Quantum-chemical density functional theory calculations using the BP86 functional in conjunction with a triple-ζ 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 Fe2(CO)9 is the triply bridged D3 h structure, whereas the most stable structures of Ru2(CO)9 and Os2(CO)9 are singly bridged C2 species. The calculated reaction energies for the formation of the cyclic trinuclear carbonyls M3(CO)12 from the dinuclear carbonyls M2(CO)9 are in agreement with experiment, as the iron complex Fe2(CO)9 is thermodynamically stable in these reactions, but the heavier homologues Ru2(CO)9 and Os2(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 D3 h structures as well as for the singly bridged C2 or C2 v species. The analysis of the orbital interactions with the help of the EDA-NOCV method suggests that the overall M→CO π backdonation is always stronger than the M←CO σ donation. The bridging carbonyls are more strongly bonded than the terminal CO ligands, and they are engaged in stronger σ donation and π 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 D3 h form of Fe2(CO)9 and C2 structures of Ru2(CO)9 and Os2(CO)9 are due to a delicate balance of several forces.