LFSE

Field Stabilization Energies, or LFSE s. The variation in LFSE across the transition-metal series is shown graphically in Fig. 8-6. It is no accident, of course, that the plots intercept the abscissa for d, d and ions, for that is how the LFSE is defined. Ions with all other d configurations are more stable than the d, d or d ions, at least so far as this one aspect is concerned. For the high-spin cases, we note a characteristic double-hump trace and note that we expect particular stability conferred upon d and d octahedral ions. For the low-spin series, we observe a particularly stable arrangement for ions. More will be said about these systems in the next chapter. 

Figure 8-6. Comparison of LFSE terms for high- and low-spin d" configurations in octahedral ligand fields.

LFSE s for tetrahedral species are computed in a similar manner. They are compared with the results for octahedral systems in Fig. 8-7. No illustration of LFSE s for low-spin tetrahedral ions is included here because, as noted in Chapter 5, the much smaller values of Aet relative to oct ensures that pairing energies P always outweigh the ligand-field terms in practice. 

Figure 8-12. Contributions to heats of hydration A = B = bond weakening due to steric activity of configuration C = LFSE as multiples of Dq D = LFSE, allowing for variation in Dq E = exchange energy F = A + B + D + E.

The successful rationalization of these transition-metal inverse spinel structures in terms of the relative LFSE s of tetrahedral and octahedral sites is another attractive vindication of ligand-field theory as applied to structure and thermodynamic properties. Once again, however, we must be very careful not to extrapolate this success. Thus, we have a clear prediction that LSFE contributions favour tetrahedral over octahedral coordination, except for d" with n = 0, 5 or 10. We do not expect to rationalize the relative paucity of tetrahedral nickel(ii) species relative to octahedral ones on this basis, however. Many factors contribute to this, the most obvious and important one being the greater stabilization engendered by the formation of six bonds in octahedral species relative to only four bonds in tetrahedral ones. Compared with that, the differences in LSFE s is small beer. Why , one asks, was our rationalization of spinel structures so successful when we neglected to include consideration of the bond count The answer is that cancellations within the extended lattice of the spinels tend to diminish the importance of this term. 

Figure 8-16. Correlation of ionic radius and LFSE with log values for divalent transition-metal complexes of 1,2-diaminoethane.

However, consideration in terms of the ionic radius or the LFSE shows that both factors predict that the maximum stabilities will be associated with nickel(ii) complexes, as opposed to the observed maxima at copper(ii). Can we give a satisfactory explanation for this The data presented above involve Ki values and if we consider the case of 1,2-diaminoethane, these refer to the process in Eq. (8.13). 

The data for the 1,2-diaminoethane complexes now parallels the trends in ionic radius and LFSE rather closely, except for the iron case, to which we return shortly. What is happening Copper(ii) ions possess a configuration, and you will recall that we expect such a configuration to exhibit a Jahn-Teller distortion - the six metal-ligand bonds in octahedral copper(ii) complexes are not all of equal strength. The typical pattern of Jahn-Teller distortions observed in copper(ii) complexes involves the formation of four short and two long metal-ligand bonds. 

Our discussion of the Irving-Williams series illustrates, as ever, an important generalization in transition-metal chemistry in many cases there is no single, simple principle which may be invoked to rationalize a given series of observations. Whilst LFSE effects are very important, they are but one of several factors controlling structure and thermodynamics. 

In order to compare the structural options for transition metal compounds and to estimate which of them are most favorable energetically, the ligand field stabilization energy (LFSE) is a useful parameter. This is defined as the difference between the repulsion energy of the bonding electrons toward the d electrons as compared to a notional repulsion energy that would exist if the d electron distribution were spherical. 

Table 9.1 Ligand field stabilization energies (LFSE) for octahedral and tetrahedral ligand distributions...

Labile species are usually main group metal ions with the exception of Cr2+ and Cu2+, whose lability can be ascribed to Jahn-Teller effects. Transition metals of classes II and III are species with small ligand field stabilization energies, whereas the inert species have high ligand field stabilization energies (LFSE). Examples include Cr3+ (3d3) and Co3+ (3d6). Jahn-Teller effects and LFSE are discussed in Section 1.6. Table 1.9 reports rate constant values for some aqueous solvent exchange reactions.8... 

The sum of the 4-electron contributions to LFSE can be calculated with the formula shown in equation 1.24 for octahedral complexes ... 

Using LFT, the change in the ligand-field stabilization energy (LFSE) for the charge disproportionation reaction (eq I) can be estimated for Mn and Co as shown in Figure 7. 

Consistent with the proposed importance of Mn valence and LFSE, low fixed valence cations (e.g., AF+, Mg +, Li+) and electronegative multivalent... 

While the piecewise linear regions and energy maximum around +4 valence of Figures 9—13 are consistent with ligand-field effects, it is important to bear in mind that LFSE cannot by itself predict the energy difference between octahedral and tetrahedral Mn. 

---