JAHN-TELLER DISTORTION THEOREM
Jahn-Teller distortion describes the geometrical distortion of molecules and ions that are associated with certain electron configurations.
This effect is most often seen in octahedral complexes of the transition metals.Jahn-Teller effect states that any non-linear molecular system in orbitally degenerate electronic state would be unstable and that it would get stabilized by undergoing distortion is its geometry and thus by causing on split in its
orbitally degenerate electronic state. In octahedral complexes six ligand molecules are arranged around the central metal ion. If we assume that the axial ligands in the octahedral complexes are removed away from the central metal to such an extent that they no longer exert any influence on the central metal ion then there will be distortion in the metal complex which is known as tetragonal distortion. Its extreme case will be that the axial ligands are removed from the metal complex then the complex will be square planar.
Jahn-Teller (1937) game explanation of such distortion which is known as Jahn-Teller theorem according to this theorem:
(i) If t2g and egorbitals of central metal ion are symmetrical (i.e., there are 0,3,5,8 and 10 electrons in d-orbitals for high spin complexes and 0,3,6 and 10 electrons in d-orbitals for low spin complexes) the octahedral complexes have no distortion i.e. have regular shape.
(ii) If t2s and eg orbitals of central metal ion are asymmetrical (i.e., there are 1,2,4 or 5 electrons in d-orbitals) the octahedral complexes have slight distortion.
(iii) If the eg orbitals of an octahedral complexes are asymmetrically filled (i.e., there are 4 and 9 electrons in high spin complexes and 7,8 and 9 electrons in low spin complexes in d-orbitals) the octahedral complexes
have strong distortion. Since above three postulates (i), (ii), (iii) describe the effect of
asymmetry of the complexes hence it is also known as Jahn-Teller effect.
It should be noted that Jahn-Tellar theorem only predicts the occurrence of a distortion, it does not predict its nature or its magnitude.
Cause of Distortion
1. We know that high spin octahedral complexes of d4 ion have either t2g2, (dz2)1(dx2-y2) or t2g3 (dz2)0 (dx2-y2)1
configuration. It means either dx2-y2 or dz2
orbital is empty therefore cation-anion interaction along the Z-axis is less than that along the X-axis and Y-axis. Since in this
case along the Z-axis inter-ionic distance is larger hence the complex shows tetragonal geometry.
2. In the case of Cu(II) ion (d9) complex, such as [Cu(NH3)4]2+ the distortion is such an extent that tetragonal geometry changes into square planar geometry. This is due to the fact that t2g-orbitals are completely filled (t2g) while eg-orbitals are incomplete (eg)3 (i.e., asymmetry or distortion). Here distortion is due to the repulsion of ligands by the electrons occupying eg orbitals.
In the case of high spin octahedral complexes of Ni2+(d8) etc. There is no distortion due to symmetry of t2g and eg orbitals. [e.g., t62g and e2g i.e., (dx2-y2)1, (dz2)1]. But the low spin octahedral complexes of d8 metal
ions exhibit distortion due to asymmetry of eg
orbitals [e.g., (dx2-y2)0, (dz2)2]. In such cases distortion is so strong that the complexes have square planar geometry.
