  It is demonstrated that the collective and single particle responses of
simple metals in the extreme long wavelength limit become identical. When
applied to alternative models of a metallic slab, this duality proves
equivalence of the plasma frequency and the surface energy barrier, which
confines electrons inside the metal. This in-turn proves also a simple, yet
powerful formula, which expresses the work function of a metals as a difference
between its free-electron plasmon and Fermi energies, and which has been shown
to be more accurate (even for complex metals) than the best available
simulations.
