Systematic comparison of crystalline and amorphous phases: Charting the landscape of water structures and transformations.

Systematically resolving different crystalline phases starting from the atomic positions, a mandatory step in algorithms for the prediction of structures or for the simulation of phase transitions, can be a non-trivial task. Extending to amorphous phases and liquids which lack the discrete symmetries, the problem becomes even more difficult, involving subtle topological differences at medium range that, however, are crucial to the physico-chemical and spectroscopic properties of the corresponding materials. Typically, system-tailored order parameters are devised, like global or local symmetry indicators, ring populations, etc. We show that a recently introduced metric provides a simple and general solution to this intricate problem. In particular, we demonstrate that a map can be traced displaying distances among water phases, including crystalline as well as amorphous states and the liquid, consistently with experimental knowledge in terms of phase diagram, structural features, and preparation routes.