Machine-Learned Probability Landscapes Reveal Charge-Controlled Structural Motifs in Gold Nanoclusters

Abstract Configurational landscapes of metallic nanoclusters (NCs), particularly identifying thermodynamically relevant basins under the combined effects of charge state and temperature, remain a major challenge for catalytic applications. This work introduces an unsupervised machine-learning framework based on nonlinear dimensionality reduction, including sketch-map, t-SNE/FIt-SNE, and UMAP, to decode the high-dimensional configurational space and physicochemical properties of bare Au13. By combining density functional theory-based replica-exchange Born–Oppenheimer molecular dynamics with Boltzmann reweighting via the multistate Bennett acceptance ratio, we constructed probability surfaces at 300 K from multiple-temperature canonical ensembles. From 2160000 sampled configurations, this framework projects complex atomistic trajectories onto low-dimensional manifolds that retain structural similarity, basin connectivity, and thermodynamic relevance. The resulting landscapes reveal that charge state and temperature cooperatively modulate the 2D/3D competition in Au13; cationic and neutral clusters retain significant populations in fluxional 3D basins, whereas anionic clusters show pronounced migration toward 2D and quasi-2D regions. Local coordination, chirality, and the center of gravity of occupied d-states further connect configurational sampling to electronic reactivity and chiral-site formation. Implemented in the DimRedPy workflow, this strategy offers a transferable and reproducible route for decoding structure–property relationships in fluxional NCs under more realistic operating conditions.