Polyhex hydrocarbons

CaHa98] G. Caporossi and P. Hansen, Enumeration of polyhex hydrocarbons up to h = 21, Journal of Chemical Information and Computer Science 38 (1998) 610-619. 

The reader is referred to the Number of Benzenoids and Poly hex Hydrocarbons subsection for the definition and classification of benzenoids and polyhex hydrocarbons, as well as for additional references for this class of compounds, which is only partially reviewed because of space limitations. Let us recall that the direct counting approach has difficulties with molecules that cannot be represented by tree-like structures, such as pericondensed polyhexes. Furthermore, the counting approach caimot separate nonplanar polyhexes (helicenes) from planar benzenoids. Consequently, for benzenoids and polyhexes, enumeration is not only a valuable tool that provides a concise description of the structures being enumerated, but also enumeration computes isomer numbers that cannot be derived otherwise. 

Use of Small Computers for Large Computations Enumeration of Polyhex Hydrocarbons. 

Already Balaban and Harary (1968) pointed out (in a footnote) the hypothetic possibilities to form Mobius counterparts of polyhex hydrocarbons. The Mobius versions of cydacenes and their zigzag-chain analogues are mentioned specifically elsewhere (Balaban 1980 1988), and the Kekule structure counts for these systems have been determined (Cyvin 1990). 

Hall GG, Dias JR (1989) The Recognition of Polyhex Hydrocarbon Radicals. J Math Chem 3 233... 

Knop JV, Muller WR, Szymanski K, Trinajstic N (1990a) Use of Small Computers for Large Calculations — Enumeration of Polyhex Hydrocarbons. J Chem Inf Comput Sci 30 ... 

Muller WR, Szymanski K, Knop JV, Nikoli6 S, Trinajstid N (1989) On Counting Polyhex Hydrocarbons. Croat Chem Acta 62 481... 

Trinajstid N (1990) On the Classification of Polyhex Hydrocarbons. J Math Chem 5 171... 

Polyhexes are used widely (see, for example, [Dia88, Bal95]) in organic chemistry they represent completely condensed PAH (polycyclic aromatic hydrocarbons) C Hm with n vertices (atoms of the carbon C), including m vertices of degree two, where atoms of the hydrogen H are adjoined (see Figure 7.1). 

If two polyhexes have the same number of edges q, then they must be isomers. Note that the number of edges is odd for every other column in the Formula Periodic Table for Benzenoid Hydrocarbons (PAH6s). Thus benzenoid hydrocarbons having formulas belonging to the ds —. .., — 2,0,2,4,... column series have q = odd number. 

Balaban and Artemi wrote very recently (1990) [63]. The enumeration of polycyclic benzenoid hydrocarbons (polyhexes, or benzenoids) continues to be a challenging problem. The field has been flourishing, not least during the very last few years, as documented by the present list of references. It contains 16 relevant publications from 1989, which can be supplemented by a few more... 

Fig. 17 is a plot of je(A) s vs- je(B) s of the corresponding equivalent polyhexes for a series of benzenoid hydrocarbons possessing one kink, i e, a hexagon with angular annelation... 

Bonchev, D. and Balaban, A.T. (1981). Topological Centric Coding and Nomenclature of Polycyclic Hydrocarbons. I. Condensed Benzenoid Systems (Polyhexes, F isenes).J.Chem.Inf.Com-put.Sci.,21,223-229. 

Cash, G.G. (1995c). Heats of Formation of Polyhex Polycyclic Aromatic Hydrocarbons from their Adjacency Matrices. J.Chem.Inf.Comput.ScL, 35, 815-818. 

D. Bonchev and A.T. Balaban, Topological Centric Coding and Nomendature of Pcdycydic Hydrocarbons. 1. Condensed Benzenoid Systems (Polyhexes, senes), J. Chem. Inf. Comput. Sd. 21 (1981), 223-9. 

Other computer programs from the same authors have been mentioned earlier in connection with the enumeration of polyhexes, and of hydrocarbons with bay regions. To compare how steeply the number of isomers increases with increasing numbers of atoms Table 11 presents the numbers of aza-benzenoids [7,122]. 

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. 

---