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We introduce the spatial correlation function $C_Q(r)$ and temporalautocorrelation function $C_Q(t)$ of the local tetrahedral order parameter$Q\equiv Q(r,t)$. Using computer simulations of the TIP5P model of water, weinvestigate $C_Q(r)$ in a broad region of the phase diagram. First we show that$C_Q(r)$ displays anticorrelation at $r\approx 0.32$nm at high temperatures$T>T_W\approx 250$ K, which changes to positive correlation below the Widomline $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits atwo-step temporal decay similar to the self intermediate scattering function,and that the corresponding correlation time $\tau_Q$ displays a dynamiccrossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for$T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the{\it local} orientational order of water molecules, and show that $\tau_Q$ canbe extracted from $S_Q$ using an analog of the Adam-Gibbs relation.

Space-Time Correlations in the Orientational Order Parameter and the Orientational Entropy of Water