as benzenoids) and those dth one hole each (as single coronoids) and discuss an extension which involves geometrically nonplanar (helicenic) systems. We shall find it expedient to define a class where the members are restricted to helicenic systems which can be represented by planar graphs. In the next section, polyhex systems which cannot be represented by planar graphs, are exemplified. 

Definition 2.5 A corohelicene (system) is a multiply connected, geometrically nonplanar (helicenic) polyhex, which is graph-theoretically planar. 

It should be made clear that the geometrical nonplanarity of helicenic polyhexes is not taken into account when the isomorphic systems of this category are enumerated and when symmetry groups are attributed to these systems. It has been ascertained, for instance, that all... 

In contrast, chromium (ITT) and cobalt(III) form 2 1 dye metal complexes that have nonplanar stmctures. Geometrical isomerism exists. The (9,(9 -dihydroxyazo dyes (22) form the Drew-Pfitzner or y rtype (23) (A = C = O) whereas o-hydroxy—o -carboxyazo dyes (24) form the Pfeiffer-Schetty or fac type (25), where A = CO 2 and C = O. 

It is often found that the ratio R (measured, for instance, by gas adsorption methods) of actual metal surface area accessible to the gas phase, to the geometric film area, exceeds unity. This arises from nonplanarity of the outermost film surface both on an atomic and a more macroscopic scale, and from porosity of the film due to gaps between the crystals. These gags are typically up to about 20 A wide. However, for film thicknesses >500 A, this gap structure is never such as completely to isolate metal crystals one from the other, and almost all of the substrate is, in fact, covered by metal. In practice, catalytic work mostly uses thick films in the thickness range 500-2000 A, and it is easily shown (7) that intercrystal gaps in these films will not influence catalytic reaction kinetics provided the half-life of the reaction exceeds about 10-20 sec, which will usually be the case. 

In contrast, chromium)III) and cobalt(IH) form 2 1 dye metal complexes that have nonplanar structures. Geometrical isomerism exists. 

Azo compound decomposition is much less susceptible to polar substituent effects, and so probably has less charge separation in the transition state,75 but is more sensitive to geometrical restrictions. Bridgehead azo compounds decompose at rates lower than expected on the basis of their tertiary nature, whereas peresters are much less strongly affected.70 The difference can be rationalized by the proposal that the transition state comes farther along the reaction coordinate in azo decomposition, so that the nonplanarity forced on the incipient radical by the ring system is felt more strongly there. 

Both of these methods may be applied to nonplanar electrodes if the results are obtained at electrolysis times sufficiently short that the diffusion layer remains thin in comparison to the radius of curvature of the nonplanar electrode surface. For example, the spherical hanging-mercurcy-drop electrode provides chronoamperometric data that deviate less than 1-2% from the linear-diffusion Cottrell equation out to times of about 1 s. With solid wire electrodes of cylindrical geometry, similar conclusions apply, but at short times surface roughness effects yields a real surface area that is larger than the geometric area. 

Geometric optimization of the dimeric mibLi systems yielded at the MP2/TZD//SCF/ SVP computing level a planar (42) and a nonplanar (43) structure, which were almost isoenergetic (relative energy ca 1 kcalmol" ) in spite of the small calculated energy difference, the authors" " proposed that the nonplanar structure 43 was the more stable at the correlated level. 

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