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A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes

Eine polycyclische konjugierte Kohlenwasserstoffe darstellende Klasse polygonaler Kohlenwasserstoffe: katakondensierte Monoheptafusene

  • Anorganische Und Physikalische Chemie
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Summary

Catacondensed monoheptafusenes consist of catafusenes annelated to a heptagon. Complete mathematical solutions are reported for the numbers of these systems. Two methods were applied: combinatorial summations and application of generating functions. Catacondensed monoheptabenzenoids (geometrically planar catacondensed monoheptafusenes) were enumerated by computer programming, and the numbers of catacondensed monoheptahelicenes (the corresponding geometrically nonplanar systems) were obtained as differences. Some of the forms of these helicenes are depicted.

Zusammenfassung

Katakondensierte Monoheptafusene bestehen aus Katafusenen, welche zu einem Heptagon verknüpft sind. Für die Zahlen der möglichen derartigen Verknüpfungen werden geschlossene mathematische Ausdrücke abgeleitet. Zwei Methoden wurden angewendet: (1) das direkte Aufsummieren der kombinatorischen Ausdrücke und (2) Summenbildung mit Hilfe von erzeugenden Funktionen. Katakondensierte Monoheptabenzenoide, darunter versteht man katakondensierte Monoheptafusene mit planarer Geometrie, wurden mittels Computersimulation abgezählt und die Zahl der katakondensierten Monoheptahelicene — dies sind die nicht planaren katakondensierten Monoheptafusene — wurden durch Differenzbildung erhalten. Einige ausgewählte Geometrien von Helicenen werden gezeigt und diskutiert.

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Authors and Affiliations

  1. Department of Physical Chemistry, The University of Trondheim, N-7034, Trondheim-NTH, Norway

    B. N. Cyvin, E. Brendsdal, J. Brunvoll & S. J. Cyvin

Authors
  1. B. N. Cyvin
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  2. E. Brendsdal
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  3. J. Brunvoll
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  4. S. J. Cyvin
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Cyvin, B.N., Brendsdal, E., Brunvoll, J. et al. A class of polygonal systems representing polycyclic conjugated hydrocarbons: Catacondensed monoheptafusenes. Monatsh Chem 125, 1327–1337 (1994). https://doi.org/10.1007/BF00811082

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  • DOI: https://doi.org/10.1007/BF00811082

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