  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 Ih. 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
non-spherical, 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 ten
years ago (Walter et al., PNAS 2008, 105, 9157).
