where E(Pt 4 Ge x +slab+adsorbate) is the energy of the MgO-supported Pt 4 Ge x cluster with one adsorbate molecule bound, and E(adsorbate) gas the energy of the ethylene or ethane molecule in gas phase. Entropic corrections are not included in our work since they are assumed to be comparable for all the clusters considered here and our goal is to compare the properties of such clusters.