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Hot Topics in Contemporary Crystallography
by Croatian Association of Crystallographers
****** Šibenik, Croatia, May, 10th to 15th, 2014 |
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Croatian Association of Crystallographers ***** Bijenička c. 54 HR-10000 Zagreb Croatia
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Absolute configuration and absolute structure: basics and evaluation Download, print and bring the handout of the Prof. Flack's presentations H. D. Flack, University of Geneva, Switzerland
Absolute configuration is a chemists' term used to specify the chirality of a molecule. Absolute structure is a crystallographers' term used to specify an orientation in a non-centrosymmetric crystal structure. The basics deals with the symmetry aspects underlying the above two concepts. In particular one touches on the definitions of chirality, enantiomorph, enantiomer and racemate. One considers the crystal structures formed by chiral and achiral molecules. The crystal-growth phenomenon of twinning by inversion in a non-centrosymmetric crystal is illustrated by the examples of quartz and hexahelicene. The basics continues by passing to considerations of the point-group symmetry of the diffraction pattern of the crystal coupled with the effect of resonant scattering. The modelling of all non-centrosymmetric crystals through twinning by inversion is treated. The rules for deducing the absolute configuration of molecules from an analysis of the diffraction pattern will be explained. The evaluation of the crystal-structure determination of non-centrosymmetric crystals is recent work which may be said to have commenced in 2007. Intensity statistics are applied to determine the expected value of Friedif, called Friedifstat which quantifies the root-mean-square intensity of Friedel opposites to the mean intensity of Friedel averages. Friedifstat may be calculated from the chemical composition of the compound and the wavelength of the radiation. Its value quantifies the resonant-scattering contribution to the diffraction intensities. Friedif values may also be calculated from the observed intensities and those calculated after completion of the crystal-structure determination. Comparison of these values allows useful statements to be made concerning whether the crystal structure is centrosymmetric or not. Another very useful technique is to compare the observed and model Friedel average intensities and those of Friedel differences. From these, one sees how good a fit has been obtained, especially for the Friedel differences. Often, indeed too often, the Friedel difference intensities are dominated by random uncertainties and systematic error, even if a strong resonant-scattering contribution is expected. Generalized Rint or Rmerge values on the Friedel-difference intensities may allow the point group of the crystal to be determined prior to structure solution. Lastly, use of the antisymmetric Friedel-difference Patterson function has been explored. This function can clearly show displaced or incorrectly-assigned atoms, and in the case of the intermetallic compound TiGePt, use of this Patterson function clearly proved that the crystal structure was non-centrosymmetric.
Figure 1. 2AD plots for gz3201 in (a) and fa3274 in (b). Both gz3201 and fa3274 have Friedifstat ~470. gz3201 shows a good fit of Dobs to Dmodel whereas for fa3274 the Dobs are dominated by random uncertainties and systematic errors. Reproduced from H. D. Flack (2013), Acta Cryst. C69, 803-807.
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The workshop is generously supported by:
Ministry of Science, Education and Sports of the Republic of Croatia
International Union of Crystallography
European Crystallographic Association
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