Quantitative Determination of Electronic Effects in Free Radicals through Open-Shell Hammett Substituent Constants

Hammett substituent constants (σ), which quantify the electronic effects of functional groups, are widely used for predicting the properties of organic compounds and investigating reaction mechanisms. While these values have been obtained for a wide range of closed-shell substituents, measurements of analogous values for open-shell substituents are rare due to challenges associated with their short lifetimes. In this report, we developed a combined experimental and computational approach for quantifying the electronic properties of open-shell substituents based on changes in nitrile vibrational frequencies (ν(C≡N)). By coupling pulse radiolysis and time-resolved infrared spectroscopy (PR-TRIR), we measured ν(C≡N) IR bands of 30 para- and meta-substituted benzonitriles bearing C-, N-, and S-centered radicals. A linear scaling relationship was obtained between these experimental values and values obtained from DFT calculations. Using these computed values, two different Hammett constants, σ_m, and σ_p⁺, were determined for a series of C-, N-, O-, S-, Si-, and B-centered radicals. The differences between σ_m and σ_p⁺ values enable the separate evaluation of inductive and resonance effects in these open-shell substituents. The results suggest that there are three classes of radicals: one is electron withdrawing (σ_m, σ_p⁺ > 0), one is electron donating (σ_m, σ_p⁺ < 0), and one is inductively withdrawing but resonance donating (σ_m > 0, σ_p⁺ < 0). Our study represents a general approach to the analysis of the electronic properties of open-shell species and has potential applications in a wide range of molecular processes involving free radical intermediates.