Molecular correlations in a supercooled liquid

We present static and dynamic properties of molecular correlation functions S_{lmn,l^′m^′n^′}(q⃗,t) in a simulated supercooled liquid of water molecules, as a preliminary effort in the direction of solving the molecular mode-coupling theory (MMCT) equations for supercooled molecular liquids. The temperature and time dependence of various molecular correlation functions, calculated from 250 ns long molecular dynamics simulations, show the characteristic patterns predicted by MMCT and shed light on the driving mechanism responsible for the slowing down of the molecular dynamics. We also discuss the symmetry properties of the molecular correlation functions that can be predicted on the basis of the C_2v symmetry of the molecule. Analysis of the molecular dynamics results for the static correlators S_{lmn,l^′m^′n^′}(q⃗) reveals that additional relationships between correlators with different signs of n and n^′ exist. We prove that for molecules with C_rv symmetry this unexpected result becomes exact at least for high temperatures.