Density Functional Theory Study of Hydrogen Atom Abstraction from a Series of para-Substituted Phenols: Why is the Hammett σ_p⁺ Constant Able to Represent Radical Reaction Rates?

The rate of hydrogen atom abstraction from phenolic compounds by a radical is known to be often linear with the Hammett substitution constant σ⁺, defined using the S_N1 solvolysis rates of substituted cumyl chlorides. Nevertheless, a physicochemical reason for the above “empirical fact” has not been fully revealed. The transition states of complexes between the 2,2-diphenyl-1-picrylhydrazyl radical (dpph·) and a series of para-substituted phenols were determined by DFT (Density Functional Theory) calculations, and then the activation energy as well as the homolytic bond dissociation energy of the O–H bond and charge distribution in the transition state were calculated. The heterolytic bond dissociation energy of the C–Cl bond and charge distribution in the corresponding para-substituted cumyl chlorides were calculated in parallel. Excellent correlations among σ⁺, charge distribution, and activation and bond dissociation energies revealed quantitatively that there is a strong similarity between the two reactions, showing that the electron-deficiency of the π-electron system conjugated with a substituent plays a crucial role in determining rates of the two reactions. The results provide a new insight into and physicochemical understanding of σ⁺ in the hydrogen abstraction from substituted phenols by a radical.