Nano Research

, Volume 5, Issue 2, pp 117–123 | Cite as

Is graphene aromatic?

Research Article


We analyze the chemical bonding in graphene using a fragmental approach, the adaptive natural density partitioning method, electron sharing indices, and nucleus-independent chemical shift indices. We prove that graphene is aromatic, but its aromaticity is different from the aromaticity in benzene, coronene, or circumcoronene. Aromaticity in graphene is local with two π-electrons delocalized over every hexagon ring. We believe that the chemical bonding picture developed for graphene will be helpful for understanding chemical bonding in defects such as point defects, single-, double-, and multiple vacancies, carbon adatoms, foreign adatoms, substitutional impurities, and new materials that are derivatives of graphene. Open image in new window


Graphene aromaticity adaptive natural density partitioning (AdNDP) chemical bonding electronic aromaticity indices multicenter indice (MCI) 


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  1. [1]
    Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666–669.CrossRefGoogle Scholar
  2. [2]
    Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-dimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197–200.CrossRefGoogle Scholar
  3. [3]
    Unarunotai, S.; Murata, Y.; Chialvo, C. E.; Mason, N.; Petrov, I.; Nuzzo, R. G.; Moore, J. S.; Rogers, J. A. Conjugated carbon monolayer membranes: Methods for synthesis and integration. Adv. Mater. 2010, 22, 1072–1077.CrossRefGoogle Scholar
  4. [4]
    Bolotin, K. I.; Sikes, K. J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H. L. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 2008, 146, 351–355.CrossRefGoogle Scholar
  5. [5]
    Morozov, S. V.; Novoselov, K. S.; Katsnelson, M. I.; Schedin, F.; Elias, D. C.; Jaszczak, J. A.; Geim, A. K. Giant intristic carrier mobilities in graphene and its bilayer. Phys. Rev. Lett. 2008, 100, 016602.CrossRefGoogle Scholar
  6. [6]
    Du, X.; Skachko, I.; Barker, A.; Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nat. Nanotechnol. 2008, 3, 491–495.CrossRefGoogle Scholar
  7. [7]
    Frank, I. W.; Tanenbaum, D. M.; Van der Zanda, A. M.; McEuen, P. L. Mechanical properties of suspended graphene sheets. J. Vac. Sci. Technol. B 2007, 25, 2558–2561.CrossRefGoogle Scholar
  8. [8]
    Scarpa, F.; Adhikari, S.; Phani, A. S. Effective elastic mechanical properties of single layer graphene sheets. Nanotechnology 2009, 20, 065709.CrossRefGoogle Scholar
  9. [9]
    Faccio, R.; Denis, P. A.; Pardo, H.; Goyenola, C.; Mombru, A. W. Mechanical properties of graphene nanoribbons. J. Phys. Condens. Matter 2009, 21, 285304.CrossRefGoogle Scholar
  10. [10]
    Stoller, M. D.; Park, S.; Zhu, Y.; An, J.; Ruoff, R. S. Graphene-based ultracapacitors. Nano Lett. 2008, 8, 3498–3502.CrossRefGoogle Scholar
  11. [11]
    Müllen, K.; Rabe, J. P. Nanographenes as active components of single-molecule electronics and how a scanning tunneling microscope puts them to work. Acc. Chem. Res. 2008, 41, 511–520.CrossRefGoogle Scholar
  12. [12]
    Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. Structural defects in graphene. ACS Nano 2011, 5, 26–41.CrossRefGoogle Scholar
  13. [13]
    Kekulé, A. Sur la constitution des substances aromatiques. Bull. Soc. Chim. Fr. (Paris) 1865, 3, 98–110.Google Scholar
  14. [14]
    Kekulé, A. Note sur quelques produits de substitution de la benzene. Bull. Acad. Roy. Belg. 1866, 119, 551–563.Google Scholar
  15. [15]
    Kekulé, A. Untersuchungen über aromatische Verbindungen. Ann. Chem. 1866, 137, 129–136.CrossRefGoogle Scholar
  16. [16]
    Hückel, P. Z. Quantentheoretische Beiträge zum Benzolproblem. Z. Phys. 1931, 70, 204–286.CrossRefGoogle Scholar
  17. [17]
    Moran, D.; Stahl, F.; Bettinger, H. F.; Schaefer, H. F. III; Schleyer, P. V. R. Towards graphite: Magnetic properties of large polybenzenoid hydrocarbons. J. Am. Chem. Soc. 2003, 125, 6746–6752.CrossRefGoogle Scholar
  18. [18]
    Schleyer, P. V. R.; Maerker, C.; Dransfeld, A.; Jiao, H. J.; Hommes, N. J. R. V. E. Nucleus-independent chemical shifts: A simple and efficient aromaticity probe. J. Am. Chem. Soc. 1996, 118, 6317–6318.CrossRefGoogle Scholar
  19. [19]
    Galeev, T. R.; Chen, Q.; Guo, J. C.; Bai, H.; Miao, C. Q.; Lu, H. G.; Sergeeva, A. P.; Li, S. D.; Boldyrev, A. I. Deciphering the mystery of hexagon holes in an all-boron graphene α-sheet. Phys. Chem. Chem. Phys. 2011, 13, 11575–11578.CrossRefGoogle Scholar
  20. [20]
    Tang, H.; Ismail-Beigi, S. Novel precursors for boron nanotubes: The competition of two-center and three-center bonding in boron sheets. Phys. Rev. Lett. 2007, 99, 115501.CrossRefGoogle Scholar
  21. [21]
    Tang, H.; Ismail-Beigi, S. Self-doping in boron sheets from first principles: A route to structural design of metal boride nanostructures. Phys. Rev. B 2009, 80, 134113.CrossRefGoogle Scholar
  22. [22]
    Yang, X.; Ding, Y.; Ni, J. Ab initio prediction of stable boron sheets and boron nanotubes: Structure, stability, and electronic properties. Phys. Rev. B 2008, 77, 041402.CrossRefGoogle Scholar
  23. [23]
    Donohue, J. The Structures of the Elements; Wiley-Interscience: New York, 1974.Google Scholar
  24. [24]
    Zubarev, D. Y.; Boldyrev, A. I. Developing paradigms of chemical bonding: Adaptive natural density partitioning. Phys. Chem. Chem. Phys. 2008, 10, 5207–5217.CrossRefGoogle Scholar
  25. [25]
    Zubarev, D. Y.; Boldyrev, A. I. Revealing intuitively assessable chemical bonding patterns in organic aromatic molecules via adaptive natural density partitioning. J. Org. Chem. 2008, 73, 9251–9258.CrossRefGoogle Scholar
  26. [26]
    Zubarev, D. Y.; Boldyrev, A. I. Deciphering chemical bonding in golden cages. J. Phys. Chem. A 2009, 113, 866–868.CrossRefGoogle Scholar
  27. [27]
    Sergeeva, A. P.; Boldyrev, A. I. The chemical bonding of Re3Cl9 and Re3Cl9 2-revealed by the adaptive natural density partitioning analyses. Comment. Inorg. Chem. 2010, 31, 2–12.CrossRefGoogle Scholar
  28. [28]
    Steiner, E.; Fowler, P. W.; Jenneskens, L. W. Counter-rotating ring currents in coronene and corannulene. Angew. Chem. Int. Ed. 2001, 40, 362–366.CrossRefGoogle Scholar
  29. [29]
    Ciesielski, A.; Cyranski, M. K.; Krygowski, T. M.; Fowler, P. W.; Lillington, M. Super-delocalized valence isomer of coronene. J. Org. Chem. 2006, 71, 6840–6845.CrossRefGoogle Scholar
  30. [30]
    Balaban, A. T.; Bean, D. E.; Fowler, P. W. Patterns of ring current in coronene isomers. Acta Chim. Slov. 2010, 57, 507–512.Google Scholar
  31. [31]
    Poater, J.; Duran, M.; Solà, M.; Silvi, B. Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches. Chem. Rev. 2005, 105, 3911–3947.CrossRefGoogle Scholar
  32. [32]
    Merino, G.; Vela, A.; Heine, T. Description of electron delocalization via the analysis of molecular fields. Chem. Rev. 2005, 105, 3812–3841.CrossRefGoogle Scholar
  33. [33]
    Bultinck, P.; Ponec, R.; Van Damme, S. Multicenter bond indices as a new measure of aromaticity in polycyclic aromatic hydrocarbons. J. Phys. Org. Chem. 2005, 18, 706–718.CrossRefGoogle Scholar
  34. [34]
    Feixas, F.; Matito, E.; Solà, M.; Poater, J. Analysis of Hückel’s [4n + 2]_rule through electronic delocalization measures. J. Phys. Chem. A 2008, 112, 13231–13238.CrossRefGoogle Scholar
  35. [35]
    Feixas, F.; Matito, E.; Duran, M.; Poater, J.; Solà, M. Aromaticity and electronic delocalization in all-metal clusters with single, double, and triple aromatic character. Theor. Chem. Acc. 2011, 128, 419–431.CrossRefGoogle Scholar
  36. [36]
    Feixas, F.; Jimenez-Halla, J. O. C.; Matito, E.; Poater, J.; Solà, M. A test to evaluate the performance of aromaticity descriptors in all-metal and semimetal clusters. An appraisal of electronic and magnetic indicators of aromaticity. J. Chem. Theory Comput. 2010, 6, 1118–1130.CrossRefGoogle Scholar
  37. [37]
    Solà, M.; Feixas, F.; Jimenez-Halla, J. O. C.; Matito, E.; Poater, J. A critical assessment of the performance of magnetic and electronic indices of aromaticity. Symmetry 2010, 2, 1156–1179.CrossRefGoogle Scholar
  38. [38]
    Poater, J.; Solà, M.; Viglione, R. G.; Zanasi, R. Local aromaticity of the six-membered rings in pyracylene. A difficult case for the NICS indicator of aromaticity. J. Org. Chem. 2004, 69, 7537–7542.CrossRefGoogle Scholar
  39. [39]
    Matito, E.; Feixas, F.; Solà, M. Electron delocalization and aromaticity measures within the Hückel molecular orbital method. J. Mol. Struct. (Theochem) 2007, 811, 3–11.CrossRefGoogle Scholar
  40. [40]
    Foster, J. P.; Weinhold, F. Natural hybrid orbitals. J. Am. Chem. Soc. 1980, 102, 7211–7218.CrossRefGoogle Scholar
  41. [41]
    Weinhold, F.; Landis, C. R. Valency and Bonding. A Natural Bond Orbital Donor-Acceptor Perspective; Cambridge University Press: Cambridge, UK, 2005.CrossRefGoogle Scholar
  42. [42]
    Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648–5652.CrossRefGoogle Scholar
  43. [43]
    Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785–789.CrossRefGoogle Scholar
  44. [44]
    Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J. Phys. Chem. 1994, 98, 11623–11627.CrossRefGoogle Scholar
  45. [45]
    Frisch, M. J. et al. Gaussian 03, (Revision D.01), Gaussian, Inc., Wallingford CT, 2004.Google Scholar
  46. [46]
    Varetto, U. Molekel, Swiss National Supercomputing Centre, Manno (Switzerland).Google Scholar
  47. [47]
    Fallah-Bagher-Shaidaei, H.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer, P. V. R. Which NICS aromaticity index for planar p rings is best? Org. Lett. 2006, 8, 863–866.CrossRefGoogle Scholar
  48. [48]
    Chen, Z.; Wannere, C. S.; Corminboeuf, C.; Puchta, R.; Schleyer P. V. R. Nucleus-independent chemical shifts (NICS) as an aromaticity criterion. Chem. Rev. 2005, 105, 3842–3888.CrossRefGoogle Scholar
  49. [49]
    Biegler-König, F. W.; Bader, R. F. W.; Tang, T. H. Calculation of the average properties of atoms in molecules. II. J. Comput. Chem. 1982, 3, 317–328.CrossRefGoogle Scholar
  50. [50]
    Matito, E. ESI-3D: Electron Sharing Indices Program for 3D Molecular Space Partitioning. Institute of Computational Chemistry: Girona, 2006. http: // (Updated March 3, 2006).Google Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Chemistry and BiochemistryUtah State UniversityLoganUSA
  2. 2.Department of Physical and Colloid ChemistryPeoples’ Friendship University of RussiaMoscowRussian Federation

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