JAHNTELLER DISTORTION
A complex will be regular octahedron when the electronic arrangement in t_{2g} and eg orbitals is symmetric (i.e., both t_{2g} and e_{g} orbitals are electronically nondegenerate) because symmetricall y arranged electrons will repel all the six ligands equally. An electronically nondegenerate means there is onl y one possible arrangement of electrons. For example, the d^{3} configuration in octahedral symmetry is nondegenerate and symmetric. Only one arrangement is possible for three electrons.
d^{3 }configuration → (t_{2g})^{3} e^{0}, only one possible arrangement ( electronically nondegenerate)
When t_{2g} and e_{g }orbitals are asymmetrically filled (i.e., either t_{2g} or e_{g} orbitals are electronicall y degenerate) the regular octahedral geometry is not the stable but it transforms into a distorted octahedral symmetry. Electronically degenerate means the situation in which an electron can be arranged in more than one orbitals of equivalent energy. For example, in octahedral Cu ^{2+} the e_{g}^{3} configuration is electronically degenerate because it has two possible arrangements of electrons i.e.,
Electronically degenerate states for e_{g}^{3}
The eg orbitals point directly towards the ligands, therefore, when e g orbitals are electronicall y degenerate (i.e., unsymmetrically filled), some ligands repelled more than the others. Therefore, there will be significant distortion in octahedral complexes. For example, octahedral complexes of d^{9 }and highspin d4 ions are o ften distorted. On the other hand, the t_{2g} orbitals lie in between the ligands; therefore, the electronically degenerate t_{2g }orbitals cause a very small distortion.
t_{2g }(sym) + e_{g }(sym) → No distortion
t_{2g} (unsym) → Slight distortion
e_{g} (unsym) → strong distortion
cases of strong distortion
d^{4} (High spin), d^{7} (low spin), d^{9}
The various configurations which cause distortion is given in the following table.
Generally, the distortion that occurs in octahedral complexes is tetragonal distortion. A tetragonal distortion means the two trans ligands on the zaxis in an octahedral complex are moved either towards or away from the metal ion/atom. Motion of trans ligands along zaxis towards the metal atom/ion is called tetragonal compression (zin distortion) and motion of these ligands away from the metal ion is called the tetragonal elongation (zout distortion).
The distortion causes by a condition called JahnTeller Theorem which states that, “Any nonlinear molecular system in a degenerate electronic state will be unstable and will undergo distortion to form a system of lower symmetry and lower energy, thereby removing the degeneracy.” When the t_{2g} set is unequall y occupied then t he distortion occur is very much smaller since t he orbitals are not pointing directly at the ligands. On the other hand when e_{g} orbitals are unsymmetrically filled, the distortion is very strong and zin or zout complexes are formed.
zOut Distortion (Tetragonal Elongation)
In a regular octahedral field, the eg orbitals (i.e., d_{x2 – y2} and d_{z}^{2}) are degenerate. However, if the eg orbitals are unsymmetrically filled i.e. either d_{x2 – y2} or dz2 contains one more electron than the other, then the eg orbitals are split. If the d_{z}^{2} orbitals contain one electron more than the d_{x2 – y2} orbitals then the ligands approaching along zaxis will be repelled more than the ligands approaching x and y axes. This is due to that electron density in d_{z}^{2} orbital is greater than that of d_{x2 – y2} orbital.
(d_{z}^{2})^{1} (d_{x2 – y2} )0 or (d_{z}^{2})^{2} (d_{x2 – y2} )^{1}
Consequently, the ligands along z axis are moved away from the metal cation relative to those on x and y axes which move towards the metal cation. Therefore, the distance between metal cation and the ligands on zaxis becomes larger and the distances between metal cation and ligands on x and y axes becomes shorter. Thus the complex undergoes a tetragonal elongation (zout distortion).
The ligands along z axis moved away from the metal cation relative to those on x and y axes which move towards the metal ion. Therefore, the d_{z}^{2} orbital will experience a decrease in repulsion from the ligands and hence energy of d_{z}^{2} orbital will decrease i.e. d_{z}^{2} orbital is stabilised. On the other hand, the d_{x2 – y2 }experiences a greater repulsion from the ligands and hence the d_{x2 – y2} will be destabilized. In a similar way, t he energies of orbitals having z component (i.e. d_{yz} and d_{zx}) will decrease and that of d_{xy }will increase in energy and a part of degenerac y of t_{2g} orbitals is removed. Therefore, the overall result is t hat both eg and t_{2g }orbitals split in two levels. Crystal field splitting in tetragonal elongation (zout) is shown below:
Crystal field splitting in tetragonal elongation (zout distortion)
zIn Distortion (Tetragonal Compression)
If the d_{x2 – y2} orbital contains one electron more than the d_{z}^{2} orbitals then the ligands approaching along x and y axes will be repelled more than the ligands approaching along zaxis. This is due to that the electron densit y in d_{x2 – y2} orbital is greater than that of d_{z}^{2} orbital.
(d_{z}^{2})^{0} (d_{x2 – y2})^{1} or (d_{z}^{2})^{1} (d_{x2 – y2})^{2}
Therefore the ligands along x and y axes are moved away from the metal cation relative to those on zaxis which move towards the metal cation. The distance between the metal cation and the ligands is shorter on zaxis because ligandligand repulsion is decreased as ligands move away from the metal cation on x and y axes. Therefore, the distance between metal cation and x and y axes becomes larger & become shorter on zaxis. Therefore the complex undergoes tetragonal compression (zin distortion).
Since the ligands on x and y axes are at longer distance from metal cation than that of ligands on zaxis, therefore the d_{x2 – y2} orbital will decrease in repulsion from the ligands and therefore the energy of d_{x2 – y2}will decrease. The d_{z}^{2 }will experience an increase in repulsion from the ligands resulting in an increase in energy. Likewise, the energies of the orbitals having x and y component (d_{xy}) orbital will decrease and that of having z component (i.e. d_{yz} and d_{zx}) will increase. The crystal field splitting in tetragonal compression (zin distortion) is shown below:
Since in tetragonal compression, four ligands on x and y axes repel the high density of electrons in d_{x2 – y2 }orbital whereas in tetragonal elongation only two ligands on z axis repel the high density of electrons in d_{z}^{2} orbitals. Therefore, there is more repulsion in tetragonal compression than that of tetragonal elongation. Therefore, tetragonal elongation is more stable than the tetragonal compression and hence tetragonal elongation is known as tetragonal distortion.
Examples of JohnTeller Distortion: The significant Johnteller distortions are generally observed in high spin d^{4} (t_{2g}^{3} e_{g}^{1}), low spin d^{7} (t_{2g}^{6} e_{g}^{1}) and d^{9} (t_{2g}^{6} e_{g}^{3}) configurations in these configurations eg orbitals are electronically degenerate and points towards the ligands directly. Compounds which undergo strong JahnTeller distortion in octahedral field are CrF_{2} and MnF_{3} (d^{4} t_{2g}^{3 }e_{g}^{1}), NaNiO_{2} (low spin, d^{7}, t_{2g}^{6} e_{g}^{1}), CuF_{2}, CuCl_{2}, CuBr_{2} (d^{9}, t_{2g}^{6} e_{g}^{3}) etc. In all these complexes the eg orbitals are unsymmetrically filled and therefore there are two longer bonds on zaxis and four shorter bonds on x and y axes.
The JahnTeller theorem does not predict which type of distortion will take place. There are two types of Jahn Teller distortions:
49 videos71 docs16 tests
