Quantum-chemical density functional theory calculations using the BP86 functional in conjunction with a triple-zeta basis set and dispersion correction by Grimme with Becke-Johnson damping D3(BJ) were performed for the title molecules. The nature of the bonding was examined with the quantum theory of atoms in molecules (QTAIM) and natural bond order (NBO) methods and with the energy decomposition analysis in conjunction with the natural orbital for chemical valence (EDA-NOCV) analysis. The energetically lowest lying form of Fe-2(CO)(9) is the triply bridged D-3h structure, whereas the most stable structures of Ru-2(CO)(9) and Os-2(CO)(9) are singly bridged C-2 species. The calculated reaction energies for the formation of the cyclic trinuclear carbonyls M-3(CO)(12) from the dinuclear carbonyls M-2(CO)(9) are in agreement with experiment, as the iron complex Fe-2(CO)(9) is thermodynamically stable in these reactions, but the heavier homologues Ru-2(CO)(9) and Os-2(CO)(9) are not. The metal CO bond to the bridging CO ligands is stronger than the bonds to the terminal CO ligands. This holds for the triply bridged D-3h structures as well as for the singly bridged C-2 or C-2v species. The analysis of the orbital interactions with the help of the EDA-NOCV method suggests that the overall M -> CO pi backdonation is always stronger than the M <- CO sigma donation. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger a donation and pi backdonation, but the formation of bridging carbonyls requires reorganization energy, which may or may not be compensated by the stronger metal ligand interactions. The lower-lying D-3h form of Fe-2(CO)(9) and C-2 structures of Ru-2(CO)(9) and Os-2(CO)(9) are due to a delicate balance of several forces.