Accelerating Global Optimization of Cerium Oxide Nanocluster Structures with High-Dimensional Neural Network...

CeO₂, characterized by its unique 4f electronic structure and high oxygen storage capacity, is widely recognized as an important catalyst and support material in energy and catalytic applications. Despite its importance, the complexity of CeO₂ nanoclusters poses challenges for structural characterization. Herein, we present a machine learning approach to accelerate the global optimization of cerium oxide nanocluster structures using a high-dimensional neural network potential (HDNNP). Our methodology integrates active learning to construct a versatile HDNNP that enables the exploration of the vast configurational space of small to medium cerium oxide clusters (CeO₂, n = 2-18, x = -1, 0, +1). The HDNNP, refined through iterative active learning, achieves an accuracy comparable to first-principles calculations. Results indicate that the configuration of the lowest energy structures varies across different intervals. At n = 9 and n = 14, there is a transition from compact structures to multilayered ordered structures, and subsequently to pyramidal structures. When n > 14, almost all structures are derived from the pyramidal structure as the core grows continuously. In addition, the electronic structures of the lowest-energy clusters are analyzed. Our findings provide insights into the size-dependent stability and electronic behavior of cerium oxide nanoclusters.