where N m denotes the number of target ions in the system for diffusion calculation, ∆⃗ r i = ⃗ r i (t + t ′ ) -⃗ r i (t) is the displacement of the i th ion; t is the time origin, while t ′ is the time difference, and the angular bracket, the average over several points in time, for statistical equal weight at each point, typically half of the total time origins are chosen. The jump frequency can also be described as