  Understanding the response of the surface of metallic solids to external
electric field sources is crucial to characterize electrode-electrolyte
interfaces. Continuum electrostatics offer a simple description of the induced
charge density at the electrode surface. However, such a simple description
does not take into account features related to the atomic structure of the
solid and to the molecular nature of the solvent and of the dissolved ions. In
order to illustrate such effects and assess the ability of continuum
electrostatics to describe the induced charge distribution, we investigate the
behaviour of a gold electrode interacting with sodium or chloride ions fixed at
various positions, in vacuum or in water, using all-atom constant-potential
classical molecular dynamics simulations. Our analysis highlights important
similarities between the two approaches, especially in vacuum conditions and
when the ion is sufficiently far from the surface, as well as some limitations
of the continuum description, namely neglecting the charges induced by the
adsorbed solvent molecules and the screening effect of the solvent when the ion
is close to the surface. While the detailed features of the charge distribution
are system-specific, we expect some of our generic conclusions on the induced
charge density to hold for other ions, solvents and electrode surfaces. Beyond
this particular case, the present study also illustrates the relevance of such
molecular simulations to serve as a reference for the design of improved
implicit solvent models of electrode-electrolyte interfaces.
