Crystal Field Theory - Octahedral Complexes

Crystal field theory describes the electronic structure of transition metal complexes based on electrostatic interactions between transition metal ions and ligand molecules. It has been used to explain certain properties of transition metal complexes such as magnetism and color.

The electrostatic interactions between the ligand molecules and the metal ion in a transition metal complex are modeled by approximating the ligands as negative point charges and calculating the net electrostatic field, or crystal field, due to these charges.

The electronic structure of the transition metal complex can then be described by examining the effect of the crystal field on the energies of the valence orbitals of the transition metal ion.

For example, when modeling the octahedral complex hexaamminecobalt(III), each amine ligand is replaced by a negative point charge, resulting in an octahedral crystal-field.

Under the influence of this field, the energies of the five d orbitals of the Co(III) ion are no longer the same.

Here, the d_x²−_y² and d_z² orbitals have higher energy than the d_xy, d_yz, and d_xz orbitals. This is attributed to the orientation of the d orbitals. The lobes of the d_x²−_y² and dz² orbitals point directly towards the ligands, accordingly, the electrons in these orbitals experience stronger repulsion from the ligand charges.

The higher energy orbitals have e_g symmetry, and are known as the e_g set of orbitals, while the lower energy orbitals have t_2g symmetry and constitute the t_2g set of orbitals. The energy difference between the two sets is known as the crystal-field splitting energy, represented by the symbol Δ_oct.

The magnitude of Δ_oct depends on the net electrostatic interaction between the metal ion and the ligand molecules. Some ligands such as carbonyl create a strong crystal field, resulting in a large value of Δ_oct. Such ligands are called strong-field ligands.

In contrast, ligands such as iodide exhibit small values of Δ_oct and are known as weak-field ligands. The ability of ligands to cause increasing values of Δ_oct is listed in the spectrochemical series.

Increase in the charge on the metal ion also increases the net electrostatic interaction within the complex, thus resulting in a higher value of Δ_oct.