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Extra info for Aromaticity of Polycyclic Conjugated Hydrocarbons
Because x has to be an integer, we have to multiply the initial coefficients 1 and x by 6, getting 6 and 6x or -4, respectively. Once all non-zero entries have been assigned with the initial steps revised in this way, we find at the top that K ) 14. Benzo[ghi]perylene is too a small structure to illustrate the power of the Platt algorithm, which can be applied with similar ease to the giant benzenoids shown in Figure 12. 466,467 NBMO’s have been of interest in various problems of chemistry. First, they play an important role in HMO theory.
At the same time, non-zero amplitudes of NBMO’s on adjacent carbon centers satisfy the zero sum rule: The coefficients of NBMO’s on adjacent atoms add to zero for each carbon atom. In the case of radicals, Platt has shown that the coefficient at the terminal carbon gives K for the underlying benzenoid hydrocarbon. This is illustrated in Figure 38 for benzo[ghi]perylene. One starts by assigning zero amplitudes to alternate carbon atoms. One then assigns “1” as the amplitude to a starting carbon atom (shown in the bottom row of carbons of benzo[ghi]perylene).
A topic closely related to enumeration and construction of benzenoid hydrocarbons is enumeration and construction constrained by specific structural requirements. An example is enumeration of benzenoid hydrocarbons having a bay region. According to Jerina and co-workers,419-421 the presence of a bay region is critical for the carcinogenic activity of benzenoid hydrocarbons. :397 Definition: A bay region is a local structural element in benzenoid hydrocarbons which involves three benzene rings arranged as in phenanthrene, of which one has to be a terminal C6H4 ring.