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.

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.

Fine structure in the transition region: reaction force analyses of water-assisted proton transfers.

We have analyzed the variation of the reaction force F(ξ) and the reaction force constant κ(ξ) along the intrinsic reaction coordinates ξ of the water-assisted proton transfer reactions of HX-N = Y (X,Y = O,S). The profile of the force constant of the vibration associated with the reactive mode, k ξ (ξ), was also determined. We compare our results to the corresponding intramolecular proton transfers in the absence of a water molecule. The presence of water promotes the proton transfers, decreasing the energy barriers by about 12 - 15 kcal mol(-1). This is due in part to much smaller bond angle changes being needed than when water is absent. The κ(ξ) profiles along the intrinsic reaction coordinates for the water-assisted processes show striking and intriguing differences in the transition regions. For the HS-N = S and HO-N = S systems, two κ(ξ) minima are obtained, whereas for HO-N = O only one minimum is found. The k ξ (ξ) show similar behavior in the transition regions. We propose that this fine structure reflects the degree of synchronicity of the two proton migrations in each case.

The reaction force constant: an indicator of the synchronicity in double proton transfer reactions.

Earlier work, both experimental and computational, has drawn attention to the transition region in a chemical reaction, which includes the traditional transition state but extends along the intrinsic reaction coordinate ξ from perturbed forms of the reactants to perturbed forms of the products. The boundaries of this region are defined by the reaction force F(ξ), which is the negative gradient of the potential energy V(ξ) of the system along ξ. The reaction force constant κ(ξ), the second derivative of V(ξ), is negative throughout the transition region. We have now demonstrated, for a series of twelve double proton transfer processes, that the profile of κ(ξ) in the transition region is an indicator of the synchronicity of the two proton migrations in each case. When they are fully or nearly fully synchronous, κ(ξ) has a single minimum in the transition region. When the migrations are considerably nonsynchronous, κ(ξ) has two minima separated by a local maximum. Such an assessment of the degree of synchronicity cannot readily be made from an examination of the transition state alone, nor it is easily detected in the profiles of V(ξ) and F(ξ).

The reaction force and the transition region of a reaction.

The reaction force F(R) and the position-dependent reaction force constant kappaF(R) are defined by F(R)=-deltaV(R)/deltaR and kappa(R)=delta2V(R)/deltaR2, where V(R) is the potential energy of a reacting system along a coordinate R. The minima and maxima of F(R) provide a natural division of the process into several regions. Those in which F(R) is increasing are where the most dramatic changes in electronic properties take place, and where the system goes from activated reactants (at the force minimum) to activated products (at the force maximum). Kappa(R) is negative throughout such a region. We summarize evidence supporting the idea that a reaction should be viewed as going through a transition region rather than through a single point transition state. A similar conclusion has come out of transition state spectroscopy. We describe this region as a chemically-active, or electronically-intensive, stage of the reaction, while the ones that precede and follow it are structurally-intensive. Finally, we briefly address the time dependence of the reaction force and the reaction force constant.

Analysis of two intramolecular proton transfer processes in terms of the reaction force.

The negative derivative of the potential energy along an intrinsic reaction coordinate defines a force that has qualitatively a universal form for any process having an energy barrier: it passes through a negative minimum before the transition state, at which it is zero, followed by a positive maximum. We have analyzed two intramolecular proton transfer reactions in terms of several computed properties: internal charge separation, the electrostatic potentials of the atoms involved, their Fukui functions, and the local ionization energies. The variation of each of these properties along the intrinsic reaction coordinate shows a marked correlation with the characteristic features of the reaction force. We present a description of the proton transfer processes in terms of this force.