Composite Structural Descriptors Reveal Microscopic Structural Heterogeneity in Liquid Water

Liquids and glasses lack long-range order yet exhibit structural organization over short and intermediate length scales that strongly influences macroscopic behavior. In water, however, the microscopic nature and extent of this structural organization remain actively debated. Here, we introduce a physically transparent framework for constructing composite structural descriptors from multidimensional joint distributions of local structural metrics targeting distinct forms of order. Using deep potential molecular dynamics with quantum-chemical accuracy, we systematically evaluate combinations of established structural metrics and identify an optimal composite descriptor Σ that synergistically integrates first-shell tetrahedral order with second-shell translational order. This descriptor robustly separates locally ordered and disordered environments and yields structural populations consistent with the two-state description of water. Information-theoretic analysis further demonstrates that structural discrimination saturates at two dimensions, with negligible gain from higher-dimensional extensions. The framework provides a general strategy for identifying minimal yet maximally informative descriptors of local order in complex disordered systems.