1 3
Top Curr Chem (Z) (2018) 376:24
each reference state along the dynamics by searching for the adiabatic state with the
greatest overlap with the reference. The energy profiles extracted for the four brightest transitions are depicted in Fig. 14c, showing clear oscillatory dynamics properly
captured by the fitting procedure (black dotted lines). Note that the energy state f 1
(red) oscillates out of phase with respect to f 2 , f 3 and f 4 .
Figure 14d, e compares simulated 2DES spectra between 0 fs and 20 fs simulated in the “quasi”-static picture (Fig. 14d) and with bath fluctuations included
(Fig. 14e). The dynamic evolution of the spectra in the static picture is approximated
by assuming fast bath fluctuations during t 1 and t 3 , inducing homogenous Lorentzian
broadening of the signals. Within this approximation, the 2DES at a waiting time
t 2 ≠ 0 can be computed with the SOS protocol (note that with a single state in the
e-manifold, the coherence term Eq. 14 vanishes), setting the pump pulse to interact
with the e-manifold of the FC point, while setting the probe pulse to interact with
the f-manifold of the snapshot reached along the trajectory at t 2 . It is apparent that
the “quasi”-static picture reproduces qualitatively the main spectral features: (a) the
GSB around 30,000 cm
−1
(shown in blue); (b) the oscillatory dynamics of the SE
between 30,000 cm
−1
and 25,000 cm
−1
, with a period of ca. 20 fs (shown in blue);
(c) the aforementioned three ESA contributions (shown in red) around 19,000 cm
−1
(f 1 ), 24,000 cm
−1
(f 2 ) and 32,000 cm
−1
(f 4 ); and (d) the time-dependent fluctuation of
the intensities, a consequence of the coordinate dependence of the TDM. However,
the static approach fails to correctly describe the spectral line shapes. This becomes
evident when slow bath fluctuations are taken into account (Fig. 14e). The vibrational progression in the L a spectrum (Fig. 14b) translates into three traces along
Ω 1 associated with the fundamental transition (28,500 cm
−1
) and two overtones.
As a consequence, the GSB and SE adopt a characteristic checkerboard pattern
[96, 97]. Another remarkable difference is that the oscillations of the ESA peaks
become less distinct. Signals showing more pronounced energy gap fluctuations
(f 4 ) appear broadened along Ω 3 and, as a consequence of this broadening, exhibit
reduced intensity compared to the static spectrum. Overall, the ESA associated with
f 1 (Ω 3 ~ 17,500 cm
−1
) constitutes the most characteristic signature of the L a state in
the Vis range. In fact, it has been observed in transient pump–probe spectra [45, 98].
The weaker ESA around 25,000 cm
−1
associated with state f 2 has been observed in
1D-PP experiments [99]. To the best of our knowledge, no transient spectra pumping the L a state and probing beyond 32,000 cm
−1
for short (< 100 fs) waiting times
has been reported in the literature; therefore, the absorption associated with f 4 is yet
to be detected experimentally and it is predicted by our simulations.
4.4 Spectral Characterization of Long‑Lived ES Intermediates
Excited states have finite lifetimes. Decay to the GS occurs either via light radiation or non-radiatively. In the second scenario, population transfer between electronic states is facilitated through non-adiabatic (e.g. singlet–singlet transfer) or
spin–orbit (e.g. singlet–triplet transfer) couplings, which are coordinate-dependent
and become large in areas where the PES of electronic states intersect. Population
transfer has a twofold effect on the appearance of the 2D electronic spectra: (i)
97
Reprinted from the journal
Top Curr Chem (Z) (2018) 376:24
each reference state along the dynamics by searching for the adiabatic state with the
greatest overlap with the reference. The energy profiles extracted for the four brightest transitions are depicted in Fig. 14c, showing clear oscillatory dynamics properly
captured by the fitting procedure (black dotted lines). Note that the energy state f 1
(red) oscillates out of phase with respect to f 2 , f 3 and f 4 .
Figure 14d, e compares simulated 2DES spectra between 0 fs and 20 fs simulated in the “quasi”-static picture (Fig. 14d) and with bath fluctuations included
(Fig. 14e). The dynamic evolution of the spectra in the static picture is approximated
by assuming fast bath fluctuations during t 1 and t 3 , inducing homogenous Lorentzian
broadening of the signals. Within this approximation, the 2DES at a waiting time
t 2 ≠ 0 can be computed with the SOS protocol (note that with a single state in the
e-manifold, the coherence term Eq. 14 vanishes), setting the pump pulse to interact
with the e-manifold of the FC point, while setting the probe pulse to interact with
the f-manifold of the snapshot reached along the trajectory at t 2 . It is apparent that
the “quasi”-static picture reproduces qualitatively the main spectral features: (a) the
GSB around 30,000 cm
−1
(shown in blue); (b) the oscillatory dynamics of the SE
between 30,000 cm
−1
and 25,000 cm
−1
, with a period of ca. 20 fs (shown in blue);
(c) the aforementioned three ESA contributions (shown in red) around 19,000 cm
−1
(f 1 ), 24,000 cm
−1
(f 2 ) and 32,000 cm
−1
(f 4 ); and (d) the time-dependent fluctuation of
the intensities, a consequence of the coordinate dependence of the TDM. However,
the static approach fails to correctly describe the spectral line shapes. This becomes
evident when slow bath fluctuations are taken into account (Fig. 14e). The vibrational progression in the L a spectrum (Fig. 14b) translates into three traces along
Ω 1 associated with the fundamental transition (28,500 cm
−1
) and two overtones.
As a consequence, the GSB and SE adopt a characteristic checkerboard pattern
[96, 97]. Another remarkable difference is that the oscillations of the ESA peaks
become less distinct. Signals showing more pronounced energy gap fluctuations
(f 4 ) appear broadened along Ω 3 and, as a consequence of this broadening, exhibit
reduced intensity compared to the static spectrum. Overall, the ESA associated with
f 1 (Ω 3 ~ 17,500 cm
−1
) constitutes the most characteristic signature of the L a state in
the Vis range. In fact, it has been observed in transient pump–probe spectra [45, 98].
The weaker ESA around 25,000 cm
−1
associated with state f 2 has been observed in
1D-PP experiments [99]. To the best of our knowledge, no transient spectra pumping the L a state and probing beyond 32,000 cm
−1
for short (< 100 fs) waiting times
has been reported in the literature; therefore, the absorption associated with f 4 is yet
to be detected experimentally and it is predicted by our simulations.
4.4 Spectral Characterization of Long‑Lived ES Intermediates
Excited states have finite lifetimes. Decay to the GS occurs either via light radiation or non-radiatively. In the second scenario, population transfer between electronic states is facilitated through non-adiabatic (e.g. singlet–singlet transfer) or
spin–orbit (e.g. singlet–triplet transfer) couplings, which are coordinate-dependent
and become large in areas where the PES of electronic states intersect. Population
transfer has a twofold effect on the appearance of the 2D electronic spectra: (i)
97
Reprinted from the journal