Classical models of anisotropic linewidth

As a starting point let us be faithful to the history of the subject and try a simple physical model due to (Johnston and Hecht, 1965) if the inhomogeneous EPR line reflects a distribution in g-values, then the anisotropy in the linewidth should be scalable to the anisotropy in the g-value. In other words, the analytical expression for g-anisotropy in terms of direction cosines, between B and the 

FIGURE 9.1 Linewidth versus standard deviation. A gaussian distribution of unit amplitude is plotted on an x-axis scale in units of the standard deviation (or sigma). At 3.15x0 the unit intensity has dropped to 0.1%. The linewidth in simulations is usually expressed as the halfwidth at half height (HWHH), which is equal to circa 1.17x0, or as twice this value that is, the full width at half height (FWHH). 

FIGURE 9.2 EPR powder pattern of the [2Fe-2S]1+ cluster in spinach ferredoxin. Trace A shows an attempt to fit the spectrum with the diagonal linewidth Equation 9.1. In trace B the spectrum is fitted with the nondiagonal g-strain Equation 9.18. Trace C shows an experiment in which the spectral features are slightly shifted (solid trace) under the influence of an external hydrostatic stress. (Data replotted from Hagen and Albracht 1982.) 

An alternative model (Venable 1967) proposes that the main cause of inhomogeneous broadening is unresolved superhyperfine interactions and, therefore, that the linewidth expression should be equivalent to the Equation 5.12 for the angular dependence of first-order hyperfine splitting  

FIGURE 9.3 Linewidth as a function of microwave frequency. The linewidth (FWHH) of the low-field gj-feature is plotted versus the frequency in L-, S-, X-, and Q-band. The left-hand panel is for the ferric low-spin heme in horse heart cytochrome c, and the right-hand panel is for the [2Fe-2S] cluster in spinach ferredoxin. (Data from Hagen 1989.) 

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