A journey into the local structural order of liquid water: from the insights earned by geometrically-inspired descriptors to the development of a brand new energy-based indicator

Abstract

In this work, we review recent efforts to develop a structural order parameter that satisfactorily accounts for water’s anomalous behavior. Over the years, a large body of evidences has been accumulated in favor of a two-liquids scenario for water. This picture considers the liquid as a mixture of two different local molecular arrangements (one well-structured, with low local density, and another unstructured, with high local density) and water’s anomalies would stem precisely from the competition between such states. Thus, the availability of a structural indicator capable of accurately discriminating both kinds of molecular arrangements is mandatory within this field and has been the subject of intense work during the past decades. In turn, comparative reports of the methods for local structure determination in liquids and glasses, including liquids with directional interactions like water, have already been performed. Thus, instead of presenting a complete account of such methods for water, we shall now focus on structural indicators that have been explicitely devised to sense the existence of the two purported water states. In this sense, we shall present indicators that have exhibited success in producing distributions with certain degree of bimodality. Some of these indicators are based on the consideration of certain structural traits like the tetrahedral order of water’s first coordination shell or the translational order up to the second shell (its inhomogeneity). However, we shall show that besides the inability of early indicators to produce clear bimodal distributions (which would enable not only the estimation of the population of the two kinds of species but that would also allow for a proper molecular classification), such indices have also exhibited a tendency to overestimate the unstructured state. We shall thus also describe strategies to overcome these limitations, like the employment of potential energy minimizations and the incorporation of water’s intermolecular interactions (hydrogen bonds), which have either improved existent indicators or proposed new ones. Within this context, a very recent proposal entirely based on energetic considerations will also be described.