The Callovo-Oxfordian clay formation (COx) is the potential host rock for long term nuclear waste repository in France. The clayey component of COx consists mostly of illite, smectite and interstratified illite/smectite (I/S) clay minerals. We performed a series of molecular dynamics (MD) computer simulations in order to quantify the molecular scale mechanisms responsible for the adsorption and transport of ions at the hydrated surfaces of illite, smectite, and I/S clays. New structural models of illite, smectite, and I/S allowed us to identify several structurally different adsorption sites at the basal surfaces of all three clay substrates. Adsorption free energy profiles above each individual adsorption site on each clay surface for a wide range of metal cations were then calculated and the metal sorption properties for the three clay surfaces are compared in terms of the preferable sorption sites and their surface distributions, most stable adsorption distances, and free energies of adsorption. The resulting equilibrium constants for surface adsorption and ion exchange were calculated and found in general agreement with available literature data. The observed discrepancies between the exchange energies obtained in the current MD simulations and the values obtained through the interpretation of recent X-ray reflectivity measurements can be attributed to the differences in the description of the exchange reaction equilibria between the experimental conditions and the simplified conditions of our simulations.