Analysis of the PC-refinement

In the present case, the analysis of the filtering procedure is straightforward: a single peak is produced, which corresponds to the orientation of one of the molecules. The second molecule is not found in this particular run, since its orientation was not among the first 240 peaks of the rotation function. This shows a problem with the $PC$-refinement strategy: if no solution is found, one cannot be sure that there is no solution. A “direct" rotation search (see Section 19.7) may help in these cases. Another aspect of the result of the filtering procedure is that sometimes several $PC$-refinements converge on the same solution. The Rotman statement provides a facility to measure the “distance" or metric between two rotation matrices by removing crystallographic redundancies. Suppose one wants to know the distance between two orientations of the search model ($\theta_1$=80.477, $\theta_2$=85.000, $\theta_3$=24.806) and ($\theta_1$=261.392, $\theta_2$=90.000, $\theta_3$= 336.243) taking into account the crystallographic symmetry. Using the Rotman statement
  a=44.144 b=164.69 c=70.17 alpha=90. beta=108.50 gamma=90.
  symmetry ( x, y, z  )
  symmetry ( -x, y+1/2, -z )
   euler=(80.477  85.000  24.806)
   euler=( 261.392  90.000 336.243)
one finds that the difference between these two orientations is about 5$^{\circ}$, due to the crystallographic symmetry.

Xplor-NIH 2023-11-10