Jahn-Teller Distortion: Z-in and Z-out

The Jahn-Teller theorem also called J.T. distortion states that any non-linear molecule or ion in an electronically degenerate ground state will undergo a geometric distortion to remove that degeneracy. In simpler terms, if a molecule has orbitals with equal energy levels that are unevenly filled with electrons, it will become unstable. In order to gain stability, the molecule distorts its shape, which lowers its symmetry and also lowers its overall energy.

The J.T. effect is commonly observed in octahedral transition metal complexes where the distortion occurs as a change in the bond lengths between the central metal ion and the surrounding ligands.

The distortion results in either an elongation (lengthening) or a compression (shortening) of the bonds along one or more axes of the molecule. For example, in an octahedral complex, the axial bonds might become longer than the equatorial bonds (elongation or z-out), or vice versa (compression or x-in). The resulting complex is thus said to be tetragonally distorted.

The J.T. theorem does not predict which type of distortion will take place except the center of symmetry will remain.
Complexes having measurable bond-length distances that can confirm the presence of J.T. distortion are examples of static J.T. distortion.
For example, in CrF₂, four Cr-F bonds are at 200 Å while two Cu-F bonds are at 234 Å.
Complexes where distortion cannot be detected at room temperature crystal structures, but other evidences show J.T. distortion are examples of dynamic J.T. distortion.
For example, The complexes of the type M₂PbCu(NO₂)₆ show dynamic Jahn-Teller distortion.
where, M = K, Rb, Cs, Tl

CSIR NET/JRF December 2013

Compounds of K₂Ba[Cu(NO₂)₆] (A) and Cs₂Ba[Cu(NO₂)₆] (B), exhibit tetragonal elongation and tetragonal compression respectively. The unpaired electrons in A and B found respectively, in orbitals

A. dz² and dx²-y²
B. dx²-y² and dz²
C. dz² and dz²
D. dx²-y² and dx²-y²

Solution:
For the compound to exhibit tetragonal elongation, the axial bonds should be lengthened. This happens when the dz² orbital is higher in energy, and the dx²-y² orbital contains the unpaired electron.
For the compound to exhibit tetragonal compression, the axial bonds should be shortened. This happens when the dx²-y² orbital is higher in energy, and the dz² orbital contains the unpaired electron.

The J.T. effect is closely related to the electronic configuration of the d-orbitals in transition metals. When the e_g orbitals (dz² and dx²-y²) are unevenly occupied, a strong J.T. distortion occurs. Unevenly occupied t_2g orbitals can also cause the J.T. effect but is very weak.

Expected J.T. Distortion in octahedral complexes
Configuration	Ground State	J.T. Distortion
d1	2T2g	Yes
d2	3T1g	Yes
d3	4A2g	No
d4	5Eg High Spin 3T1g Low Spin	Yes Yes
d5	6A1g High Spin 2T2g Low Spin	No Yes
d6	5T2g High Spin 1A1g Low Spin	Yes No
d7	4T1g High Spin 2Eg Low Spin	Yes Yes
d8	3A2g	No
d9	2Eg	Yes

GATE 2006

The set of ions expected to show Jahn-Teller distortion in their complexes is

A. Ti(III), Cu(II), High spin Fe(III)
B. Cu(I), Ni(II), High spin Fe(III)
C. Cu(II), Low spin Fe(III), Ti(III)
D. Low-spin Fe(III), Mn(II), Cu(I)

Solution:
Jahn-Teller distortion occurs when the degenerate eg orbitals are uneven occupied.
The correct option is Cu(II), Low spin Fe(III), Ti(III)

Copper(II) in [Cu(H₂O)₆]²⁺ has a d⁹ configuration, which leads to an uneven occupation of the eg orbitals. This results in a distortion of the octahedral geometry, generally an elongation of the axial Cu-O bonds.

Chelate complexes are stable due to the chelate effect but the Cu(II) complex, [Cu(en)₃]²⁺ is unstable compared to the [Cu(en)₂(H₂O)]²⁺ due to J.T. distortion. The distortion causes strain into 'en' molecule attached along z-axis.

Z-out Jahn-Teller Distortion: In this case, the energies of d-orbitals with z factor ( i.e., dz², dxz, dyz ) are lowered since the bonds along the z-axis are elongated. This is the most preferred distortion and occurs in most of the cases, especially when the degeneracy occurs in eg level.
For example, the octahedral d², d⁴ (high spin), d⁷ (low spin), d⁸ (low spin) & d⁹ configurations show the z-out distortion. Generally, it is not possible to predict the type of distortion that occurs when the degeneracy occurs in e_g level because the magnitude of CFSE is same. However it is observed that z-out distortion is more preferred.

Z-in Jahn-Teller distortion: In this case, the energies of orbitals with z factor are increased since the bonds along the z-axis are shortened. This type of distortion is observed in case of octahedral d¹ configuration. The only electron will now occupy the dxy orbital with lower energy.
For example, the octahedral d¹ configurations like Ti(III) in [Ti(H₂O)₆]³⁺ can show z-in distortion. In this case, the z-out distortion do not remove the degeneracy since even after distortion there are still two degenerate orbitals i.e., dxz and dyz available for the electron to occupy.

CSIR NET/JRF June 2014

Identify the correct statement about [Ni(H₂O)₆]²⁺ and [Cu(H₂O)₆]²⁺

A. All Ni-O and Cu-O bond lengths of individual species are equal
B. Ni-O (equatorial) and Cu-O (equatorial)
C. All Ni-O bond lengths are equal whereas Cu-O (equatorial) bonds are shorter than Cu-O (axial) bonds
D. All Cu-O bond lengths are equal whereas Ni-O (equatorial) bonds are shorter than Ni-O (axial) bonds

Solution:
[Ni(H₂O)₆]²⁺:
Ni²⁺ has a d⁸ electronic configuration in which t_2g orbitals are fully occupied, and the e_g orbitals have two electrons. This results in an even filling of the eg orbitals.
Therefore, [Ni(H₂O)₆]²⁺ does not exhibit a significant Jahn-Teller distortion. Therefore, all Ni-O bond lengths are essentially equal.

[Cu(H₂O)₆]²⁺:
Cu²⁺ has a d⁹ electronic configuration in which e_g orbitals are uneven occupied resulting in a strong Jahn-Teller distortion.
Due to the distortion, the axial Cu-O bonds are elongated. Therefore, the equatorial Cu-O bonds are shorter than the axial Cu-O bonds.

Therefore, the correct statement is:
All Ni-O bond lengths are equal whereas Cu-O (equatorial) bonds are shorter than Cu-O (axial) bonds