Multitribe evolutionary search for stable Cu–Pd–Ag nanoparticles using neural network models

We present an approach based on two bio-inspired algorithms to accelerate the identification of nanoparticle ground states. We show that a symbiotic co-evolution of nanoclusters across a range of sizes improves the search efficiency considerably, while a neural network constructed with a recently introduced stratified training scheme delivers an accurate description of interactions in multielement systems. The method's performance has been examined in extensive searches for stable elemental (30–80 atoms), binary (50, 55, and 80 atoms), and ternary (50, 55, and 80 atoms) Cu–Pd–Ag clusters. The best candidate structures identified with the neural network model have consistently lower energy at the density functional theory level compared with those found with traditional interatomic potentials.