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Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

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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. dxy, dyz and dzx) than those directed to the centres of the cube (dx2-y2 and dz2).

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

Therefore, the dxy, dyz and dzx orbitals of metal cation experience more repulsion and of higher energy than t hose of dx2 – y2 and dz2 orbitals. After splitting, the dxy. dyz and dzx destabilize (t2 set) b y a factor of 0.4 ∆t and the dx2 – y2 and dz2 orbitals (e set) are stabilized by 0.6 ∆t. The difference in energy of t2 and e set is denoted as ∆t where t stands for tetrahedral. The crystal field splitting in tetrahedral complexes is shown below.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

Since ∆t is significantly smaller than ∆o, tetrahedral complexes are high-spin. Also, since smaller amounts of energy are needed for a t2 to e transition (tetrahedral) than for an eg to t2g 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 d3, d4, d5, d6, and d7 tetrahedral complexes. Therefore, tetrahedral complexes are always high spin irrespective of strong or weak ligands.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

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 Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry
(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  Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

To these two factors, the crystal field splitting decreases I tetrahedral by a factor of 4/9 than in octahedral i.e. 

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

 

CFSE in Tetrahedral Complexes 

In tetrahedral CFSE = (no. of es in e orbital) × (–0.6 ∆t) + (no. of e-s in torbital) × (–0.4 ∆t)
or     CFSE = ne × (–0.6 ∆t) + nt2 × (+0.4∆t)

In terms of ∆o
CFSE = [ne × (–0.6) + nt2 × (+0.4 )] 4/9 ∆o
CFSE = [–0.27∆o × ne + 0.18∆o × nt2]

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

The CFSE values for various configurations of tetrahedral complexes are given in the following table.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - ChemistrySplitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - ChemistrySplitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

Square Planar Complexes 

A square planar arrangement of ligands can be formally derived from an octahedral array by removal of two trans ligands.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - ChemistrySplitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry  Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

 

If we remove the ligands lying along the z axis, then the dz2 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:

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry    Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

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 dxy and dx2 – y2 orbitals.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - ChemistrySplitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

Thus, [NiCl4]2– is paramagnetic while [Ni(CN)4]2– is diamagnetic. Alt hough [NiCl4]2– is tetrahedral and paramagnetic, [PdCl4]2– and [PtCl4]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.

Splitting Of D Orbital Energies In Fields Of Other Symmetry - Coordination Chemistry Notes | Study Inorganic Chemistry - Chemistry

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