Anomalous scattering factors

P212121 Z = 4 D = 2.01 R = 0.04 for 1,611 intensities. The compound is a minor product in the synthesis of methyl tyveloside. The pyranose conformation is a distorted 4, with Q = 66 pm 6= 162° (p=H8a. The (methylthio)carbonyl side-chain is extended. The C-S bond-lengths are 174.8, 179.1 pm. The C-I bond-length is 215.2 pm. The absolute configuration was confirmed by using the anomalous-scattering factors of the iodine atoms. 

Cromer, D. T. and Lieberman, D. (1970). Relativistic calculation of anomalous scattering factors for X-rays. /. Chemical Physics 53, 1891-1898. 

Evans, G. and Pettifer, R. E (2001). CHOOCH A program for deriving anomalous scattering factors from X-ray flourescence spectra. /. Appl. Crystallogr. 34,82-86. 

As is evident from Eqs. (1.36) and (1.37), and from the classical treatment as well, the effect of resonance on the intensity of X-ray scattering is pronounced when E E0, that is, in the vicinity of the absorption edges. Even for data collected at other wavelengths, it is necessary to correct the structure factors for anomalous scattering before the electron density can be calculated by the Fourier inversions of Eqs. (1.22) and (1.26), as further discussed in chapter 5. The anomalous scattering factors needed for this purpose are available in the literature (International Tables for X-ray Crystallography 1974, Kissel and Pratt 1990). 

Cromer, D. T. Calculation of anomalous scattering factors at arbitrary wavelengths. J. Appl. Cryst. 16, 437 (1983). 

A/" and are the real and imaginary components, respectively, of the anomalous scattering factor and they depend on both the atom type and the wavelength. 

Figure9.17 Selenobiotinyl streptavidin study, (a) Anisotropy in anomalous scattering factors for selenium. A-C spectra (thick lines) measured with the electric vector E parallel with crystal axes a, b and c respectively. Theoretical values for elemental selenium are shown as thin lines. Values off"...

D. T. Cromer and D. Liberman, Relativistic Calculation of Anomalous Scattering Factors for X-rays, Los Alamos Scientific Laboratory, LA 4403 TID 4500, July 1970. 

Measurement of X-ray absorption can be used to obtain the anomalous scattering factors. The spectrum of atomic absorption coefficients /r( ), as a function of energy, E, is related directly to the imaginary component of anomalous scattering ... 

However, if a heavy atom is contained in the molecule, equation (2) does not hold because of the anomalous scattering effect of the heavy atom. Namely if the anomalous scattering factor A/" takes a nonzero value, the intensities... 

FIGURE 55.2. Anomalous scattering factor A/ of heavy atoms found in organic molecules, where bold values are for Cu Ka and nonbold for Mo Ka. 

A teclmique that employs principles similar to those of isomorphous replacement is multiple-wavelength anomalous diffraction (MAD) [27]. The expression for the atomic scattering factor in equation (B1.8.2h) is strictly accurate only if the x-ray wavelength is well away from any characteristic absorption edge of the element, in which case the atomic scattering factor is real and Filiki) = Fthkl V- Since the diffracted... 

Atomic scattering factors corrected for anomalous dispersions were obtained from Cromer and Waber and Cromer and Liberman... 

Blessing, R. H. and Smith, G. D. (1999). Difference stmcture-factor normalization for heavy-atom or anomalous-scattering substructure determinations. /, Appl. Cryst. 32,664 670. 

The two anomalous components of the scattering factor, f" and /, are interrelated through the Kramers Kronig transforms, which have the form... 

When extinction is present in the data set, it must be corrected for before the MEM procedure is started. The structure factors must similarly be corrected for anomalous scattering, if present. Both corrections require a model for their evaluation. The independent-atom model is usually adequate for this purpose. 

The problems surrounding Hamilton s test (vide supra), as well as some misconceptions and misuses encountered in the literature, led Rogers to propose an alternative and more reliable method for determining the absolute structure58. A factor >7 is introduced which multiplies the imaginary component Aff of the anomalous scattering terms of the atomic scattering factors of all atoms (equation 11, which replaces equation 9, see Section 4.2.2,1.1), and which is treated as a variable in the least-squares refinement. 

Inconclusive results are likely to be obtained for light-atom structures because of the low amount of anomalous scattering, as well as for nearly centrosymmetric structures, especially if the heavy atoms are distributed nearly centrosymmetrically 27. In the latter case the rj value may even refine to a false minimum with a deceptively small error estimate59. This led to the development of an alternative test by Flack which also overcomes these problems39-59. Flack introduced an absolute structure parameter x, which is defined by structure factor equation 12, and which is treated as a variable in the least-squares refinement. 

The absolute configuration of a-D-glucopyranose monohydrate has also been confirmed directly by the anomalous scattering of the oxygen atoms.70 After the atomic positions had been refined, the structure factors were calculated by using the oxygen anomalous scatter-... 

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