Stacking Configurations of Triangular Au₃ and Tetrahedral Au₄ Units in Thiolate-Protected Gold Nanoclusters: Insights into Structural Stability and Growth Mechanisms

Triangular Au₃ and tetrahedral Au₄ are key structural units in the face-centered cubic gold core of thiolate-protected gold nanoclusters. Understanding their stacking arrangements is essential for elucidating the growth mechanisms of these gold cores. In this study, we design two new isomers of Au₂₉(SR)₁₉ nanoclusters via deliberately adjusting the stacking pattern of Au₃ and Au₄ based on the grand unified model and ring model to show preferable packing arrangements. Among the experimental isomer and the two newly constructed isomers of Au₂₉(SR)₁₉, the Au₃ and Au₄ units display three distinct stacking arrangements: completely independent Au₃; Au₃ sharing a vertex with one Au₄; and Au₃ sharing vertices with two Au₄. Density functional theory calculations reveal that the isomer with a completely independent Au₃ unit owns the lower relative energy, which suggests that forming independent Au₃ in thiolate-protected gold nanoclusters is relatively straightforward, while achieving alternative stacking configurations with Au₃ and Au₄ is more challenging, aligning with experimental observations. This study provides a theoretical foundation for understanding the stacking arrangements between triangular Au₃ and tetrahedral Au₄ units, offering valuable insights for designing ligand-protected gold nanoclusters featuring triangular Au₃ units.