  The structural, cohesive, electronic and optical properties of mixed SiGe:H
quantum dots are studied by Density Functional Theory (DFT) calculations on a
representative ensemble of medium size nanoparticles of the form
$Si_xGe_{47-x}:H_{60}$. The calculations have been performed in the framework
of the hybrid non-local exchange-correlation functional of Becke, Lee, Parr and
Yang (B3LYP). Besides the ground state DFT/B3LYP values we provide reliable
result for the lowest spin and symmetry allowed electronic transition based on
Time Dependent DFT (TDDFT/B3LYP) calculations. Our results show that the
optical gap depends not only on the relative concentrations of silicon,
germanium and hydrogen, but also on the relative position of the silicon and
germanium shells relative to the surface of the nanocrystal. This is also true
for the structural, cohesive and electronic properties allowing for possible
electronic and optical gap engineering. Moreover, it is found that for the
cases of nanoparticles with pure Ge or Si core, the optical properties are
mainly determined by the Ge part of the nanoparticle, while silicon seem to act
as a passivant.
