We present a systematic analysis of molecular oxygen (O$_2$) adsorption trends on bimetallic PtNi clusters and their monometallic counterparts supported on MgO(100), by means of periodic DFT calculations for sizes between 25 up to 58 atoms. O$_2$ adsorption was studied on a variety of inequivalent sites for different structural motifs, such as truncated octahedral (TO), cuboctahedral (CO), icosahedral (Ih) and decahedral (Dh) geometries. We found that O$_2$ prefers to bind on top of two metal atoms, parallel to the cluster, with an average chemisorption energy of 1.09 eV (PtNi), 1.07 eV (Pt) and 2.09 eV (Ni), respectively. The largest adsorption energy values are found to be along the edges between two neighbouring (111)/(111) and (111)/(100) facets; while FCC and HCP sites located on the (111) facets may show a chemisorption value lower 0.3 eV where often fast O$_2$ dissociation easily occurs. Our results show that, even though it is difficult to disentangle the geometrical and electronic effects on the oxygen molecule adsorption, there is a strong correlation between the calculated general coordination number (GCN) and the chemisorp- tion map. Finally, the inclusion of dispersion corrections (DFT-D) leads to an overall increase on the calculated adsorption energy values but with a negligible alteration on the general O$_2$ adsorption trends.
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