Fukui Functions, Bonding Fukui Functions, or Generalized Polarized Spin Fukui: Which Index Describes Radical Cyclizations?

In this work, the descriptive capacity of different local reactivity indices within the framework of conceptual density functional theory (cDFT) was systematically evaluated to rationalize the mechanism of Bergman, Azabergman, and intramolecular hexadehydro–Diels–Alder (HDDA) radical cyclizations. The conventional Fukui function (FF), the bonding Fukui function (BFF), and its generalization in the spin-polarized formalism (FFSP) were analyzed through a comparative study of energy profiles and local electronic redistribution. The main results show that the conventional Fukui function adequately describes the electronic charge predisposition and reproduces the symmetry or polarization of the reactive centers, whereas the bonding Fukui function characterizes the reactivity of existing π-bonds but does not identify the formation of the new σ-bond between the centers of interest. In contrast, the spin-polarized formalism reveals that the electronic reorganization associated with cyclization is dominated by spin density redistribution, with complementary contributions from the fNNo and fSSo functions at the reactive centers and their adjacent positions, respectively. These results indicate that intramolecular bond formation occurs through an electronic reorganization characterized by the generation and stabilization of a distributed biradical character. Consequently, the descriptors derived from the SP-DFT model provide the most appropriate representation of the electronic nature of these cyclizations.