Peeling the onion: a revised model of the electron count for matryoshka clusters

Abstract

We have provided a model for understanding two isoelectronic matryoshka clusters, [Sn@Cu12@Sn20](12-) and [As@Ni12@As20](3-). By dividing each of the clusters in a layer-by-layer manner and allowing each layer to follow a simple electron-filling rule, we can formulate a consistent model to explain experimental and computed properties of both matryoshka clusters that cannot be adequately explained by existing models. By analysing these clusters in a way analogous to peeling an onion, we can not only have an understanding of the structure and bonding of the two matryoshka clusters under study, but also have a generalizable model to handle certain p/d-block@d-block endohedral clusters.

An [Au13]5+ Approach to the Study of Gold Nanoclusters

“…Such an approach can be used to explain numerous gold or gold-like (with some of the gold centers replaced with other group 10−12 elements) icosahedral nanoclusters found in the literature 27−30 and could be further extended to examples such as [C@(AuL) 6 ] 2+ 31 or the inner layers of [As@Ni 12 @As 20 ] 3− 32 by allowing the central atom to follow the octet rule instead of the 18-electron rule. 33 Orbital analysis of the [Au 13 Cl 2 (PH 3 ) 10 ] 3+ cluster indeed gives rise to superatom-like valence orbitals, as shown in Figure 2.…”

“…To extend our argument to such ligated gold clusters, we consider the valence orbitals of an AuL or AuX unit to be sp hybridized; the inward-pointing sp hybrid orbitals will then resemble the Au s orbitals in the W@Au 12 cluster (note that they have the same irreducible representation), with the central Au atom formally fulfilling the 18-electron rule. Such an approach can be used to explain numerous gold or gold-like (with some of the gold centers replaced with other group 10–12 elements) icosahedral nanoclusters found in the literature − and could be further extended to examples such as [C@(AuL) 6 ] 2+ or the inner layers of [As@Ni 12 @As 20 ] 3– by allowing the central atom to follow the octet rule instead of the 18-electron rule . Orbital analysis of the [Au 13 Cl 2 (PH 3 ) 10 ] 3+ cluster indeed gives rise to superatom-like valence orbitals, as shown in Figure .…”

Endohedrally Doped Cage Clusters

“…149 Later, the [{As@Ni 12 } 3− @{As 20 } 0 ] form of [As@Ni 12 @As 20 ] 3− was confirmed by Carey et al, 859 while the same group proposed that [Sn@Cu 12 @Sn 20 ] 12− can be regarded formally as [{Sn@Cu 12 } 4− @{Sn 20 } 8− ] with the innercore having close-shell 1S 2 1P 6 2S 2 1D 10 superatomic orbitals. 860 Sheong et al 849 proposed a revised electron counting model by dividing each of the icosahedral Matryoshka clusters in a layer-by-layer manner and allowing each layer to follow a simple electron-filling rule. As illustrated in Figure 97, the octet electron rule is applicable to the core atom; each of the atoms in the middle layer should have a stable d 10 configuration; the exterior dodecahedron as 3-connected polyhedron obeys Mingos' polyhedral skeletal electron pair theory and thus requires totally 100 valence electrons.…”

Superatomic Ligand-Field Splitting in Ligated Gold Nanoclusters

“…On the other hand, as shown in Figure and Table , both ligated clusters 1 and 2 have a double-shell structure, with the icosahedral shell encapsulated inside the dodecahedral shell, resembling a Matroyoska cluster. − Such a geometric feature is preserved when optimizing the bare [Au 32 ] 8+ kernel but not in the neutral species [Au 32 ] 0 . The latter instead has a single-shell structure with the icosahedral and dodecahedral shells having almost the same radius (Table ).…”