  We study the charge induced in a Thomas-Fermi metal by an ion in vacuum,
using an atomistic description employed in constant-potential molecular
dynamics simulations, and compare the results with the predictions from
continuum electrostatics. Specifically, we investigate the effects of the
Thomas-Fermi screening length $l_{TF}$ and the position $d$ of the ion with
respect to the surface on the induced charge distribution in a graphite
electrode. The continuum predictions capture most of the features observed with
the atomistic description (except the oscillations due to the atomic sites of
the graphite lattice), provided that $d$ and $l_{TF}$ are larger than the
inter-atomic distances within the electrode. At large radial distance from the
ion, the finite $l_{TF}$ case can be well approximated by the solution for a
perfect metal using an effective distance $d+l_{TF}$. This requires a careful
definition of the effective interface between the metal and vacuum for the
continuum description. Our atomistic results support in particular an early
analytical prediction [Vorotyntsev and Kornyshev, Zh. Eksp. Teor. Fiz., 1980,
78(3), 1008] for a single charge at the interface between a Thomas-Fermi metal
and a polarizable medium, which remains to be tested in atomistic simulations
with an explicit solvent.
