Jahn–Teller effect

The Jahn-Teller effect is an important mechanism of spontaneous symmetry breaking, in molecular and solid-state systems, which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystallochemistry, molecular and solid-state physics, and materials science. The effect is named after Hermann Arthur Jahn and Edward Teller, who first reported their studies in 1937.

The Jahn-Teller Theorem

The theorem can be stated in different ways, three of which are given here:

Every nonlinear molecular system is unstable in a degenerated electronic state and will break the symmetry of the degenerated state to decrease its energy.

A non-linear polyatomic system in a spatially degenerated electronic state is spontaneously distorted in such a way that degeneration is eliminated and a new balance structure of less symmetry is reached.

Stability and degeneration are not possible simultaneously unless the molecule is linear.

Spin degeneration was an exception in the original treatment and was later treated separately.

The formal mathematical proof of the Jahn-Teller theorem relies heavily on arguments from symmetry, more specifically on the theory of molecular point groups. Jahn and Teller's argument does not assume details about the electronic structure of the system. Jahn and Teller did not make any statement about the strength of the effect, which may be so small that it cannot be measured. In fact, for electrons in nonbonding or weakly bonding molecular orbitals, the effect is expected to be weak. However, in many situations, the effect is important.

Application in transition metals

The Jahn-Teller effect is responsible for the tetragonal distortion of the hexaacuacobre ionic complex(II), [Cu(OH₂)₆]²⁺which should have an octamer geometry. The two axial distances Cu−O are 238pm], while the four equatorial distances Cu−O are ~195 pm.

Above: field linking octahédrico (left) and distorted by Jahn-Teller (right). Below: Associated energy levels of molecular orbitals.

The Jahn-Teller effect occurs in systems (generally transition metal coordination compounds) in which there are several degenerate energy levels and not equally occupied. In these cases, the Jahn-Teller theorem predicts that the system will experience a distortion, such that some of these levels will stabilize and others will destabilize. Since all the levels are not equally occupied, the destabilized ones will be the emptiest, and the system will have less energy. The theorem does not predict how strong the effect will be in each particular case.

It is most often found in octahedral complexes of transition metals. The phenomenon is most common in hexacoordinate copper(II) complexes. The electronic configuration d⁹ of this ion provides three electrons in the two degenerate e_g orbitals, leading to a doubly degenerate ground state. Such complexes are distorted along one of the molecular quadruple axes (always labeled the z-axis), which has the effect of removing orbital and electron degeneracies and lowering the overall energy. The distortion normally takes the form of lengthening the bonds to the ligands along the z-axis, but sometimes it occurs as a shortening of these bonds (the Jahn-Teller theorem does not predict the direction of the distortion, only the direction of the distortion). presence of an unstable geometry). When such stretching occurs, the effect is to decrease the electrostatic repulsion between the ligand's electron pair (Lewis base) and any electrons in orbitals with a z component, thus lowering the energy of the complex. The inversion center is preserved after the distortion. Distorting the octahedral symmetry to give an axially elongated octahedron stabilizes the d_x²-y² orbital, which becomes occupied by two electrons and destabilizes the d_z², which remains occupied by an electron.

J-T effect in high-spin complexes

In octahedral complexes, the Jahn–Teller effect is most pronounced when an odd number of electrons occupy the e_g orbitals. This situation occurs in complexes with the low-spin d⁹, d⁷, or dsup> ⁴ high spin, all of which have doubly degenerate ground states. This is because the e_g orbitals are in the same direction as the ligands, so the distortion represents a large energy stabilization.

Taking as an example a high spin complex, for example a d⁴ (t³_2ge ¹_g), the fourth d electron can occupy either the dx²-y² or the dz² orbital with equal energy. If the d_x²-y² orbital is occupied, all 4 equatorial ligands are rejected, resulting in compression of the octahedron. If, on the other hand, the dz² orbital is occupied, only the two axially arranged ligands are rejected, leading to a stretching of the octahedron in the z-direction. In both cases, the occupancy of the reduced orbital leads to an energy gain, although not very large, which is known as the Jahn-Teller stabilization energy. Whether it is stretched or compressed depends, among other things, on the counterion. For example, depending on the counterion, a [Cu(NO)₆]⁴⁻ complex is sometimes found as a compressed octahedral complex or an extended octahedral complex. Others, like [Cu(py')₆]²⁺ with py'=pyridine oxide, even have a structure that fluctuates between the two forms (see image on the left).

Strictly speaking, the effect also occurs when there is a degeneracy due to electrons in t_2g orbitals (i.e. configurations like d¹ or d², which are triply degenerate). In such cases, however, the effect is much less noticeable, because there is a much smaller decrease in repulsion by taking the ligands further away from the t_2g orbitals, which do not directly target the ligands (see table below). The same is true in tetrahedral complexes (eg manganate: the distortion is very subtle because there is less stabilization to gain because the ligands do not point directly to the orbitals). This effect also exists in d complexes. ⁸ with square-planar geometry (hybridization dsp²), where the orbitals dz², dxz and dyz are the lowest energy.

The expected effects for octahedral complexes are found in the following table:

AS: High spin

BS: Low spin

d: Weak Jahn-Teller effect (t_2g half-filled orbitals)

f: strong Jahn-Teller effect (e_g half-filled orbitals)

white: no Jahn-Teller effect expected

The Jahn–Teller effect manifests itself in the UV-VIS absorbance spectra of some compounds, where it often causes band splitting. It is readily apparent in the structures of many copper(II) complexes. However, additional detailed information about the anisotropy of such complexes and the nature of ligand binding can be obtained from the fine structure of the resonance spectra of electronic spin at low temperature.

Jahn-Teller effect in other areas of chemistry

The Jahn-Teller effect forces the radical anion of the cyclootatetraene (−1) to be not symmetrical

The underlying cause of the Jahn-Teller effect is the presence of molecular orbitals that are both degenerate and open (ie, incompletely filled). This situation is not exclusive to coordination complexes and can be found in other areas of chemistry. In organic chemistry, the phenomenon of antiaromaticity has the same cause and often sees molecules become distorted; as in the case of cyclobutadienes and cyclooctatetraenes (TOC).