Effective g-value

Spectra of radicals in a dilute single crystal are obtained for various orientations, usually with the field perpendicular to one of the crystal axes. Each spectrum usually can be analyzed as if they were isotropic to obtain an effective g-value and hyperfine coupling constants for that orientation. Since the g- and hyperfine-matrix principal axes are not necessarily the same as the crystal axes, the matrices, written in the crystal axis system, usually will have off-diagonal elements. Thus, for example, if spectra are obtained for various orientations in the crystal vy-plane, the effective g-value is ... 

FIGURE 5.9 Effective g-values for half-integer spin systems in axial symmetry. The scheme gives the values for all transitions within the Kramer s doublets of S = nl2 systems assuming gmal = 2.00 and S S S B. 

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 5.10 The rhombogram for S = 5/2. Effective g-values of the three intradoublet transitions have been plotted as a function of the rhombicity q = E/D assuming greal = 2.00 and S S S B. 

FIGURE 5.11 EPR of an S = 5/2 system with pronounced rhombicity. The X-band spectra (V = 9.31 GHz) are from high-spin FeIH in Escherichia coli iron superoxide dismutase. The observed effective g-values correspond to T = 0.24 in the S = 5/2 rhombogram. 

FIGURE 7.1 S = 3/2 rhombograms for weak-field and intermediate-field conditions. Effective g-values are plotted for v = 9.50 GHz and D = 3.0 cm"1 (weak field solid lines) or D = 0.3 cm"1 (intermediate field broken lines) as a function of the rhombicity E/D. 

Comparing the strain-induced anisotropic part of the effective g-value in Equation 9.24 with the linewidth Equation 9.18 for fully correlated g-strain reveals a remarkable correspondence they are equivalent (apart from a sign ambiguity) within the substitutions... 

The forbidden IAmsl = 2 transition occurs between levels that separate in an increasing magnetic field twice as rapidly as the levels of the regular IAmsl = 1 transitions, and so this transition is expected to be found at half field, that is, at a field corresponding to an effective g-value geff = 2xg 4. In Figure 11.1 we see the relative intensity... 

Isotropic effective g-values in high-spin systems... 

If the Ln3+ centre is a Kramers ion, the spectra can be interpreted in terms of a doublet with largely anisotropic effective -values. If one neglects the admixture of higher lying/ multiplets and considers an axial symmetry, the effective g values will be... 

Figure 10. EPR spectrum of [ZuFejS ] " recorded at 8 K. The lower panel shows energy levels and effective g>values for an S = 5/2 system with D < 0 and E/D = 0.25, where D and E are the zero field splitting parameters.

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

Effective atomic number Rule, 24 226 and cluster compounds, 24 230-231 exceptions, 24 226-227, 235 and mononuclear species, 24 234-235 Effective g values, calculation, 38 195-197 EF hand domains, calcium-binding proteins, 46 442, 443 45... 

At intermediate orientations the effective g values will also be intermediate. Consider a molecule oriented so that the magnetic field makes an angle 9 with... 

When the magnetic field is along the axis of quantization, the Zeeman interaction splits the Sj = j and = states but does not mix them. The splitting is just /SH g S there is little contribution from orbital angular momentum as there are no low-lying excited states to be mixed in by the spin-orbit coupling. Therefore, along the z direction the effective g value is about 2. 

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