Architectures, electronic structures, and stabilities of Cu-doped Ge n clusters: density functional modeling

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The present study reports the geometries, electronic structures, growth behavior, and stabilities of neutral and ionized copper-doped germanium clusters containing 1-20 Ge atoms within the framework of linear combination of atomic orbitals density functional theory (DFT) under the spin-polarized generalized gradient approximation. It was found that Cu-capped Ge(n) (or Cu-substituted Ge( n+1)) and Cu-encapsulated Ge(n) clusters mostly occur in the ground state at a particular cluster size (n). In order to explain the relative stabilities of the ground-state clusters, parameters such as the average binding energy per atom (BE), the embedding energy (EE), and the fragmentation energy (FE) of the clusters were calculated, and the resulting values are discussed. To explain the chemical stabilities of the clusters, parameters such as the energy gap between the highest occupied and the lowest unoccupied molecular orbitals (the HOMO-LUMO gap), the ionization energy (IP), the electron affinity (EA), the chemical potential (μ), the chemical hardness (η), and the polarizability were calculated, and the resulting values are also discussed. Natural atomic orbital (NAO) and natural bond orbital (NBO) analyses were also used to determine the electron-counting rule that should be applied to the most stable Ge(10)Cu cluster. Finally, the relevance of the calculated results to the design of Ge-based superatoms is discussed.