Relaxation Dynamics and Genuine Properties of the Solvated Electron in Neutral Water Clusters.

We have investigated the solvation dynamics and the genuine binding energy and photoemission anisotropy of the solvated electron in neutral water clusters with a combination of time-resolved photoelectron velocity map imaging and electron scattering simulations. The dynamics was probed with a UV probe pulse following above-band-gap excitation by an EUV pump pulse. The solvation dynamics is completed within about 2 ps. Only a single band is observed in the spectra, with no indication for isomers with distinct binding energies. Data analysis with an electron scattering model reveals a genuine binding energy in the range of 3.55-3.85 eV and a genuine anisotropy parameter in the range of 0.51-0.66 for the ground-state hydrated electron. All of these observations coincide with those for liquid bulk, which is rather unexpected for an average cluster size of 300 molecules.

The broad attention that solvated electrons in their ground and excited states have attracted over many decades can be attributed to them being among the simplest quantum solutes as well as to their important role in a wide range of fields. Many studies have focused on excess electrons in water and anion water clusters[1−37] (and refs therein). For liquid water, the excited-state relaxation dynamics of electrons has been investigated over a broad time window from femtoseconds to beyond picoseconds. This has resulted in the picture of an initially delocalized electron that relaxes to a hydrated electron within ∼1 ps; subsequent geminate recombination takes place on a much longer time scale[11,16] (and refs therein). Typically, multiphoton ionization of neat water using different detection schemes has been employed in these investigations. Recent time-resolved photoelectron studies have revealed a nonadiabatic transition from excited electronic states (p-states) to the ground electronic state (s-state) of the hydrated electron on a sub-100 fs time scale followed by slow (several 100 fs) relaxation in the ground electronic state[9,10,38] (and refs therein). Analogous studies of the relaxation dynamics in clusters—often after an s to p excitation—were conducted for different cluster sizes in photodetachment (anionic cluster) experiments[12,14,15,31,35] (and refs therein) and in neutral clusters after excitation by an extreme ultraviolet (EUV) light pulse.[39]

For the electronic ground state (s), several binding motifs (isomers) have been identified in anionic clusters including fully and partially solvated internal states and surface-bound states (refs (12), (21), (28), (40), and references therein). Distinct experimental vertical binding energies (VBEs) have been observed for the different isomers, with a strong cluster size dependence. The difference in VBE between an internal and surface state amounts to about 1 eV for a cluster of 200 molecules. Extrapolation of the cluster data to the infinite bulk results in binding energies of 3.6 and 1.6 eV for the fully solvated internal and surface-bound state, respectively, which lie 1.3 and 0.3 eV, respectively, below the value for a cluster with 200 molecules. Most experimental studies of the liquid bulk (liquid microjets) find only a single band in the range of 3.3–3.6 eV (refs (2), (8), (37), and references therein). The only exception is an additional surface-bound state at 1.6 eV reported in ref (5), which has not been reproduced so far by other studies, although a recent EUV study on neutral clusters again speculates about such as surface state.[39] A large number of overlapping bands from different species in this cluster spectrum makes an assignment to different contributions questionable.

In order to characterize the dynamics and different states of the hydrated electron, photoelectron studies record the photoelectron kinetic energies (eKEs) and in some cases the photoelectron angular distributions (PADs) usually characterized by a single anisotropy parameter β. Our recent investigation on hydrated electrons in liquid water microjets has, however, revealed that these measurement quantities are strongly influenced by electron transport scattering in the liquid and thus depend on the photon energy of the ionizing light source.[37] Typically, experimental VBEs vary by about 1 eV depending on the energy of the ionizing photon. Furthermore, the experimental PADs of the hydrated electron in the liquid correspond to an almost isotropic distribution because of electron transport scattering. Proper analysis of the data thus requires the influence of electron scattering to be taken into account.[37,41−50] We have shown that corrections of the experimental data by means of a detailed electron scattering model make it possible to retrieve a genuine (intrinsic) VBE and β for the ground state hydrated electron of 3.7 ± 0.1 eV and 0.6 ± 0.2, respectively.[37,41,42] In large clusters, the electron scattering is substantially different from that of the bulk (liquid/amorphous solid), as shown in our recent study.[51] While electron scattering cross sections in the liquid and the amorphous solid are virtually identical within experimental uncertainties, those for clusters are significantly larger and lie between the gas-[52] and condensed-phase values.[37,41,42] The reduced dielectric screening in clusters compared with that in the condensed phase provides a simple explanation for the increased scattering cross sections in the cluster.[51]

The present study investigates the relaxation dynamics in large water clusters with ∼300 molecules after above-band-gap excitation by an EUV photon from a high harmonic laser source (pump) and ionization by a UV probe pulse and the properties of the resulting ground-state solvated electron. It has so far been unknown how the behavior of the solvated electron in large neutral clusters differs from that in large anionic clusters and in liquid bulk. The role that the environment has on the properties of the solvated electron is of general interest, especially regarding confined environments and interfaces.[21] By analogy to anionic clusters, one would expect significant polarization effects shifting the VBEs of clusters relative to the bulk and possibly also isomers with different VBEs. Surprisingly, this is not what we find. By properly accounting for the effects of electron scattering in the clusters, we have evaluated genuine cluster VBEs and β parameters, which can be directly compared with the corresponding bulk values.

The experimental setup used for the measurements in the present work has been described previously.[51,53] We used a velocity map imaging (VMI)[54] spectrometer[55−58] to record time-resolved photoelectron images upon photoionization of water clusters using a pump and probe laser excitation scheme. EUV light was produced by high harmonic generation (HHG),[59] as previously described.[51] A home-built, time-preserving monochromator[60,61] was used to select the seventh harmonic (∼10.9 eV), which was used as the pump. As a probe pulse, we used 266 nm light generated by frequency tripling of the 800 nm output from a Ti:sapphire laser. A beam of neutral water clusters was produced and characterized in the same manner as in previous work.[51] For the experiments presented in this work, the average cluster size was determined to be ⟨n⟩ = 300 via the sodium-doping method.[62,63] See section S.1 in the Supporting Information (SI) for details.

The electron scattering simulations have been described previously in detail.[37,41,42,50,51] The probabilistic scattering model is based on a Monte Carlo solution of the transport equation. The scattering cross sections, angular dependences, and energy loss functions of all relevant elastic and inelastic phonon, vibron, and electronic scattering channels are explicitly taken into account. Simulations are performed for cluster scattering cross sections (models iii and iv),[51] liquid water scattering cross sections (model i),[51] and gas-phase scattering cross sections (model ii).[51] While the scattering cross sections used in models i and iii are taken directly from the previous study,[51] the cross sections in models ii and iv were adapted to account for the lower electron kinetic energies in the current study. See section S.2 in the SI for details.

Figure shows the time evolution of the vertical electron binding energy (VBE, panel a), and the full width at half-maximum (fwhm, panel b), of the binding energy spectra recorded after above-band-gap excitation with EUV light of ∼10.9 eV photon energy. The VBE increases with time and stabilizes after 1–2 ps at a value of ∼3.75 eV, while the fwhm narrows on the same time scale to stabilize at ∼1.14 eV (see section S.3 in the SI with binding energy spectra and fits at different pump–probe delays in Figure S3). The temporal increase in the VBE reflects the formation of a more strongly bound hydrated electron over time. The fast increase of the VBE by about 1 eV in the first few hundred fs cannot be fully resolved in our experiment with a pump–probe cross correlation of about 220 fs (fwhm). We assume that after 2 ps a hydrated electron in its electronic ground (s) state has formed in an equilibrated solvent environment. Direct comparison with previous studies is difficult because the time scales for equilibration depend strongly on how the electron was initially prepared.[32] Still, the overall solvation time scale of a few ps is in reasonable agreement with previously reported time scales for the formation of the ground-state hydrated electron in liquid bulk water and in anionic water clusters[12,16,23,31,32,35,36,38] (and refs therein). Considering that initial ejection lengths for excitation at ∼10.9 eV in the liquid are ∼3 nm,[11] which exceeds the cluster radius of ∼1.3 nm, it is plausible that most of the initial electron density resides near the surface. This situation closely resembles the model calculation of Herbert and co-workers for the localization of surface electrons and their internalization into the bulk.[17] Comparing the calculated time evolution of the VBE with our experimental results in Figure and accounting for the cross correlation of our experiment, we find reasonable agreement with a major change of the VBE in the first 0.5 ps. The initial β parameter (∼0.4) that we measure exceeds that of the electronic ground state (∼0.19). This might indicate an initially larger s character or less electron scattering upon ionization. The latter does not appear unreasonable for an electron residing close to the surface.

Figure 1

Evolution of the photoelectron signal as a function of the pump–probe time delay. (a) Vertical electron binding energy (VBE) and (b) full width at half-maximum (fwhm). Uncertainties are estimated not to exceed ±0.2 and ±0.3 eV for the VBE and fwhm, respectively. Lines connecting data points are intended as a guide to the eye. Data sets 1 and 2 represent independent measurement series, providing an impression of the reproducibility of the experiment.

By combining experimental photoelectron VMI images with detailed scattering simulations, we have recently determined genuine vertical binding energies and genuine β parameters for the ground-state hydrated electron in liquid bulk water.[37] Here, we retrieve genuine VBEs (Figure ) and genuine β parameters (Figure ) for the ground-state hydrated electron in large neutral water clusters from the photoelectron VMI images of the clusters recorded after ∼2 ps (Figure ). Figure a shows the experimental binding energy spectrum at ∼2 ps time delay together with two simulated spectra. For the calculated, dashed line spectrum, we used the genuine binding energy spectrum of the liquid (see the starred spectrum in Figure of Luckhaus et al.[37] and the dashed line spectrum in Figure b) and the cluster scattering cross sections (model iii from ref (51)) for the scattering calculations. The calculated, solid line spectrum was obtained by fitting a genuine binding energy spectrum (solid line in Figure b) to the experimental data using scattering calculations with the same cluster scattering cross sections (model iii in ref (51)). Contrary to the liquid bulk experiments,[37] the experimental cluster data (Figure a) were obtained for a single probe energy (266 nm), which is too low to cover the shoulder in the genuine binding energy spectrum of the liquid bulk (dashed line spectrum in Figure b). A single Gaussian is thus sufficient to represent the main part of the genuine binding energy spectrum of the clusters (full line in Figure b) covered by the experiment. Both simulations in Figure a represent the experimental spectrum very closely, suggesting that the genuine binding energy spectra of the hydrated electron in the liquid bulk and in a neutral water cluster with ∼300 molecules are similar. From the scattering correction including a sensitivity analysis using different scattering cross sections for clusters (models iii and iv from ref (51)), we derived a genuine VBE of 3.55–3.85 eV for the hydrated electron in neutral clusters (Table ). This coincides surprisingly well with the experimental liquid value of 3.7 ± 0.1 eV. As most of the liquid bulk studies, we do not find any evidence for a surface-bound electron with a VBE at 1.6 eV (Figures and S3). Contrary to the anionic clusters, the neutral clusters show only a single VBE band and, even more surprisingly, no significant shift relative to the bulk, which one would have expected from polarization effects.

Figure 2

(a) Experimental binding energy spectrum recorded at a pump–probe delay of ∼2 ps (circles). Dashed line spectrum: Simulation with genuine eBE of the liquid from Luckhaus et al.[37] (dashed line in panel b). Full line spectrum: Simulation with a single Gaussian fit for the genuine cluster eBE (full line in panel b).

Figure 3

Observable β values as a function of genuine β values (βg) simulated for different models of the electron scattering cross sections (average cluster size ⟨n⟩ = 300; see ref [51] for simulation details). Lines in between data points represent linear interpolations. The horizontal dashed line represents the experimental β value of 0.19. The gray shaded area indicates the range of genuine β parameters bracketed by cluster models iii and iv, which is consistent with the experimental β value measured for water clusters.

Table 1

Values for the Genuine VBE and Genuine β Parameter for the Solvated Electron in Liquid Water in the Bulk and at the Air/Water Interface Region, in Neutral Water Clusters, and in Anionic Water Clusters

	genuine VBE [eV]	genuine β parameter
calc. bulk from refs (17) and (21)	3.4–3.6
calc. bulk from ref (64)	3.75 ± 0.55a
calc. interfacial from refs (17) and (21)	3.1–3.2
calc. interfacial from ref (64)	3.35 ± 0.46a
exp. liquid bulk[37]	3.7 ± 0.1	0.6 ± 0.2
exp. neutral cluster (300 molecules); this work	3.55–3.85	0.51–0.66
exp. anion cluster[14] (∼50 molecules)		∼0.7 ± 0.1

The quoted uncertainty reflects the widths of the distribution. The uncertainty in the peak positions is probably on the order of ±0.1.

As a result of electron scattering, the PAD measured for bulk liquid water is almost isotropic (β close to 0).[1] Properly accounting for the scattering contributions, this leads to a genuine β parameter in the liquid bulk of 0.6 ± 0.2.[37] The value seems in fair agreement with what one would expect for an s-like orbital character of the ground-state solvated electron.[21] For clusters with ∼300 molecules, we measure a β parameter of 0.19 ± 0.12 at a ∼2 ps time delay (dashed horizontal line in Figure ). (Absolute values for β parameters are typically not measured to better than ±0.1 accuracy with VMI setups.) The measured value is again strongly reduced compared with the genuine β parameter in the cluster due to electron scattering processes. To retrieve the genuine β parameter in the clusters, we performed scattering simulations, with the results shown in Figure . The diamonds and the squares show the expected measured β parameter as a function of the genuine β parameter for scattering simulations with the cluster cross sections from models iii and iv, respectively. According to the graph, the measured β parameter of 0.19 for the clusters is consistent with a genuine β parameter in the range of 0.51–0.66, depending on the scattering cross sections used for the clusters.[51] As the VBE, the genuine β parameter of the cluster lies remarkably close to the genuine value of the liquid bulk (Table ) and to the value of ∼0.7 ± 0.1 reported for anionic water clusters containing ∼50 molecules.[14] The simulations in Figure S5 in the SI provide an idea of the cluster size dependence of the measured β parameter predicted as a function of the genuine β parameter for clusters with 100–900 molecules.

Figure also shows results for scattering simulations where we have replaced the scattering cross sections of the clusters, either by the scattering cross section of the liquid phase[37,41,42] (circles) or by those of the gas phase[52] (triangles). For liquid scattering cross sections, our experimental β parameter of 0.19 would lead to a genuine β parameter of ∼0.4, while for the gas-phase scattering cross sections a genuine β parameter of ∼1.0 would result. Neither would be fully consistent with the results of the liquid bulk. This further underlines the importance of using proper cross sections to account for electron transport in a cluster.

It is rather unexpected to find the same properties for the solvated electron in large neutral clusters as have been found in the liquid bulk, without any need for extrapolation to infinite cluster size. How could this be rationalized? As is the case for most cluster studies, we do not have direct information regarding the temperature and phase of the cluster. For our type of supersonic expansion, we know that we produce warm clusters. It is thus conceivable that we produce liquid-like clusters, i.e., with relatively high mobility of solvent molecules. This is supported by our previous study of the single-photon EUV ionization of pure water clusters generated under precisely the same conditions,[51] with ionization energies extrapolating to the liquid bulk value rather than that of the solid (see Figure 3 in ref (51)). The high temperature of our clusters might explain why we do not observe the surface-solvated electron. This is consistent with depletion of the corresponding signal for anionic clusters in warmer supersonic expansions.[12,28,40] However, the fact that the eBE spectrum both in liquid bulk and in neutral clusters shows only one band does not prove the absence of multiple isomers. It only shows that there are no isomers with significantly different VBEs. Recent calculations by Herbert and co-workers[17,21,64] have revealed similar VBE values for electrons solvated in the liquid bulk and at the air–liquid interface region (Table ). All this still does not explain why the genuine VBE of the liquid bulk is already reached in neutral clusters with 300 molecules without further extrapolation to infinite cluster size, while the VBE of anionic clusters of similar size still lies 1 eV below the bulk limit. Similar to our neutral water clusters, the bulk limit of the VBE of the solvated electron in neutral Na-doped water clusters is already reached at very small cluster sizes.[65,66] Both cases feature a charge-separated neutral ground state of the solvated electron and its counterion (H+(aq) in our case). The presence of the counterion could explain why the bulk limit is already reached in our neutral clusters, provided that the charge-separated ground state experiences the same polarization shift as the cationic state resulting after ionization.

In conclusion, we have shown that formation of the ground-state hydrated electron in neutral water clusters with about 300 molecules after above-band-gap excitation is completed within about 2 ps. This is roughly consistent with the time scale of the solvation dynamics found in the liquid bulk and in large anion clusters, hinting at similar mechanisms in the different systems. Both the genuine VBE and the genuine β parameter of hydrated electrons in large neutral clusters virtually coincide with the corresponding liquid bulk values, with only a single band in the spectrum. Contrary to anionic clusters, neither the bulk liquid nor the neutral clusters seem to give rise to different isomers with distinct VBEs. In particular, we do not find evidence for a surface-bound electron with a VBE of around 1.6 eV. That the liquid bulk value of the VBE is already reached for clusters containing about 300 molecules is rather surprising and indicates significant polarization effects in the charge-separated neutral ground state. Overall, our results suggest that the nature of the hydrated electron in neutral clusters is similar to that in the liquid bulk. Conclusive proof of this similarity, however, is not possible on the basis of VBEs and β parameters alone. It will require further investigations with other measurement methods probing different (genuine) properties and will also need the support of theoretical modeling.