Hemihedral faces

Crystals composed of the R and S enantiomers of the same racemic mixture must be related by mirror symmetry in terms of both their internal structure and external shape. Enantiomorphous crystals may be sorted visually only if the crystals develop recognizable hemihedral faces. [Opposite (hid) and (hkl) crystal faces are hemihedral if their surface structures are not related to each other by symmetry other than translation, in which case the crystal structure is polar along a vector joining the two faces. Under such circumstances the hemihedral (hkl) and (hkl) faces may not be morphologically equivalent.] It is well known that Pasteur s discovery of enantiomorphism through die asymmetric shape of die crystals of racemic sodium ammonium tartrate was due in part to a confluence of favorable circumstances. In the cold climate of Paris, Pasteur obtained crystals in the form of conglomerates. These crystals were large and exhibited easily seen hemihedral faces. In contrast, at temperatures above 27°C sodium ammonium tartrate forms a racemic compound. 

An equimolar mixture of two enantiomers is called a racemate. The separation of two enantiomers that constitute a racemate is called optical resolution or resolution. Their crystalline forms best characterize types of racemates. A racemic mixture is a crystal where two enantiomers are present in equal amounts. A conglomerate is a case where each enantiomer has its own crystalline form. Sometimes their crystals have so-called hemihedral faces, which differentiate left and right crystals. For over a hundred years, crystallization processes have been used for the separation and purification of isomers and optical resolution, both in the laboratory and on an industrial scale. 

In general, however, the occurence of spontaneous resolution of racemate is rare. Moreover cases in which the crystals of the enantiomers have visually distinct hemihedral face are extremely rare. 

G. B. Kauffman and I. Bernal, Alfred Werner s awareness of spontaneous resolutions and the meaning of hemihedral faces in optically active crystals , Structural Chem., 1993, 4 (2), 131-138. 

The first method of enantiomeric separation by direct crystallization is the mechanical technique use by Pasteur, where he separated the enan-tiomorphic crystals that were simultaneously formed while the residual mother liquor remained racemic. Enantiomer separation by this particular method can be extremely time consuming, and not possible to perform unless the crystals form with recognizable chiral features (such as well-defined hemihedral faces). Nevertheless, this procedure can be a useful means to obtain the first seed crystals required for a scale-up of a direct crystallization resolution process. When a particular system has been shown to be a conglomerate, and the crystals are not sufficiently distinct so as to be separated, polarimetry or circular dichroism spectroscopy can often be used to establish the chirality of the enantiomeric solids. 

Compounds that are optically active often form crystals with hemihedral faces. 

FIGURE 14.14. (a) Hemihedral faces (shaded) of sodium ammonium tartrate compared (b) with the holohedral faces (shaded) of the racemate. The hemihedral faces in (a) were used by Peisteur to separate left-handed and right-handed crystals. 

When the absolute structure has been determined, the result must be correlated with some physical property of the crystal, otherwise the result has no use to the chemist. The obvious correlation is with the direction of rotation of the plane of plane-polarized light, that is, whether the compound or crystal is dextrorotatory or levorotatory. Another correlation can be made with crystal appearance this was shown for zinc blende with its matte and shiny faces, and for silica and sodium ammonium tartrate crystals for the disposition of their hemihedral faces. If such data are not available, it may be necessary to list physical properties of diastereomers made with chiral complexing agents. Then, whenever this same compound is encountered by a chemist, its absolute structure is well known. 

It crystallizes in anhydrous tables belonging to the monoclinic system, with hemihedral faces. The shape of... 

Even in the case of crystalline substances, where the differences between the various forms are greater, it is not always easy to discriminate between the /-mixture and the racemic compound. The occurrence of hemihedral faces was considered by Pasteur to be a sufficient criterion for an optically active substance. It has, however, been found that hemihedry in crystals, although a frequent accompaniment of optical activity, is by no means a necessary or constant expression of this property. Other rules, also, which were given, although in some cases reliable, were in other cases insufficient and all were in so far unsatisfactory that they lacked a theoretical basis. 

It was the observation of the hemihedral crystals of sodium ammonium tartrate tetrahydrate that enabled Pasteur (1822-1895) to make a decisive step forward in stereochemistry. The problem he encountered was the contamination of the potassium salt of tartaric acid with that of another acid (which Gay-Lussac (1778-1850) called the racemic acid) that made it unsuitable for commercial use. The two acids had the same chemical composition, and Biot showed that whereas tartaric acid and its salts could rotate the plane of polarized light, the racemic acid itself was inactive. In 1848, Pastern-found the solution to this problem.He noticed that crystals of tartaric acid, like its salts, have hemihedral faces, but that the racemic sodium ammonium tartrate exists as two distinct crystals in which the hemihedral faces are mirror images of each other. One of these crystalline forms is identical to the optically active tartrate. In solution, it rotates the plane of polarized light in a dextrorotatory manner, while the other form (a mirror image of the first) is levorotatory, that is in solution it rotates the plane of polarization towards the left (Figure 2.5). 

Pasteur was convinced that there must be some molecular difference between the two salts, and he made the problem the subject of his first major piece of research. He prepared several salts of tartaric acid and found that in all cases the crystals were asymmetric (Pasteur used the term dissymmetric), and displayed hemihedral faces. Pasteur was tempted to speculate that such asymmetric crystals were typical of optically active materials, and were the manifestation of asymmetry of the molecules. He then found that crystals of the optically inactive sodium ammonium paratartrate also displayed hemihedral faces, but on careful examination he saw that two types of crystal were present, one the mirror image of the other (Figure 10.13). He carefully sorted some of the crystals by hand. Those with right-handed hemihedry gave a solution which was dextrorotatory and identical with a solution of sodium ammonium tartrate. A solution of equal concentration of the crystals with left-handed hemihedry rotated polarised light to an equal extent in the opposite direction. A solution of equal concentrations of each crystalline form was optically inactive. Pasteur thereby demonstrated that paratartaric acid was... 

Figure 10.13 The two mirror image crystals formed by sodium ammonium paratartrate. The hemihedral faces are labelled a and b...

After the recognition of chirality in molecules by Biot, the direct assignment of the absolute configuration of a chiral molecule in a chiral crystal which develops hemihedral faces has challenged the chemical crystallographer. 

In 1949 Waser [23a] tried to establish the absolute configuration of (D) - tartaric acid by correlating the relative rates of growth of the hemihedral (hkl) and (hkl) faces with the ease of attachment of the free molecule at either face in terms of intermolecular distances between the crystal and the molecule to be attached. In fact, as Turner and Lonsdale pointed out [23b], given an asymmetric molecule X-A in a polar crystal, as in Scheme 4, there is no a priori reason why, on the basis of intermolecular distances only, the attachment of an X to an A face should take place more readily than that of an A to an X face . The observed differences in development of hemihedral faces may be explained primarily in terms of surface-solvent interactions or polarizability effects. 

Crystals belonging to one of the chiral space groups appear in enantiomorphic forms. The enantiomorphous crystals in some systems may be distinguished by their hemihedral faces, if these are well developed, as in the classic experiment of Pasteur on the resolution of ammonium tartrate. Other methods which can be used for distinguishing between enantiomorphous crystals include anomalous X-ray scattering, etching techniques, and gas-solid reactions with chiral gases [28]. 

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