Chemical reactivity across electron transfer (ET), proton-coupled electron transfer (PCET),
and heterogeneous catalysis can be organized by a single stability ratio
[ \chi = \frac{\Gamma}{2\Omega} ]
where (\Gamma) is the dissipation rate and (\Omega) is the characteristic frequency
of the reactive mode.
Reactivity is maximized when the system approaches the near-critical regime
[ \chi \approx 1 ]
This point marks optimal dynamical stability, maximal information throughput,
and minimal distortion—consistent with the Symmetrical Convergence (SymC) framework
across physics, biology, and complex systems.
-
Adiabatic ET: (\chi > 1)
Overdamped, environment-dominated dynamics. -
Nonadiabatic ET: (\chi < 1)
Underdamped, structure-dominated dynamics.
This unifies Marcus regimes under a single dynamical parameter.
Mechanism selection follows from the motion of (\chi):
- Concerted PCET: (\chi) remains within the adaptive window.
- Stepwise PCET: (\chi) oscillates through underdamped / overdamped regions.
The framework replaces mechanism lookup tables with a stability criterion.
Catalyst surfaces tune substrate (\chi). Examples:
- TEMPO self-exchange: (k_{et} \propto 1/\tau_L) across solvents.
- N(_2) dissociation on Fe: barrier drop from 1.1 eV (Fe(110)) to 0.3 eV (Fe(111))
tracks the shift of (\chi \rightarrow 1).
The Sabatier principle becomes a case of critical-damping optimization.
The SymC approach:
- connects ET, PCET, and catalysis under a single mathematical rule,
- provides falsifiable predictions for solvent effects, isotope shifts, and spectra,
- reframes reactivity as a stability-controlled process,
- removes artificial boundaries between mechanistic frameworks.
The result is a coherent, dynamical theory of chemical kinetics.
- Main Manuscript: Critical Chemical Equivalence (CCE)
- Supplementary Materials: extended derivations and comparisons
- Figures & Analysis Tools: (\chi)-maps, rate predictions, and stability visualizations