Abstract: Using first-principles calculations and reactive force field molecular dynamics simulations, we study the structural properties and dynamics of a fluorine (F) atom, either adsorbed on the surface of single layer graphene (F/GE) or between the layers of AB stacked bilayer graphene (F@ bilayer graphene). It is found that the diffusion of the F atom is very different in those cases, and that the mobility of the F atom increases by about an order of magnitude when inserted between two graphene layers. The obtained diffusion constant for F/GE is twice larger than that experimentally found for gold adatom and theoretically found for C-60 molecule on graphene. Our study provides important physical insights into the dynamics of fluorine atoms between and on graphene layers and explains the mechanism behind the separation of graphite layers due to intercalation of F atoms.