A 58-electron superatom-complex model for the magic phosphine-protected gold clusters (Schmid-gold, Nanogold®) of 1.4-nm dimension

We have re-investigated the structural identity of the famous gold-phosphine-halide Au:PR₃:X compound having 55-69 gold atoms and core size of 1.4 nm (similar to "Schmid gold" or Nanogold®) from the viewpoint of the Superatom-Complex (SAC) model for ligand protected metal clusters, and in consideration of the ligand-adatom groups observed previously for the structurally known 39-atom cluster [Au₃₉(PR₃) ₁₄Cl₆]^-1. Density functional theory is used to define the formation energy of various compositions and structures, enabling a comparison of the stability of different cluster-sizes. In agreement with the SAC model, we find a strong correlation between optimal energy and delocalized electron shell closings: The 58 electron shell closing is a driving force behind the energetics. Of all compositions studied here, the energetically best one is [Au₆₉(PR₃)₂₀Cl₁₂]^-1 anion, which has a truncated decahedral 37-atom core encapsulated by 20 Au:PR₃ and 12 Au-Cl groups. It is energetically and chemically far superior to the standard models based on Au₅₅(PR₃) ₁₂X₆. Critical comparisons are made to recent experiments (NMR and mass spectrometry).