State-dependent global and local electrophilicity of the aryl cations

Two alternative approaches—vertical and adiabatic—are used to estimate global and local electrophilicity (ω and ωk+) indexes for a series of aryl cations in both the ground and first excited electronic states using the well-known Parr scheme. The energy parameters used in these methods are obtained by the B3LYP/6-311++G(2d,2p) calculations of the aryl cations and of their oxidized and reduced forms in acetonitrile medium. The ground state ω values are lower than those for the excited state, which is in accord with the maximum hardness principle. Analysis of the ω indexes calculated with more reliable adiabatic approach reveals a dependence of the ground and first excited state ω indexes on the singlet–triplet energy gap of the aryl cations. A plot of the above dependence has a hyperbola-like shape; thus, the maximum (ground state) and minimum (first excited state) ω indexes correspond to the aryl cation, for which the singlet–triplet splitting is close to zero. Moreover, the ωk+ index distribution at the ipso-carbon atoms does not obey the maximum hardness principle, since it depends on spin multiplicity, not on the electronic state spatial type. For many singlet ground state aryl cations, the ωk+ indexes at the ipso-carbon atom are lower when calculated in the excited triplet state; that is due to a strong ω delocalization onto two electrophilic centers. This explains a higher chemoselectivity of the triplet aryl cations in reactions with the π-nucleophiles compared to the corresponding singlet arylium species. Applicability of the adiabatic approach for calculation of the ω and ωk+ indexes is supported by the experimental data on the nucleophile-independent parameter E for the singlet and triplet state of the p-Me2NC6H4+ cation.