Microscopic structural descriptor of liquid water

The microscopic structure of liquid water has been believed to be the key to the understanding of the unique properties of this extremely important substance. Many structural descriptors have been developed for revealing local structural order in water, but their properties are still not well understood. The essential difficulty comes from structural fluctuations due to thermal noise, which are intrinsic to the liquid state. The most popular and widely used descriptors are the local structure index (LSI) and d₅. Recently, Russo and Tanaka [Nat. Commun. 3, 3556 (2014)] introduced a new descriptor ζ which measures the translational order between the first and second shells considering hydrogen bonding (H-bonding) in the first shell. In this work, we compare the performance of these three structural descriptors for a popular water model known as TIP5P water. We show that local structural ordering can be properly captured only by the structural descriptor ζ, but not by the other two descriptors particularly at a high temperature, where thermal noise effects are severe. The key difference of ζ from LSI and d₅ is that only ζ considers H-bonding which is crucial to detect high translational and tetrahedral order of not only oxygen but also hydrogen atoms. The importance of H-bonding is very natural, considering the fact that the locally favored structures are stabilized by energy gain due to the formation of four hydrogen bonds between the central water molecule and its neighboring ones in the first shell. Our analysis of the water structure by using ζ strongly supports the two-state model of water: water is a dynamic mixture of locally favored (ordered) and normal-liquid (disordered) structures. This work demonstrates the importance of H-bonding in the characterization of water's structures and provides a useful structural descriptor for water-type tetrahedral liquids to study their structure and dynamics.