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Spectral Signatures of Hydrated Proton Vibrations in Water Clusters

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Science  17 Jun 2005:
Vol. 308, Issue 5729, pp. 1765-1769
DOI: 10.1126/science.1113094

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Abstract

The ease with which the pH of water is measured obscures the fact that there is presently no clear molecular description for the hydrated proton. The mid-infrared spectrum of bulk aqueous acid, for example, is too diffuse to establish the roles of the putative Eigen (H3O+) and Zundel (H5O2+) ion cores. To expose the local environment of the excess charge, we report how the vibrational spectrum of protonated water clusters evolves in the size range from 2 to 11 water molecules. Signature bands indicating embedded Eigen or Zundel limiting forms are observed in all of the spectra with the exception of the three- and five-membered clusters. These unique species display bands appearing at intermediate energies, reflecting asymmetric solvation of the core ion. Taken together, the data reveal the pronounced spectral impact of subtle changes in the hydration environment.

Despite the ubiquity of aqueous acids in chemical and biological systems (17), a molecular-level description of the hydrated proton remains elusive (814). The suggestion in introductory chemistry texts that the dominant speciation occurs as “hydronium” [H3O+, also called the Eigen (9) core] is too simplistic; an alternative limiting form proposed by Zundel (10) (H2O···H···OH2)+ has long been thought to play an essential role, and the broad infrared absorptions of the aqueous proton at 1250, 1760, and 3020 cm–1 have been assigned in the context of both the Eigen and Zundel species (1517). Here, we characterize the hydrated proton using a bottom-up approach. Through recent advances in laser generation of infrared light in the 1000- to 4000-cm–1 range, we directly monitor the spectral evolution of the proton accommodation motif as water molecules are sequentially added to the hydronium ion, up to an 11-membered cluster.

Infrared spectra of bare H+ · (H2O)n clusters in the OH stretching region (2800 to 3900 cm–1, with inconsistent coverage below 2800 cm–1) have already been reported, and the observed bands are mostly attributed to water molecules remote from the proton (1823). Dangling water molecules attached to the exterior of a hydrogen-bonded network, for example, produce sharp bands arising from the symmetric (νs) and asymmetric (νa) stretches of the nonbonded OH groups. Theoretical analysis of these spectra indicated a Zundel motif for the two-, six-, seven-, and eight-membered clusters, but an embedded Eigen core for the three- to five-membered clusters (Fig. 1).

Fig. 1.

(A to G) Minimum-energy structures of H+ · (H2O)2–8. Geometries were calculated at the MP2/aug-cc-pVDZ level of theory.

The vibrations associated with the excess charge in these structures occur at much lower energies than were accessible in the early experimental studies (1823), and thus recent work has concentrated on extending the spectral range below 2100 cm–1. Spectra in this lower energy region (600 to 1900 cm–1) have already been obtained for the H5O2+ ion (2427). The patterns displayed by the bare complexes were quite complicated (24, 25), but a much simpler spectrum was obtained when H5O2+ was cooled by attachment of weakly bound Ar and, very recently, Ne atoms (26, 27). Here, we extend the argon “messenger” (18) measurements to clusters with up to 11 water molecules and survey the critical low-energy region of the vibrational spectrum. This approach allows us to characterize most of the important vibrations associated with the excess positive charge.

The H+ · (H2O)n vibrational spectra were obtained by photoevaporation of a weakly bound argon atom in a photofragmentation mass spectrometer (28, 29). The enabling experimental advance was extension of the Yale infrared laser source (Laser Vision) down to 1000 cm–1 using parametric conversion in AgGaSe2 (30). To aid in the interpretation of the spectra, we optimized the geometries of the clusters and calculated the harmonic frequencies at the MP2/aug-cc-pVDZ (31) level of theory using the Gaussian 03 program (32). For the two- to five-membered clusters, anharmonic spectra were calculated using the vibrational SCF (VSCF) method (33) as implemented in the GAMESS program (34).

We begin our discussion with the Eigen cation, H+ · (H2O)4, which has a minimum-energy structure well described as an H3O+ Eigen core, symmetrically solvated by three dangling water molecules (Fig. 1C) (9). The scaled harmonic frequencies calculated for this structure agree reasonably with the measured spectra (Fig. 2), where the outer water molecules contribute the two sharp OH stretching bands highest in energy. Most important is the strong band at 2665 cm–1, which theory (red bars) matches to the degenerate asymmetric OH stretching vibration in an intact Eigen core. Thus, the first hydration shell acts to red-shift the intrinsic OH stretching motions of the isolated H3O+ ion (35) (blue arrows labeled H3O+ νasym at the bottom of Fig. 2) by more than 860 cm–1, placing the band just below the range scanned in previous studies of this system (1820).

Fig. 2.

Vibrational predissociation spectrum of the H+ · (H2O)4 · Ar complex. The OH asymmetric stretch (νasym) and asymmetric bending (νbend) bands of bare H3O+ are denoted by arrows (35, 36), whereas the calculated harmonic spectrum (MP2/aug-cc-pVDZ level, 0.955 scaling) of H+ · (H2O)4 is displayed by bars. The Eigen core stretches are highlighted in red. The sharp bands highest in energy arise from the symmetric (νs) and asymmetric (νa) OH stretches of the dangling water molecules in the first hydration shell, with their associated intramolecular bending transitions (νb) at ∼1600 cm–1.

Several transitions are also recovered in the lower energy region. The sharp feature (νb) at 1620 cm–1 can be readily assigned to the HOH intramolecular bends of the dangling water molecules, and the weak unresolved feature emerging at 1045 cm–1 is traced to the symmetric bending motion of the H3O+ ion core along its principle axis. The broader features near 1760 and 1900 cm–1 occur just above the equatorial bends in isolated H3O+ (36). It seems likely that these transitions are due to similar bending motions in the embedded H3O+ ion, although they are not anticipated at the harmonic level, and the 1760-cm–1 transition appears markedly similar to that displayed by the isolated Zundel ion (top trace in Fig. 3). Thus, even this simple, symmetrical cluster yields spectral complexity beyond that expected at the harmonic level.

Fig. 3.

Argon predissociation spectra of H+ · (H2O)n, n = 2 to 11, with n increasing down the figure. Dangling waters attached to the exterior of the cluster network are identified by sharp features assigned to the symmetric (νs) and asymmetric (νa) OH stretches. The sharp band near 1600 cm–1 arises from the bending modes of dangling OH groups. The bands most closely associated with the motions of H atoms bearing the excess charge are highlighted in red. This stretching feature first evolves toward higher energy as the excess charge approaches maximal delocalization at n = 4, but then returns to lower energy as more water molecules are added. The persistence of the intact Zundel signature (νz) in the six- to eight-membered cluster spectra indicates that the excess charge is preferentially retained on one strongly shared proton in this size range. Bands derived from the OH stretches bridging the Zundel ion to the first hydration shell are highlighted in blue, whereas the analogous bands involving the Eigen ion are indicated in green. The purple feature in the n = 5 spectrum is assigned to the OH stretches of the H3O+ ion bound to the two single acceptor water molecules (left side of Fig. 1D). Spectral features not readily recovered at the harmonic level are denoted with an asterisk (*).

Having established the spectral signature of the symmetrically hydrated Eigen core, we can interpret the evolution of the spectra as water molecules are removed from or added to this complete hydration shell, effectively mimicking rudimentary solvent fluctuations. The 2- to 11-membered cluster spectra (Fig. 3) persistently show sharp HOH intramolecular bending bands (νbend ∼1620 cm–1) (37), as well as two to four nonbonded OH stretches centered near 3695 cm–1. The latter bands were analyzed previously (1821). Here, we are primarily interested in the broader features (highlighted in red) associated with stretching motions of the H atoms bearing the excess charge. The frequency of these strong absorptions ranges from 1000 to 2700 cm–1 depending on the degree of excess charge localization.

To unravel the information contained in these spectra, we first consider removing a water molecule from the fully hydrated Eigen core to form H+ · (H2O)3. Although the resulting cluster is structurally characterized as an Eigen-based species (Fig. 1B), the 2665-cm–1 signature band of the Eigen cation is absent from its spectrum (Fig. 3). Instead, two strong bands emerge at 1880 and 3580 cm–1. The calculations (Table 1) trace this pattern to a dramatic (∼1700 cm–1) splitting of the strong Eigen feature in H+ · (H2O)4 upon removal of a water molecule. Thus, the lowest of these transitions (highlighted in red in Fig. 3) arises from the asymmetric stretch of the two solvated protons, and the higher frequency 3580-cm–1 band involves the stretch of the unsolvated proton on the H3O+ core, which falls close to the OH stretch in bare H3O+. (35) Removal of one water molecule from the complete hydration shell around H3O+ thus leads to concentration of the excess charge onto two shared protons, pulling the two solvating water molecules closer to the Eigen core and thereby red-shifting the associated OH stretch bands. In contrast to the behavior displayed by H+ · (H2O)4, anharmonic corrections (33) are required to qualitatively recover the large observed red-shifts in the lower energy H+ · (H2O)3 stretching transitions.

Table 1.

Comparison of the calculated and measured OH-stretch vibrational frequencies for the H+ · (H2O)n, n = 2 to 6 clusters. Calculated anharmonic (VSCF) frequencies, where available, are reported in parentheses. All other values are from harmonic calculations, unscaled in the case of the shared proton in the two Zundel ions and scaled by 0.955 to account approximately for vibrational anharmonicity in all other cases.

Description νcalc (cm-1) νexpt (cm-1)
n = 2
Proton oscillation 807 (1223) 1085
H2O symmetric stretch 3552 (3546), 3558 (3538) 3520,View inline 3615View inline
H2O asymmetric stretch 3660 (3594), 3661 (3585) 3660,View inline 3695View inline
n = 3
H3O+ asymmetric stretch 2381 (1984) 1880
H3O+ symmetric stretch 2509 (2363) 2420
H2O symmetric stretch 3604 (3532), 3605 (3569) 3639
H3O+ free-OH stretch 3626 (3532) 3580
H2O asymmetric stretch 3718 (3668), 3718 (3674) 3724
n = 4
H3O+ asymmetric stretch 2804 2665
H3O+ symmetric stretch 2874
H2O symmetric stretch 3612-3613 3644
H2O asymmetric stretch 3725-3725 3730
n = 5
H3O+ stretch to AD-typeView inline H2O 2344 (1852) 1885
H3O+ asymmetric stretch 2942 2860
H3O+ symmetric stretch 2971
AD-type H2O H-bond stretch 3257 3195
H2O symmetric stretch 3615-3623 3647
AD-type H2O free-OH stretch 3695 3712
H2O asymmetric stretch 3729-3741 3740
n = 6
Proton oscillation 1209 1055
H2O in H5O2+ symmetric stretch 3128 3160
H2O in H5O2+ asymmetric stretch 3143
H2O in H5O2+ symmetric stretch 3274
H2O in H5O2+ asymmetric stretch 3320
H2O symmetric stretch 3618-3625 3650
H2O asymmetric stretch 3734-3744 3740
  • View inline* The observed OH stretch splittings are induced by the argon “messenger” atom. Our results correlate well with those of (19), where the messenger was H2.

  • View inline AD-type H2O molecules accept and donate a H-bond.

  • Removal of a second water molecule from H+ · (H2O)4 creates the isolated Zundel ion, (H2O···H···OH2)+ (Fig. 1A), which has recently been reported and discussed in detail (2427). Its infrared spectrum (top trace in Fig. 3) is dominated by a strong transition at 1085 cm–1, arising from oscillation of the shared proton along the O–O axis, with a higher energy transition at 1770 cm–1 assigned to the out-of-phase bending vibrations of the flanking water molecules (26). The ∼800-cm–1 incremental red-shift of the bands associated with the excess positive charge in going from H+ · (H2O)3 to H5O2+ is about the same as that observed upon removal of the first water molecule from the fully hydrated Eigen core. Surprisingly large spectral shifts are thus driven by changes in the hydration environment.

    We now turn to the systematic addition of water molecules to H+ · (H2O)4, nominally forming a second solvation shell. In the H+ · (H2O)5 spectrum (Fig. 3), three sharp bands appear in the high-energy nonbonded OH stretch region, consistent with the Eigen-like structure shown in Fig. 1D. Broader features also emerge that are unique to this cluster. In particular, an intense band (highlighted in purple in Fig. 3) appears ∼200 cm–1 above the 2665-cm–1 signature absorption of the H+ · (H2O)4 Eigen ion. An unusual solvation-induced blue-shift seems unlikely, given that two new bands also appear at much lower energy (1490 and 1885 cm–1). This pattern again raises the possibility that the degenerate Eigen vibrations are strongly split upon addition of the fourth water molecule, much as they were upon removal of a water molecule to form H+ · (H2O)3.

    The harmonic frequency calculations (Table 1) for the H+ · (H2O)5 structure (Fig. 1D) anticipate a splitting of the Eigen vibrations, but severely underestimate the effect, with the three OH stretch vibrations of the Eigen core predicted to occur at 2344, 2942, and 2971 cm–1. The two blue-shifted transitions are clearly derived primarily from the two protons of the Eigen core vibrating toward dangling water molecules in the first hydration shell. The calculated 2344-cm–1 OH stretch of the Eigen core, predicted to red-shift as the proton becomes solvated by a water dimer, still overshoots the experimental band at 1885 cm–1 by 459 cm–1. The strong redshift of this vibration is thus a consequence of excess charge concentration on the proton with two hydration shells coupled with pronounced vibrational anharmonicity. Vibrational self-consistent field calculations predict this stretch to resonate at 1852 cm–1, close to the experimentally observed feature. This strong anharmonicity in the excess proton stretching vibration is analogous to that observed in the H+ · (H2O)3 cluster.

    The addition of a second water molecule to H+ · (H2O)4 to give H+ · (H2O)6 creates a favorable geometry for capturing the symmetrical Zundel ion (Fig. 1E) within a complete first hydration shell. This arrangement has been identified previously (38) and is evidenced by the simple doublet in the free OH stretching region, similar to that found in the spectrum of the Eigen cation. This structure can be viewed as further stabilizing the preferentially hydrated proton in H+ · (H2O)5 such that it becomes equally shared between two oxygen atoms. The resulting H+ · (H2O)6 spectrum (Fig. 3) has a very strong transition at 1055 cm–1, nearly the same frequency as the transition associated with oscillation of the bridging proton in the isolated Zundel ion. Thus, the characteristic signature of the local, shared proton motion is virtually unperturbed upon formation of a hydration shell, in strong contrast to the more charge-delocalized Eigen arrangement, where the H3O+ stretching bands shift by almost 860 cm–1 upon hydration [i.e., in going from H3O+ to H+ · (H2O)4].

    The excess proton transitions in the spectra of the two- to six-membered clusters reveal an interesting progression in the distribution of excess charge with increasing size, first delocalizing over three protons in the Eigen cation then contracting back onto one proton in the six-membered cluster. Such oscillatory behavior naturally raises the question of whether this trend persists in the larger clusters. The spectra immediately establish that a simple repetition of the small-cluster evolution does not occur, because the 1055-cm–1 Zundel signature is maintained in the seven- and eight-membered clusters, even when strong variations in the higher energy OH stretching bands signal changes in the exterior network morphologies (Fig. 3). The calculated geometries anticipate this behavior, however, because the additional water molecules result in ring structures (Fig. 1, F and G) that preserve the quasi-symmetrical environment of the embedded Zundel motif. The character of these spectra is interesting in light of a recent paper reporting the OH stretching spectra of the bare clusters at temperature T≈ 170 K (21). In that study, the observed spectra of the six- and seven-membered clusters were assigned to a mixture of Eigen- and Zundel-based isomers, whereas the eight-membered cluster spectrum was attributed to a single Zundel-based isomer. The Ar-tagged six- to eight-membered clusters, in contrast, are all clearly dominated by Zundel-based isomers. Although the free OH stretches are similar in the three cases, notable differences arise in the lower energy H-bonded stretches in the 3200- to 3600-cm–1 range. The H+ · (H2O)8 spectrum actually appears quite similar in both the bare and Ar-tagged species, because the Ar predissociation spectrum displays sharper bands centered at almost the same locations. The bands in blue (Fig. 3) highlight the transitions associated with the OH stretches of the Zundel water molecules toward the second solvation shell, which shift toward higher energy with increasing cluster size. The isomers assigned to the observed spectra are shown in Fig. 1. These structures are also calculated to correspond to the minimum-energy isomers (after zero-point corrections).

    Although previous work anticipated a change from Zundel to Eigen structures in progressing from eight to nine water molecules (39), the change in the low-energy bands here is pronounced. The nine-membered cluster spectrum displays very broad background absorption throughout the entire 2300- to 3000-cm–1 range, reminiscent of the excess proton spectrum in bulk water (17), whereas a distinct band near the Eigen signature at 2600 cm–1 is reestablished in the 10- and 11-membered clusters. None of the clusters in the size range from 9 to 11 display absorption near the Zundel band at 1000 cm–1. The return of the embedded H+ · (H2O)4 Eigen cation is accompanied by a red-shift of the OH stretches bound to the first solvation shell (green). Notably, for nine or more water molecules, the free OH stretching bands appearing highest in energy are dominated by the doublet attributed to water molecules in AD and AAD (A is H-bond acceptor, D is H-bond donor) environments. Also noteworthy is the emergence of a relatively sharp feature near 3600 cm–1 in the spectrum of H+ · (H2O)10, which persists in the spectra of very large clusters and has been attributed to water molecules in a DDA site within the network (2123).

    The picture emerging from these cold cluster studies is that the excess proton transitions associated with the OH stretches of the Eigen cation occur highest in energy relative to the other accommodation motifs because it affords maximum charge delocalization (i.e., over three H atoms). Small asymmetries in the hydration structure around the H3O+ core result in preferential localization of the excess charge on one or two of the H atoms, as emphasized in the theoretical work by Parrinello (13) and Singer (40). This charge redistribution causes pronounced, size-dependent shifts of up to 1600 cm–1 in the characteristic absorptions nominally assigned to the excess proton. Such an extreme response to symmetry breaking would readily explain the lack of a sharp spectral signature of the hydrated proton in the bulk and would be consistent with Zundel's model of a highly polarizable excess proton (10).

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