Vibrational Coupling at the Topmost Surface of Water Revealed by

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Vibrational Coupling at the Topmost Surface of Water Revealed by Heterodyne-Detected Sum Frequency Generation Spectroscopy Yudai Suzuki, Yuki Nojima, and Shoichi Yamaguchi* Department of Applied Chemistry, Graduate School of Science and Engineering, Saitama University, 255 Shimo-Okubo, Sakura, Saitama 338-8570, Japan S Supporting Information *

ABSTRACT: Unraveling vibrational coupling is the key to consistently interpret vibrational spectra of complex molecular systems. The vibrational spectrum of the water surface heavily suffers from vibrational coupling, which hinders complete understanding of the molecular structure and dynamics of the water surface. Here we apply heterodynedetected sum frequency generation spectroscopy to the water surface and accomplish the assignment of a weak vibrational band located at the lower energy side of the free OH stretch. We find that this band is due to a combination mode of the hydrogen-bonded OH stretch and a low-frequency intermolecular vibration, and this combination band appears in the surface vibrational spectrum through anharmonic vibrational coupling that takes place exclusively at the topmost surface.

the free OD band (2745 cm−1) in the Im χ(2) spectrum of the D2O surface.37 This 2680 cm−1 band of D2O corresponds to the 3640 cm−1 band of H2O, and they tentatively assigned it to the antisymmetric stretch of D2O with two donor (D) hydrogen bonds and one acceptor (A) hydrogen bond that can be abbreviated to DDA water. In this Letter, we will experimentally prove that the 3640 cm−1 band originates from a combination mode of the hydrogen-bonded OH stretch and a low-frequency intermolecular vibration, and this combination band borrows intensity from the free OH stretch through Fermi resonance. This intensity borrowing occurs in DAA water that has one free OH bond, one donor hydrogen bond, and two acceptor hydrogen bonds at the topmost surface. Figure 1a shows the complex χ(2) spectrum of the H2O surface in the free OH region obtained by using a singlechannel HD-SFG spectrometer24,27,38 with the SSP polarization combination (S: sum frequency output, S: visible input, P: IR input) where the S and P polarizations correspond to electricfield vector perpendicular and parallel to the plane of incidence, respectively. This χ(2) spectrum is in good agreement with the spectra recorded throughout the whole OH stretch region in previous papers.23−25 The imaginary and real parts show absorptive and dispersive line shape, respectively. The Im χ(2) spectrum exhibits a sharp positive peak at 3697 cm−1 assignable to the free OH stretch of DAA water at the topmost surface. The positive sign indicates OH pointing upward to the air. A broad positive shoulder band is observed around 3640 cm−1,

T

he surface of liquid water has physicochemical properties distinct from the bulk, giving rise to surface-specific chemical reactions1 and chemical equilibria.2 Most of the unique properties of the water surface are attributed to the hydrogen bond network sharply truncated at the surface, which brings about free (dangling) OH groups with no partner to accept a hydrogen bond. The free OH at the water surface was first experimentally discovered by the Shen group using vibrational sum frequency generation (SFG) spectroscopy that has intrinsic surface selectivity and submonolayer sensitivity.3,4 Since then, SFG spectroscopy of aqueous interfaces has been reported by a number of groups,5−16 and knowledge of SFG spectra of the water surface including the bend17−20 and libration21,22 as well as stretch23−30 modes has been accumulated to an extent somehow comparable to that of IR and Raman spectra of bulk water, although thorough understanding of surface vibrational signatures of water is yet to be achieved. For elucidating the microscopic origin of the intriguing properties of the water surface, it is of particular importance to gain an insight into surface molecular structure by carrying out reliable assignment for vibrational SFG spectra. An unassigned vibrational band still exists around 3640 cm−1 as a shoulder at the lower energy side of the free OH band (3697 cm−1) in the vibrational spectrum of the water (H2O) surface.23−25 This unassigned band is recognized only in heterodyne-detected (HD-) SFG spectra that can manifest the imaginary part of the second-order nonlinear optical susceptibility (Im χ(2)),31,32 whereas it is hardly discernible in conventional SFG spectra33−36 that provide |χ(2)|2 (absolute square of χ(2)) because of its small amplitude. Benderskii and co-workers performed HD-SFG spectroscopy and observed a shoulder band around 2680 cm−1 at the lower energy side of © XXXX American Chemical Society

Received: February 9, 2017 Accepted: March 13, 2017

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Figure 1. χ(2) spectra of the surfaces of (a) H2O and (b) isotopically diluted water (H2O triply diluted by D2O) measured with the SSP polarization combination. Red and black open circles connected by dotted lines represent the experimental data of Im χ(2) and Re χ(2), respectively. Red and black solid curves represent global fits for the imaginary and real parts of χ(2), respectively. Blue curves stand for a single Lorentz function corresponding to the free OH stretch bands obtained from the global fitting analyses. The total band areas in the Im χ(2) spectra are shaded by green lines.

1/3 simply expected from the dilution ratio. Even if one takes into account nuclear quantum effects at the water surface reported by Nagata et al.,41 the ratio as much as 0.49 is too large to expect. (The present discussion does not negate a future study that may discover more enhanced nuclear quantum effects.) This apparent inconsistency can be lifted by estimating the ratio from the total band area indicated by the portion shaded with green lines in Figure 1a,b. The ratio of the shaded area in Figure 1b to that in Figure 1a is estimated at 0.31, which is compatible with 1/3 within the experimental uncertainty. The total band area is almost the same as the single Lorentz band area in the case of the isotopically diluted water, as can be obviously seen in Figure 1b. Thus, the difference of the ratios (0.49 and 0.31) originates almost solely from the contribution of the 3640 cm−1 band in Figure 1a. This strongly indicates that the 3640 cm−1 band has to be included into the estimation of the area, meaning that this band borrows intensity from the free OH stretch. Here we propose that the most probable mechanism of the intensity borrowing is Fermi resonance42 between the free OH stretch (3691 cm−1) and a combination mode of the hydrogen-bonded OH stretch (∼3450 cm−1) and a low-frequency intermolecular vibration (∼200 cm−1), as depicted in Figure 2. Within this mechanism, the 3640 cm−1 band is assigned to the combination band borrowing intensity from the free OH stretch through Fermi resonance. The vanishing of the 3640 cm−1 band upon isotopic dilution can be straightforwardly understood, because HOD cannot have the free OH and the hydrogen-bonded OH simultaneously. The red shift of the free OH stretch upon isotopic dilution can be ascribed to the removal of the energylevel repulsion characteristic of Fermi resonance.42 Although the combination mode is possible either at the surface or in the bulk, the free OH (or at least long-lived free OH) can exist only at the surface. Therefore, the anharmonic vibrational coupling in this mechanism is possible exclusively with DAA water at the topmost surface. The low-frequency intermolecular vibration of

the assignment of which is what we discuss in this paper. Figure S3 in the Supporting Information (SI) shows the |χ(2)|2 spectrum arithmetically obtained from χ(2) in Figure 1a, which agrees very well with an authentic |χ(2)|2 spectrum reported by Wang et al.33 This means that the χ(2) spectrum of the H2O surface in the present study is consistent with previous conventional SFG data that failed to indicate the existence of the 3640 cm−1 positive band.33−36 Figure 1b shows the χ(2) spectrum of the surface of isotopically diluted water obtained under the same spectroscopic condition as Figure 1a, where H2O was triply diluted by D2O, resulting in [H2O]:[HOD]:[D2O] = 1:4:4 on the assumption of isotopic scrambling. This dilution ratio indicates that two-thirds of the OH vibrational resonance is due to HOD, and one-third is due to H2O. One can notice three changes in the χ(2) spectrum upon isotopic dilution. First, Re χ(2) (the real part of χ(2)) is always less than zero in Figure 1b. This is because the resonant feature is reduced by isotopic dilution to be overwhelmed by the nonresonant background that is a real negative constant.39,40 Second, the free OH peak shows a red shift to 3691 cm −1 upon isotopic dilution. Although contribution from H2O must exist at 3697 cm−1, the present signal-to-noise ratio and the small peak-position difference (3697−3691 = 6 cm−1) do not allow for assuming two separate peaks in the spectrum. The red shift upon isotopic dilution was reported also for the free OD.37 Third, the 3640 cm−1 band almost vanishes in isotopically diluted water, which is also consistent with the isotopic dilution dependence of the free OD spectra studied by Benderskii et al.37 If one assumes that the contribution of the free OH stretch to the spectra is expressed by a single Lorentz function, one can readily separate its contribution from the others by fitting analyses (see SI for details), as shown by blue curves in Figure 1a and 1b. The ratio of the single Lorentz band area of the free OH in the isotopically diluted water (Figure 1b) to that in H2O (Figure 1a) is estimated at 0.49, which is obviously larger than 1397

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charge, following IUPAC.) The reorientation in the double layer was demonstrated by the sign change of Im χ(2) in the hydrogen-bonded OH stretch region with NaI.45 (Note that the dipole of hydrogen-bonded water at the neat water surface points downward to the bulk on average.48) The free OH band shows a marginal change in heterodyned and conventional SFG spectra,36,45,46 indicating that the topmost surface is almost unaffected. Re χ(2) and Im χ(2) at 3697 cm−1 (Figure 3) are almost independent of the NaI concentration, which is consistent with the double-layer picture, as the 3697 cm−1 band is due to the free OH at the topmost surface. Figure 3 shows that Re χ(2) and Im χ(2) at 3640 cm−1 are also almost independent of the NaI concentration, strongly indicating that the 3640 cm−1 band is not due to water molecules in the double layer where the sign of χ(2) is expected to be reversed due to the NaI-induced reorientation of water. Because it is likely that DDA water is located mainly in (or below) the double layer, the assignment of the 3640 cm−1 band to the antisymmetric stretch of DDA water37 is improbable. The assignment to the combination mode of topmost DAA water proposed in the present study is compatible with the NaI concentration dependence of χ(2) at 3640 cm−1. Figure 4 shows the χ(2) spectrum of the H2O surface in the free OH region with the SPS polarization combination (S: sum

Figure 2. Schematic energy-level diagram of Fermi resonance between the free OH stretch and the combination mode of the hydrogenbonded OH stretch and a low-frequency intermolecular vibration.

∼200 cm−1 probably has large contribution from the stretch of hydrogen bonds43 between two molecules, one of which is topmost DAA water. The assignment of the 3640 cm−1 band to the combination mode can be further supported by two more experiments. Figure 3 shows the NaI concentration dependence of χ(2) at

Figure 3. NaI concentration dependence of χ(2) at 3697 and 3640 cm−1 at the H2O surface. Red and black circles represent the experimental data of Im χ(2) and Re χ(2) at 3697 cm−1, respectively. Red and black triangles represent the experimental data of Im χ(2) and Re χ(2) at 3640 cm−1, respectively. Dotted lines just connect the data points. The top panel is a cartoon approximately illustrating the effect of the electric double layer formed by Na+ and I−. It does not intend to mean that all DDA water molecules are located within the double layer. A part of DDA molecules may exist above or below the double layer.

Figure 4. χ(2) spectrum of the H2O surface measured with the SPS polarization combination. Red and black open circles connected by dotted lines represent the experimental data of Im χ(2) and Re χ(2), respectively. Solid curves are eye guides.

3697 and 3640 cm−1 at the H2O surface. It is already wellknown that NaI forms an electric double layer “just below” the topmost surface where I− ions with higher surface preference are located “above” surface-inactive Na+ ions.9,36,44−47 According to the microscopic schematic picture of the NaI solution surface (top panel of Figure 3) established by SFG36,45,46 and MD studies,47 the static electric field between I− and Na+ reorients water molecules in the double layer with directing their permanent dipole moments upward to the air, whereas water at the topmost surface is almost unperturbed. (The direction of the dipole is defined to be from negative to positive

frequency output; P: visible input; S: IR input). This SPS spectrum is in good agreement with the theoretical prediction calculated by Morita (Figure S4 in SI).49 The vibrationally resonant feature in SPS is much smaller than in SSP (Figure 1a), resulting in Re χ(2) dominated by the nonresonant background. Positive signals due to the resonances at 3697 and 3640 cm−1 can be barely identified in the Im χ(2) spectrum (Figure 4). Nevertheless, this positive sign of the 3640 cm−1 band in SPS has significant meaning in the assignment. Wang and co-workers thoroughly described how χ(2) depends on the 1398

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ACKNOWLEDGMENTS We thank Dr. Toshiki Sugimoto (Kyoto University) for stimulating discussion. This work was supported by JSPS KAKENHI Grant Numbers JP15K13616, JP15KT0056, and JP25104005.

molecular hyperpolarizability and tilt angle of water at the surface,50 which clearly states that χ(2) in resonance with the antisymmetric stretch measured with the SPS polarization combination has the opposite sign to that with SSP (see SI for details). Then the assignment of the 3640 cm−1 positive band in SSP found in Figure 1a to the antisymmetric stretch of DDA water leads one to expect a negative band in SPS, but actually the Im χ(2) spectrum in SPS (Figure 4) definitely exhibits positive signals around 3640 cm−1. Again the assignment to DDA water is improbable. The same positive sign of the 3697 and 3640 cm−1 bands in the Im χ(2) spectrum in SPS (Figure 4) supports the assignment of the 3640 cm−1 band to the combination mode of topmost DAA water, because within the present mechanism, the 3640 cm−1 band just borrows intensity from the 3697 cm−1 band with no sign change. Finally, an additional remark is made on the assignment. Richmond and co-workers reported that AA water that has no donor hydrogen bond and two acceptor hydrogen bonds at the water/CCl4 interface exhibits the totally symmetric OH stretch at 3618 cm−1.51 Also in size-selected protonated water clusters, A water that has no donor hydrogen bond and one acceptor hydrogen bond is identified with IR spectroscopy, and it shows the totally symmetric OH stretch around 3640 cm−1.52,53 These studies may enable one to think that it is plausible to assign the 3640 cm−1 band found in the present study to the totally symmetric OH stretch of AA or A water at the topmost surface. However, this assignment cannot be reconciled with the χ(2) spectrum with the SPS polarization combination, because the Im χ(2) spectrum in SPS (Figure 4) exhibits no signal assignable to the antisymmetric OH stretch of AA or A water that is expected to show a stronger band around 3720 cm−1 than the 3640 cm−1 band in SPS. In conclusion, the present experimental results illustrate that the 3640 cm−1 shoulder band in the Im χ(2) spectrum of the water surface is assigned to the combination mode of the hydrogen-bonded OH stretch and a low-frequency intermolecular vibration. This combination band borrows intensity from the free OH stretch through Fermi resonance, that is, anharmonic vibrational coupling taking place in topmost DAA water. The present experimental study does not allow us to identify the intermolecular vibrational mode and to quantify the anharmonic coupling strength. 2D SFG spectroscopy54−59 will be very effective to gain insight into this coupling. Theoretical studies of the low-frequency modes and vibrational anharmonicity of the water surface are also awaited.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00312. Experimental details, |χ(2)|2 spectrum, fitting analysis, expressions of χ(2) in SSP and SPS, and SPS spectrum in the whole OH stretch region (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Shoichi Yamaguchi: 0000-0002-2710-5983 Notes

The authors declare no competing financial interest. 1399

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