Analysis of the Electronic Structure of Non-Spherical Ligand-Protected Metal Nanoclusters: The Case of a Box-Like Ag₆₇

In this work we introduce a new strategy to investigate the electronic shell structure of ligand-protected metal nanoclusters of polyhedral core shape. The central idea is to identify the symmetry of the Kohn–Sham molecular orbitals of an atomistic structure based on their projection onto the electronic states of a jellium system with a similar shape of the background charge density. Herein, we study the connection between a reduced atomistic model of the recently reported box-like [Ag₆₇(SR)₃₂(PR₃)₈]³⁺ nanocluster and a jellium box consisting of 32 free electrons. With this approach, we determine the symmetry of electronic states of the metal core and identify those that are involved in the lowest metal-to-metal electronic transitions. Furthermore, we define a new transition selection rule for ligand-protected metal nanoclusters with rectangular cuboid-like core. This rule differs from the one of a particle in an infinitely deep 3D potential well. The approach presented here is complementary to the angular momentum analysis of “superatom orbitals” of spherical or near spherical metal nanoclusters and opens the door to understand and predict the electronic properties and stability of several existent and new ligand-protected metal nanoclusters with nonspherical cores