Dias periodic table

Benzenoid (chemical) isomers are, in a strict sense, the benzenoid systems compatible with a formula C H, = (n s). The cardinality of C HS, viz. C HS = n, s is the number of isomers pertaining to the particular formula. The generation of benzenoid isomers (aufbau) is treated and some fundamental principles are formulated in this connection. Several propositions are proved for special classes of benzenoids defined in relation to the place of their formulas in the Dias periodic table (for benzenoid hydrocarbons). Constant-isomer series for benzenoids are treated in particular. They are represented by certain C HS formulas for which n s = In Sjl = n2 52 =. .., where (nk sk) pertains to the k times circumscribed C HS isomers. General formulations for the constant-isomer series are reported in two schemes referred to as the Harary-Harborth picture and the Balaban picture. It is demonstrated how the cardinality n s for a constant-isomer series can be split into two parts, and explicit mathematical formulas are given for one of these parts. Computational results are reported for many benzenoid isomers, especially for the constant-isomer series, both collected from literature and original supplements. Most of the new results account for the classifications according to the symmetry groups of the benzenoids and their A values (color excess). 

For books on this subject, see Gutman, I. Cyvin, S.J. Introduction to the Theory of Benzenoid Hydrocarbons, Springer NY, 1989, Dias, J.R. Handbook of Polycyclic Hydrocarbons, Part A Benzenoid Hydrocarbons, Elsevier NY, 1987, Clar, E. Polycyclic Hydrocarbons, 2 vols. Academic Press NY, 1964. For a periodic table that systematizes fused aromatic hydrocarbons, see Dias, J.R. Acc. Chem. Res., 1985, 18, 241 Top. Curr. Chem., 1990, 253, 123 J. Phys. Org. Chem., 1990, 3, 765. 

Benzenoid (chemical) isomers are, in a strict sense, the benzenoid systems compatible with a formula C HS. Several invariants, including the Dias parameter, are treated and relations between them are given. Many of the relations involve upper and lower bounds. The periodic table for benzenoid hydrocarbons is revisited and new aspects of it are pointed out. In this connection some new classes of benzenoids are defined extreme-left, protrusive and circular. Extensive tables of enumeration data for benzenoid isomers are presented. Some of their forms are displayed in figures. 

In the light of these long traditions, extensive enumerations of the isomers of benzenoid hydrocarbons is a very new area. A systematic investigation can be dated to 1982 with the first paper of Dias [7] (but see also below). He published an article series in ten parts [7-16] entitled A Periodic Table for Polycyclic Aromatic Hydrocarbons and more recent works [17, 18]. With the invention of the periodic table, Dias created orderness in the chaotic myriads of chemical formulas for benzenoid hydrocarbons, which may be written. He has also written a monograph [19] with relevance to this topic and some other reviews [20-22], Two years before Dias, Elk [23] published a paper on benzenoids, which contains explicitly the enumeration of isomers up to h = 5. It seems that the work of Elk has largely been overlooked in the context of benzenoid isomer enumeration. 

Knop et al. [5] summarized the pertinent work of Dias, his periodic table for benzenoid hydrocarbons (see also below) and enumeration of isomers. Hereby these authors [5] pointed out some erroneous omissions in the material of Dias. Many other numerical errors were later detected by Cyvin [24], Brunvoll et al. [25] and Cyvin et al. [26], These works [24-26] provide a considerable amount of supplements to the enumeration data of Dias. Further supplements are found in the present work. 

In the periodic table for benzenoid hydrocarbons [7] the formulas C HS are arranged in an array with coordinates (ds, ,). The Dias parameters (ds) are found on a horizontal axis (increasing from left to right), while the numbers of internal vertices ( ) are on a vertical axis (increasing downwards). The table extends infinitely to the right and downwards. To the left the formulas form a line in the shape of an uneven staircase, which shall be referred to as the staircase-like boundary. 

Dias [16] has stretched the analogy between the periodic table for benzenoid hydrocarbons and the Mendeleev periodic table (for elements) rather far. It can be stretched still farther by comparing the position of benzene to the unique position of hydrogen in the Mendeleev table. 

We shall refer to the generation of a class of benzenoid isomers (C HS) from other classes of benzenoid isomers as aufbau. In this we follow Dias [32-34], who apparently transferred this term from the glossary which pertains to the Mendeleev periodic table for elements. 

The C HS formulas on the staircase-like boundary are those of most interest in the present chapter. Therefore an extensive listing of these formulas is given here see Fig. 9. The values of the Dias parameter (ds), which are indicated in the figure, are supposed to facilitate the identification of the positions of the different formulas in the periodic table for benzenoid hydrocarbons the same is the case for the h values. 

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