Advertisement

Abstract

Odd electrons of benzenoid units and the correlation of these electrons having different spins are the main concepts of the molecular theory of graphene. In contrast to the theory of aromaticity, the molecular theory is based on the fact that odd electrons with different spins occupy different places in the space so that the configuration interaction becomes the central point of the theory. Consequently, a multi-determinant presentation of the wave function of the system of weakly interacting odd electrons is utterly mandatory on the way of the theory realization at the computational level. However, the efficacy of the available CI computational techniques is quite restricted in regard to large polyatomic systems, which does not allow performing extensive computational experiments. Facing the problem, computationists have addressed standard single-determinant ones albeit not often being aware of the correctness of the obtained results. The current chapter presents the molecular theory of graphene in terms of single-determinant computational schemes and discloses how reliable information about the electron-correlated system can be obtained by using either UHF or UDFT computational schemes.

Keywords

Unpaired Electron Electron Correlation Configuration Interaction Molecular Theory Benzene Molecule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author immensely appreciates fruitful discussions with I.L. Kaplan, E. Brandas, D. Tomanek. O. Ori, F. Cataldo, E. Molinary L.A. Chernozatonski who draw her attention onto different problems of the molecular theory of graphene. The author is deeply grateful to her colleagues N. Popova, V. Popova, L. Shaymardanova, B. Razbirin, D. Nelson, A. Starukhin, N. Rozhkova for support and valuable contribution into the study. A financial support provided by the Ministry of Science and High Education of the Russian Federation grant 2.8223.2013 is highly acknowledged.

References

  1. 1.
    Hoffmann R (2013) Small but strong lessons from chemistry for nanoscience. Angew Chem, Int Ed 52:93–103 CrossRefGoogle Scholar
  2. 2.
    Hoffmann R (1971) Interaction of orbitals through space and through bonds. Acc Chem Res 4:1–9 CrossRefGoogle Scholar
  3. 3.
    Hay PJ, Thibeault JC, Hoffmann R (1971) Orbital interactions in metal dimer complexes. J Am Chem Soc 97:4884–4899 CrossRefGoogle Scholar
  4. 4.
    Sheka E (2003) Violation of covalent bonding in fullerenes. In: Sloot PMA, Abramson D, Bogdanov AV et al. (eds) Computational science—ICCS2003. Lecture notes in computer science. Springer, Heidelberg, pp 386–398 Google Scholar
  5. 5.
    Sheka EF (2011) Fullerenes: nanochemistry, nanomagnetism, nanomedicine, nanophotonics. CRC Press/Taylor and Francis, Boca Raton CrossRefGoogle Scholar
  6. 6.
    Sheka EF (2003) Fullerenes as polyradicals. Internet electronic conference of molecular design, 2003, 23 November–6 December 2003. http://www.biochempress.com. November 28, paper 54
  7. 7.
    Sheka EF (2004) Odd electrons and covalent bonding in fullerenes. Int J Quant Chem 100:375–386 CrossRefGoogle Scholar
  8. 8.
    Sheka E (2009) Nanocarbons through computations: fullerenes, nanotubes, and graphene. In: The UNESCO-EOLSS encyclopedia nanoscience and nanotechnology. UNESCO, Moscow, pp 415–444 Google Scholar
  9. 9.
    Geim AK, Novoselov KS (2007) The rise of graphene. Nat Mater 6:183–191 CrossRefGoogle Scholar
  10. 10.
    Davidson E (1998) How robust is present-day DFT? Int J Quant Chem 69:214–245 CrossRefGoogle Scholar
  11. 11.
    Kaplan I (2007) Problems in DFT with the total spin and degenerate states. Int J Quant Chem 107:2595–2603 CrossRefGoogle Scholar
  12. 12.
    Takatsuka K, Fueno T, Yamaguchi K (1978) Distribution of odd electrons in ground-state molecules. Theor Chim Acta 48:175–183 CrossRefGoogle Scholar
  13. 13.
    Staroverov VN, Davidson ER (2000) Distribution of effectively unpaired electrons. Chem Phys Lett 330:161–168 CrossRefGoogle Scholar
  14. 14.
    Benard MJ (1979) A study of Hartree–Fock instabilities in Cr2(O2CH)4 and Mo2(O2CH)4. J Chem Phys 71:2546–2556 CrossRefGoogle Scholar
  15. 15.
    Lain L, Torre A, Alcoba DR et al. (2011) A study of the relationships between unpaired electron density, spin-density and cumulant matrices. Theor Chem Acc 128:405–410 CrossRefGoogle Scholar
  16. 16.
    Sheka EF, Chernozatonskii LA (2007) Bond length effect on odd electrons behavior in single-walled carbon nanotubes. J Phys Chem A 111:10771–10780 CrossRefGoogle Scholar
  17. 17.
    Sheka EF (2012) Computational strategy for graphene: insight from odd electrons correlation. Int J Quant Chem 112:3076–3090 CrossRefGoogle Scholar
  18. 18.
    Zayets VA (1990) CLUSTER-Z1: quantum-chemical software for calculations in the s,p-basis. Institute of Surface Chemistry Nat Ac Sci of Ukraine, Kiev Google Scholar
  19. 19.
    Gao X, Zhou Z, Zhao Y et al. (2008) Comparative study of carbon and BN nanographenes: ground electronic states and energy gap engineering. J Phys Chem A 112:12677–12682 CrossRefGoogle Scholar
  20. 20.
    Noodleman L (1981) Valence bond description of antiferromagnetic coupling in transition metal dimers. J Chem Phys 74:5737–5742 CrossRefGoogle Scholar
  21. 21.
    Illas F, de Moreira IPR, de Graaf C, Barone V (2000) Magnetic coupling in biradicals, binuclear complexes and wide-gap insolators; a survey of ab initio function and density functional theory approaches. Theor Chem Acc 104:265–272 CrossRefGoogle Scholar
  22. 22.
    Zvezdin AK, Matveev VM, Mukhin AA et al. (1985) Redkozemeljnyje iony v magnito-uporjadochennykh kristallakh (Rear Earth ions in magnetically ordered crystals). Nauka, Moskva Google Scholar
  23. 23.
    Van Fleck JH (1932) The theory of electric and magnetic susceptibilities. Oxford at the Clarendon Press, Oxford Google Scholar
  24. 24.
    Kahn O (1993) Molecular magnetism. VCH, New York Google Scholar
  25. 25.
    Koshino M, Ando T (2007) Diamagnetism in disordered graphene. Phys Rev B 75:235333. (8 pp) CrossRefGoogle Scholar
  26. 26.
    Nair RR, Sepioni M, Tsai I-L et al. (2012) Spin-half paramagnetism in graphene induced by point defects. Nat Phys 8:199–202 CrossRefGoogle Scholar
  27. 27.
    Sheka EF, Chernozatonskii LA (2010) Chemical reactivity and magnetism of graphene. Int J Quant Chem 110:1938–1946 Google Scholar
  28. 28.
    Sheka EF, Chernozatonskii LA (2010) Broken spin symmetry approach to chemical susceptibility and magnetism of graphenium species. J Exp Theor Phys 110:121–132 CrossRefGoogle Scholar
  29. 29.
    Shibayama Y, Sato H, Enoki T, Endo M (2000) Phys Rev Lett 84:1744 CrossRefGoogle Scholar
  30. 30.
    Enoki T, Kobayashi Y (2005) J Mater Chem 15:3999 CrossRefGoogle Scholar
  31. 31.
    Tada K, Haruyama J, Yang HX et al. (2011) Graphene magnet realized by hydrogenated graphene nanopore arrays. Appl Phys Lett 99:183111. (3 pp) CrossRefGoogle Scholar
  32. 32.
    Tada K, Haruyama J, Yang HX et al. (2011) Ferromagnetism in hydrogenated graphene nanopore arrays. Phys Rev Lett 107:217203. (5 pp) CrossRefGoogle Scholar
  33. 33.
    Sheka EF, Zayets VA, Ginzburg IYa (2006) Nanostructural magnetism of polymeric fullerene crystals. J Exp Theor Phys 103:728–739 CrossRefGoogle Scholar
  34. 34.
    Boeker GF (1933) The diamagnetism of carbon tetrachloride, benzene and toluene at different temperatures. Phys Rev 43:756–760 CrossRefGoogle Scholar
  35. 35.
    Seach MP, Dench WA (1979) Quantitative electron spectroscopy of surfaces: a standard data base for electron inelastic mean free paths in solids. Surf Interface Anal 1:2–11 CrossRefGoogle Scholar
  36. 36.
    Komolov SA, Lazneva EF, Komolov AS (2003) Low-energy electron mean free path in thin films of copper phthalocyanine. Tech Phys Lett 29:974–976 CrossRefGoogle Scholar
  37. 37.
    Takatsuka K, Fueno TJ (1978) The spin-optimized SCF general spin orbitals. II. The 22 S and 22 P states of the lithium atom. J Chem Phys 69:661–669 CrossRefGoogle Scholar
  38. 38.
    Staroverov VN, Davidson ER (2000) Diradical character of the Cope rearrangement transition state. J Am Chem Soc 122:186–187 CrossRefGoogle Scholar
  39. 39.
    Mayer I (1986) On bond orders and valences in the ab initio quantum chemical theory. Int J Quant Chem 29:73–84 CrossRefGoogle Scholar
  40. 40.
    Dewar MJS, Thiel W (1977) Ground states of molecules. 38. The MNDO method. Approximations and parameters. J Am Chem Soc 99:4899–4907 CrossRefGoogle Scholar
  41. 41.
    Zhogolev DA, Volkov VB (1976) Metody, algoritmy i programmy dlja kvantovo-khimicheskikh raschetov molekul (Methods, algorithms and programs for quantum-chemical calculations of molecules). Naukova Dumka, Kiev Google Scholar
  42. 42.
    Sheka EF, Zayets VA (2005) The radical nature of fullerene and its chemical activity. Russ J Phys Chem 79:2009–2014 Google Scholar
  43. 43.
    Lain L, Torre A, Alcoba DR et al. (2009) A decomposition of the number of effectively unpaired electrons and its physical meaning. Chem Phys Lett 476:101–103 CrossRefGoogle Scholar
  44. 44.
    Wang J, Becke AD, Smith VH Jr (1995) Eveluation of \(\langle \hat{S} \rangle^{2}\) in restricted, unrestricted Hartree-Fock, and density functional based theory. J Chem Phys 102:3477–3480 CrossRefGoogle Scholar
  45. 45.
    Cohen AJ, Tozer DJ, Handy NC (2007) Evaluation of \(\langle \hat{S} \rangle^{2}\) in density functional theory. J Chem Phys 126:214104. (4 pp) CrossRefGoogle Scholar
  46. 46.
    Lobayan RM, Bochicchio RC, Torre A et al. (2011) Electronic structure and effectively unpaired electron density topology in closo-boranes: nonclassical three-center two-electron bonding. J Chem Theory Comput 7:979–987 CrossRefGoogle Scholar
  47. 47.
    Kitagawa Y, Saito T, Ito M et al. (2007) Approximately spin-projected geometry optimization method and its application to di-chromium systems. Chem Phys Lett 442:445–450 CrossRefGoogle Scholar
  48. 48.
    Kitagawa Y, Saito T, Nakanishi Y et al. (2009) Spin contamination error in optimized geometry of singlet carbene (1A1) by broken-symmetry method. J Phys Chem A 113:15041–15046 CrossRefGoogle Scholar
  49. 49.
    Gross L, Mohn F, Moll N et al. (2009) The chemical structure of a molecule resolved by atomic force microscopy. Science 325:1110–1114 CrossRefGoogle Scholar
  50. 50.
    ‘Olympic rings’ molecule olympicene in striking image. BBC News Science and Environment (2012-05-28) Google Scholar
  51. 51.
    Fujita M, Wakabayashi K, Nakada K et al. (1996) Peculiar localized state at zigzag graphite edge. J Phys Soc Jpn 65:1920–1923 CrossRefGoogle Scholar
  52. 52.
    Nakada K, Fujita M, Dresselhaus G et al. (1996) Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys Rev B 54:17954–17961 CrossRefGoogle Scholar
  53. 53.
    Coleman J (2008) A new solution to graphene production. SPIE Newsroom. doi: 10.1117/2.1200810.1336 Google Scholar
  54. 54.
    The noise about graphene (2010) Science Centre of Barkley Lab Google Scholar
  55. 55.
    Sheka EF (2006) ‘Chemical portrait’ of fullerene molecule. J Struct Chem 47:600–607 CrossRefGoogle Scholar
  56. 56.
    Sheka EF (2007) Chemical susceptibility of fullerenes in view of Hartree-Fock approach. Int J Quant Chem 107:2803–2816 CrossRefGoogle Scholar
  57. 57.
    Sheka EF, Chernozatonskii LA (2010) Chemical reactivity and magnetism of graphene. Int J Quant Chem 110:1938–1946 Google Scholar
  58. 58.
    Allouche A, Jelea A, Marinelli F et al. (2006) Hydrogenation and dehydrogenation of graphite (0001) surface: a density functional theory study. Phys Scr T 124:91–94 CrossRefGoogle Scholar
  59. 59.
    Sheka EF (2010) Stepwise computational synthesis of fullerene C60 derivatives. Fluorinated fullerenes C60F2k. J Exp Theor Phys 111:395–412 Google Scholar
  60. 60.
    Sheka EF, Popova NA (2012) Odd-electron molecular theory of the graphene hydrogenation. J Mol Model 18:3751–3768 CrossRefGoogle Scholar
  61. 61.
    Elias DC, Nair RR, Mohiuddin TMG et al. (2009) Control of graphene’s properties by reversible hydrogenation: evidence for graphane. Science 323:610–613 CrossRefGoogle Scholar
  62. 62.
    Sheka EF (2011) Computational synthesis of hydrogenated fullerenes from C60 to C60H60. J Mol Model 17:1973–1984 CrossRefGoogle Scholar
  63. 63.
    Sheka EF, Popova NA (2011) When a covalent bond is broken? arXiv:1111.1530v1 [physics.chem-ph]
  64. 64.
    Sheka EF, Popova NA (2012) Molecular theory of graphene oxide. arXiv:1212.6413 [cond-mat.mtrl-sci]
  65. 65.
    Sheka EF, Popova NA (2012) Molecular theory of graphene oxide. Phys Chem Chem Phys 15:13304–13322 CrossRefGoogle Scholar
  66. 66.
    Dreyer DS, Park S, Bielawski CW et al. (2010) The chemistry of graphene oxide. Chem Soc Rev 39:228–240 CrossRefGoogle Scholar
  67. 67.
    Zhu Y, Shanthi M, Weiwei C et al. (2010) Graphene and graphene oxide: synthesis. Properties, and Applications Adv Mater 22:3906–3924 CrossRefGoogle Scholar
  68. 68.
    Kuila T, Mishra AK, Khanra P et al. (2013) Recent advances in the efficient reduction of graphene oxide and its application as energy storage electrode materials. Nanoscale 5:52–71 CrossRefGoogle Scholar
  69. 69.
    Wang H, Hu IH (2011) Effect of oxygen content on structures of graphite oxides. Ind Eng Chem Res 50:6132–6137 CrossRefGoogle Scholar
  70. 70.
    Fujii S, Enoki T (2010) Cutting of oxidized graphene into nanosized pieces. J Am Chem Soc 132:10034–10041 CrossRefGoogle Scholar
  71. 71.
    Xu Z, Bando Y, Liu L et al. (2011) Electrical conductivity, chemistry, and bonding alternations under graphene oxide to graphene transition as revealed by in situ TEM. ACS Nano 5:4401–4406 CrossRefGoogle Scholar
  72. 72.
    Wang S, Wang R, Liu X et al. (2012) Optical spectroscopy investigation of the structural and electrical evolution of controllably oxidized graphene by a solution method. J Phys Chem C 116:10702–10707 CrossRefGoogle Scholar
  73. 73.
    Mattevi C, Eda G, Agnoli S et al. (2009) Evolution of electrical, chemical, and structural properties of transparent and conducting chemically derived graphene thin films. Adv Funct Mater 19:2577–2583 CrossRefGoogle Scholar
  74. 74.
    Wang L, Zhao J, Sun Y-Y et al. (2011) Characteristics of Raman spectra for graphene oxide from ab initio simulations. J Chem Phys 135:184503. (5 pp) CrossRefGoogle Scholar
  75. 75.
    Saxena S, Tyson TA, Negusse E (2010) Investigation of the local structure of graphene oxide. J Phys Chem Lett 1:3433–3437 CrossRefGoogle Scholar
  76. 76.
    Ambrosi A, Chee SY, Khezri B et al. (2012) Metallic impurities in graphenes prepared from graphite can dramatically influence their properties. Angew Chem, Int Ed 51:500–503 CrossRefGoogle Scholar
  77. 77.
    Lu N, Li Zh (2012) Graphene oxide: theoretical perspectives. In: Zeng J et al. (eds) Quantum simulations of materials and biological systems. Springer, Dordrecht, pp 69–84 CrossRefGoogle Scholar
  78. 78.
    Levy N, Burke SA, Meaker KL et al. (2010) Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329:544–547 CrossRefGoogle Scholar
  79. 79.
    Georgiou T, Britnell L, Blake P et al. (2011) Graphene bubbles with controllable curvature. Appl Phys Lett 99:093103. (3 pp) CrossRefGoogle Scholar
  80. 80.
    Koenig SP, Boddeti NG, Dunn ML et al. (2011) Ultrastrong adhesion of graphene membranes. Nat Nanotechnol 6:543–546 CrossRefGoogle Scholar
  81. 81.
    Sheka EF, Popova NA, Popova VA et al. (2011) Structure-sensitive mechanism of nanographene failure. J Exp Theor Phys 112:602–611 CrossRefGoogle Scholar
  82. 82.
    Sheka EF, Popova NA, Popova VA et al. (2011) A tricotage-like failure of nanographene. J Mol Model 17:1121–1131 CrossRefGoogle Scholar
  83. 83.
    Popova NA, Sheka EF (2011) Mechanochemical reaction in graphane under uniaxial tension. J Phys Chem C 115:23745–23754 CrossRefGoogle Scholar
  84. 84.
    Sheka EF, Shaymardanova LKh (2011) C60-based composites in view of topochemical reactions. J Mater Chem 21:17128–17146 CrossRefGoogle Scholar
  85. 85.
    Sheka EF (2013) Topochemistry of spatially extended sp 2 nanocarbons: fullerenes, nanotubes, and graphene. In: Ashrafi AR, Cataldo F, Iranmanesh A et al. (eds) Topological modelling of nanostructures and extended systems. Carbon materials: chemistry and physics, vol 7. Springer, Dordrecht. doi: 10.1007/978-94-007-6413-2_5 CrossRefGoogle Scholar
  86. 86.
    Razbirin BS, Rozhkova NN, Sheka EF et al (2013) Fractals of graphene quantum dots in photoluminescence of shungite. arXiv:1308.2569v2 [cond-mat. mes-hall]
  87. 87.
    Rozhkova NN, Sheka EF Shungite as loosely packed fractal nets of graphene-based quantum dots. arXiv:1308.0794v1 [cond-mat. mtrl-sci]
  88. 88.
    Sheka EF (2009) May silicene exist? arXiv:0901.3663
  89. 89.
    Sheka EF (2013) Why sp 2-like nanosilicons should not form: insight from quantum chemistry. Int J Quant Chem 113:612–618 CrossRefGoogle Scholar
  90. 90.
    Tang S, Cao Z (2012) Site-dependent catalytic activity of graphene oxides towards oxidative dehydrogenation of propane. Phys Chem Chem Phys 14:16558–16565 CrossRefGoogle Scholar
  91. 91.
    Hsu H-C, Shown I, Wei H-Y et al. (2013) Graphene oxide as a promising photocatalyst for CO2 to methanol conversion. Nanoscale 5:262–268 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia

Personalised recommendations