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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access March 1, 2004

Fullerenes as polyradicals

  • Elena Sheka EMAIL logo
From the journal Open Physics

Abstract

We present the investigation of the electronic structure of X60 molecules (X=C, Si), containing 60 odd electrons with spin-dependent interaction between them. Conditions for the electrons to be excluded from the covalent pairing are discussed. A computational spin-polarized quantum-chemical scheme is suggested to evaluate four parameters—energy of radicalization, exchange integral, atom spin density, and squared spin— to characterize the effect quantitatively. A polyradical character of the species, weak for C60 and strong for Si60, is established.

[1] J.H. Weaver: “Fullerenes, and Fullerides: Photoemission and Scanning Tunneling Microscopy Studies”, Acc. Chem. Res., Vol. 25, (1992), pp. 143–151. http://dx.doi.org/10.1021/ar00015a00710.1021/ar00015a007Search in Google Scholar

[2] N. Matsuzawa, T. Fukunaga, and D.A. Dixon: “Electronic Structures of 1,2- and 1,4-C60X2n Derivatives with n=1, 2, 4, 6, 8, 10, 12, 18, 24, and 30”, J. Phys. Chem., Vol. 96, (1992), pp. 10747–10756. http://dx.doi.org/10.1021/j100205a03110.1021/j100205a031Search in Google Scholar

[3] A.V. Okotrub, and L.G. Bulusheva: “CKα-Spectra and Investigation of Electronic Structure of Fullerene Compounds”, Full. Sci. Techn., Vol. 6, (1998), pp. 405–432. Search in Google Scholar

[4] L.G. Bulusheva, A.V. Okotrub, A.V. Gusel'nikov, D.V. Konarev, A.L. Litvinov, and R.N. Lyubovskaya: “Electronic Structure of the Complexes of Fullerence C60 with Polyaromatic Molecules.”, Journ. Mol. Struct., Vol. 648, (2003), pp. 183–189. http://dx.doi.org/10.1016/S0022-2860(03)00027-910.1016/S0022-2860(03)00027-9Search in Google Scholar

[5] S. Nagase: “C60 Complexes with Metals”, Pure Appl. Chem., Vol. 65, (1993), pp. 675–702. Search in Google Scholar

[6] Z. Slanina and S.L. Lee: “Electrnic properties and IR Spectrum of C60”, Fullerene Sci. Technol., Vol. 2, (1994), pp. 459–464. Search in Google Scholar

[7] B.X. Lee, M. Jiang, and P.L. Cao: “A Full-Potential Linear-Muffin-Tin-Orbital Molecular-Dynamics Study on the Disordered Cage Structures of Si60 and C60 Clusters”, J. Phys.: Condens. Matter., Vol. 11, (1999), pp. 8517–8521. http://dx.doi.org/10.1088/0953-8984/11/43/31510.1088/0953-8984/11/43/315Search in Google Scholar

[8] E.F. Sheka, E.A. Nikitina, V.A. Zayets and I.Ya. Ginzburg: “Fullerene Model of Silicon Nanofibers”, JETP Letters, Vol. 71, (2001), pp. 177–181. Search in Google Scholar

[9] E.F. Sheka and E.A. Nikitina: “From Silicon Fullerenes to Nanofibers”, Doklady RAN, Vol. 378, (2001), pp. 1–6. Search in Google Scholar

[10] E.F. Sheka, E.A. Nikitina, V.A. Zayets, and I.Ya. Ginzburg: “High-Spin Silicon Fullerene Si60 and Its Oligomers”, Int. Journ. Quant. Chem., Vol. 88, (2002), pp. 441–448. http://dx.doi.org/10.1002/qua.1019210.1002/qua.10192Search in Google Scholar

[11] H.W. Kroto, J.R. Heath, S.C. O'Brien, R.F. Curl, and R.E. Smalley: “C60: Buckminsterfullerenes”, Nature, Vol. 318, (1985), pp. 162–164. http://dx.doi.org/10.1038/318162a010.1038/318162a0Search in Google Scholar

[12] P.W. Fowler and A. Ceulemans: “Electron Efficiency of the Fullerenes”, J. Phys. Chem., Vol. 99, (1995), pp. 508–510. http://dx.doi.org/10.1021/j100002a01010.1021/j100002a010Search in Google Scholar

[13] It does not seem strange any more when comparing electron affinity of the fullerene C60 molecule (2.66 eV) with those of aromatic molecules (−0.55, −0.007, 0.25, −2.45, and 0.42 eV for from benzene to pentacene, respectively). UHF calculated data by using AM1 technique (see text). Search in Google Scholar

[14] G. Herzberg: Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, 2nd Ed., Van Nostrand, Prinston, N.J., 1950, pp. 353. Search in Google Scholar

[15] V.A. Gubanov, A.I. Likhtenstein, and A.V. Postnikov: Magnetism and Chemical Bonding in Crystals (in Russian), Nauka, Moskva, 1985. Search in Google Scholar

[16] J.M. Hay and R.H. Thomson: Organic Chemistry of Stable Free Radicals, Academic Press, New York, 1955. Search in Google Scholar

[17] R. Hoffman, A. Imamura, and W.J. Hehre: “Benzenes, Dehydrogenated Molecules and the Interaction of Orbitals Separated by a Number of Sigma Bonds”, J. Amer. Chem. Soc., Vol. 90, (1968), pp. 1499–1509. http://dx.doi.org/10.1021/ja01008a01810.1021/ja01008a018Search in Google Scholar

[18] R. Hoffman: “Electronic Properties of Carbenes”, Chem. Commun., Vol. 240, (1969), pp. 1–13. Search in Google Scholar

[19] R. Hoffman: “Interaction of Orbitals Trough Space and Through Bonds”, Accounts Chem. Res., Vol. 4, (1971), pp. 1–9. http://dx.doi.org/10.1021/ar50037a00110.1021/ar50037a001Search in Google Scholar

[20] L. Salem and C. Rowland: “The Electronic Properties of Diradicals”, Angew. Chem. Intern. Edit., Vol. 11, (1972), pp. 92–111. http://dx.doi.org/10.1002/anie.19720092110.1002/anie.197200921Search in Google Scholar

[21] R. Hoffman: “Chemical Bonding in Diradicals”, J. Chem. Phys., Vol.39, (1963), pp. 1397–1401. http://dx.doi.org/10.1063/1.173445610.1063/1.1734456Search in Google Scholar

[22] R. Hoffman: “Extende Huckel Theory: Compounds of Boron and Nitrogen”, J. Chem. Phys., Vol. 40, (1964), pp. 2474–2488. http://dx.doi.org/10.1063/1.172555010.1063/1.1725550Search in Google Scholar

[23] J.W. Harrison: “The Structural Theory of Carbenes”, In: W. Kirsme (Ed.): Carbene Chemistry, 2nd Ed., Academic Press, New York, 1971, pp. 159–194. Search in Google Scholar

[24] D.E. Ellis and A.J. Freeman: “Model Calculations for the Study of Direct and Superexchange Interactions”, J. Appl. Phys., Vol. 39, (1968), pp. 424–426. http://dx.doi.org/10.1063/1.216346010.1063/1.2163460Search in Google Scholar

[25] P.J. Hay, J.C. Thibeault, and R. Hoffman: “Orbital Interaction in Metal Dimer Complexes”, J. Amer. Chem. Soc., Vol. 97 (1975), pp. 4884–4899. http://dx.doi.org/10.1021/ja00850a01810.1021/ja00850a018Search in Google Scholar

[26] I.A. Misurkin and A.A. Ovchinnikov: “Computational Techniques and Semi-Empirical Parameters in the Theory of Molecules with Conjugated Bonds” (in Russian), Uspekhi Khimii, Vol. 44, (1975), pp. 393–412. Search in Google Scholar

[27] The configuration ψ4 is usually omitted since the relevant state energy is high. Search in Google Scholar

[28] J. Pople and R. Nesbet: “Self-Consisted Orbitals for Radicals”, J. Chem. Phys., Vol. 22, (1954), pp. 571–584. http://dx.doi.org/10.1063/1.174012010.1063/1.1740120Search in Google Scholar

[29] P.O. Löwdin: “Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects”, Phys. Rev., Vol. 97, (1955), pp. 1509–1520. http://dx.doi.org/10.1103/PhysRev.97.150910.1103/PhysRev.97.1509Search in Google Scholar

[30] R. Paunz: Alternant Molecular Orbital Method, Philadelphia-London, 1967. Search in Google Scholar

[31] L. Noodleman: “Valence Bond Description of Antiferromagnetic Coupling in Transition Metal Dimers”, J. Chem. Phys., Vol. 74, (1981), pp. 5737–5743. http://dx.doi.org/10.1063/1.44093910.1063/1.440939Search in Google Scholar

[32] C.A. Daul, I. Ciofini, and A. Bencini: “Modeling Molecular Magnetism”, In: K.D. Sen (Ed): Review of Modern Quantum Chemistry, World Scientific, Singapore, 2002, pp. 1247–1294. Search in Google Scholar

[33] W. Heisenberg: “Zur Theorie des Ferromagnetism”, Ztschr. Phys., Vol. 49, (1928), pp. 619–636. Search in Google Scholar

[34] M. Benard: “The Study of Hartree-Fock Instability in Cr2(O2CH)4 and Mo2(O2CH)4”, J. Chem. Phys., Vol. 71, (1979), pp. 2546–2556. http://dx.doi.org/10.1063/1.43860910.1063/1.438609Search in Google Scholar

[35] Doubly occupied canonical molecular orbitals that describe paired electrons are omitted [31]. Search in Google Scholar

[36] L.F. Mattheis: “Effective Exchange Integral”, Phys. Rev., Vol. 123, (1961), pp. 1219–1224. http://dx.doi.org/10.1103/PhysRev.123.121910.1103/PhysRev.123.1219Search in Google Scholar

[37] V.A. Zayets: CLUSTER-Z1: Quantum-Chemical Software for Calculations in the s,p-Basis, Institute of Surface Chemistry, Nat. Ac. Sci. of Ukraine, Kiev, 1990. Search in Google Scholar

[38] M.J.S. Dewar, E.G. Zoebisch, E.F. Healey, and J.J.P. Stewart: “AM1: A New General Purpose Quantum Mechanical Molecular Model”, J. Amer. Chem. Soc., Vol. 107, (1985), pp. 3902–3909. http://dx.doi.org/10.1021/ja00299a02410.1021/ja00299a024Search in Google Scholar

[39] D.A. Zhogolev and V.B. Volkov: “Methods, Algorithms and Programs for Quantum-Chemical Calculations of Molecules (in Russian), Naukova, Dumka, Kiev, 1976. Search in Google Scholar

[40] It is easy to show that the ferromagnetic limit of \(\left( {\hat S^2 } \right)^{UHF} \) , which corresponds toS max=n, is equal to \(\left( {\hat S^2 } \right)_{\max }^{UHF} = {1 \mathord{\left/ {\vphantom {1 {4N(N + 2) = S_{\max } (S_{\max } + 1)}}} \right. \kern-0em} {4N(N + 2) = S_{\max } (S_{\max } + 1)}}\) . Search in Google Scholar

[41] Application of the above semi-empirical technique is not crucial for the study from a conceptual viewpoint. Only its highly effective computational facilities has favored the choice. Spin-polarized DFT techniques work in similar situations absolutely analogously [42, 43], however their rather modest computational efficiency seriously prevents one from carrying out an extended computational experiment which involves multiple studying of large systems at different spin multiplicity. Search in Google Scholar

[42] A.P. Ginzberg: “Magnetic Exchange in Transition Metal Complexes. 12. Calculation of Cluster Exchange Coupling Constants with the Xα-Scattered Way Method”, J. Amer. Chem. Soc., Vol. 102, (1980), pp. 111–117. http://dx.doi.org/10.1021/ja00521a02010.1021/ja00521a020Search in Google Scholar

[43] J.G. Norman, P.B. Ryan, and L. Noodleman: “Electronic Structure of 2-Fe Ferredoxin Models by Xα Valence Bond Theory”, J. Amer. Chem. Soc., Vol. 102, (1980), pp. 4279–4282. http://dx.doi.org/10.1021/ja00532a06010.1021/ja00532a060Search in Google Scholar

[44] Hereafter in the paper energetic parameters are presented by heats of formation, \(\Delta H = E_{tot} - \sum\limits_A {E_{elec}^A + EHEAT^A } \) , whereE tot =E elec +E nuc .E elec andE nuc are electronic and nuclear energies of the studied system, E elec A is the electronic energy of an isolated atom andEHEAT A is the heat of formation for atomA. All values are calculated within the same computational session. Search in Google Scholar

[45] “Brief Chemical Encyclopedia” (in Russian), Sov. enziklopedia, Moscow, 1963, pp. 799. Search in Google Scholar

[46] B.M. Bulychev and I.A. Udod: “Linear Carbon (Carbene): Approaches to Synthesis, Structure Identification, Intercalation” (in Russian), Ross. Khim. Zhurn., Vol. 39 (2), (1995), pp. 9–18. Search in Google Scholar

[47] N.I. Alekseev and G.A. Dyuzhev: “Effect of Small Clusters on the Transformation of Two-Ring Clusters into Fullerene” (in Russian), Zhurn. Tekhn. Fiz., Vol. 72, (2002), pp. 130–134. Search in Google Scholar

[48] F.N. Tomilin, P.V. Avramov, S.A. Varganov, A.A. Kuzubov, and S.G. Ovchinnikov: “A z Possible Scheme of fullerene Composition” (in Russian), Fizika Tverdogo Tela, Vol. 43, (2001), pp. 973–979. Search in Google Scholar

[49] The disclosed feature has forced us to check the tendency for a series of aromatic hydrocarbons. Calculations have convincingly shown the strengthening of the effect when going from naphthalene to pentacene for both carbon and silicon species. The results will be partially discussed in the next Section. Search in Google Scholar

[50] V. Khavryutchenko, E. Sheka, M. Aono, and D.-H. Huang: “Supercluster Quantum-Chemical Approach to the Si(111)(7×7) Surface. Charge and Spin Density”, Phys. Low-Dim. Struct., Vol. 3(4), (1998), pp. 81–106. Search in Google Scholar

[51] A generalized bond index is determined asK AB =|P AB |2+|D sp, AB |2[52], where the first term is known as Wiberg's bond index [53] which was introduced to characterize the covalence of chemical bonds in molecules with closed electron shells while the second goes from the spin density matrix. Search in Google Scholar

[52] S.G. Semenov: Evolution of the Valence Doctrine (in Russian), Moscow, Khimia, 1977, pp. 148. Search in Google Scholar

[53] K.B. Wiberg: “Application of the Pople-Santry-Segal CNDO Method to the Cyclopropylcarbonyl and Cyclobutyl Cation and to Bicyclobutane”, Tetrahedron, Vol. 24, (1968), pp. 1083–1086. http://dx.doi.org/10.1016/0040-4020(68)88057-310.1016/0040-4020(68)88057-3Search in Google Scholar

[54] P. Gaspar and B.J. Herold: “Silicon, Germanium and Tin Structural Analogs of Carbenes”, In: W. Kirsme (Ed.): Carbene Chemistry, 2nd Ed., Academic Press, New York, 1971, pp. 504–550. Search in Google Scholar

[55] R.C. Haddon, L.F. Scheemeyer, J.V. Waszczak, S.H. Glarum, R. Tycko, G. Dabbah, A.R. Kortan, A.J. Muller, A.M. Mujsce, M.J. Rosseinsky, S.M. Zahurak, A.V. Makhija, F.A. Thiel, K. Raghavachari, E. Cockayne, and V. Elser: “Experimental and Theoretical Determination of the Magnetic Susceptibility of C60 and C70”, Nature, Vol. 350, (1991), pp. 46–48. http://dx.doi.org/10.1038/350046a010.1038/350046a0Search in Google Scholar

[56] W.L. Luo, H. Wang, R.C. Ruoff, J. Cioslowski, and S. Phelps: “Susceptibility of Discontinuity in Single Crystal C60”, Phys. Rev. Lett., Vol. 73, (1994), pp. 186–190. http://dx.doi.org/10.1103/PhysRevLett.73.18610.1103/PhysRevLett.73.186Search in Google Scholar

[57] T.L. Makarova, B. Sundqvist, P. Esquinazi, R. Höhne, Y. Kopelevich, P. Scharff, V.A. Davydov, L.S. Kashevarova, and A.V. Rakhmanina: “Magnetic Carbon”, Nature, Vol. 413, (2001), pp. 716–718. http://dx.doi.org/10.1038/3509952710.1038/35099527Search in Google Scholar

[58] P.-M. Allemand, K.C. Khemani, A. Koch, F. Wudl, K. Holczer, S. Donovan, G. Grüner, and J.D. Thompson: “Organic Molec ular Soft Ferromagnetism in a Fullerene C60”, Science, Vol. 253, (1991), pp. 301–304. http://dx.doi.org/10.1126/science.253.5017.30110.1126/science.253.5017.301Search in Google Scholar

[59] E.F. Sheka: “Quantum Chemical Testing of Electron Donor-Acceptor Complexes”, In: 6 th Session of the V.A. Fock School on Quantum and Computational Chemistry. Book of Abstracts, V. Novgorod University, V. Novgorod, 2003, p. 149. Search in Google Scholar

[60] R. Brodbeck and D. Andrae: “Molecular Knots and Links”, In: 6 th Session of the V. A. Fock School on Quantum and Computational Chemistry. Book of Abstracts, V. Novgorod University, V. Novgorod, 2003, p. 88. Search in Google Scholar

[61] N.N. Volkova, E.V. Sumannen, and L.P. Smirnov: “Thermal Degradation of Hypercrosslinked Polystyrenes”, Polym. Sci. Ser. A, Vol. 45, (2003), pp. 986–992. Search in Google Scholar

[62] R.A. Kotelnikova, G.N. Bogdanov, V.S. Romanova, and Z.N. Parnes: “The Peculiarities of C60 Amino Acid Derivatives Effect on Structure and Functions of Biomembranes”, Mol. Mat., Vol. 11, (1998), pp. 111–116. Search in Google Scholar

[63] E.F. Sheka, E.A. Nikitina, and V.A. Zayats: “High-Spin Molecular Magnetism of Silicon Surfaces”, Surf. Sci., Vol. 532–535, (2003), pp. 754–759. http://dx.doi.org/10.1016/S0039-6028(03)00458-810.1016/S0039-6028(03)00458-8Search in Google Scholar

Published Online: 2004-3-1
Published in Print: 2004-3-1

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