Abstract
This chapter deals with computational and theoretical support to fullerene/nanocarbon research needed for interpretations, rationalizations, and generalizations of experimental results. In particular, predictions of various nanocarbon stabilities, or even populations, based on quantum-chemical and statistical-mechanical methods, are surveyed. The calculations are, with respect to high temperatures in fullerene electric-arc syntheses, frequently based on the Gibbs energy. Considerable thermal effects on the relative isomeric and nonisomeric populations thus revealed in the theoretical treatments originate, on molecular level, in a complex interplay between rotational, vibrational, electronic, relative potential-energy, symmetry, and chirality factors. The considered treatments are built upon a presumption of the (inter-isomeric) thermodynamic equilibrium; however, some kinetic and catalytic aspects are also included. The survey is focused on empty fullerenes, metallofullerenes, clusterfullerenes, and nonmetal endohedrals. The covered quantum-chemical treatments are the semiempirical, ab initio Hartree-Fock, density-functional theory, and perturbation approaches. The calculations have already yielded a reasonable computation-observation agreement for the isomeric systems with empty C76 till C96 cages, and mostly also when applied to metallofullerenes. This relatively large tested set supports the belief in still wider applicability of the Gibbs-energy calculations to basically all classes of nanocarbons. This chapter is complementary to this volume chapter Theoretical Prediction of Fullerene Reactivity.
Similar content being viewed by others
References
Kroto HW, Heath JR, O’Brien SC, Curl RF, Smalley RE (1985) C60: buckminsterfullerene. Nature 318:162–163
Rohlfing EA, Cox DM, Kaldor A (1984) Production and characterization of supersonic carbon cluster beams. J Chem Phys 81:3322–3330
Krätschmer W, Lamb LD, Fostiropoulos K, Huffman DR (1990) Solid C60: a new form of carbon. Nature 347:354–358
Slanina Z (2001) ISSPIC-5 in Konstanz in 1990: announcements of the C60 preparation and its structure confirmation. Int J Hist Eth Natur Sci Technol Med NTM 9:41–46
Heath JR, O’Brien SC, Zhang Q, Liu Y, Curl RF, Kroto HW, Tittel FK, Smalley RE (1985) Lanthanum complexes of spheroidal carbon shells. J Am Chem Soc 107:7779–7780
Kroto HW, Allaf AW, Balm SP (1991) C60: buckminsterfullerene. Chem Rev 91:1213–1235
Rodríguez-Fortea A, Balch AL, Poblet JM (2011) Endohedral metallofullerenes: a unique host-guest association. Chem Soc Rev 40:3551–3563
Popov AA, Yang S, Dunsch L (2013) Endohedral fullerenes. Chem Rev 113:5989–6113
Slanina Z, Uhlík F, Lee S-L, Akasaka T, Nagase S (2012) Stability computations for fullerenes and metallofullerenes. In: D’Souza F, Kadish KM (eds) Handbook of carbon Nano materials, Vol. 4. Materials and fundamental applications. World Scientific, Singapore, pp 381–429
Cioslowski J (1993) Ab initio calculations on large molecules: methodology and applications. Rev Comput Chem 4:1–33
Slanina Z, Lee S-L, Yu C-H (1996) Computations in treating fullerenes and carbon aggregates. Rev Comput Chem 8:1–62
Slanina Z (1975) Remark on the present applicability of quantum chemistry to the calculations of equilibrium and rate constants of chemical reactions. Radiochem Radioanal Lett 22:291–298
Slanina Z, Zahradnik R (1977) MINDO/2 study of equilibrium carbon vapor. J Phys Chem 81:2252–2257
Schultz HP (1965) Topological organic chemistry. Polyhedranes and prismanes. J Org Chem 30:1361–1364
Ōsawa E (1970) Superaromaticity. Kagaku 25:854–863; Chem. Abstr. 74, 75698v (1971)
Slanina Z, Zhao X, Uhlík F, Lee S-L, Adamowicz L (2004) Computing enthalpy-entropy interplay for isomeric fullerenes. Int J Quantum Chem 99:640–653
Slanina Z, Rudziński JM, Togasi M, Ōsawa E (1989) Quantum-chemically supported vibrational analysis of giant molecules: the C60 and C70 clusters. J Mol Struct (THEOCHEM) 202:169–176
Slanina Z, Lee S-L, Uhlik F, Adamowicz L, Nagase S (2007) Computing relative stabilities of metallofullerenes by Gibbs energy treatments. Theor Chem Accounts 117:315–322
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Akasaka T, Nagase S (2011) Calculations of metallofullerene yields. J Comput Theor Nanosci 8:2233–2239
Slanina Z (1986) Contemporary theory of chemical isomerism. Kluwer Academic Publishers, Dordrecht
Akasaka T, Nagase S, Kobayashi K, Wälchli M, Yamamoto K, Funasaka H, Kako M, Hoshino T, Erata T (1997) 13C and 139La NMR studies of La2@C80: first evidence for circular motion of metal atoms in endohedral dimetallofullerenes. Angew Chem Intl Ed Engl 36:1643–1645
Slanina Z (1974) Ph.D. thesis. Czech Academy of Science, Prague
Sun M-L, Slanina Z, Lee S-L (1995) Square/hexagon route towards the boron-nitrogen clusters. Chem Phys Lett 233:279–283
Zhao X, Slanina Z, Ozawa M, Osawa E, Deota P, Tanabe K (2000) C32: computations of low-energy cages with four-membered rings. Fuller Sci Technol 8:595–613
Slanina Z, Zhao X, Kurita N, Gotoh H, Uhlik F, Rudziński JM, Lee KH, Adamowicz L (2001) Computing the relative gas-phase populations of C60 and C70: beyond the traditional \( \Delta {H}_{f,298}^o \) scale. J Mol Graphics Mod 19:216–221
Slanina Z (2003) Clusters in a saturated vapor: pressure-based temperature enhancement of the cluster fraction. Z Phys Chem 217:1119–1125
Manolopoulos DE, Fowler PW (1992) Molecular graphs, point groups, and fullerenes. J Chem Phys 96:7603–7614
Fowler PW, Manolopoulos DE (1995) An atlas of fullerenes. Clarendon Press, Oxford
Schwerdtfeger P, Wirz LN, Avery J (2015) The topology of fullerenes. WIREs Comput Mol Sci 5:96–145
Manolopoulos DE, Fowler PW (1993) A fullerene without a spiral. Chem Phys Lett 204:1–7
Stone AJ, Wales DJ (1986) Topological theoretical studies of icosahedral C60 and some related species. Chem Phys Lett 128:501–503
Manolopoulos DE, May JC, Down SE (1991) Theoretical studies of the fullerenes – C34 to C70. Chem Phys Lett 181:105–111
Liu X, Klein DJ, Seitz WA, Schmalz TG (1991) Sixty-atom carbon cages. J Comput Chem 12:1265–1269
Slanina Z, Uhlík F, Sheu J-H, Lee S-L, Adamowicz L, Nagase S (2008) Stabilities of fullerenes: illustration on C80. MATCH Commun Math Comput Chem 59:225–238
Sun M-L, Slanina Z, Lee S-L (1995) AM1 computations on C59: significant eight- and nine-membered rings. Fuller Sci Technol 3:627–639
Fowler PW, Quinn CM, Redmond DB (1991) Decorated fullerenes and model structures for water clusters. J Chem Phys 95:7678–7681
Balasubramanian K (1991) Enumeration of isomers of polysubstituted C60 and application to NMR. Chem Phys Lett 182:257–262
Brendsdal E, Cyvin SJ, Cyvin BN, Brunvoll J, Klein DJ, Seitz WA (1990) Buckminster-fullerene, Part C: Hückel energy levels. In: Hargittai I (ed) Quasicrystals, networks, and molecules of fivefold symmetry. VCH Pub, New York, pp 265–276
Bochvar DA, Gal’pern EG (1973) Hypothetical systems: carbododecahedron, s-icosahedron, and carbo-s-icosahedron. Dokl Akad Nauk SSSR 209:610–612
Slanina Z, Adamowicz L (1993) One-, two- and three-dimensional structures of C20. Fuller Sci Technol 1:1–9
van Orden A, Saykally RJ (1998) Small carbon clusters: spectroscopy, structure, and energetics. Chem Rev 98:2313–2357
von Helden G, Kemper PR, Gotts NG, Bowers MT (1993) Isomers of small carbon cluster anions – linear chains with up to 20 atoms. Science 259:1300–1302
Slanina Z, Adamowicz L, François J-P, Ōsawa E (1998) Fullerenes & other carbon aggregates and the diffuse interstellar bands. In: Vigasin AA, Slanina Z (eds) Molecular complexes in Earth’s, planetary, cometary, and interstellar atmospheres. World Scientific, Singapore, pp 133–176
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Nagase S (2006) Computations of endohedral fullerenes: the Gibbs energy treatment. J Comput Meth Sci Eng 6:243–250
Slanina Z (1989) A program for determination of composition and thermodynamics of the ideal gas-phase equilibrium isomeric mixtures. Comput Chem 13:305–311
Kato H, Taninaka A, Sugai T, Shinohara H (2003) Structure of a missing-caged metallofullerene: La2@C72. J Am Chem Soc 125:7782–7783
Slanina Z, Ishimura K, Kobayashi K, Nagase S (2004) C72 isomers: the IPR-satisfying cage is disfavored by both energy and entropy. Chem Phys Lett 384:114–118
Wan TSM, Zhang HW, Nakane T, Xu ZD, Inakuma M, Shinohara H, Kobayashi K, Nagase S (1998) Production, isolation, and electronic properties of missing fullerenes: Ca@C72 and Ca@C74. J Am Chem Soc 120:6806–6807
Slanina Z, Uhlík F, Zhao X, Adamowicz L, Nagase S (2007) Relative stabilities of C74 isomers. Fulleren Nanotub Carb Nanostruct 15:195–205
Sun M-L, Slanina Z, Lee S-L, Uhlík F, Adamowicz L (1995) AM1 computations on seven isolated-pentagon-rule isomers of C80. Chem Phys Lett 246:66–72
Slanina Z, Lee S-L, Uhlík F, Adamowicz L, Nagase S (2006) Excited electronic states and relative stabilities of C80 isomers. Int J Quantum Chem 106:2222–2228
Furche F, Ahlrichs R (2001) Fullerene C80: are there still more isomers? J Chem Phys 114:10362–10367
Slanina Z, Lee S-L, Yoshida M, Ōsawa E (1996) Computations on nineteen isolated-pentagon-rule isomers of C86. Chem Phys 209:13–18
Slanina Z, Lee S-L, Adamowicz L (1997) C80, C86, C88, Semiempirical and ab initio SCF calculations. Int J Quantum Chem 63:529–535
Cross RJ, Saunders M (2005) Transmutation of fullerenes. J Am Chem Soc 127:3044–3047
Wang Z, Yang H, Jiang A, Liu Z, Olmstead MM, Balch AL (2010) Structural similarities in Cs(16)-C86 and C2(17)-C86. Chem Commun 46:5262–5264
Chen C-H, Lin D-Y, Yeh W-Y (2014) Regiospecific coordination of Re3 clusters with the sumanene type hexagons on endohedral metallofullerenes and higher fullerenes that provides an efficient separation method. Chem Eur J 20:5768–5775
Kobayashi K, Nagase S (2002) Structures and electronic properties of endohedral metallofullerenes; theory and experiment. In: Akasaka T, Nagase S (eds) Endofullerenes – a new family of carbon clusters. Kluwer Academic Publishers, Dordrecht, pp 99–119
Ichikawa T, Kodama T, Suzuki S, Fujii R, Nishikawa H, Ikemoto I, Kikuchi K, Achiba Y (2004) Isolation characterization of a new isomer of Ca@C72. Chem Lett 33:1008–1009
Slanina Z, Kobayashi K, Nagase S (2003) Ca@C72 IPR and non-IPR structures: computed temperature development of their relative concentrations. Chem Phys Lett 372:810–814
Kodama T, Fujii R, Miyake Y, Suzuki S, Nishikawa H, Ikemoto I, Kikuchi K, Achiba Y (2003) 13C NMR study of Ca@C74: cage structure and dynamics of a Ca atom inside the cage. In: Guldi DM, Kamat PV, D’Souza F (eds) Fullerenes, Vol. 13: fullerenes and nanotubes: the building blocks of next generation Nanodevices. The Electrochemical Society, Pennington, pp 548–551
Slanina Z, Kobayashi K, Nagase S (2004) Ca@C74 isomers: relative concentrations at higher temperatures. Chem Phys 301:153–157
Uhlík F, Slanina Z, Lee S-L, Adamowicz L, Nagase S (2013) Stability calculations for Eu@C74 isomers. Int J Quantum Chem 113:729–733
Xu ZD, Nakane T, Shinohara H (1996) Production and isolation of Ca@C82 (I-IV) and Ca@C84 (I,II) metallofullerenes. J Am Chem Soc 118:11309–11310
Kodama T, Fujii R, Miyake Y, Sakaguchi K, Nishikawa H, Ikemoto I, Kikuchi K, Achiba Y (2003) Structural study of four Ca@C82 isomers by 13C NMR spectroscopy Chem. Phys Lett 377:197–200
Slanina Z, Kobayashi K, Nagase S (2004) Ca@C82 isomers: computed temperature dependency of relative concentrations. J Chem Phys 120:3397–3400
Akasaka T, Wakahara T, Nagase S, Kobayashi K, Waelchli M, Yamamoto K, Kondo M, Shirakura S, Maeda Y, Kato T, Kako M, Nakadaira Y, Gao X, van Caemelbecke E, Kadish KM (2001) Structural determination of the La@C82 isomer. J Phys Chem B 105:2971–2974
Slanina Z, Kobayashi K, Nagase S (2004) Computed temperature development of the relative stabilities of La@C82 isomers. Chem Phys Lett 388:74–78
Lian YF, Yang SF, Yang SH (2002) Revisiting the preparation of La@C82 (I and II) and La2 @C80: efficient production of the “minor” isomer La@C82 (II). J Phys Chem B 106:3112–3117
Slanina Z, Uhlík F, Akasaka T, Lu X, Adamowicz L (2019) Computational modeling of the Ce@C82 metallofullerene isomeric composition. ECS J Solid State Sci Technol 8:M118–M121
Shibata K, Rikiishi Y, Hosokawa T, Haruyama Y, Kubozono Y, Kashino S, Uruga T, Fujiwara A, Kitagawa H, Takano T, Iwasa Y (2003) Structural and electronic properties of Ce@C82. Phys Rev B 68:094104-1–094104-7
Yang H, Yu M, Jin H, Liu Z, Yao M, Liu B, Olmstead MM, Balch AL (2012) Isolation of three isomers of Sm@C84 and X-ray crystallographic characterization of Sm@D3d(19)-C84 and Sm@C2(13)-C84. J Am Chem Soc 134:5331–5338
Slanina Z, Uhlík F, Nagase S, Akasaka T, Adamowicz L, Lu X (2017) Eu@C72: computed comparable populations of two non-IPR isomers. Molecules 22:1053-1–1053-8
Takata M, Nishibori E, Sakata M, Shinohara H (2002) Charge density level structures of endohedral metallofullerenes determined by synchrotron radiation powder method. New Diam Front Carb Technol 12:271–286
Jensen F (2017) Introduction to computational chemistry. Wiley, Chichester, p 319
Slanina Z (2004) Temperature development of mono- and hetero-clustering in saturated vapors. J Clust Sci 15:3–11
Alcock CB, Itkin VP, Horrigan MK (1984) Vapor pressure equations for the metallic elements: 298-2500 K. Can Metallurg Quart 23:309–313
Slanina Z, Uhlík F, Nagase S (2007) Computational evaluation of the relative production yields in the X@C74 series (X = Ca, Sr, Ba). Chem Phys Lett 440:259–262
Gromov A, Krawez N, Lassesson A, Ostrovskii DI, Campbell EEB (2002) Optical properties of endohedral Li@C60. Curr App Phys 2:51–55
Kobayashi K, Nagase S (1999) Bonding features in endohedral metallofullerenes. Topological analysis of the electron density distribution. Chem Phys Lett 302:312–316
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Akasaka T, Nagase S (2011) Computed stabilities in metallofullerene series: Al@C82, Sc@C82, Y@C82, and La@C82. Int J Quant Chem 111:2712–2718
Peres T, Cao BP, Cui WD, Khong A, Cross RJ, Saunders M, Lifshitz C (2001) Some new diatomic molecule containing endohedral fullerenes. Int J Mass Spectr 210:241–247
Suetsuna T, Dragoe N, Harneit W, Weidinger A, Shimotani H, Ito S, Takagi H, Kitazawa K (2002) Separation of N2@C60 and N@C60. Chem Eur J 8:5079–5083
Knapp C, Dinse K-P, Pietzak B, Waiblinger M, Weidinger A (1997) Fourier transform EPR study of N@C60 in solution. Chem Phys Lett 272:433–437
Saunders M, Jiménez-Vázquez HA, Cross RJ, Poreda RJ (1993) Stable compounds of helium and Neon: He@C60 and Ne@C60. Science 259:1428–1430
Zhang R, Murata M, Aharen T, Wakamiya A, Shimoaka T, Hasegawa T, Murata Y (2016) Synthesis of a distinct water dimer inside fullerene C70. Nature Chem 8:435–441
Slanina Z, Nagase S (2006) A computational characterization of N2@C60. Mol Phys 104:3167–3171
Slanina Z, Uhlík F, Adamowicz L, Nagase S (2005) Computing fullerene encapsulation of non-metallic molecules: N2@C60 and NH3@C60. Mol Simul 31:801–806
Slanina Z, Uhlík F, Nagase S, Lu X, Akasaka T, Adamowicz L (2016) Computed relative populations of D2(22)-C84 endohedrals with encapsulated monomeric and dimeric water. ChemPhysChem 17:1109–1111
Slanina Z, Uhlík F, Nagase S, Akasaka T, Lu X, Adamowicz L (2018) Cyclic water-trimer encapsulation into D2(22)-C84 fullerene. Chem Phys Lett 695:245–248
Stevenson S, Rice G, Glass T, Harich K, Cromer F, Jordan MR, Craft J, Hadju E, Bible R, Olmstead MM, Maitra K, Fisher AJ, Balch AL, Dorn HC (1999) Small-bandgap endohedral metallofullerenes in high yield and purity. Nature 401:55–57
Yang S, Liu F, Chen C, Jiao M, Wei T (2011) Fullerenes encaging metal clusters – cluster-fullerenes. Chem Commun 47:11822–11839
Slanina Z, Uhlík F, Feng L, Akasaka T, Lu X, Adamowicz L (2019) Calculations of the Lu3N@C80 two-isomer equilibrium. Fulleren Nanotub Carb Nanostruct 27:382–386
Shen W-Q, Bao L-P, Hu S-F, Gao X-J, Xie Y-P, Gao X-F, Huang W-H, Lu X (2018) Isolation and crystallographic characterization of Lu3N@C2n (2n = 80–88): cage selection by cluster size. Chem Eur J 24:16692–16698
Dunsch L, Yang SF, Zhang L, Svitova A, Oswald S, Popov AA (2010) Metal sulfide in a C82 fullerene cage: a new form of endohedral clusterfullerenes. J Am Chem Soc 132:5413–5421
Mercado BQ, Chen N, Rodriguez-Fortea A, Mackey MA, Stevenson S, Echegoyen L, Poblet JM, Olmstead MM, Balch AL (2011) The shape of the Sc-2(mu(2)-S) unit trapped in C82: crystallographic, computational, and electrochemical studies of the isomers, Sc-2(mu(2)-S)@C-s(6)-C-82 and Sc-2(mu(2)-S)@C-3v(8)-C-82. J Am Chem Soc 133:6752–6760
Slanina Z, Uhlík F, Lee S-L, Mizorogi N, Akasaka T, Adamowicz L (2011) Calculated relative yields for Sc2S@C82 and Y2S@C82. Theor Chem Accounts 130:549–554
Hao Y, Tang Q, Li X, Zhang M, Wan Y, Feng L, Chen N, Slanina Z, Adamowicz L, Uhlík F (2016) Isomeric Sc2O@C78 related by a single-step Stone-Wales transformation: key links in an unprecedented fullerene formation pathway. Inorg Chem 55:11354–11361
Slanina Z, Uhlík F, Feng L, Adamowicz L (2017) Sc2O@C78: calculations of the yield ratio for two observed isomers. Fulleren Nanotub Carb Nanostruct 25:124–127
Slanina Z, Uhlík F, Pan C, Akasaka T, Lu X, Adamowicz L (2018) Computed stabilization for a giant fullerene endohedral: Y2C2@C1(1660)-C108. Chem Phys Lett 710:147–149
Ervin KM, Gronert S, Barlow SE, Gilles MK, Harrison AG, Bierbaum VM, DePuy CH, Lineberger WC, Ellison GB (1990) Bond strengths of ethylene and acetylene. J Am Chem Soc 112:5750–5759
Slanina Z, Ōsawa E (1997) Average bond dissociation energies of fullerene. Fuller Sci Technol 5:167–175
Yu P, Shen W, Bao L, Pan C, Slanina Z, Lu X (2019) Trapping an unprecedented Ti3C3 unit inside the icosahedral C80 fullerene: a crystallographic survey. Chem Sci 10:10925–10930
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Nagase S (2008) MPWB1K calculations of stepwise encapsulations: Lix@C60. Chem Phys Lett 463:121–123
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Nagase S (2007) Alkali-metal clusters encapsulated into fullerenes: computations on Lix@C60. J Comput Meth Sci Eng 7:541–547
Mardirossiana N, Head-Gordon M (2017) Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals. Mol Phys 115:2315–2372
Slanina Z, Uhlík F, Lee S-L, Wang B-C, Adamowicz L, Suzuki M, Haranaka M, Feng L, Lu X, Nagase S, Akasaka T (2014) Towards relative populations of non-isomeric metallofullerenes: La@C76(Td) vs. La2@C76(Cs,17490). Fulleren Nanotub Carb Nanostruct 22:299–306
Suzuki M, Mizorogi N, Yang T, Uhlik F, Slanina Z, Zhao X, Yamada M, Maeda Y, Hasegawa T, Nagase S, Lu X, Akasaka T (2013) La2@Cs(17490)-C76: a new non-IPR dimetallic metallofullerene featuring unexpectedly weak metal-Pentalene interactions. Chem Eur J 19:17125–17130
Slanina Z, Uhlík F, Lee S-L, Adamowicz L, Kurihara H, Nikawa H, Lu X, Yamada M, Nagase S, Akasaka T (2014) Computations on metallofullerenes derivatized during extraction: La@C80-C6H3C12 and La@C82-C6H3Cl2. Fulleren Nanotub Carb Nanostruct 22:173–181
Feng L, Rudolf M, Trukhina O, Slanina Z, Uhlík F, Lu X, Torres T, Guldi DM, Akasaka T (2015) Tuning intramolecular electron and energy transfer processes in novel conjugates of La2@C80 and electron accepting subphthalocyanines. Chem Commun 51:330–333
Slanina Z, Uhlík F, Feng L, Akasaka T, Lu X, Adamowicz L (2020) Rotameric isomers of La2@C80 & dodecafluoro-subphthalocyanine conjugate: computational characterization. ECS J Solid State Sci Technol 9:061014
Slanina Z, Uhlík F, Juha L, Tanabe K, Adamowicz L, Ōsawa E (2004) Computations on C84O: thermodynamic, kinetic and photochemical stability. J Mol Struct (Theochem) 684:129–133
Eggen BR, Heggie MI, Jungnickel G, Latham CD, Jones R, Briddon PR (1996) Autocatalysis during fullerene growth. Science 272:87–90
Slanina Z, Zhao X, Uhlík F, Ozawa M, Ōsawa E (2000) Computational modelling of the metal and other elemental catalysis in the Stone-Wales fullerene rearrangements. J Organomet Chem 599:57–61
Slanina Z, Zhao X, Ozawa M, Adamowicz L, Ōsawa E (2000) Computational evaluations of the elemental-catalytical effects on the kinetics of the Stone-Wales isomerizations. In: Kamat PV, Guldi DM, Kadish KM (eds) Recent advances in the chemistry and physics of fullerenes and related materials: vol. 10 – Chemistry and physics of fullerenes and carbon nanomaterials. The Electrochemical Society, Pennington, pp 129–141
Walsh TR, Wales DJ (1998) Relaxation dynamics of C60. J Chem Phys 109:6691–6700
Slanina Z (1982) Sequential isomerism of activated complexes and comparisons of theoretical and observed data: a general case of a unimolecular process with one intermediate. Z Phys Chem (Wiesbaden) 132:41–54
Slanina Z (1983) Sequential isomerism of activated complexes: interfering versus noninterfering intermediate. Int J Quantum Chem 23:1553–1561
Ōsawa E, Ueno H, Yoshida M, Slanina Z, Zhao X, Nishiyama M, Saito H (1998) Combined topological and energy analysis of the annealing process in fullerene formation. Stone-Wales interconversion pathways among IPR isomers of higher fullerenes. J Chem Soc Perkin Trans 2:943–950
Lindemann FA (1922) Discussion on the radiation theory of chemical action. Trans Faraday Soc 17:598–599
Hinshelwood CN (1926) On the theory of unimolecular reactions. Proc Roy Soc London A 113:230–233
Bao JL, Zhang X, Truhlar DG (2016) Predicting pressure-dependent unimolecular rate constants using variational transition state theory with multidimensional tunneling combined with system-specific quantum RRK theory: a definitive test for fluoroform dissociation. Phys Chem Chem Phys 18:16659–16670
Levine RD (2005) Molecular reaction dynamics. Cambridge University Press, Cambridge, pp 215–224
Irle S, Zheng G, 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. J Phys Chem B 110:1453114545
Deng Q, Heine T, Irle S, Popov AA (2016) Self-assembly of endohedral metallofullerenes: a decisive role of cooling gas and metalcarbon bonding. Nanoscale 8:3796–3808
Bao L, Yu P, Pan C, Shen W, Lu X (2019) Crystallographic identification of Eu@C2n (2n = 88, 86 and 84): completing a transformation map for existing metallofullerenes. Chem Sci 10:2153–2158
Feng L, Hao YJ, Liu AL, Slanina Z (2019) Trapping metallic oxide clusters inside fullerene cages. Acc Chem Res 52:1802–1811
Cai W, Alvarado J, Metta-Magaña A, Chen N, Echegoyen L (2020) Interconversions between uranium mono-metallofullerenes: mechanistic implications and role of asymmetric cages. J Am Chem Soc 142:1311213119
Abella L, Mulet-Gas M, Rodriguez-Fortea A, Poblet JM (2016) La3N@C92: an endohedral metallofullerene governed by kinetic factors? Inorg Chem 55:3302–3306
Maeda Y, Tsuchiya T, Kikuchi T, Nikawa H, Yang T, Zhao X, Slanina Z, Suzuki M, Yamada M, Lian Y, Nagase S, Lu X, Akasaka T (2016) Effective derivatization and extraction of insoluble missing lanthanum metallofullerenes La@C2n (n = 36–38) with iodobenzene. Carbon 98:67–73
Ulusoy IS, Wilson AK (2019) Slater and Gaussian basis functions and computation of molecular integrals. In: Blinder SM, House JE (eds) Mathematical physics in theoretical chemistry. Elsevier, Amsterdam, p 43
Schwabe T, Grimme S (2007) Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability. Phys Chem Chem Phys 9:3397–3406
Menon AS, Radom L (2008) Consequences of spin contamination in unrestricted calculations on open-shell species: effect of Hartree-Fock and Mpller-Plesset contributions in hybrid and double-hybrid density functional theory approaches. J Phys Chem A 112:13225–13230
Slanina Z, Uhlík F, Bao L, Akasaka T, Lu X, Adamowicz L (2019) Calculated relative populations for the Eu@C82 isomers. Chem Phys Lett 726:29–33
Slanina Z, Uhlík F, Bao L, Akasaka T, Lu X, Adamowicz L (2020) Eu@C86 isomers: calculated relative populations. Fulleren Nanotub Carb Nanostruct 28:565–570
Zhao S, Zhao P, Cai W, Bao L, Chen M, Xie Y, Zhao X, Lu X (2017) Stabilization of giant fullerenes C2(41)-C90, D3(85)-C92, C1(132)-C94, C2(157)-C69, and C1(175)-C98 by encapsulation of a large La2C2 cluster: the importance of cluster-cage matching. J Am Chem Soc 139:4724–4728
Zhao R, Yuan K, Zhao S, Zhao X, Ehara M (2017) Quantum chemical insight into La2C96: metal carbide fullerene La2C2@C94 versus dimetallofullerene La2@C96. Inorg Chem 56:11883–11890
Li Q-Z, Zheng J-J, He L, Nagase S, Zhao X (2018) La-La bonded dimetallofullerenes [La2@C2n]−: species for stabilizing C2n (2n = 92–96) besides La2C2@C2n. Phys Chem Chem Phys 20:14671–14678
Hu SF, Shen WQ, Zhao P, Xu T, Slanina Z, Ehara M, Zhao X, Xie YP, Akasaka T, Lu X (2019) Crystallographic characterization of Er2C2@C2(43)-C90, Er2C2@C2(40)-C90, Er2C2@C2(44)-C90, and Er2C2@C4(21)-C90: the role of cage-shape on cluster configuration. Nanoscale 11:17319–17326
Liu FP, Spree L, Krylov DS, Velkos G, Avdoshenko SM, Popov AA (2019) Single-electron lanthanide-lanthanide bonds inside fullerenes toward robust redox-active molecular magnets. Acc Chem Res 52:2981–2993
Slanina Z, Uhlík F, Bao LP, Akasaka T, Lu X, Adamowicz L (2020) Calculated relative populations for the Eu@C84 isomers. Fulleren Nanotub Carb Nanostruct 29:144–148
Slanina Z (1989) Some aspects of mathematical chemistry of equilibrium and rate processes: steps towards a completely non-empirical computer design of syntheses. J Mol Struct (THEOCHEM) 185:217–228
Slanina Z, Uhlík F, Nagase S, Akasaka T, Adamowicz L, Lu X (2017) A computational characterization of CO@C60. Fulleren Nanotub Carb Nanostruct 25:624–629
Slanina Z, Uhlík F, Feng L, Adamowicz L (2016) Evaluation of the relative stabilities of two non-IPR isomers of Sm@C76. Fulleren Nanotub Carb Nanostruct 24:339–344
Yu YL, Slanina Z, Wang F, Yang Y, Lian YF, Uhlík F, Xin BF, Feng L (2020) Ho2O@D3 (85)-C92: highly stretched cluster dictated by a giant cage and unexplored isomerization. Inorg Chem 59:11020–11027
Popov AA (2017) Synthesis and molecular structures of endohedral fullerenes. In: Popov AA (ed) Endohedral fullerenes: electron transfer and spin. Springer, Cham, pp 1–34
Slanina Z, Uhlík F, Adamowicz L, Akasaka T, Nagase S, Lu X (2017) Stability issues in computational screening of carbon nanostructures: illustrations on La endohedrals. Mol Simul 43:1472–1479
Wang Y, Morales-Martínez R, Zhang X, Yang W, Wang Y, Rodriguez-Fortea A, Poblet JM, Feng L, Wang S, Chen N (2017) Unique four-electron metal-to-cage charge transfer of Th to a C82 fullerene cage: complete structural characterization of Th@C3v (8)-C82. J Am Chem Soc 139:5110–5116
Cai WT, Abella L, Zhuang JX, Zhang XX, Feng L, Wang YF, Morales-Martinez R, Esper R, Boero M, Metta-Magana A, Rodriguez-Fortea A, Poblet JM, Echegoyen L, Chen N (2018) Synthesis and characterization of non-isolated-pentagon-rule actinide endohedral metallofullerenes U@C1(17418)-C76, U@C1(28324)-C80, and Th@C1(28324)-C80: low-symmetry cage selection directed by a tetravalent ion. J Am Chem Soc 140:18039–18050
Wang YF, Morales-Martínez R, Cai WT, Zhuang JX, Yang W, Echegoyen L, Poblet JM, Rodríguez-Fortea A, Chen N (2019) Th@C1(11)-C86: an actinide encapsulated in an unexpected C86 fullerene cage. Chem Commun 55:9271–9274
Cai W, Chen C-H, Chen N, Echegoyen L (2019) Fullerenes as nanocontainers that stabilize unique actinide species inside: structures, formation, and reactivity. Acc Chem Res 52:1824–1833
Zhao Y-X, Li M-Y, Zhao P, Ehara M, Zhao X (2019) New insight into U@C80: missing U@D3(31921)-C80 and nuanced enantiomers of U@C1(28324)-C80. Inorg Chem 58:141591416
Hao D, Yang L, Wei Z, Hou Q, Li L, Jin P (2020) U2O@C76: non-isolated-pentagon-rule cages prevail with the U2O configuration determined by cage shape and dominated by multicenter bonds. Inorg Chem 59:70397048
Sure R, Hansen A, Schwerdtfeger P, Grimme S (2017) Comprehensive theoretical study of all 1812 C60 isomers. Phys Chem Chem Phys 19:14296–14305
Huffman D, Krätschmer W (1990) Solid C60 – how we found it. MRS Proc 206:601–610
Acknowledgments
The reported research has been supported by the NSFC (21171061 & 51472095), the Program for Changjiang Scholars and Innovative Research Team in University (IRT1014); by the Czech Science Foundation/GACR (P208/10/1724); by the Charles University Centre of Advanced Materials/CUCAM (CZ.02.1.01/0.0/0.0/15-003/0000417); and by the MetaCentrum (LM2010005) and CERIT-SC (CZ.1.05/3.2.00/08.0144) computing facilities. An initial phase of the research line was supported by the Alexander von Humboldt-Stiftung and the Max-Planck-Institut fur Chemie (Otto-Hahn-Institut).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this entry
Cite this entry
Slanina, Z., Uhlík, F., Adamowicz, L. (2021). Theoretical Predictions of Fullerene Stabilities. In: Lu, X., Akasaka, T., Slanina, Z. (eds) Handbook of Fullerene Science and Technology. Springer, Singapore. https://doi.org/10.1007/978-981-13-3242-5_23-1
Download citation
DOI: https://doi.org/10.1007/978-981-13-3242-5_23-1
Received:
Accepted:
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-3242-5
Online ISBN: 978-981-13-3242-5
eBook Packages: Springer Reference Chemistry and Mat. ScienceReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics