  Our theoretical examination of second and third harmonic generation from
metal-based nanostructures predicts that nonlocal and quantum tunneling
phenomena can significantly exceed expectations based solely on local,
classical electromagnetism. Mindful that the diameter of typical transition
metal atoms is approximately 3{\AA}, we adopt a theoretical model that treats
nanometer-size features and/or sub-nanometer size gaps or spacers by taking
into account: (i) the limits imposed by atomic size to fulfill the requirements
of continuum electrodynamics; (ii) spillage of the nearly-free electron cloud
into the surrounding vacuum; and (iii) the increased probability of quantum
tunneling as objects are placed in close proximity. Our approach also includes
the treatment of bound charges, which add crucial, dynamical components to the
dielectric constant that are neglected in the conventional hydrodynamic model,
especially in the visible and UV ranges, where interband transitions are
important. The model attempts to inject into the classical electrodynamic
picture a simple, perhaps more realistic description of the metal surface by
incorporating a thin patina of free-electrons that screens an internal,
polarizable medium.
