Accumulating evidence for the Zundel motif
In recent years, vibrational spectroscopy has been homing in on how water accommodates dissolved protons in acidic solution. Most such studies have examined adjacent stretching or bending modes. Dahms et al. pinpoint the vibrational dynamics of the acidic proton itself, which is sandwiched between two water molecules in a so-called Zundel motif. Comparing spectra in bulk water and in acetonitrile (a known Zundel host) revealed the persistence of this motif in aqueous acid on a subpicosecond time scale. Persistence is sustained by the hydrogen-bonding network among the surrounding water molecules.
Science, this issue p. 491
Abstract
Solvation and transport of excess protons in aqueous systems play a fundamental role in acid-base chemistry and biochemical processes. We mapped ultrafast proton excursions along the proton transfer coordinate by means of two-dimensional infrared spectroscopy, both in bulk water and in a Zundel cation (H5O2)+ motif selectively prepared in acetonitrile. Electric fields from the environment and stochastic hydrogen bond motions induce fluctuations of the proton double-minimum potential. Within the lifetime of a particular hydration geometry, the proton explores a multitude of positions on a sub-100-femtosecond time scale. The proton transfer vibration is strongly damped by its 20- to 40-femtosecond population decay. Our results suggest a central role of Zundel-like geometries in aqueous proton solvation and transport.
The hydration of excess protons in water has been described in the context of two limiting structures: In the Zundel cation (H5O2)+ (1), the proton H+ forms strong hydrogen bonds to two flanking water molecules (Fig. 1A), whereas in the Eigen complex (H9O4)+ (2), a central hydronium ion H3O+ is equally solvated by three water molecules. Although spectroscopic and theoretical analyses have identified these two and related species as stable structures in ultracold water clusters (3–6), their abundance and properties in liquid water at ambient temperature have to a large extent remained elusive.
(A) Schematic of the Zundel cation H5O2+. The arrows indicate the (O···H+···O) proton transfer coordinate z and the O···O coordinate R. (B) Anharmonic vibrational potential (left) and double-minimum potential of the Zundel cation along z (right), with a particular distortion in an external electric field (right, dotted line). (C) Linear absorption spectrum of protons solvated in H2O (top) and Zundel cations in CH3CN (bottom) measured in attenuated total reflectance and transmission mode, respectively, with a proton concentration of 0.6 M introduced to solution through HI acid dissociation, and a water concentration of 2.1 M. Solid black lines show the difference spectrum after subtraction of the H2O and CH3CN background (dotted lines). The absorption due to the v = 0 to 1 transition of the proton transfer mode z is marked in red.
In the bulk liquid, thermally activated motions of water molecules lead to pronounced structural fluctuations at femto- to picosecond time scales (7). Underlying processes range from sub-100-fs librational motions to the picosecond breaking and reformation of intermolecular H bonds. The dipolar water molecules generate strong fluctuating electric fields that act on the highly polarizable proton environment (8). As a result, the solvation geometry of the proton is expected to change rapidly, with the limiting Zundel and Eigen geometries persisting only for short periods in between H-bond breaking and reformation events. This structural flexibility and fluxionality is at the heart of proton transport in water, which, according to the traditional von Grotthuss picture, entails shuttling protons through the H-bond network of the liquid rather than hydrodynamic diffusion of particular protons over large distances. Extensive theoretical studies of the key steps of proton transport have generated conflicting views about the role of Zundel and Eigen geometries in the transport mechanism that lack experimental confirmation (9–13).
Femtosecond vibrational spectroscopy gives insight into nuclear motions and probes structural dynamics via their impact on vibrational frequencies and absorption line shapes. For solvated protons, mainly OH stretching and bending excitations of water molecules have been studied (14, 15), rather than the genuine proton degrees of freedom. We applied femtosecond infrared (IR) spectroscopy to the proton transfer vibration, which reflects changes of proton position at the hydration site directly and thus allows for an in-depth characterization of the fluctuating potential energy surface (PES) of the proton. We benchmarked results for protons solvated in liquid H2O with data for the Zundel cation, prepared as the predominant species in the polar solvent acetonitrile (8, 16). In both cases, we found strong evidence for delocalization of the proton in a double-minimum potential along the transfer coordinate z (Fig. 1A), in accordance with the view that Zundel-type complexes are a major solvation motif of the aqueous proton.
IR absorption spectra of protons solvated in bulk H2O and of Zundel cations (H5O2)+ in acetonitrile are summarized in Fig. 1C (solid lines). The broad absorption band between 900 and 1500 cm−1 (Fig. 1C, red) is dominated by the fundamental [vibrational quantum state v = 0 to 1] transition of the proton transfer mode z (17). Using HI to prepare the Zundel cation allows for direct access to this marker band unmasked by additional counterion bands of the acid used (8, 16). A quantitative analysis discussed in the supplementary materials reveals comparable intensities of this band in the acetonitrile and water samples (in water, the band is superimposed on a weak and featureless absorption background from high-frequency water librations). The OH bending and OH stretching absorptions occur at higher frequencies around 1750 cm−1 and between 3000 and 3500 cm−1. The broad absorption continuum between 1500 and 2700 cm−1 has been assigned to combination and overtones of the proton transfer vibration (8).
Two-dimensional IR (2D-IR) spectra were recorded with both samples in the range of the proton transfer fundamental transition (Fig. 2). The femtosecond IR pulses used in these measurements cover the central portion of the proton transfer absorption band, with a total bandwidth of ~250 cm−1 (Fig. 2, A and C). In Fig. 2, B and D, the absorptive 2D signal (18) is plotted as a function of excitation frequency ν1 (ordinate) and detection frequency ν3 (abscissa) for different waiting times T. Yellow-red contours predominant in the ν3-interval from 1050 to 1150 cm−1 correspond to an absorption decrease. Blue contours represent an absorption increase and occur at higher values of ν3. The line shapes of both components cover the full range of excitation frequencies ν1, with minor intensity variations and contour lines essentially parallel to the ν1 axis, even for the earliest waiting times T. These envelopes point to a negligible inhomogeneous broadening and an ultrafast, sub-100-fs correlation loss of excitation and detection frequencies. Protons in water and the Zundel cations in acetonitrile display the same behavior.
(A) 2D-IR spectra of protons in H2O integrated along the excitation frequency ν1 for different waiting times T (colored solid lines). The intensity and the field spectrum of the femtosecond pulses (~100 fs in duration) are shown as black dotted and dashed lines, respectively. (B) Absorptive 2D-IR spectra of protons in H2O for waiting times T = 0, 25, 50, and 100 fs. Yellow-red contours indicate an absorption decrease, and blue contours indicate an absorption increase. Amplitudes are scaled relative to the spectrum taken at T = 0 fs. The signal change between neighboring contour lines is 10%. (C) Same as (A) for Zundel cations in acetonitrile. (D) 2D-IR spectra of Zundel cations in acetonitrile for waiting times T = 0, 25, 50, and 100 fs.
The absorption decrease (Fig. 2, B and D, yellow-red contours) originates from the bleaching of the v = 0 ground state and stimulated emission from the v = 1 state of the proton transfer mode. Most interesting is the blue-shifted absorption increase, which is due to the v = 1 to 2 transition. The blue shift contrasts with the behavior of conventional anharmonic oscillators, displaying a red-shifted transient v = 1 to 2 absorption, but accords with a Zundel-type PES, which is discussed in more detail below.
The 2D signals decay rapidly with increasing waiting time. To assess this ultrafast relaxation, we derived pump-probe spectra from the 2D data by integrating along the ν1 axis (Fig. 2, A and C) (18). The resulting absorption changes decrease to small residual values within ~100 fs. The absorption changes observed in the acetonitrile sample (Fig. 2C) are entirely due to the solvated protons, whereas the small positive absorption change of the water sample at T = 100 fs (Fig. 2A) is caused by water librations imposing a background signal (supplementary materials) (19). Because these pump-probe spectra are limited by the bandwidth of the femtosecond pulses (dashed lines), we performed additional pump-probe measurements covering a much wider frequency range. Figure 3 displays pump-probe spectra in the range of the blue-shifted enhanced absorption and kinetics measured at a fixed probe frequency of 1280 cm−1. In both samples, the enhanced absorption exhibits a sub-100-fs population decay of the v = 1 state of the proton transfer mode, which occurs within the time resolution of the experiment and is followed by weak longer-lived signals (supplementary materials).
(A and B) IR pump-probe spectra for pump-probe delays between 25 fs and 50 ps for protons in H2O (top) and Zundel cations in acetonitrile (bottom). The absorption change ΔA = –log(Texc /T0) is plotted versus probe frequency (Texc and T0 are sample transmission with and without, respectively, excitation by pulses centered at 1200 cm−1). (Inset) Magnified view of spectra from 1140 to 1200 cm−1. (C and D) Time-resolved absorption changes at a probe frequency of 1280 cm−1 (open circles) and numerical fits (solid lines) (supplementary materials). The cross-correlation between pump and probe pulses has a width (full width at half maximum) of 200 fs.
The mechanisms and interactions governing the ultrafast dynamics of the solvated proton are manifested in our key observations: (i) the broad quasi-homogeneous 2D-IR line shapes with a blue-shifted enhanced absorption, (ii) the ultrafast decay of proton-transfer excitations on a sub-100-fs time scale, and (iii) the nearly identical response of protons solvated in water and protons forming a well-defined Zundel cation geometry in acetonitrile. In a prototypical, symmetric Zundel geometry (Fig. 1A), the vibrational PES along the proton transfer coordinate z has a double-minimum shape (Fig. 1B) (1, 5, 6, 8). The height of the central barrier separating the two minima increases with increasing O···O distance R. For the equilibrium average R ≤ 2.50 Å in the liquid phase, however, the v = 0 ground state of the proton transfer mode is above the central barrier (figs. S5 and S6). Both the v = 0 to 1 and v = 1 to 2 vibrational transitions are dipole-allowed, with the v = 1 to 2 transition exhibiting a frequency higher than that of the v = 0 to 1 transition (Fig. 1B), in contrast to a single-minimum anharmonic oscillator PES. Thus, the blue-shifted enhanced absorption in the 2D-IR and pump-probe spectra (Figs. 2 and 3) unequivocally supports the low-barrier, double-minimum character of the vibrational PES in this strongly hydrogen-bonded system.
In a polar liquid environment at ambient temperature, the hydration geometry of the proton and the outer solvation shells fluctuate on multiple time scales (7, 8, 20). Such fluctuations affect the PES of the proton transfer mode (i) through electric fields that the environment exerts on the highly polarizable hydrated proton, affecting symmetry and shape of the PES, and (ii) through stochastic induced changes to the O···O distance R, modifying height and width of the central potential barrier. Both mechanisms lead to a strong ultrafast modulation of the PES fluctuating between asymmetric and symmetric double-minimum configurations (Fig. 1B), well within the picosecond lifetimes of hydrogen bonds around the excess proton. As a result, the proton transiently explores localized and delocalized configurations, corresponding to a dynamic delocalization of the proton ground state wavefunction over a large fraction of the O···O distance. The modulation of the PES gives rise to spectral excursions, that is, spectral diffusion of the v = 0 to 1 transition of the proton transfer mode. The eminently broad homogeneous 2D line shapes of the v = 0 to 1 excitations are a direct manifestation of the fluctuating PES, with the relevant fluctuations occurring in the sub-100-fs time domain. This behavior is markedly different from protons in ultracold water clusters, where structural fluctuations are suppressed and protons are embedded in quasi-static hydration environments (3, 4).
Our simulations of the Zundel cation in acetonitrile (supplementary materials) provide quantum mechanics/molecular mechanics (QM/MM) trajectories for proton motions and dipole moment in the v = 0 ground state, and for the fluctuating electric field Ez, the environment imposes on the proton transfer coordinate z. We further derived frequency maps for the v = 0 to 1 and v = 1 to 2 transition of the proton transfer mode as a function of the O···O distance R and a static external field Ez from a 2D PES depending on R and z (figs. S5 and S7). Combining QM/MM trajectories and frequency maps, we derived the stochastic time evolution of the v = 0 to 1 and v = 1 to 2 transition frequencies and their time-averaged distributions.
We calculated the stationary absorption spectrum by means of Fourier transform of the dipole moment autocorrelation function (Fig. 4A, red line). Both the spectral position and, because of a sub-100-fs initial correlation decay, a major fraction of the width of the experimental absorption band (blue line) are reproduced. To assess the frequency range explored within a 1-ps period (a typical H-bond lifetime in aqueous systems), we calculated spectra for individual short QM/MM trajectory segments (Fig. 4B, dashed lines) and the average spectrum (Fig. 4, A and B, solid black line) of several hundred slices from a 320-ps-long trajectory (Fig. 4C). It is evident that the v = 0 to 1 transition explores a substantial fraction of the total linewidth within 1 ps.
(A) Experimental (blue line) and simulated linear absorption spectra of the proton transfer mode z. The simulated signals represent the normalized real part of the Fourier transform 
of the dipole moment autocorrelation function 
of the 320-ps QM/MM trajectory (red) and an incoherent average of 300 short time spectra (black) of independent trajectory segments of 1 ps duration. (B) Short time spectra separated by 25 ps along the QM/MM trajectory (dashed, multiplied by factor 100) and incoherent sum of 300 short time spectra (black). (C) Time series of short time spectra 
of Δt = 1 ps segments of the QM/MM trajectory. (D) Field-fluctuation correlation function (yellow) of the electric field Ez imposed by acetonitrile molecules at the position of the excess proton calculated from the QM/MM trajectory. Blue and red lines indicate time correlation functions of O···O distances R and of the 100-fs moving average of O···O distances 
.
The autocorrelation function of the electric field Ez displays an initial decay within 200 fs, followed by slower subpicosecond kinetics (Fig. 4D), which are both in agreement with experimental results for neat acetonitrile (21). The correlation functions of O···O elongations along R (Fig. 4D, blue and red lines) undergo oscillations with the 55-fs period of the O···O vibration and a damping after the Ez correlation decay. This behavior suggests that fluctuations in Ez and R are coupled; O···O motions are triggered by Ez-induced changes of the vibrational potential along R, to which the oxygen atoms respond by rearranging with their intrinsic oscillation frequency.
The time-averaged distributions of vibrational frequencies (fig. S7, E and F) show that the v = 0 to 1 transition frequency of the proton transfer mode is modulated by both the Ez fluctuations and the fluctuations in the O···O distance R. In contrast, the Ez fluctuations have negligible direct influence on the v = 1 to 2 transition frequency because of the nearly identical field dependence of the v = 1 and 2 states. Thus, the limited spectral diffusion of the v = 1 to 2 transition is predominantly caused by fluctuations in R.
On top of the structure fluctuations discussed so far, the sub-100-fs decay of the v = 1 state of the proton transfer mode causes a substantial lifetime broadening of the spectral envelopes. An analysis of the transient v = 1 to 2 absorption band (Fig. 3) discussed in the supplementary materials gives a time range of 20 fs ≤ τ1 ≤ 40 fs for the v = 1 lifetime τ1. These values are close to the 28-fs vibrational period of the proton transfer mode, which is rapidly damped by the population decay.
Our results are highly relevant for understanding proton dynamics and transport in water at the molecular level. The profound correspondence between experimental results for hydrated protons in bulk water and Zundel cations predominantly prepared in acetonitrile suggests a substantial presence of Zundel-type hydration geometries in bulk water. The full absorption recovery of the proton transfer mode within the time range of our experiments suggests a minimum lifetime of such species on the order of 1 ps, a time that is comparable with the lifetime of a hydration configuration in between two consecutive proton shuttling events. Thus, Zundel-type configurations in bulk water at ambient temperature appear to constitute not just a fleeting transition state or short-lived intermediate but rather a major hydration species subject to fluctuating electric fields from the outer water solvation shells. Persistent localization of the proton along the transfer coordinate z is suppressed by (i) the field-induced fluctuations of the double-minimum PES and (ii) the small-amplitude fluctuations in O···O distance R. The latter are limited to a range in which the barrier height in the center of the double-minimum potential remains comparable with or even smaller than the energy of the v = 0 state. Thus, the proton wave function retains a dynamically delocalized, Zundel-type character as long as the local H-bond pattern is preserved.
The sub-100-fs proton dynamics along the transfer coordinate are obviously much faster than changes in the H-bond pattern. As a result, the picosecond shuttling of a Zundel-type proton from an existing to a new hydration site—the elementary step in proton migration—requires a rearrangement of the local H-bonds, induced, for example, by breaking and forming H-bonds in the second solvation shell of the two water molecules that share the proton (10). Here, large angular jumps of outer water molecules should be important (22). Although such events are clocked in picoseconds and independent from sub-100-fs fluctuations of the proton itself, the latter allow the proton to adapt quasi-adiabatically to its new hydration geometry. Our results give evidence of the complementary roles of fluctuating electric fields and hydrogen bond dynamics in governing proton solvation and transport in aqueous systems.
Supplementary Materials
www.sciencemag.org/content/357/6350/491/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S7
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References and Notes
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- Acknowledgments: The research reported here has been funded by the Max-Born-Institute. B.P.F. gratefully acknowledges support through the Deutsche Forschungsgemeinschaft within the Emmy Noether Programme (grant FI 2034/1-1). The experimental data sets and calculation results generated and/or analyzed in the current study are archived at the Max-Born-Institute and available from the corresponding author upon reasonable request.
