Ligand-field stabilization energies

The second- and third-row d8 ions Pd2+ and Pt2+ have considerably larger splitting of the d states than does Ni2+. Consequently, the splitting is so large for these ions that only square planar complexes result, regardless of where the ligands fall in the spectrochemical series, and there are no known tetrahedral complexes of Pd2+ and Pt2+. 

Another manifestation of ligand field stabilization energy can be seen from the heats of hydration of the transition metal ions. For example, the hydration of a gaseous ion results in the formation of an aqua complex as represented by the equation 

The aqua complexes of these +2 transition metal ions are all high-spin (especially so for the +2 ions where A0 is small), so it is easy to see that for a d1 case there is an extra heat of 4Dq released. For a d2 ion, the additional heat is 8Dq, and so on, as can be seen from the values shown in Table 19.5. For a high-spin complex of a d5 ion (such as Mn2+), the LFSE 

Enthalpies of hydration for some +2 metal ions of the first transition series. 

It should be emphasized that although in principle one could determine Dq for aqua complexes in this way, it is highly impractical. First, hydration enthalpies of this magnitude are not known to high accuracy. Second, there is not a ready source of +2 gaseous metal ions, and it would also involve determining small differences between large numbers, the heats of hydration of metal ions. As a result, this is not a practical type of measurement. 

Diagram of the relative energies of electrons in d orbitals for different geometric anangements. 

The centers of gravity (mean values of the energy levels) for all term sequences were positioned on the dotted line 

Splitting of the energy levels. Both an octahedral complex (two electrons in orbitals) and a tetrahedral complex (four electrons in orbitals) are less favorable in this case. 

When ligands approach a central atom or ion, the following energetic contributions become effective  

Ligand field theory mainly considers the last contribution. For this contribution die geometric distribution of the ligands is irrelevant as long as the electrons of the central atom have a spherical distribution the repulsion energy is always the same in this case. All half and fully occupied electron shells of an atom are spherical, namely d high-spin and (and naturally t/°). This is not so for other d electron configurations. 

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. 

Find the LFSE for a d ion for both high-spin and low-spin cases. 

FIGURE 10-6 Splitting of Orbital Energies in a Ligand Field. 

Electrons t2g LFSE (A,) Energy Energy — Weak Field 

Note In addition to the LFSE, each pair formed has a positive Coulombic energy,, and each set of two electrons with the same spin has a negative exchange energy, 0,. When A If for or or when + ri(, for d or d, the strong-field arrangement (low spin) is favored. 

The most common example of LFSE in thermodynamic data appears in the exothermic enthalpy of hydration of bivalent ions of the first transition series, usually assumed to have six waters of hydration  

Experimental information on enthalpies of hydration has been measured for related reactions of the formi  

Number of cl Electrons Weak Field Arrangement LFSE (X) Coulombic Energy Exchange Energy  

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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... 

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.

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. 

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... 

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... 

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