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We investigate by Molecular-Dynamics simulations the fast mobility - therattling amplitude of the particles temporarily trapped by the cage of theneighbors - in mildly supercooled states of dense molecular (linear trimers)and atomic (binary mixtures) liquids. The mixture particles interact by theLennard-Jones potential. The non-bonded particles of the molecular system arecoupled by the more general Mie potential with variable We investigate byMolecular-Dynamics simulations the fast mobility - the rattling amplitude ofthe particles temporarily trapped by the cage of the neighbors - in mildlysupercooled states of dense molecular (linear trimers) and atomic (binarymixtures) liquids. The mixture particles interact by the Lennard-Jonespotential. The non-bonded particles of the molecular system are coupled by themore general Mie potential with variable repulsive and attractive exponents ina range which is characteristic of small $n$-alkanes and $n$-alcohols. Possiblelinks between the fast mobility and the geometry of the cage (size and shape)are searched. The correlations on a per-particle basis are rather weak.Instead, if one groups either the particles in fast-mobility subsets or thecages in geometric subsets, the increase of the fast mobility with both thesize and the asphericity of the cage is revealed. The observed correlations areweak and differ in states with equal relaxation time. Local forces between atagged particle and the first-neighbor shell do not correlate with the fastmobility in the molecular liquid. It is concluded that the cage geometry aloneis unable to provide a microscopic interpretation of the known, universal linkbetween the fast mobility and the slow structural relaxation. We suggest thatthe particle fast dynamics is affected by regions beyond the first neighbours,thus supporting the presence of collective, extended fast modes.

Weak links between fast mobility and local structure in molecular and atomic liquids