Stacking Configurations of Triangular Au<sub>3</sub> and Tetrahedral\nAu<sub>4</sub> Units in Thiolate-Protected Gold\nNanoclusters: Insights into Structural Stability and Growth Mechanisms

Triangular\nAu<sub>3</sub> and tetrahedral Au<sub>4</sub> are key\nstructural units in the face-centered cubic gold core of thiolate-protected\ngold nanoclusters. Understanding their stacking arrangements is essential\nfor elucidating the growth mechanisms of these gold cores. In this\nstudy, we design two new isomers of Au<sub>29</sub>(SR)<sub>19</sub> nanoclusters via deliberately adjusting the stacking pattern of\nAu<sub>3</sub> and Au<sub>4</sub> based on the grand unified model\nand ring model to show preferable packing arrangements. Among the\nexperimental isomer and the two newly constructed isomers of Au<sub>29</sub>(SR)<sub>19</sub>, the Au<sub>3</sub> and Au<sub>4</sub> units\ndisplay three distinct stacking arrangements: completely independent\nAu<sub>3</sub>; Au<sub>3</sub> sharing a vertex with one Au<sub>4</sub>; and Au<sub>3</sub> sharing vertices with two Au<sub>4</sub>. Density\nfunctional theory calculations reveal that the isomer with a completely\nindependent Au<sub>3</sub> unit owns the lower relative energy, which\nsuggests that forming independent Au<sub>3</sub> in thiolate-protected\ngold nanoclusters is relatively straightforward, while achieving alternative\nstacking configurations with Au<sub>3</sub> and Au<sub>4</sub> is\nmore challenging, aligning with experimental observations. This study\nprovides a theoretical foundation for understanding the stacking arrangements\nbetween triangular Au<sub>3</sub> and tetrahedral Au<sub>4</sub> units,\noffering valuable insights for designing ligand-protected gold nanoclusters\nfeaturing triangular Au<sub>3</sub> units.