where E(Pt 4 Ge n (X)/MgO) is the energy of Pt 4 Ge n cluster (n = 0-4) supported on MgO with one X molecule adsorbed, E(Pt 4 Ge n /MgO) is the energy of the bare Pt 4 Ge n cluster supported on MgO and E(X) is the energy of the isolated X molecule in gas phase (X = CO, O 2 ). The same reference E(O 2 ) is used for O 2 and 2 ✕ O adsorption.