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We use an efficient projection scheme for the Fock operator to analyze thesize dependence of silicon quantum dots (QDs) electronic properties. We comparethe behavior of hybrid, screened hybrid and local density functionals as afunction 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 screenedhybrid functionals to experimental results over a wide range of QD sizes. Wedemonstrate the size dependent behavior of the band gap, density of states,ionization potential and HOMO level shift after ionization. Those results arecompared to experiment and to other theoretical approaches, such astight-binding, empirical pseudopotentials, TDDFT and GW.

Size dependent electronic properties of silicon quantum dots - an analysis with hybrid, screened hybrid and local density functional theory