Introduction

In this particular article, We are going to discuss the Crystal field splitting in octahedral complexes, widely in the simplest manner possible.

Crystal field splitting in octahedral complexes

In a free metal cation, all the five d-orbitals are degenerate. In an octahedral complex, say {ML₆}n⁺. The metal cation is placed at the center of the octahedron. And the six ligands are at the six corners. These six corners are directed along the cartesian coordinates i.e., along x, y, and Z-axes.

Crystal field splitting in octahedral complexes

When all the six ligands are at the infinite distance from the metal cation. The five d-orbitals of the free metal cation will not be affected by the ligand electrostatic field and will remain degenerate. When the ligand moves towards the metal cation, there are two electrostatic forces. One is the attraction between metal cation and the ligands. And second is electrostatic repulsion between d-electrons of the metal cation. And lone pairs of electrons on ligands. Greater the force of attraction between the metal cation and the ligands, ligands will be closer to the metal cation. And hence more will be the repulsion between metal d- electrons and the lone pair of electrons.

When the ligands are closer to the metal cation, an electrostatic repulsion also exists among the ligands. These two repulsion cause to adopt the octahedral. That locate the ligands at the internuclear distance from the metal cation. And as far apart from one another as possible. The force of repulsion between metal d-electrons and the ligands electrons cause to increase in potential energy of the metal d-electrons. Remember that greater the force of repulsion, higher will be the potential energy. If all the six ligands approaching the metal cation surround it spherically symmetric. I.e., all the ligands are at equal distance from each of the d-orbitals.

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The energy of each of the five d-orbitals will raise by the same amount and all the five d-orbitals. In an actual octahedral complex, the spherically symmetric field is never obtained. Therefore all the five d-orbitals are not affected to the same extent. Since the two orbitals (dx²-y² and dz²) point directly towards the ligands. And three orbitals (dxy, dyz, and dzx) point in between the path of the approaching ligands. Therefore, the dx²-y² and dz² orbitals will be more strongly repelled than the dxy, dyz and dzx orbitals. Therefore, the energy of dx²-y² and dz² orbitals will be raised. And that of other three orbitals which lie far away from the ligands. And will be decreased relative to hypothetical energy state.

The five d-orbitals which were degenerate in the free metal cation. Hence are now split into two sets of orbitals of different energies. A higher energy level with two orbitals (dx²-y² and dz²) having the same energy. And a lower level with three equal energy orbitals (dxy, dyz, and dzx). The set of dx²-y² and dz² orbitals is referred to as the eg set. Which is doubly degenerate. And the set of dxy, dzy and dzx orbitals is referred to as t₂g set which is triply degenerate.

From diagram

Since the distance between the metal cation and the ligands has remained the same as that of the spherical field before splitting. Hence, This state of average energy is called the barycenter.

The separation of five d-orbitals of metal cation into two sets of different energies is called crystal field splitting. And The energy difference between two sets of orbitals which arise from an octahedral field. Is measured in terms of the parameters ∆₀ or 10Dq, where o in ∆₀ stands for octahedral.

Since the energy of barycentre remains constant. And The total energy decrease of the t₂g set must be equal to the total energy increase of eg set. Therefore since there are two eg orbitals. Hence They must increase by 0.6 or 6Dq and the three t₂g orbitals must decrease by 0.4∆₀ or 4Dq per electron. The decrease in energy of t₂g orbitals stabilizes the complex by 0.4 ∆₀. And the increase in energy of eg orbitals destabilizes the complex by 0.6∆₀.

The conclusion of Crystal field splitting in octahedral complexes

In this article Crystal field splitting in octahedral complexes, we have discussed the Crystal field splitting in octahedral complexes widely.

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