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Cite this: Phys. Chem. Chem. Phys.,
2020, 22, 10934

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Decoding the molecular water structure atcomplex interfaces through surface-specificspectroscopy of the water bending mode†
Takakazu Seki, ‡a Chun-Chieh Yu, ‡a Xiaoqing Yu,a Tatsuhiko Ohto,bShumei Sun,acd Konrad Meister,ae Ellen H. G. Backus, ad Mischa Bonn *a andYuki Nagata *a
The structure of interfacial water determines atmospheric chemistry, wetting properties of materials, andprotein folding. The challenge of investigating the properties of specific interfacial water molecules
has frequently been confronted using surface-specific sum-frequency generation (SFG) vibrational
spectroscopy using the O–H stretch mode. While perfectly suited for the water–air interface, forcomplex interfaces, a potential complication arises from the contribution of hydroxyl or amine groups ofnon-water species present at the surface, such as surface hydroxyls on minerals, or O–H and N–Hgroups contained in proteins. Here, we present a protocol to extract the hydrogen bond strength
selectively of interfacial water, through the water bending mode. The bending mode vibrationalfrequency distribution provides a new avenue for unveiling the hydrogen bonding structure of interfacial

Received 5th March 2020,
Accepted 23rd April 2020

water at complex aqueous interfaces. We demonstrate this method for the water–CaF2 and water–
protein interfaces. For the former, we show that this method can indeed single out water O–H groups

DOI: 10.1039/d0cp01269f

from surface hydroxyls, and that with increasing pH, the hydrogen-bonded network of interfacial water
strengthens. Furthermore, we unveil enhanced hydrogen bonding of water, compared to bulk water, at

rsc.li/pccp

the interface with human serum albumin proteins, a prototypical bio-interface.

Introduction
Aqueous interfaces play an important role in geology, biology,
and chemistry. The hydration structure of proteins/lipids
aﬀects their biological functions, and the interaction of waterwith solid surfaces such as mineral and metal oxide surfaces
determines surface chemistry and surface-catalytic reactions.
Understanding the structure of water at interfaces is, therefore,of great interest. So far, surface-specific techniques suchas scanning probe microscopy, X-ray spectroscopy, attenuateda

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz,
Germany. E-mail: bonn@mpip-mainz.mpg.de, nagata@mpip-mainz.mpg.debGraduate School of Engineering Science, Osaka University, 1-3 Machikaneyama,
Toyonaka, Osaka 560-8531, Japanc
Department of Physics, Applied Optics Beijing Area Major Laboratory,
Beijing Normal University, Beijing 100875, Chinad
Department of Physical Chemistry, University of Vienna, Währinger Strasse 42,1090 Vienna, AustriaeDepartment of Natural Sciences, University of Alaska Southeast, Juneau,
AK 99801, USA† Electronic supplementary information (ESI) available: Details of the SFG
measurements, the fitting procedures, and the AIMD protocols. See DOI:
10.1039/d0cp01269f‡ These authors contributed equally.

10934 | Phys. Chem. Chem. Phys., 2020, 22, 10934--10940

total reflection-infrared (ATR-IR), and sum-frequency generation (SFG) spectroscopy have been used for investigating themolecular structure and dynamics of water at interfaces.1
Among them, vibrational SFG spectroscopy has been demonstrated to be a powerful technique to probe the interfacial
water molecules at soft (biomolecule–water)2–7 and buried(solid–water) interfaces.8–17 SFG spectroscopy is active only inthe centrosymmetry-broken region and therefore probes thosemolecular responses with a non-zero net transition dipole
moment along the surface normal direction. As such, themolecules in the bulk and the molecular responses with
their transition dipole moment being parallel to the surface
are SFG-inactive. However, capturing the net contribution of theinterfacial water in the O–H stretch spectra is often highly
challenging at the complex aqueous interfaces, because thecontribution of the water O–H stretch mode is spectrally indistinguishable from that of the O–H groups chemisorbed onto thesolid surface as well as the O–H and N–H groups of proteins.
A small number of these O–H/N–H groups can overwhelm the
SFG signal, because the SFG signal of water arises from a verythin (sub-nm) water layer at the interfaces. These comparable
contributions from the water O–H groups and the other hydroxyl
groups impede a clear molecular view of the interfacial waterThis journal is © the Owner Societies 2020

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structure. For instance, a weakly hydrogen-bonded O–H stretch
peak in the SFG spectra at the water-silica interface has
been conflictingly assigned to originating from interfacial
water18,19 and silanol groups on the silica surface.15 As such,an unambiguous determination of the interfacial water contribution is essential for unveiling the microscopic structure ofwater at interfaces. A second complication is the distortion of the
SFG spectrum of the O–H stretching mode due to intra- andintermolecular vibrational coupling effects.20
The net interfacial water contribution may be measured
through the water bending mode, because the H–O–H bending
mode originates solely from the H2O water molecules and has aspectrally distinguishable frequency from other O–H bending
modes. For example, the H–O–H bending mode frequency
is 1590–1650 cm1, which is significantly distinct from thebending mode frequency of hydroxyl groups attached on solid
surfaces (300–900 cm1).21 Since the first publication of thesum-frequency generation spectrum in the frequency region of
the bending mode from the water–air interface,22 there havebeen debates about the surface- versus bulk-contribution to thesignal.23,24 We have recently demonstrated that the surface
contribution to the overall spectrum can be readily extracted,
paving the way for using the bending mode as a reporterfor determining the interfacial water structure.24 The water
bending mode may also be well-suited to study other complex
interfaces such as protein interfaces. Although the strong
amide I mode of proteins (1620–1700 cm1) masks the H–O–H
bending mode of water, the H–O–D bending mode of theisotopically diluted water (1400–1450 cm1) can provide theinformation on the interfacial water.
A drawback to probe the water bending mode with SFG
spectroscopy lies in its weak signal. The challenge in probing
the bending mode SFG signal is further increased, when thebending mode signal is weakened by using the isotopicallydiluted water; if the bending mode lineshape is distorted by theintermolecular vibrational coupling of the bending modes, one
has to obtain the characteristic frequency of the bending modethrough the isotopic dilution of water. However, knowledge ofthe vibrational coupling on the bending mode in the SFG
spectra is completely lacking. Thus, to establish a protocol toprobe the interfacial water contribution through the bending
mode SFG, one should first obtain the information on whether
the bending mode SFG response is aﬀected by vibrational
coupling, by performing experiments with isotopic dilution.
Here, we demonstrate that the lineshape of the SFG bending
mode signal is not changed upon the isotopic dilution from the
SFG measurement at the water–air interface. We further compute the SFG spectra using the ab initio molecular dynamics(AIMD) simulations and confirm that the intermolecular
coupling of the bending modes does not alter the lineshapeof the bending mode. Subsequently, we obtain the net interfacial water contribution through the water bending mode at
two aqueous interfaces. One is the water–CaF2 interface, where
we decode the contribution of the interfacial water and findthat the hydrogen bond strength is increased with increasing
pH. The other is the water–air interface in the presence of theThis journal is © the Owner Societies 2020

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human serum albumin (HSA) protein, where we use the H–O–D
bending mode and discuss the strength of the water–HSA
protein binding interaction. The successful determination of
the interfacial hydrogen bond network through the SFG water
bending mode manifests that probing the water bending modein the SFG spectra is a promising tool for understanding theinterfacial water structure.

Results
Bending mode SFG spectra of water are unchanged upon
isotopic dilution
To examine how the lineshape of the bending mode varies
upon the isotopic dilution of water, we measured the SFG(2) 2
intensity, I(2)(o) B |w(2)NR + wR | , in the H–O–H bending mode
frequency region, at the water–air interface by varying the ratio(2)
of H2O and D2O. w(2)R and wNR denote the resonant and nonresonant contributions, respectively. The measured spectra aredisplayed in Fig. 1(a). The spectrum of neat H2O is consistent
with those reported in previous studies.22,24–26 Upon isotopic
dilution, the signal intensity decreased as expected. From thefit to I(2)(o) with a Lorentzian model, we obtained the peakfrequency (obend), half width at half maximum (Gbend), andamplitude (Abend) of the bending mode of the H2O molecules
donating two hydrogen bonds24–27 (double donors; see ESI†).
The variations of obend, Gbend, and Abend are plotted in Fig. 1(b),(c), and (d), respectively.
Fig. 1(b) and (c) show that obend is independent of theH2O concentration, while Gbend shows a weak broadening withincreasing H2O concentration. Fig. 1(d) shows that Abend islinearly proportional to the H2O concentration. Here, the H2O
concentration was inferred using the equilibrium relation:28–30[HOD]2/[H2O][D2O] = 3.86.

(1)

The dotted lines in Fig. 1(b–d) show the response expectedin the absence of vibrational coupling. Clearly, we find noFig. 1 SFG responses at the isotopically diluted water–air interface.
(a) SFG intensity spectra, I(2)(o), of the H–O–H bending mode at thewater–air interface with 1/0, 2/1, 1/1, 1/2, and 0/1 H2O/D2O mixtures. Solidlines are fits to the data. (b)Variations of obend, (c) Gbend, and (d) Abend. Dottedlines are the expected results in the absence of vibrational coupling.

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Enhanced water hydrogen bond strength with increasing pH at
the water–CaF2 interface

Fig. 2 Simulated Im(w(2)
R ) spectra of the H–O–H bending mode at thewater–air interface. (a and b) The simulated spectra for the AIMD trajectories at the (a) B3LYP-D3(0) and (b) revPBE0-D3(0) levels of theory. The
standard deviations along the amplitude axis were 0.03 and 0.02 for the
B3LYP-D3(0) and revPBE0-D3(0) levels of theory, respectively.

evidence for substantial vibrational coupling between bending
modes of interfacial water.
SFG spectral calculations using AIMD trajectories at theB3LYP-D3(0) and revPBE0-D3(0) levels of theory confirm
this conclusion. The simulated imaginary part spectra of w(2)R ,Im(w(2)R ), with various cross-correlation cutoﬀ distances rt are
displayed in Fig. 2. An increase in rt means that the simulated
spectra contain the eﬀects of the intermolecular vibrational coupling between the distant water molecules. These data show thatIm(w(2)R ) is insensitive to the cross-correlation cutoﬀ rt, confirming
the notion that the eﬀects of the vibrational coupling on thebending mode spectrum are negligible and thus the SFG lineshapeof the water bending mode is not distorted by the isotopic dilution.
This ensures that the characteristic frequency of the water bending
mode can be obtained with the arbitrary H2O–D2O concentrations.
This is in stark contrast to the O–H stretch mode, for which thepeak is strongly distorted through the vibrational coupling of theO–H stretch modes20,31–33 and thus the characteristic frequency of
the O–H stretch mode can be obtained only for substantial
isotopically diluted water (e.g. 5% O–H in D2O).
This finding is important for several aspects. First, since thecharacteristic frequency of the bending mode can be obtained evenfrom the pure H2O, we do not have to reduce the bending mode
signal further by isotopic dilution to obtain the characteristicfrequency. This is a key for probing the SFG bending mode, as
the SFG bending mode signal of water is weak and thus thedetection of the bending mode signal is often challenging. Second,
not only the H–O–H bending mode but also the H–O–D bending
mode can be used for probing the interfacial water contribution;
because the H–O–D bending mode appears only when investigating
the H2O–D2O mixtures, the H–O–D bending mode can be obtained
through the systematic change of the H2O–D2O mixture composition. If the lineshape is changed through the concentration of
H–O–D, the H–O–D bending mode contribution is not accessible.
Fortunately, since the bending mode SFG lineshape is insensitive tothe intermolecular vibrational couplings, one can safely assume
that the H–O–D bending lineshape is unchanged. Investigating the
H–O–D bending mode is particularly relevant for bio-interfaces,
since the H–O–H bending mode overlaps spectrally with the amide
mode of proteins. Below, we demonstrate how measuring thewater bending mode SFG feature with the tuned H2O–D2O
concentrations can reveal the hydrogen-bonding strength ofinterfacial water at water–CaF2 and water–protein interfaces.

10936 | Phys. Chem. Chem. Phys., 2020, 22, 10934--10940

Solid–water interfaces affect the electrochemical properties
and the wetting properties of materials. The hydroxyl groupschemisorbed onto solid surfaces often complicate the vibrational
responses, causing conflicting interpretation of the water O–H
stretch mode. For example, the O–H stretch mode centered at
B3660 cm1 at the water–silica surface has been attributed tothe different molecular origins – the silanol group15 and theinterfacial water molecules.18,19 Similarly, even though the O–H
stretch mode at B3650 cm1 has been assigned to the Ca–O–H
group at the water–CaF2 interface,10,11 a possible contribution
from interfacial water cannot be strictly excluded. Here, by
probing the H–O–H bending mode, we quantify the hydrogenbond strength of the interfacial water.
We measured the SFG intensity (I(2)) spectra for the H–O–H
bending mode of the H2O–CaF2 interface. These are displayedin Fig. 3(a). The intensity spectra show a peak-like feature at
pH 2, while a dip feature was observed around 1650–1750 cm1
at pH 12 due to the destructive interference between the
non-resonant contribution and the bending mode signal. The
peak-to-dip transition with pH increasing from 2 to 12 indicatesthat the sign of the water bending mode changes. This is
attributed to flipping of the water orientation due to the changeof the sign of the CaF2 surface charge. Note that the SFG signal
at D2O–CaF2 does not show any resonant feature. The fit of
the intensity spectra (see the ESI†) indicates that the peakfrequency of the H–O–H bending mode band at pH = 2 is1633  2 cm1, while it is 1662  3 cm1 at pH = 12 in theIm(w(2)) spectra. Since a higher frequency of the bending mode
represents a stronger hydrogen bond,24,34,35 the variation of thebending mode frequency indicates that the hydrogen bondstrength of the interfacial water at the water–CaF2 interface
enhances as the pH increases.
To relate the H–O–H bending mode with the O–H stretch
mode, we measured the O–H stretch modes of HDO at theisotopically diluted water–CaF2 interface. The spectra are displayed in Fig. 3(b). Note that, to correlate the vibrational
coupling-absent H–O–H bending mode spectra with the O–H
stretch spectra which are largely modulated by the vibrational
couplings,20,36,37 we used isotopically diluted water for the O–H

Fig. 3 SFG intensity spectra at the water–CaF2 interface with pH 2 and 12.
(a) H–O–H bending mode spectra for H2O. (b) O–H stretch mode SFG
spectra for the H2O : D2O mixture (1 : 2 ratio). The pH was adjusted using
HCl or NaOH, and the total ion concentration was adjusted to be 0.1 M byadding NaCl to the solution.

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stretch mode to suppress the vibrational couplings. The following empirical relation between the bending mode and stretch
mode frequencies;24,35,38

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ogstr  ostr = a(ogbend  obend)2 + b(ogbend  obend),(2)

is employed to decode the O–H stretch spectra of water. Here,a = 0.0216 and b = 1/0.2583. ogbend and ogstr indicate gas-phasewater vibration frequencies of 1590.6 cm1 and 3706 cm1, whileo1bend and o1str indicate liquid-phase water vibration frequencies
of 1650 cm1 and 3400 cm1, respectively.36,39
Eqn (2) indicates the expected O–H stretch peak frequency,
concluded from the bend frequency of interfacial water at
pH = 2, is 3503  9 cm1, which agrees with the O–H stretch
mode frequency obtained from the fit of the intensity spectra of3426  3 cm1. Since the Ca–O–H groups are expected to beabsent at pH 2,10,11 the O–H stretch signature can be reasonably
considered to arise solely from the interfacial water. Because
the O–H stretch mode is much stronger than the non-resonant
contribution unlike the H–O–H bending mode, the nonresonant contribution is nearly zero for the O–H stretch spectra,
while the non-resonant contribution is certainly large for the
H–O–H bending mode spectra (see the ESI†). Subsequently, we
focus on the case of pH 12. The H–O–H bending mode frequencyof 1662 cm1 suggests an expected O–H stretch mode frequencyof 3320  12 cm1. This expected O–H stretch frequency is ingood agreement with the peak frequency of 3363  15 cm1 forthe 3000–3500 cm1 O–H stretch band. This suggests that the
3000–3500 cm1 O–H band arises from the interfacial water, not
the Ca–O–H groups, consistent with the previous studies.10,11
The results also demonstrate that the 3650 cm1 peak does not
originate from water, but indeed from the Ca–O–H groups. As
such, the comparison of the O–H stretch SFG spectra with thebending mode spectra can offer an unambiguous assignment of
the vibrational signatures at complex aqueous interfaces.

overwhelmed by the strong amide I mode peak (1620–1700 cm1).
To avoid the frequency overlap with the amide I mode, weprobe the H–O–D bending mode (1450–1500 cm1) instead of
the H–O–H bending mode. Although the H–O–D bending mode
frequency overlaps with the frequency of the amide II mode
(1480–1570 cm1),41 the amide II mode signal is small in the
SFG spectra, due to the small Raman cross-section of the amide
II mode.42 We would like to note that, to properly disentangle
the H–O–D bending mode contribution from the potentiallyoverlapped amide II mode, and to verify the procedure, one
needs to carefully compare the amplitude of the bending mode
against the H–O–D concentration.
We measured the SFG intensity (I(2)) at the isotopicallydiluted water–air interface in the presence of HSA interfaces
by varying the H2O/D2O concentration. Fig. 4(a) displays thevariation of the SFG spectra. In the absence of HDO – i.e. forpure H2O and D2O-, the SFG spectra are indistinguishable andshow a signal at 1410 cm1 and a relatively weak signal between
1500 and 1550 cm1, attributed to the H–C–H bending mode or
the symmetric stretch mode of R-COO, and the amide II modeof HSA, respectively. These spectral features closely resemble
the SFG spectra obtained at pH 6.3 for the water–air interface
with bovine serum albumin.43 To extract the H–O–D bending
mode contribution from the spectra for the H2O/D2O mixtures,
we fit the spectra (see the ESI†). The obtained imaginary parts of
the response are displayed in Fig. 4(b), with the H–O–D bending
contributions highlighted, while the amplitude of the H–O–D

Strong hydrogen bond network of water in the vicinity of HSA
protein
The water–protein interaction is the key for biological function
and in particular, protein folding. Although vibrational spectroscopy has been used to understand such interactions, characterizing the hydrogen bond strength of water and protein is usuallycomplicated because the vibrational signal of water is governedby the many water molecules that are not in direct contact withthe protein. Meanwhile, the SFG signal originates intrinsicallyfrom the interfacial water and proteins at the water–protein
interfaces, allowing for a selective probe of the interfacial water
structure. Proteins, however, contain the O–H groups in theirsidechains as well as N–H groups in their backbone, both ofwhich can contribute to the vibrational response in 3000 cm1 oo o 3500 cm1, along with the O–H stretch mode of theinterfacial water.40 Thus, it is prohibited to extract the net water
contribution from the O–H stretch SFG spectra.
Here, we demonstrate that the water contribution can beextracted from the bending mode SFG spectra. Probing the
H–O–H bending mode in the presence of protein is challenging,
because the H–O–H bending mode peak (1590–1650 cm1) isThis journal is © the Owner Societies 2020

Fig. 4 SFG responses at the water–air interface in the presence of HSA.
(a) SFG intensity spectra, I(2)(o), of the water–air interface in the presence of
HSA with 1/0, 3/1, 1/1, 1/3, and 0/1 H2O/D2O mixtures. The black lines are
the fit. The spectra are offset by 0.05 for clarity. (b) Imaginary part spectra of
the HSA and H–O–D water contributions obtained from the fits. The H-O-D
contribution is highlighted in blue. The spectra are offset by 0.25 for clarity.
(c) The amplitude of the H–O–D contribution vs. H2O fraction. Theoreticalprediction denoted by the black broken line is obtained from eqn (1).

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contribution is plotted in Fig. 4(c). The variation of the amplitude shows excellent agreement with the H–O–D concentration
inferred from eqn (1), confirming the peak assignment. The
center frequency for the H–O–D contribution is 1506  3 cm1.
This frequency is substantially higher than the frequency of the
H–O–D bending mode in the bulk (B1460 cm1),44 indicatingthat the interfacial water molecules near the HSA protein are
more strongly hydrogen-bonded than water in the bulk.

Discussion
Above, we have shown that the vibrational couplings and spectral overlap of the O–H stretch mode of water with other O–H
and N–H stretch modes prohibited the extraction of the interfacial water contribution from the O–H stretch mode SFG
spectra, while the SFG probe of the water bending mode allows
us to gain the information on the hydrogen bond strength of theinterfacial water. The application of the bending mode is not
only limited to the water–solid interface or the water–protein
interface but also used for studying the interfacial water at thewater–lipid/surfactant interfaces,45–47 alcohol–water mixture
interfaces,48–52 and acid aqueous solution interface.53,54
For example, 1,2-dipalmitoyl-sn-glycero-3-phospho-(1 0 -racglycerol) (DPPG) is an essential lipid for a cell membrane,
and the DPPG–water interfaces have been studied with O–H
stretch SFG to understand the water orientations.45–47 However,a DPPG lipid has multiple O–H groups in its headgroup,
prohibiting the extraction of the net interfacial water contribution.
Having established here that the characteristic frequency of thebending mode can be obtained without any isotopic dilution, it isapparent from our previous bending SFG data at the water–DPPG
interface24 that the hydrogen bond strength of water near DPPG issimilar to that in the bulk. We observed that the characteristicfrequency of the interfacial H–O–H bending mode is 1653 cm1,i.e., very similar to 1650 cm1 in the bulk liquid. The conclusionthat water at a DPPG interface is hydrogen-bonded with bulk-likestrength also affects the interpretation of the vibrational dynamics
of the O–H stretch mode near DPPG, reported to be much slower
than the bulk water vibrational dynamics.55
We point out that the bending mode SFG probe will be
powerful for unveiling the interfacial structure of water at theinterface of water–alcohol mixtures. This system is importantfor dilution processes as well as general physical chemistry,
because upon mixing with water, the structure of the water andalcohol mixture is drastically changed, resulting in the variation of the vapor pressure. The microscopic structures of thewater–alcohol interfaces have been studied with SFG in the O–
H stretch region,48–52 but the net contribution of the interfacial
water has not been accessed. The different contributions to the
O–H stretch spectrum can now be disentangled by probing thewater bending mode in the SFG measurements.
The water bending mode signal is useful not only because its
frequency carries information on the hydrogen bond strengthof the interfacial water molecules, but also because its amplitude is sensitive to the chemical compositions. Theoretical

10938 | Phys. Chem. Chem. Phys., 2020, 22, 10934--10940

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studies have suggested that, at the water–TiO2 interface, chemisorbed and physisorbed conformations of the interfacial
water molecules17 are easily distinguished through the bending
mode amplitude.56 As such, for several cases, the water bending
mode can be a very sensitive probe for the microscopic structure of the interfacial water molecules.
In summary, our combined simulations and experiments
showed that the SFG feature of the water bending mode ofinterfacial water at the water–air interface is not distorted upon
the isotopic dilution of water (Fig. 1) and thus the vibrational
coupling of the bending modes of the interfacial water is virtuallyabsent (Fig. 2). Thus, the characteristic frequency of the bending
mode can be obtained for an arbitrary mixture of the H2O–D2O
concentration, unlike the O–H stretch mode, where the characteristic frequency can be obtained only for the isotopically diluted
water.36 Since the use of the isotopic diluted water reduces the SFG
signal drastically, our findings ensure that one can use pure H2O
for gaining the maximum SFG amplitude or can use the H–O–D
bending mode for avoiding frequency overlap with the amide I
mode. We have applied this new approach for exploring the CaF2–
water interface, and found that an increase in pH enhances thehydrogen bond strength of interfacial water (Fig. 3). Even for acomplex protein–water interface, the bending mode SFG could
successfully probe the interfacial water contribution in the H–O–D
bending mode region and revealed that the interfacial water near
the HSA protein shows a stronger hydrogen bond strength thanbulk water (Fig. 4). Altogether, our work manifests that the water
bending mode is a promising tool for understanding interfacial
water structures at various complex interfaces.

Experimental details
SFG measurement
We used a femtosecond Ti:Sapphire amplified laser system(Coherent Libra, B800 nm, B50 fs, 1 kHz). The visible and IR
beams overlapped spatially and temporally at the sample surface
with their incident angles of 641 and 401 with respect to thesurface normal, respectively. All the spectra were taken in ssp(denoting s-, s-, and p-polarized SFG, visible, and IR, respectively)
polarization combination. The signals at the water–air and water–
protein interfaces were normalized to the non-resonant signal
taken from the z-cut quartz, while the signals at the water–CaF2
interface were normalized to that from the gold–CaF2 interface.
The details of the experiments can be found in the ESI.†
Computational procedure
We computed the bending mode SFG spectra based on thesurface-specific velocity–velocity correlation function formalism;57
ð1
1
2Þ;R
wðxxz
ðo Þ 
dteioti  o2 0*+X OM r_OM
ðtÞ  rOM
ðt Þ
j
j


gds ðzi ð0ÞÞgt rij ð0Þ; rt r_z;i ð0Þ 
;

ðtÞ
i; j
rOM
j
(3)

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where zi(t) is the z-coordinate of the ith oxygen atom at time t,
and gds(zi) is the function for the dividing surface to selectively
extract the vibrational responses of D2O molecules near theinterface. rOM(t) is the vector pointing from the oxygen atom (O)jto the middle point of the two hydrogen atoms (M) for watermolecule i at time t. gt(rij(0);rt) excludes the correlation of thediﬀerent water molecules, i and j, when the oxygen–oxygen
distance of water molecules i and j (rij(0)) is larger than the
cutoff distance rt.58 We chose rt = 0, 4, and 6 Å in Fig. 2. We used
the AIMD trajectories of the D2O–air interface obtained in
our previous work.59 In short, we used the B3LYP-D3(0) and
revPBE0-D3(0) levels of theory for the AIMD simulations. The
D–O–D bend frequencies were converted to the H–O–H bendfrequencies by using a factor of 1/0.735. The detail of thescaling factors of the frequency axis can be found in the ESI.†

Conflicts of interest
The authors declare no competing interest.

Acknowledgements
We thank Prof. Masanari Okuno for fruitful discussion. We
acknowledge the financial support from the MaxWater Initiative of the Max Planck Society and the ERC Starting Grant(Grant No. 336679). K. M. acknowledges the DFG for support(DFG project No. 427448850). Open Access funding provided by
the Max Planck Society.

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3 K. Engelhardt, U. Weichsel, E. Kraft, D. Segets, W. Peukert
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