Density functional theory (DFT) and time-dependent DFT (TDDFT) have been employed to examine the optical absorption spectra of bare and passivated (thiolate-, phosphine-, or carboxylate-stabilized) gold and silver nanoparticles. The location of the ligands is responsible for causing splitting in the optical absorption spectra of thiolate-stabilized nanoparticles. The choice of metal and ligand affects the thermodynamic stability of the staples on the surface of the nanoparticle, and may affect the growth of these nanoparticles. The tail group on the ligand does not greatly affect the optical properties, although it does affect the redox potentials. For bare nanoparticles, sharp optical absorption spectra can be obtained depending on the number of electrons in the system; when the number of electrons is a magic number for a given shape, the spectrum is typically sharp. For small gold nanoparticles, interband transitions are also important and can be analyzed differently than intraband transitions. The width of the absorption peak is affected by temperature. For nanoparticle aggregates, the main effect on the spectrum arises from symmetry-lowering. However, orientation also plays a role.