Calculations of the Optical Spectra of Hydrocarbon Radical Cations Based on Koopmans' Theorem

Abstract

The first few bands in the optical spectra of radical cations can often be interpreted in terms of A-type transitions that involve electron promotions from doubly occupied to the singly occupied molecular orbital (SOMO) and/or B-type transition which involve electron promotion from the SOMO to virtual molecular orbitals. We had previously demonstrated that, by making use of Koopmans' theorem, the energies of A-type transitions can be related to orbital energy differences between lower occupied MOs and the highest occupied MO (HOMO) in the neutral molecule, calculated at the geometry of the radical cation. We now propose that the energies of B-type transitions can be related similarly to energy differences between the lowest unoccupied MO (LUMO) and higher virtual MOs in the dication, also calculated at the geometry of the radical cation, by way of an extension of Koopmans' theorem to virtual MOs similar to that used sometimes to model resonances in electron scattering experiments. The optical spectra of the radical cations of several polyenes and aromatic compounds, the matrix spectra of which are known (or presented here for the first time), and for which CASSCF/CASPT2 calculations are available, are discussed in terms of these Koopmans-based models. Then the spectra of five poly(bicycloalkyl)-protected systems and that of hexabenzocoronene, compounds not amenable to higher level calculations, are examined and it is found that the Koopmans-type calculations allow a satisfactory interpretation of most of the features in these spectra. These simple calculations therefore provide a computationally inexpensive yet effective way to assign optical transitions in radical ions. Limitations of the model are discussed.

Electronic absorption spectroscopy of polycyclic aromatic hydrocarbons (PAHs) radical cations generated in oleum: A superacid medium

“…The spectrum of naphthalene radical cation is dominated by the absorption at 346 nm (not shown in Fig. 2) which corresponds to the 2 2 B 1g transition as calculated on Koopmans-based theorem and experimentally observed at 308 nm in an Ar matrix at low temperature [32]. The red shift of the 2 2 B 1g transition in oleum in comparison to the that registered in an inert medium like Ar at low temperature is due to a combination of temperature difference and matrix effect.…”

“…The radical cation of a hexa-alkylated hexabenzocoronene in an isolated matrix [33] shows a strong and broad absorption band at 555 nm followed by another broad band at 840 nm in reasonable agreement with our results. Theoretical calculations [32] also predict for the hexabenzocoronene radical cation a broad band at 450-470 nm and another peak at 750-800 nm.…”

“…Additionally, also the theoretical calculations and the assignments of the electronic transitions taken from Ref. [32] are reported as well. Surprisingly, the electronic transitions of the anthracene radical cation in oleum are all blue shifted in comparison to the anthracene radical cation in the inert Ar matrix while the opposite trend occurred in the case of naphthalene radical cation.…”

The Effects of Biological Environments on the Electron‐Relay Functionality of Tryptophan Residues in Proteins

“…According to Koopmans' theorem, the electronic coupling H 0 DA is related to the energies of the frontier MOs in the structure of the corresponding radical cation [59] or anion, [60] and it is given by Equations (3) and (4) , respectively, which are well consistent with the previous reported values of 6.85 10 10 and 2.10 10 8 S À1 . [64] The detailed calculation is given in the Supporting Information.…”

Evidence for Significant Through‐Space and Through‐Bond Electronic Coupling in the 1,4‐Diphenylcyclohexane‐1,4‐diyl Radical Cation Gained by Absorption Spectroscopy and DFT Calculations

“…This investigation has led to the first theoretical explanation of the unusually long wavelength absorption bands observed for aryl-substituted 1,4-radical cations. [30] They are often called distonic radical cations. However, this may be a misleading term because its use sometimes implies the separation of spin and positive charge in a molecule.…”