We report the interaction of hydrogen molecule with MgnRh clusters using density functional formalism with an objective to study (a) the reactivity of small sized MgnRh clusters with H-2 molecule and (b) the catalytic effect of Rh on the Mg-n cluster for adsorption and dissociation of hydrogen. From the variation of thermodynamic parameters, adsorption and chemisorption etc. with the size of the cluster, we found that the most stable lowest energy structure in the series is Mg6RH, whereas, Mg9Rh is the most effective hydrogen storage cluster. Interaction of H-2 with MgnRh cluster shows a significant reduction in the activation barrier energy, which helps in the hydrogen dissociation. The chemisorptions energy reveals that Mg9Rh cluster act as an effective catalytic agent for hydrogen adsorption and dissociation. The calculated activation barrier energy of H2-Mg9Rh has been verified by the study of intrinsic reaction coordinates (IRC) pathway between Mg9Rh and H2. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.