The electronic and optical properties of tetrahedral CdSe magic clusters (average diameter.5 nm) protected by carboxyl and amine ligands, which correspond to previously reported experimental structures, are studied using density functional theory. We find extreme ligand packing densities, capping every single dangling bond of the inorganic core, strong dependence of the Z-type metal carboxylate binding on the amount of excess amine, and potential for improved photoluminescence upon replacing phenyl ligands with alkanes. The computed absorption spectra of the Cd35Se20 cluster agree well with experiments, resolving the 0.2 eV splitting of the first exciton peak due to spin-orbit coupling. We discuss the origin of the significant broadening of the optical spectra as due to phonons and structural variations in the ligand configurations and inorganic core apexes. © 2016 American Chemical Society.