An extended form of the Evans–Polanyi equation: a simple empirical relationship for the prediction of activation energies for hydrogen-atom transfer reactions

Abstract

An empirical approach has been used to devise a simple relationship [eqn. (B)] between the activation energy for an elementary hydrogen-atom transfer reaction (A) and ground state properties A˙+ H–B → A–H + B˙(A), E_a=E_of+αΔH°(1–d)+βΔχ_AB²+γ(s_A+s_B)(B) of the reactants and products. The role of polar effects, which operate in the transition state, is emphasised and described quantitatively in terms of the difference in Mulliken electronegativities (Δχ_AB) of the radicals A˙ and B˙. Eqn. (B) reproduces the activation energies for 65 reactions, taken from the literature, within a standard error of ±2.0 kJ mol ^–1 and with a correlation coefficient of 0.988. Reactions of widely differing types are included and no distinction is made between gas-phase reactions and those which take place in non-polar solvents. Examples of hydrogen-atom transfer reactions which are not treated satisfactorily by eqn. (B) are discussed.