Butkiewicz Helena, Chodkiewicz Michał, Madsen Anders Ø, Hoser Anna A
Faculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw, 02-093, Poland.
Department of Pharmacy, University of Copenhagen, Copenhagen, Denmark.
IUCrJ. 2025 Jan 1;12(Pt 1):123-136. doi: 10.1107/S2052252524011862.
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.
自X射线衍射（XRD）诞生以来，它已经有了显著的发展，成为材料结构表征的关键工具。理论、实验技术、衍射仪和检测技术的进步使得人们能够获得高度精确的衍射图谱，远超先前的预期。由于电子密度和热运动对衍射束强度都有影响，因此从这些图谱中提取全面信息需要不同的模型。虽然电子密度建模已经取得了很大进展[例如汉森 - 科彭斯多极模型和赫希菲尔德原子精修（HAR）]，但热运动的处理在很大程度上仍未改变。我们开发了一种新方法，该方法结合了先进电荷密度模型[非球形原子模型（AAM），如HAR或可转移非球形原子模型（TAAM）]和热运动模型（简正模式精修，NoMoRe）的优势。我们将这种方法称为AAM_NoMoRe，其中我们不是针对单晶X射线衍射数据精修常规的各向异性位移参数（ADP），而是精修从周期性密度泛函理论（DFT）计算中获得的频率。在这项工作中，我们通过将其应用于模型化合物（如丙氨酸、木糖醇、萘和甘氨酸多晶型物）来证明该模型的有效性，突出了我们的方法对H原子位置及其ADP形状的影响，这些与中子数据相当。我们观察到，与仅使用AAM相比，AAM_NoMoRe处理后H原子ADP的相似性指数显著降低，与中子数据的一致性更高。由于使用了非球形形状因子（AAM），我们的方法表现出更好的拟合性能，与独立原子模型（IAM）精修相比，wR2值持续更低，与传统的NoMoRe模型相比也有显著降低。此外，我们给出了一个关键热力学性质即热容的估计，并证明了它与实验量热数据的一致性。
