Complementarity of reaction force and electron localization function analyses of asynchronicity in bond formation in Diels-Alder reactions

We have computationally compared three Diels-Alder cycloadditions involving cyclopentadiene and substituted ethylenes; one of the reactions is synchronous, while the others are slightly or highly asynchronous. Synchronicity and weak asynchronicity are characterized by the reaction force constant κ(ξ) having just a single minimum in the transition region along the intrinsic reaction coordinate ξ, while for high asynchronicity κ(ξ) has a negative maximum with minima on both sides. The electron localization function (ELF) shows that the features of κ(ξ) can be directly related to the formation of the new C-C bonds between the diene and the dienophile. There is thus a striking complementarity between κ(ξ) and ELF; κ(ξ) identifies the key points along ξ and ELF describes what is happening at those points.