Noncentrosymmetric space groups

The compounds crystallise in noncentrosymmetric space groups namely PI, P2i, C2, and P2i2i2i (but with priority of P2i) due to the chirality of the molecules. Most of the compounds have a tilted layer structure in the crystalline state. The tilt angle of the long molecular axes with respect to the layer normal in the crystal phase of the compounds is also presented in Table 18. Some compounds show larger tilt angles in the crystalline state than in the smectic phase. In the following only the crystal structures of some selected chiral liquid crystals will be discussed. 

The presence of a polar axis confers anisotropic activity to organic crystals (Curtin Paul, 1981 Desiraju, 1984b). Common polar (noncentrosymmetric) space groups adopted by organic crystals areP2i2i2i and P2i- While chiral crystals must have polar directions, polar crystals need not be chiral. Anisotropic reactivity is seen for instance in the reaction of ammonia with p-bromobenzoic anhydride, which crystallizes with a polar axis the polar axis directs the reaction, p-bromobenzoic anhydride is chiral as well as polar. Chirality of the crystalline anhydride has been exploited to resolve a racemic gaseous amine the chiral crystal preferentially reacts with one of the enantiomers of the amine. Thus when p-bromobenzoic anhydride crystals are exposed to vapours of racemic phenylethylamine, the resulting amide contains one of the enantiomers in excess. 

In the case of a-oxoamides 22, meta-substituted amides exhibit a relatively high tendency of crystallization with the chiral framework [19c]. If both observations that meta-substituted arenes prefer to crystallize in noncentrosymmetric space groups, in comparison to the ortho- and para-isomers, have some generality, then meta-substitution in an achiral compound could be an important structural... 

Jamine is most unusual in that it occurs as a racemate in Ormosia jamaicensis. Recently, jamine isolated from Ormosia costulata was found crystallized in a noncentrosymmetric space group, Pll2l2l, where it necessarily must be optically active. The structure determination (19) yielded a molecule identical to that found in the earlier publication (18). 

For noncentrosymmetric space groups, the point with the highest site symmetry and lowest multiplicity is chosen as the origin. This means that either the Ti atom or the Ca atom could be chosen as the origin since they both have the same multiplicity (one-fold) and site symmetry m3m). However, it is important to note that the Ca and Ti atom are not at the same position. The Bravais lattice is primitive, as indicated by the space group symbol. Therefore, if we allow the Ti atom positions to coincide with lattice points, the Ca atoms and O atoms cannot. 

The summation over 5 (n = 2 in the case of the example) indicates the importance of orientation in the unit cell on the magnitude of x Even large values of P in noncentrosymmetric space groups can result in small values of x depending on the details of orientation. Oudar and Zyss (25, 26) have analyzed the orientational dependence of molecules in all the polar crystallographic point groups. The maximum value of x that can be obtained for a properly phase matched interaction for optimal molecular orientation in that space group is listed in Table 6.3. The values are relative to an... 

Optical activity The crystal must belong to a noncentrosymmetric space group. 

Pyroelectricity The observation of a pyroelectric effect implies a noncentrosymmetric space group. It can only exist if there is a unique polar axis in the point group of the crystal. If no effect is observed, it is presumed (but not certain ) that the crystal possesses a center of symmetry. 

It has already been pointed out that the test for noncentrosymmetric space groups will not tell if a molecule is chiral or not, only that if the space group is centrosymmetric the molecule cannot be chiral. If, however, the molecule is chiral and only one enantiomer is present in the crystal, then anomalous dispersion can be used to determine which enantiomer is present. 

An example of tests for chirality is provided by studies of mandelic acid crystals (Figure 14.23). These crystals are polar and noncentrosymmetric, space group T 2i, but no hemihedral faees develop and therefore there are no external indications that allow one to distinguish the two ends of its polar axis b. Other techniques have to be used. In order to differentiate between the two ends of the hexagonally-shaped crystals (which were shown, by X-ray diffraction studies to have the c axis along the unique axis of the crystal). The directions of the a and b axes with respect to crystal habit were also established by X-ray diffraction studies. 

A series of N-salicylidene aniline (SA) derivatives (Figure 10.10) have been investigated for their photochromic and NLO properties. For many years, scientists have known of the photochromism of some of these molecules in the crystalline state, Among them, those that crystallize in a noncentrosymmetric space group were selected, and the NLO properties of the most stable isomer (usually OH ) were studied by SHG, along with the effect of photochromism on this property. ... 

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