# 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 e$_g$ and t$_{2g}$ 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 e$_g$* energy levels. These orbitals are antibonding; therefore, when the e$_g$ 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); t$_{2g}$* orbitals are offset by an energy value denoted δ$_1$ (with d$_{xy}$ raising by 2/3 δ$_1$ and d$_{xz}$/d$_{yz}$ lowering by 1/3 δ$_1$), and e$_g$* energy differences are denoted by δ$_2$ (with d$_x$$^2$$_{-y}$$^2$ raising by 1/2 δ$_2$ and d$_z$$^2$ lowering by 1/2 δ$_{2)}$. Complexes with the following electron configurations are likely to undergo z-out distortion:
High Spin d$^4$, High Spin d$^6$, Low Spin d$^7$, d$^9$

### 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, d$_{xy}$ are lowered from t$_{2g}$* energy levels by 2/3 δ$_1$ and d$_{xz}$/d$_{yz}$ are each raised by 1/3 δ$_1$, while d$_x$$^2$$_{-y}$$^2$ are lowered from e$_g$* energy level by 1/2 δ$_2$ and d$_z$$^2$ is raised by 1/2 δ$^2$.

### 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 d$^3$, Low Spin d$^3$, High Spin d$^5$, Low Spin d$^6$, High Spin d$^8$, Low Spin d$^8$, High Spin d$^{10}$, Low Spin d$^{10}$Template:Dashboard.wikiedu.org sandbox

## References

* 1 2 Pfennig, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: Wiley. pp. 304–305. ISBN 9781118859100.
* 1 2 3 4 5 Pfennig, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: Wiley. pp. 564–565. ISBN 9781118859100.
* ↑ "The Jahn-Teller Theorem". The Chemistry Department, The University of the West Indies at Mona, Jamaica. Retrieved 2016-06-15.
* ↑ "Coordination Chemistry II: Jahn-Teller, Square Planar Complexes, Orbital Overlap Method, and Electron Counting" (PDF). The Chemistry Department, UC Irvine. Retrieved 2016-06-15.