A novel characterization of organic molecular crystal structures for the purpose of crystal engineering

A novel analytical approach is proposed for the characterization of organic molecular crystal structures where close packing is an important factor. It requires the identification of a unique reference axis within the crystal, along which three-dimensional space is divided into close-packed blocks (CPB) and junction zones (JZ). The degree of close packing along the reference axis is quantified by a two-dimensional packing function, phi(2D), of symmetry determined by the space group. Values of phi(2D) reflect the degree of area-filling in planes perpendicular to this axis. The requirement of close packing within CPB allows the planar structures perpendicular to the reference axis to be analysed as tessellations of area-filling molecular-based cells (MBC), which are generally hexagonal. The form of these cells reflects the molecular shape in the cross-section, since their vertices are given by the centres of the voids between molecules. There are two basic types of MBC, Type 1, of glide or pseudo-glide symmetry, and Type 2, which is formed by lattice translations alone and generally requires a short unit-cell axis. MBC at layers of special symmetry are used to characterize the structures in terms of equivalent ellipses with parameters a(ell), b(ell) and chi(ell). The ratio aell/bell allows the established alpha, beta, gamma classification to be integrated into the current framework. The values of parameters aell and bell arising from all the structures considered, polynuclear aromatic hydrocarbons (PAH), substituted anthracenes and anthraquinones (SAA) and 2-benzyl-5-benzylidene (BBCP) are mapped onto a universal curve. The division of three-dimensional space into CPB and JZ is fundamentally useful for crystal engineering, since the structural perturbations brought about by substitution at hydrogen positions located within JZ are minimal. A contribution is also made to ongoing debate concerning the adoption of polar space groups, isomorphism and polymorphism.