Analysis of Localized Surface Plasmon Resonances in Spherical Jellium Clusters and Their Assemblies

Because of multiple possible applications of physicochemical properties of plasmonic metal nanoparticles and particle systems, there is high interest to understand the mechanisms that underlie the birth of localized surface plasmon resonance (LSPR). Here we studied the birth of the LSPR in spherical jellium clusters with the density of sodium and with 8, 20, 34, 40, 58, 92, 138, and 186 electrons by using the linear response time-dependent density functional theory (lr-TDDFT). The coupling of the individual plasmon resonances in dimer, trimer, tetramer, and hexamer cluster assemblies consisting of the eight-electron cluster was also studied. The Kohn-Sham electron-hole transitions contributing to the absorption peaks were analyzed using time-dependent density functional perturbation theory (TD-DFPT) and visualized using the transition contribution map (TCM) analysis. The plasmonicity of an absorption peak was analyzed by examining the number of the electron-hole (e-h) transitions contributing to it, the relative strengths of these contributions, and the radial distribution of the induced density. The main absorption peak in all the studied clusters was found to be a LSPR peak, caused by a collective excitation and with most of the induced density concentrated near the surface of the sphere. Fragmentation of the LSPR peak due to close-lying single e-h transition was observed and discussed for 20- and 40-electron clusters. The level of theory and computational and analysis methods applied in this study facilitate detailed analysis of plasmonic properties, both in energy and in real space. These methods enable the study of still significantly larger clusters and cluster assemblies, opening doors to decipher the basic quantum physics behind the collective phenomena arising in plasmonically coupled metal nano particle systems.