In another work we have determined the diffusion rates corresponding to most of the elementary diffusion processes that may occur during the growth of a single 2D adisland on Cu(111). We started by studying the diffusion of an adatom along step A and step B using the two methods: The Transition State Theory in the Harmonic Approximation (TST-HA) approach (in the classical limit) and Molecular Dynamics (MD) simulations. We show that the static activation barrier accounts quite well for the results of MD simulations. However, the prefactors obtained in the latter method are different from those given by TST-HA. Furthermore they are quite consistent with the Meyer-Neldel law. We have then determined the static barriers for other diffusion events in the presence of straight steps or in the vicinity of steps with defects, for instance around corners and kinks.