The hydrated proton (H+) in concert with the OH, is arguably the most important ion in aqueous solution, playing a prominent, if not, vital role in a variety of biological, chemical, and geological processes. It represents the essence of a concept as widely used and popularized as pH, and is obviously fundamentally involved in all acid/base chemistry. Despite recent experimental1,2,3,4,5,6,7 and theoretical advances4,8,9,10, a comprehensive molecular understanding of hydrated protons in solution remains elusive. Vibrational spectroscopy, being sensitive to hydrogen bond strength and dynamics, has been the method of choice for determining the molecular structure of the hydrated proton10. However, concentrated acid solutions give rise to extremely diffuse vibrational signatures that extend over at least 2000 cm−14,10, a fact that reflects the wide-ranging molecular distortions expected in the structural motifs, but at the same time makes the bands challenging to assign to specific species or conformers. In this sense, the structure of the hydrated proton in terms of Eigen11 (H9O4+), Zundel12,13 (H5O2+) or more delocalized motifs continues to be lively debated10. An important improvement in our understanding came from gas-phase studies of clusters of hydrated protons H+(H2O)n cryogenically cooled to 20 K1,2,14. The clusters limit the motifs accessible to the proton, generating well-resolved IR spectral features that have been directly linked to Zundel and Eigen structures, and are also used as a benchmark for testing the accuracy of different computational methods8,10,15. Though useful, the results from low-temperature gas-phase clusters are not necessarily transposable to condensed phases at ambient conditions6,16. At room temperature, we require background subtraction and the deconvolution of vibrational spectral features to obtain indirect information of the structural motifs4,15,16. A precious insight has been provided by ultrafast two-dimensional infrared (2D-IR) spectroscopy, where by connecting the coupled resonances at different frequencies, distinct species have been identified in solution6,7. The current consensus leans towards the proton in the bulk liquid being primarily hydrated by two flanking water molecules in a Zundel-like configuration4,7.

The scenario can be different at surfaces. The orientational constraints and asymmetric environment imposed by the interface may reduce the number of structural possibilities, and consequently, result in more resolved features. Vibrational sum frequency spectroscopy (VSFS), a second-order non-linear optical technique with an intrinsic surface specificity, offers the opportunity to yield vibrational spectra from molecules at interfaces17. Under the electric-dipole approximation, VSFS only detects molecules with a net polar orientation, which are typically found in the noncentrosymmetric environment of an interface18. The air/liquid surface of concentrated acid solutions has been the subject of several VSFS studies19,20,21,22,23, but they have primarily focused on the OH stretching region of interfacial water molecules (>3000 cm−1). Although some of the spectral changes observed, particularly at ~3200 cm−1, were linked to the hydrated proton21, other interpretations associate them instead to an increased number of probed water molecules in the diffuse double layer, which extends upon charging of the surface22,24. With the exception of a couple of studies on neat acid solutions20,25, where no resolved resonant features were detected, the proton continuum region (<3000 cm−1) on surfaces has largely been neglected.

Here, we use VSFS to probe the proton continuum spectral region of negatively charged liquid/vapor interfaces and identify resolved features associated with hydrated protons having a preferred orientation. The charged surfaces consist of Langmuir monolayers exposing either carboxylic acid or sulfate groups to solution. The associated negative surface potential results in surface hydronium ion concentrations that are orders of magnitude higher than in the bulk, making the spectral features detectable at ambient pH. From the analysis of the VSF spectra at different polarization combinations and comparison with gas-phase cluster, 2D-IR, and Raman/IR MCR studies, we assign the band observed at ~2540 cm−1 to the antisymmetric stretch of an Eigen-like species.


Carboxylic acid Langmuir monolayers

The starting point is the conventional homodyne SF spectra at the liquid/vapor interface of an arachidic acid Langmuir monolayer on a sodium chloride aqueous subphase at ambient pH (Fig. 1). The twenty carbon long fatty acid forms an insoluble monolayer that exposes the carboxylic acid headgroups to solution, and the hydrophobic alkyl chains towards the gas phase. The packing density can be varied by moving the barriers of the Langmuir trough. The spectra presented have been collected at a constant surface pressure of 20 mN m−1, where the monolayer is found well-packed in a tilted condensed phase with an average area per molecule of 20 Å2, as can be deduced from the surface pressure vs. molecular area isotherm (see Supplementary Note 1 and Supplementary Fig. 1). Although the intrinsic pKa of these fatty acids is similar to that of shorter chain carboxylic acids (i.e., pKa ~5), at the surface, when only the pH determining ions are present in solution, the apparent pKa is ~10.826. The negative charge and accompanying surface potential result in surface proton concentrations that are several orders of magnitude higher than in the bulk. Moreover, the charging behavior upon addition of monovalent ion salts to solution has been shown to be consistent with the Gouy–Chapman theory for concentrations ≤50 mM26,27.

Fig. 1: Interfacial spectral features of the carboxylic acid monolayer.
figure 1

VSF spectra of a perdeuterated arachidic acid (dAA) Langmuir monolayer on a 1 μM NaCl solution at pH~6 collected under the (a) SPS, and (b) SSP polarization combinations. The different polarizations provide complementary information about the surface species and their orientation. The assignements are taken from refs. 26,27,28,29 and this study (see text). Measurements are carried at 22 °C and a constant surface pressure of 20 mN m−1, corresponding to an area per molecule of ~20 Å2.

Several molecular structural details of the interfacial region can be extracted from the spectra collected at the two different polarization combinations (i.e., SPS and SSP) shown in Fig. 1. The sharp peaks found between 2050 cm−1 and 2250 cm−1 are all linked to the alkyl chain of the fatty acid, and are primarily stretching modes of the terminal methyl group26. The absence of features from CD2 groups, indicate that the monolayer is conformationally well-ordered in an all-trans configuration28, consistent with the high packing densities of the tilted condensed phase. At lower frequencies, the peak at ~1720 cm−1 observed in both polarization combinations, is assigned to the C=O stretch of the uncharged form of the carboxylic acid headgroup26,29. The spectra show no features linked to the charged carboxylate moieties, which are expected at ~1408 cm−1 and ~1535 cm−126. At pH ~6 and a NaCl concentration of 1 μM, the carboxylate modes are below the detection limit, yet the monolayer is expected to be ~0.5% deprotonated, as estimated from the Gouy–Chapman model26. Nevertheless, despite the relatively small surface charge (i.e., ~−4 mC m−2), the low ionic strength of the subphase ensure a substantial surface potential that is in the order of ~−200 mV26. At higher frequencies, between 3100 cm−1 and 3650 cm−1, the OH stretching bands from water in the interfacial region are apparent (the OH stretch from the hydrogen bonded carboxylic acid gives rise to a weak broad band centered at ~2900–2950 cm−130). The signal primarily originates from water molecules directly interacting with the carboxylic acid headgroup26,31, with only a small contribution, if any, from water molecules in the diffuse double layer. At 1 μM the Debye length (i.e., ~300 nm) is significantly longer than the non-linear coherence length of the experimental geometry (Δkz−1 ≈ 50 nm), and most of the signal generated within the diffuse double layer cancels due to destructive interference32,33.

Spectral features of hydrated protons at charged interfaces

Central to this study is the band observed at ~2540 cm−1 in the SPS spectrum (Fig. 1b), which is located far from any vibrational mode expected from the fatty acid or aqueous subphase, but within the proton continuum range of concentrated acid solutions10,20,25. To confirm that the observed vibrational mode involves the displacement of an OH bond, isotopic substitution experiments were performed using D2O. The two times heavier deuterium atoms cause the vibrational frequencies to shift within the harmonic level towards lower energies by a factor of ~1.36. The SF spectrum of an equivalent fatty acid monolayer on a D2O solution collected under the SPS polarization combination is shown in Fig. 2. In the spectrum, the broad water band that was in the case of H2O originally centered at ~3600 cm−1 is seen, as expected, to red-shift to ~2650 cm−1 in D2O. More interestingly, a peak resolved at ~1875 cm−1 proves that the ~2540 cm−1 band indeed involves an OH stretching vibration. Compared to the OH stretches of water, typically observed between 3000 cm−1 and 3600 cm−1, the significant red-shift of the ~2540 cm−1 band, indicates that the OH bonds are more strongly hydrogen-bonded, as is usually the case of water molecules surrounding the proton4,14.

Fig. 2: Isotopic substitution proves the OH stretching assignment.
figure 2

VSF spectrum collected under the SPS polarization combination of a dAA monolayer on a 1 μM NaCl solution in D2O (pD ~6.4) at a constant surface pressure of 20 mN m−1 (area per molecule ~20 Å2). Temperature. 22 °C. The assignments are taken from26,28 and this study (see text).

The peak position lies within the range generally assigned to embedded Eigen-like structures (i.e., an H3O+ core, symmetrically solvated by three water molecules)1,4,6,14. However, this classification is controversial given the extremely diffuse vibrational signature of the hydrated proton in bulk solution4,7. Although the cryogenically cooled cluster behavior cannot be readily extrapolated to the bulk liquid at room temperature, their resolved features provide useful insight. The charged delocalized Eigen cation H3O+(H2O)3 shows a characteristic peak centered at ~2660 cm−1, unambiguously assigned to the doubly degenerate antisymmetric OH stretch of the Eigen core1,3,9,14,34. This band is also observed in larger gas clusters displaying an Eigen-like motif where the hydronium core is predominantly symmetrically solvated (i.e., H+(H2O)n = 9–12), and remains detectable in even bigger clusters (i.e., n = 24), though contributions red-shifted by up to ~600 cm−1 also become apparent in the spectra1,35. In contrast, when the proton is shared by two water molecules in a Zundel-like arrangement (H2O---H---OH2)+, vibrations involving the core proton in the cluster are further red-shifted by more than 1000 cm−11,10.

Additional experimental information regarding the assignment and also molecular orientation of the hydrated proton at the surface can be extracted from the SF spectra gathered at different polarization combinations36,37. The hydrated proton feature is strongly observed in the SPS spectrum, but besides a weak non-resonant background it is essentially absent in the PPP polarization combination (Fig. 3a). This is consistent with the band being assigned to an antisymmetric OH stretch of the C3v symmetry H3O+ in the Eigen core, with its C3 axis aligned at, or close to the surface normal, as shown in the theoretical orientational analysis presented in Fig. 3b. The curves depict the expected variations in relative intensities as a function of the tilt angle for the polarization combinations SPS, SSP, and PPP, assuming a delta and a narrow Gaussian distribution of angles (see Supplementary Note 2 for details). However, though the experimental intensity in SSP is significantly weaker than for SPS (Fig. 3a), it is not negligible as predicted by the theoretical analysis for low tilt angles (Fig. 3b). The discrepancy can be accommodated by considering potential contributions from the symmetric stretch of the C3v Eigen core, which when aligned close to the surface normal, should be preferentially observed in the SSP polarized spectra (see Supplementary Note 2 for details)36,38. Although the symmetric stretch has not been experimentally resolved in any of the previous IR cluster studies, it has been theoretically estimated to lie just ~38 cm−1 red-shifted3, overlapping39, or even blue-shifted1 relative to the antisymmetric mode, with a cross-section that is almost two orders of magnitude lower than for the degenerate antisymmetric stretch9,40. Given that the SF intensity has a square dependence on the IR and Raman transition moments36,37, the significantly lower IR cross-section will have an obvious effect on the intensity of the symmetric stretching mode. Moreover, even though the mode is expected to be stronger in Raman, due to the non-Condon effect4,41, the contribution of the IR component relative to that of Raman in the SF cross-section, becomes more important at the lower OH stretching frequencies of the Eigen core. Consequently, both elements (i.e., low IR cross-section, and non-Condon effect), indicate that the SF cross-section of the H3O+ symmetric stretch will be significantly lower than for the antisymmetric mode.

Fig. 3: Polarization dependence and orientational analysis of the hydrated Eigen proton.
figure 3

a VSF spectra collected in the polarization combinations SPS, SSP, and PPP of a dAA monolayer on a 1 μM NaCl solution in H2O (surface pressure 20 mN m−1). b Theoretical curves showing the expected variations of the SF intensity of the antisymmetric stretch of H3O+ (C3v symmetry) as a function of tilt angle of the C3 axis from the surface normal for the three polarization combinations, assuming a delta distribution (solid lines), and Gaussian distribution with standard deviation of 15° (dashed lines). See Supplementary Note 2 for details of the model. The sketch depicts the orientation of the hydronium core with the arrow along the C3 axis. Experimental observations are consistent with the C3 axis aligned closed to the surface normal. In the sketch, the oxygen and hydrogen atoms of the core Eigen proton are depicted as blue and red spheres, respectively. In the flanking water molecules, oxygen atoms are in light blue, while hydrogens are illustrated as white spheres.

Fatty sulfate monolayers

To further extend the implications of the results, spectra were also collected at negatively charged surfaces that have as chargeable groups other functionalities than the carboxylic acid moiety. The SPS polarization SF spectrum of a twenty-carbon fatty sulfate Langmuir monolayer is presented in Fig. 4. At the pH and selected surface pressure of the experiment, the fatty sulfate monolayer is found in a liquid expanded phase. With an intrinsically lower pKa the fatty sulfate, even at pH 3.8, is substantially more deprotonated, but also shows a higher affinity for the other monovalent counterions (see Supplementary Note 1 for details). The presence of the hydrated proton peak at ~2540 cm−1, proves that it is not unique to surfaces displaying charged carboxylic acid groups.

Fig. 4: Hydrated protons at a negatively charged fatty sulfate interface.
figure 4

VSF spectrum collected under the SPS polarization combination of a sodium eicosyl sulfate monolayer on a pH 3.8 HCl solution at a constant surface pressure of 2.5 mN m−1 (area per molecule ~65 Å2). Temperature 22 °C. The spectral feature assigned to the hydrated Eigen proton is observed in other negatively charged interfaces besides those involving carboxylic acid moieties.


In contrast to bulk studies, the VSF results presented show compelling evidence of a narrow spectral feature linked to a specific hydrated proton configuration. The negative charge and asymmetric environment imposed by the interface are key elements for this distinction. Under the electric-dipole approximation, VSFS only detects molecules with a net polar orientation that have vibrational modes that are simultaneously Raman and IR active18,36. This typically reduces the number of bands resolved when compared with the linear vibrational spectroscopies. Moreover, the surface electric field associated with the negatively charged interface plays a fundamental role, as it not only causes a substantial increase of the surface concentration of hydrated protons, but also has a direct influence on the adopted configuration and its average net orientation. For instance, the VSF spectrum of pure water, as well as that of solutions of HCl at pH 2, and HBr at pH −0.3, show no resolved resonant features in the proton continuum range20,25, highlighting the importance of having a (partly) charged Langmuir monolayer for detecting the hydrated proton at the surface.

From the observed peak position and polarization dependence, together with the insight provided by the experimental and theoretical studies on small cold clusters, the ~2540 cm−1 can be assigned to the degenerate antisymmetric OH stretch of the H3O+ core in an Eigen-like configuration, where the three OH are equivalent (i.e., C3V symmetry). The center position is also in agreement to that proposed from calculated IR and Raman spectra for structures that can be classified as Eigen-like4. The orientational analysis for the antisymmetric stretch presented in Fig. 3b, suggest that the principal axis of the H3O+ core should be oriented close to the surface normal. Although the net polar orientation can not be directly obtained from the homodyne SF spectra presented42, the three hydrogens will most certainly be directed towards the negatively charged interface.

Interestingly, the Eigen-like VSF signal can be detected in fatty acid monolayers when the bulk hydronium ion concentration is just in the order of a few micromolar or less (i.e., pH ~6). At the negatively charged surface, however, the proton concentration is orders of magnitude higher. At low ionic strengths the charging behavior of the monolayer can be accurately predicted using the Gouy Chapman model26, thus the surface concentration of H3O+ can be estimated to be ~2.5 mM in the presence of 1 μM NaCl in the subphase (see methods). At higher monovalent salt concentrations, despite an increase of the percentage of deprotonation of the fatty acid monolayer26, the surface proton concentration is predicted to decrease due to a lowering of the surface potential as shown in Fig. 5a. In qualitative agreement with this prediction, VSF measurements carried out at higher ionic strengths show that the intensity of the H3O+ antisymmetric stretch indeed decreases with the concentration of NaCl in the subphase, at least up to 0.1 mM (Fig. 5b). The VSF intensity depends on the number of contributing oscillators squared, as well as their average orientation and distribution36,43. Provided the latter two remain constant, the VSF intensity is thus expected to be particularly sensitive to the surface concentration of Eigen-like protons (i.e., N2 dependence). In fact, although the trends are systematically reproduced, significant variations in the absolute intensities of the hydrated proton band were observed in multiple repeat experiments. Ascribed to small variations in solution pH due to CO2 absorption from the atmosphere, a detailed analysis of these fluctuations is clearly warranted but remain beyond the scope of this work.

Fig. 5: Salt dependence of the hydrated proton spectral feature: theory compared with experiments.
figure 5

a Calculated surface proton concentration as a function of NaCl in the subphase of a fatty acid Langmuir monolayer based on the Gouy Chapman model, for three different pH. b VSF spectra in the SPS polarization of a dAA monolayer on an aqueous subphase with varying concentrations of NaCl at natural pH (surface pressure 20 mN m−1, temperature 22 °C). Note that the H3O+ antisymmetric stretch intensity follows the same trend predicted for the surface proton concentration as a function of salt.

The SF signal from the hydrated proton could, in principle, originate from Eigen-like species located in direct proximity to the interface, or further away within the diffuse double layer32,44. However, the fact that the Eigen band is more strongly observed on a 1 μM NaCl subphase than at higher salt concentrations (Fig. 5b), suggests that the origin is from close proximity to the interface. Had the signal been generated from within the diffuse double layer, due to destructive interference, it would have increased with ionic strength in the concentration range considered as experimentally confirmed elsewhere when probing water molecules in the diffuse layer26,45 (i.e., the Debye screening length at 1 μM NaCl is significantly longer than the non-linear coherence length of the SF process32,33). Given that the Eigen-like proton is symmetrically hydrated, one possibility is that the hydrated proton forms a solvent separated ion pair46 with the charged carboxylate and sulfate headgroups. Nonetheless, the hydrated proton must also interact with other competing counterions present at the interface. For the fatty acid monolayers, the proton has a significantly higher affinity than other monovalent cations such as Na+ to interact with the carboxylate headgroup47. This is not the case for the sulfate headgroup48, where the presence of sodium counterions in the subphase could have a detrimental effect on the measured H3O+ core signal.

In summary, a resolved spectral feature assigned to the antisymmetric OH stretch of the H3O+ core in an Eigen-like configuration has been identified at negatively charged interfaces exposing carboxylic acid and sulfate headgroups to solution. The fact that Eigen-like protons can be detected in a biologically relevant pH range, may offer novel perspectives for understanding essential physiological functions involving proton interactions with cell membrane interfaces10. The presence of a band linked to the charge carrier opens a window of opportunities for potentially tracking the behavior of hydrated protons in a variety of conditions and systems. Moreover, VSFS could also be used in its phase-sensitive42, and time-resolved configurations49,50, to extract additional information including absolute polar orientation and vibrational dynamics. We anticipate that Eigen-like protons are not necessarily the only structural motifs with a preferred orientation that can be found at an interface, but at given conditions, other configurations, in particular, Zundel-like hydrated protons could well be the preferred species. It is hoped that the information provided here may stimulate theoretical and simulation studies of hydrated protons at charged interfaces.


Materials and preparation of solutions

NaCl (99.999% trace metal basis, Merck) was baked at 500 °C for 1 h in order to remove traces of organic contaminants. HCl 36.5% (99.999% trace metal basis, Alfa Aesar), deuterium oxide (D 99.9%, <0.8 μS cm−1 in conductivity, Cambridge Isotope Laboratories, Inc., MA, USA), chloroform (anhydrous grade, stabilized with ethanol, Merck), methanol (anhydrous, 99.8%, Merck), eicosanoic-d39 acid (97%, dAA for deuterated arachidic acid, Merck), and sodium eicosyl sulfate (>95%, Santa Cruz Biotechnology, TX, USA) were used as received. The electrolyte solutions were prepared by serial dilution in either D2O or ultrapure water from an Integral 15 Millipore system (resistivity of 18.2 MΩ.cm and TOC < 3 ppb). The solvents used for the fatty acid and fatty sulfate spreading solutions consisted of pure chloroform, and a mixture of chloroform-methanol in a 10:1 proportion, respectively.

Langmuir trough

The monolayers were formed by spreading a few microliters of the fatty acid or fatty sulfate solutions on the surface of the subphase placed in a Langmuir trough (KSV NIMA, Finland, 195 mm length, 50 mm width, and 4 mm in depth). After a waiting time of at least 10 min to ensure full solvent evaporation, the monolayers were compressed at a rate of 5 mm per minute. The surface pressure was measured using a paper Wilhelmy plate. All the VSF experiments were carried out a constant surface pressure and temperature of 22.0 ± 0.5 °C. For the fatty acid case, the surface pressure was 20 mN m−1 (~20 Å2 per molecule), while for the fatty sulfate it was set to 2.5 mN m−1 (~65 Å2 per molecule). See Supplementary Note 1 for additional details.

VSF spectrometer

The femtosecond spectrometer has been described in detail elsewhere51, and only a brief description of the key features is given here. The tuneable IR (~100 fs and 1 kHz) and visible pulses (805 nm, tuneable beam shaper, >20 ps long) are focused at the sample position in a co-propagating geometry at angles of incidence of 55° and 70°, and pulse energies of ~4 mJ cm−2 and ~12 mJ cm−2, respectively. The spectrometer features a high degree of automation that accommodates for measurements in a broad spectral region from 1000 cm−1 to 4000 cm−1. The spectra were recorded under the polarization combinations SSP (S polarized SF, S polarized visible, and P polarized IR beams), SPS, and PPP, and normalized by the non-resonant SF response from a gold substrate. The spectra presented in n.u. units have been normalized to the intensity of the CD3 symmetric stretch in the SSP spectra, and can be directly compared.

Surface hydronium concentration from the Gouy–Chapman theory

The proton concentration at the surface [H+]0 depends on that in the bulk [H+], as well as the surface potential ψ0,

$$\left[ {{\mathrm{H}}^ + } \right]_0\,=\,\left[ {{\mathrm{H}}^ + } \right]_\infty \exp \left( {\frac{{ - e\,\psi _0}}{{kT}}} \right)$$

where e, k, and T are the elemental charge, the Boltzmann factor, and temperature, respectively. The surface potential is in turn related to the degree of dissociation a of the carboxylic acid monolayer (α), and equilibrium constant Ka for the reaction HA ↔ A + H+,

$$\begin{array}{lcc}K_a\, =\,\frac{{\left[ {A^ - } \right]_0\left[ {{\mathrm{H}}^ + } \right]_0}}{{\left[ {{\mathrm{HA}}} \right]_0}}\,=\,\frac{\alpha }{{1 - \alpha }}\left[ {{\mathrm{H}}^ + } \right]_\infty \exp \left( {\frac{{ - e\,\psi _0}}{{kT}}} \right)\\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\; \to \;\psi _0\,=\,\frac{{kT}}{e}\left[ {\ln \left[ {{\mathrm{H}}^ + } \right]_\infty - \ln K_a - \ln \left( {\frac{{1 - \alpha }}{\alpha }} \right)} \right]\end{array}$$

The surface potential ψ0 also depends on the concentration of ions in solution [NaCl], and the surface charge density σ (i.e., the degree of deprotonation), through the Grahame equation52:

$$\sigma = \frac{{\alpha e}}{{{\mathrm{A}}_{\mathrm{M}}}} \, = \, \sqrt {8\varepsilon \varepsilon _0kT}\, \sin\,h \left( {\frac{{e\,\psi _0}}{{2kT}}} \right)\sqrt {\left[ {{\mathrm{NaCl}}} \right]_\infty }\\ \to \psi _0 = \frac{{{2{kT}}}}{{{e}}}\,{\mathrm{arc}}\,{\mathrm{sin}}\,h\left( {\frac{{\alpha {\boldsymbol{e}}/{\mathrm{A}}_{\mathrm{M}}}}{{\sqrt {\left[ {{\mathrm{NaCl}}} \right]_\infty 8\varepsilon \varepsilon _0{\it{kT}}} }}} \right)$$

where ε and ε0 are the dielectric constants of water and vacuum, respectively, and AM is the area per molecule (~20 Å2 per molecule). The surface potential is determined by simultaneously solving Eq. (2) and Eq. (3) and setting the pKa to 526.