In contrast to the -LPS hACF ! Q i, which exhibits no exponential decay, as shown in Figure , the hACF ! Q i for am-LPS shows a clear, fast exponential decay which can be fit to the Lipari-Szabo relation given in Equation 5 ( = 1.0). The decay time extracted from hACF ! Q for am-LPS is ⌧ SAE = 46 ns, which corresponds to a Li hopping rate of ⌧ 1 SAE = 2.17 ⇥ 10 7 s 1 . Comparing this with the hopping rate extracted from the MSD (7.0⇥10 7 s 1 ), we see that both methods predict the same order of magnitude hopping rates for Li at 300 K. The hopping rate extracted from ⌧ 1 SAE is a slight underestimation to the rate extracted from the MSD, however this is consistent with the fact that the hACF ! Q i is not sensitive to all ion hops that occur within the material, only those for which ! tm 6 = ! t0 , as discussed above.