  We observe using ab initio methods that localized surface plasmon resonances
in icosahedral silver nanoparticles enter the asymptotic region already between
diameters of 1 and 2 nm, converging close to the classical quasistatic limit
around 3.4 eV. We base the observation on time-dependent density-functional
theory simulations of the icosahedral silver clusters Ag$_{55}$ (1.06 nm),
Ag$_{147}$ (1.60 nm), Ag$_{309}$ (2.14 nm), and Ag$_{561}$ (2.68 nm). The
simulation method combines the adiabatic GLLB-SC exchange-correlation
functional with real time propagation in an atomic orbital basis set using the
projector-augmented wave method. The method has been implemented for the
electron structure code GPAW within the scope of this work. We obtain good
agreement with experimental data and modeled results, including photoemission
and plasmon resonance. Moreover, we can extrapolate the ab initio results to
the classical quasistatically modeled icosahedral clusters.
