Accelerating global search of gold–silver clusters using equivariant graph neural network

Medium-sized gold-silver clusters have been relatively underexplored due to the computational complexities associated with density functional theory (DFT) calculations and the intricate nature of their potential energy surfaces. Recently, graph neural networks (GNNs) have emerged as efficient tools for fitting these potential energy surfaces, providing both rapid computation and high accuracy. Equivariant GNNs, which incorporate vector features of nodes, are particularly adept at extracting more complex and abstract information without significantly increasing the computational burden. In this study, we develop an equivariant GNN named CCCNet that requires only coordinate and elemental information as input. This model, trained on over 1.4 × 106 cluster structures and tested on independent compositions, achieves high prediction accuracy for binding energies (MAE = 6.5 meV/atom) and atomic forces (MAE = 25.4 meV/Å). By integrating our CCCNet with a comprehensive genetic algorithm (CGA) software framework, we successfully conducted searches for global minimum structures of AumAgn clusters (where m + n = 20, 24, 30). The computational cost is remarkably less than conventional DFT calculations by about three orders of magnitude, showing the power of equivariant GNNs for accelerating structural discovery in medium-sized clusters. Several previously unknown low-energy configurations were uncovered and novel structural motifs that differ markedly from the established growth patterns were revealed. Therefore, our findings provide new insights into the stability and design principles of Au-Ag nanoclusters.