Assessing Order in Liquid, Supercooled, and Crystalline Water.

Water has strong directional interactions and forms a network of hydrogen bonds (H-bonds) in aqueous solutions. In order to assess the nature of this network as a function of the thermodynamic state, a generalized approach is introduced for enumerating the extended connectivity of H-bonding paths. By identifying and classifying rings formed from H-bonds where the donor-to-acceptor directionality can be considered, a ring summation factor metric can be constructed in a form comparable to the commonly used tetrahedral order parameter. This factor ranges between 0, where there is no closed path ring connectivity, and 1, where all potential H-bonds participate in unique closed paths. This new metric is used to explore the relative limits of water ordering in liquid, supercooled, and crystalline condensed phase systems. In liquid systems, network ordering is shown to depend on the specific state parameters and how different models for water perform at and outside of their commonly used conditions. As they are supercooled, water models that converge on a similar preferred crystalline form show a common ring distribution signature, indicating a universal characteristic ordering in the liquid environment preceding nucleation and crystal growth processes. The various crystalline ice polymorphs are observed to have unique degrees of order and distributions of ring sizes, and even different degrees of proton ordering can be identified using this approach. The detailed findings enable the identification of and subsequent remedy of potential deficiencies in tetrahedrality when characterizing the structure of crystalline water.