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 xi from perturbed forms of the reactants to perturbed forms of the products. The boundaries of this region are defined by the reaction force F(xi), which is the negative gradient of the potential energy V(xi) of the system along xi. The reaction force constant k(xi), the second derivative of V(xi), is negative throughout the transition region. We have now demonstrated, for a series of twelve double proton transfer processes, that the profile of k(xi) 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, k(xi) has a single minimum in the transition region. When the migrations are considerably nonsynchronous, k(xi) 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(xi) and F(xi).