[Ba₄@Sn₅₆]^36- as a Main-Group Second-Order Superatom. Interpenetrated Dodecahedrons as a Three-Dimensional Cluster-of-Clusters Structure

Superatomic clusters are relevant species to further understanding of bonding and structural properties of atomically precise molecular nanoparticles. Here, we explore the characteristics of ligand-free [Ba₄@Sn₅₆]^36- Zintl-ion, as a three-dimensional aggregate of clusters featuring four fused Ba@Sn₁₉ building units as an extension of the understanding in linear and cyclic superatomic cluster arrays. We provide a rational picture of the electronic shell in [Ba₄@Sn₅₆]^36- as a cluster-of-clusters motif through the recently introduced second-order superatom approach, as a three-dimensional aggregation of superatomic clusters where their shells are able to interact. The electronic structure features both tangential and radial shells from the four building Ba@Sn₁₉ units, leading to a set of 1S′²1P′⁶1D′¹⁰1F′¹⁴ and higher angular momentum shells and a second set of 2S′²2P′⁶2D′¹⁰2F′¹⁴2G′⁸ second-order shells. Thus, the current approach serves to encourage the rationalization of molecular materials conceived from cluster building blocks toward a rational guide for synthetic efforts.