Linking solid-state phenomena via energy differences in `archetype crystal structures'

Area of Science:

• Solid-state chemistry and crystallography
• Materials science
• Computational chemistry

Background:

• Categorization is fundamental to scientific understanding.
• Existing models for crystal structures struggle to fully explain disorder, polymorphism, and solid solutions.
• Disorder modeling in crystallography has limitations in explaining the occurrence and disappearance of disorder.

Purpose of the Study:

• To introduce and extend the concept of 'archetype crystal structures' to encompass disorder, polymorphism, solid solutions, special position, and high-Z' structures.
• To provide an energetic explanation for the occurrence of disorder in crystalline organic molecules.
• To demonstrate the application of archetype structures in analyzing complex crystal structures and refining disorder modeling.

Main Methods:

• Development of the 'archetype crystal structures' concept based on quantum chemical energy differences.
• Analysis of crystal structures, including disorder and special positions, using the archetype framework.
• Energetic analysis of high-Z' structures to understand their formation via archetypes.
• Comparison with existing literature and experimental least-squares refinement practices.

Main Results:

• Archetype crystal structures provide a unifying framework for understanding disorder, polymorphism, and solid solutions.
• Quantum chemical energy differences between disorder components explain the presence and absence of disorder.
• The crystal structure of oestradiol hemihydrate is analyzed, illustrating the role of space-group/subgroup relationships in explaining hydrogen-bonded hydrogen atom disorder.
• High-Z' structures are energetically understood as arising from an energy gain exceeding thermal energy (R·T) when combining diverse molecular conformations.

Conclusions:

• Archetype crystal structures offer a powerful categorization tool for solid-state molecular structures.
• The energetic approach provides a robust explanation for various structural phenomena like disorder and high-Z' structures.
• This concept has practical implications for improving disorder modeling in experimental crystallography.