  We present here a theory and a computational tool, Silicon-{\sc Qnano}, to
describe atomic scale quantum dots in Silicon. The methodology is applied to
model dangling bond quantum dots (DBQDs) created on a passivated
H:Si-(100)-(2$\times$1) surface by removal of a Hydrogen atom. The electronic
properties of DBQD are computed by embedding it in a computational box of
Silicon atoms. The surfaces of the computational box were constructed by using
DFT as implemented in {\sc Abinit} program. The top layer was reconstructed by
the formation of Si dimers passivated with H atoms while the bottom layer
remained unreconstructed and fully saturated with H atoms. The computational
box Hamiltonian was approximated by a tight-binding (TB) Hamiltonian by
expanding the electron wave functions as a Linear Combination of Atomic
Orbitals and fitting the bandstructure to {\it ab-initio} results. The
parametrized TB Hamiltonian was used to model large finite Si(100) boxes
(slabs) with number of atoms exceeding present capabilities of {\it ab-initio}
calculations. The removal of one hydrogen atom from the reconstructed surface
resulted in a DBQD state with wave function strongly localized around the Si
atom and energy in the silicon bandgap. The DBQD could be charged with zero,
one and two electrons. The Coulomb matrix elements were calculated and the
charging energy of a two electron complex in a DBQD obtained.
