Quantifying the plasmonic character of optical excitations in nanostructures

The identification of plasmons in systems below $ \sim $10 nm in size is a tremendous challenge. Any sharp distinction of the excitation character (non-plasmonic vs plasmonic) becomes blurred in this range of sizes, where quantum effects become important. Here we define a {\em plasmonicicty index} that quantifies the plasmonic character of selected optical excitations in small nanostructures, starting from first principles calculations, based on (TD)DFT. This novel approach allows us to overcome the aforementioned problems, providing a direct and quantitative classification of the plasmonic character of the excitations. We show its usefulness for model metallic nanoparticles, a prototypical C-based molecule and a paradigmatic hybrid system. Our results indicate that the plasmonicity index can be exploited to solve previously unsolvable problems about the plasmonic character of complex systems, not predictable a priori.