Practical applications of averages and differences of Friedel opposites

Abstract

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.

Analysing Friedel averages and differences

“…The validation of a structure analysis of a non-centrosymmetric crystal structure by way of plots of observed against model values of the average (A) and difference (D) intensities of Friedel opposites has been introduced by Flack et al (2011). The average and difference of Friedel opposites are defined by…”

“…A compound with an appreciable resonant-scattering contribution has D(hkl) approximately 0.01A(hkl), whereas a compound with a small resonant-scattering contribution has D(hkl) approximately 0.0001A(hkl). Flack et al (2011) made a study of 29 crystal structures published in 2007. It was found that these crystal structure determinations could be separated into three categories based on the appearance of the D obs against D model plot of the acentric reflections.…”

“…Flack et al (2011) interpreted the results of the third category as indicating that there was no problem with the D model values but that the D obs were entirely dominated by random uncertainties and systematic errors which combined to obscure, almost entirely, the resonant-scattering contribution to the difference intensity of Friedel opposites. In the second category, the results were intermediate.…”

Virtual issue on absolute structure

“…This is very much in line with the technique of comparing bond distances and angles from one particular crystal-structure determination with those given in tables of standard values. However, Dr David Watkin of the University of Oxford had the inspiration of looking at the fit of the observed to the model (calculated) intensities (Flack et al, 2011) It would seem appropriate to make some remarks based on personal experience, concerning crystallographers' understanding of the subject area of absolute structure and absolute configuration. In general, there is a deep rift in the comprehension of the subject between:…”

“…This is very much in line with the technique of comparing bond distances and angles from one particular crystal-structure determination with those given in tables of standard values. However, Dr David Watkin of the University of Oxford had the inspiration of looking at the fit of the observed to the model (calculated) intensities (Flack et al, 2011). It is customary to plot |F obs | 2 against |F model | …”