Free-standing particles were placed in a cubic cell of size 12 Å x 12 Å x 12 Å, which ensures negligible interactions between clusters in neighbouring cells while keeping calculations computationally affordable. For ceria-supported particles the oxide surface is represented by a 4x4 supercell of the CeO2(111) surface, with 12 Å of vacuum surrounding the oxide slab. For all calculations the Brillouin zone is sampled using only the Γ point. In order to describe the interaction between the frozen core electrons and the valence electrons described explicitly by the electronic wave function, VASP uses the projector augmented wave method of Blöchl. All of the levels of theory share the aforementioned common characteristics of cell size and reciprocal space sampling. The low-, mid-and high-levels of theory use the Perdew-Wang (PW91) exchange-correlation functional as it offers a good compromise between accuracy and computational cost.