Quantum calculations of dihydrogen and atomic hydrogen in contact with metal clusters Pd, Ni, Ag and bimetal clusters PdNi, PdAg have been performed using the density functional theory (DFT) methods. The potential energy surfaces for the dissociation of dihydrogen on metal clusters were calculated. The dissociation paths and the energy barriers for the activated dissociation processes were found. It was shown that in the case of Ag the H-2 dissociation process is energetically unfavourable. The energy surfaces for the interaction of atomic hydrogen with the metal clusters were also calculated. The potential barriers and the diffusion paths for the hydrogen diffusion process over the metal surface were found.