Kasha’s Rule and Koopmans’ Correlations for Electron Tunnelling through Repulsive Coulomb Barriers in a Polyanion

The long-range electronic structure of polyanions is defined by the repulsive Coulomb barrier (RCB). Excited states can decay by resonant electron tunnelling through RCBs, but such decay has not been observed for electronically excited states other than the first excited state, suggesting a Kasha-type rule for resonant electron tunnelling. Using action spectroscopy, photoelectron imaging, and computational chemistry, we show that the fluorescein dianion, Fl2–, partially decays through electron tunnelling from the S2 excited state, thus demonstrating anti-Kasha behavior, and that resonant electron tunnelling adheres to Koopmans’ correlations, thus disentangling different channels.

T he long-range electronic structure of isolated polyanions is characterized by the repulsive Coloumb barrier (RCB) that arises from the balance of long-range repulsive and shortrange attractive forces. 1−5 While often depicted as a single barrier, in reality, the RCB depends on the nuclear and electronic structure of the molecule. There is an RCB associated with each (ro)vibrational level of an electronic state, and each electronic state has its own manifold of RCBs. 6,7 Photoelectron spectroscopy, and in particular, photoelectron imaging, is wellsuited to probing RCBs of polyanions. 6−10 Photoelectron spectra are generally characterized by a cutoff in the electron kinetic energy (eKE), below which no photoelectrons are emitted, and therefore offers a direct measure of the ground state RCB height. Resonant electron tunnelling through an RCB reports on the excited state and on the pathway linking the vibrational levels of a polyanion to those of the final state with one less electron. 11−20 Hence, photoelectron spectra of resonant tunnelling give insight into the nature of the excited state RCB. The resonant tunnelling spectra typically show photoelectron emission with an eKE distribution that is independent of photon energy and yields a measure of the energy difference between the mediating resonance and the final state. 11,12 Resonant electron tunnelling through RCBs of the lowest-lying excited states, S 1 and T 1 , have been observed. 11−20 Suprisingly, however, tunnelling emission from higher-lying electronic states has, to the best of our knowledge, not been observed, suggesting that there is a Kasha-type rule 21 for electron emission by tunnelling in polyanions. In addition there are questions about the applicability of Koopmans' correlations, which have been used to interpret the photoelecton spectra of excited states, to polyanions. 22,23 Here, we show resonant tunnelling through the RCB of higher-lying electronic states, demonstrating non-Kasha behavior and that the general Koopmans' correlations hold for electron tunnelling.
Among the earliest and clearest examples of resonant tunnelling have been the studies on the doubly deprotonated fluorescein dianion (Fl 2− ) and the bisdisulizole tetra-anion. 11,12 Both studies showed a photoelectron peak with a fixed eKE distribution that was independent of photon energy. For Fl 2− , the photon energy range only covered the S 1 ← S 0 transition, 11 while for bisdisulizole, it covered >4 eV, suggesting multiple excited states were energetically accessible. 12 Kasha's rule pertains to a propensity for fluorescence from the lowest-lying excited state, 21 which can be consolidated by the fact that internal conversion (IC) between close-lying electronic states is typically faster than fluorescence in complex molecules. The photoelectron spectra of bisdisulizole are therefore consistent with an electron tunnelling analogue of Kasha's rule, where photoexcitation to a high-lying excited state is followed by a series of rapid IC processes to the S 1 state, from where the electron ultimately tunnels. The analogous electron tunneling Kasha's rule in polyanions would depend on the competition between IC and electron emission by tunnelling through the RCBs. The latter can be much faster (e.g., ∼1 ps for tunnelling through the S 1 RCB in fluorescein) 11 than fluoresence, raising the general question of whether the resonant electron tunnelling through higher-lying excited state RCBs can occur or whether Kasha's rule is followed.
We focus on the S 2 state of Fl 2− here. The S 1 state has been very well characterized. Fl 2− fluoresces strongly in aqueous solution following excitation to S 1 near 500 nm. 24 In contrast, the S 1 state of isolated Fl 2− decays by electron emission, which allowed Jockusch and co-workers to record an electronic action (absorption) spectrum of the S 1 ← S 0 transition. 25,26 Additionally, our group has previously perfomed photoelectron imaging following excitation to the S 1 state, which produced a photoelectron spectrum peaking at eKE = 1.64 eV, regardless of the photon energy. 11 We now extend both these studies to probe the S 2 state in the UV spectral range.
Frequency-resolved photoelectron imaging was performed as well as mass-resolved fragment action spectroscopy following irradiation of Fl 2− with nanosecond (ns) laser light. The photoelectron imaging apparatus has been described previously elsewhere. 27,28 Modifications have been made to allow the fragment mass and action spectra to be recorded. Fl 2− was formed via electrospray ionization of a 5 mM solution of disodium fluorescein salt (Sigma-Aldrich) in methanol. Anions were transferred to a vacuum, and Fl 2− was mass-selected using a time-of-flight spectrometer, 29 the temporal focus of which coincided with the interaction region of a velocity map imaging spectrometer, 30 where Fl 2− was excited. Tunable UV was produced by a Nd:YAG pumped optical parametric oscillator (OPO). Raw photoelectron images were deconvoluted using the polar onion peeling algorithm, 31 and the resulting photoelectron spectra were calibrated using the spectrum of iodide. Photodetachment of Fl 2− also produced the Fl − anion, which was separated using a reflectron secondary mass spectrometer. 32 The fragment action spectrum was recorded by measuring the yield of Fl − as a function of the laser wavelength from 300 to 400 nm (UV) and 400 to 600 nm (visible). Supporting electronic structure calculations were performed on both Fl 2− and Fl − using density functional theory (DFT) for ground states and time-dependent DFT with the Tamm−Dancoff approximation for the excited states, at the B3LYP level of theory with the 6-311G ++ 2d,2p basis set. 33,34 The Gaussian 16 software package was used. 35 Figure 1 shows a Fl 2− fragment action spectrum in the range λ = 600−300 nm (2.07−4.13 eV). Note that the dashed line at 400 nm (3.10 eV) highlights different ranges of the light source used, and the relative intensities on either side are not comparable. Figure 1 shows a peak at λ = 507 nm that agrees with previous measurements for the S 1 ← S 0 transition. 25 At λ = 325 nm, a second peak is seen that corresponds to excitation of the S 2 ← S 0 transition. Figure 2 shows a series of photoelectron spectra of Fl 2− recorded in the range spanning the S 2 ← S 0 transition (specific λ at which the spectra were taken are highlighted with arrows in Figure 1). Additionally, the photoelectron spectrum at λ = 520 nm is shown: this spectrum is representative of all spectra taken in the range 460 ≤ λ ≤ 540, where the excitation is resonant with the S 1 ← S 0 transition. 11 The photoelectron spectra have been plotted in terms of eKE to highlight that certain features are invariant with λ. Three features are observed: (i) a peak centered at a fixed eKE = 1.64 eV (highlighted red); (ii) a rising edge at a fixed eKE = 2.2 eV for λ ≤ 340 nm (highlighted green); and (iii) a peak that shifts to higher eKE with hν (i.e., fixed electron binding energy, eBE = hν − eKE ≈ 0.7 eV, highlighted in blue). The latter corresponds to direct detachment Fl 2− (S 0 ) + hv → Fl − (D 0 ) + e − , which was also observed in our previous study for 400 ≤ λ ≤ 440 nm. 11 From this feature, a vertical detachment energy (VDE) of ∼0.7 eV and an adiabatic detachment energy (ADE) of ∼0.5 eV can be extracted for Fl 2− . The direct detachment process, which leads to the D 0 anion state, is depicted in Figure 3a, and its shape depends on the S 0 /D 0 Franck−Condon factors.
The photoelectron spectrum at λ = 520 nm shows the resonant tunnelling through the S 1 state RCB that has been considered previously. 11 With reference to Figure 3b, the eKE of 1.64 eV corresponds approximately the energy gap between S 1 of the dianion and D 0 of the final anion state. As the S 1 state lies 2.45 eV (507 nm transition energy, Figure 1) above S 0 , the   Figure 2), where the excitation is resonant with the S 2 ← S 0 transition (see Figure 1). Therefore, at least some population is following Kasha's rule. As shown schematically in Figure 3b, excitation to S 2 can lead to IC to populate S 1 with a large amount of internal energy, and as an electron subsequently tunnels through the S 1 state RCB (RCB 1 ), internal energy will be conserved in D 0 , producing the same eKE spectrum peaking at eKE = 1.64 eV. This Kasha behavior was also observed in the bisdisulizole tetra-anion. 36 We now turn to the third feature in Figure 2, the low-energy edge to the direct detachment peak, which does not shift with eKE (highlighted in green). This edge does not correspond to a direct detachment cutoff because there is no RCB at this energy for detachment to the D 0 state. If there was, then the direct detachment peak (highlighted in blue) would not be visible in the λ = 380 nm spectrum (or the 400 ≤ λ ≤ 440 nm spectra shown previously). 11 Instead, we consider the possibility that this feature arises from resonant electron tunnelling through the RCB of the S 2 excited state (RCB 2 ). The feature peaks approximately at eKE ≈ 2.5 eV (although it is difficult to ascertain exactly because of the spectral overlap with the direct detachment highlighted in blue). The S 2 state lies at 3.82 eV (325 nm from Figure 1), and using a similar energetic argument as for S 1 resonant tunnelling, we find that the final D n state in the anion lies approximately 3.82 − 2.5 = 1.32 eV above the S 0 state. This is clearly inconsistent with the D 0 state of Fl − , which we found to be around ∼0.8 eV above S 0 . However, an excited state in Fl − following resonant electron tunnelling through RCB 2 could potentially be the final state.
The electronic structures of Fl 2− and Fl − were considered using computational chemistry, with the results summarized in Table 1. All energies for Fl 2− are quoted relative to S 0 and are considered as vertical excitations (i.e., in the S 0 geometry). For Fl − , both vertical and adiabatic energies are quoted, and the D 1 excited state is considered in the D 0 geometry. The calculated transition energies for the S 1 and S 2 states are in reasonable agreement with the fragment action spectrum (Figure 1). Similarly, the calculated VDE is in good accord with that obtained from the photoelectron spectrum ( Figure 2). Hence, the calculations have captured the essential electronic structure. On the basis of our proposed resonant tunnelling through RCB 2 , we anticipate an excited state of the anion around 1.32 eV, and our calculations indeed show that the D 1 state lies at 1.35 eV. The detachment dynamics can be schematically represented as shown in Figure 3c. But why would resonant electron tunnelling from S 2 lead to D 1 rather than D 0 ?
It is convenient to think of the first excited state as arising from the promotion of an electron from the highest-occupied molecular orbital (HOMO) to the lowest-unoccupied molecular orbital (LUMO) and subsequent excited states to promotion to successively higher-lying LUMOs (e.g., LUMO+1, LUMO+2, etc.). In a Koopmans' picture, 37 this would form the same anion state from Fl 2− whether tunnelling occurred via RCB 1 or RCB 2 . However, higher-lying states often have mixed character, including core-excited character. To assess this possibility, we considered the electron configurations of the relevant electronic states in terms of the relevant molecular orbitals of Fl 2− : HOMO, HOMO−1, LUMO, and LUMO+1 (labeled henceforth as 1, 2, 3, and 4 with increasing energy). The results of the calculations indicate that, in a Koopmans' picture, the removal of the electron in the highest-lying MO from the S 0 (1 2 2 2 ) or S 1 (55% 1 2 2 1 4 1 and 45% 1 2 2 1 3 1 ) states results in the electronic configuration of the D 0 (1 2 2 1 ) state. The S 2 (60% 1 1 2 2 3 1 and 31% 1 1 2 2 4 1 ) and D 1 states (97% 1 1 2 2 ) have predominantly core-excited character, such that electron loss from the S 2 state would result in the D 1 state in a Koopmans' picture. Hence, the calculations fully support our interpretation that the feature in Figure 2, highlighted in green, arises from resonant electron tunnelling through RCB 2 , which is associated with the S 2 electronic state.
Finally, additional evidence that two distinct detachment channels contribute to the high eKE feature for λ < 360 nm can be gained from the electron angular distributions. These are generally quantified by an anisotropy parameter, −1 ≤ β 2 ≤ +2, where β 2 < 0, = 0, and > 0 correspond to emission predominantly perpendicular, isotropic, and parallel to the laser polarization, respectively. 38 Abrupt changes in β 2 are indicative of changes in electronic character of the molecular orbital from which the  Figure 2); (b) tunnelling through RCB 1 from S 1 following excitation to either S 1 directly or to S 2 that subsequently internally converts (IC) to S 1 (highlighted in red in Figure 2); and (c) tunnelling through RCB 2 from S 2 (highlighted in green in Figure 2). Upward arrows indicate excitation and downward arrows electron emission. Dashed lines highlight the energy imparted following excitation. The gray lines indicate vibrational levels with associated RCBs for relevant electronic excited states. The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Letter electron was removed. 28,39,40 Across the high-eKE feature, the green and blue highlighted areas have distinct β 2 parameters. Specifically, the part assigned to tunnelling though RCB 2 (green) has β 2 ∼ 0, while that for direct detachment (blue) has β 2 ∼ −0.5, confirming the two distinct electron loss channels. The tunnelling feature through RCB 1 (red) has β 2 ∼ −0.2, in agreement with the previously reported value. 11 On the basis of the above, we conclude that resonant electron tunnelling occurs from both the S 1 and the S 2 states. However, why are both pathways accessible at the same photon energy? For both to be present simultaneously, IC from the S 2 to the S 1 state followed by tunnelling through RCB 1 (Figure 3b) must be competitive with electron loss via tunnelling through RCB 2 (Figure 3c). While we were not able to directly measure the tunnelling rate through RCB 2 in real time, the current experiments do provide some clues into the relative time scales of different processes. As anisotropic photoelectron angular distributions indicate tunnelling occurring on a time scale shorter than rotational dephasing, 41 the isotropic RCB 2 tunnelling feature (green) compared to the anisotropic RCB 1 tunnelling feature (red) suggests that resonant tunnelling through RCB 1 may be faster than through RCB 2 . In addition, our previous time-resolved measurements on Fl 2− found the tunnelling lifetime through RCB 1 to be ∼1 ps, 11 which is significantly faster than has been observed in many other systems. 13−17 Therefore, even if tunnelling via RCB 2 is slower than via RCB 1 , it may still be relatively fast. It has also been argued that IC from the S 2 state in Fl derivatives may be relatively slow because of the large S 1 −S 2 gap (∼0.7 eV) and the large differences in the localization of the electron density in both excited states. 26,42 Therefore, given the observation of non-Kasha's rule electron loss, it seems likely that tunnelling through RCB 2 occurs on a similar time scale to IC from S 2 to S 1 and that both processes are slower than tunnelling via RCB 1 (>1 ps).
For the other polyanionic systems where resonant tunnelling has been observed, 13−17 IC will likely outcompete electron emission, resulting in photoelectron emission that appears to adhere to Kasha's rule. This seems to be the case in the bisdisulizole tetra-anion 12 and in the protoporphyrin IX dianion. 20 We also note that Kappes and co-workers have observed competitive electron tunnelling from the lowest singlet, S 1 , and triplet, T 1 , states in the isolated Pd (II) mesotetra(4-sulfonatophenyl)porphyrin tetra-anions. 15 The observation of both S 1 and T 1 electron emission then requires that the rate of intersystem crossing relative to that of tunnelling is competitive. Finally, it should be noted that anti-Kasha's fluorescence in the condensed phase has been observed previously. 42,43 The overall picture of a single electronic RCB in a polyanion is clearly invalid, and the energetic landscape is not only spatially anisotropic, but it is also highly complex in energy with an RCB for each (ro)vibrational level of each electronic state. Additionally, not every electronic state in the dianion will correlate to the same electronic state in the final anion following removal of an electron, although a Koopmans' picture seems to hold for electron tunnelling. Note that we have solely considered the electronic RCBs and furthermore note that there are also RCBs associated with fragmentation, which will further complicate the picture. 44, 45 The multitude of electronic RCBs can stretch many electronvolts above the lowest direct detachment channel. In the present case of Fl 2− , we observe non-Kasha rule behavior either because the IC rate from S 2 to S 1 is relatively slow or because the tunnelling through the RCB is relatively fast. Generally, it is the competition between these processes that determines whether Kasha's rule will be followed. On the basis of the observation that in most cases Kasha's rule is followed, resonant electron tunnelling through high-lying excited state RCBs is not necessarily as fast (or at least significantly slower than IC) as one might intuitively expect.