Noncentrosymmetric crystallization

Optical second-harmonic generation (SHG) has recently emerged as a powerful surface probe [95, 96]. Second harmonic generation has long been used to produce frequency doublers from noncentrosymmetric crystals. As a surface probe, SHG can be caused by the break in symmetry at the interface between two centrosymmetric media. A high-powered pulsed laser is focused at an angle of incidence from 30 to 70° onto the sample at a power density of 10 to 10 W/cm. The harmonic is observed in reflection or transmission at twice the incident frequency with a photomultiplier tube. 

The EFISHG technique has also been applied to some pyridyl carbonyls of Rh1 or Ir1 by Bruce et al72,13 These complexes (e.g., (9) and (10)) contain stilbazole ligands bearing resolved 2-methylbutyloxy substituents, incorporated with the aim of encouraging noncentrosymmetric crystal packing structures. The observed 1.5- to 3-fold enhancements of (3 of the free stilbazole on complexation are attributable to the er-electron-withdrawing abilities of the metal centers.72,73... 

Figure 6. Classification of the noncentrosymmetric crystal point groups by decreasing value of the maximal efficient phase-matchable nonlinear coefficient per molecule...

Karle, J. and Karle, I.L. (1966). The symbolic addition procedure for phase determination for centrosymmetric and noncentrosymmetric crystals Acto Cryst 21, 849-859. 

Following the experimental results of Werner and his colleagues, a number of theoretical attempts were made to correlate the sign and magnitude of the optical rotation to the exact chiral molecular structure of metal complexes. These approaches have been summarized by Richardson.3 The term absolute structure is sometimes limited to a discussion of the structure of noncentrosymmetric crystals, and the term... 

A unique contribution of X-ray analysis to stereochemistry is the ability to determine directly the absolute configuration of a molecule providing that in the noncentrosymmetric crystal there is an atom present that scatters X rays anomalously (20,21). Actually, all atoms scatter X rays anomalously, but the effect is much more noticeable and more easily measured for the... 

Noncentrosymmetric crystals may generate measurable anisotropic electrical effects in response to external forces snch as temperatnre changes... 

Second harmonic generation has been used as a test for a noncentrosymmetric crystal.An example is provided by 9-methyl-lO-chloro-methylanthracene which crystallizes with disorder in the positions of the methyl and chloromethyl group and therefore it was not clear whether the space group was centrosymmetric or noncentrosymmetric. The measurement of a strong second harmonic confirmed the latter choice. 

Piezoelectric effect The generation of a small potential difference across certain crystals when they are subjected to stress (direct effect), or the change in shape of a crystal that accompanies the application of a potential difference across a crystal (inverse effect). The piezoelectric effect is only shown by noncentrosymmetric crystals. 

In 1951, Johannes Martin Bijvoet used such differences in intensity, resulting from anomalous scattering by an atom in a noncentrosymmetric crystal, to determine the chirality (absolute configuration) of the tartrate ion. Details of this method, which has been used extensively for finding the absolute configurations of natural products and for determining macromolecular structures, are given in Chapter 14. 

FIGURE 8.5. (a) The probability P E) of iJ having certain values depends on whether the structure is centrosymmetric (solid line) or noncentrosymmetric (broken line). Thus, if values are known, a plot of the number with different ranges of I E I will indicate the centrosymmetry (or lack of it) in the crystal structure, (b) The cumulative distribution curves for centrosymmetric and noncentrosymmetric crystals N Z) is the fraction of Bragg reflections with intensities (or E p values) less than or equal to Z times the mean intensity. 

FIGURE 8.28. Multiple Bragg reflections. Shown are four idealized V scans (in degrees), and the values of Osum derived from the peak profile, (a) -90°, (b) 0°, (c) -(-90°, and (d) 180°. Values intermediate between these relative phase angles these can be measured for noncentrosymmetric crystals. 

Karle, J., and Hauptman, H. The probability distribution of the magnitude of a structure factor. I. The centrosymmetric crystal. II. The noncentrosymmetric crystal. Acta Cryst. 6, 131-135 (1953). 

---