Volume 7, Issue 3, June 2019, Page: 56-61
Enumeration of Kekule Structures of Polyhex Monoradical Having Only Linear Assemblies of Benzenoid Hydrocarbons
Alphonse Emadak, Department of Inorganic Chemistry, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Robert Martin Nemba, Department of Inorganic Chemistry, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Leonel Tsassi Djoumessi, Department of Inorganic Chemistry, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Jules Cesar Epee Ndongue, Department of Inorganic Chemistry, Faculty of Science, University of Yaounde I, Yaounde, Cameroon
Received: Jun. 1, 2019;       Accepted: Jul. 9, 2019;       Published: Jul. 22, 2019
DOI: 10.11648/j.sjc.20190703.11      View  184      Downloads  92
Abstract
A mathematical process of enumeration of Kekule structures of any polybenzenoïd monoradical having only linear assemblies of benzenoid hydrocarbons is given by using a method which consisted of the excision of the radical center in order to obtain a conjugated hydrocarbon having a 12-annulene core ring appended to one or more polybenzenoïd fragments, the partition of the resulting conjugated hydrocarbon into smaller independent resonant circuits. Polyhex monoradical skeletons are obtained from a building up procedure which consists to fuse in different ways the acenaphtyl moiety with one or more polybenzenoïd fragments. Mathematical formulas are established for three cases of assemblies, one edge linear assemblies, two edges linear assemblies with two linear polybenzenoid fragments located at right angles θ = 60°, 120° or 180° and three edges linear assemblies with three linear polybenzenoid fragments located at right angles θ= 60°, 120° or 180°. Results show that the number of Kekule structures of any polybenzenoïd monoradical having only linear assemblies of benzenoid hydrocarbons increases with the number of fused benzenoids according to results compiled in the table for h equal 1, 2, 3 and 4. Difficulty to represent graphs when the number of structures increases with the number of benzenoids cannot be neglected.
Keywords
Polyhex, Enumeration, Kekule, Monoradicals, Linear Assemblies
To cite this article
Alphonse Emadak, Robert Martin Nemba, Leonel Tsassi Djoumessi, Jules Cesar Epee Ndongue, Enumeration of Kekule Structures of Polyhex Monoradical Having Only Linear Assemblies of Benzenoid Hydrocarbons, Science Journal of Chemistry. Vol. 7, No. 3, 2019, pp. 56-61. doi: 10.11648/j.sjc.20190703.11
Copyright
Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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