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This paper traces the conceptual evolution of chemical rate theory, from empirical rate constants to sophisticated quantum flux correlation functions and ensembles of reactive paths, by organizing advancements around shifts in what is computed and the meaning of a "barrier." It highlights how different theoretical frameworks, from Arrhenius to machine-learned potentials, require specific assumptions regarding kinetic models, dividing surfaces, and dynamical corrections for interpreting calculated quantities like activation free energy. The work underscores the importance of distinguishing between inferred rate constants and dynamically computed rates, particularly when analyzing experimental data like isotopic effects.
The thermodynamic interpretation of activation parameters like $\Delta G^{\ddagger}$ is shown to be critically dependent on the underlying kinetic model and dynamical assumptions, revealing subtle but significant differences across rate theories.
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 $\Delta G^{\ddagger}$, activation enthalpy $\Delta H^{\ddagger}$, activation entropy $\Delta S^{\ddagger}$, the prefactor, transmission coefficient $\kappa$, 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.