Global and local reactivity indices for electrophilic/nucleophilic free radicals

A set of five DFT reactivity indices, namely, the global electrophilicity ω° and nucleophilicity N° indices, the radical Parr function P°k, and the local electrophilicity ω°k and nucleophilicity N°k indices, for the study of free radicals (FRs) are proposed. Global indices have been tested for a series of 32 FRs having electrophilic and/or nucleophilic activations. As expected, no correlation between the proposed global electrophilicity ω° and global nucleophilicity N° has been found. Analysis of the local electrophilicity ω°k and nucleophilicity N°k indices for FRs, together with analysis of the local electrophilicity ω_k and nucleophilicity N_k indices for alkenes, allows for an explanation of the regio- and chemoselectivity in radical additions of FRs to alkenes. Finally, an ELF bonding analysis for the C-C bond formation along the nucleophilic addition of 2-hydroxyprop-2-yl FR 28 to methyl acrylate 35 evidences that the new C-C bond is formed by C-to-C coupling of two radical centres, which are properly characterized through the use of the Parr functions.