Absolute Structure Determination Research Articles

Least-squares absolute-structure refinement. Practical experience and ancillary calculations

The least-squares refinement of non-centrosymmetric crystal structures as inversion twins is presented. It is shown that the absolute-structure (twin) parameter x may be used to define the chirality or polarity of untwinned crystals. The method has been applied to 20 compounds. The least-squares refinement of the absolute-structure parameter is rapid and stable. The value of x generally falls within three e.s.d.'s of the physically meaningful range 0 ≤ x ≤ 1 and the e.s.d.'s increase as f” becomes smaller. New residual and goodness-of-fit values are defined to judge the efficiency of the method. The estimated standard deviation of x, taken with a pseudo Durbin-Watson d statistic, provides an excellent criterion for the reliability of the absolute-structure determination. Refinements on data sets including very accurately measured Friedel pairs of reflections have also been tested. The determination of the free direction(s) of origin-free space groups and an efficient algorithm for the inversion of a crystal structure that refines to x ≃ 1 are given in detail. The data and procedural structures necessary for an efficient computer implementation of absolute-structure refinement are also considered. The formulae giving the correction for the effects of anomalous dispersion on |Fobs| from an inversion-twinned crystal are given. These corrected |Fobs| are the ones to be used in an electron-density calculation. The correlation of residuals following least-squares refinement is quantified by using a pseudo Durbin-Watson d statistic. The causes of the correlation, its effect on the value of x and its e.s.d., and ways of avoiding the correlation are considered. It is shown that in using x it is more suitable to refine on |F|2 than |F|. A weighting scheme is presented and tested that increases the sensitivity of a refinement to absolute structure.

The determination of absolute structure. I. Some experiences with the Rogers η refinement

The η refinement of Rogers [Acta Cryst. (1981), A37, 734-741] has been applied to a wide range of noncentrosymmetric structures containing medium to strong anomalous scatterers; it has been shown to be an effective and robust method. The use of the general term 'absolute structure' (to signify a structure successfully distinguished from its inverse by, for example, analysis of anomalous scattering effects) is recommended.

Electric-field-induced ionic displacement and redistribution of bonding electrons in LiNbO3and LiTaO3revealed by modulation X-ray diffraction

Electric fields with alternating square wave were applied to LiNbO3 and LiTaO3 single crystals in [001] directions, and extremely small ionic displacement was directly detected by the measurement of the diffracted intensities of X-rays synchronously with the applied fields. The displacement of Nb and Li ions relative to the oxygen framework were found to be 4.9 x 10-4 and 13 x 10-4 A at E = 51.5 kV cm-1 for LiNbO3, and those of Ta and Li to be 6.8 x 10-4 and 15 x 10-4 A at E = 50 kV cm-1 for LiTaO3. The temperature factor was observed to vary with the external field, which is attributed to the change in phonon frequency of the crystal lattice. It was found from the intensity variations in the lower-indexed reflections that the displacements of the bonding electrons of Nb-O and Ta--O bonds are much larger than those of the constituent ions, which may be the origin of the electrooptic effect. The capability of the modulation technique in the absolute structure determination of crystals is demonstrated.

The pyrrolizidine alkaloids. II.

Ten years have elapsed since the pyrrolizidine alkaloids were reviewed in this series (387), and it is a not much shorter period since they formed the subject of an excellent account by Leonard (329) and a masterly summary by Boit (225). The intervening years have seen considerable activity in the isolation of new alkaloids, the determination of absolute structures, the synthesis of both the “necine” bases and “necic” acids, the study of the formation of these alkaloids in the plant and the effect of structure in hepatic cirrhosis.KeywordsMethyl EtherAbsolute ConfigurationGlutaric AcidPyrrolizidine AlkaloidAcid LactoneThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.