Ab Initio Modeling of the Vibrational Sum-Frequency Generation

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Ab Initio Modeling of the Vibrational SumFrequency Generation Spectrum of Interfacial Water Chungwen Liang, Jonggu Jeon, and Minhaeng Cho J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b00291 • Publication Date (Web): 25 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry Letters

Ab initio Modeling of the Vibrational Sum-Frequency Generation Spectrum of Interfacial Water Chungwen Liang,∗,† Jonggu Jeon,‡ and Minhaeng Cho∗,‡,¶ †Computational Modeling Core, Institute for Applied Life Sciences (IALS), University of Massachusetts Amherst, Amherst 01003, Massachusetts, USA ‡Center for Molecular Spectroscopy and Dynamics, Institute for Basic Science (IBS), Korea University, Seoul 02841, Korea ¶Department of Chemistry, Korea University, Seoul 02841, Republic of Korea E-mail: [email protected]; [email protected]

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Abstract Understanding the structural and dynamical features of interfacial water is of greatest interest in physics, chemistry, biology and material science.

Vibrational sum-

frequency generation (SFG) spectroscopy, which is sensitive to the molecular orientation and dynamics on the surfaces or at the interfaces, allows one to study a wide variety of interfacial systems. The structural and dynamical features of interfacial water at the air/water interface have been extensively investigated by SFG spectroscopy. However, the interpretations of the spectroscopic features have been under intense debate. Here, we report a simulated SFG spectrum of the air/water interface based on ab initio molecular dynamics simulations, which covers the OH stretching, bending and libration modes of interfacial water. Quantitative agreement between our present simulations and the most recent experimental studies ensures that ab initio simulations predict unbiased structural features and electrical properties of interfacial systems. By utilizing the kinetic energy spectral density (KESD) analysis to decompose the simulated spectra, the spectroscopic features can then be assigned to specific hydrogen-bonding configurations of interfacial water molecules.

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Sum-frequency generation (SFG) is one of the second order nonlinear optical (NLO) ~ ir ) and a subsequent responses of materials, which is generated after an infrared field E(ω ~ vis ) interact with a nonlinear optical material. 1–3 The second-order polarvisible field E(ω ization P~ (2) (ωSF G ) that oscillates at the frequency ωSF G (= ωir + ωvis ) is then determined by the second-order susceptibility χ(2) of the system. Due to the fact that the second order response vanishes in a centrosymmetric (bulk) material, the SFG response is exclusively enhanced at the surface or interfacial region where the centrosymmetry is broken. 4 Making use of this advantage, vibrational SFG spectroscopy 5 has been widely used to investigate the properties of molecules on surfaces or at interfaces over the past decades, such as peptide configurations, 6–9 water hydrogen bonding (H-bonding) structure, 10,11 and water dangling OH bond at the air/water interface. 12–14 Among various systems, interfacial water is of great interest in physics, chemistry, biology and material science. It is believed that the structure and dynamics of interfacial water change dramatically from those in bulk water, due to the fact that the H-bonding network is largely disturbed by the presence of interfaces. Air/water interface is one of the most studied systems for revealing the structure and dynamics of interfacial water due to its simplicity. The first SFG spectroscopy experiment 15 resolved the structural feature of interfacial water at the air/water interface by probing the OH stretching mode: a sharp peak ∼ 3700 cm−1 due to the presence of the water dangling OH bonds, and the broad band ranges from 3100 to 3600 cm−1 which originates from the H-bonded water molecules. With the development of phase-sensitive SFG spectroscopy technique capable of probing Im[χ(2) ] of the system, 13,16 the molecular orientation of interfacial water can be determined by identifying the sign of the SFG signal. It is generally assumed that the dipole orientation of the water molecules with dangling OH bonds preferentially points toward the air, while that of the H-bonded water molecules points toward the bulk phase, due to the fact that the signal of the sharp peak (∼ 3700 cm−1 ) is positive and that of the broad band (3100 ∼ 3600 cm−1 ) is negative. In particular, the existence of the positive peak around 3000 cm−1 , which was observed in

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Im[χ(2) ] spectra from the Shen group, 13,16 lacks an intuitive interpretation, and the origin of this positive signal has been under intense debate. 17–19 Now, an accord seems to have been reached that this weak low-frequency signal, even if exists, is a non-resonant background unrelated to specific molecular vibrations in this frequency region. 20–22 It was shown by several experimental studies that the feature of the positive peak around 3000 cm−1 highly relies on the spectroscopic setup and the choice of phase reference. 16,17,19,20 On the other hand, computational approaches are able to predict the SFG spectrum of interfacial water in the OH stretch region using classical MD simulations with parametrized potential models (simple point charge models, 23–25 polarizable models, 17,26 and inclusion of the three-body 27,28 and many-body 29 interactions), with mixed quantum mechanics and molecular mechanics (QM/MM) approaches, 30,31 and with density functional theory (DFT)based potentials. 32,33 The Paesani group has also reported the SFG singal based on the centroid MD 29 which incorporates nuclear quantum effects with a parametrized many-body potential model. However, there is no clear answer about whether the positive peak around 3000 cm−1 exists or not. These discrepancies among various simulation studies indicate that the calculation of SFG signal is highly sensitive to the simulation approaches and models applied. Therefore, a more robust simulation with higher level of theory is necessary to provide more insights into these controversies mentioned above. In addition, resolving the water bending and libration modes using SFG spectroscopy can provide more information for understanding the structure and dynamics of interfacial water. On one hand, two recent SFG studies 34,35 claimed different features of water bending mode ∼1650 cm−1 . On the other hand, a recent simulation work suggested that the water libration phase-sensitive SFG signal should be similar as bulk water 36 and this interpretation was contradicted by a recent experimental work, 37 due to the fact that the experimental SFG intensity (homodyne detection) is blue-shifted comparing to the resonant imaginary signal (simulation or heterodyne-detection) when the non-resonant background is considered. In this letter, we aim at modeling the full frequency range SFG spectrum from ab initio

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MD simulations of interfacial water at the air/water interface, which provides a more rigorous picture to understand its structural features. This study can be distinguished from previous attempts to obtain DFT MD based SFG signals of interfacial water 32,33 by the application of an accurate dispersion correction method, a rigorous way to extract the molecular dipole and polarizability trajectories from the DFT MD simulation, and unprecedented amount of trajectory sampling (4.9 ns in total) to produce accurate signal. In practice, ab initio simulations were performed at the DFT level using the CP2K package. 38 The exchange and correlation (XC) energy is described by the BLYP functional 39,40 and the TZV2P basis set was chosen. Dispersion interactions are accounted for by a variant of the DFT-D3 method 41 which uses the Becke-Johnson damping function 42 with damping parameters proposed by Smith et al. 43 This correction is expected to strengthen the H-bonding and simultaneously mitigate the excessive ordering of liquid structure, greatly improving liquid-state description of water. 44 The detailed simulation approach is described in the Supporting Information (SI). To obtain the resonant part of the system second-order susceptibility χ(2) , a classical time correlation function formalism 34 was employed: (2)Res χijk (ωir )

DX n

iωir = kb T

Z

∞

e−iωir t dt

t=0

αij,n (t) · µk,n (0) +

XX n

E αij,n (t) · µk,m (0)

(1)

m6=n

where the indices i, j, k refer to the Cartesian components x, y and z, and m and n to water molecules. kB and T are the Boltzmann constant and temperature. h...i denotes the ensemble average. α and µ are the molecular polarizability and dipole of the water molecule. The first term in Eq. 1 accounts for the self-correlation of the time-dependent molecular dipole and polarizability fluctuation of water molecules, and the second term accounts for the cross-correlation between a pair of water molecules. The detailed formalism and approximations that are necessary for reducing computational cost are described in the SI. In order to compare with the experimental phase-sensitive SFG measurements that 5



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Figure 1: Simulated IR (a), Raman (b), and SFGxxz(yyz) (c) spectra of interfacial water. In (c), the libration+bending regions (left) and the OH stretch region (right) are displayed.

(2)

are commonly performed under the SSP polarization scheme χSSP , we limit ourselves to (2)Res

calculate the system susceptibility χxxz

(2)Res

and χyyz

. The overall simulated SFG signal is

then the average between the two. For calculation of the time-dependent molecular dipole, we employ the maximally-localized Wannier function scheme (implemented in the CP2K package) to evaluate the instantaneous molecular dipole of each water molecule including polarization, charge transfer and many-body effects. For calculation of the time-dependent molecular polarizability, we introduce an efficient mapping scheme which has been suggested for the water hyperpolarizability calculations. 45 This allows one to accurately and efficiently determine the tensor elements of water polarizability at the level of coupled-cluster (CC) theory based on the configurations extracted from MD snapshots. The detailed mapping procedure is described in SI. We first calculated the infrared (IR) and Raman spectra from the bulk liquid water sim6


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ulation (see SI for simulation details) to validate the models that we proposed for molecular dipole and polarizability calculations (Figure 1 (a),(b)). It can be seen that our simulation well reproduces the line shapes of both experimental IR and Raman spectra. This provides the evidence that the estimation of the water molecular dipole and polarizability is reliable. However, the BLYP functional is known to underestimate the OH harmonic vibrational frequencies of an isolated water molecule by ∼160 cm−1 compared to CCSD(T) prediction 46 and this partially accounts for the observed ∼ 200 cm−1 redshift of the OH stretching mode. In addition, we found a ∼ 130 cm−1 blueshift of the libration mode which, together with the red shift of the OH stretch peak, indicates that the H-bonding strength is slightly overestimated in the current description. A more detailed discussion of this discrepancy can be found in the SI. We then modeled the SFG spectrum of interfacial water and the result is shown in Figure 1 (c). It can be seen that our simulation well reproduces the features of the OH stretching band (Figure 1 (c), right): a sharp positive peak at ∼ 3700 cm−1 , a broad negative peak between 3100 and 3600 cm−1 , and a weak positive peak around 3000 cm−1 . The simulated SFG spectrum matches the latest experimental measurement qualitatively, 20 which suggests that the positive peak around 3000 cm−1 should be weak. The simulated SFG signal corresponding to the water bending mode shows a fully positive peak at ∼ 1660 cm−1 (Figure 1 (c), left). This quantitatively matches a recent SFG measurement and simulation, 35 although the quadrupole contribution (which is suggested to be crucial) is not taken into account in our calculations. It is worth noting that another simulation study 34 predicted a different feature that the bending mode of interfacial water produces a combination of a negative low frequency peak (∼ 1660 cm−1 ) and a positive high frequency peak (∼ 1689 cm−1 ). In addition, the water libration mode exhibits a broad negative band at ∼ 800 cm−1 (Figure 1 (c), left), which is qualitatively consistent with a previous simulation study by Nagata and coworkers 36 which suggested a negative peak at ∼ 700 cm−1 . They claimed that there is a good agreement between their simulated |χ(2) |2 spectrum and a |χ(2) |2 SFG

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measurement 37 after a fitting procedure which takes into account the non-resonant signal. While the simulation study 36 suggested that the libration mode of interfacial water closely resembles that of bulk water, the experimental study 37 claimed that the libration mode of interfacial water is blue shifted ∼ 165 cm−1 compared to that of bulk water, which indicates that the libration motion of interfacial water behaves like bulk ice. Our simulation shows that the difference between the peak position in the IR spectrum of bulk water and that of the SFG spectrum of interfacial water is negligible. This supports the finding of the previous simulation study. 36 However, to our knowledge, there is no available phase-sensitive SFG experimental spectrum for direct comparison so far. Further phase-sensitive SFG measurement could be a benchmark to validate current simulation results. Since the OH stretching signal at 3000 cm−1 is under intense debate in both theoretical and experimental studies, it is important to quantify its magnitude and perform further investigation to reveal its origin. We thus calculated the depth-dependent SFG spectra using different Zc values (as described in the SI) shown in Figure 2 (a). It can be seen that the non-negligible positive signal is produced by including deeper water layers (Zc = 1 or 2 Å). On the other hand, if the calculation only includes the topmost layers of interfacial water (Zc = 4 Å), the 3000 cm−1 signal is negative. To further elucidate the origin of the positive 3000 cm−1 signal, we divided the interfacial water into five sections (according to the depth) and calculated the SFG spectra explicitly from each section (Figure 2 (b)). We found that the water molecules which are located in a deeper region from surface (|Z|=0∼4 Å) indeed contribute to the positive 3000 cm−1 signal. This illustrates that the positive 3000 cm−1 signal, if exists, does not originate from the topmost layers of interfacial water (the density profile in Figure 3 (a) yields the Gibbs dividing surface at z = 6.9 Å and the interfacial thickness 23 of 1.9 Å) and the sign of the signal can be altered by including different depths of interfacial water. We found that the depth dependence of the 3000 cm−1 signal can be explained by the H-bonding structure and the kinetic energy spectal density (KESD) 47,48 analyses of the DFT

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Figure 2: Simulated SFG spectrum of interfacial water according to (a) different depths (b) different layers.

MD trajectories. Following our previous study, 49 we first classify all the OH groups in the system into four types denoted as xOHy, according to the H-bond donating status of the OH group in question (x = h, f) and that of its conjugate OH group in the same molecule (y = h, f), regardless of the H-bond accepting status of the oxygen atom. Here, “h” and “f” represent that the OH group is making an H-bond as a donor or not, respectively. The geometric criteria of rO···O < 3.3 Å and 6 O − H · · · O > 150◦ are used for H-bond classification. 49 Using different H-bond criteria could change the quantitative results in Figures 3 and S2 to a small degree but the qualitative interpretation of the calculated SFG signal based on this analysis should remain unchanged. The population and the bond orientation of the four ˆ were calculated from the same set of DFT types of OH groups along a surface normal (k) MD trajectories as in the SFG signal calculation. The OH bond orientation is expressed by ˆ where ˆrHO is a unit vector parallel to the OH bond vector rH − rO . uHO = ˆrHO · k, z The results are plotted in Figure 3 (a) and (b) as a function of the z coordinate of the oxygen atom. The figure shows that, inside the water layer (|z| < 4 Å), ∼10% of OH groups exist as type hOHf and they are aligned in parallel with the surface normal on average. In contrast, hOHh, which is the predominant type in |z| < 4 Å, is oriented nearly randomly

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with huHO z i ≈ 0 inside the water layer. As Figure 3 (c) and (d) and Figure S2 in SI show, hOHh and hOHf are the only two types exhibiting appreciable vibration at ∼3000 cm−1 . 49 The reason for such low OH stretching vibrational frequency at 3000 cm−1 is due to the strong h-bonding interaction between hOHh/hOHf species and surrounding water molecules. However, due to their nearly isotropic orientational distribution, hOHh would not contribute much to the observed SFG signal at ∼3000 cm−1 . On the other hand, OH groups of type hOHf can be assigned as the major source of the positive 3000 cm−1 SFG signal in |z| < 4 Å, due to their significant vibration in that frequency region and their alignment in parallel with the surface normal. We note that, despite the relatively small population of ∼10% of the hOHf species, the 3000 cm−1 SFG signal due to them will be disproportionately larger because of the strong frequency dependence of the transition dipole of the OH stretch mode (non-Condon effect). 50 This may explain the large discrepancies in previous computational SFG spectra of the water/air interface mentioned above. 17,23–33 It is likely that different modeling approaches predict different population, orientation, and vibrational frequency of the singly H-bonded water molecules (hOHf), due to the fact that it is still very challenging to accurately model the intermolecular interaction between water molecules at interfaces. Although this discrepancy is fairly subtle, by taking into account different thicknesses of the water layer for the SFG signal calculation, a noticeable difference can be expected in term of the sign and amplitude of the 3000 cm−1 signal. The existence of the singly H-bonded water molecules (hOHf/fOHh) in a deeper layer (0 Å < |z| < 4 Å) and how the contribution of hOHf results in a positive 3000 cm−1 signal can be rationalized as follows. In a shallow layer (4 Å < |z| < 6 Å), hOHh, which is a predominant type in that region, strongly points toward liquid phase in search of H-bond acceptors (Figure 3 (b)). To accommodate these OH groups of type hOHh, the H-bond network right below them needs to be partially distorted. This distortion would mostly affect types hOHf/fOHh (they share same water molecules), because hOHf/fOHh are single H-bond donors and therefore expected to be less restrained in the H-bond network and

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more susceptible to structural perturbation than double donor water molecules (hOHh). This structural perturbation then introduces a subtly anisotropic alignment of hOHf and fOHh species, pointing toward the interface (huz i > 0 for z > 0) and liquid phase (huz i < 0 for z > 0), respectively. Due to the fact that the vibrational frequency of hOHf spans between 2800 and 3600 cm−1 (Figure 3 (d)) and its positive orientation with respect to the interface normal, slightly anisotropic hOHf species in a deeper water layer can give rise to a noticeable depth-dependent SFG signal at 3000 cm−1 . This finding demonstrates the high sensitivity of SFG spectroscopy to subtle molecular alignment, and it could help explaining the inconsistencies among reported experimental and theoretical SFG spectra of interfacial water. A current hypothesis derived from SFG experiments suggests that the weak low-frequency signal at 3000 cm−1 should come from a non-resonant background (with respect to different references using for the phase determination), and it is unrelated to specific molecular vibrations of interfacial water in this frequency region. 20–22 However, according to our findings, probing deeper water layers will enhance the positive 3000 cm−1 signal. It is likely that current SFG experiments only explore relatively shallow region of the interface less than ∼3 Å deep. Therefore, it could be worthwhile to further investigate the penetration depth dependence of experimental SFG signals possibly by employing visible pulses with different wavelengths or changing the incident angles of laser pulses. In summary, we have performed ab initio MD simulations of interfacial water at water/air interface. Based on the molecular configurations and the electrical properties derived from DFT and CC methods, we were able to model the full frequency range phase-sensitive SFG spectrum of interfacial water. The simulated SFG spectrum well reproduces the OH stretching, bending, and libration modes of the most recent experimental spectra, which ensures that ab initio simulations predict unbiased structural features and electrical properties of interfacial systems. We also showed that the KESD analysis provides rich information to decompose the spectroscopic features into specific H-bonding configurations of interfacial water

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Figure 3: Dependence of OH group properties on the H-bond donating status (xOHy) and the location along the surface normal (z). (a) Number density of OH groups. (b) OH bond orientation. (c) KESD of hOHh. (d) KESD of hOHf.

molecules. The present work suggests that ab initio MD simulations allow one to accurately predict the structural and dynamical properties of a wide variety of molecular surfaces and interfaces, which provides insights into interpretations of experimental measurements.

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Acknowledgement This work was supported by IBS-R023-D1.

Supporting Information Available AUTHOR INFORMAITON Corresponding Authors: Chungwen Liang, ORCID: 0000-0001-9721-6411 Minhaeng Cho, ORCID: 0000-0003-1618-1056 Notes: The authors declare no competing financial interest.

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Ab Initio Modeling of the Vibrational Sum-Frequency Generation

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