Hierarchical and chemical space partitioning in new intermetallic borides MNi₂₁B₂₀ (M = In, Sn)

The compounds MNi₂₁B₂₀ (M = In, Sn) have been synthesized and their cubic crystal structure determined (space group Pm3[combining macron]m, lattice parameters a = 7.1730(1) Å and a = 7.1834(1) Å, respectively). The structure can be described as a hierarchical partitioning of space based on a reo-e net formed by Ni3 species with large cubical, cuboctahedral and rhombicuboctahedral voids being filled according to [Ni1@Ni3₈], [M@Ni3₁₂], and [Ni2₆@B₂₀@Ni3₂₄], respectively. The [Ni₆@B₂₀] motif inside the rhombicuboctahedral voids features an empty [Ni₆] octahedron surrounded by a [B₂₀] cage recently described in E₂Ni₂₁B₂₀ (E = Zn, Ga). Position-space bonding analysis using ELI-D and QTAIM space partitioning as well as 2- and 3-center delocalization indices gives strong support to an alternative chemical description of space partitioning based on face-condensed [B@Ni₆] trigonal prisms as basic building blocks. The shortest B-B contacts display locally nested 3-center B-B-Ni bonding inside each trigonal prism. This clearly rules out the notion of [Ni₆@B₂₀] clusters and leads to the arrangement of 20 face-condensed [B@Ni2₃Ni3₃] trigonal prisms resulting in a triple-shell like situation Ni2₆@B₂₀@Ni3₂₄(reo-e), where the shells display comparable intra- and inter-shell bonding. Both compounds are Pauli paramagnets displaying metallic conductivity.