Structure determination from unindexed powder data from scratch by a global optimization approach using pattern comparison based on cross-correlation functions

A simple solution to the Rietveld refinement recipe problem

Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

Leucopterin, the white pigment in butterfly wings: structural analysis by PDF fit, FIDEL fit, Rietveld refinement, solid-state NMR and DFT-D

Leucopterin (C6H5N5O3) is the white pigment in the wings of Pieris brassicae butterflies, and other butterflies; it can also be found in wasps and other insects. Its crystal structure and its tautomeric form in the solid state were hitherto unknown. Leucopterin turned out to be a variable hydrate, with 0.5 to about 0.1 molecules of water per leucopterin molecule. Under ambient conditions, the preferred state is the hemihydrate. Initially, all attempts to grow single crystals suitable for X-ray diffraction were to no avail. Attempts to determine the crystal structure by powder diffraction using the direct-space method failed, because the trials did not include the correct, but rare, space group P2/c. Attempts were made to solve the crystal structure by a global fit to the pair distribution function (PDF-Global-Fit), as described by Prill and co-workers [Schlesinger et al. (2021). J. Appl. Cryst. 54, 776-786]. The approach worked well, but the correct structure was not found, because again the correct space group was not included. Finally, tiny single crystals of the hemihydrate could be obtained, which allowed at least the determination of the crystal symmetry and the positions of the C, N and O atoms. The tautomeric state of the hemihydrate was assessed by multinuclear solid-state NMR spectroscopy. 15N CPMAS spectra showed the presence of one NH2 and three NH groups, and one unprotonated N atom, which agreed with the 1H MAS and 13C CPMAS spectra. Independently, the tautomeric state was investigated by lattice-energy minimizations with dispersion-corrected density functional theory (DFT-D) on 17 different possible tautomers, which also included the prediction of the corresponding 1H, 13C and 15N chemical shifts in the solid. All methods showed the presence of the 2-amino-3,5,8-H tautomer. The DFT-D calculations also confirmed the crystal structure. Heating of the hemihydrate results in a slow release of water between 130 and 250 °C, as shown by differential thermal analysis and thermogravimetry (DTA-TG). Temperature-dependent powder X-ray diffraction (PXRD) showed an irreversible continuous shift of the reflections upon heating, which reveals that leucopterin is a variable hydrate. This observation was also confirmed by PXRD of samples obtained under various synthetic and drying conditions. The crystal structure of a sample with about 0.2 molecules of water per leucopterin was solved by a fit with deviating lattice parameters (FIDEL), as described by Habermehl et al. [Acta Cryst. (2022), B78, 195-213]. A local fit, starting from the structure of the hemihydrate, as well as a global fit, starting from random structures, were performed, followed by Rietveld refinements. Despite dehydration, the space group remains P2/c. In both structures (hemihydrate and variable hydrate), the leucopterin molecules are connected by 2-4 hydrogen bonds into chains, which are connected by further hydrogen bonds to neighbouring chains. The molecular packing is very efficient. The density of leucopterin hemihydrate is as high as 1.909 kg dm-3, which is one of the highest densities for organic compounds consisting of C, H, N and O only. The high density might explain the good light-scattering and opacity properties of the wings of Pieris brassicae and other butterflies.

Ambiguous structure determination from powder data: four different structural models of 4,11-di-fluoro-quinacridone with similar X-ray powder patterns, fit to the PDF, SSNMR and DFT-D

Four different structural models, which all fit the same X-ray powder pattern, were obtained in the structure determination of 4,11-di-fluoro-quinacridone (C₂₀H₁₀N₂O₂F₂) from unindexed X-ray powder data by a global fit. The models differ in their lattice parameters, space groups, Z, Z', molecular packing and hydrogen bond patterns. The molecules form a criss-cross pattern in models A and B, a layer structure built from chains in model C and a criss-cross arrangement of dimers in model D. Nevertheless, all models give a good Rietveld fit to the experimental powder pattern with acceptable R-values. All molecular geometries are reliable, except for model D, which is slightly distorted. All structures are crystallochemically plausible, concerning density, hydrogen bonds, intermolecular distances etc. All models passed the checkCIF test without major problems; only in model A a missed symmetry was detected. All structures could have probably been published, although 3 of the 4 structures were wrong. The investigation, which of the four structures is actually the correct one, was challenging. Six methods were used: (1) Rietveld refinements, (2) fit of the crystal structures to the pair distribution function (PDF) including the refinement of lattice parameters and atomic coordinates, (3) evaluation of the colour, (4) lattice-energy minimizations with force fields, (5) lattice-energy minimizations by two dispersion-corrected density functional theory methods, and (6) multinuclear CPMAS solid-state NMR spectroscopy (¹H, ¹³C, ¹⁹F) including the comparison of calculated and experimental chemical shifts. All in all, model B (perhaps with some disorder) can probably be considered to be the correct one. This work shows that a structure determination from limited-quality powder data may result in totally different structural models, which all may be correct or wrong, even if they are chemically sensible and give a good Rietveld refinement. Additionally, the work is an excellent example that the refinement of an organic crystal structure can be successfully performed by a fit to the PDF, and the combination of computed and experimental solid-state NMR chemical shifts can provide further information for the selection of the most reliable structure among several possibilities.

Solving molecular compounds from powder diffraction data: are results always reliable?

Commentary is given on a paper [Schlesinger et al. (2022). IUCrJ, 9, 406-424.] reporting on ambiguous structure determination from powder data using four different structural models of 4,11-difluoroquinacridone with similar X-ray powder patterns.

Circumventing a challenging aspect of crystal structure determination from powder diffraction data

Schmidt and co-workers [ Acta Cryst. (2022), B78, 195–213], report a strategy for structure determination from powder XRD data in which unit-cell determination and structure solution are combined within a single process, rather than handling them as sequential stages on the structure determination pathway. This strategy offers the prospect to achieve successful structure determination in cases for which conventional approaches for indexing powder XRD data prove to be challenging.