In general, two cases may be considered. The first excited state of the anion can
be referred to as either a metastable state embedded in the electronic continuum or
an electronically stable state with a particularly low electron affinity in the FranckCondon (FC) region, as was discussed earlier. The former refers to resonances of a
shape-type [51], where an electron is temporarily trapped inside the potential with a
minimum embedded in the spectral continuum. The penetration through the barrier
proceeds via tunneling which is solely a quantum effect. Such resonances, or quasibound states, embedded in the electronic continuum have been studied in atomic
and molecular cases, where both line shape and resonance position are affected by
the continuum [42, 51, 52]. The interference of a discrete autoionizing state with a
continuum results in its diluting throughout the band of actual stationary states (at
time equal to zero), whose profile has a width proportional to the square of the
interaction strength. Special complex techniques are required for proper describing
the electronic interaction of these quasi-bound states with the continuum, which
should allow line widths of the resonances to be computed and not only their
spectral locations [53]. In the case of the deprotonated GFP chromophore, we
might expect that each vibronic transition is affected by its own continuum related
to vibrational states of its neutral core. Therefore, individual resonant profiles are
hidden in smooth and mostly structureless shapes of photoabsorption bands, which
consist of trillions of individual transitions in the case of large isolated molecules.
The true experimental shape thus constitutes a challenge for theory, as opposed to
cases of atoms and simple molecules.
One way to proceed is to address a time-dependent approach and to experimentally estimate a lifetime of the autoionizing state, the inverse of which gives a line
width of the resonance. We have shown that the lifetime of the GFP chromophore
anion in the S 1 state is remarkably long compared to the characteristic timescales
for the electronic dynamics in the emission channel, which also enables internal
conversion followed by fragmentation in the ground state to occur near the threshold energies. Thus, a relatively weak coupling of the quasi-bound state to the
electronic continuum is envisaged. It is worth noting that shape resonances usually
have a rather short lifetime. For example, the resonance state of HCl
À that
correlates with the bound anionic ground state [53] has a lifetime of 20 fs, as
shown in the experiments, where the neutral molecule is vibrationally excited by
low-energy electrons [54]. In this case, the line width is equal to 0.2 eV
(1,613 cm
À1 ). The lifetime of the metastable ground state of H 2
À is further reduced
and is of the order of 1 fs, giving rise to a significant spectral broadening [55].
Alternatively, an electronically stable anion in the FC region with a very low
electron affinity can fully support the experimental finding of the substantial
lifetime in the S 1 state. Our calculated vertical detachment energy is 2.62 eV, and
that places the D 0 state vertically above the S 1 state by 0.1 eV [36]. The VDE value
has been calculated at the XMCQDPT2/CASSCF(14,14) level of theory within the
(p-type d-aug)-cc-pVTZ basis set. Oxygen atoms, which almost equally share the
negative charge due to the almost perfect resonance interaction in the pHBDI anion
(see Fig. 5.3), are treated with the entire aug-spdf diffuse shells. The electron
density is redistributed in a way that the bridge middle carbon atom (C β ) acquires
5 Photo-initiated Dynamics and Spectroscopy of the Deprotonated Green. . .
87
be referred to as either a metastable state embedded in the electronic continuum or
an electronically stable state with a particularly low electron affinity in the FranckCondon (FC) region, as was discussed earlier. The former refers to resonances of a
shape-type [51], where an electron is temporarily trapped inside the potential with a
minimum embedded in the spectral continuum. The penetration through the barrier
proceeds via tunneling which is solely a quantum effect. Such resonances, or quasibound states, embedded in the electronic continuum have been studied in atomic
and molecular cases, where both line shape and resonance position are affected by
the continuum [42, 51, 52]. The interference of a discrete autoionizing state with a
continuum results in its diluting throughout the band of actual stationary states (at
time equal to zero), whose profile has a width proportional to the square of the
interaction strength. Special complex techniques are required for proper describing
the electronic interaction of these quasi-bound states with the continuum, which
should allow line widths of the resonances to be computed and not only their
spectral locations [53]. In the case of the deprotonated GFP chromophore, we
might expect that each vibronic transition is affected by its own continuum related
to vibrational states of its neutral core. Therefore, individual resonant profiles are
hidden in smooth and mostly structureless shapes of photoabsorption bands, which
consist of trillions of individual transitions in the case of large isolated molecules.
The true experimental shape thus constitutes a challenge for theory, as opposed to
cases of atoms and simple molecules.
One way to proceed is to address a time-dependent approach and to experimentally estimate a lifetime of the autoionizing state, the inverse of which gives a line
width of the resonance. We have shown that the lifetime of the GFP chromophore
anion in the S 1 state is remarkably long compared to the characteristic timescales
for the electronic dynamics in the emission channel, which also enables internal
conversion followed by fragmentation in the ground state to occur near the threshold energies. Thus, a relatively weak coupling of the quasi-bound state to the
electronic continuum is envisaged. It is worth noting that shape resonances usually
have a rather short lifetime. For example, the resonance state of HCl
À that
correlates with the bound anionic ground state [53] has a lifetime of 20 fs, as
shown in the experiments, where the neutral molecule is vibrationally excited by
low-energy electrons [54]. In this case, the line width is equal to 0.2 eV
(1,613 cm
À1 ). The lifetime of the metastable ground state of H 2
À is further reduced
and is of the order of 1 fs, giving rise to a significant spectral broadening [55].
Alternatively, an electronically stable anion in the FC region with a very low
electron affinity can fully support the experimental finding of the substantial
lifetime in the S 1 state. Our calculated vertical detachment energy is 2.62 eV, and
that places the D 0 state vertically above the S 1 state by 0.1 eV [36]. The VDE value
has been calculated at the XMCQDPT2/CASSCF(14,14) level of theory within the
(p-type d-aug)-cc-pVTZ basis set. Oxygen atoms, which almost equally share the
negative charge due to the almost perfect resonance interaction in the pHBDI anion
(see Fig. 5.3), are treated with the entire aug-spdf diffuse shells. The electron
density is redistributed in a way that the bridge middle carbon atom (C β ) acquires
5 Photo-initiated Dynamics and Spectroscopy of the Deprotonated Green. . .
87