The identification of plasmons in systems below ∼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 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.Localized surface plasmon resonances in nanostrucures interact strongly with light allowing the confinement of electromagnetic energy down to deep subwavelength regions [1,2]. This, together with their easy tunability [3], robustness [4] and field enhancement properties [5], provides a powerful tool to manipulate light at the nanoscale, below the diffraction limit. Thus, plasmons have become of paramount importance for a wide range of applications [6][7][8] spanning from light harvesting[9] to biosensing [10]. In general terms, plasmons can be defined as electronic collective excitations that arise when the Coulomb interaction between excited states is switched on [11]. However, their theoretical description at the microscopic level is still an open and controversial issue [12]. In large nanoparticles optical and plasmonic properties are generally described by electrodynamics of continuous media, exploiting semiclassical models of the frequencydependent dielectric function [13][14][15] and the identification of plasmons is straightforward. This description has been very useful for designing applications, but fails to convey a microscopic understanding of what plasmons are. Nanoparticles and their excitations are composed of electrons and nuclei like ordinary molecules. Therefore, it must be possible to understand their excited states, including plasmons, in terms of the same elementary electron and hole excitations routinely used to interpret molecular excited states. Notably, such a microscopic description is mandatory when the system size reaches 1-2 nanometers, where the dielectric description breaks down and quantum finite-size effects [2,16] as well as the details of the atomic structure[17] play a crucial role. However, at the nanoscale, single-particle and plasmonic excitations are intrinsically mixed [18], and how to recognize a plasmonic excitation is still an unsolved problem.A few approaches have been recently proposed attempting to classify the plasmonic character of the excitations of nanosystems. [11,[19][20][21][22][23][24] In particular, Bernadotte et al. [11] formulated, in the framework of tim...