Unraveling hidden symmetry breaking in racemic compounds

Racemic compounds, consisting of an equimolar mixture of enantiomers in crystalline form, are conventionally regarded as fully symmetric and are often dismissed as a trivial phenomenon due to their abundance-as they account for a substantial fraction (90 to 95%) of entries in structural databases. Here, we uncover the symmetry-breaking hierarchical organization within racemic compounds: single-handed molecules first self-assemble into homochiral domains, which then periodically self-organize with domains of opposite chirality to form the final crystal. Using a folded-plane model by applying isometry, we introduce a quantitative descriptor (angle θ) to probe symmetry breaking in racemic compounds, directly derived from crystal symmetry and unit cell parameters. We further develop a big-data analysis tool based on coset decomposition (a method of group theory) to comprehensively examine structural data from Cambridge Structural Database. Our analysis confirms the widespread occurrence of symmetry breaking in racemic compounds. This finding challenges the traditional view of racemic crystals as inherently symmetric, revealing their hidden complexity and potential implications for crystallography, materials science, and so on.