To examine the effect of the dopant concentration on the sintering and coking propensities, different energetic characteristics of the PtGe clusters are explored. First, the ensemble-averaged formation energies are computed as: E Form (Pt 4 Ge x ) = ∑P i E(Pt 4 Ge x + slab) -E(slab) -4E(Pt) -Xμ Ge (1) where P i is the thermodynamic Boltzmann probability of isomer population. The adsorption energy of the clusters to the MgO surface is calculated as: