In this paper, a computational study, at the M06L/def2-SVP and BP86/def2-SVP levels of theory, on [M(η5–C60Me5)(CO)n] (n = 3, M = Mn(I), Tc(I), Re(I); n = 2, M = Co(I), Rh(I), Ir(I)) complexes as well as the corresponding classical half-sandwich structures, [M(η5–Cp)(CO)n], is reported. By considering the above metal complexes as an ABC system, where B is the central metal ion, A corresponds to three (or two) CO ligands and C is a η5–Cp or η5–C60Me5 ligand, four types of bonding interaction energies defined as A–BC, AB–C, A–B and B–C, as well as the total interaction energy of the complexes, were calculated and corrected for the basis set superposition error (BSSE). In the most interesting part of the paper, the possible existence of cooperativity/anticooperativity between the metal–carbonyl and the metal–(η5-ligand) bonds was also investigated for the first time. The nature of the bond in these complexes was also studied using energy decomposition analysis-natural orbital for chemical valence (EDA–NOCV) calculations.