过渡金属原子掺杂硅团簇不仅可以提高硅团簇的稳定性，还可以使其产生许多新颖的物理和化学特性，在新能源和材料领域应用广泛。本文基于密度泛函理论并结合粒子群优化算法程序卡利普索，对CoSi₁₆^-和Co₂Si₃₂^2-团簇的几何结构、电子、光谱和热力学特性进行了系统研究。结构优化发现，CoSi₁₆^-和Co₂Si₃₂^2-团簇基态结构分别为Co原子被包裹在Si笼内部的高对称D_2d和D_2h点群对称笼状结构。在此结构基础上，分析了两体系的磁性和键级等特性。此外，根据拟合的光电子能谱、红外和拉曼光谱，对两体系的主要特征峰进行了归属分析。最后，研究了体系的热力学特性，讨论了热力学参数C_v 和 S随温度变化的规律。

Doping of silicon clusters with transition metals can enhance the stability of such clusters and confer many peculiar physical and chemical properties. Therefore, this method occupies an important position in the fields of new energy and materials science. Herein, we report the geometric structures as well as electronic and thermodynamic properties of CoSi₁₆^- and Co₂Si₃₂^2- clusters using the particle swarm optimization algorithm CALYPSO searching method and density functional theory. Results indicate that the lowest structures of the CoSi₁₆^- and Co₂Si₃₂^2- clusters exhibit the highly symmetric D_2d and D_2h point structures, respectively, in which the Co atom is completely encapsulated in Si cages. Based on these structures, various electronic properties, including the magnetic properties and bond order, are systemically evaluated. In addition, the photoelectron spectra, infrared spectra, and Raman spectra are recorded to identify the main characteristic peaks of the two systems. Finally, the thermodynamic properties of the two systems are investigated. Moreover, the temperature dependence of C_v and S for the CoSi₁₆^- and Co₂Si₃₂^2- clusters is discussed.