Hückel's rule
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 rule can be used to understand the stability of completely conjugated monocyclic hydrocarbons (known as annulenes) as well as their cations and anions. The best-known example is benzene (C6H6) with a conjugated system of six pi-electrons, which equals 4n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six pi-electron system rather than addition reactions which would destroy it. The stability of this pi-electron system is referred to as aromaticity. Still, in most cases, catalysts are necessary for substitution reactions to occur.
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