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. notwithstanding many of the easy techniques of the speculation of benzenoid hydrocarbons have their origins within the nineteenth and early twentieth century, learn during this zone remains to be in lively growth. the current e-book presents an overview of an important present theoretical methods to benzenoids. Emphasis is laid at the fresh advancements of those theories, which could definitely be characterised as an important develop. Em­ phasis can be laid on functional purposes instead of on "pure" thought. The publication assumes just some effortless wisdom of natural and actual chemistry and calls for no targeted mathematical education. hence we are hoping that undergraduate scholars of chemistry might be in a position to keep on with the textual content with none hassle. because natural and actual chemists are these days no longer competently acquaint­ ed lVith the trendy concept of benzenoid molecules, we are hoping that they are going to locate this publication either valuable and informative. Our ebook can be aimed toward theoretical chemists, particularly these focused on the "topological" positive factors of natural molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for worthwhile discussions. one of many authors (1. G.) thank you the Royal Norwegian Council for clinical and business examine for monetary aid in the course of 1988, which enabled him to stick on the college of Trondheim and write the current ebook. Trondheim, July 1989 Ivan Gutman Sven J. Cyvin Contents bankruptcy 1 Benzenoid Hydrocarbons .

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1. This is achieved by successive additions starting with benzene, where the additions are restricted to one-contact additions only. A catacondensed benzenoid system may be unbranched or branched. These subclasses also may be generated specifically. The unbranched systems are obtained by one-contact additions to the ends of already generated members. It is presupposed that the computer program can identify the end hexagons, which is not a big problem. It is achieved, for instance, by keeping track of the last added hexagon for both ends.

1, (A-I) I}.. = 0 for at least one pair of vertices, ij. Here, A is the adjacency matrix. Finally, we have the non-Kekulean systems among the pericondensed benzenoids. When a computer program has the computation of the color excess (,1, see Chapter 3) built in, then the obvious non-Kekuleans are easily recognized by means of ,1 > O. Computerized procedures for obtaining the number of KEKULE structures (1<) are also available. Non-Kekulean benzenoids have K = O. 8. 16) h D3i1 3 4 5 6 7 8 9 10 II 12 * Unknown 1 0 0 1 0 0 1 1 0 3 C3h 0 0 0 I 0 0 5 I 0 21 C 2v 0 0 3 2 11 12 49 58 221 * Cs Total 0 1 4 26 130 659 3227 15919 78121 * 00 I I 7 30 141 671 3282 15979 78342 384568 4 Enumeration 40 addition, LI = 0, then the system examined is concealed non-Kekulean.

The D3h systems have three two-fold symmetry axes in the horizontal plane. ) All these three axes either (a) bisect a set of edges each, or (b) pass through vertices and edges. In the former case (a) one of the symmetry axes is horizontal with reference to the conventional orientation of the benzenoid, whereas in the latter case (b) one of the axes is vertical. The D3h benzenoid systems of the first kind (i) may have both types of two-fold symmetry axes described as (a) and (b). Hence, we subdivide these systems into (ia) and (ib) accordingly.

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