Searching for local order parameters to classify water structures at triple points

The diversity of ice polymorphs is of interest in condensed-matter physics, engineering, astronomy, and biosphere and climate studies. In particular, their triple points are critical to elucidate the formation of each phase and transitions among phases. However, an approach to distinguish their molecular structures is lacking. When precise molecular geometries are given, order parameters are often computed to quantify the degree of structural ordering and to classify the structures. Many order parameters have been developed for specific or multiple purposes, but their capabilities have not been exhaustively investigated for distinguishing ice polymorphs. Here, 493 order parameters and their combinations are considered for two triple points involving the ice polymorphs ice III-V-liquid and ice V-VI-liquid. Supervised machine learning helps automatic and systematic searching of the parameters. For each triple point, the best set of two order parameters was found that distinguishes three structures with high accuracy. A set of three order parameters is also suggested for better accuracy.