Basics of crystal field theory for octahedral complexes

In crystal field theory each ligand is considered to be a negative point charge that interacts with the electrons in orbitals on the metal ion. The diagrams show that

in octahedral complexes the bonds to the six ligands lie along the x,y and z axes
the d-orbitals are of equivalent energy in the absence of the ligands.
three d-orbitals have lobes between the axes. Two have lobes on the axes.
the d-orbitals that lie on the axes have higher energy in the presence of the ligands.

d-orbitals on Co³⁺ have same energy if no ligands

approach of NH₃ ligands
to Co³⁺ along x,y,z-axes

d(x² – y²) d(z²)

d(xy) d(yz) d(xz)

increases energy of d-orbitals on
axes and lowers energy of the others

e_g level

t_2g leve Δ_o

The two orbital groups are referred to as t_2g and e_g. Δ_o (o for octahedral) equals the difference in energy between the t_2g and e_glevels.

It is important to appreciate that the overall energy of the d-orbitals on the metal ion is unchanged. The energies of the orbitals in the e_g level added to the energies those in the t₂_g level equals the total energy of the d-orbitals in the absence of ligands.