Partial Molar Volume of the Hydrated Electron - ACS Publications

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Cite This: J. Phys. Chem. Lett. 2019, 10, 2220−2226

Partial Molar Volume of the Hydrated Electron Ireneusz Janik, Alexandra Lisovskaya, and David M. Bartels*

J. Phys. Chem. Lett. Downloaded from pubs.acs.org by AUBURN UNIV on 04/23/19. For personal use only.

Radiation Laboratory, University of Notre Dame, Notre Dame, Indiana 46556, United States ABSTRACT: The partial molar volume of the hydrated electron was investigated with pulse radiolysis and transient absorption by measuring the pressure dependence of the equilibrium constant for e−aq + NH4+ ⇔ H + NH3. At 2 kbar pressure, the equilibrium constant decreases relative to 1 bar by only 6%. Using tabulated molar volumes for ammonia and ammonium, we have the result V̅ (e−aq) − V̅ (H) = 11.3 cm3/mol at 25 °C, confirming that V̅ (e−aq) is positive and even larger than the hydrophobic H atom. Assuming on the basis of recent molecular dynamics simulations that the molar volume of the H atom is somewhat less than that of H2, we estimate V̅ (e−aq) = 26 ± 6 cm3/mol. The positive molar volume is consistent with an electron that exists largely in a small solvent void (cavity), ruling out a recent model (Larsen, R. E.; Glover, W. J.; Schwartz, B. J. Science 2010, 329, 65−69) that suggests a noncavity structure with negative molar volume.

F

volume.19 Because the water densifies around the electron in this model, its partial molar volume must be negative.20 This disagrees with the experimental determination of Borsarelli et al.,21 who used a photoacoustic method to measure the overall volume change in the ionization process

or decades, it has been accepted that electrons in polar solvents like water become solvated in a “cavity” or void, with the solvent molecules arranging such that their dipoles align with the negative charge to stabilize it.1−3 The “cavity model” was developed originally in analytic form for dielectric continuum representation of solvent,3 but starting in the 1980s, the basic assumption (electrons are repelled by the solvent molecular core due to Pauli exclusion but are stabilized by the molecular dipoles) was carried over into one-electron pseudopotential models using classical molecular dynamics to explicitly represent the solvent molecules.4,5 The widely used Schnitker−Rossky pseudopotential6 for hydrated electrons produced a cavity surrounded by six water molecules, while the later Turi−Borgis7 (TB) and polarizable Jacobson− Herbert8,9 (PEWP2) pseudopotentials, based on the Phillips−Kleinman equations, produced a four-coordinate structure. In 2010, Larson, Glover, and Schwartz10 (LGS) published an “improved” pseudopotential fit to the numerical Phillips− Kleinman solution11 that attempts to include an attractive potential region near the oxygen atom smoothed out by the TB and PEWP2 approximations. With this more structured pseudopotential, the result of the molecular dynamics simulation is a noncavity structure, likened to “plum-pudding” by the authors,10 in which the water structure densifies and the electron spin density (the pudding) is mostly between the water molecules (the plums). Critics of the LGS pseudopotential point out that it gives an overall attraction to the water monomer where it should be repulsive,12 and this results in a vertical detachment energy 1−2 eV greater than that of benchmark water cluster ab initio calculations.13 Schwartz and co-workers, while admitting that their potential overbinds the electron,14 have claimed in a number of publications15−18 that the LGS model nevertheless reproduces many more experimental observations of the hydrated electron than the earlier “cavity” pseudopotential simulations. The only experiment that seems totally at odds with the noncavity LGS model is determination of the e−aq partial molar © XXXX American Chemical Society

Fe(CN)6 4 − + hν → Fe(CN)6 3 − + (e−)aq

(1)

The molar volumes of both iron complexes are known; therefore, the electron volume could be deduced as V̅ (e−aq) = +26 cm3/mol. Could this experimental result be completely wrong? The LGS prediction20 (−116 cm3/mol) would completely change the sign of the photoacoustic response. In view of the singular importance of this (e−)aq property in settling the cavity vs noncavity controversy, we set out to measure the partial molar volume by a different technique entirely, based on pulse radiolysis of water at high pressures. The free energy of formation for the hydrated electron has been most successfully established near room temperature by Schwarz22 and by Shiraishi et al.23 using equilibrium 2 e−aq + NH4 + ⇔ H + NH3

(2)

Pulse radiolysis of water at room temperature gives rise to several free radical and molecular products according to23−25 Water ⇝ 2.5(e−)aq + 2.5(H+)aq + 2.5(OH)aq + 0.55(H)aq + 0.72(H 2O2 )aq + 0.45(H 2)aq (3)

where the coefficients represent the number of species formed per 100 eV of energy deposited, after several hundred nanoseconds of quasi-geminate or spur recombination. In the presence of appropriate concentrations of NH3 and NH4+, the initial excess of (e−)aq over (H)aq immediately following a short Received: February 15, 2019 Accepted: April 17, 2019

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The Journal of Physical Chemistry Letters radiolysis pulse can be observed (via the hydrated electron absorbance) to reach an equilibrium level, and the equilibrium constant K2 (=k2f/k2r, the ratio of forward and reverse rate constants) may be determined from several experiments with different NH3/NH4+ ratios. The equilibrium constant is directly related to the free energies of reactants and products −RT ln(K 2) = ΔG2° = ΔGf °(H) + ΔGf °(NH3) − ΔGf °(NH4 +) − ΔGf °(e−aq )

(4)

Given tabulated thermodynamic data for NH3 and NH4+ and an accurate estimate for H, the e−aq free energy is deduced. Schwarz22 measured the equilibrium at 1 atm up to 70 °C, while Shiraishi et al.23 measured to 250 °C in pressurized water. The volume change associated with the equilibrium is the pressure derivative of the free energy change, while the partial molar volume is the pressure derivative of the free energy of formation at constant temperature Figure 1. Optical absorption of the hydrated electron at 700 nm following a 0.36 Gy radiolysis pulse at 25 °C and 1 bar in the presence of variable amounts of NH3, as indicated. Both the ionic strength and total concentration of [NH3 + NH4+] remain constant at 0.100 M.

d(−RT ln(K 2) = ΔV2̅ = V̅ (H) + V̅ (NH3) − V̅ (NH4 +) − V̅ (e−aq ) dP

(5)

It follows (assuming pressure-independent molar volumes) that the equilibrium constant will be exponentially dependent on the pressure K 2(P)/K 2(0) = exp( −P ΔV2̅ /RT )

average out. Occasional very bad lamp pulses were rejected from the average. The traces were fit with a set of partial differential equations that represent the accepted reaction kinetics of the pure water radiolysis model at room temperature.28,29 In addition to the pure water reactions, the ammonia/ammonium equilibrium 2 was added as the dominant chemistry of the hydrated electron and H atom. It was also necessary to add the effect of the ammonia/ammonium buffer with a neutralization rate estimated from the diffusion limit

(6)

Using tabulated molar volumes for NH3 (24.5 cm3/mol26,27), NH4+ (12.4 cm3/mol), and (H2)aq as a model of (H)aq (25.3 cm3/mol;26,27 but see discussion), we can estimate ΔV̅ 2 = 37.4 − V̅ (e−aq) cm3/mol. If the experiment of Borsarelli et al.21 is correct, then ΔV̅ 2 = +11.4 cm3/mol, and we should measure a 60% decrease in K2 by increasing the pressure to 2 kbar. On the other hand, if the LGS model10 is correct and V̅ (e−)aq is actually negative, the pressure effect should be dramatic. Even if V̅ (e−aq) = 0, the volume change of ΔV̅ 2 = 37 cm3/mol would result in a 15× change in K2 at 2 kbar, and a negative e−aq volume would be still more extreme. The experiment to be carried out is obvious. We need to measure the equilibrium constant K2 at very high pressure using procedures similar to those of Schwarz22 and Shiraishi et al.23 Description of the experimental details can be found at the end of this Letter. Initial transient absorption measurements in our highpressure titanium cell gave short lifetimes of hydrated electrons in the ammonia/ammonium solutions. Additional flushing improved things, and it was found that application of many small radiolysis pulses gave progressively longer lifetimes until a steady state was achieved. To investigate the source of impurities and the ultimate possible hydrated electron lifetime with these reagents, a series of measurements was carried out at ambient conditions in a standard 1 cm path length silica flow cuvette using the same sample preparation technique as that for the high-pressure apparatus. Figure 1 demonstrates a series of traces acquired from NaOH/NH4ClO4 mixtures, in each case after ca. 1200 pulses of 0.36 Gy had been applied to reach a steady state. The traces are averages of 8 acquisitions of 16 shots each. At the low dose used here, with 1−2 mOD absorption, the measurement noise is overwhelmingly dominated by low-frequency fluctuations of the pulsed analyzing lamp, requiring a large number of repetitions to

NH4 + ⇔ NH3 + H+ k 7r = 2.3 × 1010 (est); K 7 = 5.43 × 10−10

(7)

To account for the ammonia-related second-order recombinations, we added30 OH + NH3 → NH 2 + H 2O

k 8 = 8.0 × 107 (ref 30) (8)

H + NH 2 → NH3

10

k 9 = 1.2 × 10 (est)

NH 2 + NH 2 → N2H4

(9)

k10 = 1.8 × 109 (ref 30) (10)

Fitting with this mechanism showed that we had not completely eliminated reactive impurities with the “radiation cleanup” procedure, and therefore, an additional pseudo-firstorder reaction was included e−aq + impurity ⇒ product

(11)

The traces shown in Figure 1 were fit to the mechanism described above, with common values for the reactions k2f and k2r but individual values for dose (amplitude) and the impurity reaction. Despite the use of arbitrary impurity reaction 11 for each trace, the forward and reverse equilibrium reactions are very well constrained by the several different NH3/NH4+ ratios employed thanks to the biexponential character of the kinetics. Even individual traces for the lower NH3 concentrations demand the final fitted values of k2f and k2r for a good fit. The 2221

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into eq 5, we can arrive at the relation V̅ (e−aq) − V̅ (H) = +11.3 cm3/mol. We should immediately point out that we are assuming pressure-independent molar volumes and assuming only a small effect of the 0.1 M ionic strength.31 These effects should amount to no more than 2−3 cm3/mol over the 2 kbar pressure range. With complete confidence, we can conclude that the volume of the hydrated electron is substantially more positive than that of the hydrophobic H atom. While this result seems to rule out a noncavity model for room temperature, a noncavity structure at higher temperature might be a real possibility. Schwartz and co-workers carried out simulations with their LGS pseudopotential model that show a change in behavior vs temperature.17,18 At lower temperature, the g(r) result for the electron center vs water oxygen atoms seems to approach the tetrahedral “cavity” structure found with other models. The distinct possibility exists that in real water the hydration structure transitions from a “cavity” motif at room temperature to a noncavity motif at high temperature. It should be noted that the bimolecular recombination reaction of hydrated electrons is diffusion-limited up to 150 °C and then abruptly becomes much slower at higher temperatures.32,33 By 250 °C, the rate constant is slower than that at room temperature. This might be explained by a change from cavity to noncavity structure. To check this possibility, a single experiment was carried out with the high-pressure cell at 200 °C. The cell leaked above 1250 bar; therefore, only a relatively large change in volume for K2 could be detected, but this is the effect being looked for. Transient absorption data for two NH3/NH4+ ratios are shown in Figure 3. The radiation cleanup procedure failed to improve

worst-case relative impurity effect is illustrated in Figure 1 for 0.09 M NH3, where the dashed line is the prediction without impurity. On the other hand, the largest impurity rate constant required is for the pure NH4+ case. This suggests that the residual impurity is actually dominated by steady-state H2O2 product of the “radiation cleanup”. Our mechanism would predict the largest production of H2O2 from OH radical recombination in the absence of NH3 scavenger. The same experiment as that shown in Figure 1 was carried out with ultrapure 99.995% NH4Cl as the source of ammonium. Radiation cleanup was still necessary to reduce impurities. Impurity rates required in the fitting were slightly smaller than those for the lower-quality 98% NH4ClO4 salt, but the overall result was very similar. Identical values of k2f = 8.96 × 105 and K2 = 1.34 were found to fit this second data set. The numbers are the same within error as those found by Schwarz22 and Shiraishi et al.23 High-pressure experiments at 25 °C were carried out once the approximate limiting electron lifetimes had been established. Radiation cleanup was required each time as the pressure was increased as this pushed in some additional solution with impurity. Figure 2 compares data collected in the

Figure 2. Pressure effect on equilibrium 2, illustrated with three different NH3/NH4+ ratios. Arrows indicate the change observed between 1 bar and 2 kbar of pressure. Least squares fits to the kinetic model are superimposed on the data.

high-pressure cell at 1 and 2000 bar of pressure. The effect of 2 kbar of pressure is to increase k2f from 1.01 ± 0.05 to 1.60 ± 0.05 × 106 M−1 s−1, but equilibrium K2 decreases by only 6%, from 1.33 ± 0.05 to 1.24 ± 0.05. It is worth noting that virtually no change to the kinetics could be detected at 1 kbar of pressure; the full 2 kbar was required to detect the small change. The immediate conclusion to be drawn is that the partial molar volume change in equilibrium 2 is quite small relative to that predicted in the introduction based on either the LGS model10 or the experimental work of Borsarelli et al.21 Application of eq 6 allows us to convert the 6% change in K2 to a volume change of +0.80 ± 0.80 cm3/mol. By inserting the tabulated molar volumes of NH3 (24.5 cm3/mol26,27) and NH4+ (12.4 cm3/mol, assuming V̅ (H+aq) = −6.4 cm3/mol)

Figure 3. Pressure effect on hydrated electron absorption at 750 nm at 200 °C in the presence of two different NH3/NH4+ ratios.

the electron lifetime at this temperature; therefore, a fresh sample was slowly pushed through the cell by one syringe and taken up by a second. The time scale for equilibration was much shorter due to the high activation energies of k2f and k2r.23 At low pressure (100 or 200 bar to prevent boiling), a biexponential decay could be found, corresponding to the expected equilibrium 2, convolved with an overall exponential decay due to impurity reactions. Pressurizing the samples to 1250 bar resulted in an increase in signal, particularly visible in 2222

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molecular-level understanding of the hydrophobic effect for small solutes.42 Therefore, we should be on firm footing if we admit a large uncertainty and estimate V̅ (H) = 15 ± 5 cm3/ mol. Using this value, we arrive at our final result, V̅ (e−aq) = +26 ± 6 cm3/mol at 25 °C, apparently in perfect agreement with Borsarelli et al.21 To evaluate their experimental results, Borsarelli et al.21 require a hydrated electron quantum yield in the photoexcitation of Fe(CN)64−. This is determined with use of a hydrated electron extinction coefficient at 720 nm of 19 000 M−1 cm−1. Recent work44 has very accurately redetermined this extinction coefficient to be 19 700 M−1 cm−1. The error will translate directly into a quantum yield estimate for (e−)aq that is slightly too high. The calculation of ΔV̅ 1 in the ferrocyanide photoionization (eq 1) will be correspondingly too low, requiring a correction from the reported 67 ± 6 to 70 ± 7 cm3/mol. Making use of the molar volumes provided by Marcus,45 we then have V̅ (e−aq) = 29 ± 7 cm3/mol in the Borsarelli et al. experiment, still well within error of our present result. Agreement will be perfect if we choose V̅ (H) = 18 cm3/ mol. High-pressure effects on the hydrated electron properties and reactions were explored up to 6.4 kbar many years ago by Hentz and co-workers, using first gamma radiolysis46,47 and then electron pulse radiolysis.35,48 An estimate of the e−aq partial molar volume was made based on the equilibrium constant for reaction 12

the second exponential of the 70 mM NH3 sample of Figure 3. An auxiliary experiment using pure water was carried out to record any pressure effect on the product of radiation yield and extinction coefficient (G × ε750) for electrons at this temperature. It was determined that the hydrated electron spectrum shifts to the blue with pressure, increasing the absorbance at 750 nm. (Radiolysis yields were shown many years ago to be insensitive to pressure up to 6.4kbar at room temperature,34 but the hydrated electron spectrum blue shifts.35) A best fit of the data in Figure 3 suggests a small decrease in K2, from 2.64 to 2.54, corresponding to a +1.1 cm3/mol volume change. (The low-pressure values of K2 = 2.64 and k2f = 1.35 × 108 M−1 s−1 agree with Shiraishi et al. at this temperature.23) Using tabulated/interpolated partial molar volumes from the HKF equation of state26,27 for NH3 (26.1 cm3/mol) and NH4+ (6.5 cm3/mol, on the basis of V̅ (H+aq) = −13.5 cm3/mol36), we have V̅ (e−aq) − V̅ (H) = +18.5 cm3/mol at 200 °C. The data of Figure 3 are certainly too poor for us to put much faith in the quantitative result for V̅ (e−aq) − V̅ (H), but qualitatively there is absolutely no indication that K2 decreases significantly with pressure at 200 °C. If V̅ (e−aq) were 0 at this temperature, the equilibrium constant K2 should decrease 10fold at 1250 bar. Even for a 40% decrease of K2, the biexponential character of the traces would disappear, leaving only a single-exponential decay due to impurities. The observation of the biexponential decays at 1250 bar allows us to claim with confidence V̅ (e−aq) − V̅ (H) > 0.0 cm3/mol at 200 °C. This result seems to rule out the possibility that the LGS noncavity model might explain anomalies of the hydrated electron self-recombination above 150 °C. Extraction of an absolute value for V̅ (e−aq) from our data requires some assumption regarding the value of V̅ (H) for the hydrogen atom in water. There is a large body of evidence that can be cited to support the thesis that H atoms are hydrophobic and have a hydration potential and thermodynamics nearly identical to that of H2.37−39 Therefore, we looked up26,27 V̅ (H2) = 25.3 cm3/mol for our initial estimates of the pressure-dependent equilibrium. Recent MD simulations of H2 and of H atoms, based on high-level ab initio calculations of the interaction potentials with water and using the highly accurate AMOEBA polarizable water model, find very similar g(r) probability functions vs water oxygen for the two species, but not identical. Smiechowski40 reports the first maximum in the H2 center of mass vs water oxygen as g(H2−Ow) = 3.27 Å and the first minimum at 5.03 Å. Pomogaeva and Chipman41 report the first maximum in the H atom vs water oxygen as g(H−Ow) = 3.0 Å and the first minimum at 4.7 Å. On the basis of this comparison, the H atom cavity is almost exactly 0.3 Å smaller than that of H2. The g(H2−Ow) function begins to rise from 0 at about 2.3 Å, whereas g(H−Ow) begins to rise at 2.0 Å. Taking the latter measurements as the radii of a spherical solvation cavity, a simple estimate of the volume difference ( 4π [(2.3)3 − (2.0)3] Å3) amounts to 10 cm3/mol. This should

e−aq + H 2O ⇔ H + OH−

(12)

The pressure effect on the equilibrium constant K12 was calculated from separate measurements of the forward and reverse rate constant activation volumes: ΔV̅ 12 = ΔV̅ ⧧12f − ΔV̅ ⧧12r. The reverse reaction rate constant k12r is quite high, 2 × 107 M−1 s−1, making its measurement relatively easy.28 The forward reaction of e−aq with water solvent is very slow under ambient conditions, and the measurement of this rate constant is very sensitive to impurities.49−51 It was demonstrated quite convincingly in a competition experiment with NO3 − scavenger that the forward reaction 12f has a large negative activation volume,47 making it quite possible to measure above 2 kbar. The overall result of Hentz and co-workers can be stated as V̅ (e−aq) − V̅ (H) = −7.6 cm3/mol, quite different from our present result using equilibrium 2. Using our present estimate for V̅ (H) = 15 cm3/mol, this would still result in a positive value for V̅ (e−)aq. It is worth noting that Hentz46 found activation volume ΔV̅ ⧧ of virtually any hydrogen atom reaction to be about −6.5 cm3/ mol, regardless of mechanism, be it H atom abstraction, addition to an unsaturated organic compound, or the reaction 12r with OH− giving e−aq. Hentz and co-workers made the very reasonable inference that V̅ (H) = +6.5 cm3/mol, a number we now consider unreasonably low. This observation of H atom activation volume invariance still lacks a suitable explanation.52 However, ΔV̅ ⧧ for reaction k2r of H with NH3 is found to have exactly the same room-temperature value in the present study. The only essential difference between our experiment and that of Hentz46 is the pressure range used. Hentz could only generate a significant difference in rates between the water reaction 12f and NO3− scavenger when the pressure was above 2 kbar. In later pulse radiolysis work, Hentz and co-workers showed that above 2 kbar the activation volumes of many hydrated electron reactions are pressure-dependent.48 The inference was drawn that e−aq is compressible, and its effective

3

be an upper limit of the volume difference between H and H2 because restructuring (densification) of water around very small hydrophobes tends to reduce the effective partial molar volume.42 From integration of the g(r) functions, Smiechowski has calculated a limiting volume for H2 of 19.8 ± 0.6 cm3/ mol.40 He notes that this value is smaller than the previously accepted 25 cm3/mol but is in much better agreement with more recent Raman scattering data for H2 in water43 and with 2223

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of NH3/NH4+ were pumped using an HPLC pump, either directly through the cell to flush the entire flow system when all syringe pump flow controlling valves were open and syringe plungers were fully pushed or into the high-pressure syringe A to fill it when the output valve of syringe B was closed. With syringe A and the cell filled, an input valve of syringe A was closed. By design, the solution can be pushed through the cell by syringe A at a constant flow rate and taken up by syringe B set to control constant pressure. When the flow of both syringes is stopped at any time under high pressure and all plumbing is leak free, the system maintains the preset pressure. At room temperature, samples were irradiated with flow stopped to apply “radiation cleanup” treatment, as described. A given sample was measured at ambient pressure and then at progressively higher pressures applied by the syringe until 2 kbar was reached.

volume becomes smaller at very high pressures. This might account for the smaller e−aq volume inferred from the Hentz experiments. It seems clear that all experimental evidence for the partial molar volume of e−aq, even that of Hentz,46 implies a positive value. We have to reject the noncavity LGS pseudopotential model10 on this basis. The partial molar volume calculated for the Turi−Borgis “cavity model” pseudopotential is actually in good agreement with the experimental results,20 and the same will certainly be true for the polarizable Jacobson−Herbert pseudopotential8 and more recently published ab initio models that give a slightly smaller central void.53−55 By disproving the noncavity LGS solvation structure, the implication is that we must also reject the LGS-based explanations for (1) the temperature dependence of the optical absorption maximum,15 (2) femtosecond polarized pump−probe “hole burning” experiments,10 (3) time-resolved photoelectron spectroscopy experiments,16 and (4) temperature dependence of the excited-state relaxation.18 However, Schwartz and co-workers have argued convincingly in these papers that existing “cavity model” pseudopotentials are incapable of reproducing these experimental observations; therefore, the need for an alternate explanation seems clear. The one-electron “cavity model” wave functions tend to be smooth but slightly distorted s-like functions, largely contained in a central void.9,56 In sharp contrast, more rigorous manyelectron ab initio wave functions feature significant p-character at the four inner oxygen atoms and nodes between the four inner protons and the central void13,53,55,57 (both properties in agreement with magnetic resonance evidence58,59). It is very reasonable to question (and we are certainly not the first to do so8,9,60) whether any one-electron pseudopotential based on the water monomer is capable of reproducing the features of the real wave function needed to model the dynamical optical properties of this species. A full many-electron treatment may be necessary.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone (574) 631-5561. Fax: (574) 631-8068. ORCID

David M. Bartels: 0000-0003-0552-3110 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-FC02-04ER15533. This is manuscript number 5236 of the Notre Dame Radiation Laboratory.

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REFERENCES

(1) Feng, D. F.; Kevan, L. Theoretical-Models for Solvated Electrons. Chem. Rev. 1980, 80 (1), 1−20. (2) Herbert, J. M.; Coons, M. P. The Hydrated Electron. In Annual Review of Physical Chemistry; Johnson, M. A., Martinez, T. J., Eds.; 2017; Vol. 68, pp 447−472. (3) Copeland, D. A.; Kestner, N. R.; Jortner, J. Excess Electrons in Polar Solvents. J. Chem. Phys. 1970, 53 (3), 1189−1216. (4) Jonah, C. D.; Romero, C.; Rahman, A. Hydrated Electron Revisited Via the Feynman Path Integral Route. Chem. Phys. Lett. 1986, 123 (3), 209−214. (5) Rossky, P. J.; Schnitker, J. The Hydrated Electron - Quantum Simulation of Structure, Spectroscopy, and Dynamics. J. Phys. Chem. 1988, 92 (15), 4277−4285. (6) Schnitker, J.; Rossky, P. J. An Electron Water Pseudopotential for Condensed Phase Simulation. J. Chem. Phys. 1987, 86 (6), 3462− 3470. (7) Turi, L.; Borgis, D. Analytical Investigations of an ElectronWater Molecule Pseudopotential. Ii. Development of a New Pair Potential and Molecular Dynamics Simulations. J. Chem. Phys. 2002, 117 (13), 6186−6195. (8) Jacobson, L. D.; Herbert, J. M. A One-Electron Model for the Aqueous Electron That Includes Many-Body Electron-Water Polarization: Bulk Equilibrium Structure, Vertical Electron Binding Energy, and Optical Absorption Spectrum. J. Chem. Phys. 2010, 133 (15), 154506. (9) Herbert, J. M.; Jacobson, L. D. Nature’s Most Squishy Ion: The Important Role of Solvent Polarization in the Description of the Hydrated Electron. Int. Rev. Phys. Chem. 2011, 30 (1), 1−48. (10) Larsen, R. E.; Glover, W. J.; Schwartz, B. J. Does the Hydrated Electron Occupy a Cavity? Science 2010, 329 (5987), 65−69. (11) Smallwood, C. J.; Larsen, R. E.; Glover, W. J.; Schwartz, B. J. A Computationally Efficient Exact Pseudopotential Method. I. Analytic

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EXPERIMENTAL METHODS Pulse radiolysis/transient absorption experiments were carried out using the 8 MeV electron linac at the Notre Dame Radiation Lab. Visible light from a pulsed 1 kW xenon lamp was detected with a fast silicon photodiode and a digital oscilloscope. A wavelength near the hydrated electron maximum at 720 nm was selected with 40 nm bandwidth interference filters. Transients observed are displayed in Figures 1−3. Samples of variable NH3/NH4+ ratios were prepared by sparging 1 L of a 0−0.090 M NaOH solution with argon and then adding solid ammonium perchlorate or ammonium chloride to make a 0.100 M solution of the added salt. The NaOH neutralized a fraction of the ammonium to yield the desired NH3/NH4+ ratio. Sparging was stopped at this point to avoid stripping out the NH3. The sample was pumped into a new high-pressure titanium optical flow cell of 1 cm path length and ∼20 μl volume with 6.35 mm thick sapphire windows (details to be published elsewhere). The flow cell was connected using 1/16 in. stainless steel tubing with SITEC fittings to output (pump A) and input (pump B) valves of two ISCO 30D syringe pumps. The temperature in the cell could be controlled by thermostatic fluid, flowing through four equally spaced 1/8 in. diameter channels in the cell body parallel to the optical cell or by using four cartridge heaters inserted into these water channels to achieve 200 °C. Solutions 2224

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