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Spanning Fullerenes as Units in Crystal Networks

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Topological Modelling of Nanostructures and Extended Systems

Part of the book series: Carbon Materials: Chemistry and Physics ((CMCP,volume 7))

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Abstract

Fullerenes are molecules consisting of tri-connected polyhedral cages of various covering. Spanning fullerenes can be obtained by deleting some atoms or bonds, thus resulting in open structures with di-connected atoms which can further join to atoms of the same or different repeating units in construction of crystal- or quasicrystal-like networks. In this chapter, a variety of spanning fullerenes, designed either by opening cages or by sequences of map operations, are used to build more complex nanostructures. Energetics of some spanning fullerenes has been calculated on optimized structures at Hartree-Fock and/or DFT level of theory. The topology of crystal networks is described in terms of Omega polynomial.

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References

  • Ashrafi AR, Jalali M, Ghorbani M, Diudea MV (2008) MATCH Commun Math Comput Chem 60:905

    CAS  Google Scholar 

  • Benedek G, Vahedi-Tafreshi H, Barborini E, Piseri P, Milani P, Ducati C, Robertson J (2003) Diamond Relat Mater 12:768

    Article  CAS  Google Scholar 

  • Blase X, Benedek G, Bernasconi M (2010) In: Colombo L, Fasolino A (eds) Computer-based modeling of novel carbon systems and their properties. Beyond nanotubes. Springer, Dordrecht, p 171

    Google Scholar 

  • Bonnet O (1853) CR Acad Sci Paris 37:529

    Google Scholar 

  • Cysewski P, Szefler B (2010) J Mol Model 16:1709

    Article  CAS  Google Scholar 

  • Diudea MV (2004) Forma (Tokyo) 19:131

    Google Scholar 

  • Diudea MV (2005) J Chem Inf Model 45:1002

    Article  CAS  Google Scholar 

  • Diudea MV (2006) Carpath J Math 22:43

    Google Scholar 

  • Diudea MV (2010a) Nanomolecules and nanostructures – polynomials and indices, vol 10. University of Kragujevac, Serbia

    Google Scholar 

  • Diudea MV (2010b) Int J Chem Model 2:155

    CAS  Google Scholar 

  • Diudea MV (2010c) MATCH Commun Math Comput Chem 63:247

    CAS  Google Scholar 

  • Diudea MV (2010d) Studia Univ Babes Bolyai Chemia 55(4):11

    CAS  Google Scholar 

  • Diudea MV, Katona G (1999) In: Newkome GA (ed) Advances in dendritic macromolecules. JAI Press Inc. Stamford, Connecticut, vol 4, p 135

    Google Scholar 

  • Diudea MV, Klavžar S (2010) Acta Chim Slov 57:565

    CAS  Google Scholar 

  • Diudea MV, Nagy CL (2007) Periodic nanostructures. Springer, Dordrecht

    Book  Google Scholar 

  • Diudea MV, Petitjean M (2008) Symmetry Cult Sci 19(4):285

    Google Scholar 

  • Diudea MV, Gutman I, Jäntschi L (2002) Molecular topology. NOVA, New York

    Google Scholar 

  • Diudea MV, John PE, Graovac A, Primorac M, Pisanski T (2003) Croat Chem Acta 76:153

    CAS  Google Scholar 

  • Diudea MV, Cigher S, Vizitiu AE, Ursu O, John PE (2006a) Croat Chem Acta 79:445

    CAS  Google Scholar 

  • Diudea MV, Stefu M, John PE, Graovac A (2006b) Croat Chem Acta 79:355

    CAS  Google Scholar 

  • Diudea MV, Cigher S, John PE (2008) MATCH Commun Math Comput Chem 60:237

    Google Scholar 

  • Diudea MV, Cigher S, Vizitiu AE, Florescu MS, John PE (2009) J Math Chem 45:316

    Article  CAS  Google Scholar 

  • Diudea MV, CsL N, Ilić A (2011) In: Putz MV (ed) Carbon bonding and structures. Springer, Dordrecht/Heidelberg/London/New York, p 273

    Google Scholar 

  • Diudea MV, Szefler B (2012) Nanotube junctions and the genus of multi-tori. Phys Chem Chem Phys 14:8111–8115

    Google Scholar 

  • Djoković DŽ (1973) J Comb Theor Ser B 14:263

    Article  Google Scholar 

  • Euler L (1758) Novi Commun Acad Sci Imp Petrop 4:109

    Google Scholar 

  • Gaussian 09, (2009) Revision A.1, Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam NJ, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ, Gaussian Inc, Wallingford

    Google Scholar 

  • Haddon RC (1987) J Am Chem Soc 109:1676

    Article  CAS  Google Scholar 

  • Haddon RC (1990) J Am Chem Soc 112:3385

    Article  CAS  Google Scholar 

  • Harary F (1969) Graph theory. Addison – Wesley, Reading

    Google Scholar 

  • Hargittai M, Hargittai I (2010) Symmetry through the eyes of a chemist. Springer, Dordrecht/ London/New York/Heidelberg, p 488

    Google Scholar 

  • John PE, Vizitiu AE, Cigher S, Diudea MV (2007) MATCH Commun Math Comput Chem 57:479

    Google Scholar 

  • Klavžar S (2008) MATCH Commun Math Comput Chem 59:217

    Google Scholar 

  • Krygowski TM, Ciesielski A (1995) J Chem Inf Comput Sci 35:203

    Article  CAS  Google Scholar 

  • Krygowski TM, Cyranski M (1996) Tetrahedron 52:1025564

    Google Scholar 

  • Lenosky T, Gonze X, Teter M, Elser V (1992) Nature 355:333

    Article  CAS  Google Scholar 

  • Levine D, Steinhardt PJ (1984) Phys Rev Lett 53:2477

    Article  CAS  Google Scholar 

  • Mackay AL (1981) Kristallografiya (Sov Phys Chrystallogr) 26:910 (517)

    Google Scholar 

  • Mackay AL, Terrones H (1991) Nature 352:762

    Article  Google Scholar 

  • Nagy CL, Diudea MV (2009) Nano studio software. Babes-Bolyai University, Cluj

    Google Scholar 

  • Nagy K, Nagy CL, Diudea MV (2011) MATCH Commun Math Comput Chem 65:163

    CAS  Google Scholar 

  • O’Keeffe M, Adams GB, Sankey OF (1992) Phys Rev Lett 68:2325

    Article  Google Scholar 

  • Schwarz HA (1865) Ãœber Minimalflächen, Monatsber. Berlin Akad

    Google Scholar 

  • Schwarz HA (1890) Gesammelte Matematische Abhandlungen. Springer, Berlin

    Book  Google Scholar 

  • Stefu M, Diudea MV (2005) CVNET software. Babes-Bolyai University, Cluj

    Google Scholar 

  • Stefu M, Diudea MV, John PE (2005) Studia Univ Babes Bolyai Chemia 50(2):165

    CAS  Google Scholar 

  • Szefler B, Diudea MV (2012) Polybenzene revisited. Acta Chim Slov 59:795–802

    Google Scholar 

  • Szefler B, Saheli M, Diudea MV (2012a) Sumanene units in P-type surface networks. Acta Chim Slov 59:177–182

    Google Scholar 

  • Szefler B, Ponta O, Diudea MV (2012b) Energetics of polybenzene multi tori. J Molec Struct 1022:89–93

    Google Scholar 

  • Szefler B, Diudea MV (2013) Strain in Platonic fullerenes. Struct Chem. doi:10.1007/s11224-013-0244-y

  • Terrones H, Mackay AL (1993) Chem Phys Lett 207:45

    Article  CAS  Google Scholar 

  • Vizitiu AE, Cigher S, Diudea MV, Florescu MS (2007) MATCH Commun Math Comput Chem 57:457

    Google Scholar 

  • Winkler PM (1984) Discrete Appl Math 8:209

    Article  Google Scholar 

Download references

Acknowledgments

The work was supported in part by the Romanian CNCSIS-UEFISCSU project PN-II-ID-PCE-2011-3-0346 and in part by the computational grant no. 133 of PCSS (Poznań, Poland).

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Authors and Affiliations

  1. Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028, Cluj, Romania

    Mircea V. Diudea

  2. Department of Physical Chemistry, Collegium Medicum, Nicolaus Copernicus University, Kurpińskiego 5, 85-950, Bydgoszcz, Poland

    Beata Szefler

Authors
  1. Mircea V. Diudea
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  2. Beata Szefler
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Corresponding author

Correspondence to Mircea V. Diudea .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Kashan, Kashan, Iran

    Ali Reza Ashrafi

  2. , Department of Materials Science, Tor Vergata University, Rome, Italy

    Franco Cataldo

  3. , Department of Mathematics, Tarbiat Modares University, Tehran, Iran

    Ali Iranmanesh

  4. Actinium Chemical Research, Rome, Italy

    Ottorino Ori

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Diudea, M.V., Szefler, B. (2013). Spanning Fullerenes as Units in Crystal Networks. In: Ashrafi, A., Cataldo, F., Iranmanesh, A., Ori, O. (eds) Topological Modelling of Nanostructures and Extended Systems. Carbon Materials: Chemistry and Physics, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6413-2_8

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