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A chiral object is one which cannot be superposed on its mirror image. The symmetry group of a chiral object contains only pure rotations, pure translations, and screw rotations. All of these operations correspond to movements which may be carried out on a rigid body. In nature, chiral objects occur as both mirror-related versions and these are called enantiomorphs. For a chiral molecule the special term enantiomer has been coined. On the other hand, an achiral object can be superposed on its mirror image and its symmetry group must contain some operations which invert its geometry, viz pure rotoinversion operations ($\overline{1}$, $m$, $\overline{3}$ ,$\overline{4}$, $\overline{6}$) or glide reflection. None of these operations can be produced by a direct movement of a rigid body.

Chirality plays a mischievous role in the packing together of molecules to form crystals. It is easy to build a spiral staircase (really it is helicoidal) from bricks. The staircase is chiral and the bricks are achiral. Are there any restrictions due to symmetry or geometry in the way that chiral or achiral molecules may be put together to form a chiral or an achiral crystal structure? In answering this question for chiral molecules we have two common cases in mind: (i) all of the enantiomers have the same chirality - the composition of the sample is said to be enantiopure or enantiomerically pure; (ii) exactly one half of the enantiomers are of one chirality and the other half of the opposite - the sample is a racemate. Of the six combinations achiral/enantiopure/racemate forming achiral/chiral crystal structures, all but one have been observed experimentally and another one is very rare. No example has been observed of a well-ordered achiral crystal structure formed of enantiopure chiral molecules. Although it may seem obvious that an enantiopure compound must form a chiral crystal structure, in fact this behaviour is due to the individuality of the molecules rather than to any underlying theorem of symmetry groups. The very rare case is the one in which a racemate forms a chiral crystal structure. At first sight this sounds counterintuitive but there is no obligation for the enantiomers either to be related one to another by a rotoinversion or a glide reflection belonging to the space group of the crystal structure or to have the same configuration in the solid state.

Crystallization of a racemate from solution or the melt frequently results in the formation of crystals with a homogeneous crystal structure containing both enantiomers in equal proportion. In the old literature this is known as a "racemic compound". However, occasionally crystallization of a racemate produces a racemic conglomerate in which the composition of each crystal is enantiopure, there being equal numbers of left-handed and right-handed crystals. In this case, a spontaneous resolution has been achieved, and this phenomenon is often quoted as one of the possible sources of enantiopurity in the biological world. The reasons for such a selectivity, undoubtedly brought about by crystal-packing requirements, is part of the mystery that shrouds the formation of crystalline solids. A comparison between the crystal structures of enantiopure compounds and their racemates shows that frequently both are formed of the same enantiopure rods or layers. The latter are packed together differently in the crystal structures of the enantiopure compounds and the racemates. A comparative study of the crystal packing of enantiopure compounds and of their racemates has been carried out[15]; no clear sign of a more compact crystal packing has been found for racemates.

Many natural products whose crystal structures appear in the Cambridge Structural Database have been isolated in enantiomerically-pure form from plants or animals. Natural compounds are chemically and biologically interesting so their crystal structures are determined more frequently than synthetic products. Thus the frequency of occurrence in the CSD of chiral crystal structures and of the 65 space groups containing only symmetry operations of the first kind (translations, pure and screw rotations) is artificially increased.

The free energies of a pair of enantiomers are identical. Nevertheless kinetic effects in the crystallization of racemates, or more generally enantiomeric mixtures, are rife and in some cases are used industrially to undertake the resolution of racemates. The key to the matter is supersaturation and the seeding of the crystallization solution. Although the effect was first mentioned in a very succinct letter to Louis Pasteur by one of his PhD students, we prefer to give a brief account of Alfred Werner's rediscovery and use of the phenomenon. Werner had synthesised a chiral complex of cobalt which did not racemize in solution. His initial product contained about 60% of the D enantiomer and 40% of the L. Taking this product into concentrated supersaturated solution, lowering the temperature and halting the crystallization at the appropriate moment, he obtained crystals of the enantiopure D. The real surprise was the composition of the remaining product in solution. This turned out to be 40% D and 60% L, the exact opposite of the starting solution. Werner had only to filter off his pure D, concentrate the remaining solution and recommence the crystallization. The second crop of crystals was, of course, the enantiopure L compound.

It is difficult, if not impossible, to ascertain the frequency of spontaneous resolution by crystallization to give a racemic conglomerate, because the chemical history of the sample and the enantiopurity of the starting materials for crystal formation and growth are seldom or never mentioned by the authors of crystallographic papers. A source of potentially extremely useful chemical information is thus lost. It is most useful to characterise both the bulk compound and the single crystal used for the diffraction studies by measurement of the optical activity, circular dichroism or enantioselective chromatography.

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Next: Polymorphism Up: (IUCr) Crystal Packing Previous: Crystal-structure descriptors

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