User:Arabi.seshappan/sandbox

Jahn-Teller Effect

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. 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 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.

Octahedral Metal-Ligand Complexes

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 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

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 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 δ₁ (with d_xy raising by 2/3 δ₁ and d_xz/d_yz lowering by 1/3 δ₁), and e_g* energy differences are denoted by δ₂ (with d_x²_-y² raising by 1/2 δ₂ and d_z² 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

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, d_xy are lowered from t_2g* energy levels by 2/3 δ₁ and d_xz/d_yz are each raised by 1/3 δ₁, while d_x²_-y² are lowered from e_g* energy level by 1/2 δ₂ and d_z² 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