Dynamical heterogeneities, the Van Hove function, and medium-range order

In supercooled liquids atoms and molecules rearrange in a correlated fashion; each of these cooperative clusters of atoms and molecules are termed a dynamical heterogeneity. Dynamical heterogeneities have historically been described by a four-point, time-dependent density correlation function, $chi (r, t)$. In this work, we show that in certain cases the distinct part of the Van Hove function, $G (r, t)$, which is a two-point correlation function, contains essentially the same information about medium-range order as $chi (r, t)$. Whereas the self part of the Van Hove function has been widely studied, the distinct part received little attention. We show that the distinct part can describe some aspects of dynamical heterogeneities related to the medium-range order, suggesting close relationships between dynamical heterogeneities and the medium-range order.