New Insights into the (A)Synchronicity of Diels–Alder Reactions: A Theoretical Study Based on the Reaction Force Analysis and Atomic Resolution of Energy Derivatives

In the present manuscript, we report new insights into the concept of (a)synchronicity in Diels–Alder (DA) reactions in the framework of the reaction force analysis in conjunction with natural population calculations and the atomic resolution of energy derivatives along the intrinsic reaction coordinate (IRC) path. Our findings suggest that the DA reaction transitions from a preferentially concerted mechanism to a stepwise one in a 0.10 Å window of synchronicity indices ranging from 0.90 to 1.00 Å. We have also shown that the relative position of the global minimum of the reaction force constant with respect to the TS is an alternative and quantifiable indicator of the (a)synchronicity in DA reactions. Moreover, the atomic resolution of energy derivatives reveals that the mechanism of the DA reaction involves two inner elementary processes associated with the formation of each of the two C-C bonds. This resolution goes on to indicate that, in asynchronous reactions, the driving and retarding components of the reaction force are mostly due to the fast and slow-forming C-C bonds (elementary processes) respectively, while in synchronous reactions, both elementary processes retard and drive the process concomitantly and equivalently.