Chemical diversity encoded in symmetry: universal distortion rules and design principles for perovskites

The quantitative relationship between chemical composition, crystal structure and functional properties in materials with complex distortions has remained elusive, creating a critical bottleneck for rational design. This is particularly relevant for the vast family of Pnma perovskites-technologically important materials where octahedral tilting governs key functionalities. While Landau theory successfully describes structural responses to external stimuli like temperature or pressure, its application to chemical diversity has been largely unexplored. Here, we bridge this gap by demonstrating that symmetry-derived order parameters serve as universal descriptors, providing a language connecting chemical bonding to distortion patterns. Through group-theoretical analysis of 227 Pnma perovskites across oxides, fluorides, halides and chalcogenides, we establish robust symmetry principles governing composition-structure relationships. Unlike empirical descriptors or non-analytical machine learning approaches, our framework provides quantitative, physics-based design rules for engineering functional properties. This work expands Landau theory into chemical space, creating a universal platform for understanding and designing functional materials, with implications extending beyond perovskites to other distorted crystal structures.