In organic chemistry

Organic chemistry

Organic chemistry is a subdiscipline within chemistry involving the scientific study of the structure, properties, composition, reactions, and preparation of carbon-based compounds, hydrocarbons, and their derivatives...

, Hückel's rule estimates whether a planar ring molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 will have aromatic

Aromaticity

In organic chemistry, Aromaticity is a chemical property in which a conjugated ring of unsaturated bonds, lone pairs, or empty orbitals exhibit a stabilization stronger than would be expected by the stabilization of conjugation alone. The earliest use of the term was in an article by August...

 properties. The quantum mechanical basis for its formulation was first worked out by physical chemist

Physical chemistry

Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

 Erich Hückel

Erich Hückel

Erich Armand Arthur Joseph Hückel was a German physicist and physical chemist. He is known for two major contributions:*The Debye–Hückel theory of electrolytic solutions...

 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

Cyclic compound

In chemistry, a cyclic compound is a compound in which a series of atoms is connected to form a loop or ring.While the vast majority of cyclic compounds are organic, a few inorganic substances form cyclic compounds as well, including sulfur, silanes, phosphanes, phosphoric acid, and triboric acid. ...

 ring molecule follows Hückel's rule when the number of its π-electrons equals 4n+2 where n is zero or any positive integer

Integer

The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...

, 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

Hückel method

The Hückel method or Hückel molecular orbital method proposed by Erich Hückel in 1930, is a very simple linear combination of atomic orbitals molecular orbitals method for the determination of energies of molecular orbitals of pi electrons in conjugated hydrocarbon systems, such as ethene,...

, although it can also be justified by considering a particle in a ring

Particle in a ring

In quantum mechanics, the case of a particle in a one-dimensional ring is similar to the particle in a box. The Schrödinger equation for a free particle which is restricted to a ring is...

 system, by the LCAO method

Linear combination of atomic orbitals molecular orbital method

A linear combination of atomic orbitals or LCAO is a quantum superposition of atomic orbitals and a technique for calculating molecular orbitals in quantum chemistry. In quantum mechanics, electron configurations of atoms are described as wavefunctions...

 and by the Pariser–Parr–Pople method

Pariser–Parr–Pople method

In molecular physics, the Pariser–Parr–Pople method applies semi-empirical quantum mechanical methods to the quantitative prediction of electronic structures and spectra, in molecules of interest in the field of organic chemistry...

.

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:

1. follow Huckel's rule, having 4n+2 electrons in the delocalized p-orbital cloud;
2. be 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.

Refinement

Hückel's rule is not valid for many compounds containing more than three fused aromatic nuclei in a cyclic fashion. For example, pyrene

Pyrene

Pyrene is a polycyclic aromatic hydrocarbon consisting of four fused benzene rings, resulting in a flat aromatic system. The chemical formula is . This colourless solid is the smallest peri-fused PAH...

 contains 16 conjugated electrons

Conjugated system

In chemistry, a conjugated system is a system of connected p-orbitals with delocalized electrons in compounds with alternating single and multiple bonds, which in general may lower the overall energy of the molecule and increase stability. Lone pairs, radicals or carbenium ions may be part of the...

 (8 bonds), and coronene

Coronene

Coronene is a polycyclic aromatic hydrocarbon comprising six peri-fused benzene rings. Its chemical formula is . It is a yellow material that dissolves in such solvents as benzene, toluene, and dichloromethane. Its solutions emit blue light fluorescence under UV light...

 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.

Three-dimensional rule

In 2000, Andreas Hirsch and coworkers in Erlangen

Erlangen

Erlangen is a Middle Franconian city in Bavaria, Germany. It is located at the confluence of the river Regnitz and its large tributary, the Untere Schwabach.Erlangen has more than 100,000 inhabitants....

, Germany

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

, formulated a rule to determine when a fullerene

Fullerene

A fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. Spherical fullerenes are also called buckyballs, and they resemble the balls used in association football. Cylindrical ones are called carbon nanotubes or buckytubes...

 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

Buckminsterfullerene

Buckminsterfullerene is a spherical fullerene molecule with the formula . It was first intentionally prepared in 1985 by Harold Kroto, James Heath, Sean O'Brien, Robert Curl and Richard Smalley at Rice University...

, with 60 π-electrons, is non-aromatic, since 60/2 = 30, which is not a perfect square

Square number

In mathematics, a square number, sometimes also called a perfect square, is an integer that is the square of an integer; in other words, it is the product of some integer with itself...

.