X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems

Enhancing hydrogen positions in X-ray structures of transition metal hydride complexes with dynamic quantum crystallography

Hirshfeld atom refinement (HAR) is a method which enables the user to obtain more accurate positions of hydrogen atoms bonded to light chemical elements using X-ray data. When data quality permits, this method can be extended to hydrogen-bonded transition metals (TMs), as in hydride complexes. However, addressing hydrogen thermal motions with HAR, particularly in TM hydrides, presents a challenge. At the same time, proper description of thermal vibrations can be vital for determining hydrogen positions correctly. In this study, we employ tools such as SHADE3 and Normal Mode Refinement (NoMoRe) to estimate anisotropic displacement parameters (ADPs) for hydrogen atoms during HAR and IAM refinements performed for seven structures of TM (Fe, Ni, Cr, Nb, Rh and Os) and metalloid (Sb) hydride complexes for which both the neutron and the X-ray structures have been determined. A direct comparison between neutron and HAR/SHADE3/NoMoRe ADPs reveals that the similarity between neutron hydrogen ADPs and those estimated with NoMoRe or SHADE3 is significantly higher than when hydrogen ADPs are refined with HAR. Regarding TM-H bond lengths, traditional HAR exhibits a slight advantage over the other methods. However, combining NoMoRe/SHADE3 with HAR results in a minor decrease in agreement with neutron TM-H bond lengths. For the Cr complex, for which high-resolution X-ray data were collected, an investigation of resolution-related effects was possible.

High-Pressure Crystallization and Thermodynamic Stability Study on the Resolution of High-Density Enantiomers from Low-Density Racemates

High-pressure recrystallization could be the cheapest clean method of resolving enantiomers from the racemates defying Wallach's rule. We have investigated the effect of pressure on sodium tartrate monohydrate (NaTa·H₂O), a notorious exception from Wallach's rule: both racemic polymorphs α-dl-NaTa·H₂O and β-dl-NaTa·H₂O are less dense than the enantiomers. According to the mobile-equilibrium principle, such high-density enantiomorphs should spontaneously separate under high pressures. The pressure dependence of the Gibbs free energy explains the preferential crystallization of mixed enantiomers of NaTa·H₂O.

How to get maximum structure information from anisotropic displacement parameters obtained by three-dimensional electron diffraction: an experimental study on metal-organic frameworks

Three-dimensional electron diffraction (3D ED) has been used for ab initio structure determination of various types of nanocrystals, such as metal-organic frameworks (MOFs), zeolites, metal oxides and organic crystals. These crystals are often obtained as polycrystalline powders, which are too small for single-crystal X-ray diffraction (SCXRD). While it is now possible to obtain accurate atomic positions of nanocrystals by adopting kinematical refinement against 3D ED data, most new structures are refined with isotropic displacement parameters (U _eq), which limits the detection of possible structure disorders and atomic motions. Anisotropic displacement parameters (ADPs, U^ij ) obtained by anisotropic structure refinement, on the other hand, provide information about the average displacements of atoms from their mean positions in a crystal, which can provide insights with respect to displacive disorder and flexibility. Although ADPs have been obtained from some 3D ED studies of MOFs, they are seldom mentioned or discussed in detail. We report here a detailed study and interpretation of structure models refined anisotropically against 3D ED data. Three MOF samples with different structural complexity and symmetry, namely ZIF-EC1, MIL-140C and Ga(OH)(1,4-ndc) (1,4-ndcH₂ is naphthalene-1,4-dicarboxylic acid), were chosen for the studies. We compare the ADPs refined against individual data sets and how they are affected by different data-merging strategies. Based on our results and analysis, we propose strategies for obtaining accurate structure models with interpretable ADPs based on kinematical refinement against 3D ED data. The ADPs of the obtained structure models provide clear and unambiguous information about linker motions in the MOFs.

Dynamics and disorder: on the stability of pyrazinamide polymorphs

The enantiotropic relationship between the four polymorphs of pyrazinamide is analyzed by means of accurate X-ray diffraction measurements, normal-mode refinement and periodic DFT calculations.

This article focuses on the structure and relative stability of four pyrazinamide polymorphs. New single crystal X-ray diffraction data collected for all forms at 10 K and 122 K are presented. By combining periodic abinitio DFT calculations with normal-mode refinement against X-ray diffraction data, both enthalpic and entropic contributions to the free energy of all polymorphs are calculated. On the basis of the estimated free energies, the stability order of the polymorphs as a function of temperature and the corresponding solid state phase transition temperatures are anticipated. It can be concluded that the α and γ forms have higher vibrational entropy than that of the β and δ forms and therefore they are significantly more stabilized at higher temperatures. Due to the entropy which arises from the disorder in γ form, it overcomes form α and is the most stable form at temperatures above ∼500 K. Our findings are in qualitative agreement with the experimental calorimetry results.

Complexity Parameters for Molecular Solids

Structural complexity measures based on Shannon information entropy are widely used for inorganic crystal structures. However, the application of these parameters for molecular crystals requires essential modification since atoms in inorganic compounds usually possess more degrees of freedom. In this work, a novel scheme for the calculation of complexity parameters (HmolNet, HmolNet,tot) for molecular crystals is proposed as a sum of the complexity of each molecule, the complexity of intermolecular contacts, and the combined complexity of both. This scheme is tested for several molecular crystal structures.