Communications: Observation of two classes of isomers of hydrated electrons in sodium-water clusters Free

The concept of the solvated electron plays a prominent role in many fields of solution chemistry and biology such as electron transfer, biological activity, and charge-induced reactivity. The low lying optical spectra of the “classical” solvated electron were observed in dilute solutions of alkali metals in ammonia.¹ Their characteristic blue color was later attributed to the presence of solvated electrons.² Hydrated electrons show similar spectral features but were observed and assigned much later due to their transient nature in bulk solutions.³ In molecular beam experiments, gas phase clusters of solvent molecules have been observed to either solve the valence electron of alkali metals or to carry an extra charge. Studying these clusters paved the way for revealing how macroscopic properties emerge microscopically as a function of cluster size.^4–9 For alkaline solvent clusters, binding energies of the solvated electron have been probed by determining the ionization potential (IP) in photoionization experiments.^6,10

The studies of the Hertel group revealed a remarkable difference for sodium microsolutions in water and ammonia with respect to the size dependent evolution of their IPs. The IPs of $Na(H2O)n$ clusters decrease from $n=1–4$ and stay constant for $n≥4$⁠, while the $Na(NH3)n$ IPs decrease from $n=1$ to 11, stay constant up to $n=19$⁠, and drop further in steps for $n≥20$ matching the macroscopic binding energies of ammoniated electrons, when scaled and extrapolated to infinity.^6,11 These observations stimulated significant theoretical efforts for understanding the nature of the sodium-water and sodium-ammonia microsolutions.^12–15 Early studies tried to rationalize the IP evolutions of small $(n=1–6)$ $Na(NH3)n$ and $Na(H2O)n$ clusters assuming a direct vertical ionization, while more recent work also discussed adiabatic contributions.^16,17 The coexistence of $Na(H2O)n$ isomer groups with distinguishable IPs has not been reported yet.

Here, we report the observation of a class of sodium-water clusters with a significantly lower IP than those previously reported. A tentative quantum chemical characterization was achieved by simulating ionization spectra of selected $Na(H2O)n$ clusters $(n≤15)$ using an ab initio quantum chemistry–molecular dynamics approach. The clusters were generated in a molecular beam machine with a reflectron time-of-flight (RETOF) mass spectrometer being described elsewhere in detail.^18,19 A water cluster beam is skimmed and crosses an atmosphere of sodium vapor created in a pickup cell (cell temperature of 490 K). The sodium doped clusters are detected by photoionization, mass resolved in the RETOF, and the ions are recorded by a multichannel plate. For the photoionization of the products, a pulsed excimer laser (LPX200i, Lambda Physics) is used for pumping a dye laser (LPD3000, Lambda Physics). This setup is particularly capable of generating molecular beams with high abundances of large clusters.^18,19 Expanding pure water at a stagnation pressure of 6.5 bar (reservoir temperature of 430 K and nozzle temperature of 440 K), a cluster size distribution with a median of $⟨n⟩=300$ is generated. The upper panel of Fig. 1 shows the associated mass spectrum of $Na(H2O)n$ recorded with a photon energy of 3.36 eV (370 nm). For the same experimental conditions, except for the lower photon energy of 2.8 eV (440 nm), a similar size distribution for large and medium sized clusters is found. A significant difference is the scarceness of clusters for $n=4–10$ in the 2.8 eV experiment and their emergence between $n=11–15$ (Fig. 1, lower panel). This observation can be interpreted such that there exist two different classes of isomers discriminated by their different IPs and the critical cluster size needed for their formation.

If this assumption holds, the plots of ion yields (for clusters above the largest critical size) versus photon energies will exhibit two regions with steep signal increases indicating the different IPs. Extrapolation of the steepest gradients to the energy axis will give the IPs. Such plots are shown in Fig. 2. The normalized ion yields are integrated over a wide size distribution $(n=45–500)$⁠, and as function of photon energy, they show two significant increases: one at 2.8 eV (isomer class II) and another at 3.2 eV (isomer class I). The first threshold we attribute to a new class of sodium water isomers with a significantly weaker bound solvated electron. Their critical size of 11 water molecules indicates that a critical distance between the hydrated electron and the sodium counterion is needed for their emergence. When a sufficient number of water molecules are present in the cluster, further addition has seemingly no effect on the efficiency of the photoionization process. This observation we know very well: the IP of 3.2 eV (3.25 eV for $n=4$⁠) for the second ion yield increase is in good agreement with the IP of 3.17 eV reported for $Na(H2O)n$ clusters for $n≥4$ up to $n=20$⁠.⁶ The signal increase in the transition region of the two isomers around 3.1 eV in Fig. 2 (middle panel) may suggest contributions of further cluster classes. However, when the total ion yields are tentatively corrected for the contribution of isomer I, a typical ion yield plot for alkali-solvent clusters results with the signal attributed to isomer II being saturated around 3.15 eV (see inserted plot). With respect to the standard IP assignment of 2.8 eV based on the steepest gradient extrapolation, one should keep in mind that the gradual signal increase and transition to saturation may reflect a spectrum of cluster geometries and contributions of autoionization.^11,17 However, the scarceness of ion yield signals below 3.05 eV for $n≤10$ and the distinguishable regions of significant signal increase show the coexistence of two cluster groups with different IPs. For isomer I in our measurement the size range is extended to about $n=500$⁠. This previously characterized cluster class shows a much higher abundance in the cluster beam compared to isomer II. However, above the critical sizes, identical size distributions are found independent of the isomer being ionized: at 440 nm it is solely isomer II; at 370 nm it is predominantly isomer I.

It is obvious to compare our findings with the related case of anionic water clusters. Figure 3 summarizes the results for $Na(H2O)n$ and $(H2O)n−$⁠. There exist at larger cluster sizes for both systems two binding motifs with different binding energies. In anionic clusters an internally solvated electron and a surface bound electron are observed.⁸ The new experimental values of 3.3 eV (internal) and 1.6 eV (surface) of the solvated electron in the liquid²⁰ are in agreement with the extrapolated vertical binding energies (VBEs) of the clusters. There exists a transitional region, where the new binding motif is established. It is between $11≤n≤15$ for isomer II of $Na(H2O)n$ and $20≤n≤50$ for isomer II of $(H2O)n−$⁠. The difference in energy, however, is much smaller for the two $Na(H2O)n$ isomers (0.4 eV compared to 1.65 eV for bulk water), which we relate to the presence of the $Na+$ counterion. As we will see, the degree of $Na+-e−$ separation distinguishes the two isomers, while different localization modes of the solvated electron are found in anionic water. In general, dependent on the expansion conditions and cluster sizes, Verlet et al.⁸ and other groups^21–23 saw a much more complex picture for anionic water with a third even weaker bound isomer and subgroups of isomer I appearing at smaller cluster sizes. We tested the effect of cluster temperature by repeating the experiment using different expansion conditions including He seeding. In the accessible range of cluster temperatures $(∼90–130K)$ (Ref. 24), we have not seen a significant effect on the critical size needed to form isomer II. The main difference, however, is the extrapolation to bulk values. Both isomers show cluster size independent IPs when their critical sizes (four $H2O$ molecules for isomer I and 15 $H2O$ molecules for isomer II) are reached. Adiabatic contributions to the photoionization process have been suggested as an explanation.^16,17 For sodium microsolutions in methanol, a pure vertical ionization could be excluded for some clusters sizes based on their comparatively simple topology. In the present study however, the assumption of a vertical ionization for IP modeling was sufficient for $n≤15$⁠, as shown below. The lower IP and the larger critical cluster size indicate that the $Na+-e−$ ion pair is more separated in isomer II. This finding may explain recent results by Kim et al.²⁵ who found that NaOH is produced either as a $Na+OH−$ contact pair or in form of isolated $Na+$ and $OH−$ ions in the Na water reaction at an ice surface. They explained their results by assuming solvated electrons being in close proximity of or separated from the Na counterion in the initial phase of reaction.

Further evidence for this assumption comes from the quantum chemical prediction of structures and modeling of ionization spectra of the $Na(H2O)n$ clusters $(n=1–4,7,15)$ using ab initio methods. The simulation protocol had two steps. In the first one, the ground state densities of the sodium-water complexes were sampled by means of ab initio molecular dynamics with a step of 40 a.u. The cluster was coupled to a Nosé–Hoover thermostat maintaining constant temperature of 250 K. The forces were calculated at the RI-PBE level with $6-31+g∗$ basis. The system was equilibrated for 2 ps for $n=1–4$ and 7 ps for $n=7$ and 15, and the production run lasted 25 ps for each cluster and isomer. In the second step, the ionization spectra were modeled with ionization energy evaluated each 50 fs. The ionization energies were calculated with the PMP2 method, which represents a reasonable compromise between accuracy and computational price for ionization processes.^26,27 For each such geometry of the neutral sodium-water cluster, the $Na+-e−$ distance and the radius of gyration were calculated by integrating the spin density of the electron. The $6-31++g∗∗(dp.)$ basis set was employed, where (dp.) stands for “doped:” one more set of Na basis functions was placed on the center of spin density calculated at the $PMP2/6-31++g∗∗$ level (for further details, see supplementary material³⁰). The TURBOMOLE and GAUSSIAN03 packages were employed for the calculations.^28,29

The calculated ionization spectra are shown in Fig. 4. The qualitative trend is the same as in the experiment, and also the quantitative agreement is rather satisfactory. Upon the solvation, the IP monotonically decreases from 4.96 eV for bare sodium (at the $MP2/6-31+g∗$ level) down to $∼3.4eV$ for $n=4$⁠. Further solvation leads to only a minor decrease in the IP (⁠$∼3.2eV$ for $n=7$⁠). For clusters with 15 water molecules, the energy landscape is already rather complicated. However, two isomers differing in their IPs can be clearly distinguished. The isomer with sodium on the surface is characterized by IP of $∼3.1eV$⁠, which is relatively close to the value found for $Na(H2O)4$⁠. Note that the decrease with respect to smaller clusters can probably be attributed to basis set deficiency or insufficient equilibration within the simulation time (32 ps).

The second isomer with sodium solvated inside the water cluster has an IP of $∼2.6eV$⁠, which is about 0.5 eV lower than the surface isomer. The interconversion between the two isomers was not observed within the simulation time. The energies of the two isomers are close enough so that both isomers can be populated (local minimum of isomer with Na inside is more stable than the isomer with Na on the surface by 0.14 eV at the $PBE/6-31+g∗$ level). We might conclude that two isomers found in our simulations most probably correspond to the isomers I and II in the current experiment.

Quantum chemistry was also used to visualize the electronic structure of the solvated sodium (Table I). Already for the binary complex, one can see the tendency for a separation between sodium and the extra electron. The distance between the $Na+$ ion and the solvated electron then further increases and amounts to approximately 2.8 Å for $Na(H2O)7$⁠. The distance is increased by additional 0.5 Å for the isomer with Na on the surface of $Na(H2O)15$⁠, while it is almost doubled for the one with Na inside. With increasing cluster size, one can also observe the expansion of the electron cloud, expressed by the radius of gyration. The general picture emerging from the quantum chemical calculations is that the electron is not bound directly to the sodium atom, but it resides on water molecules of the first solvation shell. For both isomers, the extra electron is located on the surface of the cluster (see supplementary material³⁰). Both clusters can be clearly distinguished on the basis of the $Na+-e−$ distance and the radius of gyration. As the difference between $Na+-e−$ distances for the two isomers is about 1.6 Å, we may tentatively state that one isomer corresponds to a solvent separated pair and the other to a contact ion pair.

From experiment and theory, we can conclude that $Na(H2O)n$ clusters coexist for $n≥15$ in two groups of isomers being distinguished by their different IPs of 3.2 and 2.8 eV and their different geometries expressed by the distance of the counterion to the electron distribution. The IP of both cluster types remains unchanged even for large clusters with more than 500 water molecules. This finding and the surface location of the solvated electron suggest that the sodium-water reaction on ice surfaces is initiated by the simultaneous formation of a solvent separated and a contact ion pair.²⁵ 

T.Z. acknowledges the ongoing support of Professor Martin Suhm and funding by the DFG (GRK 782, Grant No. ZE 890-1-1). P.S. would like to acknowledge Grant Agency of the Czech Republic (Grant No. P208/10/1724). M.O. is a student of the International Max Planck Research School “Dynamical Processes in Atoms, Molecules and Solids.”