Quantum Hydrodynamic Theory for Plasmonics: Impact of the Electron Density Tail

Multiscale plasmonic systems e.g. extended metallic nanostructures with sub-nanometer inter-distances) play a key role in the development of next-generation nano-photonic devices. An accurate modeling of the optical interactions in these systems requires an accurate description of both quantum effects and far-field properties. Classical electromagnetism can only describe the latter, while Time-Dependent Density Functional Theory (TD-DFT) can provide a full first-principles quantum treatment. However, TD-DFT becomes computationally prohibitive for sizes that exceed few nanometers, which are irrelevant for practical applications. In this article, we introduce a method based on the quantum hydrodynamic theory (QHT), which includes non-local contributions of the kinetic energy and the correct asymptotic description of the electron density. We show that our QHT method can predict both plasmon energy and spill-out effects in metal nanoparticles in excellent agreement with TD-DFT predictions, thus allowing a reliable and efficient calculations of both quantum and far-field properties in multiscale plasmonic systems.