The reaction force constant as an indicator of synchronicity/nonsynchronicity in [4+2] cycloaddition processes

A variety of experimental and computational analyses support the concept that a chemical reaction has a transition region, in which the system changes from distorted states of the reactants to distorted states of the products. The boundaries of this region along the intrinsic reaction coordinate ξ, which includes the traditional transition state, are defined unambiguously by the minimum and maximum of the reaction force F(ξ), which is the negative gradient of the potential energy V(ξ). The transition region is characterized by the reaction force constant κ(ξ), the second derivative of V(ξ), being negative throughout. It has recently been demonstrated that the profile of κ(ξ) in the transition region is a sensitive indicator of the degree of synchronicity of a concerted reaction: a single κ(ξ) minimum is associated with full or nearly full synchronicity, while a κ(ξ) maximum (negative) between two minima is a sign of considerable nonsynchronicity, i.e. a two-stage concerted process. We have now applied reaction force analysis to the Diels-Alder cycloadditions of the various cyanoethylenes to cyclopentadiene. We examine the relative energy requirements of the structurally- and electronically-intensive phases of the activation processes. We demonstrate that the variation of κ(ξ) in the transition region is again indicative of the level of synchronicity. The fully synchronous cycloadditions are those in which the cyanoethylenes are symmetrically substituted. Unsymmetrical substitution leads to minor nonsynchronicity for monocyanoethylene but much more - i.e. two stages - for 1,1-dicyano- and 1,1,2-tricyanoethylene. We also show that the κ(ξ) tend to become less negative as the activation energies decrease.