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A simple relation, ΔF* = (λ (1 + Δ/λ) ²) /4, derived originally for weak-overlap electron transfers, is explored in a slightly modified version for reactions with considerable resonance splitting, such as atom transfers, proton transfers, and strong-overlap electron transfers. A useful additivity property, λ_ (12) = ( (λ_ (11) + λ_ (22) ) /2, permits barriers ΔF* for cross-reactions to be computed from those of exchange reactions, λ_ (ii) /4. Some 45 barriers, calculated from some ten others, agreed with BEBO results, within a few kilocalories per mole. The agreement is analyzed and more general models for which it might occur are considered. A functional relationship between barrier and a degree-of-reaction parameter is devised to avoid commitment to too specific a model. An example where breakdown should occur is also given. Experimental data, as well as quantum mechanical calculations of barriers, will permit further tests. Corollaries of the relation include: (1) a classification of reaction barriers in terms of intrinsic (λ_ (ii) ) and extrinsic (ΔF⁰’) contributions, (2) a rate-constant relation k_ (12) ≃ (k_ (11) k_ (22) K_ (12) f_ (12) ) ^ (1/2) and modifications thereof, (3) a calculation of the local Brønsted slope α from the intercept of the ΔF* vs. ΔF⁰' plot, α = (1 + Δ/λ) /2, (4) a relation between kH/kD vs. ΔF⁰' plots and local α’s, and (5) other relations among rate constants. Throughout, ΔF* and ΔF⁰' refer to an elementary step.
R. A. Marcus (Fri,) studied this question.