Crystal Field Stabilization Energies

Recall that stable molecules contain more electrons in the lower-energy (bonding) molecular orbitals in a molecular orbital diagram than in the higher-energy (antibonding) molecular orbitals. If the lower-energy set of d orbitals (the t_2g orbitals) is selectively populated by electrons, then the stability of the complex increases. For example, the single d electron in a d¹ complex such as [Ti(H₂O)₆]³⁺ is located in one of the t_2g orbitals. Consequently, this complex will be more stable than expected on purely electrostatic grounds by 0.4Δ_o. The additional stabilization of a metal complex by selective population of the lower-energy d orbitals is called its crystal field stabilization energy (CFSE). The CFSE of a complex can be calculated by multiplying the number of electrons in t_2g orbitals by the energy of those orbitals (−0.4Δ_o), multiplying the number of electrons in e_g orbitals by the energy of those orbitals (+0.6Δ_o), and summing the two. Table 1.1 gives CFSE values for octahedral complexes with different d electron configurations. The CFSE is highest for low-spin d⁶ complexes, which accounts in part for the extraordinarily large number of Co(III) complexes known. The other low-spin configurations also have high CFSEs, as does the d³ configuration.

CFSEs are important for two reasons. First, the existence of CFSE nicely accounts for the difference between experimentally measured values for bond energies in metal complexes and values calculated based solely on electrostatic interactions. Second, CFSEs represent relatively large amounts of energy (up to several hundred kilojoules per mole), which has important chemical consequences.

Octahedral d³ and d⁸ complexes and low-spin d⁶, d⁵, d⁷, and d⁴ complexes exhibit large CFSEs.