Atoms 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. 

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). 

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... 

Cocrystallization of chiral molecules with molecules carrying heavy atoms (to exploit anomalous dispersion effects) resnlting in mnlticomponent crystals has proven useful to enable the determination of absolute structure via crystallographic studies, obviating the need to form a heavy atom salt or for chemical derivatization. In a case study, Bhatt and Desiraju demonstrated the ntility of this approach by, for example, forming multicomponent crystals comprising cholesterol and 4-iodophenol. ... 

The results of this analysis show that anomalous dispersion of light in a cesium cell is a consequence of superluminal motion of electrons and superluminal propagation of electromagnetic waves. The Feynman diagram, presented in Fig. 8, is used in the analysis, to explain the phenomena that are taking place in cesium atomic cell and that cause superluminal effects [30]. 

The results of the analysis presented here, based on the concepts of the theory of superluminal relativity [5], show that in the superluminal experiment performed by Wang et al. [6,7] the main phenomenon is distortion of curved spacetime [16] around cesium atoms, which produces superluminal processes, and the final effect is anomalous dispersion of light [30]. 

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. 

Strictly, the scattering factors / tabulated in Appendix 12 apply only when the scattered radiation has a wavelength much shorter than that of an absorption edge of the scattering atom. When these two wavelengths are nearly the same, a small correction to /must be applied in precise work. An example is given in Sec. 13-4. Ordinarily we neglect this effect, called anomalous dispersion. 

In the past 10 years, anomalous dispersion (AD) effects have been used more and more frequently to solve the phase problem. All elements display an AD effect in x-ray diffraction. However, the elements in the first and second row of the periodic table, for example, C, N, O, and so on, have negligible AD effects. For heavier elements, especially when the x-ray wavelength approaches an atomic absorption edge of the element, these AD effects can be very large. The scattering power of an atom exhibiting AD effects is... 

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