Mathematical crystal chemistry II: Random search for ionic crystals and analysis on oxide crystals registered in ICSD
Mathematical crystal chemistry views crystal structures as the optimal solutions of the mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the types of geometrical constraints, extending the concept of...
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/6yl6-fr8b |
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| Summary: | Mathematical crystal chemistry views crystal structures as the optimal solutions of the mathematical optimization problem formalizing inorganic structural chemistry. This paper introduces the minimum and maximum atomic radii depending on the types of geometrical constraints, extending the concept of effective atomic sizes. These radii define permissible interatomic distances instead of interatomic forces, constraining feasible types and connections of coordination polyhedra. The definition derives the continuous optimization problem as dense packings of flexible atomic spheres. Additionally, discrete variables and constraint functions, which give a choice of creatable types of geometrical constraints depending on the spatial order of atoms, are implemented to formalize the feasible atomic environment, such as the composition of coordination polyhedra, resulting in acceleration of structure search and decrease of the number of local minima. The framework identifies unique optimal solutions corresponding to the structures of spinel, pyrochlore (α and β), pyroxene, quadruple perovskite, cuprate superconductor YBa_{2}Cu_{3}O_{7−x}, and iron-based superconductor LaFeAsO. Notably, up to 95% of oxide crystal structure types in the Inorganic Crystal Structure Database align with the optimal solutions preserving experimental structures despite the discretized feasible atomic radii. These findings highlight the role of mathematical optimization problems as a theoretical foundation for mathematical crystal chemistry, enabling efficient structure prediction. |
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| ISSN: | 2643-1564 |