[2+3] cycloaddition of ethylene to transition metal oxo compounds. Analysis of density functional results by Marcus theory

Density functional results on the [2+3] cycloaddition of ethylene to various transition metal complexes MO₃^q and LMO₃^q (q = -1, 0, 1) with M = Mo, W, Mn, Tc, Re, and Os and various ligands L = Cp, CH₃, Cl, and O show that the corresponding activation barriers ΔE‡ depend in quadratic fashion on the reaction energies ΔE‡₀ as predicted by Marcus theory. A thermoneutral reaction is characterized by the intrinsic reaction barrier ΔE‡₀ of 25.1 kcal/mol. Both ethylene [2+3] cycloaddition to an oxo complex and the corresponding homolytic M - O bond dissociation are controlled by the reducibility of the transition metal center. Indeed, from the easily calculated M - O bond dissociation energy of the oxo complex one can predict the reaction energy ΔE₀ and hence, by Marcus theory, the corresponding activation barrier ΔE‡. This allows a systematic representation of more than 25 barriers of [2+3] cycloaddition reactions that range from 5 to 70 kcal/mol.