  The structure of the double-layer formed at the surface of carbon electrodes
is governed by the interactions between the electrode and the electrolyte
species. However, carbon is notoriously difficult to simulate accurately, even
with well-established methods such as electronic Density Functional Theory and
Molecular Dynamics. Here we focus on the important case of a lithium ion in
contact with the surface of graphite, and we perform a series of reference
Quantum Monte Carlo calculations that allow us to benchmark various electronic
Density Functional Theory functionals. We then fit an accurate carbon--lithium
pair potential, which is used in molecular Density Functional Theory
calculations to determine the free energy of the adsorption of the ion on the
surface in the presence of water. The adsorption profile in solution differs
markedly from the gas phase results, which emphasize the role of the solvent on
the properties of the double-layer.
