Hückel's rule

In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4n + 2 π-electrons, where n is a non-negative integer. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931.[1][2] The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951),[3][4] although several authors were using this form at around the same time.[5]

In agreement with the Möbius–Hückel concept, a cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4n + 2, although clearcut examples are really only established for values of n = 0 up to about n = 6.[6] Hückel's rule was originally based on calculations using the Hückel method, although it can also be justified by considering a particle in a ring system, by the LCAO method[5] and by the Pariser–Parr–Pople method.

Aromatic compounds are more stable than theoretically predicted using hydrogenation data of simple alkenes; the additional stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics are:

  1. the molecule must have 4n + 2 (a so-called "Hückel number") π electrons[7] (2, 6, 10, ...) in a conjugated system of p orbitals (usually on sp2-hybridized atoms, but sometimes sp-hybridized);
  2. the molecule must be (close to) planar (p orbitals must be roughly parallel and able to interact, implicit in the requirement for conjugation);
  3. the molecule must be cyclic (as opposed to linear);
  4. the molecule must have a continuous ring of p atomic orbitals (there cannot be any sp3 atoms in the ring, nor do exocyclic p orbitals count).
  1. ^
    • Hückel, Erich (1931). "Quantentheoretische Beiträge zum Benzolproblem I. Die Elektronenkonfiguration des Benzols und verwandter Verbindungen". Z. Phys. 70 (3–4): 204–86. Bibcode:1931ZPhy...70..204H. doi:10.1007/BF01339530. S2CID 186218131.
    • Hückel, Erich (1931). "Quanstentheoretische Beiträge zum Benzolproblem II. Quantentheorie der induzierten Polaritäten". Z. Phys. 72 (5–6): 310–37. Bibcode:1931ZPhy...72..310H. doi:10.1007/BF01341953.
    • Hückel, Erich (1932). "Quantentheoretische Beiträge zum Problem der aromatischen und ungesättigten Verbindungen. III". Z. Phys. 76 (9–10): 628–48. Bibcode:1932ZPhy...76..628H. doi:10.1007/BF01341936. S2CID 121787219.
  2. ^ Hückel, E. (1938). Grundzüge der Theorie ungesättiger und aromatischer Verbindungen. Berlin: Verlag Chem. pp. 77–85.
  3. ^ Doering, W. VON E.; Detert, Francis L. (1951-02-01). "Cycloheptatrienylium Oxide". Journal of the American Chemical Society. 73 (2): 876–877. doi:10.1021/ja01146a537. ISSN 0002-7863.
  4. ^ Doering, W. v. E. (September 1951), Abstracts of the American Chemical Society Meeting, New York, p. 24M
  5. ^ a b Roberts, John D.; Streitwieser, Andrew Jr.; Regan, Clare M. (1952). "Small-Ring Compounds. X. Molecular Orbital Calculations of Properties of Some Small-Ring Hydrocarbons and Free Radicals". J. Am. Chem. Soc. 74 (18): 4579–82. doi:10.1021/ja01138a038.
  6. ^ March, Jerry (1985). Advanced Organic Chemistry: Reactions, Mechanisms, and Structure (3rd ed.). New York: Wiley. ISBN 9780471854722. OCLC 642506595.
  7. ^ Ayub, Rabia (2017). "Excited State Aromaticity and Antiaromaticity. Fundamental Studies and Applications" (PDF). Uppsala University. p. 15. Retrieved 26 January 2022.
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