A comprehensive analysis of various properties derived from multiple high-resolution X-ray diffraction experiments is reported. A total of 13 charge-density-quality data sets of α-oxalic acid dihydrate (C2H2O4·2H2O) were subject to Hansen-Coppens-based modelling of electron density. The obtained parameters and properties were then statistically analysed yielding a clear picture of their variability across the different measurements. Additionally, a computational approach (CRYSTAL and PIXEL programs) was utilized to support and examine the experimental findings. The aim of the study was to show the real accuracy and interpretation limits of the charge-density-derived data. An investigation of raw intensities showed that most of the reflections (60-70%) fulfil the normality test and the lowest ratio is observed for weak reflections. It appeared that unit-cell parameters are determined to the order of 10(-3) Å (for cell edges) and 10(-2) ° (for angles), and compare well with the older studies of the same compound and with the new 100 K neutron diffraction data set. Fit discrepancy factors are determined within a 0.5% range, while the residual density extrema are about ±0.16 (3) e Å(-3). The geometry is very well reproducible between different data sets. Regarding the multipole model, the largest errors are present on the valence shell charge-transfer parameters. In addition, symmetry restrictions of multipolar parameters, with respect to local coordinate systems, are well preserved. Standard deviations for electron density are lowest at bond critical points, being especially small for the hydrogen-bonded contacts. The same is true for kinetic and potential energy densities. This is also the case for the electrostatic potential distribution, which is statistically most significant in the hydrogen-bonded regions. Standard deviations for the integrated atomic charges are equal to about 0.1 e. Dipole moments for the water molecule are comparable with the ones presented in various earlier studies. The electrostatic energies should be treated rather qualitatively. However, they are quite well correlated with the PIXEL results.
Single-crystal X-ray diffraction data should be collected to the highest resolution as this allows for refinement of more reliable structural, thermal and dependent parameters. The results of refinements using a Transferable Aspherical Atomic Model of electron density (TAAM) appear to be in far better agreement with neutron results than the corresponding Independent Atom Model (IAM) results for all parameters, all resolutions and all compounds, and we advocate the use of this approach instead of IAM.
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.
Although everything seems to be already well known in the field of routine structural single crystal X-ray analysis and more than 1.1 mln organic, inorganic and macromolecular structures have been solved and refined so far, even commonly used approaches in X-ray diffraction and models of electron density applied should be critically re-evaluated from time to time. It is incredible that the Independent Atom Model (IAM) of electron density, effectively introduced a century ago, is still the most common model of electron density used in structural analysis. One would even say that its success has dominated the whole field of X-ray diffraction for the past century and for years now plays, in my opinion, quite a negative role. When IAM was introduced, Max von Laue, the Braggs, and their colleagues, were using home-made pieces of equipment which could have hardly supplied qualitative information on diffraction spots. In consequence, the errors associated with the model of electron density used were overshadowed by far larger diffraction hardware errors. However, within the past century, there has been an overwhelming progress in design and production of X-ray hardware which is made for needs of both small laboratories and large scale facilities. This progress in sophisticated X-ray hardware should also accelerate progress in the quality and complexity of models of electron density used to interpret experimental results. The use of the 100 years old IAM effectively proves that even with the most modern scientific tools, one can step backward and do ca. 100 years old crystallography. In my presentation, I will discuss precision and accuracy of single crystal X-ray results obtained for multiple measurements of single crystals of oxalic acid as a function of resolution of X-ray data and quality of electron density model applied (IAM, multipole model (MM), Hirshfeld Atom Refinement (HAR) and Transferable Aspherical Atom Model of electron density (TAAM)). I will present a detailed comparison of structural, thermal and electronic parameters obtained for the same multiple diffraction data sets collected for single crystals of oxalic acid when different models of electron density are refined against collected intensities of reflections complemented by comparison to single crystal neutron diffraction and theoretical results [1]. Some practical suggestions will be presented how to estimate and improve the quality of single crystal X-ray diffraction structural results. Among others with the newer models, one can obtain more precise and accurate information on positions of H-atoms
Dedicated to Professor Bohdan Korybut-Daszkiewicz on the occasion of his 77th birthday. A number of novel tetracyano-substituted dihydrotetraaza[14] annulene (DH-TAA) analogues were obtained in a simple and convenient way by one-pot synthesis. The ligands, as well as their complexes with nickel(II), copper(II) and palladium(II) ions were characterised, including X ray structures for seven compounds. The X-ray analysis shows relatively short distances between tetraazamacrocyclic rings (3.0-3.3 Å), resulting from the presence of strong π-π interactions. Moreover, some of synthesised compounds can easily be modified in order to attach commonly used reactive groups, which makes them very promising as future components of π-interaction based supramolecular systems [a
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