Renormalized chemical kinetics and benchmark quantum mechanical rates: activation energies and tunnelling transitivities for the reactions of fluorine atoms with H2 and HD

Abstract

Experimental, theoretical and computational chemical kinetics contribute to progress both in molecular and materials sciences and in biochemistry, exploring the gap between elementary processes and complex systems. Stationary state quantum mechanics and statistical thermodynamics provide interpretive tools and instruments for classical molecular dynamics simulations for stable or metastable structures and near-equilibrium situations. Chemical reaction kinetics plays a key role at the mesoscales: time-dependent and evolution problems are typically tackled phenomenologically, and reactions through intermediates and transition states need be investigated and modelled. In this paper, scaling and renormalization procedures are developed beyond the Arrhenius equation and the Transition State Theory, regarding two key observables in reaction kinetics, the rate “constant” as a function of temperature (and its reciprocal, the generalised lifetime), and the apparent activation energy (and its reciprocal, the transitivity function). Coupled first-order equations—dependent on time and on temperature—are formulated in alternative coupling scheme they link experimental results to effective modelling, or vice versa molecular dynamics simulations to predictions. The passage from thermal to tunnelling regimes is uniformly treated and applied to converged quantum mechanical calculations of rate constants available for the prototypical three-atom reactions of fluorine atoms with both H₂ and HD: these are exothermic processes dominated by moderate tunnel, needing formal extension to cover the low-temperature regime where aspects of universal behaviour are shown to emerge. The results that have been validated towards experimental information in the 10–350 K temperature range, document the complexity of commonly considered “elementary” chemical reactions: they are relevant for modelling atmospheric and astrophysical environments. Perspectives are indicated of advances towards other types of transitions and to a global generality of processes of interest in applied chemical kinetics in biophysics and in astrochemistry.