Density functional theory (DFT) calculations combined with “stochastic kicking” (SK) global search technique were performed to investigate the structural properties of $\mathrm{E}\mathrm{u}{\mathrm{S}\mathrm{i}}_{\mathrm{n}}^{-}(1\le n\le 13)$. It was found that the Eu atom in $\mathrm{E}\mathrm{u}{\mathrm{S}\mathrm{i}}_n^{-}$ preferred to occupy the surface position up to a size of 11Si atoms. However, starting from$n$ = 12, the endohedral structures were found, as depicted by the Eu atom inserting into the center of Si frame. The global minimum structures for each size was determined by comparing with the experimental photoelectron spectroscopy (PES). Natural population analysis (NPA) coupled with spin density isosurfaces were utilized to further investigate the electronic and magnetic properties of $\mathrm{E}\mathrm{u}{\mathrm{S}\mathrm{i}}_n^{-}$. The observed magnetic moments significantly concentrates among the Eu atom, ascribed to the Eu 4f-electrons remaining largely as before encapsulating the ${\text{Si}}_n$ clusters. Meanwhile, the representative caged cluster $\mathrm{E}\mathrm{u}{\mathrm{S}\mathrm{i}}_{12}^{-}$ was subjected to density of states (DOS) and HOMO-LUMO analysis, and the results showed a significant spin polarization.

结合“随机踢”（SK）全局搜索技术进行密度泛函理论（DFT）计算，以研究结构的性能。 $\mathrm{Ë}\mathrm{ü}{\mathrm{小号}\mathrm{一世}}_{\mathrm{ñ}}^{--}（\mathrm{1个}\le ñ\le 13）$。发现in原子在$\mathrm{Ë}\mathrm{ü}{\mathrm{小号}\mathrm{一世}}_{ñ}^{--}$优选占据表面位置直至11Si原子的大小。但是，从$ñ$ = 12，发现内衬结构，如Eu原子插入Si框架的中心所示。通过与实验光电子能谱法（PES）进行比较，确定每种尺寸的整体最小结构。利用自然种群分析（NPA）与自旋密度等值面相结合来进一步研究铁的电子和磁性$\mathrm{Ë}\mathrm{ü}{\mathrm{小号}\mathrm{一世}}_{ñ}^{--}$。观察到的磁矩明显集中在Eu原子中，这归因于Eu 4f电子在包封前大致保留了下来。${\text{硅}}_{ñ}$集群。同时，典型的笼状集群$\mathrm{Ë}\mathrm{ü}{\mathrm{小号}\mathrm{一世}}_{12}^{--}$ 进行了状态密度（DOS）和HOMO-LUMO分析，结果显示出明显的自旋极化。