Hydrocarbons catacondensed

Under normal conditions the catacondensed hydrocarbons of molecular formula C4n+2H2n+4 adopt a crystal lattice104 shown schematically as Type A in Figure 13 in which the (rotational and translational) displacement of adjacent molecular planes to produce a symmetric sandwich configuration is prohibited by the interaction of neighboring molecules. These crystals exhibit a structured ( molecular ) fluorescence spectrum red-shifted by 100 cm-1 from the molecular spectrum observed in dilute solutions. 

Algorithms B and D enable the same to be done, in a more efficient way, for those benzenoid systems whose dualist graph is a tree (representing catacondensed benzenoid hydrocarbons). 

This type of Clar structure can be generated for a limited number of classes of catacondensed benzenoid hydrocarbons by defining an operation which resembles coloring [14] of the vertices of certain caterpillars but allows more flexibility. Namely, we define a Clar coloring [ 15] of the vertices of a caterpillar by the following steps ... 

The number of Kekule structures of benzenoid hydrocarbons, K, sometimes referred to as Kekule counts is a parameter of great interest to the mathematical chemist. A recent book by Cyvin and Gutman [34] is very informative of the size of this problem. Quite recently publications on these ounts even for unbranched catacondensed systems... 

All the above benzenoid hydrocarbons are catacondensed. For this class, corresponding to benzenoids without internal vertices, and represented by the general formula C4fl+2H2ft+4, the numbers of isomers are known up to h = 15 (when helicenes are excluded) [8] ... 

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]. 

First we will focus attention on selected topics relating to the equivalence between benzenoid hydrocarbons, and special types of graphs and other mathematical objects that we can associate with benzenoids- In particular we will explore relations involving caterpillar trees [3] associated with catacondensed benzenoids and their line graphs [17] called, as already mentioned, Clar graphs [4]. Also relations involving "boards" (known technically as polyominos) of special properties such as those associated with "king" and "rook" pieces of chess... 

Balaban, A.T. and Harary, F. (1968). Chemical Graphs. V. Enumeration and Proposed Nomenclature of Benzenoid Catacondensed Polycyclic Aromatic Hydrocarbons. Tetrahedron, 24, 2505-2516. 

Randic, M. (1997e). Resonance in Catacondensed Benzenoid Hydrocarbons. Int.J.Quant.Chem., 63,585-600. 

Randic, M. (1997e) Resonance in catacondensed benzenoid hydrocarbons. Int. J. Quant. Chem.,... 

El-Basil S (1993) Generation of Lattice Graphs An Equivalence Relation on Kekule Counts of Catacondensed Benzenoid Hydrocarbons. J Mol Struct (Theochem) 288 67-84... 

Figure 3. Examples of a variety ofPolycyclic Aromatic Hydrocarbons (PAHs) and the fullerene Cso- PAHs containing 5-ring structures, heteroatoms, catacondensed and open structures are expected to reside in interstellar space.

S. El-Basil, Generation of lattice graphs. An equivalence relation on Kekule counts of catacondensed benzenoid hydrocarbons, J. Mol. Struct. (Theochem.) 288 (1993) 67-84. 

Herndon WC, Biedermann PU, Agranat I (1998) Molecular structure parameters and predictions of enthalpies of formation for catacondensed and pericondensed polycyclic aromatic hydrocarbons. J Org Chem 63 7445-7448... 

Randid M, Balaban AT (2004) Partitioning of r-electrons in rings of polycyclic conjugated hydrocarbons. Part 1 catacondensed benzenoids. Polyc Atom Comp 24 173-193... 

Cioslowski J, Dobrowolski JC (2003) Structural dependence of thermodynamic stability of unbranched catacondensed benzenoid hydrocarbons. Chem Phys Lett 371 317-320... 

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