New Insights into Applicability of Electron-Counting Rules in Transition Metal Encapsulating Ge Cage Clusters

Abstract

The relative stability of Sc, Ti, and V encapsulating Ge(n) clusters in the size range n = 14-20 has been studied through first-principles electronic structure calculations based on density functional theory. Variations of the embedding energy, gap between the highest occupied and the lowest occupied molecular orbitals, ionization potential, vertical detachment energy, and electron affinity with cluster size have been calculated to identify clusters with enhanced stability. The enhanced stability of some clusters can be very well explained as due to the formation of a filled shell free-electron gas inside the Ge cages. For the first time, direct evidence of the formation of a free-electron gas is also presented. In some other clusters, enhanced stability is found to originate from geometric effects. Some clusters that may be expected to have enhanced stability from simple electron counting rules do not show that. These results provide new insights into the long-standing question of whether electron counting rules can explain the relative stability of transition metal encapsulated semiconductor clusters and show that these clusters are too complex for such simple generalizations.

Photoelectron spectroscopy and density functional calculations of AgSin− (n = 3–12) clusters

“…Kumar and Kawazoe conducted theoretical calculations on a number of TM-doped germanium clusters and predicted TiGe 16 cluster to be a Frank-Kasper polyhedron structure with a large gap between its highest-occupied-orbital (HOMO) and lowest-unoccupied-orbital (LUMO) [9]. In addition to the TiGe 16 cluster, the density functional theory (DFT) calculations of Bandyopadhyay et al on TiGe n (n=14−20) suggested that TiGe 18 cluster also has en-hanced stability [10]. The ground state structure of TiGe 12 cluster is proposed to be a remarkably stable pseudoicosahedron by Tang et al [11].…”

Electronic structures of NbGen−/0/+ (n = 1–3) clusters from multiconfigurational CASPT2 and density matrix renormalization group‐CASPT2 calculations

“…[ 1,2,4,8–10 ] Density functional theory was also employed to study the stability and electronic structures of a large number of transitions metal‐doped germanium clusters. [ 1,4–29 ] It was found in many cases that doping transition metal atom can lead to stable transition metal‐doped germanium clusters. [ 1,2,6,7,19,21 ]…”

Spin State Energetics of VGen−/0 (n = 5–7) Clusters and New Assignments of the Anion Photoelectron Spectra

“…The physical and chemical properties of transition metal‐doped germanium clusters are determined by their size, shape, and composition. In the literature, we can see a large amount of experimental and theoretical investigations on the structures of transition metal‐doped germanium clusters . It is found that doping of transition metal to pure germanium clusters can form stable cage structures that can be used as building blocks for synthesis novel materials …”