On the accuracy and precision of X-ray and neutron diffraction results as a function of resolution and the electron density model.

W Fabiola Sanjuan-Szklarz,Matthias Gutmann,Simon Grabowsky,Dylan Jayatilaka,Sławomir Domagała,Magdalena Woińska,Paulina M Dominiak,Krzysztof Woźniak

doi:10.1107/s2052252520010441

W Fabiola Sanjuan-Szklarz, Matthias Gutmann + Show 6 more

Open Access

https://doi.org/10.1107/s2052252520010441

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Abstract

X-ray diffraction is the main source of three-dimensional structural information. In total, more than 1.5 million crystal structures have been refined and deposited in structural databanks (PDB, CSD and ICSD) to date. Almost 99.7% of them were obtained by approximating atoms as spheres within the independent atom model (IAM) introduced over a century ago. In this study, X-ray datasets for single crystals of hydrated α-oxalic acid were refined using several alternative electron density models that abandon the crude spherical approximation: the multipole model (MM), the transferable aspherical atom model (TAAM) and the Hirshfeld atom refinement (HAR) model as a function of the resolution of X-ray data. The aspherical models (MM, TAAM, HAR) give far more accurate and precise single-crystal X-ray results than IAM, sometimes identical to results obtained from neutron diffraction and at low resolution. Hence, aspherical approaches open new routes for improving existing structural information collected over the last century.

Highlights

Paul Ewald (Ewald, 1948) first suggested to Max von Laue that X-rays with wavelengths comparable to the interatomic distances in crystals might produce diffraction patterns from them
A century after the work of Laue, Ewald and the Braggs, more advanced refinements of X-ray diffraction data, which provide significantly more accurate and precise structural and electronic information, are mature and ready to supplant independent atom model (IAM) refinement methods. We have shown this by comparing multiple single-crystal X-ray results with neutron data obtained for multiple measurements of single crystals of hydrated -oxalic acid and to the periodic differences between the optimized theoretical values (DFT) optimization outcome
Analysis of the dependencies of structural and thermal parameters obtained by refinement of the different models of the electron density against multiple X-ray and neutron datasets collected for single crystals of oxalic acid showed that IAM gave, in general, significantly worse accuracy and precision than the aspherical models of electron density

Summary

Introduction

Paul Ewald (Ewald, 1948) first suggested to Max von Laue that X-rays with wavelengths comparable to the interatomic distances in crystals might produce diffraction patterns from them. Max von Laue encouraged two PhD students (Paul Knipping and Walter Friedrich) to verify this hypothesis. Thereafter, they produced the very first X-ray photograph demonstrating the diffraction phenomenon. William Henry Bragg built the first X-ray spectrometer, while his son William Lawrence Bragg explained the relationship between the observed X-ray spots and the structure of crystals independently of Max von Laue. This earned Max von Laue the 1914 Nobel Prize in Physics for his discovery of X-ray diffraction by crystals, and the 1915 Nobel Prize in Physics for the Braggs for the analysis of crystal structures using X-rays. Around the time when Max von Laue received the Nobel Prize, William Henry Bragg and Arthur Holly Compton (Compton, 1915) put forward the hypothesis that each atom/ion could be modelled with a spherical electron density, put into practice in 1925, when the first spherical atomic scattering factors were calculated by Hartree (1925), which are today still used in more or less the same form

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