Crystal field theory models the effect of surrounding ligand charges or dipoles on metal atomic orbitals. Directional repulsion splits the levels. Unlike molecular orbital theory, the simplest model does not explicitly construct covalent metal–ligand bonds.
Suppression of a ground state's orbital magnetic moment by the splitting and mixing of free-ion atomic orbitals in a crystal. A nondegenerate orbital state can generally be chosen real in zero field, giving zero expectation of the imaginary orbital angular momentum operator. Spin-orbit coupling to excited states still produces residual g-factor shifts and anisotropy, so quenching is not absence of every orbital response.
Separation of metal d-orbital energies by the electrostatic field of surrounding coordination ligands. An octahedral field puts the three orbitals below the two orbitals.
In the ideal tetrahedral point-charge model, the five metal d orbitals split into a lower twofold set and an upper threefold set. Relative to their weighted barycentre their energies are and , where is the separation. For occupancies , the crystal field stabilization energy is . Under weak-field high-spin filling it is , , and zero for respectively. Shorter metal–ligand distances generally increase the splitting, so orbital filling can superimpose nonmonotonic bond-length changes on an ionic-size trend. The model alone does not determine an absolute bond length.
