Distribution of molecular centres in crystallographic unit cells

A survey has been made of the position of molecular centres in unit cells for the seven most populated space groups in the Cambridge Structural Database. Visual inspection of histograms and scattergrams reveals very clear peaks and clusters, showing preferred locations for molecules. These preferred positions are midway between centres of symmetry or screw axes. Some simple calculations of interaction energies of molecules with neighbours in a molecular coordination sphere suggest reasons for these preferred positions. These diagrams show that simplification of molecules to spheres is helpful in visualizing the prevalence of layers of molecules and tendencies to the ideal close packing of spheres.