Distortion, interaction, and conceptual DFT perspectives of MO4-alkene (M = Os, Re, Tc, Mn) cycloadditions

The reaction pathways (including the transition states) of ethylene addition to osmium tetroxide (OsO(4), and amine ligated), rhenate (ReO(4)(-)), technetate (TcO(4)(-)), and permanganate (MnO(4)(-)) have been studied by qualitative and quantitative analyses. Distortion/interaction and absolutely localized energy decomposition analyses provide new insights into why the (3 + 2) pathway is highly preferred over the (2 + 2) pathway, the origin of rate enhancement from ligated base, and reactivity differences between OsO(4), ReO(4)(-), TcO(4)(-), and MnO(4)(-). The (2 + 2) transition state has a much larger barrier than the (3 + 2) transition state because (1) the Os-O bond is stretched significantly resulting in a larger distortion energy (DeltaE(d)(double dagger)) value and (2) the transition state interaction energy (DeltaE(i)(double dagger)) is destabilizing due to large exchange repulsions overwhelming stabilizing charge-transfer terms. Base ligation lowers osmium tetroxide and ethylene distortion energies due to the ground-state O-Os-O angle being predistorted from 110 degrees to 103 degrees. Because MO(4) distortion energies are comparable, reactivity differences between OsO(4), ReO(4)(-), TcO(4)(-), and MnO(4)(-) is shown to be a function of ethylene to MO(4) charge-transfer. This interaction also dictates the position of the transition state along the reaction coordinate and corresponds to the onset of a stabilizing DeltaE(i)(double dagger) value. The conceptual DFT hardness profile and hardness response show that the (3 + 2) reaction pathway may be classified as an "allowed" pathway while the (2 + 2) reaction coordinate is best designated as "forbidden".