Exploring the stable structures of cerium oxide nanoclusters using high-dimensional neural network potential

Cerium clusters have been extensively applied in industry owing to their extraordinary properties for oxygen storage and redox catalytic activities. However, their atomically precise structures have not been studied because of the lack of a reliable method to efficiently sample their complex structures. Herein, we combined a neural network algorithm with density functional theory calculations to establish a high-dimensional potential to search for the global minimums of cerium oxide clusters. Using Ce14O28 as well as its reduced state Ce14O27 and oxidized state Ce14O29 with ultra-small dimensions of similar to 1.0 nm as examples, we found that these three clusters adopt pyramid-like structures with the lowest energies, which was obtained by exploring 100 000 configurations in large feasible spaces. Further the neural network potential-enhanced molecular dynamics calculations indicated that these cluster structures are stable at high temperature. The electronic structure analysis suggested that these clusters are highly active and easily lose oxygen. This work demonstrated that neural network potentials can be useful for exploring the stable structures of metal oxide nanoclusters in practical applications. In this work, a machine learning model is developed to construct high-dimensional neural network potential to search for the most stable structures of cerium oxide nanoclusters.