Benzenoids, modeling conjugated circuits

A number of computational approaches to the (G) have been developed and there have been widespread applications of the conjugated-circuits model, motivated both from Herndon s and from Randic s approaches. The applications extend even much beyond benzenoids. This is reviewed elsewhere by Randic et al. [76],... 

The successful accomplishments of Miillen and coworkers [22-25] who synthesized several giant benzenoid hydrocarbons will undoubtedly stimulate further theoretical interest in benzenoid hydrocarbons. It is not surprising that all the giant benzenoids that have been synthesized have 6n jt-electrons, which Clar predicted to be unusually stable. Now that the inverse problem of Clar structures has been solved we may expect novel theoretical developments in this area that may continue to expand experimentally beyond expectations. For example, the Conjugated Circuit Model, that has already been applied to giant benzenoids [26-28], may have to be modified so to take into account the prominent role of the Clar structures of benzenoids rather then considering all Kekule valence structures as equally important. Construction and enumeration of giant benzenoids and their Kekule valence structures has also received some attention [29, 30]. 

This particular class of hydrocarbons has lead to numerous investigations and probably deserves an entire chapter to be properly reviewed. Here we summarize only the major findings related to covmting. The reader further interested by polyhexes and benzenoids can consult the books of Gutman and Cyvin " as well as the books of Dias. These books, as well as that by Trinajstic," ° provide valuable information regarding the counting and enumeration of Kekule structures and the conjugated-circuit model, neither of which is reviewed here because of space limitations. 

The theory outlined in the present chapter has to be associated with the name of Milan Randid who discovered it (Randic 1976) and eventually elaborated it (Randic 1977a,b) and applied to numerous classes of conjugated molecules (Randic 1980,1982, Randic et al. 1987b, and the references cited therein). In what follows we expose only the conjugated circuit model for benzenoid hydrocarbons. One should, however, note that the model covers a much wider class of conjugated systems (Randic 1977a,b, 1982)... 

According to the conjugated circuit model, for m = 1, 2, 3,. .., one has to determine the number p of conjugated circuits of size 4 + 2 in all Kekule stmctures of the underlying benzenoid system, and compute the resonance energy as... 

Simpson-Herndon model, and the conjugated-circuits model. The calculation of the KSC can be performed with recurrence relationships, matrix methods, and explicit combinatorial expressions derived for a large number of classes of conjugated hydrocarbons various classes of cata-condensed benzenoid hydrocarbons honeycomb lattice strips polymers. 

Interpretation of statistical and other data on molecules. In this article in particular we will see how graph theoretical concepts, such as the conjugated circuits, the innate degree of freedom of Kekule valence structures, and the Clar structures, can all be combined to characterize the local and overall aromaticity of benzenoid hydrocarbons, fully benzenoid hydrocarbons, and fully aromatic compounds. In addition, we will see that these approaches that lead to the quantification of Clar s r-sextets model can be justified using chemical arguments. ... 

According to the statement made by Gutman and Cyvin in their book. Introduction to the Theory of Benzenoid Hydrocarbons, on p 80 in a section entitled The Conjugated Circuit Model The Theory outlined in this chapter has to be associated with the name of Milan Randic who discovered it and eventually elaborated it and applied it to numerous classes of conjugated molecules. ... 

The recursive approach is suitable for rigorous evaluation of the expression for resonance energies within the model of conjugated circuits for structurally related benzenoid hydrocarbons of increasing... 

Figure 54. Linear regression of REPE, as calculated by Jiang and (in units of J], and REPE, as derived from the conjugated circuits model (in units of electronvolts), for 27 of the benzenoids shown in Figure 53.

Figure 59. Benzenoids with K= and K = 38, respectively, illustrating a disagreement in the prediction of RE on the basis of the empirical log K relationship and the conjugated circuits model.

It may be of interest that isoconjugate benzenoid hydrocarbons necessarily have the same RE in Herndon s resonance theory VB model as in the conjugated circuits model, but generally they will have different RE in the HMO model and the TRE model, mentioned earlier. This clearly points to not only numerical but also conceptual differences between different graph theoretical models those based on the adjacency matrix (HMO) and that based on Kekule valence structures and conjugated circuits (VB). 

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