The mechanism of the ketene-imine Staudinger (KI-S) reaction between t-butyl-cyano ketene and N-phenyl phenylimine has been studied using DFT methods at the MPWB1K/6-311G(d) computational level. The reaction takes place through a two-step mechanism: (i) the first step is the nucleophilic attack of the imine nitrogen lone pair on the central carbon of the ketene yielding a zwitterionic (ZW) intermediate; (ii) the second step, which is the rate-and stereoselectivity-determining step, is a ringclosure process achieved by a nucleophilic attack of the terminal carbon atom of the ketene on the imine carbon atom. Due to the unfeasibility of a cis/trans and an E/Z stereoisomerisation at the ZW intermediates, trans and cis b-lactams are formed along the endo and exo stereoisomeric channels,respectively. An electron localisation function (ELF) quantum topological analysis of the bonding changes along the KI-S reaction permits a complete characterisation of the mechanism. The first step is associated with the formation of the N1-C4 single bond along the nucleophilic attack of the imine nitrogen lone pair on the central carbon of the ketene, while the second step is associated with a ringclosure process achieved by the C-to-C coupling of the C2 and C3 pseudoradical centers generated in the previous phases. The present theoretical study makes it possible to reject those analyses based on the FMO theory, in which HOMO/LUMO interactions along the nucleophilic attack of the imines on the ketenes and a feasible torquoelectronic effect along the conrotatory ring-closure step control the cis/trans stereoselectivity in the formation of b-lactams.Scheme 1 Mechanism of the KI-S reaction. ; Web: http://www. luisrdomingo.com † Electronic supplementary information (ESI) available: ELF topological analysis of bonding changes along the KI-S reaction between MCK 18 and N-methyl imine 19, and of the stationary points involved in the endo stereoisomeric path of the KI-S reaction of TBCK 11 with N-phenyl imine 12a. MPWB1K/6-311G(d) gas phase total and relative energies, total energies in benzene, and enthalpies, entropies and Gibbs free energies, computed at 80 C and 1 atm in benzene, of the stationary structures involved in the reaction of TBCK 11 with N-phenyl imine 12a. M062X/6-311G(d) Gibbs free energies and the relative ones, computed at 80 C and 1 atm in benzene, of the most relevant stationary structures involved in the reaction of TBCK 11 with N-phenyl imine 12a. MPWB1K/6-311G(d) total and relative energies, in benzene, of the stationary points along the endo and exo stereoisomeric channels associated with the KI-S reactions of N-phenyl imine 12a with the monosubtituted ketenes 15a-c. MPWB1K/6-311G(d) gas phase total and relative energies of the stationary structures involved in the reaction of MCK 18 with N-methyl imine 19.Cartesian coordinates of all species involved in the studied KI-S reactions. SeeScheme 2 Formation of cis and trans b-lactams in KI-S reactions.Scheme 3 Electrocyclic aperture of cyclobutene 5. Energies are in kcal ...