  We use an efficient projection scheme for the Fock operator to analyze the
size dependence of silicon quantum dots (QDs) electronic properties. We compare
the behavior of hybrid, screened hybrid and local density functionals as a
function of the dot size up to $\sim$800 silicon atoms and volume of up to
$\sim$20nm$^3$. This allows comparing the calculations of hybrid and screened
hybrid functionals to experimental results over a wide range of QD sizes. We
demonstrate the size dependent behavior of the band gap, density of states,
ionization potential and HOMO level shift after ionization. Those results are
compared to experiment and to other theoretical approaches, such as
tight-binding, empirical pseudopotentials, TDDFT and GW.

Chemical Physics