Hard-sphere behavior in the dynamics of all mono-atomic liquids at the de Gennes minimum

•A relation is proposed between the dynamics and the static properties of a liquid.•The relation contains no adjustable parameters.•Mono-atomic liquids that crystallize in a close packed structure adhere to it.•Liquids that do not crystallize in a close packed structure deviate from it.

We show that the position of the de Gennes minimum in scattering spectra, where the dynamics of liquids slow down, is given by a hard-sphere expression for a range of mono-atomic liquids that crystallize in a close packed structure. This expression relates the position of the minimum to the number density of the liquid, without any adjustable or unknown parameters. We argue that this implies that a liquid can be viewed as a close packed structure of the cages that represent the confinement of atoms by their neighbors. We further show that some metals deviate from this expression, namely those metals that crystallize in a structure that is not close packed. Our expression should prove very useful in identifying what liquids to study in inelastic scattering experiments given that deviations from normal fluid behavior can already be predicted based on the peak position of the static structure factor.