Theoretical relations among rate constants, barriers, and Broensted slopes of chemical reactions

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 (ΔF^0’) 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. ΔF^0' plot, α = (1 + Δ/λ)/2, (4) a relation between k_H/k_D vs. ΔF^0' plots and local α’s, and ( 5 ) other relations among rate constants. Throughout, ΔF* and ΔF^0' refer to an elementary step.