Crystal Field Theory - Crystal Field Stabilization Energy

Crystal Field Stabilization Energy

The crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands. It arises due to the fact that when the d-orbitals are split in a ligand field (as described above), some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five d-orbitals are degenerate. For example, in an octahedral case, the t_2g set becomes lower in energy than the orbitals in the barycenter. As a result of this, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field relative to the barycenter by an amount known as the CFSE. Conversely, the e_g orbitals (in the octahedral case) are higher in energy than in the barycenter, so putting electrons in these reduces the amount of CFSE.

If the splitting of the d-orbitals in an octahedral field is Δ_oct, the three t_2g orbitals are stabilized relative to the barycenter by 2/₅ Δ_oct, and the e_g orbitals are destabilized by 3/₅ Δ_oct. As examples, consider the two d5 configurations shown further up the page. The low-spin (top) example has five electrons in the t_2g orbitals, so the total CFSE is 5 x 2/₅ Δ_oct = 2Δ_oct. In the high-spin (lower) example, the CFSE is (3 x 2/₅ Δ_oct) - (2 x 3/₅ Δ_oct) = 0 - in this case, the stabilization generated by the electrons in the lower orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals.

Crystal Field stabilization is applicable to transition-metal complexes of all geometries. Indeed, the reason that many d8 complexes are square-planar is the very large amount of crystal field stabilization that this geometry produces with this number of electrons.