  Excitonic spectra are calculated for free-standing, surface passivated InAs
quantum dots using atomic pseudopotentials for the single-particle states and
screened Coulomb interactions for the two-body terms. We present an analysis of
the single particle states involved in each excitation in terms of their
angular momenta and Bloch-wave parentage. We find that (i) in agreement with
other pseudopotential studies of CdSe and InP quantum dots, but in contrast to
k.p calculations, dot states wavefunction exhibit strong odd-even angular
momentum envelope function mixing (e.g. $s$ with $p$) and large
valence-conduction coupling. (ii) While the pseudopotential approach produced
very good agreement with experiment for free-standing, colloidal CdSe and InP
dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted
spectrum does {\em not} agree well with the measured (ensemble average over dot
sizes) spectra. (1) Our calculated excitonic gap is larger than the PL measure
one, and (2) while the spacing between the lowest excitons is reproduced, the
spacings between higher excitons is not fit well. Discrepancy (1) could result
from surface states emission. As for (2), agreement is improved when account is
taken of the finite size distribution in the experimental data. (iii) We find
that the single particle gap scales as $R^{-1.01}$ (not $R^{-2}$), that the
screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$
($R^{-0.7}$), and that the eccitonic gap sclaes as $R^{-0.9}$. These scaling
laws are different from those expected from simple models.

Materials Science