Understanding the Mechanism of Nanocluster Formation from Machine-Learned Potential-based Simulations

Understanding the mechanism for the formation of metal nanoclusters is an open challenge in the nanoscience field. Computational modeling can provide molecular details of nanocluster formation that are otherwise inaccessible. However, even with advanced computational resources, simulating the nucleation of a nanocluster in solution presents significant challenges, including inaccurate energy predictions and limitations on system size and timescale. This work addresses these challenges by integrating deep neural networks (DNN) with well-tempered metadynamics (WT-Metad) to model the nucleation of an Ag$_6$(SCNH$_2$)$_6$ (a prototypical example) in solution. An unbiased neural network potential (NNP)--based molecular dynamics (MD) simulation captured the cluster's dynamic behavior, while WT-Metad simulations revealed an almost barrierless downhill transition from dispersed precursors to a nucleated state. Scaling up the system to 30 randomly distributed precursors demonstrated spontaneous nucleation at multiple sites, underscoring the method's robustness. This study presents the first successful DNN model of nanocluster formation in solution with DFT-level accuracy, paving the way for advancements in the field.