Bond energies and bonding interactions in Fe(CO)_5-n(N₂)_n (n = 0-5) and Cr(CO)_6-n(N₂)_n (n = 0-6) complexes: Density functional theory calculations and comparisons to experimental data

Metal-N₂ bond energies have been calculated for the Fe(CO)_5-n(N₂)_n (n = 1-5) and Cr(CO)_6-n(N₂)_n (n = 1-6) complexes using density-functional theory (DFT). Bond enthalpies calculated using the gradient corrected BP86 functional are in good agreement with the available experimental data. An energy decomposition procedure and a population analysis were performed for all of the complexes to quantitatively characterize the interactions of N₂ and CO with the relevant coordinatively unsaturated metal species. In all cases, the metal-N₂ bond is weaker than the metal-CO bond because CO is both a better donor and a better acceptor of electron density. Calculated bond energies for Cr-N₂ bonds for the lowest energy isomers of the chromium complexes are 24, 23, 22, 21, 20, and 25 kcal/mol for n = 1-6, respectively. The trend of decreasing bond energy with added N₂ ligands is a result of weaker orbital interactions. The exception is Cr(N₂)₆, which is predicted to be more stable than the CO containing complexes. This increase in stability is ascribed to the absence of a CO Irans effect. In contrast, the Fe-N₂ bond energies for the lowest energy isomers in the series are 24, 17, 14, 10, and 5 kcal/mol for n = 1-5, respectively. Although iron has a larger orbital interaction with dinitrogen ligands than chromium, the 16-electron iron complexes have to deform substantially when going from their ground triplet states to their finalpentacoordinated singlet geometries. An energy cost that increases as the number of N₂ ligands increases is associated with this deformation. For chromium complexes, this deformation term does not significantly decrease the bond energy, but the magnitude of this term becomes the dominant factor in the differences in bond energies in the dinitrogenated iron complexes.