Further Validation of Quantum Crystallography Approaches

Abstract

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.

First Experimental Quantitative Charge Density Studies of Advanced Intermediate of Vitamin D Analogues

“…Moreover, our research on quantum crystallography methods showed that quantum crystallography models may be used for the reconstruction of the electron density. The methodological correctness of this approach was proved by us in our previous studies [ 14 , 15 ]. Therefore, in this work we additionally present results of reconstruction of charge density of final crystal structures of vitamin D analogues (PRI-1730 and PRI-1731, Figure 2 ) which were obtained using the transferable aspherical atom model (TAAM).…”

“…This study is also an example that quantum crystallography methods may be used for the refinement of low-resolution data even when the quality of the data is not very high (in terms of measurement statistics and data resolution). When we performed the methodological work to prove this approach, we used the model compounds which did not exceed 25 atoms [ 14 , 15 ]. On the contrary, vitamin D analogues have more than 70 atoms.…”

Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement

“…We have compared these (Table 1) using values from the similarity index S 12 (see the supporting information for definitions of the descriptors) as introduced by Whitten & Spackman (2006), an average absolute difference and relative difference in ADP tensor components. It has been suggested that very good agreement for ADP values was achieved for S 12 that is equal to or smaller than 1 with an in-house source measurement refined with HAR (Wanat et al, 2021). Good agreement between X-ray and neutron structures should not be taken for granted as HAR is very sensitive to the quality of the X-ray data.…”

Influence of modelling disorder on Hirshfeld atom refinement results of an organo-gold(I) compound

“…This is an iterative procedure, where 'tailor-made' aspherical atomic scattering factors (Hirshfeld, 1977), obtained by quantum mechanical methods, are used to refine the atomic positions and ADPs in the standard, least-squares structure refinement until convergence. Previous work reported that HAR provides more accurate hydrogen atom positions (Woin ´ska et al, 2016(Woin ´ska et al, , 2021Malaspina et al, 2020) than IAM and enables refinement of hydrogen ADP values (Wanat et al, 2021). Furthermore, HAR utilizing relativistic Hamiltonians was also successfully applied to heavy elements (Pawle ˛dzio et al, 2021;Buc ˇinsky ´et al, 2019Buc ˇinsky ´et al, , 2016.…”