Studies on Cu-doped germanium clusters in the neutral and mono-anion states CuGe_n^−/0 (n = 4–13) are carried out employing a double-hybrid density functional mPW2PLYP scheme. The global minimal structure, spectral property, HOMO–LUMO gap, and stability of CuGe_n^−/0 (n = 4–13) were confirmed. The results showed that the global minimal structures of the anionic clusters are Cu-substituted for a Ge in the ground state of anionic Ge_n+1⁻ with n ≤ 8, and Cu atom is encapsulated into germanium cages starting from n = 9. For neutral, it is also Cu-encapsulated into cage-like Ge framework with n ≥ 9. The spectra information including adiabatic electron affinity, vertical detachment energy and simulated photoelectron spectroscopy were presented. The HOMO–LUMO gap, atomization energy, and second energy difference for CuGe_n^−/0 (n = 4–13) clusters along with NICS of CuGe₁₂⁻ were evaluated to examine the thermodynamic and chemical stability. The results revealed that anionic cluster CuGe₁₂⁻ with a high-symmetry endohedral I_h configuration possessed a perfect thermodynamic stability and chemical reactivity, making it possible as appropriate building block for new multi-functional semiconductor materials.

 采用双杂化密度泛函mPW2PLYP方案对中性和单阴离子态CuGe _n- ^{/ 0}（n = 4-13）的Cu掺杂锗团簇进行了研究。 证实了整体最小结构，光谱性质，HOMO-LUMO间隙和CuGe _n- ^{/ 0}（n = 4-13）的稳定性。结果表明，阴离子簇的全局最小结构的Cu-取代的Ge中的阴离子Ge的基态_{Ñ 1} ^- ，其中n≤8，和Cu原子被封装成锗笼从开始Ñ =9。对于中性，它也被Cu封装到n≥9的笼状Ge框架中。给出了包括绝热电子亲和力，垂直脱离能和模拟光电子能谱的光谱信息。的HOMO-LUMO能隙，雾化能量，和第二能量差为CuGe _ñ ^{- / 0}（Ñ 与CuGe的NICS沿= 4-13）簇₁₂ ^-进行评估，以检查的热力学和化学稳定性。结果表明，阴离子簇CuGe ₁₂ ^-具有高对称性富勒烯我_ħ 构型具有完美的热力学稳定性和化学反应性，使其有可能成为新型多功能半导体材料的合适基础。