Triphenylsilanol–4,4′-bipyridyl (4/1): theZ′ = 4 polymorph revisited

High-Z′ structures of organic molecules: their diversity and organizing principles

A list has been compiled of 284 well determined organic structures having more than four crystallographically independent molecules or formula units (i.e. Z′ > 4). Another 22 structures were rejected because the space group or unit cell was probably misassigned; the rate for that type of error is then only 7%. The space-group frequencies are unusual; half the structures are in Sohncke groups, partly because the fraction of enantiopure structures of resolvable enantiomers is higher than for lowerZ′ structures. Careful investigation of the 284 structures has shown that they are very diverse; no simple classification can describe them all. Organizing principles have, however, been recognized for almost all of them. The most common features are simple modulations and hydrogen-bonded aggregates; only 14% of the structures have neither. In 50% of the structuresnmolecules are related by a pseudotranslation that would be a crystallographic translation but for small molecular displacements and rotations. In 70% of the structures there are aggregates (e.g. n-mers, columns or layers) held together by strong intermolecular interactions; those aggregates usually have approximate local symmetry. Because then-fold modulations and then-mers often haven<Z′, 85% of the structures withZ′ > 5 have several features that combine to give the highZ′ value. The number of different molecular conformations is usually small,i.e.one or two in 84% of the structures. More exotic packing features, such as ordered faults and alternating layers of different types, are found inca30% of the structures. A very few structures are so complex that it is difficult to understand how the crystals could have formed.

From direct-space discrepancy functions to crystallographic least squares

Crystallographic least squares are a fundamental tool for crystal structure analysis. In this paper their properties are derived from functions estimating the degree of similarity between two electron-density maps. The new approach leads also to modifications of the standard least-squares procedures, potentially able to improve their efficiency. The role of the scaling factor between observed and model amplitudes is analysed: the concept of unlocated model is discussed and its scattering contribution is combined with that arising from the located model. Also, the possible use of an ancillary parameter, to be associated with the classical weight related to the variance of the observed amplitudes, is studied. The crystallographic discrepancy factors, basic tools often combined with least-squares procedures in phasing approaches, are analysed. The mathematical approach here described includes, as a special case, the so-called vector refinement, used when accurate estimates of the target phases are available.