Structural, electronic and optical properties of germanium clusters doped with palladium and platinum atoms MGe_n (M=Pd,Pt and n=1-20) are investigated in the framework of the density-functional theory. From n ≥ 10 or 11, the cage-like structures where the doping atom is totally encapsulated inside a Ge_n cage are favored. Relative stabilities of different MGe_n clusters have been analyzed from the average binding energies, second energy differences, HOMO–LUMO gap, and the vertical ionization potential and electronic affinity. Our results show that the clusters of MGe_n (M=Pd,Pt) with n = 10, 12, 16 and 18 exhibit relative high stability. Optical absorption spectra are predicted to be unable to discriminate the endohedral and exohedral structures.

在密度泛函理论的框架下研究了掺杂有钯和铂原子MGe _n（M = Pd，Pt和n = 1-20）的锗团簇的结构，电子和光学性质。从n≥10或11开始，倾向于使用笼状结构，其中掺杂原子被完全封装在Ge _n笼中。从平均结合能，第二能差，HOMO-LUMO间隙，垂直电离势和电子亲和力分析了不同MGe _n团簇的相对稳定性。我们的结果表明MGe _n的簇n ＝ 10、12、16和18的（M ＝ Pd，Pt）表现出相对高的稳定性。预测光吸收光谱不能区分内面和外面结构。