The direct synthesis of H2O2 over Pd catalysts is a promising alternative to the industrial Riedl-Pfleiderer process. We studied the size effects of Pd catalysts ranging from subnano clusters to extended surfaces using first-principles calculations. Compared to the high-coordinated terrace sites of extended Pd surfaces, the low-coordinated terrace and edge sites of clusters showed lower H2O2 selectivities. Bader charge analysis proved that low-coordinated terrace sites of clusters donated more electrons to adsorbed O-2 than the extended surfaces, thus enhancing the undesired dissociation of O-2. Accordingly, with the decline in the size of Pd nanoparticles (NPs), the increase in low-coordinated active sites results in the drop in H2O2 selectivity. Moreover, both site coordination and site geometry play critical roles in the performance of Pd active sites. Our findings provide a molecular understanding of size effects of Pd NPs on this reaction, which is consistent with the reported experimental results. (C) 2018 Elsevier Inc. All rights reserved.