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Splitting of d Orbital Energies in Fields of Other Symmetry
Tetrahedral Complexes: In tetrahedral complexes, none of the ligands approach directly any of the d orbitals. However, the ligands come closer to t he orbitals directed to edges of the cube (i.e. d_{xy}, d_{yz} and d_{zx}) than those directed to the centres of the cube (dx^{2}y^{2} and d_{z}^{2}).
Therefore, the d_{xy}, d_{yz} and d_{zx} orbitals of metal cation experience more repulsion and of higher energy than t hose of dx^{2} – y^{2} and d_{z}^{2} orbitals. After splitting, the d_{xy}. d_{yz} and d_{zx} destabilize (t_{2} set) b y a factor of 0.4 ∆t and the d_{x2 – y2} and d_{z}^{2} orbitals (e set) are stabilized by 0.6 ∆_{t}. The difference in energy of t_{2} and e set is denoted as ∆t where t stands for tetrahedral. The crystal field splitting in tetrahedral complexes is shown below.
Since ∆_{t} is significantly smaller than ∆_{o}, tetrahedral complexes are highspin. Also, since smaller amounts of energy are needed for a t_{2} to e transition (tetrahedral) than for an eg to t_{2g} transition (octahedral), corresponding octahedral and tetrahedral complexes often have different colours.
Tetrahedral complexes are always high spin because:
(a) ∆t = 4/9 ∆_{0} i.e. ∆t is much smaller than ∆_{0}.
(b) ∆t is alwa ys much smaller than the pairing energy.
Due to these reasons, no pairing occurs in d^{3}, d^{4}, d^{5}, d^{6}, and d^{7} tetrahedral complexes. Therefore, tetrahedral complexes are always high spin irrespective of strong or weak ligands.
The crystal field splitting in tetrahedral complexes is smaller than that in octahedral complexes. It is observed that
∆t = 4/9 ∆_{0}
(a) In octahedral there are six ligands whereas in tetrahedral low ligands come to interact with metal ions. Hence the repulsion decreases by a factor of
(b) In octahedral, all the six ligands come along the axes while in tetrahedral they come between the axes. Therefore, again repulsion is decreases by a factor of
To these two factors, the crystal field splitting decreases I tetrahedral by a factor of 4/9 than in octahedral i.e.
CFSE in Tetrahedral Complexes
In tetrahedral CFSE = (no. of e^{–}s in e orbital) × (–0.6 ∆_{t}) + (no. of e^{}s in t_{2 }orbital) × (–0.4 ∆_{t})
or CFSE = ne × (–0.6 ∆_{t}) + nt_{2} × (+0.4∆_{t})
In terms of ∆_{o}
CFSE = [ne × (–0.6) + nt_{2} × (+0.4 )] 4/9 ∆_{o}
CFSE = [–0.27∆_{o} × ne + 0.18∆_{o} × nt_{2}]
The CFSE values for various configurations of tetrahedral complexes are given in the following table.
Square Planar Complexes
A square planar arrangement of ligands can be formally derived from an octahedral array by removal of two trans ligands.
If we remove the ligands lying along the z axis, then the d_{z}^{2} orbital is greatly stabilized; the energies of the dyz and dxz orbitals are also lowered, although to a smaller extent. The resultant ordering of the metal d orbitals is shown below:
The fact that square planar d8 complexes such as [Ni(CN)_{4}]^{2–} are diamagnetic is a consequence of the relatively large energy difference between the d_{xy }and d_{x2 – y2} orbitals.
Thus, [NiCl_{4}]^{2–} is paramagnetic while [Ni(CN)_{4}]^{2–} is diamagnetic. Alt hough [NiCl_{4}]^{2–} is tetrahedral and paramagnetic, [PdCl_{4}]^{2–} and [PtCl_{4}]^{2–} are square planar and diamagnetic. This difference is a consequence of the larger crystal field splitting observed for second and third row metal ions compared with their first row congener; Pd(II) and Pt(II) complexes are invariably square planar.
Other Crystal Fields
Crystal field splittings for some common geometries with the relative splittings of the d orbitals with respect to ∆o is given below. But this comparison is only valid for MLx type complexes containing like ligands, and so only applies to simple complexes.
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