Reply to the 'Comment on "Topography of the Free Energy Landscape on the Claisen-Schmidt Condensation: Solvent and Temperature Effect in the Rate-Controlling Step"' by N. D. Coutinho, H. G. Machado, V. H. Carvalho-Silva and W. A. da Silva, Phys. Chem. Chem. Phys., 2021, 23, 6738.

In the Comment on our paper on the description of the Gibbs Free energy profile of Claisen-Schmidt condensation, it is claimed that our calculations are flawed due to inconsistencies with experimental isotope effects in aqueous acetonitrile. In this Reply, we presented rigorous arguments, ambiguities in the Comment and new calculations confirming the consistency of our results: (i) small differences in the relative energetic barriers in both experimental and theoretical curves make the assignment of the rate-limiting step debatable, making the concept of RCS questionable; (ii) it is shown how the misinterpretation of the elementary steps and of the overall processes rate constants led the Comment to incorrect conclusions about the behavior of the inverse isotopic effect; (iii) neglect in the Comment of the inverse kinetic isotope effect in step R2 due to the hybridization conversion, and of the inverse equilibrium isotopic effect for step R1 to describe an overall iKIE > 1, (iv) an erroneous suggestion in the Comment that the disagreement between experimental kinetic parameters is due to the fact that acetonitrile is not used in previous experimental works, when contradictorily the literature recommends it as being indispensable to allow kinetic accuracy; and (v) new calculations improved by explicit-implicit hybrid treatment again ensure that step R4, and not step R5, can assume the role of RCS in protic solvents. Recognizing that questioning is an excellent path for promoting understanding, we hope that the answers provided here will help to clarify and expand the pertinent topics under discussion.

Topography of the free energy landscape of Claisen-Schmidt condensation: solvent and temperature effects on the rate-controlling step.

Recent studies have found that hydroxide elimination and the C[double bond, length as m-dash]C bond formation step in base-promoted aldol condensation have a strong influence on the overall rate of the reaction, in contrast to the well-accepted first enolization or C-C bond formation step. Here, applying theoretical models to the prototypical reaction of chalcone formation, the complete free energy profile of Claisen-Schmidt condensation is assessed, revealing how a protic solvent and a slight increase in temperature can induce the second enolization as the rate-controlling step (RCS). It is also observed: i) the nonexistence of a step with a much higher energetic barrier than the others, making the concept of RCS debatable; and ii) that the overall inverse kinetic isotopic effect does not exclude second enolization as a RCS in protic continuum medium. We expect that these results can expand the understanding of the decisive role of physicochemical factors on the choose of the RCS in the aldol condensation.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions.

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.