Advanced Inorganic Chemistry/Jahn-Teller Distortion (3.6)

= Jahn-Teller Effect = The Jahn-Teller Effect, governed by the Jahn-Teller Theorem, is a phenomenon in which non-linear molecules are stabilized via symmetric geometric distortions along one of their vibrational axes. The theorem does not predict what type of distortion will occur; however, it does note that this distortion will lower the complex's symmetry, energy, and degeneracy. The phenomenon exclusively affects systems with electronic degeneracy, and it primarily affects systems with an odd number of electrons. This effect was first described and published by Hermann Arthur Jahn and Edward Teller in 1937, and has since been well documented in octahedral transition-metal complexes.

Octahedral Metal-Ligand Complexes
In the crystal field representation of metal-ligand octahedral complexes, the molecular orbitals that are used to indicate the type of distortion are the metal's d-orbitals; these are antibonding orbitals with eg and t2g symmetry. In octahedral complexes, the distortion occurs such that the axial ligands- those along the z-axis- are either pushed away from the central metal or towards it (seen in figure 1). The type of distortion is dependent on the complex's d-orbital configuration.

Z-out Distortion
Complexes most likely to have z-out distortion are those whose ground state have electrons in the eg* energy levels. These orbitals are antibonding; therefore, when the eg level is populated, the metal-ligand bond is weakened and destabilization occurs along the z-axis. As a result, energy levels of x-y planar orbitals are stabilized and lowered, whereas z-oriented orbitals are destabilized and raised (seen in figure 2). Stabilizations and destabilizations are symmetric (as seen in figure 3); t2g* orbitals are offset by an energy value denoted δ1 (with dxy raising by 2/3 δ1 and dxz/dyz lowering by 1/3 δ1), and eg* energy differences are denoted by δ2 (with dx2-y2 raising by 1/2 δ2 and dz2 lowering by 1/2 δ2). Complexes with the following electron configurations are likely to undergo z-out distortion:

High Spin d4, High Spin d6, Low Spin d7, d9

Z-in Distortion
Complexes with z-in distortion are those whose ground state energy is lowered by having occupied z-oriented orbitals lower in energy. Once again, stabilizations and destabilizations due to the distortions are symmetric (seen in figure 4); however, this time, dxy are lowered from t2g* energy levels by 2/3 δ1 and dxz/dyz are each raised by 1/3 δ1, while dx2-y2 are lowered from eg* energy level by 1/2 δ2 and dz2 is raised by 1/2 δ2.

No Distortion
There are some complexes that do not undergo Jahn-Teller distortion; these are complexes whose overall energy will not be altered by any change in individual orbital energy. These complexes have the following d-orbital configurations:

High Spin d3, Low Spin d3, High Spin d5, Low Spin d6, High Spin d8, Low Spin d8, High Spin d10, Low Spin d10