Conjugated circuit theory

As it turns out though even the simplified VB-theoretic formulations giving rise to conjugated-circuit theory or even just Kekule-structure enumeration, may become challenging for sufficiently large (perhaps formally infinite) systems, or for non-Kekulean (i.e., radicaloid) systems. It might oft be convenient if explicit enumeration of Kekule structures could be avoided. Notably for such cases there are some few alternative sorts of means by which to obtain some partial information about the system, within a VB-theoretic context. 

Fig. 2. The resonance energy per site, relative to graphite, computed from conjugated circuit theory as a function of p, the number of bonds contained in two pentagonal rings.

The intimate contact with conjugated circuits theory also may be indicated. This theory concerns a formulation for the resonance energy of molecular structures G which support at least one (fully paired) Kekule structure. Within a Kekule structure k on G, a conjugated n-circuit is defined to be a cycle (in G) which exhibits alternating pairing in k around the cycle. Then the resonance energy is... 

The conjugated-circuits model is one of the simplest quantitative models that has been reasonably well studied. As already mentioned this model may be motivated from classical chemical bonding theory (extended a la Clar s classical empiricist argument) or from Simpson s existential quantum-theoretic argument [ 121 ], or from a quantum chemical derivation indicated in our hierarchy of section 3.2. But beyond derivation of the model there is the question of its solution, such as we now seek to address. 

Klein DJ, Seitz WA, Schmalz TG (1990) Conjugated-Circuit Computations for Conjugated Hydrocarbons [in] Computational Chemical Graph Theory (Rouvray DH, E t). Nova, New York... 

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 above should have sufficed to show not only that our paper was not plagiarism, but that this information was available for the reviewer, who was incompetent and superficial, yet arrogant and irresponsible. Chemists who have not heard of conjugated circuits should not evaluate publications on chemical graph theory whether considering benzenoid or non-benzenoid conjugated hydrocarbons. Period. 

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)... 

This paper presents a novel and impressively revealing application of graph theory to chemistry. I am amazed how the simple concept of conjugated circuits is utilized to provide a wealth of qualitative and quantitative information about conjugated... 

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... 

Kekule valence structures have been around for over 135 years. They have received considerable attention, particularly in the early developments of the VB method from about 1935 to 1960, and yet conjugated circuits remained a hidden treasure . It was only with the revival of chemical graph theory in the mid-1960s that topological and combinatorial features of chemical structure received a fresh attention. This revival of chemical graph theory owes... 

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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