A tetrahedral entropy for water

We introduce the space-dependent correlation function C Q(r) and time-dependent autocorrelation function C Q(t) of the local tetrahedral order parameter Q ≡ Q(r,t). By using computer simulations of 512 waterlike particles interacting through the transferable interaction potential with five points (TIP5 potential), we investigate C Q(r) in a broad region of the phase diagram. We find that at low temperatures C Q(t) exhibits a two-step time-dependent decay similar to the self-intermediate scattering function and that the corresponding correlation time τQ displays a dynamic cross-over from non-Arrhenius behavior for T > T W to Arrhenius behavior for T < T W, where T W denotes the Widom temperature where the correlation length has a maximum as T is decreased along a constant-pressure path. We define a tetrahedral entropy S Q associated with the local tetrahedral order of water molecules and find that it produces a major contribution to the specific heat maximum at the Widom line. Finally, we show that τQ can be extracted from S Q by using an analog of the Adam–Gibbs relation.