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The electronic structures of a variety of experimentally identified gold andsilver nanoclusters from 20 to 246 atoms, either unprotected or protected byseveral types of ligands, are characterized by using point group specificsymmetry analysis. The delocalized electron states around the HOMO-LUMO energygap, originating from the metal s-electrons in the cluster core, show symmetrycharacteristics according to the point group that describes best the atomicarrangement of the core. This indicates strong effects of the lattice structureand overall shape of the metal core to the electronic structure, which cannotbe captured by the conventional analysis based on identification of sphericalangular momentum shells in the superatom model. The symmetry analysis discussedin this paper is free from any restrictions regarding shape or structure of themetal core, and is shown to be superior to the conventional spherical harmonicsanalysis for any symmetry that is lower than Ih. As an immediate application,we also demonstrate that it is possible to reach considerable savings incomputational time by using the symmetry information inside a conventionallinear-response calculation for the optical absorption spectrum of the Ag55cluster anion, without any loss in accuracy of the computed spectrum. Our workdemonstrates an efficient way to analyze the electronic structure ofnon-spherical, but atomically ordered nanocrystals and ligand-protectedclusters with nanocrystal metal cores and it can be viewed as thegeneralization of the superatom model demonstrated for spherical shapes tenyears ago (Walter et al., PNAS 2008, 105, 9157).

Point Group Symmetry Analysis of the Electronic Structure of Bare and Protected Metal Nanocrystals