Statistical analysis of multipole-model-derived structural parameters and charge-density properties from high-resolution X-ray diffraction experiments

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.