Exploring the Chemical Space of Metal Clusters via Machine Learning

Atomic clusters serve as the embryos of materials, yet their enormous and compositionally complex chemical space has long hindered systematic exploration of thermodynamic stability. Here, a unified first-principles and machine-learning framework is developed to enable large-scale mapping of metal cluster thermodynamics. By introducing a progressive sampling strategy integrated with a composition-based deep learning model, the intrinsic sampling bottleneck associated with exponentially expanding chemical spaces is alleviated. Based on ~45,000 global-minimum structures obtained via automated first-principles calculations, a composition-based deep learning model, the Cluster Transformer Encoder Network, enables reliable predictions of atomization energies (~50 meV/atom accuracy) for 9.13 million metal cluster compositions, covering 30 d-block metals and 4 main-group elements. The resulting thermodynamic trends reveal strong correlations between cluster atomization energies and bulk cohesive energies and highlight heteronuclear stabilization and the stability of noble-metal-doped oxide clusters. This work establishes a general strategy for efficient exploration of chemically complex cluster spaces and advances a holistic understanding of the collective properties of metal clusters.