200px|thumb|right|[[Benzene, the most widely recognized aromatic compound with six delocalized π-electrons (4n + 2, for n = 1).]]

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. 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:

  1. the molecule must have 4n&nbsp;+&nbsp;2 (a so-called "Hückel number") π electrons (2, 6, 10, ...) in a conjugated system of p orbitals (usually on sp<sup>2</sup>-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 sp<sup>3</sup> atoms in the ring, nor do exocyclic p orbitals count).

Monocyclic hydrocarbons

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 (C<sub>6</sub>H<sub>6</sub>) with a conjugated system of six π electrons, which equals 4n&nbsp;+&nbsp;2 for n&nbsp;=&nbsp;1. The molecule undergoes substitution reactions which preserve the six π electron system rather than addition reactions which would destroy it. The stability of this π electron system is referred to as aromaticity. Still, in most cases, catalysts are necessary for substitution reactions to occur.

The cyclopentadienyl anion () with six π electrons is planar and readily generated from the unusually acidic cyclopentadiene (pK<sub>a</sub> 16), while the corresponding cation with four π electrons is destabilized, being harder to generate than a typical acyclic pentadienyl cations and is thought to be antiaromatic. Similarly, the tropylium cation (), also with six π electrons, is so stable compared to a typical carbocation that its salts can be crystallized from ethanol. and the triboracyclopropenyl dianion () are considered examples of a two π electron system, which are stabilized relative to the open system, despite the angle strain imposed by the 60° bond angles.

Planar ring molecules with 4n π electrons do not obey Hückel's rule, and theory predicts that they are less stable and have triplet ground states with two unpaired electrons. In practice, such molecules distort from planar regular polygons. Cyclobutadiene (C<sub>4</sub>H<sub>4</sub>) with four π electrons is stable only at temperatures below 35&nbsp;K and is rectangular rather than square.

Polycyclic hydrocarbons

Hückel's rule is not valid for many compounds containing more than one ring. For example, pyrene and trans-bicalicene contain 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&nbsp;+&nbsp;2 rule. Indeed, Hückel's rule can only be theoretically justified for monocyclic systems.

See also

  • Baird's rule (for triplet states)

References