Slow Dynamics of Water Molecules in Supercooled States

We perform long molecular dynamics simulations of liquid water in normal and supercooled states for times up to 50 ns. We observe the onset of a cage effect at 0.25 ps followed by diffusion at much longer time. The diffusion constant has a power-law temperature dependence. The long-time single-particle dynamics of supercooled water is dominated by a two-step process, beta and alpha relaxations, familiar in the mode-coupling theory of supercooled simple liquids. Over length scales comparable to the cage size alpha decay is characterized by a relaxation rate having a $q^2$ to $q$ crossover close to the kinetic glass transition temperature.