Aromatic sextet theory

In sharp contrast to cyclopentadiene is cycloheptatriene (41), which has no unusual acidity. This would be hard to explain without the aromatic sextet theory, since, on the basis of resonance forms or a simple consideration of orbital overlaps. 

Many researchers tried to explain the secret of the Clar s aromatic sextet theory, or hypothesis from quantum-chemical points of view. However, those trials have been failing until the graph and combinatorial theories came to be applied to this challenging problem [9,10]. In the following discussion it will be shown how various techniques and concepts of the graph theory are useful for realizing and formulating not only the fantastic theory of Clar but also the mathematical beauty of the structural formula of aromatic hydrocarbons. 

Several applications of the BG-concept were put forward by Kirby [12, 13]. It has been shown recently [23] that the number of 2-factors of a benzenoid system equals the number of 1-factors ( = perfect matchings) of the branching graph. This latter result is of considerable relevance in Clar s aromatic sextet theory. 

Various algebraic and combinatorial aspects of Claris aromatic sextet theory are outlined in the recent book [3] and the recent reviews [50, 51, 89]. Therefore, in this paragraph we will just point out a few details related to the author s own research and mention the most recent developments in the filed. 

In most cases the ef-values closely follow the conjugation pattern anticipated by the Clar aromatic sextet theory [12, 126], Three typical examples of this kind are perylene (1), dibenzo[g,p]chrisene (2) and coronene (3) ... 

The effect of the biphenyl rule is small and is usually screened by much stronger conjugation modes (e.g. those taken into account by resonance, conjug-ated-circuit and/or Clar-aromatic-sextet theories [64]), In some exceptional cases, however, the biphenyl rule can completely invert the conjugation pattern anticipated by the classical theories. This particularly occurs in benzenoid... 

So the presented results show that the Clar hypergraph has properties quite different from the traditional molecular graph. These differences are best manifested in the case of topological indices. The Clar aromatic sextet theory was introduced without a theoretical foundation and without any mathematical formalism. Its remarkable success... 

The finding that for every benzenoid graph G another graph C G) can be constructed [139], such that Sez(G) = ln(C(G)), had already been mentioned (Theorem 4.6 3.4). The graph C(G) is of some relevance in Clar s aromatic sextet theory. The name Ciar graph has been proposed for C(G). 

Armit and Robinson introduced the notion of six-member rings in unsaturated compounds associated with the k electron aromatic sextet that bestows on them unusual stability, for which they have introduced the circle notation. Robinson later abandoned this novel model to characterize benzenoid compounds. It was Clar who not only adopted the notion of aromatic sextets, but significantly developed the model into a theory, which could explain several regularities of selected properties of these compounds. Clar s aromatic sextet theory assigns to individual benzenoid hydrocarbons novel structural formulas, which are obtained by following the rules summarized in Table 11.1. 

K. P. Vijayalakshmi and C. H. Suresh, Pictorial representation and validation of Clar s aromatic sextet theory using molecular electrostatic potentials. New J. Chem. 34 (2010) 2132-2138. 

F. Zhang, X. Guo, and H. Zhang, Advances of Clar s aromatic sextet theory and Randic s conjugated circuit model. Open Org. Chem. J. (Suppl. 1-M6) (2006) 87-111. 

Ring bond orders (RBO)—quantitative representation of Clar s aromatic sextet theory (Randid) [22]... 

Before leaving the arena of ring bond orders, let us mention that it may be of considerable interest to see how ring bond orders based on Coulson s bond orders (using HMO [16], then PPP [25], and other more advanced computations, including ab initio calculations) would parallel Clar s aromatic sextet theory. 

Suresh CH, Gadre SR (1999) Clar s aromatic sextet theory revisited via molecular electrostatic potential topography. J Org Chem 64 2505-2512... 

Here must be mentioned the aromatic sextet theory developed by Erich Clar [109], within which some Kekule stmctures are represented via Clar formulas whereas some are fully ignored. Details of Clar s theory can be found in [38, pp. 93-116] and [109, 110], but cannot be further elaborated in this survey. 

Gutman I, Radenkovic S, Antic M, Durdevic J (2013) A test of Clar aromatic sextet theory. J Serb Chem Soc 78 1539-1546... 

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