Anomalous scattering groups

Structure of the MoFe Protein. Extensive spectroscopic studies of the MoEe proteia, the appHcation of cluster extmsion techniques (84,151), x-ray anomalous scattering, and x-ray diffraction (10,135—137,152) have shown that the MoEe proteia contains two types of prosthetic groups, ie, protein-bound metal clusters, each of which contains about 50% of the Ee and content. Sixteen of the 30 Ee atoms and 14—16 of the 32—34... 

X-ray crystallographic analysis also revealed that the crystal of thioamide la was chiral, the space group P2i2i2i. The absolute configuration of (-)-rotatory crystals of la, where the optical rotation was assigned on the basis of CD spectra in a KBr pellet, was determined by the X-ray anomalous scattering method as (-)-(M)-la for the helicity. When (-)-rotatory crystals were irradiated at 0 °C until the reaction conversion reached 100% yield, the asymmetric induction in... 

However, FriedeFs law no longer holds if a compound containing an anomalous scatterer, besides other elements, crystallizes in a non-centrosymmetric space group then the following inequalities between Friedel pairs apply ... 

If, for a set of reflections hkl, the Friedel opposites, or any other reflections equivalent by point group symmetry, have not been measured, a determination of absolute configuration can be attempted using the following method. The structure refinement (including anomalous scattering) is carried out separately for the two enantiomorphic models (one obtained from the other... 

X-ray crystallographic analysis revealed that the crystals of thioamide 32b are chiral and the space group is P2 L lx. Dextrorotatory crystals were irradiated at 0°C until the reaction conversion reached 81 % yield. As expected, the asymmetric induction was observed, and optically active 33b (55% ee) was isolated (Table 5). As a consequence of the suppression of the reaction conversion yield from 81% to 17%, the enantiomeric purity rose up to 74% ee. p-Thiolactam 33b with only Z-configuration was isolated, and the absolute configuration of ( + )-33b was determined as (3S,4S)-isomer by the x ray anomalous scattering method. 

The structure of Ca ascorbate dihydrate was simultaneously determined by two independent groups (12,13), and their data and results were subsequently compared and analyzed by Abrahams et al. (14). Some general conclusions could be drawn from this investigation with respect to the given values of standard deviations, to the effect of anomalous scattering on atomic coordinates, and to the absolute configuration of the molecule in question. 

When the anomalous scattering is present, the structure amplitude even for a centrosymmetric crystal becomes a complex number. This is shown in Eqs. 2.107 and 2.108. The first (general expression) is easily derived by combining Eqs. 2,101 and 2.103 and rearranging it to group both the real and imaginary components. 

Excellent and detailed treatments of the use of anomalous dispersion data in the deduction of phase information can be found elsewhere (Smith et al., 2001), and no attempt will be made to duplicate them here. The methodology and underlying principles are not unlike those for conventional isomorphous replacement based on heavy atom substitution. Here, however, the anomalous scatterers may be an integral part of the macromolecule sulfurs (or selenium atoms incorporated in place of sulfurs), the iron in heme groups, Ca++, Zn++, and so on. Anomalous scatterers can also be incorporated by diffusion into the crystals or by chemical means. With anomalous dispersion techniques, however, all data necessary for phase determination are collected from a single crystal (but at different wavelengths) hence non-isomorphism is less of a problem. 

Resolution of the Difficulty Some years earlier we4 had added anomalous scattering terms to the usual least squares program. In 1966 the polar dispersion error was discovered.5 When the above problem came to our attention, we felt that the difficulty might be in an incorrect space group determination. Ensuing calculations using our modified least squares program quickly revealed that the difficulty arose from the... 

Because of anomalous scattering by H, the results for the as-precipitated Ni(OH)2 could not be refined. Nevertheless, cell constants and the O-H bond distance could be determined. The results showed that the as-precipitated material was different from the well-crystaUized material. The unit cell dimensions were ao = 3.119 A and Co = 4.686 A. Also the O-H bond length was 1.08 A, a value similar to that previously reported by Szytula et al. in a neutron diffraction study of Ni(OH)2 [23]. The O-H bond in both well-crystalhzed and as-precipitated materials is parallel to the c-axis. The difference between wellelectrochemically active. The differences between the materials are attributed to a defective structure that arises from the large concentration of surface OH ion groups in the high-surface-area material [22]. These are associated with absorbed water. This is a consistent with an absorption band in the infrared at 1630 cm . This is not seen in the well-crystallized material. 

While it is very easy, when one knows the structure of the crystal and the wavelength of the rays, to predict the diffraction pattern, it is quite another matter to deduce the crystal structure in all Its details from the observed pattern and the known wavelength. The first step is lo determine the spacing of the atomic planes from the Bragg equation, and hence the dimensions of the unit cell. Any special symmetry of the space group of the structure will be apparent from space group extinction. A Irial analysis may (hen solve the structure, or it may be necessary to measure the structure factors and try to find the phases or a Fourier synthesis. Various techniques can be used, such as the F2 series, the heavy atom, the isomorphous series, anomalous atomic scattering, expansion of the crystal and other methods. 

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