[Sn@Cu12@Sn20]12− represents an archetypal intermetalloid structure composed of several concentric polyhedral shells displaying a highly spherical shape. This feature paves the way to understanding the electronic structure of multilayered structures in terms of interacting superatomic shells. As a result, [Sn@Cu12@Sn20]12− can be regarded formally as [{Sn@Cu12}4−@{Sn20}8−], which ensures a favorable electronic configuration with a sizable HOMO–LUMO gap for the inner core [Sn@Cu12]4−. The interaction between the [Sn@Cu12]4− and [Sn20]8− layers involves a concentric bonding interaction of s-, p- and d-type. The approach employed here is suggested and demonstrated to be a useful strategy for rationalizing multilayer endohedral clusters, which can be extended to nanoparticles or even to less symmetrical systems.
![Graphical abstract: Interaction in multilayer clusters: a theoretical survey of [Sn@Cu12@Sn20]12−, a three-layer matryoshka-like intermetalloid](http://hg.y866.cn/compound/lib/scimg/usr/1/C4RA16660D.jpg)