Octahedron, crystal field splitting

Figure V l l. (a) CoC>6 octahedron. Solid and open circles indicate cobalt and oxygen ions, respectively, (b) C0O2 layer, c and at axes are along (1,1,1) and (—1,1,0) directions in xyz coordinate system shown in (a). The numbers (0 12) on solid circles are the labels of Co sites, (c) The crystal-field splitting of the distorted CoC>6 octahedron. e g is used to distinguish from the eg (x2-y2 and 3z2-r2) states...

We will briefly consider the crystal field splitting of the rf-orbitals in four-coordinate, tetrahedral complexes. The cube, octahedron and tetrahedron are related geometrically. Octahedral coordination results when ligands are placed in the centers of cube faces, while tetrahedral coordination results when ligands are placed on alternate comers of a cube, as shown in Fig. 10.9. 

Figure 19.1 Crystal-field splitting of 3d one-electron levels in octahedral and tetrahedral environment within the (TM)06 octahedron.

Based on the spin Hamiltonian of equation (1), EPR and Mossbauer spectra of various siderophores have been analyzed. The parameters obtained are listed in Table 3. AU siderophores have some features in common. Isomer shifts and quadrupole splittings are typical for high-spin Fe +. The internal field is on the order of — 55T. For comparison, the internal field of the isolated Fe + ion is —63 T, FeFs exhibits a value of -62 T, and FeCb of -48.6 T. The internal field of siderophores indicates a high degree of ionicity and is typical for an isolated FeOe octahedral configuration. The X-values near 0.333 listed in Table 3 reflect a nearly complete rhombic distortion of the FeOe octahedron arising from crystal fields at the nucleus with syrmnetries lower than C3. Similarly, C NMR spectra of alumichromes show that the hydroxamate carbonyl functionalities are inequivalent, since two carbonyl... 

The crystal field optical transitions of Cr + in an octahedral site are shown in Fig. 26. The splitting of the upper energy levels by the weak trigonal distortion ( 350 cm ) (67,168-170) of the octahedron cannot be resolved in powder samples of chromia-alumina. The optical reflectance spectra shown in Fig. 27 show a gradual shift of the absorption maxima near 17,000 and 23,000 cm (15,39,171) due to the lattice expansion that results when chromia is added to an alumina lattice. The optical spectra conform to the Tanabe and Sugano (168,172-174) theoretical calculations. The Racah parameter varied with the chromium content (15,171), Variable temperature (169,175) and variable pressure (176,177) optical spectra have been obtained for ruby samples. 

The Jahn-Teller distortion has another consequence. The d states that split in energy in an octahedral crystal field into the tj and e pair are further spilt in a Jahn-Teller environment (Figure 1.7). In the case of an elongated octahedron, the most common situation is that the set are split slightly, but there is a bigger splitting for the e pair, with the d j orbital at an appreciably lower energy than the d 2 2 orbital. This means that the orbital that is preferentially occupied will be d 2 and orbital... 

This is the famous crystal-field operator for an octahedron, which splits the ai-shell into eg and t2g subshells. The crystal-field interaction is usually parameterized by the crystal-field parameter, lODq, which corresponds to the splitting of the eg and t2g orbitals. The term in brackets here is the octahedral invariant of rank 4. In the multipole expansion this corresponds to a hexadecapole operator. In normalized form it reads... 

The separation between the e and t2 levels in a tetrahedron is smaller than the separation between t2g and eg levels in an octahedron. Within the assumptions of crystal field theory the e-t2 splitting in a tetrahedron is 4/9 (44%) of the value of the t2g-eg splitting in an octahedron. While many assumptions used in simple crystal field theory are not completely valid, a value of 40 to 50% is a reasonable rough approximation. As an example the t2g-e. splitting in Ti(H20)4 is 1.1 eV. 

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