Dynamics of 1,3-dipolar cycloadditions: energy partitioning of reactants and quantitation of synchronicity

The dynamics of 1,3-dipolar cycloadditions of nine 1,3-dipoles with ethylene and acetylene have been explored by quasiclassical trajectory and single trajectory calculations in the retro-cycloaddition direction to compute energy partitioning of reactants among relative translation, vibration, and rotation. The results are interpreted with an expanded version of Polanyi's Rules for bimolecular reactions, and three trends are evident. (1) Relative translation of reactants is the main contributor to surmounting the barrier, since all transition states (TSs) are early with respect to sigma bond formation. (2) Vibrational excitation in the 1,3-dipole bending modes required for reaction is related to the lateness of the TS with respect to dipole bending: diazonium betaines (late TS, dipole bending required) > nitrilium betaines > azomethine betaines (early TS, dipole bending least important). This is also the order of the activation barriers (high --> low). (3) The previously reported linear correlation between activation barriers and the energy required to distort reactants to their TS geometries are understandable in terms of the requirements for vibrational excitation computed here. For the 1,3-dipolar cycloadditions, single trajectory calculations, which contain no zero point vibrational energy, give reasonable estimates of the mean energy partitioning of reactants derived from potential energy barrier release. The timing of bond formation and relative reactivities of different 1,3-dipoles are discussed.