Relaxation Mechanism of the Hydrated Electron

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Science  20 Dec 2013:
Vol. 342, Issue 6165, pp. 1496-1499
DOI: 10.1126/science.1246291

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Relaxing in a Water Jet

High-energy irradiation of liquid water and its solutes can transiently liberate electrons, which act as potent chemical reductants, but they are challenging to characterize precisely. Seeking to bridge the gap between liquid and gas, Elkins et al. (p. 1496) report results from photoelectron spectroscopy of hydrated electron dynamics in a liquid jet. The results reveal a very rapid transition from the electronic excited state to the ground state, prior to full relaxation of the solvent shell.


The relaxation dynamics of the photoexcited hydrated electron have been subject to conflicting interpretations. Here, we report time-resolved photoelectron spectra of hydrated electrons in a liquid microjet with the aim of clarifying ambiguities from previous experiments. A sequence of three ultrashort laser pulses (~100 femtosecond duration) successively created hydrated electrons by charge-transfer-to-solvent excitation of dissolved anions, electronically excited these electrons via the sp transition, and then ejected them into vacuum. Two distinct transient signals were observed. One was assigned to the initially excited p-state with a lifetime of ∼75 femtoseconds, and the other, with a lifetime of ∼400 femtoseconds, was attributed to s-state electrons just after internal conversion in a nonequilibrated solvent environment. These assignments support the nonadiabatic relaxation model.

The hydrated electron eaq is a species of fundamental interest in the chemistry of water. It has been implicated in phenomena ranging from aerosol nucleation to radiation damage in DNA (1). As the simplest quantum solute, with only a single electronic degree of freedom, it has been the focus of many experimental and theoretical studies over the years (24). Nonetheless, many of its key attributes remain controversial. For example, the standard picture (5) of an electron residing in a cavity of radius ∼2.4 Å has been repeatedly questioned (6). Another unresolved issue concerns the relaxation mechanism of eaq subsequent to electronic excitation. This mechanism, which represents a subtle interplay between solute-solvent interactions and electronically nonadiabatic dynamics, is of critical importance in hydrated electron chemistry and radiation biology, given that excited states of eaq are considerably more reactive than its ground state (7). The relaxation dynamics of eaq upon excitation have been studied in bulk water by using transient absorption (TA) (810) and resonance Raman spectroscopy (11). Complementary studies have also been carried out in size-selected water cluster anions by using time-resolved photoelectron spectroscopy (TRPES) (12). In this work, we connect these very disparate experimental techniques using TRPES of hydrated electrons in liquid water microjets in order to resolve key questions regarding the relaxation mechanism of eaq.

The hydrated electron has a characteristic electronic spectrum peaking at 720 nm that is attributed to excitation from its ground s-state to a manifold of excited p-states within the solvent cavity (13). The proposed relaxation mechanism after sp excitation is shown in Fig. 1. It comprises solvent relaxation in the p-state, p→s internal conversion (IC), and solvent relaxation in the s-state. These three processes are characterized by time constants τp, τIC, and τs. In TA experiments by Barbara and coworkers (8), the sp transition was excited with a femtosecond pump pulse, and the resulting dynamics were followed by the absorption of a broadband femtosecond probe pulse. Three time scales of 50 to 80 fs, 200 to 400 fs, and ~1.1 ps were identified and have been largely reproduced by other laboratories (9, 10). However, the assignment of these lifetimes to particular physical phenomena has been a matter of some debate. Two basic models (Fig. 1) are proposed: the “adiabatic” model and the “nonadiabatic” model (2). The adiabatic model assigns the rapid time scale (50 to 80 fs) to τp, the intermediate time scale to τIC, and the slow time scale to τs. Alternatively, the nonadiabatic model assigns the fastest observable time scale to τIC and the slower two to τs. From TA alone, one cannot easily distinguish between the two models, and differing theoretical treatments have favored both models (14, 15).

Fig. 1 Proposed relaxation mechanism of the electronically excited hydrated electron.

Initial p-state solvent relaxation is followed by IC and then s-state solvent relaxation. Adiabatic (left) and nonadiabatic (right) models differ primarily in τIC.

TRPES of anionic water clusters (H2O)n, provides a different perspective on hydrated electron relaxation dynamics (1619). In these experiments, the excess electron is electronically excited with a femtosecond pump pulse and then photodetached with a femtosecond probe pulse. The resulting time-dependent photoelectron spectra show a transient feature clearly associated with the cluster excited state and directly yield τIC at each cluster size. These experiments show that τIC decreases from 190 to 60 fs with increasing cluster size up to 200 water molecules. Extrapolating this trend to the bulk (n→∞) limit implies τIC ~ 60 fs for eaq. This trend suggests that the fastest time constant seen in the TA experiments corresponds to τIC, which is consistent with the nonadiabatic relaxation model (Fig. 1).

The validity of this conclusion depends on whether water cluster anions are in fact gas-phase analogs of eaq, which is a subject of considerable discussion (2, 20, 21). Recent experiments on liquid water microjets (22) have tested this correspondence directly by using photoelectron spectroscopy to measure the vertical detachment energy (VDE) of ground state hydrated electrons in liquid jets (2326). The value obtained, 3.3 to 3.5 eV, agrees well with the extrapolated VDE obtained from photoelectron spectra of water cluster anions (18, 27, 28) and raises the question of whether the cluster dynamics will also extrapolate to an observable bulk quantity. We report TRPES experiments on liquid water jets that directly yield the p-state lifetime of eaq, resolving which of the two models in Fig. 1 is more appropriate. Our results provide the missing link between the time-resolved water cluster anion experiments and the TA work on bulk hydrated electrons.

The principle of the experiment, in which three femtosecond laser pulses interact with a liquid water jet, is outlined in Fig. 2 and in Eq. 1: Embedded Image (1)The first pulse, hν1, is centered at 239 nm and generates hydrated electrons via charge transfer to solvent (CTTS) excitation of a precursor anion; results are reported here for a 100 mM solution of I, but identical results were obtained by using Fe(CN)64–. The time (Δt12) between hν1 and the pump pulse hν2 (800 nm, 1.55 eV, and 85 fs) is held at 200 ps so as to ensure a population of equilibrated, ground-state hydrated electrons (29). The pump pulse lies within the sp absorption band and excites an electron to the p-state manifold. The probe pulse hν3 (266 nm, 4.65 eV, and 125 fs) then detaches the electron to vacuum. The resulting photoelectron kinetic energy (eKE) distribution is measured as a function of Δt23. Because TRPES measures the energy of populated states relative to vacuum, electrons ejected from the p-state will have higher eKE than those ejected from the s-state, which enables us to distinguish between them. The experimental set-up comprises a liquid jet source described elsewhere (25, 30), a 1-kHz femtosecond laser system, and a magnetic bottle electron spectrometer (26, 31).

Fig. 2 Energy diagram of experiment.

Three femtosecond laser pulses interact with the liquid jet.

Shown in Fig. 3 are TRPE spectra using two background subtraction schemes. The eKE scale is corrected for the liquid jet streaming potential as described previously (30, 32). The photoelectron spectrum is shown in Fig. 3A, with the individual one-color contributions from hν1 and hν3 subtracted from the three-pulse spectra. Each ultraviolet beam causes a delay-invariant two-photon signal from detachment of the precursor anion, which we treat as background. A short-lived transient feature above 2.0 eV and a broad, intense feature centered at 1.2 eV are shown in Fig. 3A. The latter corresponds to a VDE (=hν3 – 1.2 eV) of 3.45 eV and is readily assigned to detachment from the s-state of eaq on the basis of previous work (2326). Recent experiments (33, 34) suggest that the escape depth in liquid water for photoelectrons in this eKE range (1 to 3 eV) is at least 5 nm, which is approximately a factor of 20 larger than the cavity radius of eaq. These results imply that the detached electrons seen here are not predominantly sampled from the jet surface.

Fig. 3 Time-resolved photoelectron spectra.

The plots show three-pulse spectra from which (A) the contribution from each one color spectrum has been subtracted and (B) the (hν1 + hν3) two-color spectrum has been subtracted. (C) Spectra from (B) at early times, showing curve at 167 fs subtracted.

The result of subtracting the (hν1 + hν3) two-pulse spectrum from the three-pulse spectrum is shown in Fig. 3B at each delay time. These difference spectra show how the photoelectron signal changes with the addition of the pump pulse, hν2. Here, positive signal is induced by hν2, whereas negative-going signal represents depletion by hν2. The depleted signal overlaps the ground-state feature in Fig. 3A. The positive signal in Fig. 3B exhibits a shoulder from 2.3 to 2.6 eV at the earliest delays that disappears within 100 fs. By 230 fs (Fig. 3B, green trace), the signal has evolved into a smaller transient feature peaking around 1.7 eV that continues to decay and shift toward lower eKE on a significantly longer time scale. The early-time behavior of the shoulder at high eKE can be more readily discerned by subtracting the curve at 230 fs from those at earlier times. The result, shown in Fig. 3C, is a peak centered around 2.5 eV.

To gain further insight into these dynamics, integrated signal is shown in Fig. 4 as a function of delay over three energy intervals indicated in Fig. 3A. Data are shown as points, and the solid lines are fitting functions. These regions are well fit by a simple, sequential three-step mechanism (Embedded Image), with time constants τ1 = 75 ± 20 fs and τ2 = 410 ± 40 fs. In Fig. 4, the blue curve is associated with I in the mechanism, red with II, and green with III. The fitting functions for each step in the mechanism are a convolution of the measured pump-probe cross-correlation (115 fs), with the kinetic rate equation for each step (supplementary text).

Fig. 4 Integrated intensity as a function of delay over three eKE intervals.

Colors are the same as in Fig. 3A.

The blue curve in Fig. 4 corresponds to eKEs separated from the ground-state feature by ∼hν2 and is assigned to the initially excited p-state. The green curve indicates that the ground state is initially depleted by the pump pulse but that its population recovers as the p-state relaxes. The existence of an intermediate state II is inferred from the observation that ground-state recovery is noticeably slower than decay of the blue curve. With reference to Fig. 1, state II can be assigned either to p-state signal subsequent to solvent relaxation in the excited state, or to s-state signal just after IC, in which the electron is surrounded by a vibrationally excited, nonequilibrium distribution of solvent molecules. This assignment determines whether the decay of the blue signal in Fig. 4 corresponds to relaxation within the p-state or to IC to the s-state.

The latter assignment is supported by several factors. First, as shown in Fig. 3A, the energy interval corresponding to feature II falls on the high-eKE edge of the ground-state spectrum but clearly lies within the eKE range of the ground state, just where one would expect to see a contribution from vibrationally hot s-state signal. A close examination of Fig. 3B suggests that for Δt12 ≥ 230 fs, the pump-induced signal shifts toward lower eKE as it loses intensity, as one might expect for signal associated with solvent relaxation on the ground state.

Moreover, assigning the red signal to the relaxed p-state signal would indicate an energy shift of around –0.8 eV within the p-state subsequent to photoexcitation, as seen from the difference between the blue and red energy windows and the data in Fig. 3B. Quantum-classical molecular dynamics simulations of hydrated electron pump-probe signal using various electron-water pseudopotentials do not support such a large energy shift (6, 14); instead, they find the p-state energy remains nearly constant, whereas the s-state energy exhibits large fluctuations. It thus appears more reasonable to attribute the decay of the blue signal I to IC, and the decay (recovery) of the red (green) signal to solvent relaxation on the s-state subsequent to IC. This assignment then yields τ1 = τIC = 75 ± 20 fs, whereas τ2 = τs = 410 ± 40 fs represents the time constant for solvent relaxation subsequent to IC.

Our value of 75 ± 20 fs for τIC supports the nonadiabatic relaxation mechanism shown in Fig. 1, apparently resolving the ambiguity from the TA experiments (which yielded similar time constants). Moreover, this value is remarkably consistent with the extrapolated τIC of 60 fs obtained from size-selected water cluster anions, suggesting that both the relaxation dynamics and the VDEs for water cluster anions can be extrapolated to bulk values. The data as interpreted here also yield a measurement of the VDE for the p-state of the hydrated electron, 2.2 ± 0.2 eV, taking the center of the eKE distribution in Fig. 3C to be 2.5 eV.

We next considered whether our results show any evidence for p-state relaxation. Our more recent work on water cluster anions showed the p-state photoelectron signal shifting to lower eKE on the same time scale as IC, implying that these two processes occur in parallel (18). Similar dynamics are suggested here by Fig. 3C, which shows the early-time signal shifting toward lower eKE as it disappears. However, this p-state signal overlaps the hot s-state signal, which is shifting in the same direction, so the trend in Fig. 3C should be viewed with caution. We do not see evidence for the slowest time constant (1.1 ps) seen in the TA experiments, possibly because relatively few data points were taken at long time delays.

The experiments presented here open up the possibility of tracking solvated electron dynamics in methanol and other solvents, in which similar mechanistic issues have been raised from TA experiments (35). Furthermore, with differing excitation schemes (36) it should be possible to probe the relaxation dynamics of prehydrated and conduction-band electrons in liquid water jets. These electrons are more highly excited and delocalized than are the p-state electrons probed here, and their energetics and dynamics have been investigated but are not as well-characterized (3739). Hence, TRPES in liquid jets offers considerable potential for unraveling electron dynamics in water and other solvents.

Supplementary Materials

Materials and Methods

Supplementary Text

Fig. S1

Reference (40)

References and Notes

  1. Acknowledgments: This research is supported by the National Science Foundation (NSF) under grant CHE-1011819. The data presented in this paper are available upon request sent to
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