DFT study on the mechanisms and diastereoselectivities of Lewis acid-promoted ketene-alkene [2 + 2] cycloadditions: what is the role of Lewis acid in the ketene and C = X (X = O, CH₂, and NH) [2 + 2] cycloaddition reactions?

The detailed mechanisms and diastereoselectivities of Lewis acid-promoted ketene-alkene [2 + 2] cycloaddition reactions have been studied by density functional theory (DFT). Four possible reaction channels, including two noncatalyzed diastereomeric reaction channels (channels A and B) and two Lewis acid (LA) ethylaluminum dichloride (EtAlCl2) catalyzed diastereomeric reaction channels (channels C and D), have been investigated in this work. The calculated results indicate that channel A (associated with product R-configurational cycloputanone) is more energy favorable than channel B (associated with the other product S-configurational cyclobutanone) under noncatalyzed condition, but channel D leading to S-configurational cyclobutanone is more energy-favorable than channel C, leading to R-configurational cycloputanone under a LA-promoted condition, which is consistent with the experimental results. And Lewis acid can make the energy barrier of ketene-alkene [2 + 2] cycloaddition much lower. In order to explore the role of LA in ketene and C = X (X = O, CH2, and NH) [2 + 2] cycloadditions, we have tracked and compared the interaction modes of frontier molecular orbitals (FMOs) along the intrinsic reaction coordinate (IRC) under the two different conditions. Besides by reducing the energy gap between the FMOs of the reactants, our computational results demonstrate that Lewis acid lowers the energy barrier of the ketene and C = X [2 + 2] cycloadditions by changing the overlap modes of the FMOs, which is remarkably different from the traditional FMO theory. Furthermore, analysis of global reactivity indexes has also been performed to explain the role of LA catalyst in the ketene-alkene [2 + 2] cycloaddition reaction.