Communication: dynamical embedding: correct quantum response from coupling TDDFT for a small cluster with classical near-field electrodynamics for an extended region.

We show how to obtain the correct electronic response of a large system by embedding; a small region is propagated by TDDFT (time-dependent density functional theory) simultaneously with a classical electrodynamics evolution using the Near-Field method over a larger external region. The propagations are coupled through a combined time-dependent density yielding a common Coulomb potential. We show that the embedding correctly describes the plasmonic response of a Mg(0001) slab and its influence on the dynamical charge transfer between an adsorbed H2O molecule and the substrate, giving the same spectral shape as full TDDFT (similar plasmon peak and molecular-dependent differential spectra) with much less computational effort. The results demonstrate that atomistic embedding electrodynamics is promising for nanoplasmonics and nanopolaritonics.