Effect of Internal Energy on the Repulsive Coulomb Barrier of Polyanions

The nature of the repulsive Coulomb barrier in isolated molecular polyanions is studied by means of the photodetachment dynamics of the $S_1$ excited state of the fluorescein dianion which is bound solely by the repulsive Coulomb barrier. Photoelectron spectra reveal a feature at a constant electron kinetic energy, regardless of the excitation energy. This is explained by using an adiabatic tunneling picture for electron loss through successive repulsive Coulomb barriers correlating to vibrationally excited states. This physical picture is supported by time-resolved photoelectron spectra, showing that the tunneling lifetime is also invariant with excitation energy.

Figure 1

PE spectra of the doubly deprotonated fluorescein dianion, with its chemical structure shown in (a). (b) Deconvoluted PE image taken at 2.48 eV (500 nm) and (c) resultant PE spectra taken over a 0.8 eV energy range.

Figure 2

Time-resolved PE spectra following excitation to $S_1$. (a) Representative PE spectra when pump and probe pulses are temporally overlapped and when the pump arrives after the probe. (b) Integrated PE signal of the $S_1$ feature at three different excitation energies, indicating an invariance of the lifetime with respect to excitation energy.

Figure 3

Effect of internal energy on RCB. (a) shows two scenarios in which the height of the outer RCB is (i) constant or (ii) changes with internal energy. The case for the fluorescein dianion is shown in (b), where $R$ is the $[\mathrm{fl}-2\mathrm{H}{]}^{-}$ to $e-$ distance. The RCBs correlating to the $S_0$ state (right) and to the $S_1$ state (left) are shown. With increasing excitation energy, and hence internal energy in $S_1$, there is a progression of RCBs correlating to $[\mathrm{fl}-2\mathrm{H}{]}^{-}$ with higher internal energy. Tunneling through these RCBs leads to PEs with constant kinetic energy (downward arrows), as shown on the left-hand side. Once above the RCB for $S_0$, a direct detachment channel opens up leading to a PE spectrum determined by the Franck-Condon factors between the dianion in its $S_0$ state and the monoanion in its $D_0$ state. This is shown on the right-hand side for excitation at 3.10 eV.