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. global minimum, but not always. This observation has been noted both by workers who have exhaustively explored packing parameter space (Williams, 1969; van Eijck, Mooij & Kroon, 1995) or have used Monte Carlo methods plus simulated annealing to take statistical samples of the total space and proceed to a local minimum (Karfunkel & Gdanitz, 1992). What is certain is the importance of the principle of close packing. The present study takes the approach of looking at the total available data on packing of molecular crystals to identify certain tendencies in packing and certain commonly occurring patterns. If such patterns exist then these will have implications as regards the methods of prediction, if only on the basis of probability of occurrence.