Electrons in Finite-Sized Water Cavities: Hydration Dynamics Observed in Real Time

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Science  22 Oct 2004:
Vol. 306, Issue 5696, pp. 672-675
DOI: 10.1126/science.1102827


We directly observed the hydration dynamics of an excess electron in the finite-sized water clusters of Embedded Image with n = 15, 20, 25, 30, and 35. We initiated the solvent motion by exciting the hydrated electron in the cluster. By resolving the binding energy of the excess electron in real time with femtosecond resolution, we captured the ultrafast dynamics of the electron in the presolvated (“wet”) and hydrated states and obtained, as a function of cluster size, the subsequent relaxation times. The solvation time (300 femtoseconds) after the internal conversion [140 femtoseconds for Embedded Image] was similar to that of bulk water, indicating the dominant role of the local water structure in the dynamics of hydration. In contrast, the relaxation in other nuclear coordinates was on a much longer time scale (2 to 10 picoseconds) and depended critically on cluster size.

The nature of the solvated electron, which was first observed in liquid ammonia in 1864, continues to pose several fundamental problems. When the solvent medium is water, the hydrated electron becomes essential to a myriad of physical, chemical, and biological processes. In a simple picture of an electron in a cavity, the description of the hydrated electron state structure is analogous to that of a hydrogen atom, with a ground state of s-type and an excited state of p-type character. However, the hydrated electron is far more complex, because of the ultrafast dynamics of structural change, solvation, and recombination. After postulation of the existence of the hydrated electron and the discovery of its absorption, experimental and theoretical efforts have focused on studies in bulk water in which the “cavity” is surrounded by a continuum of other water molecules.

A key issue for understanding electron hydration is knowledge of the time scales involved: the motion of water molecules toward the equilibrium structure and the lifetime of the electron in the different states it occupies. In bulk water, early femtosecond transient absorption studies (1, 2) resolved electron hydration dynamics using excitation by two ultraviolet photons to eject bound electrons from water molecules or solute anions. During the succeeding decade, different research groups have provided a vast amount of experimental data on the time scales of relaxation and the theoretical underpinnings of the hydrated electron system (312). Among these was the first three-pulse experiment (3), in which a population of ground-state hydrated electrons created by an initial laser pulse was subsequently studied using two additional pulses, the first of which excited the electrons from the s- to the p-state and the second of which probed either state. More recently, studies have been made with pulses as short as 5 fs in order to elucidate the different relaxation pathways (5, 9). In these bulk studies, there remain unanswered questions, especially regarding the microscopic molecular structure and dynamics of hydration.

Mesoscopic clusters (13, 14) are ideal for forming finite-sized nanoscale water cavities for electron hydration, and because of the charge of the electron, it is in principle possible to select a particular size of cluster and study its isolated structure and dynamics. Results from such studies provide insight into the bulk behavior. For example, accurate spectra of neutral water dimers are predictive of the properties of larger clusters and bulk water (15). For electrons in water clusters, Haberland and co-workers (16) first reported the experimental observation of Embedded Image clusters, and, in a series of comprehensive studies, the Johnson (1719) and Bowen (20, 21) groups have elucidated the size dependence of spectroscopic properties, examining the role of the core motif in reaching bulk hydration.

The structure of these finite-sized clusters has been studied both experimentally and theoretically, addressing the issue of surface and interior electron binding (18, 20, 2224). Theoretical studies (23, 24) of small Embedded Image clusters, n ≤ 14, predict that the electron lies at the surface. Earlier calculations by the groups of Landman and Jortner (22) indicated that for small clusters (n ≤ 32), the electron tends to remain on the surface, whereas for the larger ones (n = 64 and 128), the electron is in the interior. Recent work for n = 24 indicates that although three isomers (with the electron inside or outside at the surface) are energetically similar, the vertical detachment energy closest to the experimental value is that of the isomer with the electron inside (25). Despite these extensive studies, the only report of real-time dynamics of water cluster anions has been that of a preliminary p-state lifetime, limited by laser pulse duration, for a cluster of unspecified size (19).

We present here direct observation of the femtosecond dynamics of electrons in water clusters varying in size up to n = 35. We focused our attention on the dynamics in systems with different solvation cavities (n = 15, 20, 25, 30, and 35). The finite-sized clusters were selectively intercepted by femtosecond pulses to promote the electron from the s- to the p-state (Fig. 1A) (26). We followed subsequent relaxation dynamics by monitoring the evolution of the photoelectron (PE) spectrum with kinetic energy resolution (27). The latter proved critical, as did the resolution of kinetic energy of ions (28), for deciphering different pathways of dynamics. This PE energy resolution allowed us to address whether hydration proceeds while the electron is in the ground (s-type) and/or excited (p-type) states. For the cavity sizes under study, the behavior observed can be correlated to that of bulk-type hydration.

Fig. 1.

(A) Schematic representation of the s- and p-states of the hydrated electron, based on fig. 14 of (5). (B) Experimental mass spectrum of Embedded Image generated by the ion source in our apparatus. A series of Embedded Image peaks is seen at low mass. amu, atomic mass units.

We generated the negatively charged water clusters by crossing a continuous electron beam (1 keV) with a jet of water vapor, using nitrogen as a carrier gas at 150 to 250 kPa. After ∼100 μs of drift time, application of a properly timed voltage pulse accelerated Embedded Image clusters into the field-free time-of-flight region, where the desired size was intercepted with femtosecond laser pulses (29). A typical cluster size distribution is shown in Fig. 1B. The laser pulses (110 fs) were generated from a Ti:sapphire oscillator and amplified by regenerative and multipass amplifiers. The 800-nm laser output was frequency doubled to generate a 400-nm pulse. The residual 800-nm light was used as the excitation pulse, and the 400-nm laser pulse, delayed in time, was used as the probe to photodetach electrons. Photoelectrons were collected by a magnetic-bottle PE spectrometer, and the metastable anions and photofragments were detected by a linear reflectron mass spectrometer. We recorded transients by integrating the PE intensity in selected electron kinetic energy (eKE) windows as a function of the delay time.

A conceptual illustration of our experiments and methodology is shown in Fig. 2. When a particular size of Embedded Image is selectively excited by the 800-nm femtosecond laser pulse, the excess electron is promoted to the p-state (Fig. 2A). The coordinate-labeled solvation represents all nuclear motions of the solvent that strongly affect the electrostatic environment and thus the energy of the electron. As a result of the electronic transition, the electron charge distribution is significantly changed, driving a rearrangement of water molecules around the electron that corresponds to displacement along the solvation coordinate with characteristic time τp. Similarly, when the excited state relaxes down to the ground state by internal conversion with characteristic time τic, displacement along the solvation coordinate will reverse, and the solvent will move back toward its original configuration with characteristic time τs. Because the pump photon energy, which is several times greater than the binding energy of surface water molecules (30), is retained in these isolated clusters, the flow of energy from the solvation coordinate into other nuclear coordinates will lead to the eventual evaporation of water molecules (Fig. 2A, left). The fact that 800-nm absorption ultimately leads to evaporation is confirmed by our mass spectra of anionic fragments and has been reported elsewhere (31).

Fig. 2.

(A) A schematic illustration of the solvation and evaporative dissociation exhibited in the hydrated electron clusters. The upward arrow represents the excitation to the p-state. The relaxation and dissociation pathways are depicted and labeled by their characteristic times as follows: τp, solvation in p-state, τic, internal conversion, τs, solvation in s-state, τr, relaxation and evaporation. hν, photon energy. (B) Probing of different transient states of the solvated electron by energy and time resolution. Left: An energy-level diagram illustrating the changes in PE distribution originating from anion populations with different electronic and solvation energies. The upward arrows indicate the 400-nm probe pulse that detached the electron, and the downward arrows correspond to the kinetic energy of the detached electron (the eKE). Right: The resulting PE spectra are plotted together on a common energy axis, with a, b, and c indicating points with differing sensitivities to the location of the transient state. The distribution shown is for a moderate weakening of the force constant and displacement of minimum position between the anion and the neutral potentials, as confirmed by Franck-Condon calculation. Asterisk indicates an excited electronic state.

The PE spectra were used to follow these dynamics and disentangle the pathways. The energy level diagram (Fig. 2B) shows qualitatively how the energy content in the solvation coordinate of the anion is expected to affect the eKE of the electron ejected upon absorption of the 400-nm probe pulse. Franck-Condon considerations indicate that the eKE distribution broadens asymmetrically as the amount of energy in the solvation coordinate increases in a given electronic state (yellow to red); a change in electronic state causes the spectrum to shift position (yellow to blue). The degree of broadening depends on the relative flatness and equilibrium position displacement of the neutral's and anion's solvation coordinate potentials. With this picture in mind, solvation dynamics in both the p- and s-states can be followed by monitoring the dependence on probe delay time of the production of detached electrons with various values of eKE (e.g., the energies labeled a, b, and c in Fig. 2B).

The PE spectrum of Embedded Image upon irradiation by the 400-nm femtosecond pulse confirmed ejection of the excess electron by vertical detachment, producing the characteristic eKE distribution (Fig. 3A, top). When the clusters were irradiated by both 800-nm and 400-nm pulses, the PE spectrum changed with delay time, as indicated in the difference spectra (Fig. 3A, bottom). The same spectra are also shown in a three-dimensional representation (Fig. 3B). It is apparent that different regions of the PE spectrum exhibit distinct temporal behaviors, and we focused only on the three particular regions labeled a, b, and c. As indicated by the ribbons in Fig. 3B, at high eKE above the onset of the PE spectrum (region a), a new peak appeared at time zero and disappeared by 0.7 ps. The PE intensity near the onset (region b) decayed with time, whereas the PE signal near the peak of the spectrum (region c) displayed an abrupt drop at time zero and a rise at positive time.

Fig. 3.

(A) Top: PE spectrum of Embedded Image obtained by irradiation with the 400-nm pulse only. Bottom: Time-dependent PE difference spectra at several time delays of the 400-nm probe pulse relative to the 800-nm excitation pulse. Each spectrum was constructed by subtracting the reference at 100 ps from the PE spectrum at the time specified. Regions a, b, and c indicate the energy windows of interest. (B) Three-dimensional representation of the time-dependent PE spectra. The intensity trends in region a, b, and c are indicated by yellow, red, and blue ribbons. (C) Femtosecond transients of Embedded Image and Embedded Image obtained by integration of the three different gated regions (a, b, and c) as a function of delay time. The transients of region b for Embedded Image and Embedded Image are also shown.

To quantify the trends shown by the ribbons in Fig. 3B, we obtained transients by integrating the PE intensity as a function of the delay time for each energy window. The same forms of apparent temporal behaviors were evident for both n = 30 and n = 35 clusters (Fig. 3C). The greater level of detail provided by the transients revealed that the fast decay for region a is not limited by laser pulse duration, as the asymmetry is evident, and there are two distinct time scales of decay for region b. We also compared with region b results obtained for Embedded Image and Embedded Image. For Embedded Image, n = 15, 20, and 25, only transients for region b were measured (Fig. 4A) (32).

Fig. 4.

(A) Femtosecond transients of Embedded Image (where n = 15, 20, 25, 30, or 35) obtained by integration of the PE signals in region b. The short- and long-range scans are shown in the left and right columns, respectively. (B) Time constants τs (squares) and τr (circles) versus cluster size n. The solid curves indicate the observed trends. (C) Observed relaxation rate 1/τr (circles) and the scaled RRKM rates for the hydrogen-bond breakage 1/τevp (triangles). The RRKM rate is scaled by ∼11,000 to match the observed rate for n = 35. The solid curves indicate the observed trend, and the dashed curve indicates the theoretical trend.

The temporal behavior observed in the time-dependent PE spectra of Embedded Image and Embedded Image elucidates the ultrafast dynamics. The instantaneous rise and the fast decay in region a (at high eKE) represent vertical excitation to the p-state followed by rapid relaxation to the s-state. As discussed earlier, an isolated peak of a-type character should rise within our pulse duration and decay with the p-state lifetime. Moreover, this peak temporally changes at an eKE shift of ∼1 eV, which corresponds to the s- to p-state energy gap (19), as predicted conceptually (Fig. 2B). In bulk water (4, 5, 33), the inertial solvent motions (libration) are expected to occur before the internal conversion. In the clusters, the decay of the a-peak gives the time scale for population transfer to the s-state, with an effective time constant, τeff, for inertial motion and internal conversion (τp and τic). Single exponential fits to the region a data give corresponding Ceff values of 170 fs (n = 30) and 140 fs (n = 35) (Fig. 3C). Given the short time scale of these motions, coherent effects may be present (4, 34), but a kinetic description suffices for the behavior observed here.

After the internal conversion, the electron becomes presolvated in the ground state, and solvation of the electron (τs) follows, as revealed by the short time behavior in region b and c. Relaxation (τr) after solvation can be most clearly seen in the long time behavior in region b (Fig. 4A, right). To account for the delayed return of population from the p- to the s-state, a proper kinetic analysis must also include the influence of τeff on the transients of regions b and c (35). The results (Figs. 3C and 4A) give τs values of 300 fs (the range for the clusters studied was ±150 fs with our current analysis) and τr values ranging from 2 to 10 ps, depending on cluster size (Fig. 4A). For the different clusters n = 15 to n = 35 (Fig. 4B), the time scale of solvation was within a factor of two and was similar to that of electrons in bulk water. It was also on the order of the time scale of the diffusive rotational and translational motions of bulk water around molecular probes (33). The solvent rearrangement time we obtained here for the s-state of these large clusters is about the same as that found for electron hydration after excitation of a charge transfer band of I(H2O)n for n = 5 and n = 6 (36). Such weak size dependence and the similarity between bulk and clusters indicate that the dynamics of hydration are in large part controlled by the local structure of water molecules in immediate contact with the electron.

The longer relaxation times are determined by the energy content in the s-state, the rate of intramolecular vibrational energy redistribution (IVR), and hydrogen-bond breakage (Fig. 4, B and C). Because these times increase with cluster size, we excluded both time-dependent solvation and IVR as rate-determining and considered evaporation. Manifestation of evaporation in the transients was expected because the process alters the PE spectra as a result of change in cluster size and internal energy. We calculated the statistical rate constants for clusters undergoing evaporation by one water molecule (1/τevp). Using Rice-Ramsperger-Kassel-Marcus theory (37), we obtained rate constants that were slower or much slower than the experimental observation, depending on the particular values of frequencies and the reaction barrier; for example, for n = 35, τevp ranged from ∼1 ns to 15 μs versus the observed value of 10 ps. The discrepancy would indicate a nonstatistical behavior (40). However, there have been reports that such clusters may live for much longer times (31), and because the internal energy needs to be determined, the results for the Embedded Image and Embedded Image systems should be extended with variation of energy and cluster initial temperature. The experimental time scale for relaxation (2 to 10 ps) of the clusters at finite temperature is not that different from that of hydrogen-bond making/breaking dynamics in bulk at room temperature (33).

Our observations demonstrate that solvation dynamics in mesoscopic hydrated electron clusters can be probed directly in real time. From the energy- and time-resolved PE spectra, we were able to follow the ultrafast processes that occur in the presolvated and hydrated states of the electron. With size-selection capability, we also observed the behavior of the rates of solvation and relaxation as a function of cluster size. For the clusters studied, our time-resolved data display solvation dynamics similar to those of the hydrated electron in bulk water, suggesting a local-water-structure model for hydration, and the pathways of electronic relaxation, solvation, and hydrogen-bond breakage have distinctly resolvable time scales. Mesoscopic scale clusters can thus provide the elementary dynamics and, as such, represent simplified model systems to study the behavior of bulk systems.

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