Atomistic Details of Nanocluster Formation from Machine-Learned-Potential-Based Simulations

Understanding the mechanism for the formation of metal nanoclusters is an open challenge in nanoscience. Computational modeling can provide molecular details of nanocluster formation that are otherwise inaccessible. However, simulating nanocluster nucleation in solution presents significant challenges, including inaccurate energy predictions and limitations on the system size and time scale. This work addresses these challenges by combining deep neural networks (DNNs) with well-tempered metadynamics (WT-MetaD) to model the nucleation of a prototypical nanocluster, Ag₆(SCNH₂)₆ in methanol. A neural-network-potential-based unbiased molecular dynamics simulation captured the cluster's dynamic behavior, while WT-MetaD simulations revealed an almost barrierless transition from dispersed precursors to a nucleated state. The method's robustness was further demonstrated by scaling up to 30 randomly distributed precursors, which resulted in spontaneous nucleation. This study presents the first successful DNN model of nanocluster formation in solution with density-functional-theory-level accuracy, paving the way for advancements in the field.