Local-order metric for condensed-phase environments

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, $S$ and $\ensuremath{\delta}S$, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that $S$, $\ensuremath{\delta}S$, and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.