  The standard hydrodynamic Drude model with hard-wall boundary conditions can
give accurate quantitative predictions for the optical response of noble-metal
nanoparticles. However, it is less accurate for other metallic nanosystems,
where surface effects due to electron density spill-out in free space cannot be
neglected. Here we address the fundamental question whether the description of
surface effects in plasmonics necessarily requires a fully quantum-mechanical
approach, such as time-dependent density-functional theory (TD-DFT), that goes
beyond an effective Drude-type model. We present a more general formulation of
the hydrodynamic model for the inhomogeneous electron gas, which additionally
includes gradients of the electron density in the energy functional. In doing
so, we arrive at a Self-Consistent Hydrodynamic Model (SC-HDM), where spill-out
emerges naturally. We find a redshift for the optical response of Na nanowires,
and a blueshift for Ag nanowires, which are both in quantitative agreement with
experiments and more advanced quantum methods. The SC-HDM gives accurate
results with modest computational effort, and can be applied to arbitrary
nanoplasmonic systems of much larger sizes than accessible with TD-DFT methods.
Moreover, while the latter typically neglect retardation effects due to
time-varying magnetic fields, our SC-HDM takes retardation fully into account.
