In this computational study, we report on the stability
of cyclic
phosphinyl radicals with an aim for a systematical assessment of stabilization
effects. The radical stabilization energies (RSEs) were calculated
using isodesmic reactions for a large number of carbocyclic radicals
possessing different ring sizes and grades of unsaturation. In general,
the RSE values range from −1.2 to −14.0 kcal·mol–1, and they show practically no correlation with the
spin populations at the P-centers. The RSE values correlate with the
reaction Gibbs free energies calculated for the dimerization of the
studied simple radicals. Therefore, the more easily accessible RSE
values offer a cost-effective estimation of global stability in a
straightforward manner. To explore the effect of unsaturation on the
RSE values, delocalization energies were determined using appropriate
isodesmic reactions. Introducing unsaturations beside the P-center
into the backbone of the rings leads to an additive increase in the
magnitude of the delocalization energy (∼10, 20, and 30 kcal·mol–1, respectively, for radicals with one, two, and three
CC bonds in the conjugation). Parallelly, the spin populations
at the P-centers also dwindle gradually by ∼0.1 e in the same
order, indicating that the lone electron delocalizes over the π-system.
Radicals containing exocyclic CC π-bonds were also investigated,
and all of these radicals have rather similar stabilities independently
of the ring size, outlining the primary importance of the two exocyclic
π-bonds in the conjugation. Among the radicals involved in our
study, those with the best electronic stabilization are the unsaturated
three-, five-, six-, and seven-membered rings containing the maximum
number of conjugated vinyl fragments. The largest delocalization energy
of 31.5 kcal·mol–1 and the lowest obtained
spin population of 0.665 e were found for the fully unsaturated seven-membered
radical (phosphepin derivative). Importantly, the electronic stabilization
effects alone are insufficient for stabilizing the radicals in monomeric
forms epitomized by the exothermic dimerization energies (−40
to −58 kcal·mol–1). Therefore, it is
essential to apply sterically demanding bulky substituents on the
α-C-atoms. Tweaking the steric congestion enabled us to propose
radicals that are expected to be stable against dimerization and,
consequently, may be realistic target species for synthetic investigations.
The effects contributing to the stability of radicals having sterically
encumbered substituents have also been explored.