Walking the unit sphere

Biochemical EPR samples are almost always collections of randomly oriented molecules (frozen) aqueous solutions in which each paramagnetic molecule points in a different direction. In order to generate simulations of these powder EPR spectra we have to calculate the individual spectrum for many different orientations and then add these all up to obtain the powder pattern. Numerical procedures that generate sufficient spectra to approximate a powder pattern are collectively known as walking the unit sphere algorithms. Here is the basic procedure  

FIGURE 6.3 Quantification on the first half of an isolated peak. The spectrum is from the [2Fe-2S] cluster in the enzyme adenosine phosphosulfate reductase from Desulfovibrio vulgaris (Verhagen et al. 1993). The inset shows the asymmetrical low-field -feature the vertical line at the peak position indicates the rightmost integration limit for quantification on half 

FIGURE 6.4 Vectors to describe a walk on the unit sphere. The orientation of a vector b of unit length along the dipolar magnetic field vector B in a Cartesian molecular axes system xyz is defined by the two polar angles 9 between b and the z-axis, and cp between the projection of b on the x-y plane and the x-axis. 

A computer program to generate S(B) in pseudo-code would be something along the following lines 

INPUT g-values git linewidth r, frequency v, field limits INPUT stepwidth in solid angle dcosB, dip spectral points n NULL absorption-array 

---