Anomalous dispersion of X-rays

Single crystals of ferroelectric TGS grown from solution generally contain domains of the two enantiomorphous phases (110). This juxtaposition of enantiomorphous domains may be explained in terms of the minor deviations of the crystal structure from a centrosymmetric arrangement. The relative concentrations of the two enantiomorphous phases in a single crystal may be determined by means of anomalous dispersion of X-rays (111,112). 

Determination of Absolute Configuration 4.2.2.1. Based on Anomalous Dispersion of X-rays Introduction... 

The discovery by Bijvoet (22) of the method of anomalous dispersion of X-rays gave a means of establishing the absolute configurations of particular enantiomers, and, in 1955, the first report of the absolute stereochemistry of an octahedral complex appeared. This concerned the important ion (+)-[Co(en)3]3+ which had the configuration (10) shown in (II). 

The experimental method used to determine the chirality or absolute structure of a molecule or crystal structure involves the use of the anomalous dispersion of X-rays by one or more atoms in the structure. We will now describe this effect and how Bijvoet used it to determine the absolute configuration of (-l-)-tartaric acid from the differences in the intensities of the hkl and iM Bragg reflections. 

During 1972-3 great concern was felt regarding the correctness of results based on the Bijvoet method of anomalous dispersion of X-rays. Calculations by Tanaka and his co-workers (Chimia, 1972, 26, 271 Chem. Comm., 1973, 21, 22) appeared to indicate a contradiction between Bijvoet determinations for some compounds and ab initio calculations of the absolute configurations of the same compounds based on chiroptical measurements. This was taken as an indication that the Bijvoet treatment was giving the wrong answer. 

Patterson, A. L. Treatment of anomalous dispersion in X-ray diffraction data. Acta Cryst. 16, 1255-1256 (1963). 

Table 1. Correction Terms Af and Af" for Anomalous Dispersion of Some Elements, Which Commonly Occur in Organic Compounds, at Three X-ray Wavelengths25...

PROBLEM 11.23.2 The Bragg reflections are symmetrical to reflection and transmission. However, Bijvoet showed that if there is "anomalous dispersion"—that is, a small amount of X-ray absorption (usually due to elements with high atomic number (Z > 60)—then asymmetry occurs, and this facilitates structure solution. 

Centrosymmetric crystal structure A crystal structure whose space group, and therefore arrangement of atoms, contains a center of symmetry. When the origin of the unit cell is at a center of symmetry, the relative phase angle for each Bragg reflection is either 0° or 180° in the absence of X-ray anomalous dispersion. 

The X-ray study was extended to a determination of absolute configuration. The problem of the phase angle was solved by the Bijvoet method taking advantage of the anomalous dispersion of copper radiation... 

Because part of the anomalous dispersion component is jt/2 out of phase with the isomorphous, real component, the net observable effect is a breakdown of Friedel s law regarding the perfect equality of the magnitudes of and If-h-k-i- That is, the two need not be absolutely equivalent but can demonstrate some slight difference A I anom = fhki — f-h-k-i- This difference will normally be imperceptible and within the expected statistical error of most X-ray diffraction intensity measurements, but with care in data collection, and judicious choice of X-ray wavelength, it can be measured and used to obtain phase information in conjunction with isomorphous replacement phase determination, or even independently, as described in Chapter 8. 

In the case of x-ray diffraction, important advances include the use of robotics to ensure successful growth of crystals, the development of synchrotron sources for macromolecular crystallography, the use of direct methods and anomalous dispersion in phasing, and the development of automated methods of map htting. 

The high brilliance at ultra-short wavelengths (0.15 A) of the higher harmonics from X-ray undulators would allow X-ray diffraction from macromolecular crystals totally free of absorption errors whilst stimulating the K edge anomalous dispersion of high atomic number elements (e.g. mercury, platinum, etc). 

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