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 parameterdcovering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant andd< 0, to those whered> 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered ford= 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution ifd> 0 or for a negative binomial distribution ifd< 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) thesuper-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) thesub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) theanti-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'.
Dipartimento di Chimica, Biologia e Biotecnologie, Università di Perugia, via Elce di Sotto 8, 06123 Perugia, Italy vincenzoaquilanti@yahoo.it.|Instituto de Física, Universidade Federal da Bahia, 40210 Salvador, Brazil.|Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche, 00016 Rome, Italy.
Vincenzo
V
Aquilanti
Instituto de Química, Universidade de Brasília, Caixa Postal 4478, 70904-970 Brasília, Brazil.
Nayara Dantas
ND
Coutinho
Grupo de Química Teórica e Estrutural de Anápolis, Campus de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás, CP 459, 75001-970 Anápolis, GO, Brazil fatioleg@gmail.com.
Valter Henrique
http://orcid.org/0000-0002-7411-0099
VH
Carvalho-Silva
anti-Arrhenius; d-transition state theory; deformed Arrhenius; sub-Arrhenius; super-Arrhenius