Thermodynamic stability is an essential property of crystalline materials, and its accurate calculation requires a reliable description of the thermal motion - phonons - in the crystal. Such information can be obtained from periodic density functional theory (DFT) calculations, but these are costly and in some cases insufficiently accurate for molecular crystals. This deficiency is addressed here by refining a lattice-dynamics model, derived from DFT calculations, against accurate high-resolution X-ray diffraction data. For the first time, a normal-mode refinement is combined with the refinement of aspherical atomic form factors, allowing a comprehensive description and physically meaningful deconvolution of thermal motion and static charge density in the crystal. The small and well diffracting L-alanine system was used. Different lattice-dynamics models, with or without phonon dispersion, and derived from different levels of theory, were tested, and models using spherical and aspherical form factors were compared. The refinements indicate that the vibrational information content in the 23 K data is too small to study lattice dynamics, whereas the 123 K data appear to hold information on the acoustic and lowest-frequency optical phonons. These normal-mode models show slightly larger refinement residuals than their counterparts using atomic displacement parameters, and these features are not removed by considering phonon dispersion in the model. The models refined against the 123 K data, regardless of their sophistication, give calculated heat capacities for L-alanine within less than 1 cal mol-1 K-1 of the calorimetric measurements, in the temperature range 10-300 K. The findings show that the normal-mode refinement method can be combined with an elaborate description of the electron density. It appears to be a promising technique for free-energy determination for crystalline materials at the expense of performing a single-crystal elastic X-ray diffraction determination combined with periodic DFT calculations.

中文翻译：

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针对弹性衍射数据改进的电子密度和晶格动力学的组合模型。结晶L-丙氨酸的热力学性质。

热力学稳定性是晶体材料的基本属性，其精确计算需要可靠地描述晶体中的热运动-声子。可以从周期性密度泛函理论（DFT）计算中获得此类信息，但这些信息昂贵，并且在某些情况下对于分子晶体而言不够准确。通过针对精确的高分辨率X射线衍射数据改进从DFT计算得出的晶格动力学模型，可以解决此不足。首次将常模精细化与非球面原子形状因子的精细化结合在一起，从而可以对晶体中的热运动和静电荷密度进行全面的描述以及在物理上有意义的反卷积。使用了小型且衍射良好的L-丙氨酸系统。测试了来自不同理论水平的具有或不具有声子扩散的不同晶格动力学模型，并比较了使用球形和非球形形状因数的模型。改进表明，23 K数据中的振动信息内容太小而无法研究晶格动力学，而123 K数据似乎保留了声学和低频光子的信息。这些正常模式模型显示的精炼残差比使用原子位移参数的模型的残差略大，并且这些特征并未通过考虑模型中的声子色散而消除。根据123 K数据精炼的模型，无论其复杂程度如何，都可以在不到1 cal mol-1 K-1的量热测量值范围内计算出L-丙氨酸的热容量，在10-300 K的温度范围内。发现表明，正常模式的细化方法可以与电子密度的详细描述相结合。这似乎是一种有前途的晶体材料自由能测定技术，但要进行单晶弹性X射线衍射测定并结合定期DFT计算来进行。