Cata-condensed system

John, P.E., Malhon, R.B. and Gutman, I. (1998). An Algorithm for Counting Spanning Trees in Labeled Molecular Graphs Homeomorphic to Cata-Condensed Systems. J.Chem.Inf Corn-put. ScL, 38,108-112. 

In the present review we shall not aim at such exhaustive enumerations of all possible systems, but we shall expand the ring sizes to include also four- and eight-membered rings, which were also included in the preceding section. Stmctures of the systems that will be discussed in this section are presented in Fig. 8.20 (bicyclic and tricyclic cata-condensed systems). Fig. 8.21 (tetracyclic cata-condensed systems) and Fig. 8.22 (peri-condensed systems). 

A comparison of equations (4) and (5) shows that the extension of the cata-condensed system by one benzene ring in both neutral and protonated azides leads to a bathochromic shift of the band by 6400 cm" on average. 

All that is needed to complete the canonical name is to locate the remaining bonds, as well as the location of the hydrogen atoms, by the above described system. For example, Figure 10 illustrates the names of the seven tetrabenzenes (5 cata-condensed, 1 peri-condensed and 1... 

The structural parameter Ham/Car, which gives the ratio of substitutable edge atoms to total aromatic atoms, is important because it is a measure of the average aromatic ring system which is independent of molecular weight measurements. Figure 2 shows the Ham/Car values for some typical 1-7 cata-condensed aromatic ring systems. When the Ham/... 

The role of Young diagrams in the ordering of chemical structures is explained by their relation to alkane hydrocarbons and unbranched cata-condensed benzenoid systems. 

The 4ti + 2 rule appears to ax)piy not only to monocyclic systems, but also to cata-condensed hydrocarbons, in which every unsaturated carbon atom lies on the perimeter of the molecule. An example is the azulene molecule which may be regarded as a conjugated cycle of ten bonds with a relatively unimportant cross-link. 

To reveal the effect of the size and charge on azide photoactivity, the structures of linear cata-condensed heteroaromatic azides from azidopyridine to azidoazahexacene (the size of aromatic -system from 6 to 26 e) are calculated by semiempirical (PM3), ab initio (HF/6-31G ) and DFT (B3LYP/6-31G ) methods. Joint consideration of the experimental and quantum-chemical data results in the conclusion that the azide photoactivity depends on the nature of molecular orbital (MO) that is filled in the lowest excited singlet (Si) state. If the antibonding cnn -MO, which is localized on the azido group and is empty in the ground (So) state, is filled the Si state, the azide is photoactive (cp > 0.1). However, when the size of the Ti-system increases above a certain threshold, aromatic -MO is filled instead of the aNN -MO in the Si state, and the azide becomes photoinert (

positively charged azides, respectively. 

Thus, heteroaromatic azides proved to be convenient objects for studying general structure-reactivity relationship in aromatic azide photochemistry. On the example of the series of cata-condensed heteroaromatic azides from azidopyridine to azidoazahexacene (the size of aromatic 7t-system from 6 to 26 e), the size and charge effects, that is, the dependence of photodissociation quantum yield on the size of the azide 7t-system and its charge, were investigated both quantum-chemically and experimentally. These effects are interrelated the size effect depends on the charge of the azide molecule and vice versa, the charge effect depends on the size of the azide 7t-system. 

This count includes benzenoid hydrocarbons that would be unstable by having eight or more linearly fused benzene rings. For comparison, the total number of peri-condensed benzenoids with n = benzene rings is about twice the number of cata-condensed benzenoids (A/ = 41 764), to which one should add 78 350 non-Kekulean structures (systems for which one cannot write Kekule valence structures), giving a total of just over 120 000 possible structures for analysis. 

Definition A cata-condensed benzenoid hydrocarbon is a system built from fused benzene rings such that two adjacent rings have no other common adjacent rings. 

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