We study (through computer simulation) the variation of the band gap as a function of sizes and shapes of small Silicon (Si) dots using pseudo-potential approach. We have used empirical pseudo-potential Hamiltonian and a plane wave basis expansion and a basic tetrahedral structure. It is found that the gap decreases for increasing dot size. Furthermore, the band gap increases as much as 0.13eV on passivation the surface of the dot with hydrogen. So both quantum confinement and surface passivation determine the optical and electronic properties of Si quantum dots. Visible luminescence is probably due to radiative recombination of electrons and holes in the quantum confined nanostructures. The effect of passivation of the surface dangling bonds by hydrogen atoms and the role of surface states on the gap energy as well as on the HOMO-LUMO states has also been examined. We have investigated the entire energy spectrum starting from the very low lying ground state to the very high lying excited states for silicon dots having 5, 18, 17 and 18 atoms. The results for the size dependence of the HOMO-LUMO gap and the wave functions for the bonding-antibonding states are presented and the importance of the confinement and the role of hydrogen passivation on the confinement are also discussed.