The Difference in HMO and PPP Bond Orders

The Pariser-Parr-Pople molecular orbital calculations, as already mentioned earlier in Chapter 2, consider contributions to MO arising from electron repulsions. The resulting calculations produced more reliable % electron molecular orbitals in comparison to the Hiickel MO approach, which completely ignore electron-electron repulsions. The Coulson bond orders, based on PPP MO wavefunctions, are thus expected to be different and better than Coulson bond orders based on HMO. A comparison between the two MO bond order models could have been done in 1953 when PPP was introduced, but it waited almost 10 years for its first consideration [94,95]. The comparison is of interest because all CC bonds need not be equally affected, and the comparison may point to changes in molecular geometry due to the influence of the % electron-electron repulsion. 

FIG U RE 3.8 Fries structures for a selection of smaller benzenoid hydrocarbons. Anthracene, pyrene, and ovalene have two Fries structures. 

This result, which even today appears not to be widely known, is very interesting and instructive. Unexpectedly, a comparison of two distinct MO calculations offers information of considerable interest for the VB model. In VB calculations, the starting point is the assumption that all Kekuld valence structures have the same weight. The Fries rule suggests that some Kekuld valence structures appear to be more important than others. 

A simple new weighting scheme, for example, could be to take the count of rings having three C=C bonds as the weight of Kekule valence structures. The model can 

FIGURE 3.9 The weights of Kekule valence structures of smaller benzenoid hydrocarbons based on the count of benzene rings with three C=C bonds. 

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Pauling bond orders were correlated with experimental CC bond lengths in numerous benzenoid hydrocarbons and have offered insights into the variations in CC bonds in these molecules. Pauling bond orders found additional application in quantum chemistry whether used alone or combined with their counterpart in HMO, the Coulson bond orders [21], One such illustration, outlined in Chapter 3 in the section "The Difference in HMO and PPP Bond Orders showed that the differences between the simple Huckel MO calculations and more elaborate self-consistent-field MO calculations, known as the Pariser-Parr-Pople MO method [22], points to so-called Fries valence structures. These are Kekule valence structures that have the largest number of benzene rings with three C=C bonds [23]. Pauling bond orders continue to be of interest in structural chemistry. For example, recently S. Narita and... 

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