In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. The succinct expression as the 4n+2 rule has been attributed to von Doering (1951), although several authors were using this form at around the same time.
A cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4n+2 where n is zero or any positive integer, although clearcut examples are really only established for values of n = 0 up to about n = 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 and by the Pariser–Parr–Pople method.
Aromatic compounds are more stable than theoretically predicted by alkene hydrogenation data; the "extra" stability is due to the delocalized cloud of electrons, called resonance energy. Criteria for simple aromatics are:
- the molecule must follow Hückel's rule, having 4n+2 electrons in the delocalized, conjugated p-orbital cloud;
- the molecule must be able to be planar;
- the molecule must be cyclic; and,
- every atom in the ring must be able to participate in delocalizing the electrons by having a p-orbital or an unshared pair of electrons.
Hückel's rule is not valid for many compounds containing more than three fused aromatic nuclei in a cyclic fashion. For example, pyrene contains 16 conjugated electrons (8 bonds), and coronene contains 24 conjugated electrons (12 bonds). Both of these polycyclic molecules are aromatic, even though they fail the 4n+2 rule. Indeed, Hückel's rule can only be theoretically justified for monocyclic systems.
In 2000, Andreas Hirsch and coworkers in Erlangen, Germany, formulated a rule to determine when a fullerene would be aromatic. They found that if there were 2(n+1)2 π-electrons, then the fullerene would display aromatic properties. This follows from the fact that an aromatic fullerene must have full icosahedral (or other appropriate) symmetry, so the molecular orbitals must be entirely filled. This is possible only if there are exactly 2(n+1)2 electrons, where n is a nonnegative integer. In particular, for example, buckminsterfullerene, with 60 π-electrons, is non-aromatic, since 60/2 = 30, which is not a perfect square.
- 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. 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.
- Hückel, E. (1938), Grundzüge der Theorie ungesättiger und aromatischer Verbindungen, Berlin: Verlag Chem, pp. 77–85.
- Doering, W. v. E. (September 1951), Abstracts of the American Chemical Society Meeting, New York, p. 24M Missing or empty
- See Roberts et al. (1952) and refs. therein.
- March, Jerry (1985), Advanced Organic Chemistry: Reactions, Mechanisms, and Structure (3rd ed.), New York: Wiley, ISBN 0-471-85472-7
- Roberts, John D.; Streitweiser, 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
- Hirsch, Andreas; Chen, Zhongfang; Jiao, Haijun (2000), "Spherical Aromaticity in Ih Symmetrical Fullerenes: The 2(N+1)2 Rule", Angew. Chem., Int. Ed. Engl. 39 (21): 3915–17, doi:10.1002/1521-3773(20001103)39:21<3915::AID-ANIE3915>3.0.CO;2-O.