Towards a new frontier of computational plasmonics: The density functional tight binding (DFTB) method

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 propone the time dependent Density Functional Tight-Binding Method (TDDFTB) as an efficient and reliable method to describe the optical propreties of metallic clusters, molecules and their relative interactions at the atomistic level. We present a new empirical strategy to improve the TDDFTB performances and overcome its limits in reproducing ab-initio TDDFT spectra for tetrahedral closed-shell Ag„ clusters and report on our best results for hand-tuned on-site energies. With the proposed parametrization TDDFTB gives results comparable to the reference ones but within a computational time less than 0.1%.