An ab initio study on the allene-isocyanic acid and ketene-vinylimine [2 + 2] cycloaddition reaction paths.

The reaction paths of [2 + 2] cycloadditions of allene (H2C=C=CH2) to isocyanic acid (HN=C=O) and ketene (H2C=C=O) to vinylimine (H2C=C=NH), leading to all the possible 14 four-membered ring molecules, were investigated by the MP2/aug-cc-pVDZ method. In the two considered reactions, the 2-azetidinone (beta-lactam) ring compounds were predicted to be the most stable thermodynamically in the absence of an environment. Although 4-methylene-2-azetidinone is the most stable product of the ketene-vinylimine cycloaddition, its activation barrier is higher than that for 4-methylene-2-iminooxetane by ca. 6 kcal/mol. Therefore, the latter product can be obtained owing to kinetic control. The activation barriers in the allene-isocyanic acid reactions are quite high, 50-70 kcal/mol, whereas in the course of the ketene-vinylimine cycloaddition they are equal to ca. 30-55 kcal/mol. All the reactions studied were found to be concerted and mostly asynchronous. Simulation of the solvent environment (toluene, tetrahydrofuran, acetonitrile, and water) by using Tomasi's polarized continuum model with the integral equation formalism (IEF-PCM) method showed the allene-isocyanic reactions remained concerted, yet the activation barriers were somewhat higher than those in the gas phase, whereas the ketene-vinylimine reactions became stepwise. The larger the solvent dielectric constant, the lower the activation barriers found. The lowest-energy pathways in the gas phase and in solvent were confirmed by intrinsic reaction coordinate (IRC) calculations. The atoms in molecules (AIM) analysis of the electron density distribution in the transition-state (TS) structures allowed us to distinguish pericyclic from pseudopericyclic from nonplanar-pseudopericyclic types of reactions.