Rhombic crystal field

Fig. 8.24 Energy splitting of

FIGURE 5.16 Crystal-field pictures for the low-spin d5 system in deformed octahedra. (a) relative energy of d-orbitals for an octahedron with strong crystal field (b) d-orbitals of the T2s set in a rhombically distorted octahedron (c) three possible electron configurations of increasing total energy (d) the term scheme for the configurations in (c). 

Figure 27 (a) The splitting of the one-electron energy levels of the copper(II) ion in crystal fields of axial and rhombic symmetry (b) The splitting of the one-electron energy levels of the copper(II) ion in crystal fields of tetrahedral, cu-distorted octahedral, trigonal octahedral and trigonal bipyramidal symmetry... 

In the high-spin ferrous ion, spin-orbit interactions mix the ground state wave functions with the excited states. If the ground state is assumed to have dZ2 symmetry, then the following expressions apply for an ion in a crystal field with both rhombic and axial distortions (Edwards et al. (70). 

A small rhombic splitting in7the g values is also calculated (g g = 0.017). As a rhombic splitting was also indicated by our crystal field computations (11), a higher resolution EPR spectrum than the previously considered X-band data was obtained. Figure 18 shows the results of Q-band EPR on a frozen sample of spinach plastocyanin. A rhombic splitting of 0.017 is clearly discernable, in agreement with the adjusted Xa calculation. 

Lanthanide complexes with axial symmetry (i.e., possessing at least a threefold axis, see sect. 2.4.2) are exclusively considered because the principal magnetic z axis coincides with the molecular symmetry axis (Forsberg et al., 1995) and the c 2 spherical tensor operators do not contribute to the crystal-field potentials (Gorller-Walrand and Binne-mans, 1996). The rhombic term of Bleaney s approach V6B Hi (eqs. (42), (46)) thus vanishes and the crystal-field independent methods (eqs. (51), (53)) can be used without complications. 

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... 

Figure 9 The crystal field splitting of Fe and Fe d orbitals in cubic O/, tetragonal D41, and rhombic C2 environments (a). Only the latter two are typically observed for metal porphyrinoid complexes. The axial and rhombic ligand field parameters are denoted as A and V. The low-, intermediate- and high-spin states for Fe and Fe " based on a tetragonal environment (b). (Reprinted from Mack, Stillman and Kobayashi, Elsevier 2007)...

Hje and Hrj, are the tetragonal and rhombic crystal fields, respectively Hso is the spin-... 

The term with fi as a coefficient represents the cubic crystal field energy and arises from coupling with higher excited states (32). This contribution can usually be neglected except for those ions with nearly cubic symmetry. If there is rhombic symmetry then the (rj, f, ) axes... 

It might be worthwhile to point out that in the wide variety of crystal fields possible, the symmetry at the metal site can be orthorhombic which has fewer symmetry operations than an axially symmetric complex for example. However, the strength of the axial distortion might disturb the local environment more severely (as in the heme complexes) in contrast to the weak rhombic departures from cubic symmetry in the sideramines discussed later. The electronic wave functions which determine the hyperfine interactions depend on the parameters X and fi which reflect the degree of asymmetry in the local environment. 

In each of the iron transport proteins there is a rhombic crystal field which is strong enough to make E comparable to D, (Actually, D is rather weak in these cases.) In fact E = D/3 or A = 1/3 is the condition for which the extreme rhombic asymmetry exists (33, 36). A value for A >1/3 merely implies that the principal axis of the zero field splitting is no longer the z axis. 

Centres in octahedral symmetry with rhombic distortion Strong crystal field... 

Interestingly, the mathematical treatment leading to Eq. (44) is very general and any paramagnetic system, for which Bleaney s approach requires two independent crystal-field parameters may benefit from its use for testing isostructurality, as demonstrated with the structural analyses of rhombic mononuclear (Terazzi et al., 2006) and polynuclear (Ouali et al., 2004) lanthanide complexes. 

If we have the analysis of a large number of low-spin ferric compounds, they may be conveniently summarized on a crystal field diagram such as Figure 8. Here we have plotted the tetragonal field (A/A) as abscissa and V/A, which we have termed the rhombicity, as ordinate. All of these compounds, with the exception of the ones labelled with... 

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