Kekuld valence-bond structures

The dissociation of hexaphenylethane leads to the formation of two triphenylmethyl radicals. With the central carbon atom in the trivalent state eight Kekuld structures are possible the nine carbon atoms in the ortho and para positions in the three rings may also be in a trivalent state and thus in all, 36 valence bond structures are possible for the free radical. As a result of the resonance among these structures there is a gain in energy of the free radical by 50 kcals, with the result that the dissociation energy of hexaphenylethane is as low as 11-12 kcals. 

The comparison of bond orders based on the HMO and PPP methods has shown some interesting results on benzenoid hydrocarbons illustrated in Figure 3.8. In this figure, are shown selected Kekuld valence structures of 10 smaller benzenoid hydrocarbons. In these structures, the bonds shown as C=C are the bonds for which Coulson bond orders based on the PPP MO have increased, suggesting an increase in CC double bond character. It is very intriguing that the results represent individual Kekule valence structures. Due to symmetry, in the case of anthracene, pyrene, and ovalene, there are two symmetry equivalent Kekuld structures similarly affected both are shown in Figure 3.8. A close look at the valence structures of Figure 3.8 shows that these are... 

In the case of benzene, both Kekuld valence structures are equivalent, being identical except for their orientation in space. In naphthalene, two of the three structures are symmetry-related, but the third structure is different. The question is How different is the symmetry non-equivalent structure With a close look at the naphthalene Kekule valence structures it is easy to see that the unique Kekule structure of naphthalene has two rings each having three C=C bonds just as have Kekule structure of benzene. The other two Kekuld valence structures of naphthalene have but a single benzene ring with three C=C bonds. 

Let us examine the seven Kekuld valence structures of benzanthracene illustrated in Figure 11.11, which have been arbitrarily labeled 1-7. We now introduce the notion of adjacency of Kekule valence structures, which depends on the distributions of C=C bonds in individual benzene rings of two structures following the rules two Kekule structures K, and are adjacent, a = 1, if C=C bonds in Kekule structures K, and are in the same location in all rings except one, where they exchange positions with C-C bonds a, = 0 otherwise. 

Occasionally, one comes across benzenoid hydrocarbons with several Kekule valence structures that have the same number of benzene rings with alternating double and single bonds however, some of those structures are distinct, that is, symmetry non-equivalent. Hence, such Kekule valence structures need not be equally important for the aromaticity of these compounds. In order to find out how important individual Kekuld valence structures are, we propose a model in which the relative weight of Kekuld valence structures is given by their contribution to molecular resonance energy (RE). 

In benzene, each carbon atom uses three valence electrons to bond to the hydrogen atom and two adjacent carbons. That leaves one valence electron, which scientists first thought was shared in a double bond with an adjacent carbon. In 1865, August Kekuld proposed that the carbon atoms in benzene were arranged in a flat ring with alternating single and double bonds between the carbon atoms. There are two possible structural representations of benzene due to resonance in which the donble bonds can form between two different carbon atoms. 

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