Tetrahedral crystal field

Although Fc304 is an inverse spinel it will be recalled that Mn304 (pp. 1048-9) is normal. This contrast can be explained on the basis of crystal field stabilization. Manganese(II) and Fe" are both d ions and, when high-spin, have zero CFSE whether octahedral or tetrahedral. On the other hand, Mn" is a d and Fe" a d ion, both of which have greater CFSEs in the octahedral rather than the tetrahedral case. The preference of Mn" for the octahedral sites therefore favours the spinel structure, whereas the preference of Fe" for these octahedral sites favours the inverse structure. 

Tetrahedral complexes arc also common, being formed more readily with cobali(II) than with the cation of any other truly transitional element (i.e. excluding Zn ). This is consistent with the CFSEs of the two stereochemistries (Table 26.6). Quantitative comparisons between the values given for CFSE(oct) and CFSE(let) are not possible because of course tbc crystal field splittings, Ao and A, differ. Nor is the CFSE by any means the most important factor in determining the stability of a complex. Nevertheless, where other factors are comparable, it can have a decisive effect and it is apparent that no configuration is more favourable than d to the adoption of a tetrahedral as opposed to... 

An S term, like an s orbital, is non-degenerate. Therefore, while the effect of a crystal field (of any symmetry) will be to shift its energy, there can be no question of its splitting. The ground term for the configuration is S. In an octahedral crystal field, this is relabelled Aig, in tetrahedral symmetry, lacking a centre of inversion, it is labelled M]. 

The three p orbitals are directed along the three cartesian axes and so, in an octahedral crystal field, suffer equal repulsion from point charges sited on those axes. The energies of the three p orbitals, therefore, remain degenerate. Similarly, a free-ion P term remains unsplit in octahedral or tetrahedral crystal fields and is labelled Tig or Ti respectively. 

The crystal field energy level diagram for tetrahedral complexes. The d orbitals are split into two sets, with three orbitals destabilized relative to the two others. 

C20-0014. Draw crystal field splitting diagrams that show the electron configurations for the following complex ions (a) [Cr (H2 (b) [IrCle] (c) [V (en)3] and (d) [NiCl4] (tetrahedral). 

A quantitative consideration on the origin of the EFG should be based on reliable results from molecular orbital or DPT calculations, as pointed out in detail in Chap. 5. For a qualitative discussion, however, it will suffice to use the easy-to-handle one-electron approximation of the crystal field model. In this framework, it is easy to realize that in nickel(II) complexes of Oh and symmetry and in tetragonally distorted octahedral nickel(II) complexes, no valence electron contribution to the EFG should be expected (cf. Fig. 7.7 and Table 4.2). A temperature-dependent valence electron contribution is to be expected in distorted tetrahedral nickel(n) complexes for tetragonal distortion, e.g., Fzz = (4/7)e(r )3 for com-... 

High-valent iron can occur in a wide variety of electronic configurations. Figure 8.25 (a-c, e-i) presents a summary of the corresponding one-electron crystal-field states for the 3(/, 3J, and 3J electron configurations, allocated to HS and LS states in distorted octahedral and tetrahedral symmetry. Part d, in addition, depicts the case of low-low-spin iron(IV) found in some trigonal... 

I shall take the simple view that most metal oxide structures are derivatives of a closest packed 02 lattice with the metal ions occupying tetrahedral or octahedral holes in a manner which is principally determined by size, charge (and hence stoichiometry) and d configuration (Jj). The presence of d electrons can lead to pronounced crystal field effects or metal-metal bonding. The latter can lead to clustering of metal atoms within the lattice with large distortions from idealized (ionic) geometries. 

Although Chapter 25 does not address directly why some compounds with coordination 4 are tetrahedral and some are square planar, it is possible to surmise that the answer lies with (1) Crystal Field Theory and the energies of the d orbitals involved bonding and (2) how many unpaired electrons the metal complex has. 

A low-spin to high-spin transition relates to the crystal field splitting of the d-orbitals in an octahedral or tetrahedral crystal field. However, even in cases where the energy difference between two spin states is much larger, electronic transitions are observed. An atom with total spin quantum number S has (22 + 1) orientations. In a magnetic field the atom will have a number of discrete energy levels with... 

Figure 5.6 Energy level diagram of the splitting of the J-orbitals of a transition metal ion as a result of (a) octahedral co-ordination and (b) tetrahedral coordination, according to the crystal field theory. (From Cotton and Wilkinson, 1976 Figure 23-4. Copyright 1976 John Wiley Sons, Inc. Reprinted by permission of the publisher.)...

At an early stage in the development of ligand field theory, it was found that A the splitting parameter for tetrahedral MX4, should be equal to (4/9) of A0, the splitting parameter for octahedral MX6, and experimental data are in good agreement with this prediction. However, this takes no account of the fact that the M—X distance in tetrahedral MX4 is usually some 8—10% shorter than in octahedral MX6. In the pointcharge crystal field model, A is proportional to R-5, so that if the difference in R between MX4 and MX6 is taken into account, we predict (At/A0) to be 0.6—0.7, compared with the experimental value of about 0.5. An AOM treatment (131) leads to better results, since here we find ... 

The regular cube used in Figure 5.5 to represent different symmetry centers suggests that these symmetries can be easily interrelated. In particular, following the same steps as in Appendix A2, it can be shown that the crystal field strengths, lODq, of the tetrahedral and cubic symmetries are related to that of the octahedral symmetry. Assuming the same distance A-B for all three symmetries, the relationships between the crystalline field strengths are as follows (Henderson and Imbusch, 1989) ... 

F ure 5.6 The energy-level scheme for the crystal field splitting of a d electron in different symmetries (a) octahedral, (b) tetrahedral, and (c) cubic. 

There have been few studies of substitution in complexes of nickel(II) of stereochemistries other than octahedral. Substitution in 5-coordinated and tetrahedral complexes is discussed in Secs. 4.9 and 4.8 respectively. The enhanced lability of the nickel(II) compared with the cobalt(II) tetrahedral complex is expected from consideration of crystal field activation energies. The reverse holds with octahedral complexes (Sec. 4.8). 

Figure 1.18 shows energy levels for d orbitals in crystal fields of differing symmetry. The splitting operated by the octahedral field is much higher than that of the tetrahedral field (A = lower than the effect imposed by the square... 

Figure 1.18 Crystal field splitting for d orbitals A = square-planar field B = octahedral field C = tetrahedral field.

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