Relative diffusion and memory effects in supercooled water

The relative motion of tagged pairs of water molecules, which are in a given state of the pair configuration space at the initial time, is followed along simulated trajectories in the supercooled liquid. The initial state selects particles of the first coordination shell with specific relative orientations. This allows one to study the effects produced by the local orientational order on the translational dynamics. The states of the first coordination shell, indicated as transition states (TS) in the structural study, show higher mobility than the hydrogen bonded (HB) ones. The memory of the initial state results completely last only after 20 ps. In the first 10 ps the memory effects produce an increasing difference between the mean square displacements of pairs originally tagged as TS and HE pairs. Between 10 and 20 ps, the relative motions relax toward the normal diffusion regime along trajectories with a fractal dimension higher and lower than 2 for TS and HE pairs, respectively. This fact and the evaluation of the average lifetime of Il bonds suggest that the time length of the anomalous diffusion regime and the memory time are determined by the dynamics of the hydrogen bond network rearrangements. Our approach can be relevant to understand the interplay between structure and dynamics in orientationally disordered media and, particularly, to interpret the results of recent studies on protein hydration water and confined water.