Rhombicity parameter

The ratio 7Z) is the so-called rhombicity parameter. With some algebra, and... 

The values of the rhombicity parameters are conventionally limited to the range 0 < EjD < 1/3 without loss of generality. This corresponds to the choice of a proper coordinate system, for which /)zz (in absolute values) is the largest component of the D tensor, and /) is smaller than Dyy. Any value of rhombicity outside the proper interval, obtained from a simulation for instance, can be projected back to 0 < EID < 1/3 by appropriate 90°-rotations of the reference frame, that is, by permutations of the diagonal elements of D. To this end, the set of nonconventional parameters D and EID has to be converted to the components of a traceless 3x3 tensor D using the relationships... 

A semiquantitative indication of complex distortion is also possible with the ESR spectra of Mn11. For unchelated Mn11 in zeolite Y, the values of the axial and rhombic parameter are small, most of the spectral intensity in X band being accumulated close to geff = 2 with a broad distribution of axial sites. This is observed for the bpen and bpb complexes, while for bpeh and bppn a feature around g = 4.3 is prominent. The complex distortion estimated form ESR thus follows the sequence derived from IR. 

Mossbauer spectroscopy can also be used to obtain information about fine structure parameters like zero-field splitting D and rhombicity parameter E D. The zero-field splitting is a second-order effect, which can be classically visualized as resulting from the circular currents generated in the atomic shell by the electron spin. In Section 3.10.5, we describe how D and E D can be calculated. 

Figure 11. The best fit has been found for 5 = 0.7 0.01 nuns, Aitg =—3.25 0.01 nuns, " =(2.11, 2.19, 2.00), "T/ nMn = (-45, 10, 19) T, tj = 0.74 0.1, D = 7.2 0.5 cm, and EID = 0.16 0.02. The zero-field splitting parameter D = 7.2 0.5 cm is comparable to that found for rabredoxin from Clostridium pasteurianum (D = 7.6cm Surprisingly, the rhombicity parameter E/D = 0.16 0.02 differs somewhat from that of rubre-doxin from C. pasteurianum (E/D = 0.28). The hyperfine coupling tensor has been determined to be A = (-14.5, -9.2, -27.5) T. The anisotropy of the hyperfine conpling tensor is cansed by spin-orbit confribntions to the internal magnetic hyperfine field.

The situation resembles the case of zero-field splitting in mononuclear systems (Section 8.4) the energy levels are split by the axial parameter into a Kramers doublet and a single level the rhombic parameter removes the degeneracy completely. 

Figure 8 Mossbauer spectrum of a frozen aqueous solution of [ Fe +]-ferrioxamine B (12mM) employing BSA (lOOmM) as a dilutant to minimize spin-spin relaxation. The solid line represents a simulation based on a spin Hamiltonian line width = 0.35 mm s zero-field splitting, D = 1.2 cm E rhombicity parameter, E/D = 0.33 8 = 0.52mms A q = —0.84mms asymmetry parameter, rj = and isotropic hyperfine coupling tensor Axx/gN/XN = Ayy/gNMN = Azz/gx/XN = —22.1 T. The simulation does not completely fit the experimental data. This discrepancy is caused by relaxation effects that are not dealt with in the spin Hamiltonian simulation...

Xmax, nm absorption maxima, (per iron) absroption coefficient, AE, mm/s quadrupole splitting, 5, mm isomer shift, F, nm/s line width, D, cm l zero-field splitting, X rhombic parameter, p qurtic parameter... 

The fine structure interaction (Fig. 16) is only valid when the electron spin is greater than Vi and only has Axial and Orthorhombic representations, as it is a traceless tensor. D is the axial zero field splitting and EID, the rhombicity parameter, can vary between 0 (axial symmetry) and 1/3 (rhombic symmetry). 

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