Dynamic Response at Metal Surfaces: Violation of Sum Rules by Density-Functional-Based Random Phase Approximation

Abstract

It is shown that the use of the random phase approximation (RPA) to determine the response of a metal surface to an external electromagnetic field in conjunction with a local density description of exchange and correlation in the ground state violates the force sum rule and the surface f-sum rule. As a result, the static image plane is located too close to the surface and the effective number of electrons available for excitation near a metal surface is underestimated, giving incorrect values for the first and first inverse frequency moments of the dynamic induced charge. All previous RPA-LDA calculations of the surface photoelectric effect, the surface plasmon dispersion, the vibrational lifetime of adsorbates due to electron-hole excitations, etc. are affected by these sum rule violations. These inconsistencies can be avoided by treating electron-electron interaction contributions to the induced field on the same footing as in the ground state.