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Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

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Abstract

To gain insight into the structures and stability of F4F6 polyhedrons formed by squares and hexagons, a density functional theory study was performed on all isomers of F4F6 polyhedrons with sizes from 8 to 60. The calculated results demonstrate that the six squares tend to isolate from each other, i.e. these F4F6 polyhedrons obey the isolated square rule. Those isomers with fewer B44 bonds (square-square adjacencies) are more stable than those with more B44 bonds, i.e. they obey square adjacency penalty rule. Both of the two rules in F4F6 polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F5F6 fullerenes and can be used to screen the lowest energy isomers of F4F6 polyhedrons as IPR and PAPR do in classic fullerenes. Structural analysis demonstrates that the pyramidalization of carbon atoms at the square-square adjacencies determines the stability of corresponding structures.

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References

  1. Kroto H W, Heath J R, O’Brien S C, Curl R F, Smalley R E. C60: Buckminsterfullerene. Nature, 1985, 318: 162–163

    Article  CAS  Google Scholar 

  2. Kroto H W. The stability of the fullerenes Cn, with n = 24, 28, 32, 36, 50, 60 and 70. Nature, 1987, 329: 529–531

    Article  CAS  Google Scholar 

  3. Prinzbach H, Weiler A, Landen-berger P, Wahi F, Worth J, Scott L T, Gelmont M, Olevano D, Issendorff B. Gas-phase production and photoelectron spectroscopy of the smallest fullerene, C20. Nature, 2000, 407: 60

    Article  CAS  Google Scholar 

  4. Buhl M, Hirsch A. Spherical aromaticity of fullerenes. Chem Rev, 2001, 101: 1153–1184

    Article  CAS  Google Scholar 

  5. Xie S Y, Gao F, Lu X, Huang R B, Wang C R, Zhang X, Liu M L, Deng S L, Zheng L S. Capturing the Labile Fullerene[50] as C50Cl10. Science, 2004, 304: 699

    Article  CAS  Google Scholar 

  6. Chen Z, King R B. Spherical aromaticity: Recent work on fullerenes, polyhedral boranes, and related structures. Chem Rev, 2005, 105: 3613–3642

    Article  CAS  Google Scholar 

  7. Lu X, Chen Z. Curved Pi-conjugation, aromaticity, and the related chemistry of small fullerenes <C60 and single-walled carbon nanotubes. Chem Rev, 2005, 105: 3643–3696

    Article  CAS  Google Scholar 

  8. Diaz-Tendero S, Martin F, Alcami M. Structure and electronic properties of fullerenes C52 q+: Is C52 2+ an exception to the pentagon adjacency penalty rule? Chem Phys Chem, 2005, 6: 92–100

    CAS  Google Scholar 

  9. Campbell E E B, Fowler P W, Mitchell D, Zerbetto F. Increasing cost of pentagon adjacency for larger fullerenes. Chem Phys Lett, 1996, 250: 544–548

    Article  CAS  Google Scholar 

  10. Albertazzi E, Domene C, Fowler P W, Heine T, Seifert G, Alsenoyd C V, Zerbettoe F. Pentagon adjacency as a determinant of fullerene stability. Phys Chem Chem Phys, 1999, 1: 2913–2918

    Article  CAS  Google Scholar 

  11. Slanina Z, Ishimura K, Kobayashi K, Nagase S. C72 isomers: The IPR-satisfying cage is disfavored by both energy and entropy. Chem Phys Lett, 2004, 384: 114–118

    Article  CAS  Google Scholar 

  12. Díaz-Tendero S, Alcamí M, Martín F. Fullerene C50: Sphericity takes over, not strain. Chem Phys Lett, 2005, 407: 153–158

    Article  CAS  Google Scholar 

  13. Sun M L, Slanina Z, Lee S L. Square/hexagon route towards the boron-nitrogen clusters. Chem Phys Lett, 1995, 233: 279–283

    Article  CAS  Google Scholar 

  14. Wu H S, Xu X H, Stout D L, Jiao H. The structure and stability of B N cages: A computational study. J Mol Model, 2005, 12: 1–8

    Article  CAS  Google Scholar 

  15. Fowler P W, Heine T, Manolopoulos D E, Mitchell D, Orlandi G, Schmidt R, Seifert G, Zerbetto F. Energetics of fullerenes with four-membered rings. J Phys Chem, 1996, 100: 6984–6991

    Article  CAS  Google Scholar 

  16. Gao Y D, Herndon W C. Fullerenes with four-membered rings. J Am Chem Soc, 1993, 115: 8459–8460

    Article  CAS  Google Scholar 

  17. Qian W Y, Bartberger M D, Pastor S J, Houk K N, Wilkins C L, Rubin Y. C62, a non-classical fullerene incorporating a four-membered ring. J Am Chem Soc, 2000, 122: 8333–8334

    Article  CAS  Google Scholar 

  18. Ayuela A, Fowler P W, Mitchell D, Schmidt R, Seifert G, Zerbetto F. C62: Theoretical evidence for a nonclassical fullerene with a heptagon. J Phys Chem, 1996, 100: 15634–15636

    Article  CAS  Google Scholar 

  19. Domene M C, Fowler P W, Mitchell D, Seifert G, Zerbetto F. Energetics of C20 and C22 fullerene and near-fullerene carbon cages. J Phys Chem A, 1997, 101: 8339–8344

    Article  CAS  Google Scholar 

  20. Cui Y H, Chen D L, Tian W Q, Feng J K. Structures, stabilities, and electronic and optical properties of C62 fullerene isomers. J Phys Chem A, 2007, 111: 7933–7939

    Article  CAS  Google Scholar 

  21. Haddon R C. Measure of nonplanarity in conjugated organic molecules: Which structurally characterized molecule displays the highest degree of pyramidalization? J Am Chem Soc, 1990, 112: 3385–3389

    Article  CAS  Google Scholar 

  22. Haddon R C. Chemistry of the fullerenes: The manifestation of strain in a class of continuous aromatic molecules. Science, 1993, 261: 1545–1550

    Article  CAS  Google Scholar 

  23. http://www.mathematik.uni-bielefeld.de/~CaGe/

  24. Bürgi H B, Blanc E, Schwarzenbach D, Liu S Z, Lu Y J, Kappes M M, Ibers J A. The structure of C60: Orientational disorder in the low-temperature modification of C60. Angew Chem Int Ed, 1992, 31: 640–643

    Article  Google Scholar 

  25. Frisch M J, Trucks G W, Schlegel H B, Scuseria G E, Robb M A, Cheeseman J R, Montgomery J A, Vreven T, Kudin K N, Burant J C, Millam J M, Iyengar S S, Tomasi J, Barone V, Mennucci B, Cossi M, Scalmani G, Rega N, Petersson G A, Nakatsuji H, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda, Y, Kitao O, Nakai H, Klene M, Li X, Knox J E, Hratchian H P, Cross J B, Adamo C, Jaramillo J, Gomperts R, Stratmann R E, Yazyev O, Austin A J, Cammi R, Pomelli C, Ochterski J W, Ayala P Y, Morokuma K, Voth G. A, Salvador P, Dannenberg J J, Zakrzewski V G, Dapprich S, Daniels A D, Strain M C, Farkas O, Malick D K, Rabuck A D, Raghavachari K, Foresman J B, Ortiz J V, Cui Q, Baboul A G, Clifford S, Cioslowski J, Stefanov B B, Liu G, Liashenko A, Piskorz P, Komaromi I, Martin R L, Fox D J, Keith T, Al-Laham M A, Peng C Y, Nanayakkara A, Challacombe M, Gill P M W, Johnson B, Chen W, Wong M W, Gonzalez C, Pople J A. Gaussian 03, Revision B, 05. Gaussian Inc, Pittsburgh, PA, 2003

    Google Scholar 

  26. Balaban A T. From chemical topology to 3D geometry. J Chem Inf Comput Sci, 1997, 37: 645–650

    CAS  Google Scholar 

  27. Schmalz T G, Seitz W A, Klein D J, Hite G E. Elemental carbon cages. J Am Chem Soc, 1988, 110: 1113–1127

    Article  CAS  Google Scholar 

  28. Qian W, Chuang S C, Amador R B, Jarrosson T, Sander M, Pieniazek S, Khan S I, Rubin Y. Synthesis of stable derivatives of C62: The first nonclassical fullerene incorporating a four-membered ring. J Am Chem Soc, 2003, 125: 2066–2067

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. School of Chemistry and Chemical Engineering, Southwest University, Chongqing, 400715, China

    LiHua Gan, Jian Liu & Jian Zou

  2. Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment, Ministry of Education, Chongqing University, Chongqing, 400044, China

    LiHua Gan, ZuoHua Liu & BaiZhan Li

  3. College of Computer and Information Science, Southwest University, Chongqing, 400715, China

    Li Li

  4. College of Chemistry and Chemical Engineering, Chongqing University, Chongqing, 400044, China

    ChangYuan Tao

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  1. LiHua Gan
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  2. Jian Liu
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  5. Li Li
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Correspondence to LiHua Gan.

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Supported from Southwest University, China (Grant No. SWNUB2005002) and Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment within Ministry of Education, Chongqing University (Grant No. KLVF-2007-5)

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Gan, L., Liu, J., Zou, J. et al. Carbon polyhedrons formed by squares and hexagons obeying isolated square rule. Sci. China Ser. B-Chem. 52, 1085–1089 (2009). https://doi.org/10.1007/s11426-009-0139-3

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  • DOI: https://doi.org/10.1007/s11426-009-0139-3

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