Atomic-scale structure of static screening in noble-metal nanoparticles from clusters to the conductor limit

Abstract

The static screening response of a metallic nanoparticle is encoded in its induced charge density. Integrated observables such as the dipole moment or the polarizability do not determine this density, because many different screening profiles yield the same integrals. We show that in noble-metal nanoparticles the screening charge is atomically structured, with facet, edge, and vertex sites responding differently from a smooth classical conductor. This structure survives in a surface layer of about one atomic width even when the integrated response has reached the conductor limit, and it is absent from continuum descriptions. To resolve it across size, morphology, and composition, we calibrate an atomistic charge-dipole model for Ag and Au nanoparticles directly to first-principles induced-density profiles. The calibration includes the short-range kinetic and exchange-correlation contribution to the hardness kernel that a purely electrostatic model omits, reducing the induced-density-profile error by about a factor of 2.5. A single averaged parameter set per element predicts clusters withheld from the fit and transfers without adjustment to Ag/Au core-shell, alloyed, and elongated particles. A continuous fast multipole implementation of the model scales almost linearly with the number of atoms and reaches several-million-atom particles, far beyond the reach of first-principles methods.