From Clusters to Nanocrystals: The Continuous Evolution of Copper Clusters Revealed by Machine Learning

The evolution of cluster structure with size and the critical size for the transition from cluster to nanocrystal have long been fundamental problems in nanoscience. Solving this problem is still a big challenge due to limitations of experimental technology and computational methods. Here, we proposed a machine learning force field (MLFF) that can generalize well to various copper systems ranging from small clusters to large clusters and bulk. The continuous evolution of copper clusters CuN towards nanocrystal was revealed by investigating clusters in a wide size range (7 ≤ N ≤ 17885) based on MLFF simulated annealing (SA). For small CuN (N < 40), electron counting rule and geometric symmetry play a major role in stability. For large CuN (N > 80), geometric magic number rule plays a dominant role and the evolution of clusters is based on the formation of more and more icosahedral shells. For medium size CuN (40 ≤ N ≤ 80), both electron counting rule and geometric magic number rule contribute. The critical size from cluster to nanocrystal was calculated to be around 8200 atoms (about 6 nm in diameter). Our results shed light on the structural evolution of copper clusters and lay the methodological foundation for subsequent research on other cluster systems.