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Enumeration of polycarborane isomers: especially dicarboranes

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Abstract

Various sorts of isomer enumeration problems are addressed in the context of polycarboranes, with special illustrative focus on the case of dicarboranes, for which then various numerical results are given. A systematic and general Pólya-theoretic methodology is used to make the computations, including some new techniques being applicable to a wide range of nano-structures built from a framework of like local subunits.

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References

  1. Müller J., Base K., Magnera T.F., Michl J.: J. Am. Chem. Soc. 114, 9721–9722 (1992)

    Article  Google Scholar 

  2. Jiang W., Harwell D.E., Mortimer M.D., Knobler C.B., Hawthorne M.F.: Inorg. Chem. 35, 4355–4359 (1996)

    Article  CAS  Google Scholar 

  3. Oliva J.M., Klein D.J., Schleyer P.V.R., Serrano-Andres L.: Pure & Appl. Chem. 81, 719–729 (2009)

    Article  CAS  Google Scholar 

  4. Yannopoulos S.N., Zouganelis G.D., Nurmohamed S., Smith J.R., Bouropoulos N., Calabrese G., Fatouros D.G., Tsibouklis J.: Nanotechnology 21, 085101 (2010)

    Article  CAS  Google Scholar 

  5. Pólya G.: Kombinatorische Anzahlbestimmungen fur Gruppen, Graphen und chemische Verbindungen. Acta Math. 68, 145–254 (1937)

    Article  Google Scholar 

  6. Pólya G., Read R.C.: Combinatorial Enumeration of Groups, Graphs, and Chemical Compounds. Springer, New York (1987)

    Book  Google Scholar 

  7. A. Kerber, Applied Finite Group Actions, 2nd Revised and Expanded Edition (Springer, Berlin, 1999); see the Wreath product on pp. 64–65, Theorem 2.2.12

  8. Harary F., Palmer E.: Graphical Enumeration. Academic Press, New York and London (1973)

    Google Scholar 

  9. Balasubramanian K.: A generalized wreath product method for enumeration of stereo and position isomers of polysubstituted organic compounds. Theore. Chim. Acta 51, 37–54 (1979)

    Article  CAS  Google Scholar 

  10. G. James, A. Kerber, page 160 and formula 4.4.10 in The Representation Theory of the Symmetric Group, Encyclopedia of of Mathematics, vol. 16, ed. by G.-C. Rota (Addison-Wesley, Reading, 1981)

  11. Balasubramanian K.: Chemical group theory techniques and applications. Chem. Rev. 85, 599–618 (1985)

    Article  CAS  Google Scholar 

  12. Bytautas L., Klein D.J.: Alkane isomer combinatorics: stereostructure enumeration and graph-invariant and molecular-property distributions. J. Chem. Inf. & Comp. Sci. 39, 803–818 (1999)

    Article  CAS  Google Scholar 

  13. Bytautas L., Klein D.J., Schmalz T.G.: All acyclic hydrocarbons: formula periodic table and property overlap plots via chemical combinatorics. New J. Chem. 24, 329–336 (2000)

    Article  CAS  Google Scholar 

  14. Cox J.D., Pilcher G.: Thermochemistry of Organic and Organometallic Compounds. Academic Press, NY (1970)

    Google Scholar 

  15. Benson S.W.: Thermochemical Kinetics. Wiley, NY (1976)

    Google Scholar 

  16. Klein D.J., Bytautas L.: Directed reaction graphs as posets. Commun. Math. & Comp. Chem. (MatCh) 42, 261–290 (2000)

    CAS  Google Scholar 

  17. Ivanciuc T., Ivanciuc O., Klein D.J.: Posetic quantitative superstructure/activity relationships (QSSARs) for chlorobenenes. J. Chem. Inf. & Model. 45, 870–879 (2005)

    Article  CAS  Google Scholar 

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Correspondence to Josep M. Oliva.

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Rosenfeld, V.R., Klein, D.J. & Oliva, J.M. Enumeration of polycarborane isomers: especially dicarboranes. J Math Chem 50, 2012–2022 (2012). https://doi.org/10.1007/s10910-012-0017-7

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  • DOI: https://doi.org/10.1007/s10910-012-0017-7

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