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Structure/formula informatics of isomeric sets of fluoranthenoid/fluorenoid and indacenoid hydrocarbons

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Abstract

The systematics of fluoranthenoid/fluorenoid and indacenoid hydrocarbons is studied. Successive circumscribing a set of isomeric structures that result in a constant number of isomers at each circumscribing step gives what is called a constant-isomer series. Constant-isomer series have a repetitive isomer number pattern in which those series with the same isomer number have a one-to-one matching in topology among their membership. The general formulas of the matching constant-isomer sets of indacenoids are reproduced by \({{\rm C}_{{{4p}^{2}}{+1}}{\rm H}_{4p+1}}\) and \({{\rm C}_{{{4p}^{2}}{+4p+3}}{\rm H}_{4p+3}}\), respectively, by successively inputting p  =  1, 2, 3, . . ., and the general formula for the unique indacenoid constant-isomers is reproduced by \({{\rm C}_{{p^{2}}{+3p+4}}{\rm H}_{2p+4}}\). Similar general formulas for the fluoranthenoid/fluorenoid hydrocarbon constant-isomer series are also presented.

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References

  1. Hagen S., Christoph H., Zimmermann G.: High temperature synthesis to bowl-shaped subunits of fullerenes. Tetrahedron 51, 6961–6970 (1995)

    Article  CAS  Google Scholar 

  2. Han J., Jaffe R.: Energetics and geometries of carbon nanoconic tips. J. Chem. Phys. 108, 2817–2823 (1998)

    Article  CAS  Google Scholar 

  3. Dias J.R.: Handbook of Polycyclic Hydrocarbons. Part B. Polycyclic Isomers and Heteroatom Analogs of Benzenoid Hydrocarbons. Elsevier, New York (1988)

    Google Scholar 

  4. Dias J.R.: Series of fluorenoid/fluoranthenoid hydrocarbons having a constant number of isomers. Chem. Phys. Lett. 185, 10–15 (1991)

    Article  CAS  Google Scholar 

  5. Dias J.R.: Studies in deciphering the information content of chemical formulas: a comprehensive study of fluorenes and fluoranthenes. J. Chem. Inf. Comput. Sci. 32, 2–11 (1992)

    CAS  Google Scholar 

  6. Dias J.R.: Deciphering the information content of chemical formulas: chemical and structural characteristics and enumeration of indacenes. J. Chem. Inf. Comput. Sci. 32, 203–209 (1992)

    CAS  Google Scholar 

  7. Dias J.R.: Indacenoid isomers of semibuckminsterfullerene (buckybowl) and their topological characteristics. J. Chem. Inf. Comput. Sci. 35, 148–151 (1995)

    CAS  Google Scholar 

  8. Fowler P.W., Mithchell D.: Electronic and steric factors in the stability of a protofullerene framework: indacenoid isomers of C30H12. J. Chem. Inf. Comput. Sci. 35, 874–878 (1995)

    CAS  Google Scholar 

  9. Cyvin S.J.: Generalization of extremal hexagonal animals. J. Math. Chem. 9, 389–390 (1992)

    Article  Google Scholar 

  10. Cyvin S.J.: Graph-theoretical studies on fluoranthenoids and fluorenoids. Part 1. J. Molec. Struct. (Theochem) 262, 219–231 (1992)

    Article  Google Scholar 

  11. Cyvin S.J., Cyvin B.N., Brunvoll J.: Graph-theoretical studies on fluoranthenoids and fluorenoids. Part 2. J. Molec. Struct. (Theochem) 281, 229–236 (1993)

    Article  Google Scholar 

  12. Cyvin S.J., Cyvin B.N., Brunvoll J.: General formulations for some polycyclic hydrocarbons. Constant-isomer series and a formula index. Chem. Phys. Lett. 201, 273–277 (1993)

    Article  CAS  Google Scholar 

  13. Brunvoll J., Cyvin B.N., Cyvin S.J., Brinkmann G., Bornhoft J.: Enumeration of chemical isomers of polycyclic conjugated hydrocarbons with six-membered and five-membered rings. Z. Naturforsch. 51a, 1073–1078 (1996)

    Google Scholar 

  14. Bally T., Chai S., Neuenschwander M., Zhu Z.: Pentalene: formation, electronic, and vibrational stucture. J. Am. Chem. Soc. 119, 1869–1875 (1997)

    Article  CAS  Google Scholar 

  15. Scott L.T., Necula A.: Synthesis and characterization of the three dicyclopentapyrenes. J. Org. Chem. 61, 386–388 (1996)

    Article  CAS  Google Scholar 

  16. Hagan S., Bratcher M.S., Erickson M.S., Zimmeremann G., Scott L.T.: Novel syntheses of three C30H12 bowl-shaped polycyclic aromatic hydrocarbons. Angew. Chem. Int. Ed. Engl. 36, 406–408 (1997)

    Article  Google Scholar 

  17. Sarobe M., Jenneskens L.W.: Benz[mno]aceanthrylene, a transient intermediate for cyclopenta[cd]pyrene. J. Org. Chem. 62, 8247–8250 (1997)

    Article  CAS  Google Scholar 

  18. Tsefrikas V.M., Scott L.T.: Geodesic polyarenes by flash vacuum pyrolysis. Chem. Rev. 106, 4868–4884 (2006)

    Article  CAS  Google Scholar 

  19. Harary F., Harborth H.: Extremal animals. J. Combinat. Inf. System Sci. 1, 1–8 (1976)

    Google Scholar 

  20. Brunvoll J., Cyvin B.N., Cyvin S.J.: Enumeration of poly-5-catafusenes representing a class of catacondensed polycyclic conjugated hydrocarbons. J. Chem. Inf. Comput. Sci. 36, 91–99 (1996)

    CAS  Google Scholar 

  21. Cyvin S.J., Cyvin B.N., Brunvoll J., Fuji Z., Xiaofeng G., Tosić R.: Graph-theoretical studies on fluoranthenoids and fluorenoids: enumeration of some catacondensed systems. J. Molec. Struct. (THEOCHEM) 104, 179–185 (1993)

    Article  CAS  Google Scholar 

  22. Cyvin S.J., Cyvin B.N., Brunvoll J.: General formulations for some polycyclic hydrocarbons. Di-q-polyhexes. Chem. Phys. Lett. 240, 601–604 (1995)

    Article  CAS  Google Scholar 

  23. Cyvin B.N., Brunvoll J., Cyvin S.J.: Di-5-catafusenes: a subclass of indacenoids. MATCH Commun. Math. Computer Chem. 33, 35–46 (1996)

    CAS  Google Scholar 

  24. Cyvin S.J., Brunvoll J., Cyvin B.N.: Supplementary notes on indacenoids with application to semibuckminsterfullerene. MATCH Commun. Math. Computer Chem. 33, 47–56 (1996)

    CAS  Google Scholar 

  25. Ge M., Sattler K.: Observation of fullerene cones. Chem. Phys. Lett. 220, 192–196 (1994)

    Article  CAS  Google Scholar 

  26. Sattler K.: Scannig tunneling microscopy of carbon nanotubes and nanocones. Carbon 33, 915–920 (1995)

    Article  CAS  Google Scholar 

  27. Ebbessen T.W.: Cones and tubes; geometry in the chemistry of carbon. Acc. Chem. Res. 31, 558–566 (1998)

    Article  Google Scholar 

  28. Balaban A.T., Klein D.J.: Graphitic cones. Carbon 32, 357–359 (1994)

    Article  CAS  Google Scholar 

  29. Klein D.J., Balaban A.T.: The eight classes of positive-curvature graphitic nanocones. J. Chem. Inf. Model. 46, 307–320 (2006)

    Article  CAS  Google Scholar 

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  1. Department of Chemistry, University of Missouri, Kansas City, MO, 64110-2499, USA

    Jerry Ray Dias

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  1. Jerry Ray Dias
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Dias, J.R. Structure/formula informatics of isomeric sets of fluoranthenoid/fluorenoid and indacenoid hydrocarbons. J Math Chem 48, 313–329 (2010). https://doi.org/10.1007/s10910-010-9671-9

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  • DOI: https://doi.org/10.1007/s10910-010-9671-9

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