Abstract
Conic carbon radicals with non-trivial automorphism groups are topologically possible when the curvature originates from 1, 3 or 5 pentagons in the otherwise hexagonal graphene sheet. By splitting determinants of quotient graphs, we determine the bonding nature of the last occupied and first unoccupied Hückel orbitals of the radicals constituting the three infinite series with the most plausible topologies. Each member of the series with three pentagons at the tip has one electron in the first anti-bonding orbital, each member of the series with one or five pentagons at the tip has one vacancy in the last bonding orbital, and none of the radicals have any un-bonding orbital. Within the limits of the Hückel model, this implies, respectively, stable conic cations and anions. The quotient graphs also give the collected Hückel energy for each of the one-dimensional irreducible representations of the point groups.
Similar content being viewed by others
References
Hückel E. (1931) Z. Phys. 70: 204
Fowler P.W., Steer J.I. (1987) J. Chem. Soc. Chem. Commun. 18: 1403
Manolopoulus D.E., Woodall D.R., Fowler P.W. (1992) J. Chem. Soc. Faraday Trans. 88: 2427
X. Fan, R. Buczko, A.A. Puretzky, D.D. Geohegan, J.Y. Howe, S.T. Pantelides and S.J. Pennycook, Phys. Rev. Lett. 90 (2003) 145501-1.
Ge M., Sattler K. (1994) Chem. Phys. Lett. 220: 192
Krishnan A., Dujardin E., Treacy M.M.J., Hugdahl J. (1997). Nature 388: 451
Kværner’s patent no PCT/NO98/00093 for production of micro domain particles by use of a plasma process.
US Patent No. 6,290,753 B1 issued Sept. 18, 2001, to A. T. Skjeltorp and A. Maeland.
H. Heiberg-Andersen, in: Handbook of Theoretical and Computational Nanotechnology, eds. M. Rieth and W. Schommers (American Scientific Publishers, 2006).
Murrell J.N., Kettle S.F.A., Tedder J.M. (1978). The Chemical Bond. Wiley, New York
Mintmire J.W., Dunlap B.I., White C.T. (1992) Phys. Rev. Lett. 68: 631
Akagi K., Tamura R., Tsukada M., Itoh S., Ihara S. (1995) Phys. Rev. Lett. 74: 2307
Dresselhaus M.S., Dresselhaus G., Eklund P.C. (1995). Science of Fullerenes and Carbon Nanotubes. Academic Press, New York
Heiberg-Andersen H., Skjeltorp A.T. (2005) J. Math. Chem. 38: 589
Kroto H.W. (1987). Nature 329: 529
Klein D.J., Schmaltz T.G., Hite T.G., Seitz W.A. (1986) J. Am. Chem. Soc. 108: 1301
Schmaltz T.G., Seitz W.A., Klein D.J., Hite T.G. (1988) J. Am. Chem. Soc. 110: 1113
Taylor R. (1991) Tetrahedron Lett. 32: 3731
Taylor R., Walton R.M. (1993). Nature 363: 685
R.C. Haddon and K. Raghavachari, in: Buckministerfullerenes, eds. W.E. Billups and M.A. Ciufolini (VCH Press, New York, 1993).
Raghavachari K., Rohlfing C.M. (1993) J. Phys. Chem. 96: 2463
Ebbesen T.W. (1998) Acc. Chem. Res. 31: 558
Treacy M.M.J., Kilian J. (2001) Mater. Res. Soc. Symp. Proc. 675: 1
Cvetković D.M., Doob M., Sachs H. (1980). Spectra of Graphs. Academic Press, New York
Bhatia R. (1997). Matrix Analysis. Springer-Verlag, New York
Godsil C., Royle G. (2001). Algebraic Graph Theory. Springer-Verlag, New York
Milić M. (1964) IEEE Trans. Circuit Theory CT-11: 423
H. Sachs, Habilitationsschrift Univ. Halle, Math.-Nat. Fak. (1963)
Sachs H. (1964) Polynom. Publ. Math. Debrecen 11: 119
Spialter L. (1964) J. Chem. Doc. 4: 269
Cvetković D.M., Gutman I., Trinajstić N. (1974) J. Chem. Phys. 61: 2700
Asratian A.S., Denley T.M.J., Häggkvist R., Bollobas B. (1998). Bipartite Graphs and their Applications. Cambridge University Press, Cambridge
Gutman I., Trinajstić N. (1973) Croat. Chem. Acta 45: 539
Dewar M.S.J., Longuet-Higgins H.C. (1952) Proc. R. Soc. (London) A 214: 482
Graovac A., Gutman I., Trinajstić N., Živković (1972) Theoret. Chim. Acta 26: 67
Weyl H. (1911) Math. Ann. 71: 441
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heiberg-Andersen, H., Skjeltorp, A.T. Spectra of Conic Carbon Radicals. J Math Chem 42, 707–727 (2007). https://doi.org/10.1007/s10910-006-9103-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10910-006-9103-z