Data-Driven Topological Analysis of Polymorphic Crystal Structures

Abstract: Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of materials. Accurate identification and prediction of polymorphic structures are critical for materials design, drug development, and device optimization, as unknown or overlooked polymorphs may lead to unexpected performance or stability issues. Despite its significance, predicting polymorphism directly from a chemical composition remains a challenging problem due to the complex interplay between molecular conformations, crystal packing, and symmetry constraints. In this study, we conduct a comprehensive data-driven analysis of polymorphic materials from the Materials Project database, uncovering key statistical patterns in their composition, space group distributions, and polyhedral building blocks. We discover that frequent polymorph pairs across space groups, such as (71, 225), display recurring topological motifs that persist across different compounds, highlighting topology not symmetry alone as a key factor in polymorphic recurrence. We reveal that many polymorphs exhibit consistent local polyhedral environments despite differences in their symmetry or packing. Additionally, by constructing polyhedron connectivity graphs and embedding their topology, we successfully cluster polymorphs and structurally similar materials even across different space groups, demonstrating that topological similarity serves as a powerful descriptor for polymorphic behavior. Our findings provide new insights into the structural characteristics of polymorphic materials and demonstrate the potential of data mining and machine learning for accelerating polymorph discovery and design.