where r i is the net displacement of a migrating ion after n hops, while a is the average distance for a single hop. Therefore, an accurate calculation of the ionic transport properties requires the sampling of a large-enough number of migration events, which requires that all mobile species are tracked during the simulation. One of the important parameters required by a kMC simulation are the migration barriers (E b s), which are the energy barrierers that the mobile ion must overcome to complete a successful hop. E b ultimately determines the probability of occurrence a given ionic hop. Typically, E b s are evaluated using the nudged elastic band (NEB) method in combination with density functional theory (DFT). . In a NEB calculation, one performs a constrained relaxation of a specific number of virtually connected "images", between the initial and final positions of a migration event, along a guessed minimum energy pathway (MEP). The relaxation is constrained to maintain a uniform spacing between the images (i.e., as uniform as possible), through the addition of fictitious spring forces. Other tools, such as force fields and machine-learned interatomic potentials, can also be used to determine E b instead of DFT, and kMCpy is also compatible with such tools.