Many theoretical studies already dealt with the interaction of one H-2 molecule with a metallic surface, but so far none aimed at the description of the interaction of additional layers of molecules, which is the goal of the present work. A model system consisting of a cluster of 13 Cu atoms and two/three H-2 molecules has been used to calculate with highly correlated wavefunctions the interaction of successive layers of H-2 with a surface of copper already covered by chemisorbed, dissociated H-2 molecules. A second H-2 molecule, approaching the Cu surface with different orientations, on top of a first one, is not dissociated and its physisorption interaction with the surface is calculated to be in the range 600-1000 cm(-1), approximately twice that of the first H-2 molecule. The physisorption interaction of H-2 molecules forming a third layer is estimated to be in the range of 60-100 cm(-1), which is much smaller than the interaction of the second layer with the surface but still larger than the H-2/H-2 interaction between a pair of isolated molecules. It is shown that this effect mainly results from the interactions with the ions H- and Cu+ formed on the surface. (c) 2006 Elsevier B.V. All rights reserved.