The Bending Mode of Water: A Powerful Probe for Hydrogen Bond Structure of Aqueous Systems

Insights into the microscopic structure and dynamics of the water’s hydrogen-bonded network are crucial to understand the role of water in biology, atmospheric and geochemical processes, and chemical reactions in aqueous systems. Vibrational spectroscopy of water has provided many such insights, in particular using the O–H stretch mode. In this Perspective, we summarize our recent studies that have revealed that the H–O–H bending mode can be an equally powerful reporter for the microscopic structure of water and provides more direct access to the hydrogen-bonded network than the conventionally studied O–H stretch mode. We discuss the fundamental vibrational properties of the water bending mode, such as the intermolecular vibrational coupling, and its effects on the spectral lineshapes and vibrational dynamics. Several examples of static and ultrafast bending mode spectroscopy illustrate how the water bending mode provides an excellent window on the microscopic structure of both bulk and interfacial water.

W ater plays an important role in many biological and chemical processes. The hydration structure of proteins and lipids affects their biological functions, and the interaction of water with solid surfaces such as mineral and metal oxide surfaces determines surface chemistry and surface−catalytic reactions. In addition to these critical roles in natural and industrial processes, the fundamental physical properties of condensed phase (liquid-and solid-state bulk water) and interfacial water, e.g., anomalously high surface tension, high viscosity, high boiling point, and so forth, have also attracted a great deal of attention. Some of these unique features have been attributed to the cooperative hydrogen-bond network of multiple water molecules. 1 Thus, to unveil the physics underlying the unique properties of water, a molecular-level understanding of the structure and dynamics of the hydrogenbond network is essential.
Vibrational spectroscopy techniques have provided detailed information on the microscopic hydrogen-bond structure of water in aqueous solutions, primarily via the O−H stretch mode of water. 2  The data points were experimentally obtained by measuring the frequencies of water in various media. 6 The blue and red lines represent the relations of eqs 1 and 2, respectively. moieties are present in the sample. The broad O−H stretch band of water then overlaps with other vibrational bands such as the O−H stretch mode of alcohols and biomolecules as well as their N−H stretch/amide A modes. Disentangling the different modes is a formidable challenge, which cannot be resolved, for instance, by H/D isotopic substitution, because of rapid proton exchange. Also, vibrational couplings such as energy splitting between the O−H stretch modes and Fermi resonance with bending overtone often complicate the interpretation of the O−H stretch mode spectra and dynamics.
Compared to the stretch mode, the H−O−H bending mode has several advantages. Because the bending mode of water is unique to water molecules, it is spectrally separated from the C−O−H and C−N−H bending modes of alcohols and biomolecules. Essentially, water has only one bending mode in a molecule, which means there is no intramolecular bending mode−bending mode vibrational coupling. In addition to these advantages, the bending frequency can provide information on the hydrogen-bond strength of water, in a manner very similar to the stretch mode frequency.
A very similar coefficient of −1/0.259 was obtained from ab initio calculations. 7 When the nonlinear term is included in eq 1, one can add the additional condition satisfying the stretch and bend frequencies in liquid water (ω bend l = 1650 cm −1 and ω str l = 3400 cm −1 ) to eq 1. 8,9 This is given as 10 The vibrational nature of the water bending mode, however, has been much less investigated than the stretch mode, presumably because of its weaker absorbance. In contrast to the O−H stretch mode, it has been unclear how isotopic dilution affects the spectral shape and the vibrational dynamics of the bending mode, i.e., bending mode−bending mode and bending mode−other vibrational mode couplings have not been fully elucidated. 2 At the interface, it has been controversially discussed whether the bending mode signal in surface-specific vibrational spectra arises from the interfacial water molecules 7,11,12 or from the bulk. 13 As such, despite the potential advantage of using the bending mode probe to explore the hydrogen-bond network, fundamental knowledge on the vibrational nature of the bending mode is still lacking.
In this Perspective, recent spectroscopic advances on the water bending mode will be introduced, followed by a discussion of the fundamental vibrational properties of the bending mode in bulk liquid, the vibrational dynamics, and the surface specificity and coupling nature of the bending mode of the interfacial water. Subsequently, several examples of probing the bending mode of water are discussed. Finally, the key results are summarized.
First, we examined the static spectra of the water bending mode in pure bulk water through the comparison of the stretch and the bending modes. Figure 2a shows that the use of isotopically diluted water (HOD in D 2 O) changes the lineshapes of the O−H stretch mode in both the IR and Raman spectra of neat H 2 O. 14,15 The shoulder at ∼3200 cm −1 diminishes while the ∼3400 cm −1 contribution persists upon isotopic dilution, resulting in an overall narrowing of the vibrational line shape. These spectral variations are well reproduced by simulations using the frequency-mapping technique ( Figure 2b) and can be explained by intermolecular intramode (i.e., stretch mode−stretch mode) coupling as well as intramolecular intermode coupling mainly due to the Fermi resonance between the stretch and the overtone of the bending mode. 16,17 The intra/intermolecular intra/inter-mode couplings for the O−H stretch mode and H−O−H bending mode are summarized in Tables 1 and 2, respectively. How does the lineshape of the bending mode change upon isotopic dilution of water? Recently, we compared the experimentally determined lineshapes of the H−O−H bending mode of neat H 2 O and isotopically diluted water by carefully subtracting the H−O−D bending mode contribution from the measured spectra, which is plotted in Figure 2c. 18 The data show that the peak frequency is slightly shifted to higher frequencies (∼7 cm −1 ) upon isotopic dilution. At the same time, the full width at half-maximum (fwhm) of the bending mode is rather insensitive to the isotopic composition, in stark contrast to the stretch mode. Modeling and detailed analysis of bending mode spectra are, however, still largely unexplored. One of the pioneering works for the bending mode has been reported by Ni and Skinner. 7 Figure 2d displays the simulated bending mode IR spectra with and without the intermolecular intramode (bending mode−bending mode) coupling. Figure  2d shows a slight blue-shift (∼10 cm −1 ) of the uncoupled oscillators, relative to the coupled mode, in reasonable agreement with the experimental data. 18 However, the simulation indicates a substantial narrowing of the H−O−H bending mode spectra upon isotopic dilution, in contrast to the experimental spectra in Figure 2c. As such, theoretical modeling of the IR bending mode spectra is challenging. Furthermore, a theoretical calculation of the Raman response of the bending mode is lacking.
Overall, the experimental lineshapes indicate that intermolecular intramode coupling of the bending mode causes only minimal distortion of the lineshape, and shifts the peak position of the bending mode spectra of water, but the shift is very tiny. This is in contrast with the stretch mode response, which is strongly affected by a complex interplay of intramolecular intermode and intermolecular intramode couplings. Thus, the water bending mode in bulk water is a more direct reporter of the hydrogen-bond network.
The H−O−H bending mode frequency is responsive to the hydrogen-bond strength of the system of interest.
The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Perspective Next, we turn our attention to the vibrational dynamics of liquid water, which plays an important role in chemical processes occurring in aqueous media, for example, by facilitating energy dissipation during chemical reactions.
Time-resolved spectroscopies, including pump−probe IR or two-dimensional IR (2D-IR) spectroscopy, have been used to quantify the time scales of the vibrational dynamics such as vibrational energy relaxation, orientational memory decay, and spectral diffusion. 19,20 When vibrationally exciting the O−H stretch mode, the excess vibrational energy relaxes from the O−H stretch mode to lower-frequency modes (e.g., the H− O−H bending mode at 1650 cm −1 , the librational mode at 600−800 cm −1 , and the hydrogen-bond stretch mode at 180 cm −1 ), i.e., vibrational energy relaxation. Because the infrared excitation light is typically linearly polarized, it preferentially excites water molecules with transition dipole moments aligned along the field polarization. The decay of orientation memory, i.e., excitation anisotropy, has also been used to characterize  The lineshape of the bending mode is less sensitive to vibrational coupling of water than the stretch mode, being a direct probe for hydrogen-bond network.  21 This acceleration of the dynamics of the O− H stretch mode arises from two mechanisms. 24     In contrast, isotopic dilution of water has a smaller effect on the frequency mismatch between the H−O−H bending mode and the overtone of the librational mode, and this intramolecular intermode coupling remains largely unchanged. Hence, one can expect the vibrational energy relaxation of the H−O−H bending mode to be insensitive to the isotopic dilution. This is also borne out by experiment: we found that the vibrational lifetime of the H−O−H bending model is invariant to the isotopic composition, with a time scale of ∼200 fs. 18 This fast vibrational energy relaxation of the bending mode arises from the ultrafast energy transfer of the bending mode to the higher-frequency side of the librational motion. 28 To obtain the orientational memory dynamics, transient spectra at different polarization combinations are recorded to determine the anisotropy decay. 2  The orientation of the transition dipole moments associated with the bending and stretch modes are aligned, roughly, along the bisector axis of the H−O−H angle and the O−H axis, respectively. As such, for sufficiently low OH concentrations, for which energy transfer is negligible, the anisotropy decay of the two modes reflects the reorientational motion of water along those two molecular coordinates. From simulations and experiments, the decay of the rotational correlation function of the bisector axis and the O−H axis of water are known to be very similar, with a decay time of 1.5−2 ps. 29 This time constant is similar to the time constant of the anisotropy decay when pumping and probing the O−H stretch mode of isolated HDO in D 2 O, while the anisotropy decay when pumping and probing the H−O−H bending mode is much faster than 1.5−2 ps. Currently, this is understood as the mixing of the bending mode and other vibrational modes; because of strong vibrational mixing, 18,22,30,31 the orientation of the transition dipole moment is rapidly randomized. As such, the anisotropy decay of the bending mode is much faster than the actual molecular reorientation, even for isotopically diluted water.
Finally, we discuss the spectral diffusion of the bending mode. 2D-IR spectroscopy can provide the time scale of the spectral diffusion, reflecting the memory loss of the excitation frequency. So far, only a few studies have been done to understand the spectral diffusion of the bending vibration. 30,32,33 Figure 4  The hydrogen-bond structure at the air−water interface has been studied by vibrational sum-frequency generation (VSFG) spectroscopy over the past two decades. Because of the optical selection rule of SFG, the SFG signal arises only from the interface where inversion symmetry is broken, i.e., not from isotropic bulk water. Because SFG signal is resonantly enhanced by interfacial vibrational transitions, it can provide vibrational and structural information on specifically interfacial water. This region is limited to the topmost few layers of water at the water−air interface. 3 The intramolecular intermode coupling of the bending mode of water is much stronger than its intermolecular intramode coupling.
The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Perspective The first SFG intensity spectrum (the square of the effective surface nonlinear susceptibility, |χ eff (2) | 2 ) of the bending mode at the air−water interface was experimentally measured in 2012, 48 and then the imaginary part of the SFG susceptibility, (Im(χ bend (2) )), was reported. 13 This Im(χ bend (2) ) spectrum shows a positive band. In contrast, MD simulations show that the imaginary part of the bending mode SFG spectrum exhibits both positive and negative features. 7,11,49 Tahara and coworkers attributed this discrepancy of the experimentally measured and simulated Im(χ bend (2) ) to the bulk quadrupole  The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Perspective contribution; the simulation had assumed that the SFG signal arises solely from the interface because the interfacial dipole contribution is stronger than the bulk quadrupole contribution (electric dipole approximation), 50 while the experimental data may contain not only the leading contribution of the interfacial dipole but also contributions from the bulk quadrupole. 51 If the bulk quadrupole indeed dominates the bending mode signal, there is no chance to extract the interfacial water contribution from the SFG bending mode signal.
To explore the origin of the water SFG bending signal, one can take advantage of the fact that the sign of the Im(χ bend (2) ) SFG signal will change if the transition dipole moment flips its orientation along with the interfacial water molecules themselves. On the other hand, if the bending mode signal is governed by the proposed bulk quadrupole contribution, the sign of the Im(χ bend (2) ) will remain unchanged upon flipping the orientation of the interfacial water molecules. 51 By identifying the negative/positive change of Im(χ bend (2) ) upon going from a positively to a negatively charged interface, 52 one could elucidate whether Im(χ bend (2) ) arises from interfacial water or from bulk water.
As the presence of surface charge will induce the formation of the electrical double layer (EDL), the obtained SFG signal, χ eff (2) , originates from two contributions: one arises from the water molecules interacting with surface molecules in the Stern layer, χ stern (2) , while the other originates from the water molecules which can flip their orientations in response to the surface electric field in diffuse layer, χ Diffuse (2) . Thus, extracting the χ Diffuse (2) contribution from the χ eff (2) spectrum is needed in order to address the sign of the change of the Im(χ stern (2) ). The χ Diffuse (2) is strongly dependent on the degree of screening of the surface charge by electrolytes in solution and therefore depends on ion concentration c. The overall response can be approached by 53−55 where Φ(c), κ(c), and Δk z denote the surface potential, the inverse of the Debye length, and the mismatch of the wavevectors along the surface normal (z-axis) in the reflected SFG configuration, respectively. We measured the SFG intensity (|χ eff (2) | 2 ) spectra by varying the ion concentrations, which are displayed in Figure 5a,b. Note that the spectral shape may be affected by beam geometries (Fresnel factors). The SFG spectra at the watercharged lipids interface showed a sharp C=O stretch peak at ∼1710 cm −1 and the bending mode peak at ∼1650 cm −1 . These spectra show that the interference between the 1710 cm −1 C=O stretch peak and the 1650 cm −1 water bend peak is different for the positively and negatively charged interfaces. By obtaining complex χ eff (2) from a Lorentzian fit of the SFG intensity and subsequently disentangling Stern and diffuse layer contributions from χ eff (2) via eq 4, one can obtain the Im(χ bend (2) ) and Im(χ bend (3) Φ (c)) spectra where Stern (2) bend (2) χ χ ≅ in our notation and 1 . These spectra at the negatively and positively charged interfaces are displayed in Figure 5c,d. The opposite sign of the Im(χ bend (2) ) response for the positively and negatively charged interfaces manifests that the bending mode contribution arises from the interfacial water molecules.
Having established that the bending mode signal arises from interfacial water molecules, we further confirm that the vibrational spectral response Im(χ bend (2) ) is insensitive to the isotope composition, as established for the bending mode of bulk water. Figure 6a displays the variation of the SFG intensity spectra at the water−air interface by varying the H 2 O/D 2 O concentration. Even the pure D 2 O spectrum, which does not have any resonances in the displayed frequency region, has tilted features, which is the signature of the tail of the O−D stretch mode (∼2400 cm −1 ). The non-negligible contribution from the O−D stretch mode implies that the bending mode SFG signal is much weaker than the stretch mode SFG signal.
By fitting the intensity spectra with a Lorentzian model, we obtain the Im(χ bend (2) ) response of the bending mode ( Figure  6b). 10 The spectra show that the isotopically diluted water and neat H 2 O data are similar within the error, which is in line with the bending mode of bulk water, discussed above. A relatively large deviation at ∼1600 cm −1 between refs 10 and 56 indicates that capturing the bending mode signal is still challenging. One can compare these bending mode SFG spectra with the O−H stretch mode SFG spectra. To have a coherent discussion about the bending mode of bulk water, we show the O−H stretch mode Im(χ str (2) ) spectra upon isotopic dilution in Figure 6c. The spectra differ slightly for reports from different groups. 57−59 So far, a commonly observed feature in the Im(χ str (2) ) spectra is the reduced low-frequency side of the negative peak around 3300 cm −1 and the 3600 cm −1 positive shoulder peak upon the isotope dilution. As a result, the isotopic dilution alters the lineshape of the O−H stretch The SFG bending mode can provide information on the interfacial hydrogen-bond network. The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Perspective SFG spectra, unlike the bending mode SFG spectra. This further demonstrates that the use of the bending mode is beneficial to identify the aqueous interfacial structure without isotopically diluting water. Above, we have described the vibrational nature of the water bending mode in the IR, Raman, and SFG spectra, in comparison with the water stretch mode. We have shown that the bending mode is insensitive to the intermolecular intramode (bending mode−bending mode) vibrational coupling, allowing us to connect the vibrational spectra with the net water structure in the aqueous system, without isotope dilution. What have the recent studies clarified using the bending mode probe? Here, we pick two examples: a study of the microscopic structure of alcohol−water binary mixtures and a study of water at protein−water interfaces. Both examples make use of the fact that the H−O−H bending mode arises solely from water molecules with no interference from other modes, unlike the O−H stretch mode for which alcohol and biomolecules also contribute. Thus, the observation based on the bending mode can provide clear evidence of the water contribution for these samples.
First, we focus on the water−alcohol mixtures, a model system of hydrophobic hydration. Water molecules surrounding a hydrophobic moiety of a molecule have been proposed to form tetrahedral or cluster-like structures, 60 which may explain the unique properties of water−alcohol mixtures, such as enhanced heat capacity. To clarify to what extent the water hydrogen-bond network in water−alcohol mixtures varies with changing the temperature, the IR spectra of the water bending mode have been measured for various water−alcohol mixtures. 61 Figure 7 displays temperature-dependent IR spectra of the water bending mode in various water−alcohol mixtures. The data show that increasing temperature induces a red-shift of the H−O−H bending mode frequency. As is accounted for in Figure 1, the red-shift of the bending mode frequency means that the hydrogen-bond of water is weakened. As a result, the IR spectra show that the hydrogen-bond strength of water is weakened at elevated temperatures. The interesting point is that the red-shift of the bending mode peak frequency upon increasing temperature amounts to only 0.05 cm −1 /°C for pure water, while it is 0.38 cm −1 /°C on average for alcohol−water mixtures. Furthermore, alcohols with longer alkyl chains tend to induce a larger frequency shift, indicating a more substantial weakening induced by temperature for longer alkyl chains. The observation that the hydrogen-bond strength of water is stronger in the presence of alcohol than in the pure water is linked with the enhanced heat capacity of the water−alcohol mixture. 62 Owing to the interference of the different O−H stretch modes of alcohols and water, this information cannot be obtained from the O−H stretch response. As such, the bending mode spectroscopy unraveled the variation of the hydrogen-bond network in the water−alcohol mixture.
The  64 We extracted the net water contribution at the human serum albumin (HSA) protein−water interface using the H−O−D bending mode. The SFG intensity spectra are displayed in Figure 8a, while Figure 8b shows the Im(χ bend (2) ) spectra obtained through the Lorentzian model fit  (Figure 8c), confirming the peak assignment. The H−O−D bending mode contribution exhibits substantially higher peak frequency in the presence of HSA (∼1510 cm −1 ) than for bulk water (∼1460 cm −1 ). This indicates that interfacial water molecules near the HSA protein are more strongly hydrogen-bonded than water in the bulk. This observation seems to be linked with the fact that the HSA protein has a negatively charged site, which strongly modulates the hydrogen-bond strength of the interfacial water. As such, the water bending mode spectroscopy opens a path to extract information on water in bulk and at interfaces from the vibrational spectra of complex aqueous solutions.
In summary, we have presented new insights into the nature of water's bending mode and recent advancements in static and time-resolved water bending mode spectroscopy. We have demonstrated that the bending mode static spectral feature and also the vibrational dynamics can report directly on the hydrogen-bonded network, as the bending mode is sensitive to hydrogen bonding yet not obscured by intermolecular vibrational coupling effects. This makes the bending mode an excellent complement to the O−H stretch mode, which has The Journal of Physical Chemistry Letters pubs.acs.org/JPCL Perspective been traditionally studied as a reporter of the microscopic structure and dynamics of water's hydrogen-bond network, and for which intermolecular vibrational coupling effects do play a role. Several fundamental properties of the bending mode remain unknown. The vibrational properties of the bending mode in ice are not well understood. 68 Even though time-resolved vibrational spectroscopy in the bulk has revealed the vibrational dynamics to be insensitive to the local molecular environments for bulk liquid water, this observation may not apply to interfacial water. Time-resolved surface vibrational spectroscopy needs to be carried out to explore the energy transfer of bending mode excitation at the air−water (ice) interface to understand the energy flow at the interface. Bending mode spectroscopy can further provide a powerful way to (re)explore the microscopic hydrogen-bond network of various aqueous systems, which can be applied to further understand complicated phenomena such as liquid−liquid phase separation or hydrogen-evolution reactions at the surface of catalysts in situ/operando.   The water bending mode can decode the net water contribution from various complex aqueous systems such as water−liquid mixture and solid−water and protein−water interfaces. We are grateful for financial support from the MaxWater initiative from the Max Planck Society and the DAAD project based personnel exchange program (#57526761).