The diffusion property of the intercalated species in the graphite materials is at the heart of the rate performance of graphite-based metal-ion secondary battery. Here we study the diffusion process of a AlCl 4 molecule within graphite -a key component of a recently reported aluminum ion battery with excellent performance -via molecular dynamics (MD) simulations. Both ab-initio MD (AIMD) and semiempirical tight-binding MD simulations show that the diffusion process of the intercalated AlCl 4 molecule becomes rather inhomogeneous, when the simulation time exceeds approximately 100 picoseconds. Specifically, during its migration in between graphene layers, the intercalated AlCl 4 molecule may become stagnant occasionally, and then recovers its normal (fast) diffusion behavior after halting for a while. When this phenomenon occurs, the linear relationship of the mean squared displacement (MSD) versus the duration time is not fulfilled. We interpret this peculiar behavior as a manifestation of inadequate sampling of rare event (the stagnation of the molecule), which does not yet appear in short-time MD simulations. We further check the influence of strains present in graphite intercalated compounds (GIC) on the diffusion properties of AlCl 4 , and find that their presence in general slows down the diffusion of the intercalated molecule, and is detrimental to the rate performance of the GIC-based battery.