Jahn-Teller effect
The Jahn-Teller effect, sometimes also known as Jahn-Teller distortion, describes the geometrical distortion of non-linear molecules under certain situations. The effect is named after Hermann Arthur Jahn and Edward Teller, who proved, using group theory, that non-linear degenerate molecules cannot be stable. The theorem essentially states that any non-linear molecule with a degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy. This also has the effect of lowering the overall energy of the complex.

# In transition metal chemistry
The Jahn-Teller effect is most often encountered in octahedral complexes of the transition metals, and is very common in six-coordinate copper(II) complexes. The d9 electronic configuration of this ion gives three electrons in the two degenerate eg orbitals, leading to a doubly-degenerate electronic ground state. Such complexes distort along one of the molecular fourfold axes (always labelled the z axis), which has the effect of removing the orbital and electronic degeneracies and lowering the overall energy. The distortion normally takes the form of elongating the bonds to the ligands lying along the z axis, but occasionally occurs as a shortening of these bonds instead (the Jahn-Teller theorem does not predict the direction of the distortion, only the presence of an unstable geometry). When such an elongation occurs, the effect is to lower the electrostatic repulsion between the electron-pair on the Lewis basic ligand and any electrons in orbitals with a z component, thus lowering the energy of the complex. If the undistorted complex would be expected to have an inversion centre, this is preserved after the distortion.
In octahedral complexes, the Jahn-Teller effect is most pronounced when an odd number of electrons occupy the eg orbitals; i.e., in d9, low-spin d7 or high-spin d4 complexes, all of which have doubly-degenerate ground states. This is because the eg orbitals involved in the degeneracy point directly at the ligands, so distortion can result in a large energetic stabilisation. Strictly speaking, the effect should also occur when there is a degeneracy due to the electrons in the t2g orbitals (i.e configurations such as d1 or d2, both of which are triply degenerate). However, the effect is much less noticeable, because there is a much smaller lowering of repulsion on taking ligands further away from the t2g orbitals, which don't point directly at the ligands involved (see the table below).  The same is true in tetrahedral complexes; distortion is less because there is less stabilisation to be gained because the ligands are not pointing directly at the orbitals.
The expected effects for octahedral coordination are given in the following table:
w: weak Jahn-Teller effect (t2g orbitals unevenly occupied), s: strong Jahn-Teller effect expected (eg orbitals unevenly occupied), blank: no Jahn-Teller effect expected.
The Jahn-Teller effect can be demonstrated experimentally by investigation of the UV-VIS absorbance spectra of inorganic compounds, where it often causes splitting of bands. It is also readily apparent in the crystal structures of many copper(II) complexes.

# In organic chemistry
The Jahn-Teller effect is also sometimes encountered in organic chemistry, as in the case of cyclooctatetraene .  The cited reference however is in disagreement with another paper in which the pseudo Jahn-Teller effect (also sometimes called the "second order Jahn-Teller effect") is apparently not present in the D4h transistion structure .  A clear case however is the case of the COT radical anion, wherein the traditional frost circle  MO diagram (image at right) shows clearly a non-equally filled set of degenerate orbitals.  This configuration therefore distorts according to the Jahn-Teller effect (see reference for computational detail of distortion specifics) .