  We analyze the electronic structure of group III-V semiconductors obtained
within full potential linearized augmented plane wave (FP-LAPW) method and
arrive at a realistic and minimal tight-binding model, parameterized to provide
an accurate description of both valence and conduction bands. It is shown that
cation sp3 - anion sp3d5 basis along with the next nearest neighbor model for
hopping interactions is sufficient to describe the electronic structure of
these systems over a wide energy range, obviating the use of any fictitious s*
orbital, employed previously. Similar analyses were also performed for the
II-VI semiconductors, using the more accurate FP-LAPW method compared to
previous approaches, in order to enhance reliability of the parameter values.
Using these parameters, we calculate the electronic structure of III-V and
II-VI nanocrystals in real space with sizes ranging upto about 7 nm in
diameter, establishing a quantitatively accurate description of the band-gap
variation with sizes for the various nanocrystals by comparing with available
experimental results from the literature.
