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. despite the fact that the various uncomplicated recommendations of the speculation of benzenoid hydrocarbons have their origins within the nineteenth and early twentieth century, learn during this zone continues to be in lively enlargement. the current ebook offers an overview of an important present theoretical methods to benzenoids. Emphasis is laid at the fresh advancements of those theories, which may definitely be characterised as an important enhance. Em phasis can also be laid on useful purposes instead of on "pure" idea. The booklet assumes just some common wisdom of natural and actual chemistry and calls for no unique mathematical education. consequently we are hoping that undergraduate scholars of chemistry can be capable of persist with the textual content with none trouble. on account that natural and actual chemists are these days no longer safely acquaint ed lVith the fashionable thought of benzenoid molecules, we are hoping that they're going to locate this e-book either worthwhile and informative. Our publication is additionally aimed toward theoretical chemists, specifically these all for the "topological" positive factors of natural molecules. The authors are indebted to Dr. WERNER SCHMIDT (Ahrensburg, FRG) for important discussions. one of many authors (1. G.) thank you the Royal Norwegian Council for medical and business study for monetary aid 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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3. 9. 6 Classification According to the Number of Internal Vertices or the Number of External Vertices, and Enumeration of Chemical Isomers An important classification of benzenoid systems follows their number of internal vertices. Then" the class defined by n i = 0 is coincident with the class of catacondensed benzenoid systems. Benzenoid systems with odd numbers n i , viz. 1,3,5, ... , are necessarily oJJVious non-Kekuleans. Systems with n i = 2,4,6, ... may be either Kekulean or non-Kekulean.
4. 5. 5 Pericondensed Benzenoid Systems The pericondensed benzenoid systems also may be obtained by specific generation. One starts with phenalene, the smallest pericondensed system, and executes the additions of all kinds: one-, two-, three-, four-, and five-contact additions. 4 Enumeration 38 It is more interesting that the classes of normal and normal pericondensed benzenoid systems also seem to be available from specific generations. The principles are based on a conjecture that says any normal benzenoid with h + 1 hexagons may be generated by adding one hexagon to a normal benzenoid with h hexagons (CYVIN and GUTMAN 1986a)*.
6 Classification According to the Number of Internal Vertices or the Number of External Vertices, and Enumeration of Chemical Isomers An important classification of benzenoid systems follows their number of internal vertices. Then" the class defined by n i = 0 is coincident with the class of catacondensed benzenoid systems. Benzenoid systems with odd numbers n i , viz. 1,3,5, ... , are necessarily oJJVious non-Kekuleans. Systems with n i = 2,4,6, ... may be either Kekulean or non-Kekulean. Introduce the notation * external vertices = n e • Then ne is also the number of edges of the perimeter.