Physical and Chemical Properties of Unsupported (MO2) n Clusters for M = Ti, Zr, or Ce and n = 1–15: A Density Functional Theory Study Combined with the Tree-Growth Scheme and Euclidean Similarity Distance Algorithm

Metal-oxide clusters, (MO2) n , have been widely studied along the years by experimental and theoretical techniques, however, our atomistic knowledge is still far from satisfactory for systems such as ZrO2 and CeO2, which play a crucial role in nanocatalysis. Thus, with the aim to improve our atomistic understanding of the physical and chemical properties of the metal-oxide clusters as a function of size, n, we performed a systematic ab initio density functional theory study of the (MO2) n clusters, where M = Ti, Zr, or Ce and n = 1–15. In this work, the trial atomic configurations were obtained by a tree-growth (TG) scheme combined with the Euclidean similarity distance (ESD) algorithm. Using the (TiO2) n clusters, we validated the TG-ESD algorithm, which found the same putative global minimum configurations (pGMCs) reported in the literature for most of the (TiO2) n systems, and in a few cases, there are lower energy configurations than previous data. From our analyses, the structural parameters of the (MO2) n clusters show an asymptotic behavior toward the values obtained from the nonoptimized bulk fragments, and hence, the differences between the asymptotic (MO2) n values and the bulk values are due to the surface and relaxation effects. We found a very similar increase in the binding energy with increased n for both systems, in particular for large n values, which is associated with an increase in the coordination of the core atoms toward the bulk values, whereas the magnitude of the binding energy is largely determined by the ionic contribution due to the charge transfer among the cation and oxygen atoms. From the relative stability function, the most stable clusters are (TiO2)6 pGMC, (ZrO2)8 pGMC, and (CeO2)10 pGMC. As expected, from the density of states, we found discrete energy levels for smaller n, which form the valence and conduction bands separated by an energy gap for large n values, and hence, the evolution of the highest occupied molecular orbital–lowest unoccupied molecular orbital energy separation was obtained for the studied metal oxides.