Towards understanding high-Z' organic molecular crystals through the superspace method.

大约90%的分子晶体在单位晶胞中具有一个对称无关的分子(对于共晶体，每个组分一个分子)。Z‘被定义为单位晶胞中的公式单元的数目Z除以空间群的倍数。因此，90%的晶体结构被表征为Z‘=1(或在特殊情况下为Z’&lt；1)。Z‘=1的丰度可以从这样的论点中理解，即晶态将包含分子在最佳环境中的最佳构象。当不同的交互无法同时优化时，可能会出现值Z‘&gt；1。Z‘&gt；4的值被认为是高Z’值。在已知的有机分子晶体结构中，约有0.1%是高Z‘结构。最近的两篇综述文章-由Steed&Steed(2015)和C.BRock(2016)-强调了高Z‘结构对于理解晶体堆积的重要性，特别是多态。晶体结构决定了药物和农用化学品的溶解度、稳定性和生物利用度。因此，它在工业上具有重要意义。高Z‘晶体结构具有大的晶胞，其中包含分子在不同构象和不同环境中的Z’拷贝。这一特性使它们成为超空间方法的理想候选者。在超空间方法中，晶体结构被描述为基本结构的调制，后者被描述为小的单胞。调制提供了分子的Z‘拷贝之间的差异的直接表示。可替换地，调制可以是不相称的，其结果是不存在超级小区并且未定义Z‘。本项目的目的是证明超空间方法对高Z‘晶体结构的理解将导致对这些结构的理解，而不是经典的大单胞方法。为此，将对三种具有生物重要性的物质的晶体结构进行超空间描述：环吡喃(Z‘=12；制药)、二水糖精钠(Z’=16；人工甜味剂)和胆固醇(Z‘=16，存在于动物生活中)。通过对晶体结构在不同温度下的X射线衍射，可以得到超空间模型。高Z‘结构模型将针对晶体结构可能存在的不可公度性进行测试。相变将被研究，因为它们可能发生在无公度和高Z‘晶体结构之间。晶体结构的超空间描述将阐明伪对称性，并将表征导致Z‘值高的相互作用。

About 90% of the molecular crystals possess a single symmetry-independent molecule in the unit cell (in case of cocrystals, one molecule of each of the constituents). Z' is defined as the number of formula units in the unit cell, Z, divided by the multiplicity of the space group. Therefore, 90% of the crystal structures are characterized by Z' = 1 (or Z' < 1 in special cases). The abundance of Z' = 1 can be understood from the argument, that the crystalline state will contain the molecule in its optimal conformation in the optimal environment. Values Z' > 1 can occur, when the different interactions cannot be simultaneously optimized. A value of Z' > 4 is considered to be a high Z' value. About 0.1% of the known crystal structures of organic molecular crystals are high-Z' structures. Two recent review articles---by Steed & Steed (2015) and C. Brock (2016)---stress the importance of high-Z' structures for understanding crystal packing in general and polymorphism in particular. The crystal structure determines the solubility, stability and bioavailability of pharmaceuticals and agrochemicals. It is, therefore, of great industrial importance. High-Z' crystal structures possess large unit cells containing Z' copies of the molecule in different conformations and different environments. This property makes them ideal candidates for the superspace approach. Within the superspace approach, the crystal structure is described as a modulation of a basic structure, the latter being characterized by a small unit cell. The modulation provides a direct representation of the differences between the Z' copies of the molecule. Alternatively, the modulation can be incommensurate, with the consequence that a supercell does not exist and Z' is not defined. The present project is intended to demonstrate that the superspace approach to high-Z' crystal structures will lead to an understanding of these structures that goes beyond the classical approach with a large unit cell. For this purpose, the superspace description will be developed for the crystal structures of three substances of biological importance: Ciclopirox (Z' = 12; Pharmaceutical), Sodium saccharine dihydrate (Z' = 16; artificial sweetener) and cholesterol (Z' = 16; present in animal life). Superspace models will be obtained by x-ray diffraction for the crystal structures at several temperatures. The high-Z' structure model will be tested against a possible incommensurability of the crystal structure. Phase transitions will be investigated, as they may occur between incommensurate and high-Z' crystal structures. The superspace description of the crystal structures will elucidate pseudo-symmetries, and it will characterize the interactions that are responsible for the high value of Z'.