The sizes, shapes, relaxed atomic positions, eigenvalues, and total energies are calculated for selected ultra-small CdSe clusters using SIESTA, a software package for electronic structure calculations and molecular dynamics simulations of molecules and solids. The properties of these bare clusters with small numbers of constituent atoms are studied using density functional theory (DFT) for energy calculations and the conjugate gradient approximation as well as simulated annealing type of molecular dynamics techniques in relaxing the structure to find the lowest energy configurations.The ab-initio norm-conserving pseudopotentials, the exchange-correlation approximation, and parameters used in the computations by Siesta software is verified using FHI98PP, a package used to generate and test the ab-initio norm-conserving pseudopotentials. The initial position of the atomic co-ordinates is determined using ancillary software written in Matlab. / Department of Physics and Astronomy