Nayara D. Coutinho

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 Tolmans 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’.

Description of the effect of temperature on food systems using the deformed Arrhenius rate law: deviations from linearity in logarithmic plots vs. inverse temperature

In order to account for the deviations from the Arrhenius rate law for the effect of temperature on food processes, we adopt an alternative approach inspired by the deformed exponential based on the Euler limit. The non-enzymatic browning of onions and the growth of bacteria were chosen to validate our proposal, which provides a better description than other formulas previously tested for these systems. These results show that the deformed Arrhenius rate law is suitable for describing the effect of rate-temperature on different food systems and suggest a relationship between the kinetic behavior of food processes and classical collective phenomena.

Kinetics of the OH+HCl→H2O+Cl reaction: Rate determining roles of stereodynamics and roaming and of quantum tunneling: Kinetics of the OH+HCl→H2O+Cl Reaction: Rate Determining Roles of Stereodynamics and Roaming and of Quantum Tunneling

The OH + HCl → H2O + Cl reaction is one of the most studied four‐body systems, extensively investigated by both experimental and theoretical approaches. Here, as a continuation of our previous work on the OH + HBr and OH + HI reactions, which manifest an anti‐Arrhenius behavior that was explained by stereodynamic and roaming effects, we extend the strategy to understand the transition to the sub‐Arrhenius behavior occurring for the HCl case. As previously, we perform first‐principles on‐the‐fly Born–Oppenheimer molecular dynamics calculations, thermalized at four temperatures (50, 200, 350, and 500 K), but this time we also apply a high‐level transition‐state‐theory, modified to account for tunneling conditions. We find that the theoretical rate constants calculated with Bell tunneling corrections are in good agreement with extensive experimental data available for this reaction in the ample temperature range: (i) simulations show that the roles of molecular orientation in promoting this reaction and of roaming in finding the favorable path are minor than in the HBr and HI cases, and (ii) dominating is the effect of quantum mechanical penetration through the energy barrier along the reaction path on the potential energy surface. The discussion of these results provides clarification of the origin on different non‐Arrhenius mechanisms observed along this series of reactions.

The \( {\mathbf{HI}}\,\varvec{ + }\,{\mathbf{OH}}\, \to \,{\mathbf{H}}_{{\mathbf{2}}} {\mathbf{O}}\, + \,{\mathbf{I}} \) Reaction by First-Principles Molecular Dynamics: Stereodirectional and anti-Arrhenius Kinetics

Exemplary of four-atom processes, the series of reactions between OH and HX to give H2OþX (here X is a halogen atom) is one of the most studied theoretically and experimentally: the kinetics for X = Br and I manifests an unusual anti-Arrhenius behavior, namely a marked decrease of the rate constants as the temperature increases, and this has intrigued theoreticians for a long time. Motivation of the work reported in this paper is the continuation of the investigation of the stereodirectional dynamics of these reaction as the prominent reason for the peculiar kinetics, started in previous papers on X = Br. A first-principles Born-Oppenheimer ‘canonical’ molecular dynamics approach involves trajectories step-by-step generated on a potential energy surface quantum mechanically calculated on-the-fly, and thermostatically equilibrated in order to correspond to a specific temperature. Previous refinements of the method permitted a high number of trajectories at 50, 200, 350 and 500 K, for which the sampling of initial conditions allowed us to characterize the stereodynamical effect. It was confirmed also for X = I that the adjustment of the reactants’ mutual orientation in order to encounter the entrance into the ‘cone of acceptance’ is crucial for reactivity. The aperture angle of this cone is dictated by a range of directions of approach compatible with the formation of the specific HOH angle of the product water molecule; and consistently the adjustment is progressively less effective at higher the kinetic energy. Thermal rate constants from this molecular dynamics approach are discussed: provided that the systematic sampling of the canonical ensemble is adequate as in this case, quantitative comparison with the kinetic experiments is obtained.

First-Principles Molecular Dynamics and Computed Rate Constants for the Series of OH-HX Reactions (X = H or the Halogens): Non-Arrhenius Kinetics, Stereodynamics and Quantum Tunnel

This paper is part of a series aiming at elucidating the mechanisms involved in the non-Arrhenius behavior of the four-body OH + HX (X = H, F,Cl, Br and I) reactions. These reactions are very important in atmospheric chemistry. Additionally, these four-body reactions are also of basic relevance for chemical kinetics. Their kinetics has manifested non-Arrhenius behavior: the experimental rate constants for the OH + HCl and OH + H2 reactions, when extended to low temperatures, show a concave curvature in the Arrhenius plot, a phenomenon designated as sub-Arrhenius behavior, while reactions with HBr and HI are considered as typical processes that exhibit negative temperature dependence of the rate constants (anti-Arrhenius behavior). From a theoretical point of view, these reactions have been studied in order to obtain the potential energy surface and to reproduce these complex rate constants using the Transition State Theory. Here, in order to understand the non-Arrhenius mechanism, we exploit recent information from ab initio molecular dynamics. For OH + HI and OH + HBr, the visualizations of rearrangements of bonds along trajectories has shown how molecular reorientation occurs in order that the reactants encounter a mutual angle of approach favorable for them to proceed to reaction. Besides the demonstration of the crucial role of stereodynamics, additional documentation was also provided on the interesting manifestation of the roaming phenomenon, both regarding the search for reactive configurations sterically favorable to reaction and the subsequent departure of products involving their vibrational excitation. Under moderate tunneling regime, the OH + H2 reaction was satisfactory described by deformed-Transition-State Theory. In the same reaction, the catalytic effect of water can be assessed by path integral molecular dynamics. For the OH + HCl reaction, the theoretical rate coefficients calculated with Bell tunneling correction were in good agreement with experimental data in the entire temperature range 200–2000 K, with minimal effort compared to much more elaborate treatments. Furthermore, the Born-Oppenheimer molecular dynamics simulation showed that the orientation process was less effective than for HBr and HI reactions, emphasizing the role of the quantum tunneling effect of penetration of an energy barrier in the reaction path along the potential energy surface. These results can shed light on the clarification of the different non-Arrhenius mechanisms involved in four-body reaction, providing rate constants and their temperature dependence of relevance for pure and applied chemical kinetics.

Description of deviations from Arrhenius behavior in chemical kinetics and materials science

The Arrhenius law has been used successfully to describe the temperature dependence for a considerable number of rate processes in many areas of molecular science. In order to provide a description of non-Arrhenius processes, we illustrate a formula permitting to evaluate prototypes systems where the temperature dependence of the rate constant is concave (super-Arrhenius), convex (sub-Arrhenius), or may change the curvature (anti-Arrhenius) in the semilog plots against reciprocal temperature. Modern experimental techniques and theoretical approaches are providing an ample phenomenology for deviations especially at low temperatures.The Arrhenius law has been used successfully to describe the temperature dependence for a considerable number of rate processes in many areas of molecular science. In order to provide a description of non-Arrhenius processes, we illustrate a formula permitting to evaluate prototypes systems where the temperature dependence of the rate constant is concave (super-Arrhenius), convex (sub-Arrhenius), or may change the curvature (anti-Arrhenius) in the semilog plots against reciprocal temperature. Modern experimental techniques and theoretical approaches are providing an ample phenomenology for deviations especially at low temperatures.