Howard D. Flack

Reporting and evaluating absolute-structure and absolute-configuration determinations

Detailed practical and numerical information is provided for undertaking and evaluating absolute-structure and absolute-configuration determinations. The interpretation of numerical values of x, the Flack [Acta Cryst. (1983), A39, 876–881] parameter, and its standard uncertainty u are explained in terms of the inversion-distinguishing power. Moreover, the conditions to obtain reliable values of x(u) are detailed. Further explanatory material is provided on the use of right-handed axes, valid intensity data, the application to macromolecular structures, the dangers of polar-dispersion errors, Euclidean normalizers of space groups, the detection and reporting of molecular symmetry, enantiopurity and optical activity in solution. New CIF data names are introduced.

Use of intensity quotients and differences in absolute structure refinement

Differences and quotients can be defined using Friedel pairs of reflections and applied in refinement to enable absolute structure to be determined precisely even for light atom crystal structures.

Absolute structure and absolute configuration

Fundamental notions concerning absolute structure and absolute configuration, and their determination from single-crystal diffraction measurements, are presented and reviewed. A glossary of terms with definitions useful in this field is provided. For absolute structure and its determination, the separate but interacting influences of the structure and the inversion-distinguishing power of an X-ray diffraction experiment with dispersive scatterers are examined. Important experimental and algorithmic details of the current methods used for absolute-structure determination are provided. Characterization of crystals for absolute-structure determination and of molecules for absolute-configuration determination are treated. Attention is given to the analysis of absolute structure and absolute configuration in twinned crystals.

The evaluation of transmission factors and their first derivatives with respect to crystal shape parameters

Methods, implemented into a computer program (LSABS), are described which calculate transmission factors and their first derivatives with respect to the positions of the faces of a convex polyhedral monocrystal. Both Gaussian and analytical integration procedures are considered in detail. LSABS has been implemented as a module of the Xtal system of programs. It functions independently of the instrument used to collect the intensity data. Test results obtained with this program are compared with standard literature values. Correlation coefficients of an absorption-corrected intensity data set of calcite, CaCO3 are reported. The need for transmission factor derivatives in the refinement of crystal shape and in the elimination of correlated absorption-corrected structure amplitudes is explained.

Practical applications of averages and differences of Friedel opposites

The practical use of the average and difference intensities of Friedel opposites at different stages of structure analysis has been investigated. It is shown how these values may be properly and practically used at the stage of space-group determination. At the stage of least-squares refinement, it is shown that increasing the weight of the difference intensities does not improve their fit to the model. The correct form of the coefficients for a difference electron-density calculation is given. In the process of structure validation, it is further shown that plots of the observed and model difference intensities provide an objective method to evaluate the fit of the data to the model and to reveal insufficiencies in the intensity measurements. As a further tool for the validation of structure determinations, the use of the Patterson functions of the average and difference intensities has been investigated and their clear advantage demonstrated.

Louis Pasteur's discovery of molecular chirality and spontaneous resolution in 1848, together with a complete review of his crystallographic and chemical work.

Pasteurs chemical and crystallographic work is described. The article commences with a brief overview of related science (chemical structure, crystallography, optical activity) before and after 1848, the year of the discovery of molecular chirality and spontaneous resolution. Concerning this discovery, three separate and varying reports are described. These are: (i) the publications in the scientific literature, (ii) the early (auto)biographies and (iii) Pasteurs handwritten laboratory notebooks. The three versions give differing views on the topic. Subsequently all of Pasteurs crystallographic and chemical work is passed in review, a topic very rarely broached. Pasteurs view in later life on this part of his work is examined. The article concludes with a discussion of the term dissymmetry used by Pasteur.

Statistical descriptors in crystallography: Report of the IUCr Subcommittee on Statistical Descriptors

The Subcommittee has attempted to elucidate the nature of problems encountered in the definition and use of statistical descriptors as applied to crystallography and to propose procedural improvements. The report contains (a) a dictionary of statistical terms established for use by experimentalists; (b) a description of the statistical basis for refinement procedures; (c) sections dealing with defects in the physical model used for refinement, and with the choice and significance of weighting schemes; and (d) recommendations, some of which may be readily implemented, whilst others may require a long-term effort to bring them into general use.

The mean-square Friedel intensity difference in P1 with a centrosymmetric substructure.

For non-centrosymmetric structures in space group P1 containing a centrosymmetric substructure, analytical expressions have been obtained for various functions of the diffraction intensity of Friedel opposites. These functions are the average intensity of Friedel opposites, the mean difference in intensity of Friedel opposites and the mean-square difference in intensity of Friedel opposites. A Bijvoet intensity ratio is defined for the evaluation of resonant-scattering effects in non-centrosymmetric and pseudo-centrosymmetric structures. Analysis of these expressions confirms that both resonant and non-resonant atoms are necessary to produce differences in intensity between Friedel opposites and also shows that in some circumstances atoms may lie on a centrosymmetric substructure without diminishing the Bijvoet intensity ratio. The effects of the real component of resonant scattering, of the variation of the scattering factors with sin theta/lambda, of isotropic atomic displacement parameters, of a crystal twinned by inversion, of atoms in special positions and of weak reflections are considered. Software is available for the evaluation of the Bijvoet intensity ratio.

Statisical descriptions in crystallography. II. Report of a Working Group on Expression of Uncertainty in Measurement

The Working Group has examined recent recommendations for evaluating and expressing uncertainty in measurement [Guide to the Expression of Uncertainty in Measurement, International Organization for Standardization (ISO, 1993)]. The present publication updates an earlier report of the IUCr Subcommittee on Statistical Descriptors [Schwarzenbach, Abrahams, Flack, Gonschorek, Hahn, Huml, Marsh, Prince, Robertson, Rollett & Wilson (1989). Acta Cryst. A45, 63-75]. This new report presents the concepts of standard uncertainty, of combined standard uncertainty, and of Type A and Type B evaluations of standard uncertainties. It expands the earlier dictionary of statistical terms, recommends replacement of the term estimated standard deviation (e.s.d.) by standard uncertainty (s.u.) or by combined standard uncertainty (c.s.u.) in statements of the statistical uncertainties of data and results, and requests a complete description of the experimental and computational procedures used to obtain all results submitted to IUCr publications.

Applications and properties of the Bijvoet intensity ratio

An empirical relationship of use in prediction and evaluation is established between the standard uncertainty of the Flack parameter and the Bijvoet intensity ratio. The expected value of this ratio may be calculated from the chemical composition of the compound and the X-ray wavelength. Structure analyses published with intensity data have allowed various properties of the Bijvoet intensity ratio to be studied. It is found that, although the Bijvoet intensity ratio has a strong dependence on sin theta/lambda, extrapolation to sin theta/lambda = 0 of model intensity pairs leads to values satisfactorily close to those expected. Moreover, it is shown that there is no symmetry enhancement for general reflections of the Bijvoet ratio in agreement with theory. The behaviour of some special reflections is examined. Two methods of correcting the observed Bijvoet ratio for systematic and random effects have been tested and found to be unsatisfactory. Evidence is produced to show that standard uncertainties provided with intensities are unrealistic and that measurement protocols need improvement.