I find this is very interesting. May I suggest another way to answer the question – with the help of Avnir's continuous symmetry measure S(Cs) for the permutation that permutes each atom with itself. It measures the distance of each structure to a structure with the same vertices and connectivity, but with Cs symmetry. The measure is zero if the structure is symmetric (i.e. planar) and rises as the structure deviates from planarity. In the attached figure I drew a torsion map similar to the one in above representing 961 fragments of azobenzene from the CSD database and colored them by their S(Cs) level. Note that the color scale is not linear. Statistically most of the structures are very closed to planarity (median S(Cs) is 0.065 and the average is 0.82). The method can also be used to distinguish between cis and trans azobenzene since they belong to different symmetry point groups.
Please see http://telem.openu.ac.il/csm/ for more details on the method.

Sincerely,

Dr. Inbal Tuvi-Arad

Department of Natural Sciences

The Open University of Israel

]]>