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

Abstract

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.