Since we are interested in correlations between dierent molecules, we focus herein solely on the analysis of the distinct dynamical atom-atom correlation functions, both in r and k space. The time dependence of these functions for the The main panel of Fig. shows the decay of the OO and OH main peaks of the pair correlation functions of Fig. , in the range of 0-2 ps, while the inset focus on the long time scale (with vertical log scale). The rst feature which is immediately apparent is the hierarchy of time decays, the fastest for water and slowest for ethanol, with a narrower dierence between the 2 alcohols. This feature alone indicates that the temporal decay of charged atom correlations is vastly dierent for water and the 2 alcohols, despite the static correlations presenting appealing similarities. The second feature is that time decays between the various atom-atom correlation show more dierence between themselves for water than for the alcohols, indicating that the charged group motions are more homogeneous for alcohols than for water. Going into specic details, for water, the OH decay is the fastest, while the OO decay is the slowest, which seems contradictory: if the OH contact decorrelates very fast, then the auxiliary OO contact should also decay accordingly. The only way to reconcile these contradictory decays is that the rotation of the OH arm is such that it re-establish the OO contact. This is the jump rotation motion advertised in recent investigations , and is found to be contained in the dynamics of a classical model of water. For alcohols, it is the opposite which is found, namely that the OO decay is faster than the OH decay, denoting that the hydrogen bonding holds the hydroxyl group clusters. The long time decay shown in the inset suggests a near exponential behaviour, as expected for equilibrium liquids with simple diusion, and a perfect isotropy for all atoms. It is seen that water and methanol have a similar decay, while ethanol has a markedly slower decay, suggesting slower global dynamics, which is also compatible with the higher viscosity of this liquid. Fig. shows the time decays of the various peak positions we discussed in Fig. , through the total intermediate scattering function F t (k, t), and the inset shows the log scale version, to underline the quasi-exponential decays. While the dynamics in r-space is directly intuitive as referring to actual atom motions, that in k-space is more dicult to grasp, since k-peaks reect global trends.