Analysis of the resonant raman spectra of viologens and of their radical cations using range-separated hybrid density functionals

The UV/vis absorption spectra and resonance Raman spectra of methyl viologens and p-phenylene-extended viologens have been simulated by using the LC-BLYP range-separated hybrid exchange-correlation functional with different range-separating parameters (μ). In most cases, the shape of the UV/vis absorption bands and the relative Raman intensities, which find their common origins in the geometrical relaxation upon electronic excitations, depend strongly on the μ value: the larger the μ values, the more long-range Hartree-Fock (HF) exchange, the larger the geometrical relaxations, and the more complex the UV/vis absorption bands, whereas the resonance Raman signatures depend more on the presence or not of a dominating normal coordinate of relaxation. For the first excited state of the methyl viologen/p-phenylene- extended viologen radical cations, the μ values matching best the experimental UV/vis spectra are 0.03/0.13 bohr^-1, whereas for the second excited state, they amount to 0.28-0.33/0.18 bohr^-1. The first excited state of the radical cations is associated with an increase of the aromatic character and the second excited state to an increase of the quinoid character, like the first excited state of the dications. In the case of the resonant Raman spectra, a μ value of 0.08-0.13 bohr^-1 is adequate to reproduce the experimental spectrum of MV²⁺, whereas for MV ^+̇, the Raman spectrum in resonance with the first excited state is better described by μ = 0.03-0.08 bohr^-1 and the resonance with the second excited state by μ = 0.13-0.18 bohr^-1. Without discussing the ability of these functionals to estimate the excitation energies, these results on the vibronic signatures show that there is not a unique range-separating parameter to achieve general agreement with experiment. Rather, for the transitions increasing the quinoid character, the best μ value is globally larger than for describing the transitions where the aromatic character increases. Moreover, going from methyl viologens to extended viologens, the best μ values change. Besides demonstrating that an appropriate exchange correlation (XC) functional can reproduce, for a given excited state, most of the vibronic effects, this study has also scrutinized the strong interplay between the oxidation state and the vibronic structures of viologens as well as the effect on inserting a p-phenylene group between the two pyridinium moieties. In particular, these vibronic effects are often dominated by a vibrational normal mode (DC8) that consists of the combination of aromatic-to-quinoid distortions with CH wagging motions. Its large resonant Raman intensity has been attributed to its character matching the change of geometry upon excitation, which is also related to the HOMO-LUMO/SOMO topologies. In addition to the DC8 activity, the I_DC6/I_DC5 ratio has been proposed as a signature of the extended viologen oxidation state.