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Jahn-Teller Effect

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Figure 1: Geometric representation of octahedral complexes and their distortions (caused by Jahn-Teller effect). From left to right: z-out distorted octahedron, ground state octahedron, z-in distorted octahedron.

The Jahn-Teller Effect, governed by the Jahn-Teller Theorem, is a phenomenon in which non-linear molecules with electronic degeneracy undergo symmetric geometric distortion along one of its vibrational axes in order to stabilize the complex.[1][2] 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.[1] The phenomenon exclusively affects systems with orbital 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.[3]

Octahedral Metal-Ligand Complexes

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Figure 2: The energy levels of eg* and t2g* orbitals of octahedral complexes, alongside their z-in and z-out distorted counterparts. These distortions are caused by the Jahn-Teller Effect. From left to right: z-in distorted octahedral energy levels, ground state octahedral energy levels, z-out distorted octahedral energy levels.

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.[2]

Z-out Distortion

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Figure 3: The energy levels of d-orbitals in octahedral complexes that have undergone z-out Jahn-Teller 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).[2] Complexes with the following electron configurations are likely to undergo z-out distortion: [2]

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

Z-in Distortion

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Figure 4: Energy levels of the d-orbitals in octahedral complex that has undergone z-in Jahn-Teller 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.[2]

No Distortion

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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:[4]

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

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