Motivated by the recent experiments by Wang et al. (Angew. Chem., Int. Ed. 2012, 51, 6154-6157), in which the alkylamine-capped magic-size (CdSe)13 has been isolated for the first time, we report on the computational modeling of the putative low-lying isomers of (CdSe)13, both bare and ligand-protected. According to Density Functional Theory (DFT) calculations, the core@cage configuration Se@Cd13Se12, consisting of a Se atom incarcerated in the center of a puckered Cd13Se12 cage, lies lower in energy than fullerene- and wurtzite-like structures. Methylamine-capped nanoclusters present average bond energies per ligand of about 20 kcal mol(-1), while bond energy decomposition schemes show this interaction to be mostly electrostatically-driven. The computed Time-Dependent-DFT (TDDFT) spectrum of the lowest-lying methylamine-protected (CdSe)13 isomer essentially coincides with the experiment, with a notable blueshift of the absorption features induced by the ligands. The LUMO has been found to be the acceptor orbital for all the lowest-lying electronic excitations, in both the bare and methylamine-capped clusters, which could explain the narrow emission profiles inherent in semiconductor nanostructures. In addition, the attachment of pyridine and aniline molecules has been evaluated. Interestingly, the molecular orbitals of these aromatic amines located on the edges of the valence and conduction bands may act as trap states, in agreement with experimental evidences. In the particular case of pyridine molecules, unoccupied orbitals intrude into the HOMO-LUMO gap of the cluster.