Molecular geometries, electronic properties, and vibrational spectroscopies of TM@C 24 and TM@C 24 H 12 (TM = Cr, Mo, and W) in their different spin configurations have been systematically investigated with the hybrid DFT-(U)B3PW91 functional. The results show that the TM atoms bind over the pentagon ring inside C 24 cage, and they move gradually toward the center of C 24 cage along with the increasing atomic radii. The most stable Mo@C 24 H 12 and W@C 24 H 12 are in their spin-triplet states. The analyses of dissociation energy and energy gap reveal that TM@C 24 (TM = Cr, Mo, and W) and Cr@C 24 H 12 are not only thermodynamically stable, but also considerably stable kinetically. Meanwhile, natural population analyses tell us that the two cages act as electron acceptors, and the transferred charge from the W atom to C 24 cage is the largest in the endohedral metallofullerenes. Additionally, the vibrational frequencies and active infrared intensities may be used as evidence to characterize these unknown species.