Jahn–Teller Distortion

The Jahn–Teller distortion is a vital process of spontaneous symmetry breaking in molecular and solid-state systems, which has far-reaching consequences in different fields, and is accountable for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science.

It was named after Hermann Arthur Jahn and Edward Teller, who first documented cases about it in 1937. It explains the geometrical distortion of molecules and ions that is stemmed from specific electron mechanisms. Its theorem indicates that any non-linear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy because the distortion lowers the overall energy of the species.

As stated earlier, it is a geometric distortion of a non-linear molecular system that reduces its symmetry and energy. This distortion is typically observed among octahedral complexes where the two axial bonds can be shorter or longer than those of the equatorial bonds are.

This effect is most often seen in octahedral complexes of the transition metals. The phenomenon is usually observed in six-coordinate Copper (II) complexes. The D9 electronic configuration of this ion gives three electrons in the two degenerate orbitals, leading to a doubly degenerate electronic ground state.

Such complexes distort along with one of the molecular fourfold axes (always labeled the z-axis), which has the effect of removing the orbital and electronic degeneracies and lowering the overall energy. The distortion usually 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 (in essence, it 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. The inversion center is preserved after the distortion.

Octahedral Complexes

In octahedral complexes, the Jahn–Teller distortion is most pronounced when an odd number of electrons occupy the EG orbitals. This situation arises in complexes with the configurations d9, low-spin d7, or high-spin d4 complexes, all of which have doubly degenerate ground states. In such compounds, the EG orbitals involved in the degeneracy, point directly at the ligands, so distortion can result in a large energetic stabilization.

Strictly speaking, the effect also occurs when there is a degeneracy due to the electrons in the t2g orbitals (i.e. configurations such as d1 or d 2, both of which are triply degenerate). In such cases, 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 do not point directly at the ligands.

The same is true in tetrahedral complexes (e.g. manganate: distortion is very subtle because there is less stabilization to be gained because the ligands are not pointing directly at the orbitals).

Jahn-Teller Theorem

In 1937, Hermann Jahn and Edward Teller postulated a theorem stating, "Stability and degeneracy are not possible simultaneously unless the molecule is a linear one," in regards to its electronic state. This leads to a break in degeneracy, which stabilizes the molecule and by consequence, reduces its symmetry.

Since 1937, the theorem has been revised, which Housecroft and Sharpe have eloquently phrased as "any non-linear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy, thereby removing the degeneracy." This is most commonly observed with transition metal octahedral complexes, however, it can be observed in tetrahedral compounds as well.

For a given octahedral complex, the five d atomic orbitals are split into two degenerate sets when constructing a molecular orbital diagram. These are represented by the sets' symmetry labels: t2g ( dxz, dyz, dxy ) and eg (dz2 and dx2−y2). When a molecule possesses a degenerate electronic ground state, it will distort to remove the degeneracy and form a lower energy (and by consequence, lower symmetry) system. The octahedral complex will either elongate or compress the z ligand bonds.

Elongation and Compression

Elongation occurs when the degeneracy is broken by the stabilization (lowering in energy) of the d orbitals with a z component, while the orbitals without a z component are destabilized (higher in energy). This is due to the dxy and dx2−y2 orbitals having a greater overlap with the ligand orbitals, resulting in the orbitals being higher in energy.

Since the dx2−y2 orbital is antibonding, it is expected to increase in energy due to elongation. The dxy orbital is still nonbonding but is destabilized due to the interactions. Jahn-Teller elongations are well documented for copper (II) octahedral compounds. Compression happens when the degeneracy is broken by the stabilization (lowering in energy) of the d orbitals without a z component, while the orbitals with a z component are destabilized (higher in energy)

It should however be noted that when an octahedral complex exhibits elongation, the axial bonds are longer than the equatorial bonds. For compression, it is the reverse; the equatorial bonds are longer than the axial bonds. Elongation and compression effects are dictated by the amount of overlap between the metal and ligand orbitals. Thus, this distortion varies greatly depending on the type of metal and ligands. In general, the stronger the metal-ligand orbital interactions are, the greater the chance for the effect to be observed.

Finally, for Jahn–Teller distortion to occur in transition metals there must be degeneracy in either the t2g or eg orbitals. The electronic states of octahedral complexes depend on the number of d-electrons and the splitting energy, Δ. When Δ is large and is greater than the energy required to pair electrons, electrons pair in t2g before occupying eg. On the other hand, when Delta is small and is less than the pairing energy, electrons will occupy eg before pairing in t2g. The Δ of an octahedral complex is dictated by the chemical environment (ligand identity), and the identity and charge of the metal ion.