Mechanism of cycloaddition reactions between ketene and N-silyl-, N-germyl-, and N-stannylimines: a theoretical investigation.

A theoretical study of the cycloaddition reactions of ketene and N-silyl-, N-germyl-, and N-stannylimines were performed at the B3LYP/6-311+G(d,p) theory level using the LANL2DZ effective core potential for Ge and Sn and taking into account the effect of diethyl ether solvent by means of the polarizable continuum model method. According to the obtained results the reaction between ketene and N-germylimine is a two-step process due to the effect of solvent, whereas the cycloaddition of ketene and N-silylimine follows a three-step mechanism because in this case the evolution of the electronic energy along the reaction coordinate predominates over the effect of solvent. For N-stannylimine the two- and three-step mechanisms are competitive. In all the cases the rate-determining barrier corresponds to the evolution of the azadiene intermediate. The cycloaddition of ketene and N-germylimine is kinetically the most favorable reaction of the three studied by us and can take place as a domino process. In the three cases the isomerization of the imine through the inversion at the nitrogen atom is easier than the formation of the azadiene intermediate so that the three processes would afford the trans-beta-lactam.