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

• Applicant: Professor Dr. Sander van Smaalen
• Subject Area: Mineralogy, Petrology and Geochemistry
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 389490692

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'.

• DFG Programme: Research Grants