Enantiomers homochirality classes

Finally, reference must be made to the important and interesting chiral crystal structures. There are two classes of symmetry elements those, such as inversion centers and mirror planes, that can interrelate. enantiomeric chiral molecules, and those, like rotation axes, that cannot. If the space group of the crystal is one that has only symmetry elements of the latter type, then the structure is a chiral one and all the constituent molecules are homochiral the dissymmetry of the molecules may be difficult to detect but, in principle, it is present. In general, if one enantiomer of a chiral compound is crystallized, it must form a chiral structure. A racemic mixture may crystallize as a racemic compound, or it may spontaneously resolve to give separate crystals of each enantiomer. The chemical consequences of an achiral substance crystallizing in a homochiral molecular assembly are perhaps the most intriguing of the stereochemical aspects of solid-state chemistry. 

Racemic acid has now been shown to consist of an equimolar mixture of (A,A)-tartaric acid and the unnatural (A S)-enantiomer and is obtained as a monohydrate species. The compound crystallizes in the triclinic class (space group PI), with the unit cell consisting of one molecule of (i ,i )-tartaric acid, one molecule of (A S)-tartaric acid, and two water molecules [26], This heterochiral unit cell is significantly different from the homochiral unit cell a = 8.06 A, b = 9.60 A, c = 4.85 A, a = 70.4°, P = 97.2°, and y = 112.5°. The unit cell of racemic acid contains a center of symmetry, while that of tartaric acid does not. 

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