We report calculations using a previously reported model of lithium perchlorate in polyethylene oxide in order to understand the mechanism of lithium transport in these systems. Using an algorithm suggested by Voter, we find results for the diffusion rate which are quite close to experimental values. By analysis of the individual events in which large lithium motions occur during short times, we find that no single type of rearrangement of the lithium environment characterizes these events. We estimate the free energies of the lithium ion as a function of position during these events by calculation of potentials of mean force and thus derive an approximate map of the free energy as a function of lithium position during these events. The results are consistent with a Marcus-like picture in which the system slowly climbs a free energy barrier dominated by rearrangement of the polymer around the lithium ions, after which the lithium moves very quickly to a new position. Reducing the torsion forces in the model causes the diffusion rates to increase.