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Structures and Stability of Fullerenes, Metallofullerenes, and Their Derivatives

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Abstract

This chapter describes general principles in the stability and bonding of empty fullerenes, endohedral fullerenes, and exohedral derivatives of empty fullerenes. First, an overview of the structural properties of empty fullerenes is given. The problem of isomers’ enumeration is described and the origin of the intrinsic steric strain of the fullerenes is discussed in terms of POAV (π-orbital vector analysis) leading to the isolated pentagon rule (IPR). Finally, theoretical studies of the isomers of fullerenes are discussed. In the second part of the chapter, bonding phenomena and molecular structures of endohedral metallofullerenes (EMFs) are reviewed. First, the bonding situation in EMFs is discussed in terms of ionic/covalent dichotomy. Then, the factors determining isomers of EMFs, including those favoring formation of non-IPR cage isomers, are reviewed. In the third part, general principles governing addition of atomic addends and trifluoromethyl radicals to fullerenes are analyzed.

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References

  • Achiba, Y., Kikuchi, K., Aihara, Y., Wakabayashi, T., Miyake, Y., & Kainosho, M. (1995). Higher fullerenes – structure and properties. Science and technology of fullerene materials. Materials Research Society symposium proceedings, Pittsburg.

    Google Scholar 

  • Achiba, Y., Fowler, P. W., Mitchell, D., & Zerbetto, F. (1998a). Structural predictions for the C116 molecule. Journal of Physical Chemistry A, 102(34), 6835–6841.

    CAS  Google Scholar 

  • Achiba, Y., Miyake, Y., Ishiwatari, H., Kainosho, M., & Kikuchi, K. (1998b). NMR characterization of higher fullerenes up to C 94. Materials Research Society 1998 Fall Meeting. Boston.

    Google Scholar 

  • Akasaka, T., Wakahara, T., Nagase, S., Kobayashi, K., Waelchli, M., Yamamoto, K., Kondo, M., Shirakura, S., Okubo, S., Maeda, Y., Kato, T., Kako, M., Nakadaira, Y., Nagahata, R., Gao, X., Van Caemelbecke, E., & Kadish, K. M. (2000). La@C82 anion. An unusually stable metallofullerene. Journal of the American Chemical Society, 122(38), 9316–9317.

    Google Scholar 

  • Al-Matar, H., Sada, A. K. A., Avent, A. G., Taylor, R., & Wei, X. W. (2002). Methylation of [70]fullerene. Journal of the Chemical Society-Perkin Transactions, 2, 1251–1256.

    Google Scholar 

  • Albertazzi, E., Domene, C., Fowler, P. W., Heine, T., Seifert, G., Van Alsenoy, C., & Zerbetto, F. (1999). Pentagon adjacency as a determinant of fullerene stability. Physical Chemistry Chemical Physics, 1(12), 2913–2918.

    CAS  Google Scholar 

  • Alvarez, M. M., Gillan, E. G., Holczer, K., Kaner, R. B., Min, K. S., & Whetten, R. L. (1991). La2C80 – a soluble dimetallofullerene. Journal of Physical Chemistry, 95(26), 10561–10563.

    CAS  Google Scholar 

  • Alvarez, L., Pichler, T., Georgi, P., Schwieger, T., Peisert, H., Dunsch, L., Hu, Z., Knupfer, M., Fink, J., Bressler, P., Mast, M., & Golden, M. S. (2002). Electronic structure of pristine and intercalated Sc3N@C80 metallofullerene. Physical Review B, 66(3), 035107.

    Google Scholar 

  • Attalla, M. I., Vassallo, A. M., Tattam, B. N., & Hanna, J. V. (1993). Preparation of hydrofullerenes by hydrogen radical-induced hydrogenation. Journal of Physical Chemistry, 97(24), 6329–6331.

    CAS  Google Scholar 

  • Austin, S. J., Fowler, P. W., Orlandi, G., Manolopoulos, D. E., & Zerbetto, F. (1994). Relative stabilities of C76 isomers – a numerical test of the fullerene isolated-pentagon rule. Chemical Physics Letters, 226(1–2), 219–225.

    CAS  Google Scholar 

  • Austin, S. J., Fowler, P. W., Manolopoulos, D. E., Orlandi, G., & Zerbetto, F. (1995). Structural motifs and the stability of fullerenes. Journal of Physical Chemistry, 99(20), 8076–8081.

    CAS  Google Scholar 

  • Avdoshenko, S. M., Goryunkov, A. A., Ioffe, I. N., Ignat’eva, D. V., Sidorov, L. N., Pattison, P., Kemnitz, E., & Troyanov, S. I. (2006). Preparation, crystallographic characterization and theoretical study of C70(CF3)16 and C70(CF3)18. Chemical Communications, (23), 2463–2465.

    Google Scholar 

  • Avent, A. G., Benito, A. M., Birkett, P. R., Darwish, A. D., Hitchcock, P. B., Kroto, H. W., Locke, I. W., Meidine, M. F., O’Donovan, B. F., Prassides, K., Taylor, R., Walton, D. R. M., & van Wijnkoop, M. (1997). The structure of fullerene compounds. Journal of Molecular Structure, 437, 1–9.

    Google Scholar 

  • Avent, A. G., Clare, B. W., Hitchcock, P. B., Kepert, D. L., & Taylor, R. (2002). C60F36: There is a third isomer and it has C 1 symmetry. Chemical Communications, 2006(20), 2370–2371.

    Google Scholar 

  • Bader, R. F. W. (1990). Atoms in molecules – a quantum theory. Oxford: Oxford University Press.

    Google Scholar 

  • Balasubramanian, K. (1991). Enumeration of isomers of polysubstituted C60 and application to NMR. Chemical Physics Letters, 182(3–4), 257–262.

    CAS  Google Scholar 

  • Beavers, C. M., Zuo, T. M., Duchamp, J. C., Harich, K., Dorn, H. C., Olmstead, M. M., & Balch, A. L. (2006). Tb3N@C84: An improbable, egg-shaped endohedral fullerene that violates the isolated pentagon rule. Journal of the American Chemical Society, 128(35), 11352–11353.

    CAS  Google Scholar 

  • Beavers, C. M., Chaur, M. N., Olmstead, M. M., Echegoyen, L., & Balch, A. L. (2009). Large metal ions in a relatively small fullerene cage: The structure of Gd3N@C 2(22010)-C78 departs from the isolated pentagon rule. Journal of the American Chemical Society, 131(32), 11519–11524.

    CAS  Google Scholar 

  • Birkett, P. R., Hitchcock, P. B., Kroto, H. W., Taylor, R., & Walton, D. R. M. (1992). Preparation and characterization of C60Br6 and C60Br8. Nature, 357(6378), 479–481.

    CAS  Google Scholar 

  • Birkett, P. R., Avent, A. G., Darwish, A. D., Kroto, H. W., Taylor, R., & Walton, D. R. M. (1993). Preparation and 13C NMRspectroscopiccharacterizationofC60Cl6. Journal of the Chemical Society- ChemicalCommunications,1993(15), 1230–1232.

    Google Scholar 

  • Birkett, P. R., Avent, A. G., Darwish, A. D., Kroto, H. W., Taylor, R., & Walton, D. R. M. (1995). Formation and characterization of C70Cl10. Journal of the Chemical Society-Chemical Communications, (6), 1995683–684.

    Google Scholar 

  • Boltalina, O. V., Street, J. M., & Taylor, R. (1998). C60F36 consists of two isomers having T and C3 symmetry. Journal of the Chemical Society-Perkin Transactions, 2(3), 649–653.

    Google Scholar 

  • Boltalina, O. V., Ioffe, I. N., Sidorov, L. N., Seifert, G., & Vietze, K. (2000a). Ionization energy of fullerenes. Journal of the American Chemical Society, 122(40), 9745–9749.

    CAS  Google Scholar 

  • Boltalina, O. V., Lukonin, A. Y., Street, J. M., & Taylor, R. (2000b). C60F2 exists! Chemical Communications, 2000(17), 1601–1602.

    Google Scholar 

  • Boltalina, O. V., Markov, V. Y., Troshin, P. A., Darwish, A. D., Street, J. M., & Taylor, R. (2001). C60F20: “Saturnene”, an extraordinary squashed fullerene. Angewandte Chemie-International Edition, 40(4), 787–789.

    CAS  Google Scholar 

  • Boltalina, O. V., Darwish, A. D., Street, J. M., Taylor, R., & Wei, X. W. (2002). Isolation and characterisation of C60F4, C60F6, C60F8, C60F7CF3 and C60F2O, the smallest oxahomofullerene; the mechanism of fluorine addition to fullerenes. Journal of the Chemical Society-Perkin Transactions, 2(2), 251–256.

    Google Scholar 

  • Boltalina, O. V., Popov, A. A., & Strauss, S. H. (2009). Physicochemical properties and the unusual structure of fullerenes: Single-crystal X-ray structures of fullerenes and their derivatives. In H. Dodziuk (Ed.), Strained hydrocarbons: Beyond the Van’t Hoff and Le Bel hypothesis (pp. 225–238). Weinheim: Wiley-VCH.

    Google Scholar 

  • Campanera, J. M., Bo, C., Olmstead, M. M., Balch, A. L., & Poblet, J. M. (2002). Bonding within the endohedral fullerenes Sc3N@C78 and Sc3N@C80 as determined by density functional calculations and reexamination of the crystal structure of Sc3N@C78 ⋅Co(OEP) ⋅1.5(C6H6) ⋅0.3(CHCl3). Journal of Physical Chemistry A, 106(51), 12356–12364.

    Google Scholar 

  • Campanera, J. M., Bo, C., & Poblet, J. M. (2005). General rule for the stabilization of fullerene cages encapsulating trimetallic nitride templates. Angewandte Chemie-International Edition, 44(44), 7230–7233.

    CAS  Google Scholar 

  • Campbell, E. E. B., Fowler, P. W., Mitchell, D., & Zerbetto, F. (1996). Increasing cost of pentagon adjacency for larger fullerenes. Chemical Physics Letters, 250(5–6), 544–548.

    CAS  Google Scholar 

  • Cao, B. P., Wakahara, T., Tsuchiya, T., Kondo, M., Maeda, Y., Rahman, G. M. A., Akasaka, T., Kobayashi, K., Nagase, S., & Yamamoto, K. (2004). Isolation, characterization, and theoretical study of La2@C78. Journal of the American Chemical Society, 126(30), 9164–9165.

    CAS  Google Scholar 

  • Cao, B., Nikawa, H., Nakahodo, T., Tsuchiya, T., Maeda, Y., Akasaka, T., Sawa, H., Slanina, Z., Mizorogi, N., & Nagase, S. (2008). Addition of adamantylidene to La2@C78: Isolation and single-crystal X-ray structural determination of the monoadducts. Journal of the American Chemical Society, 130, 983–989.

    CAS  Google Scholar 

  • Chai, Y., Guo, T., Jin, C. M., Haufler, R. E., Chibante, L. P. F., Fure, J., Wang, L. H., Alford, J. M., & Smalley, R. E. (1991). Fullerenes with metals inside. Journal of Physical Chemistry, 95(20), 7564–7568.

    CAS  Google Scholar 

  • Chaur, M. N., Melin, F., Elliott, B., Kumbhar, A., Athans, A. J., & Echegoyen, L. (2008). New M3N@C2n endohedral metallofullerene families (M = Nd, Pr, Ce; n = 40–53): Expanding the preferential templating of the C88 cage and approaching the C96 Cage. Chemistry – A European Journal, 14(15), 4594–4599.

    Google Scholar 

  • Chen, Z. F., Cioslowski, J., Rao, N., Moncrieff, D., Buhl, M., Hirsch, A., & Thiel, W. (2001). Endohedral chemical shifts in higher fullerenes with 72–86 carbon atoms. Theoretical Chemistry Accounts, 106(5), 364–368.

    CAS  Google Scholar 

  • Chen, Z. F., & Thiel, W. (2003). Performance of semiempirical methods in fullerene chemistry: Relative energies and nucleus-independent chemical shifts. Chemical Physics Letters, 367(1–2), 15–25.

    CAS  Google Scholar 

  • Chen, D. L., Q., T. W., Feng, J. K., & Sun, C. C. (2008). C68 fullerene isomers, anions, and their metallofullerenes: Charge-stabilizing different isomers. ChemPhysChem, 9, 454–461.

    Google Scholar 

  • Cioslowski, J., Rao, N., & Moncrieff, D. (2000). Standard enthalpies of formation of fullerenes and their dependence on structural motifs. Journal of the American Chemical Society, 122(34), 8265–8270.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1993). Structures and stabilities of hydrofullerenes C60H n . Theochem-Journal of Molecular Structure, 281, 45–52.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1994a). An analysis of the 63 Possible isomers of C60H36 containing a threefold axis – a new structure for C60H20. Theochem-Journal of Molecular Structure, 315, 71–83.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1994b). Structures and stabilities of hydrofullerenes – completion of a tetrahedral fused quadruple crown structure and a double crown structure at C60H36. Theochem-Journal of Molecular Structure, 304, 181–189.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1994c). Structures and stabilities of hydrofullerenes. Completion of crown structures at C60H18 and C60H24. Theochem-Journal of Molecular Structure, 303, 1–9.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1995a). Stereochemical patterns in bromofullerenes C60Br2 to C60Br12. Theochem-Journal of Molecular Structure, 340, 125–142.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1995b). Stereochemical patterns in bromofullerenes, C60Br12 to C60Br24. Theochem-Journal of Molecular Structure, 358, 79–94.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1996). Fullerene hydrides based on skew pentagonal pyramidal arrangements of hydrogen atoms. Theochem-Journal of Molecular Structure, 363, 179–190.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1997). An analysis of the 94 possible isomers of C60F48 containing a three-fold axis. Journal of Molecular Structure-Theochem, 389, 97–103.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1999a). The structures of C60F36 and new possible structures for C60H36. Journal of Molecular Structure-Theochem, 466, 177–186.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (1999b). The structures of C70X n , X=H, F, Br, C6H5 and n = 2–12. Theochem-Journal of Molecular Structure, 491, 249–264.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (2001). Structures and stabilities of adducts of carbenes and fullerenes, C60(CR2) n , R = H, CH3, C4H9 and n = 1–6. Journal of Molecular Structure-Theochem, 548, 61–91.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (2002a). Structures of C60H n and C60F n , n = 36–60. Journal of Molecular Structure-Theochem, 589, 209–227.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (2002b). Structures, stabilities and isomerism in C60H36 and C60F36. A comparison of the AM1 Hamiltonian and density functional techniques. Journal of Molecular Structure-Theochem, 589, 195–207.

    Google Scholar 

  • Clare, B. W., & Kepert, D. L. (2003a). Early stages in the addition to C60 to form C60X n , X=H, F, Cl, Br, CH3, C4H9. Journal of Molecular Structure-Theochem, 621(3), 211–231.

    CAS  Google Scholar 

  • Clare, B. W., & Kepert, D. L. (2003b). Structures, stabilities and isomerism in C60H n , n = 2–36. A comparison of the AM1 Hamiltonian and density functional techniques. Journal of Molecular Structure-Theochem, 622(3), 185–202.

    Google Scholar 

  • Cortés-Guzmán, F., & Bader, R. F. W. (2005). Complementarity of QTAIM and MO theory in the study of bonding in donor–acceptor complexes. Coordination Chemistry Reviews, 249(5–6), 633–662.

    Google Scholar 

  • Cremer, D., & Kraka, E. (1984). Chemical bonds without bonding electron density – Does the difference electron-density analysis suffice for a description of the chemical bond? Angewandte Chemie-International Edition in English, 23(8), 627–628.

    Google Scholar 

  • Darwish, A. D., Avent, A. G., Taylor, R., & Walton, D. R. M. (1996). Structural characterisation of C60H18; a C3v symmetry crown. Journal of the Chemical Society-Perkin Transactions, 2(10), 2051–2054.

    Google Scholar 

  • Darzynkiewicz, R. B., & Scuseria, G. E. (1997). Noble gas endohedral complexes of C60 buckminsterfullerene. Journal of Physical Chemistry A, 101(38), 7141–7144.

    CAS  Google Scholar 

  • Dennis, T. J. S., Kai, T., Asato, K., Tomiyama, T., & Shinohara, H. (1999). Isolation and characterization by 13C NMR spectroscopy of [84]fullerene minor isomers. Journal of Physical Chemistry A, 103(44), 8747–8752.

    CAS  Google Scholar 

  • Diener, M. D., & Alford, J. M. (1998). Isolation and properties of small-bandgap fullerenes. Nature, 393(6686), 668–671.

    CAS  Google Scholar 

  • Dixon, D. A., Matsuzawa, N., Fukunaga, T., & Tebbe, F. N. (1992). Patterns for addition to C60. Journal of Physical Chemistry, 96(15), 6107–6110.

    CAS  Google Scholar 

  • Dorozhkin, E. I., Ignat’eva, D. V., Tamm, N. B., Goryunkov, A. A., Khavrel, P. A., Ioffe, I. N., Popov, A. A., Kuvychko, I. V., Streletskiy, A. V., Markov, V. Y., Spandl, J., Strauss, S. H., & Boltalina, O. V. (2006a). Synthesis, characterization, and theoretical study of stable isomers of C70(CF3) n (n = 2, 4, 6, 8, 10). Chemistry – A European Journal, 12(14), 3876–3889.

    Google Scholar 

  • Dorozhkin, E. I., Ignat’eva, D. V., Tamm, N. B., Vasilyuk, N. V., Goryunkov, A. A., Avdoshenko, S. M., Ioffe, I. N., Sidorov, L. N., Pattison, P., Kemnitz, E., & Troyanov, S. I. (2006b). Structure of 1,4,10,19,25,41-C70(CF3)6, isomer with unique arrangement of addends. Journal of Fluorine Chemistry, 127(10), 1344–1348.

    CAS  Google Scholar 

  • Dorozhkin, E. I., Goryunkov, A. A., Ioffe, I. N., Avdoshenko, S. M., Markov, V. Y., Tamm, N. B., Ignat’eva, D. V., Sidorov, L. N., & Troyanov, S. I. (2007). Synthesis, structure, and theoretical study of lower trifluoromethyl derivatives of [60]fullerene. European Journal of Organic Chemistry, 2007(30), 5082–5094.

    Google Scholar 

  • Dunsch, L., & Yang, S. (2007). Metal nitride cluster fullerenes: Their current state and future prospects. Small, 3(8), 1298–1320.

    CAS  Google Scholar 

  • Dunsch, L., Georgi, P., Krause, M., & Wang, C. R. (2003). New clusters in endohedral fullerenes: The metalnitrides. Synthetic Metals, 135(1–3), 761–762.

    Google Scholar 

  • Dunsch, L., Krause, M., Noack, J., & Georgi, P. (2004). Endohedral nitride cluster fullerenes – formation and spectroscopic analysis of L3 − x M x N@C2n (0 ≤ x ≤ 3; n = 39, 40). Journal of Physics and Chemistry of Solids, 65(2–3), 309–315.

    CAS  Google Scholar 

  • Dunsch, L., Yang, S., Zhang, L., Svitova, A., Oswald, S., & Popov, A. A. (2010). Metal sulfide in a C82 fullerene cage: A new form of endohedral clusterfullerenes. Journal of the American Chemical Society, 132(15), 5413–5421. doi: 10.1021/ja909580j.

    CAS  Google Scholar 

  • Ettl, R., Chao, I., Diederich, F., & Whetten, R. L. (1991). Isolation of C76, a chiral (D 2) allotrope of carbon. Nature, 353(6340), 149–153.

    CAS  Google Scholar 

  • Farrugia, L. J., Evans, C., Lentz, D., & Roemer, M. (2009). The QTAIM approach to chemical bonding between transition metals and carbocyclic rings: A combined experimental and theoretical study of (η5 -C5H5)Mn(CO)3, (η6 -C6H6)Cr(Co)3, and (E)-5 -C5H4)CF = CF(η5 -C5H4)​(η5 -C5H5)2Fe2. Journal of theAmerican Chemical Society, 131(3), 1251–1268.

    CAS  Google Scholar 

  • Fowler, P. W., & Manolopoulos, D. E. (1995a). An atlas of fullerenes. Oxford: Claredron Press.

    Google Scholar 

  • Fowler, P. W., & Zerbetto, F. (1995b). Charging and equilibration of fullerene isomers. Chemical Physics Letters, 243(1–2), 36–41.

    CAS  Google Scholar 

  • Fowler, P. W., Rogers, K. M., Somers, K. R., & Troisi, A. (1999). Independent sets and the prediction of addition patterns for higher fullerenes. Journal of the Chemical Society-Perkin Transactions, 2(10), 2023–2027.

    Google Scholar 

  • Furche, F., & Ahlrichs, R. (2001). Fullerene C80: Are there still more isomers? Journal of Chemical Physics, 114(23), 10362–10367.

    CAS  Google Scholar 

  • Gakh, A. A., & Tuinman, A. A. (2001). ‘Fluorine dance’ on the fullerene surface. Tetrahedron Letters, 42(41), 7137–7139.

    CAS  Google Scholar 

  • Gakh, A. A., Romanovich, A. Y., & Bax, A. (2003). Thermodynamic rearrangement synthesis and NMR structures of C 1, C 3, and T isomers of C60H36. Journal of the American Chemical Society, 125(26), 7902–7906.

    CAS  Google Scholar 

  • Gan, L. H., & Yuan, R. (2006). Influence of cluster size on the structures and stability of trimetallic nitride fullerenes M3N@C80. ChemPhysChem, 7(6), 1306–1310.

    CAS  Google Scholar 

  • Goryunkov, A. A., Kuvychko, I. V., Ioffe, I. N., Dick, D. L., Sidorov, L. N., Strauss, S. H., & Boltalina, O. V. (2003). Isolation of C60(CF3) n (n = 2, 4, 6, 8, 10) with high compositional purity. Journal of Fluorine Chemistry, 124(1), 61–64.

    CAS  Google Scholar 

  • Goryunkov, A. A., Ioffe, I. N., Kuvychko, I. V., Yankova, T. S., Markov, V. Y., Streletskii, A. A., Dick, D. L., Sidorov, L. N., Boltalina, O. V., & Strauss, S. H. (2004a). Trifluoromethylated [60]fullerenes: Synthesis and characterization. Fullerenes Nanotubes and Carbon Nanostructures, 12(1–2), 181–185.

    CAS  Google Scholar 

  • Goryunkov, A. A., Markov, V. Y., Ioffe, I. N., Bolskar, R. D., Diener, M. D., Kuvychko, I. V., Strauss, S. H., & Boltalina, O. V. (2004b). C74F38: An exohedral derivative of a small-bandgap fullerene with D 3 symmetry. Angewandte Chemie-International Edition, 43(8), 997–1000.

    CAS  Google Scholar 

  • Goryunkov, A. A., Dorozhkin, E. I., Ignat’eva, D. V., Sidorov, L. N., Kemnitz, E., Sheldrick, G., & Troyanov, S. I. (2005). Crystal and molecular structures of C70(CF3)8 ⋅PhMe. Mendeleev Communications, 15(6), 225–227.

    Google Scholar 

  • Goryunkov, A. A., Ignat’eva, D. V., Tamm, N. B., Moiseeva, N. N., Loffe, I. N., Avdoshenko, S. M., Markov, V. Y., Sidorov, L. N., Kemnitz, E., & Troyanov, S. I. (2006a). Preparation, crystallographic characterization, and theoretical study of C70(CF3)14. European Journal of Organic Chemistry, 2006, 2508–2512.

    Google Scholar 

  • Goryunkov, A. A., Kareev, I. E., Ioffe, I. N., Popov, A. A., Kuvychko, I. V., Markov, V. Y., Goldt, I. V., Pimenova, A. S., Serov, M. G., Avdoshenko, S. M., Khavrel, P. A., Sidorov, L. N., Lebedkin, S. F., Mazej, Z., Zemva, B., Strauss, S. H., & Boltalina, O. V. (2006b). Reaction of C60 with KMnF4 – isolation and characterization of a new isomer of C60F8 and re-evaluation of the structures of C60F7(CF3) and the known isomer of C60F8. Journal of Fluorine Chemistry, 127(10), 1423–1435.

    CAS  Google Scholar 

  • Goryunkov, A. A., Dorozhkin, E. I., Tamm, N. B., Ignat’eva, D. V., Avdoshenko, S. M., Sidorov, L. N., & Troyanov, S. I. (2007). Synthesis and molecular structure of 1,6,11,16,18,24,27,36-C60(CF3)8. Mendeleev Communications, 17(2), 110–112.

    CAS  Google Scholar 

  • Haddon, R. C. (1993). Chemistry of the fullerenes - the manifestation of strain in a class of continuous aromatic-molecules. Science, 261(5128), 1545–1550.

    CAS  Google Scholar 

  • Haser, M., Almlof, J., & Scuseria, G. E. (1991). The equilibrium geometry of C60 as predicted by 2nd-Order (MP2) perturbation-theory. Chemical Physics Letters, 181(6), 497–500.

    CAS  Google Scholar 

  • Haufler, R. E., Conceicao, J., Chibante, L. P. F., Chai, Y., Byrne, N. E., Flanagan, S., Haley, M. M., Obrien, S. C., Pan, C., Xiao, Z., Billups, W. E., Ciufolini, M. A., Hauge, R. H., Margrave, J. L., Wilson, L. J., Curl, R. F., & Smalley, R. E. (1990). Efficient production of C60 (Buckminsterfullerene), C60H36, and the solvated buckide ion. Journal of Physical Chemistry, 94(24), 8634–8636.

    CAS  Google Scholar 

  • Heath, J. R., O’Brien, S. C., Zhang, Q., Liu, Y., Curl, R. F., Tittel, F. K., & Smalley, R. E. (1985). Lanthanum complexes of spheroidal carbon shells. Journal of the American Chemical Society, 107(25), 7779–7780.

    CAS  Google Scholar 

  • Henderson, C. C., & Cahill, P. A. (1993). C60H2 - synthesis of the simplest C60 hydrocarbon derivative. Science, 259(5103), 1885–1887.

    CAS  Google Scholar 

  • Hennrich, F. H., Michel, R. H., Fischer, A., Richard-Schneider, S., Gilb, S., Kappes, M. M., Fuchs, D., Burk, M., Kobayashi, K., & Nagase, S. (1996). Isolation and characterization of C80. Angewandte Chemie-International Edition in English, 35(15), 1732–1734.

    CAS  Google Scholar 

  • Hirsch, A., & Brettreich, M. (2005). Fullerenes. Chemistry and reactions. Weinheim: Wiley.

    Google Scholar 

  • Hirsch, A., & Vostrowsky, O. (2001). C60 hexakisadducts with an octahedral addition pattern - a new structure motif in organic chemistry. European Journal of Organic Chemistry, 2001, 829–848.

    Google Scholar 

  • Hitchcock, P. B., & Taylor, R. (2002). Single crystal X-ray structure of tetrahedral C60F36: The most aromatic and distorted fullerene. Chemical Communications, 2002(18), 2078–2079.

    Google Scholar 

  • Hitchcock, P. B., Avent, A. G., Martsinovich, N., Troshin, P. A., & Taylor, R. (2005). C 2 C70F38 is aromatic, contains three planar hexagons, and has equatorial addends. Chemical Communications, 2005(1), 75–77.

    Google Scholar 

  • Ignat’eva, D. V., Goryunkov, A. A., Tamm, N. B., Ioffe, I. N., Avdoshenko, S. M., Sidorov, L. N., Dimitrov, A., Kemnitz, E., & Troyanov, S. I. (2006). Preparation, crystallographic characterization and theoretical study of two isomers of C70(CF3)12. Chemical Communications, 2006(16), 1778–1780.

    Google Scholar 

  • Iiduka, Y., Wakahara, T., Nakahodo, T., Tsuchiya, T., Sakuraba, A., Maeda, Y., Akasaka, T., Yoza, K., Horn, E., Kato, T., Liu, M. T. H., Mizorogi, N., Kobayashi, K., & Nagase, S. (2005). Structural determination of metallofuIlerene Sc3C82 revisited: A surprising finding. Journal of the American Chemical Society, 127(36), 12500–12501.

    CAS  Google Scholar 

  • Iiduka, Y., Wakahara, T., Nakajima, K., Tsuchiya, T., Nakahodo, T., Maeda, Y., Akasaka, T., Mizorogi, N., & Nagase, S. (2006). 13C NMR spectroscopic study of scandium dimetallofullerene, Sc2@C84 vs. Sc2C2@C82. Chemical Communications, 2006(19), 2057–2059.

    Google Scholar 

  • Inoue, T., Tomiyama, T., Sugai, T., Okazaki, T., Suematsu, T., Fujii, N., Utsumi, H., Nojima, K., & Shinohara, H. (2004). Trapping a C2 radical in endohedral metallofullerenes: Synthesis and structures of (Y2C2)@C82 (Isomers I, II, and III). Journal of Physical Chemistry B, 108(23), 7573–7579.

    CAS  Google Scholar 

  • Irle, S., Zheng, G. S., Elstner, M., & Morokuma, K. (2003). From C2 molecules to self-assembled fullerenes in quantum chemical molecular dynamics. Nano Letters, 3(12), 1657–1664.

    CAS  Google Scholar 

  • Irle, S., Zheng, G. S., Wang, Z., & Morokuma, K. (2006). The C60 formation puzzle “solved”: QM/MD simulations reveal the shrinking hot giant road of the dynamic fullerene self-assembly mechanism. Journal of Physical Chemistry B, 110(30), 14531–14545.

    CAS  Google Scholar 

  • Karataev, V. I. (1998). Anomalous properties of C74 fullerene. Molecular Crystals and Liquid Crystals Science and Technology Section C-Molecular Materials, 11(1–2), 57–58.

    CAS  Google Scholar 

  • Kareev, I. E., Kuvychko, I. V., Popov, A. A., Lebedkin, S. F., Miller, S. M., Anderson, O. P., Strauss, S. H., & Boltalina, O. V. (2005). High-temperature synthesis of the surprisingly stable C 1-C70(CF3)10 isomer with a para 7-meta-para ribbon of nine C6(CF3)2 edge-sharing hexagons. Angewandte Chemie-International Editionv, 44(48), 7984–7987.

    CAS  Google Scholar 

  • Kareev, I. E., Shustova, N. B., Kuvychko, I. V., Lebedkin, S. F., Miller, S. M., Anderson, O. P., Popov, A. A., Strauss, S. H., & Boltalina, O. V. (2006). Thermally stable perfluoroalkylfullerenes with the skew-pentagonal-pyramid pattern: C60(C2F5)4O, C60(CF3)4O, and C60(CF3)6 Journal of the American Chemical Society, 128(37), 12268–12280.

    Google Scholar 

  • Kareev, I. E., Shustova, N. B., Peryshkov, D. V., Lebedkin, S. F., Miller, S. M., Anderson, O. P., Popov, A. A., Boltalina, O. V., & Strauss, S. H. (2007). X-ray structure and DFT study of C 1-C60(CF3)12. A high-energy, kinetically-stable isomer prepared at 500 degrees C. Chemical Communications, 2007(16), 1650–1652.

    Google Scholar 

  • Kareev, I. E., Kuvychko, I. V., Shustova, N. B., Lebedkin, S. F., Bubnov, V. P., Anderson, O. P., Popov, A. A., Boltalina, O. V., & Strauss, S. H. (2008a). C 1-(C84C 2(11))(CF3)12: Trifluoromethylation yields structural proof of a minor C84 cage and reveals a principle of higher fullerene reactivity. Angewandte Chemie-International Edition in English, 47, 6204–6207.

    CAS  Google Scholar 

  • Kareev, I. E., Popov, A. A., Kuvychko, I. V., Shustova, N. B., Lebedkin, S. F., Bubnov, V. P., Anderson, O. P., Seppelt, K., Strauss, S. H., & Boltalina, O. V. (2008b). Synthesis and X-ray or NMR/DFT structure elucidation of Twenty-One new trifluoromethyl derivatives of soluble cage isomers of C76,C78, C84, and C90. Journal of the American Chemical Society, 130, 13471–13489.

    CAS  Google Scholar 

  • Kato, H., Taninaka, A., Sugai, T., & Shinohara, H. (2003). Structure of a missing-caged metallofullerene: La2@C72. Journal of the American Chemical Society, 125(26), 7782–7783.

    CAS  Google Scholar 

  • Kemnitz, E., & Troyanov, S. I. (2009). Connectivity patterns of two C90 isomers provided by the structure elucidation of C90Cl32. Angewandte Chemie International Edition, 48(14), 2584–2587.

    CAS  Google Scholar 

  • Kepert, D. L., & Clare, B. W. (1996). Stereochemical patterns formed by addition to fullerene C60. Coordination Chemistry Reviews, 155, 1–33.

    CAS  Google Scholar 

  • Kessler, B., Bringer, A., Cramm, S., Schlebusch, C., Eberhardt, W., Suzuki, S., Achiba, Y., Esch, F., Barnaba, M., & Cocco, D. (1997). Evidence for incomplete charge transfer and la-derived states in the valence bands of endohedrally doped La@C82. Physical Review Letters, 79(12), 2289–2292.

    CAS  Google Scholar 

  • Kikuchi, K., Nakahara, N., Wakabayashi, T., Suzuki, S., Shiromaru, H., Miyake, Y., Saito, K., Ikemoto, I., Kainosho, M., & Achiba, Y. (1992). NMR characterization of isomers of C78, C82 and C84 fullerenes. Nature, 357(6374), 142–145.

    CAS  Google Scholar 

  • Kobayashi, K., & Nagase, S. (1997a). Structures of the Ca@C82 isomers: A theoretical prediction. Chemical Physics Letters, 274(1–3), 226–230.

    CAS  Google Scholar 

  • Kobayashi, K., Nagase, S., Yoshida, M., & Osawa, E. (1997b). Endohedral metallofullerenes. Are the isolated pentagon rule and fullerene structures always satisfied? Journal of the American Chemical Society, 119(51), 12693–12694.

    Google Scholar 

  • Kobayashi, K., & Nagase, S. (1998). Structures and electronic states of M@C82 (M = Sc, Y, La and lanthanides). Chemical Physics Letters, 282(3–4), 325–329.

    CAS  Google Scholar 

  • Kobayashi, K., & Nagase, S. (1999). Bonding features in endohedral metallofullerenes. Topological analysis of the electron density distribution. Chemical Physics Letters, 302(3–4), 312–316.

    Google Scholar 

  • Kobayashi, K., & Nagase, S. (2002a). A stable unconventional structure of Sc2@C66 found by density functional calculations. Chemical Physics Letters, 362(5–6), 373–379.

    CAS  Google Scholar 

  • Kobayashi, K., & Nagase, S. (2002b). Structures and electronic properties of endohedral metallofullerenes; theory and experiment. In T. Akasaka & S. Nagase (Eds.), Endofullerenes: A new family of carbon custers (pp. 99–119). Dordrecht: Kluwer.

    Google Scholar 

  • Kobayashi, K., Nagase, S., & Akasaka, T. (1995). A theoretical study of C80 and La2@C80. Chemical Physics Letters, 245(2–3), 230–236.

    CAS  Google Scholar 

  • Kobayashi, K., Sano, Y., & Nagase, S. (2001). Theoretical study of endohedral metallofullerenes: Sc3 − n La n N@C80 (n = 0–3). Journal of Computational Chemistry, 22(13), 1353–1358.

    CAS  Google Scholar 

  • Komatsu, K., Murata, M., & Murata, Y. (2005). Encapsulation of molecular hydrogen in fullerene C60 by organic synthesis. Science, 307(5707), 238–240.

    CAS  Google Scholar 

  • Kovalenko, V. I., & Khamatgalimov, A. R. (2003). Open-shell fullerene C74: Phenalenyl-radical substructures. Chemical Physics Letters, 377 (3–4), 263–268.

    CAS  Google Scholar 

  • Krapp, A., & Frenking, G. (2007). Is this a chemical bond? A theoretical study of Ng2@C60 (Ng = He, Ne, Ar, Kr, Xe). Chemistry – A European Journal, 13(29), 8256–8270.

    Google Scholar 

  • Krätschmer, W., Lamb, L. D., Fostiropoulos, K., & Huffman, D. R. (1990). Solid C60 – a new form of carbon. Nature, 347(6291), 354–358.

    Google Scholar 

  • Krause, M., & Dunsch, L. (2005). Gadolinium nitride Gd3N in carbon cages: The influence of cluster size and bond strength. Angewandte Chemie-International Edition, 44(10), 1557–1560.

    CAS  Google Scholar 

  • Krause, M., Popov, A., & Dunsch, L. (2006). Vibrational structure of endohedral fullerene Sc3N@C78(D 3h ’): Evidence for a strong coupling between the Sc3N cluster and C78 cage. ChemPhysChem, 7(8), 1734–1740.

    CAS  Google Scholar 

  • Krause, M., Ziegs, F., Popov, A. A., & Dunsch, L. (2007). Entrapped bonded hydrogen in a fullerene: The five-atom cluster Sc3CH in C80. Chemphyschem, 8(4), 537–540.

    CAS  Google Scholar 

  • Kroto, H. W. (1987). The Stability of the fullerenes C24, C28, C32, C36, C50, C60 and C70. Nature, 329(6139), 529–531.

    CAS  Google Scholar 

  • Kroto, H. W., Heath, J. R., Obrien, S. C., Curl, R. F., & Smalley, R. E. (1985). C60 – Buckminsterfullerene. Nature, 318(6042), 162–163.

    CAS  Google Scholar 

  • Lamparth, I., Maichlemossmer, C., & Hirsch, A. (1995). Reversible template-directed activation of equatorial double-bonds of the fullerene framework – regioselective direct synthesis, crystal-structure, and aromatic properties of T h -C66(COOEt)12. Angewandte Chemie-International Edition in English, 34(15), 1607–1609.

    CAS  Google Scholar 

  • Liu, D., Hagelberg, F., & Park, S. S. (2006). Charge transfer and electron backdonation in metallofullerenes encapsulating NSc3. Chemical Physics, 330(3), 380–386.

    CAS  Google Scholar 

  • Lu, J., Zhang, X. W., Zhao, X. G., Nagase, S., & Kobayashi, K. (2000). Strong metal-cage hybridization in endohedral La@C82, Y@C82 and Sc@C82. Chemical Physics Letters, 332(3–4), 219–224.

    CAS  Google Scholar 

  • Lu, X., Nikawa, H., Nakahodo, T., Tsuchiya, T., Ishitsuka, M. O., Maeda, Y., Akasaka, T., Toki, M., Sawa, H., Slanina, Z., Mizorogi, N., & Nagase, S. (2008). Chemical understanding of a Non-IPR metallofullerene: Stabilization of encaged metals on fused-pentagon bonds in La2@C72. Journal of the American Chemical Society, 130, 9129–9136.

    CAS  Google Scholar 

  • Macchi, P., & Sironi, A. (2003). Chemical bonding in transition metal carbonyl clusters: Complementary analysis of theoretical and experimental electron densities. Coordination Chemistry Reviews, 238–239, 383–412.

    Google Scholar 

  • Manolopoulos, D. E., May, J. C., & Down, S. E. (1991). Theoretical-studies of the fullerenes – C34 to C70. Chemical Physics Letters, 181(2–3), 105–111.

    CAS  Google Scholar 

  • Matsuzawa, N., Dixon, D. A., & Fukunaga, T. (1992). Semiempirical calculations of dihydrogenated buckminsterfullerenes, C60H2. Journal of Physical Chemistry, 96(19), 7594–7604.

    CAS  Google Scholar 

  • Matta, C. F., & Boyd, R. J. (Eds.). (2007). The quantum theory of atoms in molecules. From solid state to DNA and drug design. Weinheim: Wiley.

    Google Scholar 

  • Mercado, B. Q., Beavers, C. M., Olmstead, M. M., Chaur, M. N., Walker, K., Holloway, B. C., Echegoyen, L., & Balch, A. L. (2008). Is the isolated pentagon rule merely a suggestion for endohedral fullerenes? The structure of a second egg-shaped endohedral fullerene—Gd3N@C s (39663)-C82. Journal of the American Chemical Society, 130(25), 7854–7855.

    CAS  Google Scholar 

  • Miyake, Y., Minami, T., Kikuchi, K., Kainosho, M., & Achiba, Y. (2000). Trends in structure and growth of higher fullerenes isomer structure of C86 and C88. Molecular Crystals and Liquid Crystals, 340, 553-558.

    CAS  Google Scholar 

  • Muthukumar, K., & Larsson, J. A. (2008). A density functional study of Ce@C82: Explanation of the Ce preferential bonding site. Journal of Physical Chemistry A, 112, 1071–1075.

    CAS  Google Scholar 

  • Mutig, T., Ioffe, I. N., Kemnitz, E., & Troyanov, S. I. (2008). Crystal and molecular structures of C 2-C70(CF3)8 ⋅1.5PhMe. Mendeleev Communications, 18, 73–75.

    Google Scholar 

  • Nagase, S., Kobayashi, K., & Akasaka, T. (1997). Recent progress in endohedral dimetallofullerenes. Theochem-Journal of Molecular Structure, 398, 221–227.

    Google Scholar 

  • Nagase, S., Kobayashi, K., & Akasaka, T. (1999). Unconventional cage structures of endohedral metallofullerenes. Journal of Molecular Structure-Theochem, 462, 97–104.

    Google Scholar 

  • Neretin, I. S., Lyssenko, K. A., Antipin, M. Y., Slovokhotov, Y. L., Boltalina, O. V., Troshin, P. A., Lukonin, A. Y., Sidorov, L. N., & Taylor, R. (2000). C60F18, a flattened fullerene: Alias a hexa-substituted benzene. Angewandte Chemie-International Edition, 39(18), 3273–3276.

    CAS  Google Scholar 

  • Nishibori, E., Takata, M., Sakata, M., Taninaka, A., & Shinohara, H. (2001). Pentagonal-dodecahedral La2 charge density in [80-I h ]fullerene: La2@C80. Angewandte Chemie-International Edition, 40(16), 2998–2999.

    CAS  Google Scholar 

  • Nishibori, E., Ishihara, M., Takata, M., Sakata, M., Ito, Y., Inoue, T., & Shinohara, H. (2006a). Bent (metal)2C2 clusters encapsulated in (Sc2C2)@C82(III) and (Y2C2)@C82(III) metallofullerenes. Chemical Physics Letters, 433(1–3), 120–124.

    CAS  Google Scholar 

  • Nishibori, E., Narioka, S., Takata, M., Sakata, M., Inoue, T., & Shinohara, H. (2006b). A C2 molecule entrapped in the pentagonal-dodecahedral Y2 cage in Y2C2@C82(III). ChemPhysChem, 7(2), 345–348.

    CAS  Google Scholar 

  • Olmstead, M. H., de Bettencourt-Dias, A., Duchamp, J. C., Stevenson, S., Marciu, D., Dorn, H. C., & Balch, A. L. (2001). Isolation and structural characterization of the endohedral fullerene Sc3N@C78. Angewandte Chemie-International Edition, 40(7), 1223–1225.

    CAS  Google Scholar 

  • Olmstead, M. M., Lee, H. M., Duchamp, J. C., Stevenson, S., Marciu, D., Dorn, H. C., & Balch, A. L. (2003). Sc3N@C68: Folded pentalene coordination in an endohedral fullerene that does not obey the isolated pentagon rule. Angewandte Chemie-International Edition, 42(8), 900–903.

    CAS  Google Scholar 

  • Omelyanyuk, N. A., Goryunkov, A. A., Tamm, N. B., Avdoshenko, S. M., Ioffe, I. N., Sidorov, L. N., Kemnitz, E., & Troyanov, S. I. (2007). New trifluoromethylated derivatives of [60]fullerene, C60(CF3) n with n = 12 and 14. Chemical Communications, 2007(45), 4794–4796.

    Google Scholar 

  • Popov, A. A. (2009). Metal-cage bonding, molecular structures and vibrational spectra of endohedral fullerenes: Bridging experiment and theory. Journal of Computational and Theoretical Nanoscience, 6(2), 292–317.

    CAS  Google Scholar 

  • Popov, A. A., & Dunsch, L. (2008). Hindered cluster rotation and 45Sc hyperfine splitting constant in distonoid anion radical Sc3N@C80, and spatial spin charge separation as a general principle for anions of endohedral fullerenes with metal-localized lowest unoccupied molecular orbitals. Journal of the American Chemical Society, 130(52), 17726–17742.

    CAS  Google Scholar 

  • Popov, A. A., & Dunsch, L. (2009). The bonding situation in endohedral metallofullerenes as studied by quantum theory of atoms in molecules (QTAIM). Chemistry – A European Journal, 15(38), 9707–9729.

    Google Scholar 

  • Popov, A. A., Senyavin, V. M., Granovsky, A. A., & Lobach, A. S. (2004). Vibrational spectra and molecular structure of the hydrofullerenes C60H18, C60D18 and C60H36 as studied by IR and Raman spectroscopy and first-principle calculations. In T. N. Veziroglu (Ed.), Hydrogen materials science and chemistry of carbonnanomaterials (Vol. 172, pp. 347–356). NATO Science Series II: Mathematics, Physics and Chemistry. Dordrecht: Kluwer Academic.

    Google Scholar 

  • Popov, A. A., Senyavin, V. M., Boltalina, O. V., Seppelt, K., Spandl, J., Feigerle, C. S., & Compton, R. N. (2006). Infrared, Raman, and DFT vibrational spectroscopic studies of C60F36 and C60F48. Journal of Physical Chemistry A, 110(28), 8645–8652.

    CAS  Google Scholar 

  • Popov, A. A., & Dunsch, L. (2007a). Structure, stability, and cluster-cage interactions in nitride clusterfullerenes M3N@C2n (M = Sc, Y; 2n = 68–98): A density functional theory study. Journal of the American Chemical Society, 129(38), 11835–11849.

    CAS  Google Scholar 

  • Popov, A. A., Kareev, I. E., Shustova, N. B., Lebedkin, S. F., Strauss, S. H., Boltalina, O. V., & Dunsch, L. (2007b). Synthesis, spectroscopic and electrochemical characterization, and DFT study of seventeen C70(CF3) n derivatives (n = 2, 4, 6, 8, 10, 12). Chemistry – A European Journal, 14(1), 107–121.

    Google Scholar 

  • Popov, A. A., Kareev, I. E., Shustova, N. B., Stukalin, E. B., Lebedkin, S. F., Seppelt, K., Strauss, S. H., Boltalina, O. V., & Dunsch, L. (2007c). Electrochemical, spectroscopic, and DFT study of C60(CF3) n frontier orbitals (n = 2–18): The link between double bonds in pentagons and reduction potentials. Journal of the American Chemical Society, 129(37), 11551–11568.

    CAS  Google Scholar 

  • Popov, A. A., Krause, M., Yang, S. F., Wong, J., & Dunsch, L. (2007d). C78 cage isomerism defined by trimetallic nitride cluster size: A computational and vibrational spectroscopic study. Journal of Physical Chemistry B, 111(13), 3363–3369.

    CAS  Google Scholar 

  • Raghavachari, K. (1992). Ground state of C84: Two almost isoenergetic isomers. Chemical Physics Letters, 190(5), 397–400.

    CAS  Google Scholar 

  • Reimers, J. R., Cai, Z.-L., Bilic, A., & Hush, N. S. (2003). The appropriateness of density-functional theory for the calculation of molecular electronics properties. Annals of the New York Academy of Sciences, 1006, 235–251.

    CAS  Google Scholar 

  • Rogers, K. M., & Fowler, P. W. (1999). A model for pathways of radical addition to fullerenes. Chemical Communications, 1999(23), 2357–2358.

    Google Scholar 

  • Rodriguez-Fortea, A., Alegret, N., Balch, A. L., & Poblet, J. M. (2010). The maximum pentagon separation rule provides guideline for the structures of endohedral metallofullerenes. Nature Chemistry, 2(11), 955–961.

    CAS  Google Scholar 

  • Ruchardt, C., Gerst, M., Ebenhoch, J., Beckhaus, H. D., Campbell, E. E. B., Tellgmann, R., Schwarz, H., Weiske, T., & Pitter, S. (1993). Bimolecular radical formation through H-transfer 3. Transfer hydrogenation and deuteration of buckminsterfullerene C60 by 9,10-dihydroanthracene and 9,9, 10,10[D4]dihydroanthracene. Angewandte Chemie-International Edition in English, 32(4), 584–586.

    Google Scholar 

  • Samokhvalova, N. A., Khavrel, P. A., Markov, V. Y., Samokhvalov, P. S., Goryunkov, A. A., Kemnitz, E., Sidorov, L. N., & Troyanov, S. I. (2009). Isolation and structural characterization of the most stable, highly symmetric isomer of C60(CF3)18. European Journal of Organic Chemistry, 2009(18), 2935–2938.

    Google Scholar 

  • Sandall, J. P. B., & Fowler, P. W. (2003). The energies of some isomers of C60F8: The use of experimental and theoretical considerations to limit candidate structures. Organic & Biomolecular Chemistry, 1(6), 1061–1066.

    CAS  Google Scholar 

  • Sato, Y., Yumura, T., Suenaga, K., Moribe, H., Nishide, D., Ishida, M., Shinohara, H., & Iijima, S. (2006). Direct imaging of intracage structure in titanium-carbide endohedral metallofullerene. Physical Review B, 73(19), 193401.

    Google Scholar 

  • Saunders, M., Jimenezvazquez, H. A., Cross, R. J., & Poreda, R. J. (1993). Stable compounds of Helium and Neon – He@C60 and Ne@C60. Science, 259(5100), 1428–1430.

    CAS  Google Scholar 

  • Schmalz, T. G., Seitz, W. A., Klein, D. J., & Hite, G. E. (1988). Elemental carbon cages. Journal of the American Chemical Society, 110(4), 1113–1127.

    CAS  Google Scholar 

  • Shao, N., Gao, Y., Yoo, S., An, W., & Zeng, X. C. (2006). Search for lowest-energy fullerenes: C98 to C110. Journal of Physical Chemistry A, 110(24), 7672–7676.

    CAS  Google Scholar 

  • Shao, N., Gao, Y., & Zeng, X. C. (2007). Search for lowest-energy fullerenes 2: C38 to C80 and C112 to C120. Journal of Physical Chemistry C, 111(48), 17671–17677.

    CAS  Google Scholar 

  • Shi, Z. Q., Wu, X., Wang, C. R., Lu, X., & Shinohara, H. (2006). Isolation and characterization of Sc2C2@C68: A metal-carbide endofullerene with a non-IPR carbon cage. Angewandte Chemie-International Edition, 45(13), 2107–2111.

    CAS  Google Scholar 

  • Shimotani, H., Ito, T., Iwasa, Y., Taninaka, A., Shinohara, H., Nishibori, E., Takata, M., & Sakata, M. (2004). Quantum chemical study on the configurations of encapsulated metal ions and the molecular vibration modes in endohedral dimetallofullerene La2@C80. Journal of the American Chemical Society, 126(1), 364–369.

    CAS  Google Scholar 

  • Shinohara, H. (2000). Endohedral metallofullerenes. Reports on Progress in Physics, 63(6), 843–892.

    CAS  Google Scholar 

  • Shustova, N. B., Kuvychko, I. V., Bolskar, R. D., Seppelt, K., Strauss, S. H., Popov, A. A., & Boltalina, O. V. (2006). Trifluoromethyl derivatives of insoluble small-HOMO–LUMO-gap hollow higher fullerenes. NMR and DFT structure elucidation of C2-(C74 -D 3h )(CF3)12, C s -(C76 -T d (2))(CF3)12, C 2-(C78 -D 3h (5))(CF3)12, C s -(C80-C2v (5))(CF3)12, and C 2-(C82 -C 2(5)) (CF3)12. Journal of the American Chemical Society, 128(49), 15793–15798.

    Google Scholar 

  • Shustova, N. B., Newell, B. S., Miller, S. M., Anderson, O. P., Bolskar, R. D., Seppelt, K., Popov, A. A., Boltalina, O. V., & Strauss, S. H. (2007). Discovering and verifying elusive fullerene cage isomers: Structures of C 2 -p 11-(C74 -D 3h )(CF3)12 and C 2 -p 11-(C78 -D 3h (5))(CF3)12. Angewandte Chemie-International Edition, 46(22), 4111–4114.

    CAS  Google Scholar 

  • Shustova, N. B., Chen, Y.-S., Mackey, M. A., Coumbe, C. E., Phillips, J. P., Stevenson, S., Popov, A. A., Strauss, S. H., & Boltalina, O. V. (2009). Sc3N@(C80 -I h (7))(CF3)14 and Sc3N@(C80 -I h (7))(CF3)16. Endohedral metallofullerene derivatives with exohedral addends on four and eight triple-hexagon junctions. Does the Sc3N cluster control the addition pattern or vice versa? Journal of the American Chemical Society, 131(48), 17630–17637.

    Google Scholar 

  • Shustova, N. B., Mazej, Z., Chen, Y.-S., Popov, A. A., Strauss, S. H., & Boltalina, O. V. (2010). Saturnene revealed: X-ray crystal structure of D 5d -C60F20 formed in reactions of C60 with A x MF y fluorinating agents (A = Alkali Metal; M = 3d Metal). Angewandte Chemie International Edition, 49, 812–815.

    CAS  Google Scholar 

  • Shustova, N. B., Peryshkov, D. V., Kuvychko, I. V., Chen, Y.-S., Mackey, M. A., Coumbe, C. E., Heaps, D. T., Confait, B. S., Heine, T., Phillips, J. P., Stevenson, S., Dunsch, L., Popov, A. A., Strauss, S. H., & Boltalina, O. V. (2011). Poly(perfluoroalkylation) of metallic nitride fullerenes reveals addition-pattern guidelines: Synthesis and characterization of a family of Sc3N@C80(CF3) n (n = 2–16) and their radical anions. Journal of the American Chemical Society, 133(8), 2672–2690.

    CAS  Google Scholar 

  • Simeonov, K. S., Amsharov, K. Y., & Jansen, M. (2007). Connectivity of the chiral D 2-symmetric isomer of C76 through a crystal-structure determination C76Cl18 ⋅TiCl4. Angewandte Chemie-International Edition, 46(44), 8419–8421.

    CAS  Google Scholar 

  • Simeonov, K. S., Amsharov, K. Y., Krokos, E., & Jansen, M. (2008). An Epilogue on the C78-fullerene family: The discovery and characterization of an elusive isomer. Angewandte Chemie International Edition, 47, 6283–6285.

    CAS  Google Scholar 

  • Slanina, Z., Zhao, X., Deota, P., & Osawa, E. (2000). Relative stabilities of C92 IPR fullerenes. Journal of Molecular Modeling, 6(2), 312–317.

    CAS  Google Scholar 

  • Slanina, Z., Ishimura, K., Kobayashi, K., & Nagase, S. (2004a). C72 isomers: The IPR-satisfying cage is disfavored by both energy and entropy. Chemical Physics Letters, 384(1–3), 114–118.

    CAS  Google Scholar 

  • Slanina, Z., Zhao, X., Uhlik, F., Lee, S. L., & Adamowicz, L. (2004b). Computing enthalpy-entropy interplay for isomeric fullerenes. International Journal of Quantum Chemistry, 99(5), 640–653.

    CAS  Google Scholar 

  • Slanina, Z., Chen, Z. F., Schleyer, P. V., Uhlik, F., Lu, X., & Nagase, S. (2006a). La2@C72 and Sc2@C72: Computational characterizations. Journal of Physical Chemistry A, 110(6), 2231–2234.

    CAS  Google Scholar 

  • Slanina, Z., Uhlik, F., & Nagase, S. (2006b). Computed structures of two known Yb@C74 isomers. Journal of Physical Chemistry A, 110(47), 12860–12863.

    CAS  Google Scholar 

  • Slanina, Z., Uhlik, F., Sheu, J. H., Lee, S. L., Adamowicz, L., & Nagase, S. (2008). Stabilities of fullerenes: Illustration on C80. Match-Communications in Mathematical and in Computer Chemistry, 59, 225–238.

    CAS  Google Scholar 

  • Spielmann, H. P., Weedon, B. R., & Meier, M. S. (2000). Preparation and NMR characterization of C70H10: Cutting a fullerene pi-system in half. Journal of Organic Chemistry, 65(9), 2755–2758.

    CAS  Google Scholar 

  • Stevenson, S., Rice, G., Glass, T., Harich, K., Cromer, F., Jordan, M. R., Craft, J., Hadju, E., Bible, R., Olmstead, M. M., Maitra, K., Fisher, A. J., Balch, A. L., & Dorn, H. C. (1999). Small-bandgap endohedral metallofullerenes in high yield and purity. Nature, 401(6748), 55–57.

    CAS  Google Scholar 

  • Stevenson, S., Fowler, P. W., Heine, T., Duchamp, J. C., Rice, G., Glass, T., Harich, K., Hajdu, E., Bible, R., & Dorn, H. C. (2000). Materials science – A stable non-classical metallofullerene family. Nature, 408(6811), 427–428.

    CAS  Google Scholar 

  • Stevenson, S., Mackey, M. A., Stuart, M. A., Phillips, J. P., Easterling, M. L., Chancellor, C. J., Olmstead, M. M., & Balch, A. L. (2008). A distorted tetrahedral metal oxide cluster inside an icosahedral carbon cage. Synthesis, isolation, and structural characterization of Sc43-O)2@I h -C80. Journal of the American Chemical Society, 130(36), 11844–11845.

    Google Scholar 

  • Sun, G. Y. (2003a). Assigning the major isomers of fullerene C88 by theoretical 13C NMR spectra. Chemical Physics Letters, 367(1–2), 26–33.

    CAS  Google Scholar 

  • Sun, G. Y. (2003b). Theoretical 13C NMR chemical shifts of the stable isomers of fullerene C90. Chemical Physics, 289(2–3), 371–380.

    CAS  Google Scholar 

  • Sun, G. Y., & Kertesz, M. (2000). Theoretical 13C NMR spectra of IPR isomers of fullerenes C60, C70, C72, C74, C76, and C78 studied by density functional theory. Journal of Physical Chemistry A, 104(31), 7398–7403.

    CAS  Google Scholar 

  • Sun, G. Y., & Kertesz, M. (2001a). Identification for IPR isomers of fullerene C82 by theoretical 13C NMR spectra calculated by density functional theory. Journal of Physical Chemistry A, 105(22), 5468–5472.

    CAS  Google Scholar 

  • Sun, G. Y., & Kertesz, M. (2001b). Isomer identification for fullerene C84 by 13C NMR spectrum: A density-functional theory study. Journal of Physical Chemistry A, 105(21), 5212–5220.

    CAS  Google Scholar 

  • Sun, G. Y., & Kertesz, M. (2002). 13C NMR spectra for IPR isomers of fullerene C86. Chemical Physics, 276(2), 107–114.

    CAS  Google Scholar 

  • Tagmatarchis, N., Avent, A. G., Prassides, K., Dennis, T. J. S., & Shinohara, H. (1999). Separation, isolation and characterisation of two minor isomers of the [84]fullerene C84. Chemical Communications, 1999(11), 1023–1024.

    Google Scholar 

  • Tagmatarchis, N., Arcon, D., Prato, M., & Shinohara, H. (2002). Production, isolation and structural characterization of [92]fullerene isomers. Chemical Communications, 2002(24), 2992–2993.

    Google Scholar 

  • Takata, M., Nishibori, E., Sakata, M., & Shinohara, H. (2003). Synchrotron radiation for structural chemistry – endohedral natures of metallofullerenes found by synchrotron radiation powder method. Structural Chemistry, 14(1), 23–38.

    CAS  Google Scholar 

  • Tamm, N. B., Sidorov, L. N., Kemnitz, E., & Troyanov, S. I. (2009a). Crystal structures of C94(CF3)20 and C96(C2F5)12 reveal the cage connectivities in C94(61) and C96(145) fullerenes. Angewandte Chemie International Edition, 48, 9102–9104.

    CAS  Google Scholar 

  • Tamm, N. B., Sidorov, L. N., Kemnitz, E., & Troyanov, S. I. (2009b). Isolation and structural X-ray investigation of perfluoroalkyl derivatives of six cage isomers of C84. Chemistry – A European Journal, 15(40), 10486–10492.

    Google Scholar 

  • Tan, K., & Lu, X. (2005). Ti2C80 is more likely a titanium carbide endohedral metallofullerene (Ti2C2)@C78. Chemical Communications, 2005(35), 4444–4446.

    Google Scholar 

  • Tan, Y.-Z., Xie, S.-Y., Huanh, R.-B., & Zheng, I.-S. (2009). The stabilization of fused-pentagon fullerene molecules. Nature Chemistry, 1, 450–460.

    CAS  Google Scholar 

  • Tebbe, F. N., Harlow, R. L., Chase, D. B., Thorn, D. L., Campbell, G. C., Calabrese, J. C., Herron, N., Young, R. J., & Wasserman, E. (1992). Synthesis and single-crystal X-ray structure of a highly symmetrical C60 derivative, C60Br24. Science, 256(5058), 822–825.

    CAS  Google Scholar 

  • Troyanov, S. I., & Kemnitz, E. (2005). Synthesis and structures of fullerene bromides and chlorides. European Journal of Organic Chemistry, 2005(23), 4951–4962.

    Google Scholar 

  • Troyanov, S. I., Popov, A. A., Denisenko, N. I., Boltalina, O. V., Sidorov, L. N., & Kemnitz, E. (2003). The first X-ray crystal structures of halogenated [70]fullerene: C70Br10 and C70Br10 ⋅3Br2. Angewandte Chemie-International Edition, 42(21), 2395–2398.

    CAS  Google Scholar 

  • Troyanov, S. I., Dimitrov, A., & Kemnitz, E. (2006). Selective synthesis of a trifluoromethylated fullerene and the crystal structure of C60(CF3)12. Angewandte Chemie-International Edition, 45(12), 1971–1974.

    CAS  Google Scholar 

  • Troyanov, S. I., Goryunkov, A. A., Dorozhkin, E. I., Ignat’eva, D. V., Tamm, N. B., Avdoshenko, S. M., Ioffe, I. N., Markov, V. Y., Sidorov, L. N., Scheurel, K., & Kemnitz, E. (2007). Higher trifluoromethylated derivatives of C60, C60(CF3)16 and C60(CF3)18 – Synthesis, structure, and theoretical study. Journal of Fluorine Chemistry, 128(5), 545–551.

    CAS  Google Scholar 

  • Troyanov, S. I., & Tamm, N. B. (2009a). Cage connectivities of C88(33) and C92(82) fullerenes captured as trifluoromethyl derivatives, C88(CF3)18 and C92(CF3)16. Chemical Communications, 2009(40), 6035–6037.

    Google Scholar 

  • Troyanov, S. I., & Tamm, N. B. (2009b). Crystal and molecular structures of trifluoromethyl derivatives of fullerene C86, C86(CF3)16 and C86(CF3)18. Crystallography Reports, 54(4), 598–602.

    CAS  Google Scholar 

  • Tsuchiya, T., Wakahara, T., Maeda, Y., Akasaka, T., Waelchli, M., Kato, T., Okubo, H., Mizorogi, N., Kobayashi, K., & Nagase, S. (2005). 2D NMR characterization of the La@C82 anion. Angewandte Chemie-International Edition, 44(21), 3282–3285.

    CAS  Google Scholar 

  • Valencia, R., Rodriguez-Fortea, A., & Poblet, J. M. (2007). Large fullerenes stabilized by encapsulation of metallic clusters. Chemical Communications, (40), 4161–4163.

    Google Scholar 

  • Valencia, R., Rodríguez-Fortea, A., & Poblet, J. M. (2008). Understanding the stabilization of metal carbide endohedral fullerenes M2C2@C82 and related systems. Journal of Physical Chemistry A, 112(20), 4550–4555.

    CAS  Google Scholar 

  • Wakabayashi, T., Kikuchi, K., Suzuki, S., Shiromaru, H., & Achiba, Y. (1994). Pressure-controlled selective isomer formation of fullerene-C78. Journal of Physical Chemistry, 98(12), 3090–3091.

    CAS  Google Scholar 

  • Wakahara, T., Kobayashi, J., Yamada, M., Maeda, Y., Tsuchiya, T., Okamura, M., Akasaka, T., Waelchli, M., Kobayashi, K., Nagase, S., Kato, T., Kako, M., Yamamoto, K., & Kadish, K. M. (2004). Characterization of Ce@C82 and its anion. Journal of the American Chemical Society, 126(15), 4883–4887.

    CAS  Google Scholar 

  • Wakahara, T., Nikawa, H., Kikuchi, T., Nakahodo, T., Rahman, G. M. A., Tsuchiya, T., Maeda, Y., Akasaka, T., Yoza, K., Horn, E., Yamamoto, K., Mizorogi, N., Slanina, Z., & Nagase, S. (2006). La@C72 having a non-IPR carbon cage. Journal of the American Chemical Society, 128(44), 14228–14229.

    CAS  Google Scholar 

  • Wang, C. R., Kai, T., Tomiyama, T., Yoshida, T., Kobayashi, Y., Nishibori, E., Takata, M., Sakata, M., & Shinohara, H. (2000a). C66 fullerene encaging a scandium dimer. Nature, 408, 426–427.

    CAS  Google Scholar 

  • Wang, C. R., Sugai, T., Kai, T., Tomiyama, T., & Shinohara, H. (2000b). Production and isolation of an ellipsoidal C80 fullerene. Chemical Communications, (7), 557–558.

    Google Scholar 

  • Wang, C. R., Kai, T., Tomiyama, T., Yoshida, T., Kobayashi, Y., Nishibori, E., Takata, M., Sakata, M., & Shinohara, H. (2001). A scandium carbide endohedral metallofullerene: (Sc2C2)@C84. Angewandte Chemie-International Edition, 40(2), 397–399.

    CAS  Google Scholar 

  • Wang, T.-S., Chen, N., Xiang, J.-F., Li, B., Wu, J.-Y., Xu, W., Jiang, L., Tan, K., Shu, C.-Y., Lu, X., & Wang, C.-R. (2009). Russian-Doll-Type metal carbide endofullerene: Synthesis, isolation, and characterization of Sc4C2@C80. Journal of the American Chemical Society, 131(46), 16646–16647.

    CAS  Google Scholar 

  • Wu, J., & Hagelberg, F. (2008). Computational study on C80 enclosing mixed trimetallic nitride clusters of the form Gd x M3-x N (M = Sc, Sm, Lu). Journal of Physical Chemistry C, 112(15), 5770–5777.

    CAS  Google Scholar 

  • Xiao, Z., Wang, F. D., Huang, S. H., Gan, L. B., Zhou, J., Yuan, G., Lu, M. J., & Pan, J. Q. (2005). Regiochemistry of [70]fullerene: Preparation of C70((OOBu)-tBu) n , (n = 2, 4, 6, 8, 10) through both equatorial and cyclopentadienyl addition modes. Journal of Organic Chemistry, 70(6), 2060–2066.

    CAS  Google Scholar 

  • Xu, L., Cai, W. S., & Shao, X. G. (2006). Prediction of low-energy isomers of large fullerenes from C132 to C160. Journal of Physical Chemistry A, 110(29), 9247–9253.

    CAS  Google Scholar 

  • Xu, L., Cai, W. S., & Shao, X. G. (2007). Performance of the semiempirical AM1, PM3, MNDO, and tight-binding methods in comparison with DFT method for the large fullerenes C116–C120. Journal of Molecular Structure-Theochem, 817(1–3), 35–41.

    CAS  Google Scholar 

  • Xu, L., Cai, W., & Shao, X. (2008). Systematic search for energetically favored isomers of large fullerenes C122-C130 and C162-C180. Computational Materials Science, 41, 522–528.

    CAS  Google Scholar 

  • Yamada, M., Wakahara, T., Tsuchiya, T., Maeda, Y., Kako, M., Akasaka, T., Yoza, K., Horn, E., Mizorogi, N., & Nagase, S. (2008). Location of the metal atoms in Ce2@C78 and its bis-silylated derivative. Chemical Communications, (5), 558–560.

    Google Scholar 

  • Yang, S., Popov, A. A., & Dunsch, L. (2007a). The role of an asymmetric nitride cluster on a fullerene cage: The non-IPR endohedral DySc2N@C76. Journal of Physical Chemistry B, 111(49), 13659–13663.

    CAS  Google Scholar 

  • Yang, S. F., Popov, A. A., & Dunsch, L. (2007b). Violating the isolated pentagon rule (IPR): The endohedral non-IPR cage of Sc3N@C70. Angewandte Chemie-International Edition, 46(8), 1256–1259.

    CAS  Google Scholar 

  • Yang, S., Yoon, M., Hicke, C., Zhang, Z., & Wang, E. (2008). Electron transfer and localization in endohedral metallofullerenes: Ab initio density functional theory calculations. Physical Review B, 78, 115435.

    Google Scholar 

  • Yang, H., Beavers, C. M., Wang, Z., Jiang, A., Liu, Z., Jin, H., Mercado, B. Q., Olmstead, M. M., & Balch, A. L. (2010). Isolation of a small carbon nanotube: The surprising appearance of D 5h (1)-C90. Angewandte Chemie International Edition, 49(5), 886–890.

    CAS  Google Scholar 

  • Yanov, I., Kholod, Y., Simeon, T., Kaczmarek, A., & Leszczynski, J. (2006). Local minima conformations of the Sc3N@C80 endohedral complex: Ab initio quantum chemical study and suggestions for experimental verification. International Journal of Quantum Chemistry, 106(14), 2975–2980.

    CAS  Google Scholar 

  • Yumura, T., Sato, Y., Suenaga, K., & Iijima, S. (2005). Which do endohedral Ti2C80 metallofullerenes prefer energetically: Ti2@C80 or Ti2C2@C78? A theoretical study. Journal of Physical Chemistry B, 109(43), 20251–20255.

    CAS  Google Scholar 

  • Zalibera, M., Rapta, P., & Dunsch, L. (2007). In situ ESR–UV/VIS/NIR spectroelectrochemistry of an empty fullerene anion and cation: The C82:3 isomer. Electrochemistry Communications, 9(12), 2843–2847.

    CAS  Google Scholar 

  • Zhang, J., Hao, C., Li, S. M., Mi, W. H., & Jin, P. (2007). Which configuration is more stable for La2@C80, D 3d or D 2h ? Recomputation with ZORA methods within ADF. Journal of Physical Chemistry C, 111(22), 7862–7867.

    CAS  Google Scholar 

  • Zhao, X., Slanina, Z., Goto, H., & Osawa, E. (2003). Theoretical investigations on relative stabilities of fullerene C94. Journal of Chemical Physics, 118(23), 10534–10540.

    CAS  Google Scholar 

  • Zheng, G. S., Irle, S., & Morokuma, K. (2005). Performance of the DFTB method in comparison to DFT and semiempirical methods for geometries and energies Of C20–C86 fullerene isomers. Chemical Physics Letters, 412(1–3), 210–216.

    CAS  Google Scholar 

  • Zuo, T. M., Beavers, C. M., Duchamp, J. C., Campbell, A., Dorn, H. C., Olmstead, M. M., & Balch, A. L. (2007). Isolation and structural characterization of a family of endohedral fullerenes including the large, chiral cage fullerenes Tb3N@C88 and Tb3N@C86 as well as the I h and D 5h isomers of Tb3N@C80. Journal of the American Chemical Society, 129(7), 2035–2043.

    CAS  Google Scholar 

  • Zuo, T., Walker, K., Olmstead, M. M., Melin, F., Holloway, B. C., Echegoyen, L., Dorn, H. C., Chaur, M. N., Chancellor, C. J., Beavers, C. M., Balch, A. L., & Athans, A. J. (2008). New egg-shaped fullerenes: Non-isolated pentagon structures of Tm3N@C s (51365)-C84 and Gd3N@C s (51365)-C84. Chemical Communications, 2008(9), 1067–1069.

    Google Scholar 

  • Zywietz, T. K., Jiao, H., Schleyer, R., & de Meijere, A. (1998). Aromaticity and antiaromaticity in oligocyclic annelated five-membered ring systems. Journal of Organic Chemistry, 63(10), 3417–3422.

    CAS  Google Scholar 

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Acknowledgments

I would like to thank my colleagues in IFW Dresden, Moscow State University, and Colorado State University for a fruitful collaboration in the studies of fullerenes. A majority of the computations were performed using facilities of Scientific Research Center of the Moscow State University. Financial support from Alexander von Humboldt Foundation and DFG are deeply acknowledged.

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Popov, A.A. (2012). Structures and Stability of Fullerenes, Metallofullerenes, and Their Derivatives. In: Leszczynski, J. (eds) Handbook of Computational Chemistry. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0711-5_19

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