Analytical Approaches to Identify Plasmon-like Excited States in Bare and Ligand-Protected Metal Nanoclusters

Noble metal nanoclusters containing dozens to hundreds of metal atoms are of great interest because of their unique optical properties. Classical electrodynamics fails to describe the optical properties of clusters smaller than a few nanometers, so quantum-mechanical models are needed to describe these clusters. However, it is challenging to identify which features of the computed excited states indicate plasmon-like character, particularly in a way that is generalizable to the ligand-protected clusters that are commonly studied in experiments. We present an analytical method to identify plasmon-like excited states using three quantifiable indicators that must be considered in combination: (1) large superatomic character, (2) large collectivity among single-particle excitations, and (3) large additivity of contributions of these single-particle excitations to the transition dipole moment. Visualizing these three indicators on a single plot enables rapid classification of hundreds of excited states into plasmon-like, collective, single-particle, or interband categories or as intermediate between these categories. This method is used to identify excited states with plasmon-like character in both bare and ligand-protected Ag clusters at the TDDFT level. Using these three nearly orthogonal indicators in combination provides more information than any one criterion can provide.