Interaction in multilayer clusters: a theoretical survey of [Sn@Cu12@Sn20]12−, a three-layer matryoshka-like intermetalloid

Abstract

[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.