Silver sulfide clusters with size less than 2 nm are of much interest in photoelectric devices, such as photoconductive devices, infrared detectors and superconductors. The electronic structures of [Ag(Ag₂S)_n]⁺ (n = 1–9) clusters are investigated using the combined method of genetic algorithm (GA) and density functional theory (DFT). Results reveal that S atoms prefer to be at the tip of the structure, and Ag atoms tend to form S-Ag-S unit between two S atoms. With the increase of cluster size, the open structure evolves into closed centre-hollow structure. According to the stability analysis, [Ag(Ag₂S)₆]⁺ is a magic number cluster due to its high HOMO-LUMO gap, big average energy and high second-order energy difference. Ag-S bonds, S-Ag-S and triangular Ag₃S₃ units play key roles in stabilizing [Ag(Ag₂S)_n]⁺ clusters. According to the electron affinity energy analysis, the clusters are easier to get electrons when n = 1, 3, 5 and 9. Based on the charge analysis of the studied clusters, the charges on Ag and S atoms are positive and negative, respectively, which indicates that the charge transfer from Ag to S occurs in cluster. Infrared and Raman spectra are dependent on the symmetries of the clusters. The molecular orbitals of [Ag(Ag₂S)₆]⁺ and [Ag(Ag₂S)₈]⁺ present superatomic properties. We hope that the clusters studied here could provide valuable data for future experimental and theoretical study of cationic silver sulfide clusters.

a The second-order energy differences (Δ₂E). b Energy gaps (E_g). c Average binding energies (E_b) versus cluster size, n

尺寸小于2 nm的硫化银簇对光电器件非常感兴趣，例如光电导器件，红外探测器和超导体。[Ag（Ag ₂ S）_n ] ⁺（n  = 1–9）团簇的电子结构使用遗传算法（GA）和密度泛函理论（DFT）的组合方法进行研究。结果表明，S原子更喜欢位于结构的顶端，而Ag原子倾向于在两个S原子之间形成S-Ag-S单元。随着团簇尺寸的增加，开放结构演变成封闭的中空结构。根据稳定性分析，[Ag（Ag ₂ S）₆ ] ⁺由于其高HOMO-LUMO间隙，大平均能量和高二阶能量差，它是一个幻数簇。Ag-S键，S-Ag-S和三角形Ag ₃ S ₃单元在稳定[Ag（Ag ₂ S）_n ] ⁺簇中起关键作用。根据电子亲和能分析，当n  = 1、3、5和9时，这些簇更容易获得电子。根据所研究簇的电荷分析，Ag和S原子上的电荷分别为正和负。这表明从Ag到S的电荷转移发生在簇中。红外光谱和拉曼光谱取决于团簇的对称性。[Ag（Ag ₂ S）₆的分子轨道] ⁺和[Ag（Ag ₂ S）₈ ] ^+具有超原子性质。我们希望这里研究的簇可以为阳离子硫化银簇的未来实验和理论研究提供有价值的数据。

一个二阶能量差（Δ ₂ ë）。b能隙（E _g）。c平均结合能（E _b）与团簇大小n