  We report on a theoretical derivation of the electronic dielectric response
of semiconductor nanocrystals using a tight-binding framework. Extending to the
nanoscale the Hanke and Sham approach [Phys. Rev. B 12, 4501 (1975)] developed
for bulk semiconductors, we show how local field effects can be included in the
study of confined systems. A great advantage of this scheme is that of being
formulated in terms of localized orbitals and thus it requires very few
computational resources and times. Applications to the optical and screening
properties of semiconductor nanocrystals are presented here and discussed.
Results concerning the absorption cross section, the static polarizability and
the screening function of InAs (direct gap) and Si (indirect gap) nanocrystals
compare well to both first principles results and experimental data. We also
show that the present scheme allows us to easily go beyond the continuum
dielectric model, based on the Clausius-Mossotti equation, which is frequently
used to include the nanocrystal surface polarization. Our calculations indicate
that the continuum dielectric model, used in conjunction with a size dependent
dielectric constant, underestimates the nanocrystal polarizability, leading to
exceedingly strong surface polarization fields.
