Transition-State Damping and Rate Turnover in Chemical Reaction Dynamics

This version refines the theoretical presentation of the transition-state damping framework, expands the cross-domain comparison across catalysis, electron transfer, and PCET systems, and adds improved derivations, statistical treatment, and reproducibility documentation. Chemical reaction dynamics has a well-developed thermodynamic description of barrier crossing, but a less operational account of the dynamical conditions governing whether a reactive trajectory commits productively or recrosses. This work shows that near a transition state this behavior is organized by a dimensionless damping ratio, χ = Γₑff/(2Ωₜₛ), separating oscillatory recrossing from overdamped sluggishness and reaching optimal monotonic commitment near χ ≈ 1. Established descriptions of barrier crossing in electron transfer, proton-coupled electron transfer, and heterogeneous surface reactivity yield locally equivalent damped-generator dynamics near the transition state despite distinct microscopic origins. Three calibrated estimator routes connect χ to spectroscopic linewidths, solvent longitudinal relaxation times, and electronic friction coefficients, each with explicit validity bounds. Worked examples illustrate solvent-dependent turnover in TEMPO electron transfer and promoter-dependent N₂ activation on Fe surfaces. The damping descriptor complements thermodynamic rate theory by quantifying when barrier crossing is limited by recrossing, overdamped sluggishness, or near-critical commitment.