Strategies to Calculate Fukui Functions and Applications to Radicals with SOMO–HOMO Inversion

This work explores an efficient and numerically accurate procedure to obtain the Fukui function from fractional orbital occupation calculations. The energy- and density-linearity conditions are investigated in the context of using optimally tuned range-separated hybrid functionals for the calculation of the Fukui function. The methodology is then used to study the reactivity of organic radicals exhibiting energetic inversion between the singly occupied molecular orbital (SOMO) and the highest occupied molecular orbital (HOMO), that is, SOMO–HOMO inversion (SHI). The Fukui function correctly identifies the reactive sites of the molecules investigated, but additional computed quantities, such as radical reaction energies and vertical ionization potentials, are needed to distinguish SHI systems from conventional radicals.