First principle study on the structures and properties of Ag_m(Ag₂S)₆ (m = 3–12) clusters

Genetic algorithm (GA) combined density functional theory (DFT) method is used to obtain the structures of Ag_m(Ag₂S)₆ (m = 3–12) clusters. The size of the studied clusters is less than 2 nm. The computational results reveal that the six S atoms in Ag_m(Ag₂S)₆ (m = 3–12) clusters exist in S–Ag-S units, and the S–Ag-S units further form Ag₃S₃ or Ag₄S₄ units. The S atoms all bind with three or four Ag atoms to form μ₃ or μ₄-S. Other Ag atoms not in S–Ag-S units tend to form Ag₃, Ag₄, Ag₅ or Ag₆ cores to stabilize the structure. The evolution of the global minimum (GM) structures manifests that as the addition of Ag atom to Ag_m(Ag₂S)₆ cluster one by one, the number of Ag_n cores increases and the molecular framework unit changes from Ag₃S₃ to Ag₄S₄. When m ≤ 10, the silver cores gather at one side of the cluster and are wrapped by the cage molecular framework formed by Ag₃S₃ and Ag₄S₄ from one side. When m is bigger than 10, the molecular framework is not big enough to wrap the silver cores. Then, the silver cores are separated on the left and right sides of the molecular framework. The stability and ionization potentials of the clusters present odd–even oscillation, because the number of valence electrons is odd or even. Ag₈(Ag₂S)₆ and Ag₁₀(Ag₂S)₆ clusters are more stable than other clusters because of their high second-order difference energies. Ag₇(Ag₂S)₆ and Ag₁₁(Ag₂S)₆ clusters are easy to get electrons to form anionic clusters, resulting in big electron affinities. The sulfur atoms in the clusters obtain electrons to become negatively charged, whereas silver atoms loose valence electrons to become positively or negatively charged. The direction of electron transfer in the clusters is from silver to sulfur.