Catalytic reactions perform best if the interaction between the adsorbates and the surface is not too strong and not too weak. This relates to the d-band occupancy of the metals. In this respect, hydrogenation of propenal or acrolein on silver surface rises up the question whether H2 proceeds in the mechanism of the reaction as molecule or dissociates on silver. Silver having an electronic configuration 4d105s1 cannot dissociate the strong bond of H2. However, it is known that even on gold provided the gold particles are very small molecules such as O2 can dissociatively chemisorb. Aiming elucidation of the reaction mechanism, small clusters of silver atoms are considered (mimicking small particles) by checking first their stability by means of theoretical calculations. Next, adsorption of hydrogen was allowed in order to estimate whether the adsorption energy is exothermic or not. In this context, computational calculations carried out by means of Density Functional Theory for small silver clusters indicated that rhombic structure was the most stable configuration. Adsorption of hydrogen on rhombic silver cluster yielded negative value of the adsorption energy suggesting that hydrogen can dissociatively be adsorbed on small particle and step surfaces as well.