STRUCTURES WITH Z'>1: PROBLEMS AND OPPORTUNITIES. Carolyn Pratt Brock, Department of Chemistry, University of Kentucky, Lexington, KY 40506-0055, USA
Structures with Z'>1 (more than one independent formula unit in the asymmetric unit) frequently present crystallographic difficulties. Such structures are nearly always pseudosymmetric, at least locally. Data-to-parameter ratios are often low and least-squares refinements unstable or slow to converge. Structure solution can be a problem, especially if the molecules are approximately planar. Even if everything goes smoothly there is the nagging worry that additional symmetry has been overlooked and will be found by an alert Editor, Referee, or interested reader.
Examples (some published, some not) will be discussed. In several the use of constraints, including the rigid-group approximation, was very important.
Consideration of structures with Z'>1 may also lead to greater understanding of crystal packing. Only about 7% of the structures in the Cambridge Structural Database have Z'>1; crystallization with Z'<1 is the norm. (The tendency to low Z' values may explain why crystals containing two different stereoisomers are rare.) Certain classes of compounds are, however, especially likely to crystallize with Z'>1. Among these are the monoalcohols CnHmOH and vic-diols CnHm(OH)2. Optimization of H-bonding interactions in these compounds often rules out a unit cell having Z'<1. Other Z'>1 structures reveal multi-molecule packing units that have internal structure incompatible with translational symmetry. Probably such aggregates exist in solution but are found only rarely in the solid state. Finally, many Z'>1 crystals, especially those grown at one temperature and studied at a lower temperature, can be viewed as having commensurately modulated structures.
*Research supported in part by the Kentucky EPSCoR program (NSF Grant EHR-91-08764).