Au ₆₀ ^-: The Smallest Gold Cluster with the High-Symmetry Icosahedral Core Au ₁₃

Among coinage metal nanoclusters with 55 atoms, only Ag ₅₅ ^- and Cu ₅₅ ^- are the geometric magic-number clusters, as both exhibit icosahedral symmetry. Au ₅₅ ^- , however, exhibits much lower symmetry due largely to the strong relativistic bonding effect. In this study, we collect a much larger population (>10,000 isomers) of low-energy isomers of Au ₅₅ ^- to Au ₆₀ ^- by using the combined density-functional theory and basin-hopping global optimization method. We also include the spin-orbit effect in the density-functional theory computation to achieve simulated photoelectron spectra in quantitative fashion. Remarkably, we uncover that the Au ₁₃ core with the highest icosahedral (I _h ) symmetry emerges at the size of Au ₆₀ ^- . Stability analysis suggests that Au ₅₇ ^- with 58 valence electrons, an electronic magic number, is the relatively more stable cluster in the size range considered. Overall, in this size range we reveal a compromise between the trend toward having a perfect icosahedral 13-atom core and the strong relativistic bonding effect.