Global Optimization and Structural Evolution of Platinum Clusters (PtN , N=6-50) via Deep Potential and Hybrid Evolutionary Algorithm

Abstract

Platinum (Pt) clusters hold significant potential in catalysis and nanoelectronics due to their unique size-dependent physicochemical properties.However, searching for global minimum structures with first-principles accuracy remains a formidable computational challenge as the cluster size increases. This study presents a search strategy combining the Deep Potential (DP) model with an improved Hybrid Differential Evolution (HDE) algorithm. Through rigorous ab initio molecular dynamics (AIMD) sampling within a temperature range of 300-1500 K, a high-quality dataset was constructed to train a DP model exhibiting excellent energy prediction accuracy (MAE < 0.011 eV/atom) and cross-size generalization capability. Utilizing the DP-HDE framework, we extended the ground-state structure search of Pt clusters up to 50 atoms at near first-principles accuracy for the first time, breaking the size bottleneck of traditional high-precision calculations. Energy analysis demonstrates that the structures identified in this work are more stable than those derived from empirical potentials (the S-C potential), and a series of magic number sizes (10, 17, 30, 36, 42, 43) was successfully identified. Structural analysis reveals an evolutionary path from pyramidal cage-like (N ≤ 21) to layer-like (22 ≤ N ≤ 44) and then to multi-shell (N ≥ 45) structures. Furthermore, descriptors such as radial distribution functions, similarity functions, and coordination number distributions were introduced to quantitatively analyze the structural properties and evolution patterns of Pt clusters. This study provides an efficient and reliable theoretical tool for understanding the structural evolution of medium-to-large-sized clusters.