A Hard−Soft Acid−Base and DFT Analysis of Singlet−Triplet Gaps and the Addition of Singlet Carbenes to Alkenes

The electronic structures of sixteen carbenes and four alkenes calculated at the B3LYP/6-31G* level were used to carry out a hard−soft acid−base investigation of carbene singlet−triplet gaps and of the addition of carbenes to alkenes. The carbenes chosen include examples where the ground state varies from triplet to singlet state and examples that have been characterized as nucleophilic, electrophilic, or ambiphilic based on their reactivity with alkenes having varying electron demands. We confirmed that singlet−triplet gaps calculated by DFT methods with the B3LYP functional correlate well with experimentally known values of carbenes spanning over 70 kcal/mol. Correlations between electron-density-based parameters and singlet−triplet gaps, or with carbene−alkene reactivity, were analyzed to gain insight into the electronic structure of the carbenes and their acid−base tendencies. A good correlation was found between the singlet−triplet energy gap and the condensed softness for electrophilic attack at the triplet carbene carbon [ (T)], which reflects the level of carbene stability upon electron donation. Trends in electron donation between carbenes and alkenes with different electrophilicities and nucleophilicities analyzed by the electronegativity equalization principle correlate well with Moss' reactivity indices. We also found that interaction energies calculated between alkenes and carbenes are most favorable with parameters that reflect mutual electron donation, reflecting the simultaneous acidity and basicity of carbenes and alkenes.