energies, when both processes are IVR-mediated in the vicinity of the planar
minimum in S 1 (governed by crossing a transition state or a pseudo-transition
state). At higher energies, the emission active modes are directly excited, and the
electron-emission dynamics may occur within a timescale of vibrational
decoherence. Support to this comes from the experiment [10], where the IC channel
essentially vanishes at energies higher than 2.75 eV (450 nm). To completely
surpass IC, PD should be ultrafast and non-statistical.
5.4.4 Spectral Shape and Excited-State Nuclear Dynamics
Both absorption spectra and excited-state decay are determined by photo-initiated
dynamics, usually occurring, however, on different timescales and influenced by
different factors. However, a lifetime broadening may influence spectral shapes, as,
for example, in the cases of auto-detaching resonance excited-states embedded in
the electronic continuum or dissociative states that directly lead to molecular
fragmentation. In the case of the GFP chromophore anion, two characteristic
timescales may be outlined: a timescale of a hundred of femtoseconds, when the
early-time adiabatic nuclear dynamics in S 1 defines the spectral shape of
photoabsorption, and a picosecond timescale of the non-adiabatic dynamics in the
excited-state decay channels at low excitation energies. As discussed earlier, the
excited-state decay of the isolated anion is mostly governed by crossing barriers
upon twisting in internal conversion. The corresponding barrier heights are remarkably small both in the gas phase and in solution, giving rise to the similar excitedstate lifetime components found experimentally [15, 63]. Upon fixing a planarity of
the chromophore, e.g., in the protein, internal conversion becomes largely
prohibited, and other decay channels, like fluorescence, play an essential role in
electronic de-excitation. The question then arises how similar the early-time
nuclear dynamics of the GFP chromophore anion in vacuo and inside the protein
is. We discuss below a remarkable similarity between the early-time dynamics in
these environments and outline possible implications of the intrinsic photophysical
properties of the light-absorbing molecular unit to the photoresponse of the GFP
proteins as a whole.
The simulated spectra of the GFP chromophore anion in the gas phase and inside
the protein have been obtained using a time-domain formalism within the BornOppenheimer approximation for separating the nuclear and electronic motion.
According to this formalism, the spectra are formulated in terms of Fourier
transforms of appropriate autocorrelation functions [64]. An explicit formula for
the overlap of the thermally-averaged initial ground-state vibrational wave function
evolving in S 1 at time t with those at t ¼ 0 can be derived in the double harmonic
parallel-mode approximation [65]. The latter assumes a simplified picture of multidimensional ground and excited-state harmonic potential energy surfaces
displaced relative to each other along each normal mode. Neither frequency change
nor Duschinsky rotation is assumed to occur upon electronic transition. The details
of this approach can be found elsewhere [48]. The protein simulations are described
94
A.V. Bochenkova and L.H. Andersen
minimum in S 1 (governed by crossing a transition state or a pseudo-transition
state). At higher energies, the emission active modes are directly excited, and the
electron-emission dynamics may occur within a timescale of vibrational
decoherence. Support to this comes from the experiment [10], where the IC channel
essentially vanishes at energies higher than 2.75 eV (450 nm). To completely
surpass IC, PD should be ultrafast and non-statistical.
5.4.4 Spectral Shape and Excited-State Nuclear Dynamics
Both absorption spectra and excited-state decay are determined by photo-initiated
dynamics, usually occurring, however, on different timescales and influenced by
different factors. However, a lifetime broadening may influence spectral shapes, as,
for example, in the cases of auto-detaching resonance excited-states embedded in
the electronic continuum or dissociative states that directly lead to molecular
fragmentation. In the case of the GFP chromophore anion, two characteristic
timescales may be outlined: a timescale of a hundred of femtoseconds, when the
early-time adiabatic nuclear dynamics in S 1 defines the spectral shape of
photoabsorption, and a picosecond timescale of the non-adiabatic dynamics in the
excited-state decay channels at low excitation energies. As discussed earlier, the
excited-state decay of the isolated anion is mostly governed by crossing barriers
upon twisting in internal conversion. The corresponding barrier heights are remarkably small both in the gas phase and in solution, giving rise to the similar excitedstate lifetime components found experimentally [15, 63]. Upon fixing a planarity of
the chromophore, e.g., in the protein, internal conversion becomes largely
prohibited, and other decay channels, like fluorescence, play an essential role in
electronic de-excitation. The question then arises how similar the early-time
nuclear dynamics of the GFP chromophore anion in vacuo and inside the protein
is. We discuss below a remarkable similarity between the early-time dynamics in
these environments and outline possible implications of the intrinsic photophysical
properties of the light-absorbing molecular unit to the photoresponse of the GFP
proteins as a whole.
The simulated spectra of the GFP chromophore anion in the gas phase and inside
the protein have been obtained using a time-domain formalism within the BornOppenheimer approximation for separating the nuclear and electronic motion.
According to this formalism, the spectra are formulated in terms of Fourier
transforms of appropriate autocorrelation functions [64]. An explicit formula for
the overlap of the thermally-averaged initial ground-state vibrational wave function
evolving in S 1 at time t with those at t ¼ 0 can be derived in the double harmonic
parallel-mode approximation [65]. The latter assumes a simplified picture of multidimensional ground and excited-state harmonic potential energy surfaces
displaced relative to each other along each normal mode. Neither frequency change
nor Duschinsky rotation is assumed to occur upon electronic transition. The details
of this approach can be found elsewhere [48]. The protein simulations are described
94
A.V. Bochenkova and L.H. Andersen