Energy minimisation calculations and molecular dynamics simulations have been used to investigate the motion of single adatoms on the (100) faces of model face-centred-cubic metals. The potentials used were introduced by Sutton and Chen [Philos. Mag. Lett. 61 (1990) 139] and include a many-body term which should give a reasonable realistic description of the surface, including inward relaxation of the surface layer. These potentials are characterised by a pair of exponents, and Sutton and Chen assigned different exponents to different metals. Two mechanisms for migration of surface atoms were found, a direct motion of the adatom across the surface and exchange of the adatom with a substrate atom. The preferred mechanism depends on the exponents used in the potential, that is on the particular metal modelled. This difference arises because the activation energy for the exchange process is strongly dependent on the exponents in the Sutton-Chen potential. The pre-exponential factor or inherent diffusivity was investigated for two Sutton-Chen potentials using molecular dynamics simulations and found to be somewhat larger for the exchange process; the reasons for this are discussed. The values are in agreement with experiment. The simulation results show that the exchange mechanism results in diagonal motion. For the potential assigned to platinum exchange occurs, but for rhodium it does not. This is in agreement with experiment, but the results for iridium are in contradiction with experiment, probably due to a lack of angle-dependent terms in the potential. Such terms are less likely to be important in metals with full or nearly full d shells and predictions are made about the mechanisms of adatom diffusion on such metals.