Hydrated hydronium: a cluster model of the solvated electron?

Abstract

Ab initio (ROHF, CASSCF, CASPT2) and DFT/B3LYP calculations have been performed for the electronic ground state and the lowest excited singlet states of the water dimer and hydronium–water clusters. It has been found that a barrierless hydrogen-transfer reaction path exists in the first excited singlet state of the water dimer, leading to OH and H₃O radicals. The microsolvation of the hydronium radical has been investigated, considering up to two solvation shells of water molecules. Solvated H₃O is found to be a charge-separated complex, consisting of the hydronium cation and a localized electron cloud, which are connected by a water network. Results are reported on the stability of these clusters and their electronic and vibrational spectroscopic properties. The calculated electronic and vibrational spectra of the clusters exhibit striking similarities with the spectral signatures of the hydrated electron. It is argued that H₃O(H₂O)_n clusters could be the carriers of the characteristic spectroscopic properties of the hydrated electron.

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1. Introduction

The hydrated electron is a unique species, which is generated by radiolysis or photolysis of liquid water.¹ Its distinctive properties are the broad and intense absorption spectrum,² centered near 720 nm, its high rate of diffusion and its high reactivity.³ Despite many years of research on the production mechanism of the hydrated electron, its reaction kinetics and its spectroscopy, the microscopic structure of this species remains an enigma. Recent measurements with unprecedented time resolution have yielded a wealth of data on the mechanism of formation of the hydrated electron and its electronic and vibrational spectroscopy, without providing a definitive clue, however, what the structure of the equilibrated hydrated electron may be.^4–10

In early theoretical descriptions of the electron solvated in water or ammonia, continuum or semicontinuum models were adopted, see the review ref. 11 and references therein. In the more recent theoretical works, the focus has been on molecular dynamics simulations of a quantum mechanical electron in a classical water environment, see, e.g., refs. 12–15. These computer simulations are based on the qualitative picture of a localized electronic charge distribution existing in a cavity of the hydrogen-bonded network of water molecules, the so-called cavity model. While this model and its computational realizations have been able to account for many of the observed phenomena, they have failed so far to provide a quantitatively accurate description of the CW absorption spectrum.¹⁶ The most recent data on the lifetime of the excited p state of the hydrated electron obtained with very high time resolution^6,9 are not in agreement with the predictions of the earlier computer simulations.^14,15 A long-standing puzzle not easily explained by the cavity model is the observation that hydrated electrons in neat water are produced by photon absorption near the bottom of the first absorption band (≈6 eV),^8,17 at much lower energy than the expected ionization potential of liquid water (≈9 eV).^7,18

The persistent difficulties encountered with the cavity model have led to repeated proposals of alternative models which associate the unique spectroscopic and kinetic properties of the hydrated electron with a molecular species or a small cluster in the liquid environment.¹¹ Robinson and collaborators^19,20 and Tuttle and Golden,²¹ for example, have argued that solvent–anion complexes of the type H₃O–OH⁻ may be carriers of the spectroscopic properties of the hydrated electron. More recently, Muguet has suggested that the hydrated electron should be viewed as an itinerant H₃O or H₅O₂ radical in water.²²

In recent ab initio investigations of reaction paths for the photochemistry of clusters of pyrrole, indole and phenol with water molecules, the present authors have found that the dominant reaction process in the electronically excited state is an intracluster hydrogen-transfer process from the chromophore to the aqueous environment.^23–25 It has been shown that the hydrogen-transfer photochemistry is governed by an optically dark state of ¹πσ^* character, which is repulsive with respect to the NH stretching coordinate of indole and the OH stretching coordinate of phenol, respectively. Excited-state geometry optimization has revealed that the 1 : 1 cluster of indole (phenol) with water relaxes to a configuration in which an indolyl (phenoxy) radical is hydrogen-bonded to a hydronium radical.^24,25 Calculations for indole (phenol) (H₂O)_n clusters have shown, furthermore, that the preferred structure of the water network after hydrogen atom transfer is that of a solvated hydronium ion and a solvated diffuse electron cloud.^24,25 In view of the fact that UV excitation of indole and phenol in liquid water leads to the formation of hydrated electrons with high quantum yields,^26,27 it appears likely that these computational findings for indole–water and phenol–water clusters have some bearing on the enigma of the microscopic structure of the hydrated electron.

Here we report the essentials of a similar computational study on neat hydronium–water clusters. We focus on the possible photochemical formation mechanism of the H₃O radical and on the structure, stability and spectroscopic signatures of small clusters of the type H₃O(H₂O)_3m with m = 0,1,2. A more comprehensive analysis of the structure and properties of H(H₂O)_n clusters, including the hydrated dihydronium radical, will be reported elsewhere.²⁸

The H₃O radical has been the subject of a number of theoretical investigations,^29–32 mostly in the context of identifying radiative transitions between Rydberg states, stimulated by the observation of optical emission spectra of the ammonium radical by Herzberg.³³ An early paper by Schwartz³⁴ and more recent work by Muguet²² have pointed out that the 3s → 3p absorption of H₃O falls into the energy range of the absorption spectrum of the hydrated electron. Muguet has also calculated the absorption spectrum of the dihydronium radical, H₅O₂.²² No calculations on H(H₂O)_n clusters beyond H₅O₂ are known to the authors.

It is well known from many computational studies on negatively charged water clusters and anion–water complexes that the modeling of an excess electron in water by finite-size clusters in an intricate problem.^35–41 The long-range polarization forces and the Pauli repulsion of the excess electron by the surrounding water molecules are not accounted for in finite cluster models. On the other hand, several experimental investigations, e.g. on the ionization potentials and excitation energies of alkali–water clusters, have shown that these spectroscopic properties converge rather fast with increasing cluster size.⁴² This encourages us to look for correlations between the spectroscopic properties of individual hydronium–water clusters and the spectroscopic signatures of the hydrated electron. We hope that this unconventional viewpoint stimulates experimental work on the spectroscopic properties of these clusters and thus possibly opens an alternative approach towards the understanding of the solvated electron in water.

2. Computational methods

The geometry of H₃O(H₂O)_n (henceforth abbreviated as H₃OW_n) clusters in the electronic ground state has been optimized at the restricted open-shell Hartree–Fock (ROHF) level and with density-functional theory (DFT), employing the B3LYP functional. A non-standard basis set was used. The 6-31+G** split valence double-zeta Gaussian basis set with polarization functions on all atoms and standard diffuse functions on the oxygen atoms⁴³ was additionally supplemented with diffuse s and p functions (ζ = 0.02) for the oxygen atoms. Harmonic vibrational frequencies and IR intensities of the fundamentals have been calculated at the DFT level. The GAUSSIAN 98 package has been used for these electronic ground-state calculations.⁴⁴

For the construction of the hydrogen-transfer reaction path in the ¹A″(πσ*) excited state of the water dimer, and the hydrogen-detachment reaction path in the ground state of hydronium and hydrated hydronium, the coordinate-driven minimum-energy-path approach was adopted. For a given value of the OH bond length of one of the water molecules or of H₃O, all remaining coordinates were optimized at the complete-active-space self-consistent-field (CASSCF) level. For the water dimer, the 9a′, 10a′ and 2a″ orbitals have been included in the active space. For the construction of the potential-energy functions along the reaction coordinate, multi-reference second-order perturbation theory as implemented in the GAMESS program⁴⁵ has been applied, taking the state-averaged CASSCF wavefunction of the S₀ and ¹A″(πσ*) states as the reference. For these calculations on the water dimer, a more extended basis set has been used: the 6-311++G** basis was supplemented with an additional set of diffuse Gaussians (exponent ζ = 0.02) on the oxygen atoms.

The energies of the lowest excited states of the clusters were calculated at the ground-state DFT/B3LYP-optimized geometries with the aid of the CASPT2 method (second-order perturbation theory based on the CASSCF reference).⁴⁶ In the CASSCF/CASPT2 calculations 7 electrons were distributed within 10 orbitals and the energies of the 4 lowest doublet states were averaged with equal weights. In the calculation of the oscillator strengths, the CASPT2 energies were combined with transition dipole moments calculated from CASSCF wavefunctions by means of the CASSI (complete-active-space state interaction) method. The CASPT2 calculations were performed with the MOLCAS-4 package,⁴⁷ using the ANO-L basis set of split-valence double-zeta quality, augmented with polarization functions on all atoms and additional diffuse s and p Gaussian functions of exponent 0.02 at the oxygen atoms.

3. Results and discussion

3.1 Photochemistry of the water dimer

In this subsection we briefly discuss the formation mechanism of the hydronium radical via a photoinduced hydrogen-transfer process in water clusters.

Fig. 1 shows the CASPT2 potential-energy (PE) profiles of the S₀ and S₁ states for the hydrogen-transfer reaction path in the water dimer. The reaction path has been optimized in the S₁(πσ*) state; the energy of the S₀ state is calculated at the same geometries. It can be seen that the vertically excited S₁(πσ*) state of the dimer correlates, without barrier, with a configuration which corresponds to a hydrogen-bonded OH–H₃O biradical complex. The π and σ* CASSCF orbitals of the ¹πσ* state of the OH–H₃O complex are shown as inserts in Fig. 1. It is seen that the π orbital remains on the OH radical, while the σ* orbital is transferred, together with the proton, to form the H₃O Rydberg molecule. The photochemistry of the H₂O dimer can thus be characterized as a concerted electron and proton transfer process.

Fig. 1 MP2 PE functions of the S₀ (circles) and S₁(πσ*) (squares) electronic states of the water dimer, calculated along the minimum-energy reaction path for hydrogen transfer. The reaction path has been optimized in the S₁(πσ*) state; the S₀ energies are calculated at the same geometries. The π and σ* CASSCF natural orbitals of the ¹πσ* state obtained at the S₀ (left) and S₁ (right) equilibrium geometries are shown as inserts.

The analysis of the wavefunction of the electronic ground state reveals an increasing admixture of the ion-pair configuration along the reaction path. The ground state correlates adiabatically with the OH⁻H₃O⁺ ion-pair configuration,^48,49 while the excited state of the water dimer correlates with the OH–H₃O biradical complex. The ion-pair configuration does not exist as a minimum on the ground-state PE surface. The shallow plateau of the S₀ PE function of the water dimer seen around R_OH = 1.8 Å in Fig. 1 develops into a local minimum for a larger water cluster.^48,50 Thus the OH⁻H₃O⁺ ion-pair configuration is stabilized by solvation.

The important aspect of Fig. 1 is the existence of a barrierless reaction path from the vertically excited water dimer in the S₁(πσ*) state to the OH–H₃O radical pair. This property of the water dimer is not expected to be significantly changed by the presence of additional water molecules. Photoexcitation within the first absorption band of water clusters is thus expected to yield hydroxyl and hydronium radicals as primary products. The fact that the onset of the first absorption band of liquid water coincides with the threshold for the production of hydrated electrons^8,17 strongly suggests that the H₃O radical is involved in the photolytic production of the hydrated electron (the OH radical is not a candidate for the hydrated electron, as it does not absorb in the visible and infrared regions.⁸)

The present results for the S₁(πσ*) PE function of the water dimer differ from those of ref. 51. The latter calculations have predicted a substantial barrier for the hydrogen-transfer process in the S₁ state of the water dimer. This barrier is a computational artifact. It arises from the omission of diffuse basis functions, which are essential for the description of the σ* Rydberg orbital, and the lack of excited-state geometry optimization in the calculations of ref. 51.

Knowing that H₃O in its ²A₁ electronic ground state is readily formed by photodissociation of water clusters, we focus in the following on the structure of the electronic ground state of the isolated and micro-solvated hydronium radical and the spectroscopic properties of these species.

3.2 Geometric and electronic structure of H₃O(H₂O)_3m, m = 0, 1, 2, clusters

H₃O is a marginally stable hypervalent radical which has been characterized, in its deuterated form, by mass spectroscopic methods.^52,53Ab initio calculations have shown that the H₃O Rydberg radical corresponds to a shallow local minimum of the H + H₂O/H₂ + OH PE surface.^29–32 The barrier for decay into H + H₂O is too low to allow for a significant lifetime of the vibrational ground state.^29,30 H₃O itself is certainly too short-lived to be associated with the solvated electron, which has a lifetime of the order of microseconds in pure liquid water.²

Although neutralized ion-beam studies have shown that the hydronium radical is stabilized by solvation,⁵³ it seems that hydronium–water clusters have not been investigated so far by accurate ab initio calculations. We have performed geometry optimizations of selected H₃OW_n clusters with n < 10.²⁸ A comprehensive discussion of the possible structures of H₃OW_n clusters and their relative stabilities is beyond the scope of the present paper. We restrict our attention here to the H₃OW₃ and H₃OW₆ complexes, which correspond to the closing of the first and second solvation shells of the H₃O radical.

The most stable H₃OW₃ cluster processes C₃ symmetry. The C_3v isomer, however, is only 0.6 kcal mol⁻¹ higher in energy at this level of theory (DFT/B3LYP). The minimum-energy structure is shown in Fig. 2 as a stick model. The length of the hydrogen bond between H₃O and H₂O is 1.551 Å (1.559 Å for the C_3v isomer), indicating a fairly strong hydrogen bond. The corresponding bond length in H₃O⁺W₃ is 1.533 Å. The HOH bond angle of the central H₃O unit is 107.0° (107.4° for the C_3v isomer), significantly smaller than in the H₃O⁺W₃ cluster (115.0°).

Fig. 2 Equilibrium geometries in the electronic ground state of H₃O and the H₃OW₃ and H₃OW₆ clusters. The left panel shows the view along the symmetry axis, the right panel shows a side view.

The lowest-energy conformation of the H₃OW₆ cluster possesses C_3v symmetry. The C₃ isomer is higher by 3.7 kcal mol⁻¹ in this case. The C_3v structure is illustrated in the lower part of Fig. 2. The length of the hydrogen bond between H₃O and H₂O for the two isomers is 1.528 and 1.501 Å, respectively, indicating an even stronger hydrogen bond than in the H₃OW₃ cluster. The second water shell is more weakly bound, as indicated by the hydrogen bond lengths (1.956 and 1.657 Å for the two isomers, respectively). The addition of the second solvation shell changes the HOH bond angle of the central H₃O unit only moderately (105.4° and 110.1°, for the two isomers, respectively). It is worth noticing that the structure of the C₃ isomer, in particular, is approaching that of the H₃O⁺W₆ cluster, for which the corresponding values are: 1.504 Å, 1.730 Å and 114.0°.

A remarkable aspect of the electronic structure of hydrated hydronium is illustrated in Fig. 3. This figure displays the singly occupied ROHF molecular orbital of H₃O, H₃OW₃ and H₃OW₆. It is seen that the 3s Rydberg-type orbital of H₃O detaches from the H₃O⁺ ionic core in H₃OW₃ and H₃OW₆. In the H₃OW₃ complex, the hydronium cation forms strong hydrogen bonds with three water molecules, which in turn solvate the charge distribution of the unpaired electron. In the H₃OW₆ complex, two water shells separate the H₃O⁺ cation and the electronic cloud.

Fig. 3 The singly occupied highest molecular orbital of H₃O, H₃OW₃ and H₃OW₆, calculated at the ROHF level.

The trend illustrated by Fig. 3 continues when further solvation shells of water molecules are added. The very stable and rigid H₃O⁺ ion enforces a three-fold symmetry of all clusters of the type H₃OW_3m, m = 1, 2, 3...... In calculations for clusters up to m = 3 we have found that the unpaired electron prefers to localize outside the hydrogen-bonded water network.²⁸

The hydronium radical thus dissolves into a solvated hydronium cation and a solvated electron cloud in an aqueous environment by a spontaneous charge-separation process. This finding, together with the results of the preceding subsection, suggests a close relationship between hydrated hydronium clusters of various sizes and the hydrated electron in liquid water.

The structures shown in Fig. 3 exhibit similarities with the structures found in ab initio calculations on solvated halogen anions.^39–41 With the exception of F⁻(H₂O)_n,³⁹ these clusters prefer structures where the anion is located on the surface and the non-hydrogen-bonded H atoms are oriented towards the negative ion.^40,41 Interesting structural similarities also exist with HCl(H₂O)_n clusters. The global minimum of the HCl(H₂O)₄ cluster is a zwitterionic Cl⁻(H₂O)₃ H₃O⁺ structure⁵⁴ with a similar geometry as the H₃O(H₂O)₃ cluster in Fig. 3.

3.3 Stability of hydrated hydronium

Fig. 4 shows CASPT2 PE profiles along the minimum-energy path for the detachment of a hydrogen atom from H₃O (a) and H₃OW₃ (b). Fig. 4(a) illustrates the well-known fact that the hydronium radical is less stable by about 21 kcal mol⁻¹ than the H + H₂O dissociation limit.^29,30 The local PE minimum of C_3v symmetry is separated by a barrier of about 3.6 kcal mol⁻¹ from the H + H₂O dissociation channel.^29,30 Our result of 2.7 kcal mol⁻¹ is in reasonable agreement with that value.

Fig. 4 MP2 PE functions of the D₀ state of H₃O (a) and H₃OW₃ (b), calculated along the minimum-energy reaction path for hydrogen detachment.

Fig. 4(b) shows the corresponding energy profile for the removal of a hydrogen atom from the H₃OW₃ cluster. The rearrangement of the cluster during this dissociation process is illustrated by several snapshots of the geometric structure along the reaction path. The hydrogen-detachment process involves a hydrogen shift from the central hydronium unit to one of the terminal waters via a Zundel-type transition state. The terminal hydronium then dissociates, yielding an (H₂O)₄ cluster and an H atom.

It is seen that hydrogen detachment from H₃OW₃ is a considerably less exothermic process than hydrogen detachment from H₃O. Moreover, the barrier separating H₃OW₃ from the dissociation channel is found to be 7.0 kcal mol⁻¹ and is thus significantly larger than the barrier in bare H₃O. This finding is in agreement the results of neutralized ion beam experiments, which have demonstrated enhanced stability of the H₃OW₃ cluster.⁵³

Calculations of the type shown in Fig. 4(b) have to be extended to larger clusters. It is strongly suggested by the present preliminary results, however, that H₃OW_3m, m = 1, 2, 3...., clusters are considerably more stable and long-lived than the bare hydronium radical. It is an interesting open question whether H₃OW_n clusters are thermodynamically stable with respect to hydrogen detachment for n → ∞. In any case, larger H₃OW_n clusters should be at least kinetically stable with respect to the hydrogen-detachment reaction. It should thus be possible to obtain spectroscopic data on size-selected H₃OW_n clusters.

It has recently been shown by Jouvet and collaborators^55,56 and Fujii and collaborators⁵⁷ that long-lived NH₄(NH₃)_n clusters are formed by UV excitation of phenol–ammonia clusters via a hydrogen-transfer reaction in the excited state and subsequent dissociation. Ishiuchi et al. have shown that it is possible to obtain size-specific IR spectra of these clusters by double-resonance techniques.⁵⁷ Although excited-state hydrogen transfer is less facile in phenol–water than in phenol–ammonia clusters,^25,55 it should be possible to obtain in this way spectroscopic information on size-selected H₃OW_n clusters.

It is an obvious consequence of the PE function of Fig. 4(b) that D₃O(D₂O)_n clusters are kinetically more stable than H₃O(H₂O)_n clusters. This isotope effect is well known for hydronium–water clusters in the gas phase.^52,53 On the other hand, the proposed connection of the solvated electron with hydronium–water cluster structures can provide the explanation of an unexpected isotope effect in the liquid phase: the yield of solvated electrons at short (picosecond) times in pulse radiolysis experiments in heavy water is substantially higher than in water.⁵⁸

3.4 Electronic and vibrational spectra of H₃O and hydrated H₃O

It has been noted previously that the 3s → 3p transition in H₃O is expected to fall into the energy range of the absorption spectrum of the hydrated electron.^20,34 More recently, Muguet has calculated the vertical excitation spectrum of hydronium (and dihydronium) with a MCSCF-propagator method.²² He reported 2.0 eV for the 3s → 3p(E) excitation energy of bare H₃O. Employing a reaction field continuum model of solvation, Muguet has estimated the excitation energy of hydronium in liquid water to be in the range 1.8–2.0 eV.²²

Fig. 5 shows the present CASPT2 vertical electronic excitation energies and oscillator strengths of H₃OW_3m clusters for m = 0, 1, 2. The thick bar represents the excitation energy and oscillator strength (to be multiplied by two) of the degenerate ²E(p_xy) state, while the thin bar represents the ²A(p_z) state. The excitation energy of the ²E state of H₃O is found to be 2.20 eV, in good agreement with the result of Muguet.²²

Fig. 5 Vertical electronic excitation spectra of H₃O (a), H₃OW₃ (b) and H₃OW₆ (c), calculated at the CASPT2 level. Bold sticks denote transitions from D₀ to the degenerate ²E(p_x,y) state, thin sticks represents transitions to the ²A(p_z) state.

It is seen that microsolvation of H₃O by three water molecules shifts the excitation energy markedly to the red, to 1.06 eV for the ²E state. This reflects the fact that H₃OW₃ is not a solvated Rydberg molecule (for which a blue shift of the absorption spectrum is expected), but a microsolvated electron–ion complex. In H₃OW₆ the ²E and ²A₂ excitation energies are close to each other, near 1.5 eV. The sum of the oscillator strengths is close to unity, decreasing slightly for larger clusters.

The calculated excitation energies of small H₃OW_3m clusters essentially cover the energy range of the absorption of the hydrated electron, which extends from about 0.8 to about 3.0 eV.^1,2 The electronic absorption of a statistical distribution of H₃OW_n clusters thus can provide a partial explanation of the large width of the absorption spectrum of the hydrated electron. The inclusion of nuclear-motion effects is indispensable, of course, for a quantitative simulation of the spectrum.

The calculated vibrational spectra of H₃O, H₃OW₃ and H₃OW₆ are shown in Fig. 6. The spectra have been obtained in the harmonic approximation with the DFT/B3LYP method. Thick bars represent degenerate vibrational levels (their intensity has to be multiplied by two), thin bars, nondegenerate levels. While the harmonic approximation is questionable for H₃O, it should be reasonably accurate for H₃OW₃ and the larger clusters (cf.Fig. 4). The H₃O spectrum has been included in Fig. 6 to point out that already the bare H₃O radical exhibits a very intense absorption of the OH stretch vibration. Its intensity exceeds that of the most intense absorption of the H₂O molecule by nearly two orders of magnitude. For H₃OW₃, an even more intense absorption (I ≈ 6000 km mol⁻¹) is predicted near 3500 cm⁻¹, which shifts to ≈3300 cm⁻¹ in H₃OW₆ (note that these are harmonic estimates; the fundamentals of OH stretch vibrations are expected to be lower than the harmonic vibrational frequencies by about 150 cm⁻¹). The intense OH stretch absorptions above 3000 cm⁻¹ in H₃OW₃ and H₃OW₆ are associated with the water molecules in the first solvation shell of the electron cloud. The OH stretch vibration of the H₃O⁺ unit is less intense and located near 2500 cm⁻¹ in H₃OW₃ and H₃OW₆. It is expected that the OH stretch lines are strongly broadened, a phenomenon which is generally observed for the stretching vibrations of OH groups directly involved in hydrogen bonding.⁵⁹

Fig. 6 Vibrational spectra of H₃O (a), H₃OW₃ (b), and H₃OW₆ (c), calculated in the harmonic approximation at the DFT/B3LYP level. Bold sticks denote transitions to degenerate (E) vibrational levels, thin sticks represent transitions to nondegenerate (A) levels. The dashed lines connect the OH stretching bands of H₃O with those of the central H₃O⁺ unit of the clusters.

Intense IR absorptions in the range 3200–3400 cm⁻¹ have been detected by Johnson and collaborators in negatively charged water clusters as well as in X⁻H₂O (X = Br, I) clusters.^60–62 These characteristic lines have been assigned to “free OH groups interacting with the excess electron”.^60–62 The existence of these fingerprint OH vibrations in H₃OW_3m clusters is a clear signature of the charge-separated structure of these species. Moreover, the value of ≈2500 cm⁻¹ found for the OH stretch vibration of the H₃O⁺ unit in H₃OW_3m clusters is very close to that found for the OH stretch vibration of the hydronium cation in protonated water clusters.⁶³ This observation provides additional evidence for the charge-separation process in H₃OW_3m clusters.

To the knowledge of the authors, experimental IR spectra of size-selected H₃OW_n clusters have not yet been reported. Very recently, the first transient midinfrared spectra of the hydrated electron in water and heavy water have been obtained by Laenen et al.¹⁰ A strong transient absorption positioned at ≈2.9 μm (3450 cm⁻¹) in H₂O corresponds well in frequency and intensity to the present prediction for H₃OW₃ and H₃OW₆ clusters.

4. Conclusions

It has been shown that a barrierless hydrogen-transfer reaction takes place in the S₁ state of the water dimer, yielding the hydroxyl radical and the hydronium radical. The same hydrogen-transfer process can be expected to take place in larger water clusters and in liquid water, yielding solvated hydroxyl and hydronium radicals. We have explored in some detail the microsolvation of the hydronium radical using ab initio and DFT methods. The structure and the spectroscopic properties of selected H₃OW_n clusters have been discussed with respect to the possible relationship of these species with the hydrated electron. The conclusions of this investigation can be summarized as follows:

(i) H₃O radicals are formed by a barrierless hydrogen-transfer reaction in the lowest excited singlet state of water clusters. This finding strongly suggests that the H₃O radical should be involved in the sequence of ultrafast processes following photoabsorption in liquid water.

(ii) Microsolvation of the H₃O radical leads to a charge-separated complex, consisting of a hydronium cation and a localized electron cloud, which are connected by a water network. The particularly stable H₃O⁺ species enforces a rather rigid structure of these complexes, especially for closed solvation shells, H₃OW_3m, m = 1, 2, 3.... For the clusters investigated so far (m < 4),²⁸ the electron cloud localizes outside the water network, being solvated by a shell of three water molecules.

(iii) The H₃OW₃ cluster is considerably more stable than the bare H₃O radical with respect to the detachment of a hydrogen atom, but is still a metastable species. The activation energy for the decomposition of the H₃OW₃ complex is estimated as 7 kcal mol⁻¹.

(iv) The vertical excitation energies of the s → p electronic transition of H₃OW_3m clusters scatter between 1.1 and 3.0 eV. The first solvation shell (m = 1) induces a large redshift of the s → p transition, which is followed by a gradual, but not monotonic, blueshift when additional solvation shells are added (m = 2, 3....).²⁸ The absorption lines of different clusters cover roughly the energy range of the absorption spectrum of the hydrated electron. The sum of the oscillator strengths of the D₀ → ²E(p_xy) and D₀ → ²A(p_z) transitions is close to unity. The rigidity of the water network associated with the H₃O⁺-electron charge-separated complex can provide an explanation of the amazing shape stability²¹ of the absorption spectrum of the hydrated electron.

(v) H₃OW_3m clusters are predicted to exhibit a very intense (4000–6000 km mol⁻¹) OH stretch absorption in the range between 3400 cm⁻¹ (H₃OW₃) and 3200 cm⁻¹ (larger clusters). This IR absorption represents the OH stretch vibration of the water molecules in the first solvation shell of the electron. It is suggested that this absorption can be considered as a fingerprint of the hydrated electron.

A substantiation of the proposed connection between the properties of individual H₃OW_n clusters and the properties of the hydrated electron in water requires ab initio molecular-dynamics simulations for a hydronium radical in a large ensemble of water molecules at finite temperature. Even short of such simulations, it can be concluded that the empirical model potentials employed in current simulations of the hydrated electron (see refs. 14, 15 and references therein) should be scrutinized whether they are able to reproduce the present ab initio results for clusters. A major limitation of the simulations supporting the cavity model of the hydrated electron may be the assumption of rigid (or at least nondissociating) water molecules. This assumption is called into question by the present ab initio results on the photochemistry of water clusters.

Acknowledgements

The authors would like to thank Francis Muguet and Dominik Marx for stimulating discussions. This work has been supported by the Deutsche Forschungsgemeinschaft and the Committee for Scientific Research of Poland (grant No. 3T09A 082 19).

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