This book is based on my PhD thesis where I explored the electronic structure calculation of semiconductor quantum dots.All the calculations are based on density functional theory based ab-initio method.The optical properties of Silicon cluster and Quantum Confinement Effect were studied.Also the adsorption of Silicon clusters on metallic (Au/Ag) and insulating(MgO)surface were investigated in order to understand the charge transfer process between adsorbates and surfaces.This can be leading towards catalytic behavior as well studying the gas phase clusters on different surfaces.Also by exploring the nature of optical spectra of Silicon cluster one can understand the optical response of Nano cluster and this may lead to creation of Nano crystalline Silicon Solar Cell.The extensive study of electronic structure optimization of different nano cluster in different size regime had been done by keeping in mind the gloabal minimum structures.For all the calculations VASP, CPMD and PARSEC were used as computing code along with several fortran codes as the post processing program. The readers will be beneficial in terms of getting a profound knowledge in electronic structure calculations