Exploring the validity of the Glidewell–Lloyd extension of Clar’s π-sextet rule: assessment from polycyclic conjugated hydrocarbons

  • Ouissam El Bakouri
  • Jordi Poater
  • Ferran Feixas
  • Miquel Solà
Regular Article
Part of the following topical collections:
  1. Festschrift in honour of A. Vela


The Clar π-sextet rule was formulated as a tool to qualitatively assign the local aromatic character of six-membered rings in benzenoid species. This simple rule has been widely validated both experimentally and theoretically. In 1984, Glidewell and Lloyd reported an extension of this rule to polycyclic conjugated hydrocarbons having rings with any even number of carbon atoms in their structure. In this work, we assess the validity of the Glidewell–Lloyd extension in 69 polycyclic conjugated hydrocarbons composed of different combinations of four-, six-, and eight-membered rings. Our results support the validity of this extension with some exceptions that are discussed. Finally, a minor modification to the rule is proposed.


Glidewell–Lloyd’s rule Clar’s π-sextet rule Polycyclic conjugated hydrocarbons Aromaticity Clamped benzenes Double bonds in ring junctions 



This work has been supported by the Ministerio de Economía y Competitividad (MINECO) of Spain (Project CTQ2014-54306-P) and the Generalitat de Catalunya (Project 2014SGR931, Xarxa de Referència en Química Teòrica i Computacional, ICREA Academia 2014 prize for M.S., and Grant No. 2014FI_B 00429 to O.E.B.). The EU under the FEDER Grant UNGI10-4E-801 (European Fund for Regional Development) has also funded this research.

Supplementary material

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Supplementary material 1 (DOCX 7146 kb)


  1. 1.
    Hückel E (1931) Quantentheoretische Beiträge zum Benzolproblem I: Die Elektronenkonfiguration des Benzols und verwandter Verbindungen. Z Phys 70:104–186CrossRefGoogle Scholar
  2. 2.
    Hückel E (1931) Quanstentheoretische Beiträge zum Benzolproblem II: Quantentheorie der induzierten Polaritäten. Z Phys 72:310–337CrossRefGoogle Scholar
  3. 3.
    Hückel E (1932) Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen: III. Z Phys 76:628–648CrossRefGoogle Scholar
  4. 4.
    Hückel E (1937) The theory of unsaturated and aromatic compounds. Z Elektrochem 43(752–788):827–849Google Scholar
  5. 5.
    Clar E (1972) The aromatic sextet. Wiley, New YorkGoogle Scholar
  6. 6.
    Solà M (2013) Forty years of Clar’s aromatic π-sextet rule. Front Chem 1:22CrossRefGoogle Scholar
  7. 7.
    Portella G, Poater J, Bofill JM, Alemany P, Solà M (2005) Local aromaticity of [n]Acenes, [n]Phenacenes, and [n]Helicenes (n = 1–9). J Org Chem 70:2509–2521CrossRefGoogle Scholar
  8. 8.
    Glidewell C, Lloyd D (1984) MNDO study of bond orders in some conjugated bi- and tri-cyclic hydrocarbons. Tetrahedron 40:4455–4472CrossRefGoogle Scholar
  9. 9.
    Vol’pin ME (1960) Non-benzenoid aromatic compounds and the concept of aromaticity. Russ Chem Rev 29:129–160CrossRefGoogle Scholar
  10. 10.
    Randić M (2003) Aromaticity of polycyclic conjugated hydrocarbons. Chem Rev 103:3449–3605CrossRefGoogle Scholar
  11. 11.
    Ginsburg D (1959) Non-benzenoid aromatic compounds. Interscience Publishers Inc., New YorkGoogle Scholar
  12. 12.
    Breslow R (2014) Novel aromatic and antiaromatic systems. Chem Rec 14:1174–1182CrossRefGoogle Scholar
  13. 13.
    Miyoshi H, Nobusue S, Shimizu A, Tobe Y (2015) Non-alternant non-benzenoid kekulenes: the birth of a new kekulene family. Chem Soc Rev 44:6560–6577CrossRefGoogle Scholar
  14. 14.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Revision A.02, Gaussian Inc, PittsburghGoogle Scholar
  15. 15.
    Becke AD (1993) Density-functional thermochemistry. III: the role of exact exchange. J Chem Phys 98:5648–5652CrossRefGoogle Scholar
  16. 16.
    Lee C, Yang W, Parr RG (1988) Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B 37:785–789CrossRefGoogle Scholar
  17. 17.
    Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ (1994) Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem 98:11623–11627CrossRefGoogle Scholar
  18. 18.
    Frisch MJ, Pople JA, Binkley JS (1984) Self-consistent molecular orbital methods 25: supplementary functions for Gaussian basis sets. J Chem Phys 80:3265–3269CrossRefGoogle Scholar
  19. 19.
    Poater J, Duran M, Solà M, Silvi B (2005) Theoretical evaluation of electron delocalization in aromatic molecules by means of atoms in molecules (AIM) and electron localization function (ELF) topological approaches. Chem Rev 105:3911–3947CrossRefGoogle Scholar
  20. 20.
    Feixas F, Matito E, Poater J, Sola M (2015) Quantifying aromaticity with electron delocalisation measures. Chem Soc Rev 44:6434–6451CrossRefGoogle Scholar
  21. 21.
    Bultinck P, Ponec R, Van Damme S (2005) Multicenter bond indices as a new measure of aromaticity in polycyclic aromatic hydrocarbons. J Phys Org Chem 18:706–718CrossRefGoogle Scholar
  22. 22.
    Matito E, Duran M, Solà M (2005) The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization. J Chem Phys 122:014109CrossRefGoogle Scholar
  23. 23.
    Kruszewski J, Krygowski TM (1972) Definition of aromaticity basing on the harmonic oscillator model. Tetrahedron Lett 13:3839–3842CrossRefGoogle Scholar
  24. 24.
    Krygowski TM (1993) Crystallographic studies of inter- and intra-molecular interactions reflected in benzenoid hydrocarbons: nonequivalence of indices of aromaticity. J Chem Inf Comput Sci 33:70–78CrossRefGoogle Scholar
  25. 25.
    Giambiagi M, de Giambiagi MS, dos Santos CD, de Figueiredo AP (2000) Multicenter bond indices as a measure of aromaticity. Phys Chem Chem Phys 2:3381–3392CrossRefGoogle Scholar
  26. 26.
    Bader RFW, Stephens ME (1975) Spatial localization of the electronic pair and number distributions in molecules. J Am Chem Soc 97:7391–7399CrossRefGoogle Scholar
  27. 27.
    Fradera X, Austen MA, Bader RFW (1999) The Lewis model and beyond. J Phys Chem A 103:304–314CrossRefGoogle Scholar
  28. 28.
    Fradera X, Poater J, Simon S, Duran M, Solà M (2002) Electron-pairing analysis from localization and delocalization indices in the framework of the atoms-in-molecules theory. Theor Chem Acc 108:214–224CrossRefGoogle Scholar
  29. 29.
    Matito E, Poater J, Solà M, Duran M, Salvador P (2005) Comparison of the AIM delocalization index and the Mayer and fuzzy atom bond orders. J Phys Chem A 109:9904–9910CrossRefGoogle Scholar
  30. 30.
    Bader RFW (1990) Atoms in molecules: a quantum theory. Clarendon, OxfordGoogle Scholar
  31. 31.
    Bader RFW (1991) A quantum theory of molecular structure and its applications. Chem Rev 91:893–928CrossRefGoogle Scholar
  32. 32.
    Matito E (2006) ESI-3D: electron sharing indexes program for 3D molecular space partitioning. http://iqc.udg.es/~eduard/ESI. Girona: Institute of Computational Chemistry and Catalysis
  33. 33.
    Keith A (2014) AIMall (v. 14.11.23). Overland Park: TK Gristmill Software (http://www.tkgristmill.com)
  34. 34.
    Portella G, Poater J, Solà M (2005) Assessment of the Clar’s aromatic pi-sextet rule by means of PDI, NICS, and HOMA indicators of local aromaticity. J Phys Org Chem 18:785–791CrossRefGoogle Scholar
  35. 35.
    Zubarev DY, Boldyrev AI (2008) Revealing intuitively assessable chemical bonding patterns in organic aromatic molecules via adaptive natural density partitioning. J Org Chem 73:9251–9258CrossRefGoogle Scholar
  36. 36.
    Popov IA, Boldyrev AI (2012) Chemical bonding in coronene, isocoronene, and circumcoronene. Eur J Org Chem 2012:3485–3491CrossRefGoogle Scholar
  37. 37.
    Kabuto C, Oda M (1980) Crystal and molecular structure of 9,10-diphenylbicyclo[6.2.0]decapentaene a 10 π aromatic compound. Tetrahedron Lett 21:103–106CrossRefGoogle Scholar
  38. 38.
    Papadakis R, Ottosson H (2015) The excited state antiaromatic benzene ring: a molecular Mr Hyde? Chem Soc Rev 44:6472–6493CrossRefGoogle Scholar
  39. 39.
    Baird NC (1972) Quantum organic photochemistry. II: resonance and aromaticity in the lowest 3.pi.pi.* state of cyclic hydrocarbons. J Am Chem Soc 94:4941–4948CrossRefGoogle Scholar
  40. 40.
    Roberts JD, Streitwieser A, Regan CM (1952) Small-ring compounds. X: molecular orbital calculations of properties of some small-ring hydrocarbons and free radicals1. J Am Chem Soc 74:4579–4582CrossRefGoogle Scholar
  41. 41.
    Platt JR (1949) Classification of spectra of cata-condensed hydrocarbons. J Chem Phys 17:484–495CrossRefGoogle Scholar
  42. 42.
    Soncini A, Havenith RWA, Fowler PW, Jenneskens LW, Steiner E (2002) Control of the diatropic pi ring current in strained benzenes: effects of annelation with cyclopropa, cyclobuta, and cyclobutadieno clampling groups. J Org Chem 67:4753–4758CrossRefGoogle Scholar
  43. 43.
    Frank NL, Baldridge KK, Siegel JS (1995) Synthesis and characterization of trisbicyclo[2.1.1]hexabenzene, a highly strained bicycloannelated benzene. J Am Chem Soc 117:2102–2103CrossRefGoogle Scholar
  44. 44.
    Fowler PW, Havenith RWA, Jenneskens LW, Soncini A, Steiner E (2001) Survival and extinction of delocalised ring currents in clamped benzenes. Chem Commun (22):2386–2387Google Scholar
  45. 45.
    Grant Hill J, Karadakov PB, Cooper DL (2006) The spin-coupled picture of clamped benzenes. Mol Phys 104:677–680CrossRefGoogle Scholar
  46. 46.
    Feixas F, Matito E, Poater J, Solà M (2007) Aromaticity of distorted benzene rings: exploring the validity of different indicators of aromaticity. J Phys Chem A 111:4513–4521CrossRefGoogle Scholar
  47. 47.
    Feixas F, Matito E, Poater J, Solà M (2008) On the performance of some aromaticity indices: a critical assessment using a test set. J Comput Chem 29:1543–1554CrossRefGoogle Scholar
  48. 48.
    Solà M, Feixas F, Jiménez-Halla JOC, Matito E, Poater J (2010) A critical assessment of the performance of magnetic and electronic indices of aromaticity. Symmetry 2:1156–1179CrossRefGoogle Scholar
  49. 49.
    Poater J, Visser R, Solà M, Bickelhaupt FM (2007) Polycyclic benzenoids: why kinked is more stable than straight. J Org Chem 72:1134–1142CrossRefGoogle Scholar
  50. 50.
    Poater J, Bickelhaupt FM, Solà M (2007) Didehydrophenanthrenes: structure, singlet-triplet splitting, and aromaticity. J Phys Chem A 111:5063–5070CrossRefGoogle Scholar
  51. 51.
    Dewar MJS, Li W-K (1974) MINDO [modified intermediate neglect of differential overlap]/3 study of the bisdehydrobenzenes. J Am Chem Soc 96:5569–5571CrossRefGoogle Scholar
  52. 52.
    Feixas F, Vandenbussche J, Bultinck P, Matito E, Solà M (2011) Electron delocalization and aromaticity in low-lying excited states of archetypal organic compounds. Phys Chem Chem Phys 13:20690–20703CrossRefGoogle Scholar
  53. 53.
    Rosenberg M, Dahlstrand C, Kilså K, Ottosson H (2014) Excited state aromaticity and antiaromaticity: opportunities for photophysical and photochemical rationalizations. Chem Rev 114:5379–5425CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institut de Química Computacional i Catàlisi (IQCC) and Departament de QuímicaUniversitat de GironaGironaSpain
  2. 2.Departament de Química Inorgànica i Orgànica and Institut de Química Teòrica i Computacional (IQTCUB)Universitat de BarcelonaBarcelonaSpain
  3. 3.Institució Catalana de Recerca i Estudis Avançats (ICREA)BarcelonaSpain

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