The crystal and molecular structures of a series of structurally related analogues of 1,25-dihydroxyvitamin D2 and of the first analogue with all hydroxyl groups protected were established with single crystal X-ray structural analysis. With the use of the new structural data, we proposed that the A-ring conformation depends on hydrogen bonding of the hydroxyl groups of the A-ring. The A-ring of the 1α-hydroxylated vitamin D analogues exists in the solid state in a preferred chair β-conformation induced by direct hydrogen bonds between the 1-OH and 3-OH hydroxyl groups. In the same A-ring conformation, the vitamin D analogue interacts with the vitamin D receptor. Indirect hydrogen bonds between the A-ring hydroxyl groups, such as the ones through the water molecule, or hydrogen bonds between the A-ring hydroxyl groups and side-chain hydroxyl groups, induce the α-conformation. Theoretical calculations performed in vacuo showed that the β-form has a slightly lower energy than the α-form. Not only the hydroxyl groups but also the exocyclic methylene highly influences intermolecular interactions including the hydrogen bond pattern in the crystal lattices.

The Independent Atom Model (IAM) of electron density is used in routine X-ray data analysis. However, this model does not give a quantitative description of the electron-density distribution. A better model that allows for modelling of aspherical charge density deformations is introduced by the Hansen–Coppens variant of the multipole model of electron density. However, the application of this model requires crystals of excellent quality and high-resolution XRD data which are quite often difficult criteria to fulfil. Therefore, Mo Kα and Cu Kα data of three model compounds (tricyclic imide, xylitol and methyluracil) were refined using IAM and new methods which enabled the refinement and reconstruction of charge density based on the Cu Kα data. These methods were the Bond-Oriented Deformation Density (BODD) model, Hirshfeld Atom Refinement (HAR) and the Transferable Aspherical Atom Model (TAAM). The final results were compared to the model obtained from neutron diffraction experiments. Our results demonstrated not only that Cu Kα data may be refined using BODD, HAR and TAAM methods, but also revealed systematic errors arising from the use of Cu Kα data. These errors were a result of the limited information in the low-resolution data set that manifested as higher values for the anisotropic displacement parameters (ADPs) and smaller maxima and minima of the residual electron density for the Cu Kα data compared to the Mo Kα data. Notably, these systematic errors were much less significant than those found for the IAM. Therefore, the application of BODD, HAR and TAAM on Cu Kα data has a more significant influence on the final results of refinement than for the Mo Kα data.

In this work, two methods of high-resolution X-ray data refinement: multipole refinement (MM) and Hirshfeld atom refinement (HAR) – together with X-ray wavefunction refinement (XWR) – are applied to investigate the refinement of positions and anisotropic thermal motion of hydrogen atoms, experiment-based reconstruction of electron density, refinement of anharmonic thermal vibrations, as well as the effects of excluding the weakest reflections in the refinement. The study is based on X-ray data sets of varying quality collected for the crystals of four quinoline derivatives with Cl, Br, I atoms and the -S-Ph group as substituents. Energetic investigations are performed, comprising the calculation of the energy of intermolecular interactions, cohesive and geometrical relaxation energy. The results obtained for experimentally derived structures are verified against the values calculated for structures optimized using dispersion-corrected periodic density functional theory. For the high-quality data sets (the Cl and -S-Ph compounds), both MM and XWR could be successfully used to refine the atomic displacement parameters and the positions of hydrogen atoms; however, the bond lengths obtained with XWR were more precise and closer to the theoretical values. In the application to the more challenging data sets (the Br and I compounds), only XWR enabled free refinement of hydrogen atom geometrical parameters, nevertheless, the results clearly showed poor data quality. For both refinement methods, the energy values (intermolecular interactions, cohesive and relaxation) calculated for the experimental structures were in similar agreement with the values associated with the optimized structures – the most significant divergences were observed when experimental geometries were biased by poor data quality. XWR was found to be more robust in avoiding incorrect distortions of the reconstructed electron density as a result of data quality issues. Based on the problem of anharmonic thermal motion refinement, this study reveals that for the most correct interpretation of the obtained results, it is necessary to use the complete data set, including the weak reflections in order to draw conclusions.

Quantum crystallography is a fast-developing multidisciplinary area of crystallography. In this work, we analyse the influence of different charge density models (i.e., the multipole model (MM), Hirshfeld atom refinement (HAR), and the transferable aspherical atom model (TAAM)), modelling of the thermal motion of hydrogen atoms (anisotropic, isotropic, and with the aid of SHADE or NoMoRe), and the type of radiation used (Mo Kα and Cu Kα) on the final results. To achieve this aim, we performed a series of refinements against X-ray diffraction data for three model compounds and compared their final structures, geometries, shapes of ADPs, and charge density distributions. Our results were also supported by theoretical calculations that enabled comparisons of the lattice energies of these structures. It appears that geometrical parameters are better described (closer to the neutron values) when HAR is used; however, bonds to H atoms more closely match neutron values after MM or TAAM refinement. Our analysis shows the superiority of the NoMoRe method in the description of H-atom ADPs. Moreover, the shapes of the ADPs of H atoms, as well as their electron density distributions, were better described with low-resolution Cu Kα data in comparison to low-resolution Mo Kα data.

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