Symmetry, conjugated chains

The perturbation and symmetry theories can be used to find molecular orbitals of conjugated chains and to explain the aromaticity 4n + 2 rule. 

FIGURE 63.2 Essentially all carotenoids, which are widespread in nature, possess certain common chemical features — a polyisoprenoid structure, a long conjugated chain of double bonds in the central portion of the molecule, and near symmetry around the central double bond. This basic structure can be modified in a variety of ways, most prominently by cyclization of the end groups and by the introduction of oxygen functions, to yield a large family of > 600 compounds, exclusive of cis/trans isomers. 

FIGURE 1.13 Schematic representation of the one-electron energy diagram for a polaron (a) localized on a single conjugated chain and (b) delocalized over two cofacial chains. The symmetry of the orbitals and the relevant electronic excitations are indicated. 

C—C a bond to be cleft (Fig. 7.34). The LU of the C—C a part will conjugate with the HO of the n part of the ground-state polyene moiety in case of reaction, so that the orbital symmetry relations clearly determines the direction of bond fission. The direction of change is indicated by arrows. In this manner, in the thermal opening, the (4 )-chain will be... 

At present, it is common knowledge that not only the photoreactivity, but also the stereochemistry, of the photoproduct is predictable from crystallographic information of starting olefin substrates. This ability of olefinic crystals to dimerize has been widely applied to the topochemical photocycloaddition polymerization of conjugated diolefinic compounds, so called "four-center type photopolymerizations" (7,8). All the photopolymerizable diolefin crystals are related to the center of symmetry mode (centrosymmetric -type crystal) and thus give polymers having cyclobutanes with a 1,3-trans configuration in the main chain on irradiation. 

The largest component of the Y-tensor is in the conjugation direction. Therefore,.even though no particular bulk symmetry is required for nonzero x > a medium in which all conjugated polymeric chains align in the same direction should have a larger x value along the chain direction relative to that in an amorphous or disordered form of the same polymer. Studies of x in ordered or stretch-oriented polymers as discussed below confirm this prediction. Finally, the polymeric chains should pack as closely as possible in order to maximize the hyperpolarizability density and hence x ... 

Previously in Chapter 3 we introduced the Huckel molecular orbital theory and applied it to the n system of a number of conjugated polyene chains. In this section we will apply this approximation to cyclic conjugated polyenes, taking advantage of the symmetry properties of these systems in the process. 

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