Ligand Field Stabilization
Yet is there any other basic evidence to support the theory that we have dwelt on so much? One of the key pillars of the theory is that there should be some inherent stabilization of compounds as a result of introducing a field of ligands around the central metal ion, expressed in terms of the so-called ligand field stabilization energy. Recall that in an octahedral field, electrons in diagonal orbitals are stabilized (by -4D) and those in axial orbitals are destabilized (by +6Dq) relative to the spherical field situation. By summing up the energy values for all d electrons in the set, we arrive at the overall stabilization or ligand field stabilization energy (LFSE), which will thus vary with n in d", as shown in Table 7.9.
Table 7.9 Ligand field stabilization energies (LFSE given in D1 = A/10) for the various d" configurations.
Configuration.
For example, for high spin d3, we have three electrons in the 12g level (3 x -4Dq) and two in the eg level (2 x +6Dq) for an overall LFSE of zero; however, for low spin d3, all five electrons lie in the f2g level (5 × -4D1) for an overall LFSE of -20Dq. The concept is simple, and for high-spin produces a pattern as shown in the inset of Figure 7.6.
There is experimental evidence that supports this trend. For example, hydration energies for M(II) ions of the first row transition metals exhibit a W-shaped pattern, as a result of crystal field stabilization superimposed on the expected periodic increase (Figure 7.6), consistent with this model. Likewise, the measured lattice energies of transition metal fluorides (MF2) display a very similar pattern. The predominance of low spin do complexes is also consistent with the model, as there is a significant difference in LFSE between spin states in favour of low spin in the model. However there are concerns with the model that have attracted criticism; for example, one might anticipate low spin d3 more often than is observed. However it is a simple and sufficient model to use at a basic level.
Figure 7.6 Predicted LFSE for high-spin d0 to d10 (inset) and variation in hydration energy for first-row M2+ transition metal ions, which mirrors this trend, superimposed on a general increase with atomic number.
