Molecular dynamics (MD) simulations of SPC/E water have been performed to characterize anomaly of water such as density maximum and minimum observed in temperature dependence and polyamorphism related them. Two important factors to explain the density anomaly of the system are considered in the present work. First, the changes in network of hydrogen bonds of water with temperatures is characterized by the thermodynamical quasi-equilibration among different kinds of local polyhedra (O atoms around O atom connected by hydrogen bonding), where applicability of the van’t Hoff analysis is confirmed. As a result of this treatment, change of water structure with decreasing temperature can be characterized as the transition from “heterogeneous network” to “homogeneous network”. This explanation differs from that based on simple mixing of two (or several) components nor that by development of typical hydrogen networks only. Second, one needs to consider oscillating structures of coordination shells. Quantitative comparison of local density with different length scales revealed that inclusion of longer length scale structures is required for convergence of the density. Namely, the density of water is not a simple sum of the different size of units but is determined by the coordination shells including sparse regions. These concepts are also useful to characterize the polyamorphism of water. With increasing pressure at 200 K, the transition from “homogeneous network” to “heterogeneous network” occurs. The change corresponds to that from “low density water (LDW)” to “high density water (HDW)”, which accompanied with a large change of distribution of coordination numbers in longer length scales.
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