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. The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951), although several authors were using this form at around the same time. 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. 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 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: the molecule must have 4n + 2 (a so-called "Hückel number") π electrons (2, 6, 10, ...) in a conjugated system of p orbitals (usually on sp2-hybridized atoms, but sometimes sp-hybridized); the molecule must be (close to) planar (p orbitals must be roughly parallel and able to interact, implicit in the requirement for conjugation); the molecule must be cyclic (as opposed to linear); 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). 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 π electrons, which equals 4n + 2 for n = 1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it.