Crystal Field Theory

Crystal Field Theory is a model that describes the non-degeneracies of electron orbital states, usually d or f orbitals, due to static electric field produced by a surrounding charge distribution.

Octahedral Crystal Field Diagram

Assuming the ligands are acting as negative point charges around the central metal ion, as the ligands and the d_x²-y² and d_z² orbitals lie on the same axes, there is a large electronic repulsion. Thus, these orbitals will form the doubly degenerate high energy orbitals. For the d_xy, d_yz, and d_xz orbitals, since they bisect the negative charges, there is less repulsion between the ligands and the orbitals. Therefore, these orbitals will form the triply degenerate low energy set of orbitals.

Tetrahedral Crystal Field Diagram

Assuming the ligands are acting as negative point charges around the central metal ion, for the d_xy, d_yz, and d_xz orbitals, they will experience a stronger electronic repulsion due to closer proximity with the ligands. Thus, they will form the triply degenerate high energy set of orbitals. As the ligands and the d_x²-y² and d_z² orbitals are less close to each other, they will experience a weaker electronic repulsion and thus will form the doubly degenerate low energy set of orbitals.