Plasmon Character Index: An Accurate and Efficient Metric for Identifying and Quantifying Plasmons in Molecules

Plasmons, which are collective and coherent oscillations of charge carriers driven by an external field, play an important role in applications such as solar energy harvesting, sensing, and catalysis. Plasmons can be found in bulk and nanomaterials, and in recent years, plasmons have also been identified in molecules and these molecules have been utilized to build plasmonic devices. As molecular plasmons can no longer be described by classical electrodynamics, a description using quantum mechanics is necessary. Many methods have been developed to identify and quantify molecular plasmons based on the properties of plasmonic excitations. However, there is not currently a method that is widely accepted, connects to collectivity and coherence, and is computationally practical. Here we develop a metric to accurately and efficiently identify and quantify plasmons in molecules. A number, which we call plasmon character index (PCI), can be calculated for each electronic excited state and describes the plasmonicity of the excitation. PCI is developed from the collective and coherent excitation picture in orbitals and shows excellent agreement with the predictions from scaled time-dependent density functional theory but is vastly more computationally efficient. Therefore, PCI can be a useful tool in identifying and quantifying plasmons and will inform the rational design of plasmonic molecules and small nanomaterials.