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1 Hydrogen bonding at the water surface revealed by isotopic dilution spectroscopy Igor V. Stiopkin, 1,2 Champika Weeraman, 1,3 Piotr A. Pieniazek, 4 Fadel Y. Shalhout, 1,5 James L. Skinner, 4 and Alexander V. Benderskii1 1,5* 1 Department of Chemistry, Wayne State University, Detroit, MI Current address: Department of Chemistry, University of Wisconsin-Madison, Madison, WI Current address: Steacie Institute for Molecular Sciences, National Research Council, Ottawa, ON, Canada 4 Department of Chemistry, University of Wisconsin-Madison, Madison, WI Current address: Department of Chemistry, University of Southern California, Los Angeles, CA 989 * Corresponding author. alex.benderskii@usc.edu 1. Experimental Details: HD-SFG We use the broad-band SFG scheme, where a femtosecond (broad-band) infrared (IR) pulse excites the vibrational coherence and a picosecond (narrow-band) visible pulse up-converts it into the SFG signal. 1,2 Using another recent technical development, a 35 fs time-delay was introduced between the IR and visible pulses in order to maximize the SFG signal and at the same time improve spectral resolution and reduce the nonresonant background. 3 While the conventional homodyne detection directly measures the intensity of the SFG signal emitted by the sample, the HD-SFG technique records an interference pattern of the SFG optical field and a reference beam (the so-called local oscillator, LO). The amplitude and phase of the SFG signal are obtained using broad-band spectral 1

2 interferometry (SI), 4,5 by setting a 2.5 ps time delay between the SFG signal and LO pulses which are made collinear and passed through a monochromator. This produces a fringe pattern in the frequency domain, recorded by a CCD detector. HD-SFG interferograms were recorded using 1 min. acquisition time. The phase drift between the signal and LO pulses was measured to be less than λ/1 over 1 min, so that phase fluctuations did not affect the contrast of the inteference fringes. Standard SI analysis including inverse and forward Fourier transforms as well as filtering in the time domain was implemented to recover phase and amplitude of the SFG spectrum. 4,5 All recorded spectra were all phased with respect to a single selected reference, the 1% H 2 O spectrum, using the fringes in the off-resonant part of the interferogram above 28 cm. 5 After phasing, 2-5 interferograms were averaged for each isotopic dilution (Fig. 2). The spectral phase of all SFG signals was then set such that the imaginary part of the SFG spectrum is zero in the off-resonance part of the spectrum, around 282 cm. This part of the spectrum agrees with the phase-sensitive SFG measurements by Tian and Shen 6 where the imaginary part of χ (2) for the air/water interface of 1% to 33% O:H 2 O solutions were measured to be close to zero around 28 cm. Additionally, this is also consistent in that the frequency-independent nonresonant background term is purely real in the spectral curve fitting. We note that the peak amplitudes and frequencies of the free OD in HOD and O extracted from the fitting are practically insensitive to the value of the absolute phase of the SFG spectrum. 2

3 SSP PPP 2 1 HOD O 1% 2 HOD O 1% Amplitude, a.u. 1 75% 5% Amplitude, a.u % 5% 25% 25% Frequency, cm Frequency, cm Figure 2. Heterodyne-detected vibrational SFG spectra of the free OD stretch at the air/water interface of isotopic mixtures H 2 O:HOD: O. The D/H mole fraction is indicated in each spectrum. Left panel shows spectra recorded for SSP polarization combination of SFG-vis-IR beams; Right panel shows PPP spectra. Solid blue and red lines are the experimentally measured real and imaginary parts of the SFG signal. Dashed lines represent the fitting to a sum of Lorentzian terms and a nonresonant background, B (2) NR j i j ( IR ) ANRe j ( IR j) i as described in the text; The components of the resonant j part of the response used in the fitting are shown as shaded Lorentzian peaks. The two narrow peaks with interchanging amplitudes (shaded orange and yellow) are assigned, respectively, to the free OD of O and HOD molecules at the interface, as detailed in the text. 3

4 The uncertainty in determining absolute frequencies, δω= 2 cm, is due to the SFG spectrometer calibration (performed using the liquid DMSO/air interface as the frequency standard) and curve fitting. The estimated uncertainty in the reported value of the shift between the free OD of HOD and O, δδ= 1.5 cm is somewhat smaller due to cancellation of the frequency calibration error. Peak Frequency, cm Peak Area, a.u SSP cm HOD/ O Fraction 4 A. B. Peak Frequency, cm Peak Area, a.u C. D PPP E. F. cm HOD/ O Fraction Figure 3. A, B: Peak areas from spectral fitting (Lorentzian B j Γ j ) of the free OD of DOD peak (blue squares), and free OD of HOD peak (red squares), as a function of isotopic dilution. The scaling expected based on isotopic scrambling, taking into account that O has two potential free ODs while HOD has one, is shown in solid lines (right axis). C, D: Peaks frequencies (Ω j from Lorentzian fit) of the free OD of DOD peak, blue circles, and free OD of HOD peak, red circles, as a function of isotopic dilution. E, F: Line widths (Γ j from Lorentzian fit) of the free OD of DOD peak, blue diamonds, and free OD of HOD peak, red diamonds, as a function of isotopic dilution. Left panel shows the fitting results for SSP spectra, right - for PPP spectra. The lines between experimental points are to guide the eye only. 4

5 2. MD simulations and spectral calculations. We simulated slabs of 512 SPC/E H 2 O and O molecules for 2 ns. The former trajectory was directly used to study dilute HOD in H 2 O. Box dimensions were 25Å x 25Å x 8Å and the temperature was maintained at 3K. The simulated slab has two surfaces, and the contributions to the sum-frequency spectrum from each surface have equal magnitude but opposite sign. Therefore, a spectral calculation for the full slab produces no signal. To compare with experiment we need to calculate the signal from a single interface, and to do this, we need to assign molecules to the upper or lower parts of the slab. In this work we follow the usual convention of doing this by oxygen position: 8,9 If the oxygen atom of a water molecule is in the upper half-slab, then the entire molecule is assigned to that slab. A more extensive discussion of this partitioning issue is presented elsewhere. 7 Spectral simulations were performed using the mixed quantum/classical approach. The O-H (D) oscillators are treated quantum mechanically, while the rest of the system is treated as a classical bath. The resulting time-correlation function expressions for the susceptibility have been given elsewhere. 8,9 Within our ES/MD (electronic structure/molecular dynamics) approach the required polarizabilites, transition dipoles, frequencies, and intramolecular couplings are obtained from a limited number of ab initio calculations on clusters from bulk water simulations. 1 To make extensive calculations possible these are hence expressed as linear or quadratic functions of the electric field on hydrogen atoms, referred to as spectroscopic maps. Intermolecular coupling is represented within the transition dipole moment model. In particular, the electric field map of the intramolecular coupling in O obtained from ab initio calculations on water clusters combined with the MD simulations was used to evaluate 5

6 the intramolecular coupling between the free OD and the other OD stretch on the same O molecule at the interface, γ S ~48 cm (Fig. 4E), scaled down from the gas-phase value of γ 6 cm (23, 26) due to the local interfacial environment. P(ω ij ) E. FreeOD -intra FreeOD -inter Bulk - inter intra Gas-phase -intra ω ij, cm ij Figure 4. E. Distribution of the coupling strengths: intramolecular coupling in surface O molecules that have a free OD, i.e. coupling between the free OD and the other OD (γ S, black line); intermolecular coupling between OD stretches of bulk-phase water molecules (blue); intermolecular coupling of the free OD to OD stretches on other waters (red); intramolecular coupling in the gas-phase O molecule, 6 cm (yellow). The following criteria were used for identifying the free OD molecules: (1) ODstretch frequency is above 268 cm ; (2) molecule is positioned within 6 Å of the Gibbs dividing surface; (3) the angle between the free OD vector and the vector from D to the nearest oxygen of another water molecule is larger than 9 o. The spectrum calculated using only OD oscillators tagged as free according to this definition coincides with the spectrum calculated for the whole system above 268 cm. Analysis of the MD trajectories yields 23% of water molecules at the air/water interface having free OD, in agreement with earlier MD simulations 11 and experiments Spectral feature at 268 cm The experimentally measured SSP spectra of pure O show a broad shoulder with positive imaginary part at ~268 cm (Γ~5 cm ) (indicated by black arrow in Fig. 6

7 4B,C). This feature decreases with isotopic dilution (Fig. 2), suggesting that it is a result of vibrational coupling between the OD chromophores. It is not observed in the PPP spectra at any isotopic dilution (Fig. 2). Im[ (2) ] (a.u.) SSP B. C. HOD DOD IR frequency (cm ) 1 Im[ (2) ] (a.u.) SSP DOD HOD Frequency, cm Figure 4. B. Experimentally recorded Im[χ (2) ] SSP spectra of the air/water interface of pure O (blue) and 25%:75% O:H 2 O mixture (red). C. Theoretically calculated Im[χ (2) ] SSP spectra for free OD of isolated surface HOD molecule in H 2 O (red) and O molecule in pure O (blue). The simulations faithfully reproduce this feature, including its isotopic dilution and polarization dependence. Fig. 4C shows the calculated SSP spectra, which correspond to a single tensor element of the second order nonlinear susceptibility, χ (2) XXZ. Fig. 5 shows all calculated elements of the χ (2) tensor. Note that the PPP spectrum includes several tensor elements, but is dominated by the ZZZ element, whereas the SSP spectrum contains only the XXZ element. 7

8 Frequency, cm Figure 5. Calculated χ (2) tensor elements for the coupled (dashed lines) and uncoupled (solid lines) cases. Note that the 268 cm shoulder is present only for the XXZ element and only in the coupled case. Selectively turning off inter- vs. intramolecular coupling in the simulations suggests the intramolecular coupling as the origin of this feature. Analysis of the MD trajectories by the hydrogen bond classes 13 shows that this 268 cm feature is due to O molecules with 2 donor and 1 acceptor hydrogen bonds. While these molecules are on-average oriented with both hydrogens down, the intramolecular coupling in O switches on an antisymmetric linear combination of the two local modes which has the higher frequency. Its transition dipole moment is an upward pointing vector difference, giving positive contribution to Im[ (2) ]. Thus, the 268 cm peak can be thought of as the manifestation of the asymmetric stretch character of O, with the caveat that the intermolecular coupling (which is relatively strong for these bulk-like molecules) 8

9 delocalizes the excitations over several molecules and thus renders the asymmetric/symmetric designation meaningless. References 1. L. J. Richter, T. P. Petralli-Mallow, J. C. Stephenson, Opt. Lett. 23, 1594 (1998). 2. A. N. Bordenyuk, A. V. Benderskii, J. Chem. Phys. 122, (25). 3. I. V. Stiopkin, H. D. Jayathilake, C. Weeraman, A. V. Benderskii, J. Chem. Phys. 132, (21). 4. L. Lepetit, G. Cheriaux, M. Joffre, J. Opt. Soc. Am. B 12, 2467 (1995). 5. I. V. Stiopkin, H. D. Jayathilake, A. N. Bordenyuk, A. V. Benderskii, J. Am. Chem. Soc. 13, 2271 (28). 6. C. S. Tian, Y. R. Shen, J. Am. Chem. Soc. 131, 279 (29). 7. P. A. Pieniazek, C. J. Tainter, and J. L. Skinner, Interpretation of the water surface vibrational sum-frequency spectrum, submitted for publication (211). 8. Auer, B. M. & Skinner, J. L. Vibrational sum-frequency spectroscopy of the liquid/vapor interface for dilute HOD in O. J. Chem. Phys. 129, (28). 9. Auer, B. M. & Skinner, J. L. Vibrational Sum-Frequency Spectroscopy of the Water Liquid/Vapor Interface. J. Phys. Chem. B 113, (29). 1. Corcelli, S. A., Lawrence, C. P. & Skinner, J. L. Combined electronic structure/molecular dynamics approach for ultrafast infrared spectroscopy of dilute HOD in liquid H 2 O and O. J. Chem. Phys. 12, (24). 11. Morita, A. & Hynes, J. T. A theoretical analysis of the sum frequency generation spectrum of the water surface. Chem. Phys. 258, (2). 12. Du, Q., Superfine, R., Freysz, E. & Shen, Y. R. Vibrational Spectroscopy of Water at the Vapor Water Interface. Phys. Rev. Lett. 7, (1993). 9