Anomalous Dispersion Effects

The anomalous components of the total scattering are wavelength dependent and the use of radiation close to an absorption edge may increase or optimise the contribution due to the anomalously scattering atoms. Ramaseshan (1962) pointed out that data collected at multiple wavelengths optimising the anomalous dispersion effects would improve the quality of phase determination. 

The anomalous dispersion effects do not alter the validity of FriedeFs law (equations 7 and 8), if... 

Our IBM 7040 least-squares programme was modified to cope with this situation. After several cycles of refinement of the gold atomic parameter, a c-axis difference electron-density projection was computed. On the resulting map it WM possible to locate the fluorine atoms there are only two independent fluorines, one in the general position x, y, z), 12(c), and the other in the special position (J, 0, 0), 6(o). Structure factors were calculated by use of the scattering factors of the International Tables for Au and F, that for gold being corrected for the real part of the anomalous dispersion effect B was taken as 2-0 A. ... 

Anomalous X-ray dispersion effects will cause intensity differences if the structure is noncentrosymmetric and contains an atom that scatters anomalously. Friedel s Law, which states that the X-ray diffraction pattern of a crystal is centrosymmetric even if the crystal structure is not, will not be obeyed. This means that, in the presence of anomalous dispersion effects, I hkl) If the structure is... 

To determine the absolute configuration of optically active organic compounds, there are two nonempirical methods. One is the Bijvoet method in the X-ray crystallographic structure analysis, which is based on the anomalous dispersion effect of heavy atoms. - The X-ray Bijvoet method has been extensively applied to various chiral organic compounds since Bijvoet first succeeded in determination of the absolute stereochemistry of tartaric acid in 1951. The second method is a newer one based on the circular dichroism (CD) spectroscopy. Harada and Nakanishi have developed the CD dibenzoate chirality rule, a powerful method for determination of the absolute configuration of glycols, which was later generalized as the CD exciton chirality method. 8 The absolute stereochemistry of various natural products has been determined by application of this nonempirical method. 

It is well known that the absolute configuration of chiral compounds was first determined by the Bijvoet using X-ray crystallography [1]. In X-ray crystallography, since the anomalous dispersion effect of heavy atoms can be measured accurately under proper conditions, the absolute stereostructure obtained is unambiguous and reliable. In addition, the molecule can be projected as a three-dimensional structure, and, therefore, the method has been employed extensively. However,... 

Despite repeated recrystallizations, both diastereomers 43a and 43b were obtained only as amorphous solids. Therefore, the first-eluted fraction (-)-43a was reduced with LiAlH4 to yield enantiopure glycol (-)-42, which was further converted to 4-bromobenzoate (-)-44 (Fig. 9.7a). By recrystallization from EtOH, (-)-44 gave good single crystals suitable for X-ray analysis, and consequently its absolute configuration was explicitly determined as S by the Bijvoet pair measurement of the anomalous dispersion effect of the bromine atom contained (Fig. 9.7b) [40]. 

As in the case of LAXS measurements, the anomalous dispersion effects, arising when the energy is closed to the absorption edge, can be used with the SAXS technique. FONTAINE did ASAXS experiments, at LURE-DCl, to probe the distribution of Zn atoms in phase separated Ai—Zn alloys He measured the variation of SAXS from Guinier-Preston zones when the energy is scanned below the Zn absorption edge (Fig. 5). 

Anomalous dispersion effects have been used for a considerable time, to some extent, in crystal structure analyses. In combination with a tunable synchrotron X-ray source there is considerable scope for a dramatically increased use and benefit of these small but significant effects. 

The anomalous dispersion effect is associated with the ejection of photoelectrons from inner shell electrons in an atom. The normal scattering describes the interaction of all the electrons in the atom with the X-ray beam. The radial distribution of the electrons in an atom can be calculated using quantum mechanics, originally by Hartree s self-consistent field method (Hartree 1933). In figure 9.12 this distribution is given for rubidium, which has a K edge at 0.8155 A the mean radius for... 

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