RESONANCE ENERGIES OF LARGE CONJUGATED HYDROCARBONS BY A STATISTICAL-METHOD
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We developed a theoretical method for studying the aromatic stability of large molecules, molecules having a dozen and more fused benzene rings. Such molecules have so far often been outside the domain of theoretical studies. Combining the statistical approach and a particular graph theoretical analysis, it is possible to derive the expressions for molecular resonance energy for molecules of any size. The basis of the method is enumeration of conjugated circuits in random Kekul valence structures. The method has been applied to evaluation of the resonance energies of conjugated hydrocarbons having about a dozen fused benzene rings. The approach consists of (1) construction of random Kekul valence structures, (2) enumeration of conjugated circuits within the generated random valence structures, and (3) application of standard statistical analysis to a sufficiently large sample of structures. The construction of random valence forms is nontrivial, and some problems in generating random structures are discussed. The random Kekul valence structures allow one not only to obtain the expression for molecular resonance energies (RE) and numerical estimates for RE, but also they provide the basis for discussion of local molecular features, such as ring characterization and Pauling bond orders. Copyright 1987 John Wiley & Sons, Inc.
