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 thepresence of a static electric field in the semi-infinite jellium model. The calculation is based on theHohenberg-Kohn-Sham theory with a nonlocal approximation for the exchange-correlationenergy and potential. For different metallic density r s = 2, 3, 4 we present numerical results for themean position and the spread of the induced charge density. The results for the centroid of thecharge induced by a small field are discussed and compared with the image plane position valuesobtained from the exchange-correlation potential