Electrodynamics methods have been proved to be useful and powerful tools to theoretically study localized and delocalized surface plasmons. Anyway the recent progresses achieved in fabrication techniques to control sub-nanomater structures and features has lead to search for more rigorous approaches able to theoretically describe nonlocality or the spill-out of conduction electrons, effects well visible in very narrow junctions or sub-nanometers gaps. The main shortcoming of the classical approaches consists, in fact, in losing the intrinsic atomistic structure of matter and in neglecting the quantum mechanical effects. Standard atomistic ab-initio time dependent density functional theory (TDDFT) seems to be the most suitable approach for a complete quantum mechanical treatment of plasmons but it becomes computationally unaffordable for particles sizes of several hundreds of atoms. Here we alternatively …