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.