Critical Chemical Equivalence(CCE): The SymC Principle Governing Catalysis and Reactivity

The ratio χ = Γ/(2Ω) — damping rate to characteristic frequency — organizes chemical reactivity across multiple domains. This paper demonstrates that (i) adiabatic versus nonadiabatic electron transfer corresponds to χ > 1 versus χ < 1, (ii) concerted versus stepwise proton-coupled electron transfer reflects whether χ remains within or oscillates through the critical window, and (iii) catalytic bond activation occurs when the catalyst tunes the substrate toward χ ≈ 1. This framework unifies Marcus theory, proton-coupled electron transfer mechanism selection, and the Sabatier principle under a single stability criterion derived from the Symmetrical Convergence (SymC) postulate. Illustrative comparisons with TEMPO self-exchange kinetics showing k_et ∝ 1/τ_L across solvents, and N₂ dissociation on Fe surfaces where barrier reduction from 1.1 eV (Fe(110)) to 0.3 eV (Fe(111)) tracks χ moving toward unity, are consistent with the framework’s predictions. The approach yields falsifiable predictions for solvent effects, isotope effects, and spectroscopic signatures across all three domains.