Electron density profiles at charged metal surfaces in the weighted density approximation

We present a selfconsistent calculation of the electron distribution at metal surfaces in the presence of a static electric field in the semi-infinite jellium model. The calculation is based on the Hohenberg-Kohn-Sham theory with a nonlocal approximation for the exchange-correlation energy and potential. For different metallic density rs=2, 3, 4 we present numerical results for the mean position and the spread of the induced charge density. The results for the centroid of the charge induced by a small field are discussed and compared with the image plane position values obtained from the exchange-correlation potential.