Prediction of the Au₄S crystal via a superatom network model: from clusters to solids

Owing to their unique properties, thiolate-protected gold clusters (denoted as Au_n(SR)_m) have attracted intense research interest both experimentally and theoretically. The superatom complex (SAC) and superatom network (SAN) models are significantly well-known concepts to explain the electronic stability of Au_n(SR)_m. Based on the structural characters of Au_n(SR)_m, the tetrahedral Au₄ unit was found to be an elementary building block and used to design a series of tetrahedron-network clusters. In this work, we first build a Au₂₂(μ₄-S)(SH)₁₂ cluster consisting of a network of four non-conjugated tetrahedral Au₄ units and confirm that it is a local minimum on the potential energy surface by density functional theory calculations. Chemical bonding analysis by the AdNDP method reveals that the electronic structure of Au₂₂(μ₄-S)(SH)₁₂ follows the SAN (4 × 2e) model. Based on the structural character of the Au₂₂(μ₄-S)(SH)₁₂ cluster, we utilize the diamond lattice as a template to construct a stable Au₄S crystal in which each S atom binds to four Au₄ superatoms. The computational results demonstrate that the structure has rather good dynamic and thermal stabilities, and it is an indirect semiconductor with a band gap of 2.68 eV at the HSE06 level. Chemical bonding analysis performed by the SSAdNDP method reveals that the Au₄S can be seen as a SAN crystal. These bonding patterns and properties of the solid provide references for further investigation of cluster-assembled materials.