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, φ_2D, of symmetry determined by the space group. Values of φ_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 χ_ell. The ratio a_ell/b_ell allows the established α, β, γ classification to be integrated into the current framework. The values of parameters a_ell and b_ell 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.