Bond Energies and Bonding Interactions in Fe(CO)₅_-<i>_n</i>(N₂)<i>_n</i> (<i>n</i> = 0−5) and Cr(CO)₆_-<i>_n</i>(N₂)<i>_n</i>\n(<i>n</i> = 0−6) Complexes:  Density Functional Theory Calculations and Comparisons to\nExperimental Data

Abstract

Metal−N₂ bond energies have been calculated for the Fe(CO)₅_-<i>_n</i>(N₂)<i>_n</i> (<i>n</i> = 1−5) and Cr(CO)₆_-<i>_n</i>(N₂)<i>_n</i> (<i>n</i> =\n1−6) complexes using density-functional theory (DFT). Bond enthalpies calculated using the gradient corrected\nBP86 functional are in good agreement with the available experimental data. An energy decomposition\nprocedure and a population analysis were performed for all of the complexes to quantitatively characterize\nthe interactions of N₂ and CO with the relevant coordinatively unsaturated metal species. In all cases, the\nmetal−N₂ bond is weaker than the metal−CO bond because CO is both a better donor and a better acceptor\nof electron density. Calculated bond energies for Cr−N₂ bonds for the lowest energy isomers of the chromium\ncomplexes are 24, 23, 22, 21, 20, and 25 kcal/mol for <i>n</i> = 1−6, respectively. The trend of decreasing bond\nenergy with added N₂ ligands is a result of weaker orbital interactions. The exception is Cr(N₂)₆, which is\npredicted to be more stable than the CO containing complexes. This increase in stability is ascribed to the\nabsence of a CO trans effect. In contrast, the Fe−N₂ bond energies for the lowest energy isomers in the series\nare 24, 17, 14, 10, and 5 kcal/mol for <i>n</i> = 1−5, respectively. Although iron has a larger orbital interaction\nwith dinitrogen ligands than chromium, the 16-electron iron complexes have to deform substantially when\ngoing from their ground triplet states to their final pentacoordinated singlet geometries. An energy cost that\nincreases as the number of N₂ ligands increases is associated with this deformation. For chromium complexes,\nthis deformation term does not significantly decrease the bond energy, but the magnitude of this term becomes\nthe dominant factor in the differences in bond energies in the dinitrogenated iron complexes.