Intermolecular interactions between HR (R = F, OH, H2O+) and the hydride and NO ligands of Mo(H)(CO)2(L)2(L‘) (where cis-ligand L = PH3, NH3; trans-ligand L‘ = NO, Cl, H) and the W(H)(CO)2(NO)(PH3)2 complex have been studied using HF/3-21G and DFT (B3LYP, BLYP, B3PW91) methods. The structure of the complexes depends upon the nature of the trans-ligand and the proton donor ability of HR. H···H bonding exists in the case of poor and moderate proton donors HR and the strong π-acceptor trans-ligand. A strong σ-donor cis-ligand strengthens the H···H bonding. The change from poor proton donor to strongly acidic HR leads to a η2-H2 structure. The dihydride structure is formed with replacement of a π-acceptor trans-ligand by a σ-donor as a result of greater nucleophilicity of the metal atom. Energy decomposition analysis shows that the H···H bond consists of a large electrostatic component, with a small but significant contribution from both charge transfer and polarization, distinct from the pattern of the conventional H-bond wherein polarization makes a more minor contribution. Whereas HF/3-21G predicts a preference for a H···O interaction, the DFT approaches favor H···H. B3PW91 results are in the best agreement with available experimental data.