Surface plasmon dependence on the electron density profile at metal surfaces.

We use an extension of the hydrodynamic model to study nonlocal effects in the collective plasmon excitations at metal surfaces and narrow gaps between metals, including the surface spill-out of conduction band electrons. In particular, we simulate metal surfaces consisting of a smooth conduction-electron density profile and an abrupt jellium edge. We focus on aluminum and gold as prototypical examples of simple and noble metals, respectively. Our calculations agree with the dispersion relations measured from planar surfaces for these materials. Systems involving small gaps display a regime of tunnelling electrons, which is partially captured by the overlap of electron densities. This extension of the hydrodynamic model to cope with inhomogeneous density profiles provides a relatively fast and accurate way of describing the optical response of metal surfaces at subnanometer distances.