an additional negative charge upon the S 0 ! S 1 excitation. Since the most weakly
bound electron in the S 1 state populates this particular orbital, the basis set is
augmented with an additional diffuse function of the p-type centered at C β with a
particularly small exponent equal to À10. The π
∗ orbital of this highly diffuse shell
is included in the active space spanned by almost all valence-type π and π
∗ orbitals
(14,13) and is used to mimic an electron ejection. Importantly, electronic ground
and detached states are treated in a balanced way within a state-averaging procedure in the frame of a single calculation.
The calculated vertical detachment and excitation energies, as well as origin
shifts (minimum displacements) between the S 0 and S 1 electronic states of the anion
and between the anion S 1 state and the ground neutral D 0 state may be used for a
pictorial representation of vibrational resonances embedded in the electronic continuum for the GFP chromophore anion in S 1 . Figure 5.15 shows quadratically
approximated potential energy surfaces for the three states as a function of the two
emission-active mode coordinates. They refer to the totally symmetric in-plane
medium and high-frequency stretching modes. If not being coupled to the nuclear
motion, electron detachment would never occur, since the S 1 state is electronically
bound in the FC region. These are vibrational resonances that enable electron
autodetachment (VAD). The crossing point of the S 1 and D 0 surfaces is importantly
located outside the FC region; hence even at energies where this crossing occurs
(~2.7 eV), vibrations are required to reach this point (autodetachment through
vibrational Feshbach resonances, VFRAD). At the crossing point, the states are
electronically degenerate, and this can be distinguished from VAD that occurs even
below the crossing point. In VAD, the energy has to be transferred from the nuclei
to the electrons through their (non-adiabatic) coupling. Such a mechanism enables
electron emission in the cases, where the state of a molecular anion and its neutral
counterpart do not cross at all [56].
The mode-specificity in VAD comes from the calculated S 1 /D 0 origin shifts. The
larger the shift is, the more active is a particular mode in the electron emission. It
serves as a reaction coordinate, since electron ejection has to be accompanied by the
nuclear rearrangements along this particular mode. Furthermore, the non-adiabatic
couplings in VAD should depend on vibrational overlap between the final vibrational wavefunction and the derivative of the initial vibrational wavefunction with
respect to the corresponding nuclear coordinates. At low excitation energies, the
final state refers to the ground vibrational level, and such overlap is larger if the two
surfaces are displaced farther along the corresponding normal modes.
Remarkably, the PD-active modes are those that are excited upon the S 0 !S 1
transition. This means that the S 1 surface is shifted in the same direction with
respect to both the S 0 and D 0 surfaces. This is easily recognised by comparing the
corresponding equilibrium geometry parameters in S 0 , S 1 and D 0 (see Fig. 5.15).
Upon excitation of the PD-active modes in the blue part of the spectrum, electron
ejection becomes a dominating channel.
A special consideration is needed for the lowest-energy PD pathway at excitation energies in the red part of the S 0 !S 1 absorption band. One can superficially
come to the striking conclusion that PD occurs even below VDE. However,
88
A.V. Bochenkova and L.H. Andersen
bound electron in the S 1 state populates this particular orbital, the basis set is
augmented with an additional diffuse function of the p-type centered at C β with a
particularly small exponent equal to À10. The π
∗ orbital of this highly diffuse shell
is included in the active space spanned by almost all valence-type π and π
∗ orbitals
(14,13) and is used to mimic an electron ejection. Importantly, electronic ground
and detached states are treated in a balanced way within a state-averaging procedure in the frame of a single calculation.
The calculated vertical detachment and excitation energies, as well as origin
shifts (minimum displacements) between the S 0 and S 1 electronic states of the anion
and between the anion S 1 state and the ground neutral D 0 state may be used for a
pictorial representation of vibrational resonances embedded in the electronic continuum for the GFP chromophore anion in S 1 . Figure 5.15 shows quadratically
approximated potential energy surfaces for the three states as a function of the two
emission-active mode coordinates. They refer to the totally symmetric in-plane
medium and high-frequency stretching modes. If not being coupled to the nuclear
motion, electron detachment would never occur, since the S 1 state is electronically
bound in the FC region. These are vibrational resonances that enable electron
autodetachment (VAD). The crossing point of the S 1 and D 0 surfaces is importantly
located outside the FC region; hence even at energies where this crossing occurs
(~2.7 eV), vibrations are required to reach this point (autodetachment through
vibrational Feshbach resonances, VFRAD). At the crossing point, the states are
electronically degenerate, and this can be distinguished from VAD that occurs even
below the crossing point. In VAD, the energy has to be transferred from the nuclei
to the electrons through their (non-adiabatic) coupling. Such a mechanism enables
electron emission in the cases, where the state of a molecular anion and its neutral
counterpart do not cross at all [56].
The mode-specificity in VAD comes from the calculated S 1 /D 0 origin shifts. The
larger the shift is, the more active is a particular mode in the electron emission. It
serves as a reaction coordinate, since electron ejection has to be accompanied by the
nuclear rearrangements along this particular mode. Furthermore, the non-adiabatic
couplings in VAD should depend on vibrational overlap between the final vibrational wavefunction and the derivative of the initial vibrational wavefunction with
respect to the corresponding nuclear coordinates. At low excitation energies, the
final state refers to the ground vibrational level, and such overlap is larger if the two
surfaces are displaced farther along the corresponding normal modes.
Remarkably, the PD-active modes are those that are excited upon the S 0 !S 1
transition. This means that the S 1 surface is shifted in the same direction with
respect to both the S 0 and D 0 surfaces. This is easily recognised by comparing the
corresponding equilibrium geometry parameters in S 0 , S 1 and D 0 (see Fig. 5.15).
Upon excitation of the PD-active modes in the blue part of the spectrum, electron
ejection becomes a dominating channel.
A special consideration is needed for the lowest-energy PD pathway at excitation energies in the red part of the S 0 !S 1 absorption band. One can superficially
come to the striking conclusion that PD occurs even below VDE. However,
88
A.V. Bochenkova and L.H. Andersen