Advancing dynamic quantum crystallography: enhanced models for accurate structures and thermodynamic properties

By implementing the aspherical atom model to normal mode refinement, we obtained accurate structures [including H-atom positions and anisotropic displacement parameters (ADPs)] and heat capacity from single-crystal X-ray diffraction data.

X-ray diffraction (XRD) has evolved significantly since its inception, becoming a crucial tool for material structure characterization. Advancements in theory, experimental techniques, diffractometers and detection technology have led to the acquisition of highly accurate diffraction patterns, surpassing previous expectations. Extracting com­prehensive information from these patterns necessitates different models due to the influence of both electron density and thermal motion on diffracted beam intensity. While electron-density modelling has seen con­siderable progress [e.g. the Hansen–Coppens multipole model and Hirshfeld Atom Refinement (HAR)], the treatment of thermal motion has remained largely unchanged. We have developed a novel method that combines the strengths of the advanced charge-density models [Aspherical Atom Models (AAMs), such as HAR or the Transferable Aspherical Atom Model (TAAM)] and the thermal motion model (normal modes refinement, NoMoRe). We denote this approach AAM_NoMoRe, wherein instead of refining routine anisotropic displacement parameters (ADPs) against single-crystal X-ray diffraction data, we refine the frequencies obtained from periodic density functional theory (DFT) calculations. In this work, we demonstrate the effectiveness of this model by presenting its application to model com­pounds, such as alanine, xylitol, naphthalene and glycine polymorphs, highlighting the influence of our method on the H-atom positions and shape of their ADPs, which are com­parable with neutron data. We observe a significant decrease in the similarity index for H-atom ADPs after AAM_NoMoRe in com­parison to only AAM, aligning more closely with neutron data. Due to the use of aspherical form factors (AAM), our approach demonstrates better fitting performance, as indicated by consistently lower wR2 values com­pared to the Independent Atom Model (IAM) refinement and a significant decrease com­pared to the traditional NoMoRe model. Furthermore, we present the estimation of a key thermodynamic property, namely, heat capacity, and demonstrate its alignment with experimental calorimetric data.