A first-principles study of small Cd<sub>n</sub>Se<sub>n</sub> Quantum Dots (QD) (`n' =6, 12, 13, and 33) has been performed for application to QD solar cell development. We separately assess the effects of the particle size and the passivating ligands upon the optimized structure and the energy gap (from a density functional theory (DFT) calculation) and the corresponding absorption spectrum (from a time-dependent density functional theory (TDDFT) calculation). The structures of four thiol ligands, namely -- cysteine (Cys), mercaptopropionic acid (MPA), and their reduced-chain analogues, are investigated. We have documented significant passivation effects of the surfactants upon the structure and the optical absorption properties of the CdSe quantum dots: The surface Cd-Se bonds are weakened, whereas the core bonds are strengthened. A blue shift of the absorption spectrum by ~0.2 eV is observed. Also, the optical absorption intensity is enhanced by the passivation. By contrast, we have observed that varying the length of ligands yields only a minor effect upon the absorption properties: a shorter alkane chain might induce a slightly stronger interaction between the -NH<sub>2</sub> group and the nearest surface Se atom, which is observed as a stronger ligand binding energy. For Cd<sub>12</sub>Se<sub>12</sub>, which is regarded as the `non-magic' size QD, neither the self-relaxation nor the ligand passivation could fully stabilize the structure or improve the poor electronic properties. We also observe that the category of thiol ligands possesses a better ability to open the band gap of CdSe QD than either phosphine oxide or amine ligands. Our estimation of the absorption peak of the Cys-capped QDs ranges from 413 nm to 460 nm, which is consistent to the experimental peak as 422 nm.