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 MV
2+
, 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.