Molecular shape and crystal packing: a database study

Abstract

The relationship between molecular shape and packing patterns in molecular crystals has been investigated using the Cambridge Structural Database (CSD). The methodology for molecular shape uses the enclosing box based on the principal axes of inertia, with some descriptors of the amount of void space between the van der Waals surface and the faces of the rectangular box. The ratio of the molecular volume to the volume of the box, and some counts of atom types describing chemical character were also found useful. Packing descriptors are based on the molecular coordination shell of neighbours in contact with a reference molecule, usually 14–16. A set of 16 vectors between molecular centres are sorted by magnitude and stored in tabular form for a set of 133 448 CSD entries, together with other descriptors such as unit cell, space group, H-bonds, etc. A computer program was written to search the table file by molecular shape within specified tolerance ranges. This allows one to select a set of molecules most similar in shape to a given target molecule, and cluster the packing patterns. Cluster analysis on the sets of 16 sorted coordination distances often shows visually recognisable structural patterns. Methods for detection of 1D and 2D substructures are discussed. There is broad correlation of packing patterns and molecular shapes classed as rods, discs and spheres and packing patterns based on partition of the 14 distances by largest gap. Case studies showing clustering of packing patterns are presented, using sets of molecules judged most similar to target CSD molecules.