Field Stabilization Energies

Electronic Configurations and Crystal Field Stabilization Energies for Metal Ions in Octahedral Fields 

What happens when we extend these arguments to systems containing degenerate energy levels such as those produced in a metal by an octahedral crystal field Table 41 shows the possible electronic configurations that result for varying numbers of delectrons. Note that electrons are removed from a transition metal in the order ns electrons first, then n — l)delectrons. It follows, for example, that, whereas the electronic configuration of titanium is [Ar] V 3d, that of Ti is [Ar]3 / Ti, then, is called a d case.) 

For the d case, the CFSEs are different for the high- and low-spin cases. For the low-spin case, there are now four electrons in the 2 set, but two of them must be paired. In the unsplit state, no pairing is necessary. Accordingly, the CFSE is 4( A ) minus i the pairing energy that is, since it costs energy to pair two of the electrons. 

P must be subtracted from the stabilization energy that otherwise results from four electrons occupying the 2 set. For the high-spin case, three electrons are fA lower in energy but one is A higher. Therefore, the CFSE is 3( A ) — 1( A ), or just A . Having now calculated these CFSEs, can we decide which configuration is more stable  

As in the nondegenerate example previously described, the relative stability of the two cases comes down to the difference between A and P. To see this more clearly, the expressions for the CFSEs in each case are recast as follows  

Nickel acetate tetrahydrate forms coordination complexes with poly(4-vinylpyri-dine) (P4VP) and increases the glass-transition temperature of this amorphous polymer by 102°C when the Ni concentration is 36mol%. The complete concentration dependence of the effect of NF on P4VP s is summarized in Table 6.  

Mole Fraction Nickel Acetate Glass-Transition Temperature (°C) T —T g,complex g,P4VP (°C) 

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Many of the spinel-type compounds mentioned above do not have the normal structure in which A are in tetrahedral sites (t) and B are in octahedral sites (o) instead they adopt the inverse spinel structure in which half the B cations occupy the tetrahedral sites whilst the other half of the B cations and all the A cations are distributed on the octahedral sites, i.e. (B)t[AB]o04. The occupancy of the octahedral sites may be random or ordered. Several factors influence whether a given spinel will adopt the normal or inverse structure, including (a) the relative sizes of A and B, (b) the Madelung constants for the normal and inverse structures, (c) ligand-field stabilization energies (p. 1131) of cations on tetrahedral and octahedral sites, and (d) polarization or covalency effects. ... 

Ligand-Field Stabilization Energies 8.2.3 Contributions to the Chelate Effect - The Entropy... 

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 8-7. A comparison of high-spin octahedral and tetrahedral ligand-field stabilization energies for various d" configurations.

Table 1.3 Esti mated values of the four components of the contribution made by ligand field stabilization energy to the lattice enthalpy of KsCuFe, to the hydration enthalpy of Ni (aq), AH (Ni, g), and to the standard enthalpy change of reaction 13.

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...

Relative ligand field stabilization energies for 3d ions. Thick lines octahedral field ... 

The ligand field stabilization is expressed in the lattice energies of the halides MX2. The values obtained by the Born-Haber cycle from experimental data are plotted v.v. the d electron configuration in Fig. 9.5. The ligand field stabilization energy contribution is no more than 200 kJ mol-1, which is less than 8% of the total lattice energy. The ionic radii also show a similar dependence (Fig. 9.6 Table 6.4, p. 50). 

Table 17.4 Ligand field stabilization energies for Mn304, Fe304 and Co304. Values for high-spin complexes in all cases except for octahedral Co ...

Decide whether the following compounds should form normal or inverse spinels using the ligand field stabilization energy as the criterion ... 

Table 17.4 Ligand Field Stabilization Energies in Dq Units. ...

The graph shows what has become known as the "double-humped" appearance that reflects the fact that the ligand field stabilization energy for the aqua complexes begins at 0, increases to 12 Dq, then drops to 0 on going from d° to d5 and repeats the trend on going from d6 to d10 (see Table 17.4). 

Determine the ligand field stabilization energy for d°-d10 ions in tetrahedral complexes. Although there are no low-spin tetrahedral complexes, assume that there are. 

Another factor that affects trends in the stability constants of complexes formed by a series of metal ions is the crystal field stabilization energy. As was shown in Chapter 17, the aqua complexes for +2 ions of first-row transition metals reflect this effect by giving higher heats of hydration than would be expected on the basis of sizes and charges of the ions. Crystal field stabilization, as discussed in Section 17.4, would also lead to increased stability for complexes containing ligands other than water. It is a pervasive factor in the stability of many types of complexes. Because ligands that form tt bonds... 

The ligand field stabilization energy is only one aspect of the formation of a transition state. Because the reactions are carried out in solutions, solvation of the transition state and the entering ligand may have enough effect to assist in the formation of a particular transition state. Also, the fact that some... 

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