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

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 wR 2 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.