Electronic Structure Progression across the ACu ₂ Q ₂ (MQ ₂ ) _<i>n</i> Semiconductor Series

Moving beyond the engineering of known materials and elemental substitution within common structure types is critical for designing unique properties. Here, we present a new homologous series, ACu₂Q₂(MQ₂)<i>_<i>n</i></i> (A = Sr, Ba, 2Na; MQ₂ = ZrS₂, HfSe₂), establishing 11 new members. In β-BaCu₂Q₂ and Na₂Cu₂Se₂ (<i>n</i> = 0), the [Cu₂Q₂]^2- motifs extend in two dimensions, whereas those in α-BaCu₂Q₂ extend in three dimensions. Hence, there are two structural evolutions within the ACu₂Q₂(MQ₂)<i>_<i>n</i></i> family driven by the polymorphism of the host structures. MQ₂ (<i>n</i> → ∞) displays 2D layers of edge-sharing [MQ₆]^8- octahedra that are 1-octahedron-thick and connected via van der Waals bonding. Each insertion of MQ₂ into ACu₂Q₂ incorporates [MQ₆]^8- octahedra extending infinitely in one direction, confined to being 1-octahedron-thick in the second direction, with <i>n</i> controlling the number of [MQ₆]^8- octahedra in the third direction. Therefore, increasing <i>n</i> predictively expands the [Cu₂M<i>_<i>n</i></i>Q_2<i>n</i>+2]^2- network in the direction controlled by <i>n</i> and relative to the A⁺/A²⁺ ions. We demonstrate that for a given set of elements, one can enforce a "Host(Insertion)<i>_<i>n</i></i>" formula to systematically evolve both crystal and electronic structures from the host (<i>n</i> = 0) to the insertion (<i>n</i> → ∞) materials through intermediate values of <i>n</i>. Specifically, the energetic misalignment of the electronic band extrema of the parents predictively determines the band extrema and the resulting band gaps of all intermediate <i>n</i> members.