  Quantum size effects on the permittivity of metal nanoparticles are
investigated using the quantum box model. Explicit upper and lower bounds are
derived for the permittivity and relaxation rates due to quantum confinement
effects. These bounds are verified numerically, and the size-dependence and
frequency-dependence of the empirical Drude size parameter is extracted from
the model. Results suggest that the common practice of empirically modifying
the dielectric function can lead to inaccurate predictions for highly uniform
distributions of finite-sized particles.
