in [36]. The total propagation time in simulating absorption profiles is set to 500 fs
based on the characteristic timescale of ~100 fs in the early-time decay of the
autocorrelation function at room temperature, which defines a spectral resolution.
The time-independent approach based on explicit calculation of the Franck-Condon
factors has also been applied to supplement results on the early-time excited-state
nuclear dynamics with detailed insights into the origin of observed spectral
features. Both formalisms produce exactly the same final spectral shapes under
the above-mentioned approximations.
Although approximations made for treating a nuclear problem in calculating
absorption profiles may be thought of as an oversimplified approach, it is important
to underline that a highly reliable prediction of the ground-to-excited state minimum displacements (origin shifts) play the most crucial role in simulating major
spectral features. Here, we use a highly correlated multistate multi-reference
perturbation theory in its invariant XMCQDPT2 version, formulated recently
[57]. One way to validate an electronic structure method used for calculating an
excited-state gradient is to compare the final overall widths in the experimental and
simulated spectra. By the time-energy uncertainty principle the broadest feature of
the spectrum, its width, is determined by the shortest feature in time. This feature
refers to the initial dynamics of vibrational wave packet moving downhill along the
path of steepest descent, which is anti-parallel to the gradient at the initial FC point
on the upper electronic potential energy surface. The steeper the upper surface in
the FC region is, the faster is the decay and the broader is the shape of the
absorption profile. As a result, the initial S 1 gradient essentially determines the
major spectral feature of the spectrum, its total width.
As seen in Fig. 5.18, the simulated vibrational profile of the isolated GFP
chromophore anion is rather broad and do not give precise spectroscopic information. The broadening is caused by the large manifold of contributing vibrational
levels. Active low-frequency modes, which are also excited in the ground electronic
state at room temperature, completely wash out all fine structures upon temperature
increase (compare the blue and red lines in Fig. 5.18). Importantly, spectral profiles
of relatively large isolated biological chromophores are inherently smooth and
mostly structureless. For resolved structures to appear in the spectrum, there should
be a nice recurrence in the autocorrelation function in the time domain [64]. In other
words, all nuclei should simultaneously come close to the initial FC point. The
larger the molecule is, the larger is the number of active vibrational modes excited
upon absorption; hence, larger displacements in the multidimensional phase space
and a poor recurrence in the time domain are expected.
The calculated shape of the isolated anion at room temperature is well consistent
with the prompt action spectrum (see Fig. 5.11), provided that the first peak in the
action spectrum at 482 nm is corrected for the multiple-photon contribution.
Structures at 482, 469, 452, and 421 nm practically coincide with those found
experimentally (482, 472, 452, and 422 nm). Importantly, the major spectral
feature, its total width, is fully accounted for. As a result, by comparing the
experimental and theoretical shapes directly, we show that a nuclear dynamic
broadening is responsible for the observed absorption profile in the gas phase.
5 Photo-initiated Dynamics and Spectroscopy of the Deprotonated Green. . .
95
based on the characteristic timescale of ~100 fs in the early-time decay of the
autocorrelation function at room temperature, which defines a spectral resolution.
The time-independent approach based on explicit calculation of the Franck-Condon
factors has also been applied to supplement results on the early-time excited-state
nuclear dynamics with detailed insights into the origin of observed spectral
features. Both formalisms produce exactly the same final spectral shapes under
the above-mentioned approximations.
Although approximations made for treating a nuclear problem in calculating
absorption profiles may be thought of as an oversimplified approach, it is important
to underline that a highly reliable prediction of the ground-to-excited state minimum displacements (origin shifts) play the most crucial role in simulating major
spectral features. Here, we use a highly correlated multistate multi-reference
perturbation theory in its invariant XMCQDPT2 version, formulated recently
[57]. One way to validate an electronic structure method used for calculating an
excited-state gradient is to compare the final overall widths in the experimental and
simulated spectra. By the time-energy uncertainty principle the broadest feature of
the spectrum, its width, is determined by the shortest feature in time. This feature
refers to the initial dynamics of vibrational wave packet moving downhill along the
path of steepest descent, which is anti-parallel to the gradient at the initial FC point
on the upper electronic potential energy surface. The steeper the upper surface in
the FC region is, the faster is the decay and the broader is the shape of the
absorption profile. As a result, the initial S 1 gradient essentially determines the
major spectral feature of the spectrum, its total width.
As seen in Fig. 5.18, the simulated vibrational profile of the isolated GFP
chromophore anion is rather broad and do not give precise spectroscopic information. The broadening is caused by the large manifold of contributing vibrational
levels. Active low-frequency modes, which are also excited in the ground electronic
state at room temperature, completely wash out all fine structures upon temperature
increase (compare the blue and red lines in Fig. 5.18). Importantly, spectral profiles
of relatively large isolated biological chromophores are inherently smooth and
mostly structureless. For resolved structures to appear in the spectrum, there should
be a nice recurrence in the autocorrelation function in the time domain [64]. In other
words, all nuclei should simultaneously come close to the initial FC point. The
larger the molecule is, the larger is the number of active vibrational modes excited
upon absorption; hence, larger displacements in the multidimensional phase space
and a poor recurrence in the time domain are expected.
The calculated shape of the isolated anion at room temperature is well consistent
with the prompt action spectrum (see Fig. 5.11), provided that the first peak in the
action spectrum at 482 nm is corrected for the multiple-photon contribution.
Structures at 482, 469, 452, and 421 nm practically coincide with those found
experimentally (482, 472, 452, and 422 nm). Importantly, the major spectral
feature, its total width, is fully accounted for. As a result, by comparing the
experimental and theoretical shapes directly, we show that a nuclear dynamic
broadening is responsible for the observed absorption profile in the gas phase.
5 Photo-initiated Dynamics and Spectroscopy of the Deprotonated Green. . .
95