Conjugated-circuit model, and

We will briefly review various VB approximate methods here and show that the conjugated circuits method can be related to VB approaches and that, therefore, it has a sound quantum chemistry basis. This is needed because later we will relate Clar s /r-sextet model to the conjugated circuits model and will show that, therefore, one can justify Clar s empirical approach by quantum chemical arguments. 

In chemistiy, priority is to be given to experimental facts, not to calculations. Clar has offered experimental facts to support his model of the aromatic jr-sextet, but as we know, theoretical chemists have for the most part ignored his works. Recall the opening remark by R. G. Parr in this section. That is what has happened to Clar s aromatic jr-sextet. Now, with the synthesis of helical [/j]phenylenes by Vollhardt and co-workers, we may expect additional quantum chemical computations from theoretical circles. These are welcome. However, to fully appreciate the conjugated circuits model and the work of Clar, and to accept his model of the aromatic jr-sextet, apparently requires some imagination, or at least a... 

Different circuit counts are designated as <4n+2) or (4,) and are obtained by the summation of all (4n + 2) or An) conjugated circuits. When the conjugated circuits model (CCM) is applied, the RE of a polycyclic conjugated molecule (CCMRE) may be determined as follows, taking into account that the REs are additive within the model in question (76CPL68),... 

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],... 

Several qualitative models, e.g. Platt s ring perimeter model [88], Clar s model [89] and Randic s conjugated circuits model [90-92] have either been or are frequently used for the rationalisation of their properties. All these qualitative models rationalise the properties of aromatic and anti-aromatic hydrocarbons in terms of the Hiickel [4n+2] and [4n] rules. The extra stability of a PAH, due to 7t-electron delocalisation, can also be determined, computationally or experimentally, by either considering homodesmotic relationships [36] or by the reaction enthalpy of the reaction of the PAH towards suitable chosen reference compounds [93],... 

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]. 

However, in the 4, 8 semiregular planar lattice (Fig. 2) both the angle strain and the antiaromaticity contribute to destabilization in the conjugated circuits model there are 10- and 14-membered circuits with small positive contributions R2, Rsas well as 4-, 8- and 12-membered rings with appreciable negative coefficients Qi, Q2, 03. 

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. 

Plavsic D, Nikolic S, Trinajstic N (1992) The Conjugated-Circuit Model - Application to Non—Alternant Hydrocarbons and a Comparison with Some Other Theoretical Models of Aromaticity. J Mol Struct (Theochem) 277 213... 

D.J. Klein, Graph theoretically formulated electronic-structure theory, Internet Electronic J. Mol. Des. 2 (2003) 814—834. http //www.hiochempress.com D.J. Klein and N. Trinajstic, Foundations of conjugated-circuit models. Pure Appl. Chem. 61 (1989) 2107-2115. 

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. 

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... 

Randid M, Nikolid S, Trinajstic N (1987) The conjugated circuit model on the selection of parameters for computing the resonance energies. In King RB, Rouvray DH (eds) Graph theory and topology in chemistry. Elsevier, Amsterdam, pp 429 147... 

Although the conjugated-circuit model [33] suggested that the linear [N]phenylenes are more stable than their angular isomers, the application of ah initio methods proved the opposite [126]. Schulman and Disch s examination of the problem by modem DFT methods placed the stabilization of 15 vs. 9b at 2.4 kcal mol [53]. Branched [4]phenylene 21b is the most stable of the five... 

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. 

The conjugated-circuit model is a simple valence-bond resonance-theoretic model introduced for the study of aromaticity and conjugation of polycyclic conjugated systems which can be used to compute their r-resonance energies, RE. This model is a measure of the aromaticity in conjugated systems. Developed initially for polycyclic conjugated... 

On the other hand, if a model is simple, empirical, and parametric, that does not necessarily means that it has no firm, apparently hidden link to generally accepted fundamental laws, such as those of quantum chemistry. Just as the opposite may be the case, a model that is thought to be based on basic axioms may turn out not to reflect this deep connection with quantum chemistry. It thus was found, mostly through the work of D. J. Kleln, that the conjugated circuits model has a quite firm foundation in quantum chemical principles, while as we all know, the Hiickel molecular orbital (MO) model that started as a quantum chemical model turned out to be a consequence of molecular topology, rather than an intricate interaction of r-electrons governed by the Schrodinger equation. 

The conjugated circuits model, as will be seen, offers insight into aromaticity that has been so far missing, and in that sense in our view it will be found... 

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. ... 

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