Formula Periodic table, for

The vast majority of aromatic compounds have a closed loop of six electrons in a ring (the aromatic sextet), and we consider these compounds first. It is noted that a formula periodic table for the benzenoid polyaromatic hydrocarbons has been developed. ... 

Formula Periodic Table for Benzenoids 3.1 Structure of Table PAH6... 

Table PAH6. Formula periodic table for benzenoid polycyclic aromatic hydrocarbons (PAH6)... 

By merging our prior aufbau concept with the Formula Periodic Table for Benzenoid Hydrocarbons (Table PAH6), the enumeration process itself will have a... 

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. 

Dias JR (1990) A Formula Periodic Table for Benzenoid Hydrocarbons and the Aujbau and Excised Internal Structure Concepts in Benzenoid Enumerations. J Math Chem 4 17-30... 

Klein DJ Periodic Tables and the Formula Periodic Table for all Acyclic Hydrocarbons. Proceedings of Wiener Conference on Periodic Tables, in press... 

Dias, J, Formula Periodic Table for Benzenoid Hydrocarbons, Top. Curr. Chem. 1990, 153, 123-143,... 

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. 

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. 

Assume a formula C HS which corresponds to a benzenoid hydrocarbon. Then the coordinates of the periodic table for benzenoid hydrocarbons are readily obtained from Eqs. (1) and (6) as... 

The formulas at the extreme left in the periodic table for benzenoid hydrocarbons, except C10H8 (naphthalene), represent exclusively strictly pericondensed benzenoids [12, 16, 21], viz. the pericondensed extreme-left benzenoids. Formulas for ds< 0 and not at the extreme left represent both strictly pericondensed and non-strictly pericondensed benzenoids. For ds > 0 there are no strictly pericondensed benzenoids [56]. 

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). 

Fig. 2. The periodic table for benzenoid hydrocarbons (dot diagram) with asterisks an asterisk indicates that the numbers of Kekulean and non-Kekulean benzenoids are known (separately) for the formula in that particular position. For the significance of the full-drawn staircase line, see the text...

The formulas in the first row of the periodic table for benzenoid hydrocarbons (C4M.2H2Ji+4) correspond to the catacondensed systems with h > 1. Since there are no other formulas above this row, all the C4h+2H2h+4 (h > 1) benzenoids are generated by the scheme (b) exclusively [16, 31]. 

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. 

In order to prove Proposition 1 (a) consider the diagram below where each box represents a formula in the periodic table for benzenoid hydrocarbons. Suppose... 

Fig. 9. Formulas (C HS) on the staircase-like boundary of the periodic table for benzenoid hydrocarbons. The formula for benzene (C6H6) is added...

The answer to the above question is therefore Look up the formula for the ground forms with the same 5 as in G, but one unit less in j. Subtract C2, which means moving two places up and one place to the right in the periodic table for benzenoids. 

The formulas of tiie binary compounds of hydrogen may be correlated with the position of the combined element in the periodic table. For the elements in the first two rows of the periodic table these compounds are the following ... 

Mendel eff had no room in his Periodic Table for an element with this atomic weight he had, however, a vacancy for one,of 9 and in his table dated 1869 (p. 170) he placed beryllium between lithium and boron, ascribing to it a valency of two. Confirmation was afforded when in 1884 Nilson and Pettersson determined the vapour density of its chloride, showing its formula to be BeCl2, and again when in 1887 Mallardf observed that crystallised beryllia is isomorphous with crystallised zinc oxide, ZnO, and must therefore have a similar structure, namely BeO. 

Applying kr and R, for purely single and double bonds, constants a and b are estimated. This formula works well for the bonds between atoms of elements in the second row of the Periodic Table. For longer bonds formula (9) is used [48]. 

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