By Professor Dr. Ivan Gutman, Professor Dr. Sven Josef Cyvin (auth.)
In the final hundred years benzenoid hydrocarbons have continually attracted the eye of either experimental and theoretical chemists. even if the various uncomplicated options of the speculation of benzenoid hydrocarbons have their origins within the nineteenth and early twentieth century, study during this quarter continues to be in lively growth. the current publication offers an summary of crucial present theoretical techniques to benzenoids. Emphasis is laid at the contemporary advancements of those theories, that may definitely be characterised as an important boost. Em phasis can also be laid on sensible purposes instead of on "pure" conception. The ebook assumes just some straightforward wisdom of natural and actual chemistry and calls for no unique mathematical education. hence we are hoping that undergraduate scholars of chemistry might be capable of persist with the textual content with none hassle. considering that natural and actual chemists are these days no longer adequately acquaint ed lVith the trendy idea of benzenoid molecules, we are hoping that they're going to locate this publication either valuable and informative. Our publication is usually aimed toward theoretical chemists, in particular these occupied with the "topological" gains of natural molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for invaluable discussions. one of many authors (1. G.) thank you the Royal Norwegian Council for clinical and commercial learn for monetary help in the course of 1988, which enabled him to stick on the collage of Trondheim and write the current ebook. Trondheim, July 1989 Ivan Gutman Sven J. Cyvin Contents bankruptcy 1 Benzenoid Hydrocarbons .
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Additional resources for Introduction to the Theory of Benzenoid Hydrocarbons
Below is a schematic survey. -. I I 3. Benzenoids ofD2h and C2h symmetries fall into two categories: (i) the system has a central hexagon; (ii) the center bisects an edge which is called the central edge. 7 More about Symmetry 4. A benzenoid of C2v symmetry has no center, but a unique symmetry axis which is two-fold. ) This axis either bisects edges (a), or passes through vertices and edges (b). The benzenoid may always be oriented (within the usual conventions) so that this axis is (a) horizontal or (b) vertical.
Usually, but not always, the number of hexagons (h) is the leading parameter. Thus the enumeration for h = 1,2, 3,4, etc. is to be executed. 1 shows the results of enumerations for h = 2, 3, and 4, which account for all possible benzenoid systems with these numbers of hexagons. For larger h values, it is of interest to subdivide the total amount of benzenoids into different classes. In this connection we speak about classification. The enumeration ofbenzenoid systems may be traced back to KLARNER (1965), who followed up a suggestion of GOLOMB (1954).
N. = 0 1- catacondensed benzenoid system n. = 2 1- n. 3 Coloring of Vertices Any hexagon of a catacondensed benzenoid system is of the mode L 1 , L 2 , A 2 , or A 3. If A3-modes are absent, then the catacondensed system is unbranched. Otherwise it is branched. 3 Coloring of Vertices The vertices of a benzenoid system can be divided in to two groups, such that vertices from the same group are never adjacent. It is customary to speak about coloring of vertices, which means that the vertices are colored by two colors (say black and white), so that adjacent vertices never have the same color.