Space groups enantiomorphic

In literature, SOHNCKE space-group types are often termed chiral space groups , which is not correct. Most chiral molecular compounds do not crystallize in a chiral (enantiomorphic) space group. For details see [86]. 

Finally, one should be cautioned that, occasionally, substances form chiral single crystals of nearly racemic composition. For example, hexahelicene crystals grown from racemic solutions apparently undergo spontaneous resolution, displaying the enantiomorphic space group P2[2,2, however, the e.e. in the crystal is only —2%. This material (and probably others as well) has a lamellar, twinned structure in which alternating layers, 20 p,m thick, of optically pure (/ )-( + )-and (M)-( — )-hexahelicene are perfectly aligned to build up the observed crystal (266). 

While a collection of molecules that are all of the same chirality (e.g., a D- or L-amino acid or a naturally occurring protein) must form a chiral crystal, inherently nonchiral molecules are not barred from doing so, if they crystallize in one of the 11 pairs of enantiomorphous space groups. In that event, which is rather rare, there will, of course, be an equal probability of forming either enantiomorph and a batch of crystals will normally contain both. A couple of real examples are (NH4)3Tc2C18 3H20 (P3,21 and P3 >21) and SntTa Cl (P6 22 and P6522). 

The next step is for a protein crystallographer to mount a small perfect crystal in a closed silica capillary tube and to use an X-ray camera to record diffraction patterns such as that in Fig. 3-20. These patterns indicate how perfectly the crystal is formed and how well it diffracts X-rays. The patterns are also used to calculate the dimensions of the unit cell and to assign the crystal to one of the seven crystal systems and one of the 65 enantiomorphic space groups. This provides important information about the relationship of one molecule to another within the unit cell of the crystal. The unit cell (Fig. 3-21) is a parallelopiped... 

Optical Networks crystallize in chiral (enantiomorphic) space groups and can therefore be related to homochiral compounds. 

Some space groups are enantiomers of others. There are 11 such pairs, listed in Table 4.6 (Chapter 4) and Table 14.2. If the (+) isomer of a chiral molecule crystallizes in one of these space groups, the (-) isomer will crystallize in the enantiomorphous space group. The systematic absences in the Bragg reflections are the same for both members of these pairs of space groups, but anomalous dispersion can aid in distinguishing between them. Several proteins have crystallized in enantiomorphous space groups. 

In a few cases, the space group cannot be determined uniquely from the symmetry of the reciprocal lattice and the systematic absences. In these cases, however, only a choice between two specific possibilities remains. The two choices are usually enantiomorphic space groups, such as P6 and P65. 

Similarly, the symmetry of the mixed crystal system composed of (E)-cin-namamide (host) and (E)-2-thienylacrylamide (guest, 8% occluded) is lower than that of the host crystal (P2j/c). The selective occlusion of the guest arises from repulsive sulfur- n interactions. The -l-b end and the -b end of the mixed crystal are enantiomorphic (space group PI) and underwent topochemical [2-1-2] photodimerization in 40-69% enantiomeric excess (Scheme 8) [29]. 

For intrinsically chiral species that are inert enough to be resolved conventionally, the measurement of natural optical activity in crystals has the same advantages as single crystal absorption measurements. In addition, however, it also affords the opportunity to determine rotational strengths of species which do not exhibit optical activity in solution. There are two classes of such materials 1) intrinsically achiral chromophores which crystallize in enantiomorphous space groups, and 2) intrinsically chiral but labile chromophores which spontaneously resolve on crystallization. 

The enantiomorphs of a nonplanar disulfide sometimes become separated in crystals. Thus, diphenyl disulfide (43) and probably also di-p-tolyl disulfide (43) crystallize in enantiomorphous space groups with only one enantiomorph per unit cell, and so do barium tetrasulfide monohydrate (1) and sodium tetrathionate dihydrate (101). The same applies, of course, to L-cystine and other optically active disulfides. 

Rikken proposed that the EMCA effect could also result from the simultaneous application of a magnetic field and a current to a crystal with an enantiomorphous space group, and that it is a universal property. He showed the existence of this effect in the case of chiral single-walled carbon nanotubes.For most of the investigated tubes, a dependence of the resistance is observed that is odd in both the magnetic field and the current. These observations confirm the existence of EMCA not only for a macroscopic chiral conductor but also for a molecular conductor with chirality on the microscopic level. 

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