Fullerenes as polyradicals

• Authors: Elena Sheka
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

Fullerenes X60 (X=C, Si); polyradicals; quantum chemistry; 31.10.+z; 31.15.Ct' 81.05.Tp; 82.20.Wt

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2004
• Volume: 2
• Issue: 1
• Pages: 160-182

Dates

published

1 - 3 - 2004

online

1 - 3 - 2004

Contributors

author

Elena Sheka

• Peoples' Friendship University of Russia, ul. Ordjonikidze, 3, 117923, Moscow, Russia

References

• [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/ar00015a007[Crossref]
• [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/j100205a031[Crossref]
• [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.
• [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)00027-9[Crossref]
• [5] S. Nagase: “C60 Complexes with Metals”, Pure Appl. Chem., Vol. 65, (1993), pp. 675–702.
• [6] Z. Slanina and S.L. Lee: “Electrnic properties and IR Spectrum of C60”, Fullerene Sci. Technol., Vol. 2, (1994), pp. 459–464.
• [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/10.1088/0953-8984/11/43/315[Crossref]
• [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. [Crossref]
• [9] E.F. Sheka and E.A. Nikitina: “From Silicon Fullerenes to Nanofibers”, Doklady RAN, Vol. 378, (2001), pp. 1–6.
• [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.10192[Crossref]
• [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/10.1038/318162a0[Crossref]
• [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/j100002a010[Crossref]
• [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).
• [14] G. Herzberg: Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules, 2nd Ed., Van Nostrand, Prinston, N.J., 1950, pp. 353.
• [15] V.A. Gubanov, A.I. Likhtenstein, and A.V. Postnikov: Magnetism and Chemical Bonding in Crystals (in Russian), Nauka, Moskva, 1985.
• [16] J.M. Hay and R.H. Thomson: Organic Chemistry of Stable Free Radicals, Academic Press, New York, 1955.
• [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/ja01008a018[Crossref]
• [18] R. Hoffman: “Electronic Properties of Carbenes”, Chem. Commun., Vol. 240, (1969), pp. 1–13.
• [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/ar50037a001[Crossref]
• [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.197200921[Crossref]
• [21] R. Hoffman: “Chemical Bonding in Diradicals”, J. Chem. Phys., Vol.39, (1963), pp. 1397–1401. http://dx.doi.org/10.1063/1.1734456[Crossref]
• [22] R. Hoffman: “Extende Huckel Theory: Compounds of Boron and Nitrogen”, J. Chem. Phys., Vol. 40, (1964), pp. 2474–2488. http://dx.doi.org/10.1063/1.1725550[Crossref]
• [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.
• [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/10.1063/1.2163460[Crossref]
• [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/ja00850a018[Crossref]
• [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.
• [27] The configuration ψ4 is usually omitted since the relevant state energy is high.
• [28] J. Pople and R. Nesbet: “Self-Consisted Orbitals for Radicals”, J. Chem. Phys., Vol. 22, (1954), pp. 571–584. http://dx.doi.org/10.1063/1.1740120[Crossref]
• [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.97.1509[Crossref]
• [30] R. Paunz: Alternant Molecular Orbital Method, Philadelphia-London, 1967.
• [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/10.1063/1.440939[Crossref]
• [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.
• [33] W. Heisenberg: “Zur Theorie des Ferromagnetism”, Ztschr. Phys., Vol. 49, (1928), pp. 619–636. [Crossref]
• [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/10.1063/1.438609[Crossref]
• [35] Doubly occupied canonical molecular orbitals that describe paired electrons are omitted [31].
• [36] L.F. Mattheis: “Effective Exchange Integral”, Phys. Rev., Vol. 123, (1961), pp. 1219–1224. http://dx.doi.org/10.1103/PhysRev.123.1219[Crossref]
• [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.
• [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/ja00299a024[Crossref]
• [39] D.A. Zhogolev and V.B. Volkov: “Methods, Algorithms and Programs for Quantum-Chemical Calculations of Molecules (in Russian), Naukova, Dumka, Kiev, 1976.
• [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 \(\left( {\hat S^2 } \right)_{\max }^{UHF} = {1 \mathord{\left/ {\vphantom {1 {4N(N + 2) = S_{\max } (S_{\max } + 1)}}} \right. \kern-0em} {4N(N + 2) = S_{\max } (S_{\max } + 1)}}\) .
• [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.
• [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/ja00521a020[Crossref]
• [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/ja00532a060[Crossref]
• [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.
• [45] “Brief Chemical Encyclopedia” (in Russian), Sov. enziklopedia, Moscow, 1963, pp. 799.
• [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.
• [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.
• [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.
• [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.
• [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.
• [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.
• [52] S.G. Semenov: Evolution of the Valence Doctrine (in Russian), Moscow, Khimia, 1977, pp. 148.
• [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)88057-3[Crossref]
• [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.
• [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/10.1038/350046a0[Crossref]
• [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.73.186[Crossref]
• [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/10.1038/35099527[Crossref]
• [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.253.5017.301[Crossref]
• [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.
• [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.
• [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.
• [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.
• [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)00458-8[Crossref]

Identifiers

DOI

10.2478/BF02476279