Self-consistent density functional calculation of the image potential at a metal surface

It is well known that the exchange-correlation (XC) potential at a metal surface has an image-like asymptotic behaviour given by -1/4(z-z₀), where z is the coordinate perpendicular to the surface. Using a suitable fully non-local functional prescription, we evaluate self-consistently the XC potential with the correct image behaviour for simple jellium surfaces in the range of metallic densities. This allows a proper comparison between the corresponding image-plane position, z₀, and other related quantities such as the centroid of an induced charge by an external perturbation. As a by-product, we assess the routinely used local density approximation when evaluating electron density profiles, work functions, and surface energies by focusing on the XC effects included in the fully non-local description.