Rendiconti Lincei. Scienze Fisiche e Naturali

, Volume 29, Issue 4, pp 787–802 | Cite as

From statistical thermodynamics to molecular kinetics: the change, the chance and the choice

  • Vincenzo AquilantiEmail author
  • Ernesto P. Borges
  • Nayara D. Coutinho
  • Kleber C. Mundim
  • Valter H. Carvalho-SilvaEmail author
The Quantum World of Molecules


A survey on the principles of chemical kinetics (the “science of change”) is presented here. This discipline plays a key role in molecular sciences, however, the debate on its foundations had been open for the 130 years since the Arrhenius equation was formulated on admittedly purely empirical grounds. The great success that this equation has had in the development of experimental research has motivated the need of clarifying its relationships with the foundations of thermodynamics on the one hand and especially with those of statistical mechanics (the “discipline of chances”) on the other. The advent of quantum mechanics in the Twenties and the scattering experiments by molecular beams in the second half of last century have validated collisional mechanisms for reactive processes, probing images of single microscopic events; molecular dynamics computational techniques have been successfully applied to interpret and predict phenomena occurring in a variety of environments: the focus here is on a key aspect, the effect of temperature on chemical reaction rates, which in cold environments show departure from Arrhenius law, so arguably from Maxwell–Boltzmann statistics. Modern developments use venerable mathematical concepts arising from “criteria for choices” dating back to Jacob Bernoulli and Euler. A formulation of recent progress is detailed in Aquilanti et al. 2017.

Graphical abstract


Arrhenius equation Tolman activation energy Super-Arrhenius Sub-Arrhenius 



The authors acknowledge the Brazilian funding agencies Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for financial support. Valter H. Carvalho-Silva thanks PrP/UEG for research funding through the PROBIP and PRO´-PROJETO programs, also thanks CNPq for research funding through the Universal 2016—Faixa A program. Ernesto P. Borges acknowledges National Institute of Science and Technology for Complex Systems (INCT-SC). Vincenzo Aquilanti acknowledgments financial support for the Italian Ministry for Education, University and Research, MIUR. Grant no. SIR2014(RBSI14U3VF) and Elvira Pistoresi for this assistance in the preparation of her manuscript.


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Copyright information

© Accademia Nazionale dei Lincei 2018

Authors and Affiliations

  • Vincenzo Aquilanti
    • 1
    • 2
    Email author
  • Ernesto P. Borges
    • 3
  • Nayara D. Coutinho
    • 1
  • Kleber C. Mundim
    • 4
  • Valter H. Carvalho-Silva
    • 5
    Email author
  1. 1.Dipartimento di Chimica, Biologia e BiotecnologieUniversità di PerugiaPerugiaItaly
  2. 2.Istituto di Struttura della Materia, Consiglio Nazionale delle RicercheRomeItaly
  3. 3.Instituto de FísicaUniversidade Federal da BahiaSalvadorBrazil
  4. 4.Instituto de QuímicaUniversidade de BrasíliaBrasíliaBrazil
  5. 5.Grupo de Química Teórica e Estrutural de Anápolis, Campus de Ciências Exatas e Tecnológicas Henrique SantilloUniversidade Estadual de GoiásAnápolisBrazil

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