Linking solid-state phenomena via energy differences in ‘archetype crystal structures’

Abstract

Solid-state phenomena like disorder, polymorphism but also the occurrence of high-Z′ crystal structures can be linked via energy differences in ‘archetype crystal structures’, which will permit better prediction of their occurrence.

Categorization underlies understanding. Conceptualizing solid-state structures of organic molecules with ‘archetype crystal structures’ bridges established categories of disorder, polymorphism and solid solutions and is herein extended to special position and high-Z′ structures. The concept was developed in the context of disorder modelling [Dittrich, B. (2021). IUCrJ, 8, 305–318] and relies on adding quantum chemical energy differences between disorder components to other criteria as an explanation as to why disorder – and disappearing disorder – occurs in an average structure. Part of the concept is that disorder, as probed by diffraction, affects entire molecules, rather than just the parts of a molecule with differing conformations, and the finding that an R·T energy difference between disorder archetypes is usually not exceeded. An illustrative example combining disorder and special positions is the crystal structure of oestradiol hemihydrate analysed here, where its space-group/subgroup relationship is required to explain its disorder of hydrogen-bonded hydrogen atoms. In addition, we show how high-Z′ structures can also be analysed energetically and understood via archetypes: high-Z′ structures occur when an energy gain from combining different rather than overall alike conformations in a crystal significantly exceeds R·T, and this finding is discussed in the context of earlier explanations in the literature. Twinning is not related to archetype structures since it involves macroscopic domains of the same crystal structure. Archetype crystal structures are distinguished from crystal structure prediction trial structures in that an experimental reference structure is required for them. Categorization into archetype structures also has practical relevance, leading to a new practice of disorder modelling in experimental least-squares refinement alluded to in the above-mentioned publication.