Resonance condition rhombicity

In general, no simple, consistent set of analytical expressions for the resonance condition of all intradoublet transitions and all possible rhombicities can be derived with the perturbation theory for these systems. Therefore, the rather different approach is taken to numerically compute all effective g-values using quantum mechanics and matrix diagonalization techniques (Chapters 7-9) and to tabulate the results in the form of graphs of geff,s versus the rhombicity r = E/D. This is a useful approach because it turns out that if the zero-field interaction is sufficiently dominant over... 

Figure 5. Visualisation of the EPR-resonance condition for a subset of molecules and the corresponding giso-curves for a rhombic model g-tensor at several effective g-factor values. The g-sphere and the principal values on the g-ellipsoid are marked with arrows. The corresponding powder EPR spectrum in absorption and first derivative mode is shown in the top left panel.

Electron Paramagnetic Resonance Spectra. Only two of these complexes exhibit well-resolved EPR spectra. A narrow, isotropic signal observed at g = 2.005 for the trinuclear complex 12 at low temperatures is consistent with an S = 1/2 ground state169), but a detailed description of the electronic properties of the complex remains to be developed. The [Fe(MoS4)2]3 ion shows a rhombic S = 3/2 EPR spectrum that is very solvent dependent and, under certain conditions, is somewhat similar in apperance to that of FeMo-com). For example, in frozen aqueous solution, the apparent g values are 5.3,2.6, and 1.7181). If complex 14 also proves to have an S = 3/2 ground state, a somewhat similar EPR spectrum at low temperature would be expected as well. 

Recent work by Peterson et al (1974) and Carnevale et al (1976) on the ESR of borate glasses raises the possibility of a different kind of explanation for some sharp g — 4.3 resonances. In glasses, random distributions of the effective g values, which obviously depend upon random distributions in the values of D and , are invoked to show that even when the symmetry at each site is notionally axial, described by 2 and g 6, a strong negative correlation between and g distributions can produce a sharp g 4 resonance. Such an explanation avoids the requirement of extremely large line widths often needed to simulate the ESR spectra because of Fe in glasses. Neither the correlation explanation nor the involvement of fourth-order terms in the conditions (24) are meant to convey the idea that the extreme rhombic condition E/D = 1/3 never occurs. It must, however, be stressed that it would seem most unlikely that the extreme rhombic condition would be rigorously fulfilled in all cases where g = 43 lines are found. 

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