Mathematical crystal chemistry: A mathematical programming approach to crystal structures of inorganic compounds

R Koshoji and T Ozaki, PHYSICAL REVIEW MATERIALS, 8, 113801 (2024).

DOI: 10.1103/PhysRevMaterials.8.113801

Efficient heuristics have predicted many functional materials such as high-temperature superconducting hydrides, while inorganic structural chemistry explains why and how the crystal structures are stabilized. Building upon the foundational insights of inorganic structural chemistry, we propose a mathematical programming formalism to search and systematize structural prototypes of crystals. By integrating empirical principles that govern the spatial arrangement of anions and their effects on cations, we define the objective functions: minimizing the unit cell volume and assigning discrete geometrical constraints including chemical bonds. This formulation introduces inequality constraints on interatomic distances derived from inorganic chemistry, substantially narrowing the search space for feasible structures. The method has been effectively applied to generate various oxide structures, including spinel, pyrochlore-alpha, and K2NiF4, demonstrating its ability to explore candidate crystal structures of complex inorganic compounds.

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