Origins of Tetrahedral Order in Ice.

The many-body decomposition of the lattice energies in seven ice polymorphs (ice Ih, II, VIII, IX, XIII, XIV, XV) reveals an intriguing correlation between the polymorph's local tetrahedral order, its density, and the inherent cooperativity of its hydrogen bond network. Low-pressure ice phases demonstrate significant cooperative effects, accounting for up to approximately 25% of the lattice energy and exhibit nearly perfect local tetrahedral order. In contrast, high-pressure ice phases exhibit smaller cooperative effects (around 6%) and local structures that are less tetrahedral. The distinct local tetrahedral order encompassing nearest neighbors in these ice polymorphs is attributed to the hydrogen bond cycles in the extended network (heterodromic, antidromic and homodromic), which represents a unifying feature that profoundly influences cooperativity based on cycle size and connectivity. These findings facilitate the establishment of a novel causality between structure and stability while they further identify cooperativity as the key descriptor of hydrogen bonding characteristics across the ice phase diagram.