This journal is c the Owner Societies 2013 Phys. Chem. Chem. Phys., 2013, 15, 7311--7320 7311 Cite this: Phys. Chem. Chem. Phys., 2013, 15, 7311 The reaction force constant as an indicator of synchronicity/nonsynchronicity in [4+2] cycloaddition processes Diana Yepes, a Oscar Donoso-Tauda, a Patricia Pe ´rez, a Jane S. Murray, bc Peter Politzer bc and Pablo Jaque* a 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 x, which includes the traditional transition state, are defined unambiguously by the minimum and maximum of the reaction force F(n), which is the negative gradient of the potential energy V(n). The transition region is characterized by the reaction force constant k(n), the second derivative of V(n), being negative throughout. It has recently been demonstrated that the profile of k(n) in the transition region is a sensitive indicator of the degree of synchronicity of a concerted reaction: a single k(n) minimum is associated with full or nearly full synchronicity, while a k(n) 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 k(n) 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 k(n) tend to become less negative as the activation energies decrease. Diels–Alder cycloaddition A concerted chemical reaction is one that takes place in a single kinetic step, without the involvement of a metastable inter- mediate. 1 If just one bond is broken and one formed, then in Dewar’s terminology it is a ‘‘one-bond’’ reaction. 2 An example is nucleophilic substitution at a saturated carbon: X  +RY - XR+Y  (1) ‘‘Multi-bond’’ means that two or more bonds are broken and/or formed, as in a double proton transfer: AH a + BH b - AH b + BH a (2) The bond breaking and formation may be synchronous – i.e. proceeding in unison – or nonsynchronous. If sufficiently non- synchronous, the reaction may be described as ‘‘two-stage’’. 2 A very important reaction in organic synthesis is the Diels–Alder cycloaddition of an alkene to a diene, producing a cyclohexene; the prototype for this is, (3) Depending upon the natures of the reactants and the con- ditions, a rich array of six-membered carbocyclic structures can be generated. The process is stereospecific; the addition is syn (suprafacial) with respect to both the alkene and the diene, and the endo isomer is generally preferred. 1 Diels–Alder reactions have been investigated very exten- sively, both experimentally and computationally. 1–10 They are in the multi-bond category, since formally three p bonds are a Departamento de Ciencias Quı ´micas, Facultad de Ciencias Exactas, Universidad Andres Bello, Avenida Repu ´blica 275, Santiago, Chile. E-mail: pjaque@unab.cl b CleveTheoComp LLC, 1951 W. 26th Street, Suite 409, Cleveland, OH 44113, USA c Department of Chemistry, University of New Orleans, New Orleans, LA 70148, USA Received 23rd November 2012, Accepted 17th January 2013 DOI: 10.1039/c3cp44197k www.rsc.org/pccp PCCP PAPER Downloaded by Universite Pierre et Marie Curie on 25/04/2013 03:06:36. Published on 18 January 2013 on http://pubs.rsc.org | doi:10.1039/C3CP44197K View Article Online View Journal | View Issue