Question

How do 'd' orbitals split in an octahedral crystal field?

Answer 1

According to Crystal Field Theory, as a ligand approaches the metal ion, the electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges. Thus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy.

The most common type of complex is octahedral; here six ligands form an octahedron around the metal ion. In octahedral symmetry the d-orbitals split into two sets with an energy difference, where the $d_{xy}{d}_{yz}{d}_{zx}$ orbitals will be lower in energy than the $d_{z^2}{d}_{x^2-y^2}$, which will have higher energy, because the former group is farther from the ligands than the latter and therefore experience less repulsion.