Corrections to the Local Density Approximation: Gradient Expansion versus Wave-Vector Analysis for the Metallic Surface Problem

We present strong evidence that the first gradient correction to the local density approximation for exchange and correlation is inappropriate near physical metallic surfaces, in that it fails to improve the energy and worsens the density profile. Further evidence is presented for the validity of the wave-vector analysis procedure, in that it is shown to be correct both for slowly varying and for rapidly varying density profiles.