# Introduction

In this particular article Crystal Field Splitting in Tetrahedral Complexes we are going to discuss about Crystal Field Splitting in Tetrahedral Complexes in detail with there appropriate examples.

## Crystal field splitting in tetrahedral complexes

A regular tetrahedral geometry is obtained when a metal cation or atom is placed at the centre of a cube. And four ligands occupy the alternate corners of the cube as shown in fig.

The x,y and z- axes are passed through the centres of the faces of the cube. None of the ligands approach directly any of the metal d-orbitals. Instead they all approach to some degree in between the metal d-orbitals.

### Theory

It can be seen from the fig that the three orbitals (dxy, dzy, dzx ) are far apart by 1/2 (=0.5 ) from each of the ligands. Where as the two orbitals (d*x²-y² *and d*z²)* are relatively little far apart by l√2/2 =0.71 l, where l is the length of the side of the cube. In other words we can say that the d*xy, *d*zy, *dzx orbital are half the diagonal (l√2/2) of the face of cube away.

This indicates that the ligands come closer to the orbitals directed to edges of the cube (i.e., d*xy, *d*zy and *d*zx)* than to those directed to the centers of the cube (i.e.,d*x²-y² *and d*z²). *Each of the five d-orbitals in tetrahedral field is representedin fig.

The dxy, dzy and dzx orbitals of metal cation, experience more repulsion from the ligands and are of higher energy than those of the dx²-y² and dz² orbitals. To maintain the rule of centre of gravity, the dxy, dzy, dzx orbitals are 0.4 ∆t above the bary centre and the dx²-y² and dz² orbitals are 0.6∆t below the barycenter. The g subscript is not used with t₂ and e sets because the tetrahedral complexes have no inversion centre. The difference in energy of e and t₂ sets is represented by ∆t, where t stands aor tetrahedral. The crystal field splitting in tetrahedral complexes is shown in fig.

The crystal field splitting is just reverse of the octahedral complexes.

#### Difference in Crystal Field Splitting in Tetrahedral and octahedral

The crystal field splitting in tetrahedral complexes is smaller than that in octahedral complexes. Because there are two third ligands of octahedral complexes and none of the ligands approach the metal d-orbitals. For the same metals, ligand and metal- ligand distance, it is observed that ∆t = 4/9∆₀ because:

- The number of ligands are 2/3 of the octahedral complex, therefore the splitting of the d-orbitals is also two third.
- None of the ligands point directly towards any of the five d-orbitals. Therefore the splitting is reduced by roughly two third. In tetrahedral and octahedral complexes the dxy, dzy, and dzx orbitals are at 45⁰, i.e.,at equal distance from the ligands. Therefore in both the comlexxes, each ligand repels these orbitals in equal amount. In octahedral complexes, the ligands approach directly to and dz² orbitals and repel them strongly. But in tetrahedral complexes these orbitals are at √2l/2= 0.71 l as compared to that of octahedral complexes.

Therefore in tetrahedral complexes, the ligands repel these orbitals 2/3 times than that of octahedral complexes. Thus, due to this fact, splitting decreases by 2/3rd in tetrahedral complexes as compare to octahedral complexes.

Therefore, ∆t = 2/3×2/3×∆₀ or ∆t =4/9∆₀.

Tetrahedral complexes are always high spin because (1) ∆t = 4/9∆₀ i.e., ∆t is much smaller than octahedral splitting ∆₀ and (2) ∆t is always less than the pairing energy. Due to these two reasons no pairing of electrons occurs in d³, d⁴, d⁵, d⁶ and d⁷ tetrahedral complexes. Therefore the tetrahedral complexes of these configuration are always high spin whether the ligands are strong or weak.

##### Conclusion of Crystal Field Splitting in Tetrahedral Complexes

In order to read this article we have learnt many important information about crystal Field Splitting in tetrahedral complexes in most simplest manner.

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