Crystal fields octahedral

Mulliken symbols The designators, arising from group theory, of the electronic states of an ion in a crystal field. A and B are singly degenerate, E doubly degenerate, T triply degenerate states. Thus a D state of a free ion shows E and Tj states in an octahedral field. 

The and 72 states are broadened as a result of slight variations in the crystal field. The 72 and E states are sharper but the E state is split into two components, 29 cm apart, because of the slight distortion of the octahedral field. Population inversion and... 

Figure 19.16 The possible high-spin and low-spin configurations arising as a result of the imposition of an octahedral crystal field on a transition metal ion.

Figure 22.9 Energy Level diagram for a ion in an octahedral 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. 

The difference in energy between the two groups is called the crystal field splitting energy and given the symbol A, (the subscript o stands for octahedral ). 

The poor data on PuF6 are probably best interpreted as a very small TIP of about 150 x 10-6 emu indicating a singlet ground state and a large crystal field splitting of the octahedral compound ( 5). 

We are concerned with what happens to the (spectral) d electrons of a transition-metal ion surrounded by a group of ligands which, in the crystal-field model, may be represented by point negative charges. The results depend upon the number and spatial arrangements of these charges. For the moment, and because of the very common occurrence of octahedral coordination, we focus exclusively upon an octahedral array of point charges. 

In an octahedral crystal field, for example, these electron densities acquire different energies in exactly the same way as do those of the J-orbital densities. We find, therefore, that a free-ion D term splits into T2, and Eg terms in an octahedral environment. The symbols T2, and Eg have the same meanings as t2g and eg, discussed in Section 3.2, except that we use upper-case letters to indicate that, like their parent free-ion D term, they are generally many-electron wavefunctions. Of course we must remember that a term is properly described by both orbital- and spin-quantum numbers. So we more properly conclude that a free-ion term splits into -I- T 2gin octahedral symmetry. Notice that the crystal-field splitting has no effect upon the spin-degeneracy. This is because the crystal field is defined completely by its ordinary (x, y, z) spatial functionality the crystal field has no spin properties. 

The ground term of the cP configuration is F. That of is also F. Those of and d are " F. We shall discuss these patterns in Section 3.10. For the moment, we only note the common occurrence of F terms and ask how they split in an octahedral crystal field. As for the case of the D term above, which splits like the d orbitals because the angular parts of their electron distributions are related, an F term splits up like a set of / orbital electron densities. A set of real / orbitals is shown in Fig. 3-13. Note how they comprise three subsets. One set of three orbitals has major lobes directed along the cartesian x or y or z axes. Another set comprises three orbitals, each formed by a pair of clover-leaf shapes, concentrated about two of the three cartesian planes. The third set comprises just one member, with lobes directed equally to all eight corners of an inscribing cube. In the free ion, of course, all seven / orbitals are degenerate. In an octahedral crystal field, however, the... 

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 effects of an octahedral crystal field upon each of the ground terms is shown in Fig. 3-20. This diagram was constructed as follows. From our previous discussions, + Eg, F Tig + Tig + Aig (with Ti, always in the middle), and... 

Here we comment on the shape of certain spin-forbidden bands. Though not strictly part of the intensity story being discussed in this chapter, an understanding of so-called spin-flip transitions depends upon a perusal of correlation diagrams as did our discussion of two-electron jumps. A typical example of a spin-flip transition is shown inFig. 4-7. Unless totally obscured by a spin-allowed band, the spectra of octahedral nickel (ii) complexes display a relatively sharp spike around 13,000 cmThe spike corresponds to a spin-forbidden transition and, on comparing band areas, is not of unusual intensity for such a transition. It is so noticeable because it is so narrow - say 100 cm wide. It is broad compared with the 1-2 cm of free-ion line spectra but very narrow compared with the 2000-3000 cm of spin-allowed crystal-field bands. 

In octahedral symmetry, the F term splits into Aig + T2g + Tig crystal-field terms. Suppose we take the case for an octahedral nickel(ii) complex. The ground term is 2g. The total degeneracy of this term is 3 from the spin-multiplicity. Since an A term is orbitally (spatially) non-degenerate, we can assign a fictitious Leff value for this of 0 because 2Leff+l = 1. We might employ Van Vleck s formula now in the form... 

Now take the case for an octahedral vanadium(iii) ion. For d, the ground term is Tig. The spatial degeneracy of a 7 term is three-fold and we describe this with Leff = 1. Using (5.10) we find eff = VlO. So for this Tig term, the crystal field has quenched some, but not all, of the angular momentum of the parent free ion F term. 

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