What Rate Theories Compute: Chemical kinetics from Arrhenius to machine-learned potentials

Abstract

Major advances in chemical rate theory changed what was computed and what a barrier meant. I organize this conceptual history around those changes, while retaining the controlled corrections and limiting relations between theories. The calculated quantities include an empirical rate constant, a collision count, a thermodynamic activation free energy, a statistical flux across a dividing surface, a stochastic escape rate, an energy-resolved microcanonical rate, a quantum flux correlation function, and an ensemble of reactive paths computed with electronic-structure or machine-learned potentials. I compare the assumptions with the limits stated by the pioneering authors. A rate constant is inferred from measurements under a stated rate law; its temperature dependence defines an apparent activation energy $E_a$. Activation free energy $ΔG^{\ddagger}$, activation enthalpy $ΔH^{\ddagger}$, activation entropy $ΔS^{\ddagger}$, the prefactor, transmission coefficient $κ$, and saddle height require a kinetic model and, where relevant, a standard state, dividing surface, ensemble, and dynamical correction for their interpretation in a rate calculation. In hydrogen transfer by soybean lipoxygenase-1, similar single-isotope activation parameters accompany a large change in isotope-sensitive dynamics. Five rate benchmarks illustrate the errors different comparisons test and motivate seven reporting items. These distinctions guide comparisons of rates and interpretations of activation parameters.