Modeling of metal nanoparticles: Development of neural-network interatomic potential inspired by features of the modified embedded-atom method

Interatomic potential plays a key role in ensuring the accuracy and reliability of molecular-dynamics simulation results. While most empirical potentials are benchmarked against a set of carefully chosen bulk material properties, recent advances in machine learning have seen the emergence of neural-network-based mathematical potentials capable of describing highly complex potential energy surfaces for a variety of systems. We report here the development of a neural-network interatomic potential (NNIP) with modified embedded-atom method background density as fingerprint functions, which could accurately model the energetics of metallic nanoparticles and clusters (Cu as a representative example) widely used in catalysis. To appropriately account for the diverse chemical environments encountered in nanoparticles/nanoclusters, an extensive set of atomic configurations (totaling 18 084) were calculated using density-functional-theory (DFT) at the Perdew-Burke-Ernzerhof level. In addition to standard bulk properties such as cohesive energies and elastic constants, the sampled configurations also include a substantial number of differently oriented crystal facets and differently sized nanoparticles and nanoclusters, greatly expanding the value range of NNIP features that was otherwise quite limited. The complex energy potential surface of Cu can be faithfully reproduced, with an average error of 0.011 eV/at for energy states within 3 eV of the ground state. As an illustration, the developed NNIP is used to simulate the molecular dynamics of copper nanoparticles, and good agreement is achieved between DFT and the NNIP.