Direct methods and refinement in electron and X-ray crystallography – diketopiperazine revisited

Abstract

AbstractTexture diffraction data in pioneering Russian electron crystallographic studies inspired the invention of modern precession methods for collecting single crystal data. (Although oblique texture patterns contain overlapped reflections, the similarity to precession methods is a result of averaging intensities over an angular distribution of crystallites within the large area sampled by the incident electron beam.) Using texture diffraction amplitudes originally measured by Vainshtein, the crystal structure of diketopiperazine has been re-determined using automated direct methods (SIR97) and refined by block diagonal least squares. This determination was carried out in parallel with an equivalent direct methods study of a larger X-ray data set from the same material published by Degeilh and Marsh, followed by least squares refinement, reproducing the original results. After both refinements, the electron crystallographic bonding parameters for heavy atoms are found to be similar to derived X-ray crystallographic parameters. On the other hand, C–H and N–H distances are more accurately determined by electron crystallography than by X-ray crystallography since the light atom positions are more easily detected in ensuing maps. Surprisingly the least squares refinement against the electron diffraction data did not require a restraint on the magnitude of atomic incremental movement; moreover the atomic temperature factors could be refined, producing results that were more reasonable than expected from the very low overall B value found from a Wilson plot.