Proton as the simplest of all catalysts for [2+2] cycloadditions: DFT study of acid-catalyzed imine metathesis

Abstract

The mechanism of imine metathesis was studied as a prototype reaction for the impact that heteroatom substitution has on thermally forbidden [2 + 2] addition reactions using high-level density functional theory in combination with a continuum solvation model. The intuitively expected high activation barriers were confirmed for N-alkyl- and N-aryl-substituted imine reactants with transition state free energies of 78.8 and 68.5 kcal/mol, respectively, in benzene. The computed reaction energy profiles were analyzed to discover possible strategies for lowering the transition state energy. Protonation of the imine nitrogen was proposed as a possible catalytic route and was explicitly modeled. The computed reaction energy profile shows that protonation of one of the imine reactants has an enormous effect on the overall rate of metathesis and lowers the activation barrier by as much as 37.3 and 30.6 kcal/mol for the N-alkyl and N-aryl reactants, respectively. These results suggest that acid-catalyzed imine metathesis should be amenable at elevated temperatures. Furthermore, the protonation of both reactants of the metathesis reaction is predicted to be not productive owing to electrostatic repulsion of the reactants, thus suggesting that there should be an optimum pH for the catalytic turnover. A detailed analysis of the catalytic mechanism is presented, and the primary driving force for the catalysis is identified. Upon protonation of the imine nitrogen, the key [2 + 2]-addition step becomes asynchronous and one of the two intermolecular N-C bonds is formed before traversing the transition state, resulting in a substantial net decrease of the overall energy requirement. The general applicability of this intuitively understandable mechanism for designing structural features for lowering the energy of transition state structures is explored.