Essentially, the H R is a ratio between the average MSD of all the mobile atoms and the MSD of the center of mass of all the mobile atoms (denominator ). As the center of mass of the target ions is equivalent to a single particle behavior, it is a fluctuating quantity. Thus, in practice, several independent runs are counted for better statistics. The ionic conductivity, σ, can be linked to the diffusion coefficient, D r , according to the Nernst-Einstein equation,