Abstract
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 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, 9157−916218599443).
Highlights
Symmetry lays the foundation to understanding the electronic structure and spectroscopic transitions of small molecules, giving point group assignments of single-electron orbitals and dictating rules for allowed and forbidden dipole transitions between the quantum states.[1]
Theoretical and computational research on chemical and optical properties of nanoclusters relies on examination of the electronic states and the corresponding wave functions computed from the density functional theory (DFT)
We have introduced an improved and generalized way to analyze electronic states of metal clusters that have nanocrystalline cores, i.e., atomic arrangements with specific point group symmetries
Summary
Symmetry lays the foundation to understanding the electronic structure and spectroscopic transitions of small molecules, giving point group assignments of single-electron orbitals and dictating rules for allowed and forbidden dipole transitions between the quantum states.[1]. Larger clusters are expected to be stabilized by a favorable atomic packing of the metal, creating a series of atomic “magic numbers” Very recently, both stabilization mechanisms were demonstrated to be present simultaneously in cluster synthesis.[25] several known compositions and structures of ligand-protected gold and silver nanoclusters have strongly nonspherical core shapes and free-electron counts that do not match with expected electronic “magic numbers”. Were projected onto the jellium wave functions of a threedimensional (3D) quantum box, which aided the assignment of symmetries based on box quantization.[26] This method, was constrained to the cuboidal shape of the cluster core and required a reference calculation of the corresponding jellium box. We demonstrate significant savings in CPU time when the symmetry information is used inside the linearresponse calculation of the optical absorption spectrum of 1
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