Crystal field lower symmetry

Generally, the crystal field lowers the symmetry of the free molecule. Chemical equivalence in the free molecule may occasionally be preserved as crystallographic equivalence in the solid. Chemical inequivalence in the free molecule cannot be reconciled with crystallographic equivalence in the solid by crystal field effects. 

This is an immediate consequence of the lowering of the symmetry as, even in the regular octahedral geometry, group theory tells us that the highest dimension of the irreducible representation is three. This is the basis of Crystal Field Theory, whose deeply symmetry-based formalism was developed by Bethe in 1929 [16]. 

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... 

Under the action of a crystal field component of lower symmetry each state of Ok will split up further. Under tetragonal symmetry (D ), Tig and Eg decompose as follows ... 

If, in addition to the cubic crystal field, a component of lower symmetry is present, such as one having tetragonal or trigonal symmetry (as for the Al sites in a-AUOa), further splitting will occur as shown in Fig. 24. Crystal field splittings for other configurations in both the weak and strong field cases are summarized in a review article by Moffitt and Ballhausen... 

The electronic spectrum (36) of the pol5uner is dominated by a very broad ultraviolet band, with shoulders at 280 and 470 m/t, which tails into the visible region and is responsible for the deep brown color of the polymer. Very weak crystal field excitations are found at 640 and 880 m. From the latter transition one can estimate that for high-spin Fe +, Dq = 1100 cm i. This value is typical of Fe3+ in octahedral coordination with oxygen ligands, but the X-ray evidence (see below) indicates that the coordination is tetrahedral, so that Dq seems anomalously high. However, the coordination symmetry is actually lower than tetrahedral, since both hydroxide and oxide ligands are involved. 

Lower Symmetry Crystal Fields There are two common types of distortion from an octahedral symmetry. One distortion alters the charges along the z axis, giving rise to what is called a tetragonal field in which the... 

A prediction of crystal field theory as outlined in the preceding subsections is that the crystal field splitting parameter, A, should be rather critically dependent upon the details of the crystal lattice in which the transition metal ion is found, and that the splittings of the /-orbital energies should become larger and quite complicated in lattices of symmetry lower than cubic. The theory could not be expected to apply, for example, to the spectra of transition metal ions in solution. 

In symmetries lower than cubic the (/-orbitals mix with the donor atom s—p hybrid orbitals to varying extents in molecular orbitals of appropriate symmetry. However, the mixing is believed to be small and the ligand field treatment of the problem proceeds upon the basis that the effective d-orbitals still follow the symmetry requirements as (/-orbitals should. There will be separations between the MOs which can be reproduced using the formal parameters appropriate to free-ion d-orbitals. That is, the separations may be parameterized using the crystal field scheme. Of course, the values that appear for the parameters may be quite different to those expected for a free ion (/-orbital set. Nevertheless, the formalism of the CFT approach can be used. For example, for axially distorted octahedral or tetrahedral complexes we expect to be able to parameterize the energies of the MOs which house the (/-orbitals using the parameter set Dq, Ds and Dt as set out in Section 6.2.1.4 or perhaps one of the schemes defined in equations (11) and (12). 

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