How do ‘d’ orbitals split in an octahedral crystal field?

In octahedral crystal field theory, when ligands approach a central metal ion, they interact with the metal's d orbitals. This interaction leads to a splitting of the d orbitals into different energy levels, resulting in what is known as "crystal field splitting."

In an octahedral crystal field, the d orbitals of the central metal ion are split into two sets of energy levels: three lower-energy orbitals and two higher-energy orbitals. This splitting pattern is a result of the electrostatic interaction between the negatively charged ligands and the positively charged metal ion.

Here's how the d orbitals split in an octahedral crystal field:

Three lower-energy orbitals (t2g orbitals): These orbitals experience less repulsion from the surrounding ligands and, as a result, have lower energy. The three d orbitals that fall into this group are dxy, dxz, and dyz. They remain closer to their original energy levels.

Two higher-energy orbitals (eg orbitals): These orbitals experience greater repulsion from the ligands and, therefore, have higher energy. The two d orbitals that fall into this group are dx²-y² and dz². They move to higher energy levels due to the interaction with the ligands.

This splitting of the d orbitals into t2g and eg sets results in an energy difference between them, which can be observed in various spectroscopic techniques, such as UV-Vis spectroscopy and magnetic susceptibility measurements. The energy separation between the t2g and eg sets is often referred to as Δo (delta-o), which represents the crystal field splitting parameter in octahedral crystal field theory.

The crystal field splitting in octahedral coordination environments can lead to different electronic configurations and magnetic properties, depending on the occupancy of the d orbitals, making it an important concept in coordination chemistry and the understanding of transition metal complexes.