Recently,an outstanding example of ketene-alkene [2+2] cycloaddition reactions promoted by Lewis acid is first reported by Rasik and co-workers.[1] To the best of our knowledge,the mechanisms and diastereoselectivities of Lewis acid-promoted ketene-alkene [2+2] cycloadditions have not been investigated in theory,and why Lewis acid can promote the reaction and inverse the diastereoselectivity of the ketene-alkene [2+2] cycloadditions has remained unexplored by now.In this work,we have performed the theoretical study on the mechanisms and diastereoselectivities of Lewis acid-promoted ketene-alkene [2+2] cycloadditions and explored the role of LA in ketene and C=X(X=O,CH2,and NH)[2+2] cycloadditions using the frontier molecular orbitals(FMOs)along the intrinsic reaction coordinate(IRC).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.