Catafusenes, benzenoids

Table 16. Numbers of branched catafusenes benzenoids and helicenes...

It is interesting to compare isomeric catafusenic benzenoids such as anthracene and phenanthrene their 14 n-electrons are partitioned differently (4.75 + 4.50 + 4.75, and 5.2 + 3.6 + 5.2, respectively) and this difference accounts for their different properties. Of course, the propensity of anthracene to react with dienopWles and the unsaturated behavior of carbons 9 and 10 in both these catafusenes has subtler explanations. 

In the present section the catafusenes (catacondensed simply connected poly hexes cf. Sect. 5.1) are treated. However, in contrast to the Harary-Read numbers (first column of Table 7) we shall be interested in the numbers of unbranched and branched systems separately. The numbers of unbranched catafusenes (Table 10) are known from algebraic formulas (cf. Sect. 5.2), but now we are interested in the unbranched catacondensed benzenoids and helicenes separately. Likewise we shall treat the numbers of branched catacondensed benzenoids and helicenes separately. 

Balaban, A.T. and Artemi, C. (1989). Chemical Graphs. Part 51. Enumeration of Nonbranched Catafusenes According to the Nmnbers of Benzenoid Rings in the Catafusene and Its Longest Linearly Condensed Portion. Polycyclic Aromatic Compounds, 1,171-189. 

Balaban, A.T. (1993a). Benzenoid Catafusenes Perfect Matchings, Isomerization, Automeriza-tion. Pure ApplChem., 65,1-9. 

Isomer Enumeration of Catafusenes, C4 +2H2n+4 Benzenoid and Helicenic Hydrocarbons. 

Fig. 8.2 Examples of benzenoids and their dualist graphs trees for non-branched catafusenes (top three benzenoids), branched catafusenes (middle row), a perifusene and a coronafusene (bottom row)...

The following notation will be used throughout this review the number of carbon atoms, hence also of 71-electrons, will be denoted by n = D/2, the number of double bonds by D, the number of rings by R, and the numbers of Kekule structures by K. For benzenoid catafusenes, = 4R + 2, and their formulas are C4R+2H2R+6, or alternatively C2r 4(CH)2r+6, which immediately shows the number (2R - 4) of internal or quaternary carbon atoms participating in the fusion of rings. While clearly all benzenoids are alternant hydrocarbons, not all alternants are benzenoid (e. g. biphenylene). 

A final average of EC values over all rings then provides a global aromaticity index per benzenoid ring. We recall that all catafusenes have the molecular formula C4r+2H2r+ and that each of the n = 4R -h 2 carbon atoms contributes with one... 

In Table 8.1 we illustrate the coding of catafusenes for benzenoids with five and six condensed rings. 

Branched benzenoids Catafusenes with five condensed rings 01(.) [2/12] 1... 

All nmi-branched catafusenes have C = Cj = 0, and sj = 0. There are srane interesting correlations among r and r, illustrating the grouping of catafusenes into several classes with common structural features of their dualists, as discussed in detail in two side-by-side papers (Balaban and Randic 2(X)8 Randic and Balaban 2008). Whenever a benzenoid ring in catafusenes or perifusenes has at least three... 

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