Model for single-particle dynamics in supercooled water

We analyze a set of 10 M-step molecular dynamics (MD) data of low-temperatu re SPC/E model water with a phenomenological analytical model. The motivati on is twofold: to extract various k-dependent physical parameters associate d with the single-particle or the self-intermediate scattering functions (S ISFs) of water at a deeply supercooled temperature and to apply this analyt ical model to analyse of new high resolution quasielastic neutron scatterin g data presented elsewhere. The SISF of the center of mass computed from th e MD data show clearly time-separated two-step relaxations with a well defi ned plateau in between. We model the short time relaxation of the test part icle as a particle trapped in a harmonical potential well with the vibratio nal frequency distribution function having a two-peak structure known from previous inelastic neutron scattering experiments. For the long time part o f the relaxation, we take the alpha relaxation suggested by mode-coupling t heory. The model fits the low-temperature SISK over the entire time range f rom 1 fs to 10 ns, allowing us to extract peak positions of the vibrational density of states, the structural relaxation rats 1/tau of the cage (the p otential well) and the stretch exponent beta. The structural relaxation rat e has a power law dependence on the magnitude of the wave vector transfer k and the stretch exponent varies from 0.55 at large k to unity at small k.