The mean square displacement is a very important way of calculating diffusion. The slope of the mean square plot vs. time provides the diffusion coefficient. With molecular dynamics we can investigate the rate of diffusion for many different liquids over a wide range of temperatures and densities. The results can be compared with experiment or we can even predict experimental results when they are difficult to obtain. This is a very powerful way of looking at molecular motion, we can even look at the motion of atoms in solids which is difficult to measure experimentally.
Diffusion in solids usually proceeds by hopping; the atoms jump from place to place rather than simply drift. The energy required for a hop can be calculated from the slope of the Arrhenius plot, the steeper the slope the more energy is required. In liquids diffusion is relatively easy and so the Arrhenius slope is much less.