Surface-response functions obtained from equilibrium electron-density profiles

Surface-response functions are one of the most promising routes for bridging the gap between fully quantum-mechanical calculations and phenomenological models in quantum nanoplasmonics. Among all currently available recipes for obtaining such response functions, the use of ab initio methods remains one of the most conspicuous trends, wherein the surface-response functions are retrieved via the metal's non-equilibrium response to an external time-dependent perturbation. Here, we present a complementary approach to approximate one of the most appealing surface-response functions, namely the Feibelman d-parameters, yield a finite contribution even when they are calculated solely with the equilibrium properties of the metal, described under the local-response approximation (LRA) but with a spatially varying equilibrium electron density, as input. Using model calculations that mimic both spill-in and spill-out of the equilibrium electron density, we show that the obtained d-parameters are in qualitative agreement with more elaborate, but also more computationally demanding, ab initio methods. The analytical work presented here illustrates how microscopic surface-response functions can emerge out of entirely local electrodynamic considerations.