The electronic structures of a variety of experimentally identified gold and silver nanoclusters from 20 to 246 atoms, either unprotected or protected by several types of ligands, are characterized by using point group specific symmetry analysis. The delocalized electron states around the HOMO-LUMO energy gap, originating from the metal s-electrons in the cluster core, show symmetry characteristics according to the point group that describes best the atomic arrangement of the core. This indicates strong effects of the lattice structure and overall shape of the metal core to the electronic structure, which cannot be captured by the conventional analysis based on identification of spherical angular momentum shells in the "superatom" model. The symmetry analysis discussed in this paper is free from any restrictions regarding shape or structure of the metal core, and is shown to be superior to the conventional spherical harmonics analysis for any symmetry that is lower than I h. As an immediate application, we also demonstrate that it is possible to reach considerable savings in computational time by using the symmetry information inside a conventional linear-response calculation for the optical absorption spectrum of the Ag55 cluster anion, without any loss in accuracy of the computed spectrum. Our work demonstrates an efficient way to analyze the electronic structure of nonspherical, but atomically ordered nanocrystals and ligand-protected clusters with nanocrystal metal cores, and it can be viewed as the generalization of the superatom model demonstrated for spherical shapes 10 years ago ( Walter, M.; et al. Proc. Natl. Acad. Sci. U. S. A. 2008 , 105 , 9157 - 9162 ).

中文翻译：

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裸露和受保护的金属纳米晶体的电子结构的点群对称性分析。

通过使用点组特异性对称分析，可以表征未经保护或受几种配体保护的20至246个原子的各种实验确定的金和银纳米簇的电子结构。源于团簇核中金属s电子的HOMO-LUMO能隙附近的离域电子状态根据最能描述核原子排列的点群显示对称性。这表明晶格结构和金属芯的整体形状对电子结构的强大影响，而基于“超原子”模型中球形角动量壳的识别的常规分析无法捕捉到这种影响。本文讨论的对称性分析不受金属芯形状或结构的任何限制，对于任何低于1 h的对称性，均优于传统的球谐分析。作为直接的应用，我们还证明了通过在常规线性响应计算中使用Ag55团簇阴离子的光吸收光谱的对称线性信息中的对称信息，可以节省大量的计算时间，而不会降低计算精度。光谱。我们的工作展示了一种有效的方法，可以分析非球形但原子有序的纳米晶体和具有纳米晶体金属核的配体保护簇的电子结构，