  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.
