In this paper we present some calculations which describe the process of physisorption and dissociation of molecular hydrogen on a Ag(111) surface. The stability of chemisorbed atomic hydrogen with respect to physisorbed molecular hydrogen is discussed. We use a cluster type approach in the framework of the local approximation of the density functional theory. Size effects are studied by considering Ag5, Ag7, Ag10 and Ag12 clusters. It is shown that localized electronic states contamine the physisorption region. On the other hand the physisorption energy is roughly independent of the size of the system. This is not the case for the chemisorption where it is well known that binding energies vary significantly with the size of the cluster. In order to compare the relative energies of both chemisorbed and physisorbed states, two kinds of treatments are needed. While the binding energy may be obtained directly when the adsorbed molecule is above the jellium edge, the electronic delocalization effects have to be taken into account when the hydrogen atoms are embedded in the electronic sea of the surface. In this way, it is shown that the dissociation process is not allowed for molecular H-2 on a Ag(111) surface.
