Hückel's rule
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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. It was first expressed succinctly as the 4n+2 rule by von Doering in 1951. 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 6). Hückel's rule was based on calculations using the Hückel method, although it can also be justified by considering a particle in a ring system.
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 - (1) follow Huckel's rule, having 4n+2 electrons in the delocalized cloud, (2) are able to be planar and are cyclic, (3) every atom in the circle is able to participate in delocalizing the electrons by having a p orbital or an unshared pair of electrons.
[edit] Refinement
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.
The Hückel method and Pariser-Parr-Pople method are a more precise means of estimating the properties of a π-system.
[edit] Three-Dimensional Rule
In 2000, chemists in Germany formulated a rule to determine when a fullerene would be aromatic. In particular, 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 only possible 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.
