We have carried out long time scale simulations where the “dimer method” [G. Henkelman and H. Jónsson, J. Chem. Phys. 111, 7010 (1999)] is used to find the mechanism and estimate the rate of transitions within harmonic transition state theory and time is evolved by using the kinetic Monte Carlo method. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assigned to lattice sites and a list of all possible transitions does not need to be specified beforehand. Rather, the relevant transitions are found on the y during the simulation. An application to the diffusion and island formation of Al adatoms on an Al(100) surface is presented.