Molecular Dynamics Simulations of SFG Librational Modes Spectra of

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Molecular Dynamics Simulations of SFG Librational Modes Spectra of Water at the Water-Air Interface Remi Khatib, Taisuke Hasegawa, Marialore Sulpizi, Ellen H.G. Backus, Mischa Bonn, and Yuki Nagata J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b06371 • Publication Date (Web): 03 Aug 2016 Downloaded from http://pubs.acs.org on August 8, 2016

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The Journal of Physical Chemistry

Molecular Dynamics Simulations of SFG Librational Modes Spectra of Water at the Water-Air Interface Rémi Khatib,1 Taisuke Hasegawa,2 Marialore Sulpizi,*1 Ellen, H. G. Backus,3 Mischa Bonn,3 Yuki Nagata*3

1. Institute of Physics, Johannes Gutenberg University Mainz, Staudingerweg 7, D-55099 Mainz, Germany

2. Department of Chemistry, Graduate School of Science, Kyoto University, Sakyoku, Kyoto 606-8502, Japan

3. Department for Molecular Spectroscopy, Max Planck Institute for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany

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Abstract

At the water-air interface, the hydrogen-bond network of water molecules is interrupted, and accordingly the structure and dynamics of the interfacial water molecules are altered considerably compared with the bulk. Such interfacial water molecules have been studied by surface-specific vibrational sum-frequency generation (SFG) spectroscopy probing high frequency O-H stretch and H-O-H bending modes. In contrast, the low-frequency librational mode has been much less studied with SFG. Since this mode is sensitive to the hydrogen-bond connectivity, understanding the librational mode of the interfacial water is crucial for unveiling microscopic view of the interfacial water. Here, we compute the SFG librational mode spectra at the water-air interface by using molecular dynamics simulation. We show that the modeling of the polarizability has a drastic effect on the simulated librational mode spectra, while the spectra are less sensitive to the force field models and the modeling of the dipole moment. The simulated librational spectra display a peak centered at ~700 cm-1, which is close to the infrared peak frequency of the liquid water librational mode of 670 cm-1. This indicates that the librational mode of the interfacial water at the water-air interface closely resembles that of bulk liquid water.

I.

Introduction

Probing vibrational modes in liquids is a unique way of gaining molecular-level insight into their local structure and dynamics. For liquid water, the O-H stretching mode has been proved frequently to extract information on the local hydrogen-bond strength.1,2 Moreover, the H-O-H


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bending mode of water has provided information on the conformation of water clusters.3–5 In contrast to the O-H stretching and H-O-H bending modes, the librational mode is mixed with the delocalized translational mode, causing a very broad spectral feature in the range from 100 to 1000 cm-1.6 This librational mode has been known to be a good reporter for the connectivity of the hydrogen-bond network.7 The peak frequency of the librational mode is substantially blueshifted when the temperature is lowered and liquid water turns into ice; librational mode frequencies of liquid water is ~670 cm-1,8 while those of microporous amorphous ice, annealed ice, and crystalline ice are 770, 810, 840 cm-1, respectively.9 Furthermore, confinement of water has a strong impact on the libration mode;10,11 the peak frequency of the librational mode of the confined water is red-shifted compared with the crystal ice, suggesting a softening of the water structure in a confined environment.12 When moving from the bulk to the interface, an interface-specific vibrational technique is required to identify the contribution of the molecules located specifically at the interface. Sum-frequency generation (SFG) spectroscopy is a nonlinear optical technique which combines IR and visible pulses and permits us to selectively address vibrational modes of interfacial molecules. In this technique the contribution from the molecules in the bulk vanishes, owing to the selection rules, thus allowing us to probe the vibrational response of the interfacial molecules.13 The liquid water-air interface has been extensively investigated by SFG in the O-H stretch frequency region.14–21 A sharp peak at 3700 cm-1 in the SFG spectrum evidences that the water hydrogen-bond network is interrupted at the interface, with dangling O-H groups appearing. In addition, the SFG spectra indicate the presence of the O-H groups hydrogen-


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bonded to the other water molecules. The analyses based on the static17,18 and time-resolved22– 24

SFG studies have revealed that the interfacial water molecules are, in terms of both structure

and dynamics, very similar to bulk water. These are also supported by the number of SFG spectra simulation.25–33 Furthermore, the similarity of the interfacial water and bulk water is also consistent with the similar H-O-H bending mode frequency in the SFG spectrum of the water-air interface and in the IR spectrum of the bulk.34–37 In contrast to the O-H stretching and H-O-H bending SFG spectra, much less is known about the librational modes of the interfacial water molecules. The librational region of the SFG spectra has been measured only very recently,38 providing an important piece of the SFG water puzzle. The SFG intensity spectrum at room temperature exhibits a main band centered around 830 cm-1 at the water-air interface, which is at higher frequency than the librational mode in bulk liquid water at the same temperature (670 cm-1), and more similar to bulk ice (840 cm-1). This raises a question whether the libration mode of the interfacial water is similar to that in the ice, in contrast to the O-H stretching and H-O-H bending modes. The SFG spectra in the libration region for a water-air interface were simulated with the SPC water model by Space and co-workers,39,40 much before the experimental measurement.38 This simulation predicted a SFG peak of the libration mode at ~875 cm-1.39 Subsequent calculations with the ab initio-based POLI2VS force field model41 exhibits a residence at ~600 cm-1.36 A ~ 300 cm-1 difference in the libration peak position between these simulations36,39 suggests that the computational algorithm and/or the force field model have a strong impact on the SFG spectra in this region. In fact, theoretical vibrational spectroscopy studies of bulk liquid water have pointed out that the vibrational spectra for the librational and translational


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modes are very sensitive to the force field model and/or optical response calculations; Bosma et al. showed that the anisotropy component of the polarizability strongly affects the Raman spectra of water.42 A recent study by Hamm has demonstrated that the bulk librational mode spectra (THz, Raman, and 2D THz-Raman spectra) also strongly depend on the force field models and the optical response calculation.43 Combined, these studies suggest that a systematic investigation of the low-frequency (ω < 1000 cm-1) region of the SFG spectra is certainly needed. Therefore, we simulate the librational mode SFG spectra at the water-air interfaces with various force field models and approaches for computing the dipole moments and polarizabilities. We show that the simulated librational SFG spectra are quite sensitive to the modeling of the polarizability, whereas they are much less sensitive to the force field models and the modeling of the dipole moment. Simulated SFG spectra with the precise models provide a peak frequency at ~700 cm-1 in the imaginary part of the SFG spectra, which differs significantly from the IR peak frequency of 840 cm-1 for the ice and is rather similar to that of 670 cm-1 for the liquid water. We found that the simulated imaginary spectra with a peak frequency of ~700 cm-1 can be consistent with the experimentally measured SFG intensity spectrum with a peak frequency of 830 cm-1, due to the non-resonant contribution. These manifest that the libration mode of the interfacial water resembles that of the bulk water. This article is organized as follow. In section II, we describe the methods, including the different simulation setups and models and the details on the SFG spectra calculations. In section III, the results are presented with a discussion about the impact of the intermolecular coupling and temperature. Conclusions are given in section IV.


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II.

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Computational Details

A. MD Simulation To examine the effects of the force field model on the librational SFG features, we used both polarizable and non-polarizable force field models. For the polarizable force field models, we used two models which have already successfully been used to reproduce the bulk properties of water; the POLI2VS force field model41 and inexpensive AMOEBA (iAMOEBA) force field model.44 The POLI2VS force field model is designed to reproduce the IR and Raman vibrational spectra of bulk water and has been applied to the water-air interface to compute the SFG response,36 while the iAMOEBA model is an optimized version of the AMOEBA force field45 which is one of the most widely used polarizable water models. As non-polarizable rigid-body force field models, we used the SPC/E46 and TIP4P47 models. For all the simulations, a cell with its size of 45 Å × 45 Å × 80 Å was used, which contained 2400 water molecules. Periodic boundary conditions were employed in all directions. The electrostatic interactions were calculated using either the Ewald summation (POLI2VS model) or the particle mesh Ewald method (SPC/E, TIP4P, and iAMOEBA models). We integrated the equation of motion with a time step of 0.4 fs (POLI2VS), and 1 fs (SPC/E, TIP4P) at 300 K, while we used a time step of 0.1 fs at ~300 K for the iAMOEBA model. For the polarizable POLI2VS and iAMOEBA models, MD trajectories over 5.3 ns were recorded in the NVT and NVE ensembles, respectively, after 1 ns NVT-MD run for equilibration. For the nonpolarizable models, we obtained over 30 ns NVT MD trajectories after 2 ns equilibration NVTMD runs. For the NVT ensemble, the temperature was controlled using the Nose-Hoover chain


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thermostat for POLI2VS, TIP4P, and SPC/E model, while it was controlled by using the Langevin integrator for iAMOEBA model. Nose-Hoover chain thermostats were composed of 3 chains for TIP4P and SPC/E models and 10 chains for POLI2VS model. The time constant for the thermostat was set to 1 ps for all the NVT simulations. We used an in-house MD code for the POLI2VS model, the OpenMM code48 for iAMOEBA model, and the CP2K code49 for the SPC/E and TIP4P models. For the rigid-body SPC/E and TIP4P models, the molecular conformations were fixed by using the SHAKE algorithm. In this study, we used the molecular (xyz) frame for defining the molecular dipole moment and polarizability, while the laboratory (XYZ) frame was used for computing the SFG spectra. For the molecular frame, the z-axis was defined to be parallel to the H-O-H angle bisector of a water molecule, the y-axis perpendicular to the molecular plane defined by the three atoms of a water molecule, while the x-axis perpendicular to the z-axis on the molecular plane. For the laboratory frame, the Z-axis was normal to the interface. The point of origin of the Z-axis was set to the center of mass of the whole system. These definitions are schematically given in Figure 1.


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Figure 1: Schematics of the reference frames: (Left) Molecular frame (xyz), (Right) laboratory frame (XYZ). ZG is the position of the Gibbs dividing surface, while Zc1 and Zc2 are the parameters used in Eq. (3).

B. SFG Spectra Calculations The resonant term of the Y-polarized SFG susceptibility, , generated by the Y-polarized ,

visible and Z-polarized IR pulses, can be computed from the time-correlation function of the

dipole moment and polarizability. With the truncated correlation function formalism, the SFG susceptibility reads:50 , , , = , sin

, & , = 〈" #$% '( 0*+, 0,,

,

(1)

+ " " #$% '( 0*#$% (. 0 +, 0,., # ' . 0; *〉

.0

(2)

where = 2ℏ /'1 − 78−2ℏ * is the harmonic quantum correction factor,45 μi,Z(t)

and αi,YY(t) denote the Z-component of the dipole moment and the YY-component of the

polarizability of water molecule i at time t, respectively, while Zi(0) is the Z-coordinate of the

center of mass of molecule i at time t = 0. 〈… 〉 denotes the statistical average. We set Tmax= 600

fs. In addition, since the ab initio-based force field without nuclear quantum effects gives

slightly higher vibrational frequencies, we scaled the frequencies down by 2 % only for the simulation with the POLI2VS model.36,41 Since the water slab contains two, oppositely facing,


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water-air interfaces, we introduced #$% to flip the orientation of the water molecules near one

interface as well as to separate the two interfacial regions, which was given by: #$% ( = sign( ×

1 if (%? ≤ |( |

| |CD

(4)

C. Modeling of Dipole Moment and Polarizability To investigate the impact of the dipole moment and polarizability models on the librational SFG spectra, five different models for the dipole moment/polarizability were used in this study; the POLI2VS

model,

single-point

(isotropic/anisotropic)

models,

and

three-point

(isotropic/anisotropic) models. The model which is the most crude but has been frequently used for calculating the Raman spectra43,51–55 is the single-point dipole moment/polarizability model, in which a point dipole moment/polarizability is placed at the center of mass (M) of a water molecule. More precise modeling employs the three-point model for the dipole moment and polarizability, where the point dipole moment and polarizability are located at the atom sites.56,57 For these single-point and three-point models, the induced dipole moment and


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polarizability have been calculated from the dipole-induced dipole model in self-consistent field equations as:

where

Q. 'K. + KLM KLM = −N ∑.0 P . *,

Q . 'N. + N.LM *, NLM = −N ∑.0 P BU * Q. = RE STV BU − &RD 'ST P X. X. , W T T BU

BU

Y? Z = 1 − 1 + Z +

Y Z = 1 − 1 + Z +

$D

$D

$ ,

+

$V [

(5) (6)

(7) (8) $ .

(9)

K^] (N^] ) denotes the gas-phase dipole moment (polarizability) of water molecule i, while K]_` ]

(N]_` ] ) represents the induced dipole moment (polarizability). a is a parameter for screening the

short-range electrostatic interactions, which was set to 4.607 Å-1 58 for the three-point models

and infinite for the single-point models. In all the cases a cutoff of >10 Å has been used to compute the induced dipoles and polarizabilities in Eqs. (5) and (6). For the single-point models, we used Avila’s59 and Huiszoon’s60 polarizability and Morita’s dipole moment.25 Huiszoon’s polarizability has been frequently used for the calculation of Raman spectra. Although its anisotropic components are overestimated compared with the gas-phase experimental data, it reproduces the experimentally measured third-order librational Raman spectra.42,55 The polarizability of Avila model59 is obtained from the accurate gas phase ab initio-calculation and is more isotropic compared with Huiszoon’s polarizability. Note that this comparison – about the impact of the anisotropy of polarizability models on vibrational spectra – is similar to the discussion reported in Reference 43. For the three-point models, K^] was taken from the permanent dipole moments at the atom sites which ACS Paragon Plus Environment

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were given in the POLI2VS model,41 while N^] for a single molecule was set to be equal to the

Avila model.59 Note that we did not take into account the intramolecular electrostatic

interactions. The polarizability is thus only induced via the intermolecular interaction through the dipole-induced dipole model. For the isotropic three-point model, the point polarizabilities at the atom sites (αH / αO) were set to satisfy the ratio αH / αO = 1.3368 / 2.5694, where these ratio was obtained from Reference 58. For the anisotropic three-point model, the point polarizability at the hydrogen atom site was obtained from the gas-phase POLI2VS model,41 and the point polarizability at the oxygen atom site was set such that the total molecular polarizability was equal to the Avila model.59 These values are summarized in Table 1.

Table 1: Permanent point dipole moments/polarizabilities used for calculation of the librational SFG spectra. All the values are given in atomic units. +b,c Model Site(a) Isotropic (Avila) M 0.000 Singlepoint Anisotropic (Huiszoon) M 0.000 O 0.000 Isotropic (Avila) H ±0.063d Threepoint O 0.000 Anisotropic (Avila) H ±0.063d a from Reference 25 b

from Reference 59

c

from Reference 60

d

from Reference 41

+d,c ,bb,c 0.728a 9.92b 0.728a 10.97c 0.540d 4.86 0.049d 2.53 0.540d 5.50 0.049d 2.21d

,ee,c ,dd,c ,bd,c 9.32b 9.58b 0.00 c c 8.68 10.09 0.00 4.57 4.70 0.00 2.38 2.44 0.00 5.85 5.76 0.00 d d 1.73 1.91 ±0.58d

Beyond the point polarizability models, ab initio-based many body interaction approaches provide more accurate estimation of the dipole moment and polarizability. In this


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approach, according to ab initio-calculations, atomic dipole moments and atomic polarizabilities as well as atomic charges are integrated into the force field. The other force field parameters are adjusted to reproduce several target properties which can be either macroscopic or microscopic. These force field models have been used for the calculations of the vibrational IR and Raman spectra of water.41,61,62 Among these ab initio-based many body force field models, we used the POLI2VS model.41 In this model, the same dipole moment and polarizability were used in the MD simulation and optical response calculation.

III.

Results

A. Model Dependency of SFG Libration Spectra To examine the impact of using different methods to infer the dipole moment/polarizability ,

modeling on the SFG librational mode spectra, we calculated Im spectra from the SPC/E MD trajectories. Figures 2(a-d) show the spectra with the single-point (isotropic/anisotropic) and three-point (isotropic/anisotropic) models, while Figure 2(e) (2(f)) shows the spectra calculated with the dipole moment obtained from the single-point isotropic model (three-point anisotropic model) and the polarizability obtained from the three-point anisotropic model (single-point isotropic model). The different lines in each panel indicate the spectra with various intermolecular cross-correlation cutoff rt. The red lines in Figures 2(a-d) (rt = 0 Å) show strikingly different spectra, indicating that the different dipole moment/polarizability modeling dramatically affects the SFG librational mode spectra. In particular, there is no noticeably large peak in the frequency region of 400 cm-1 < ω < 1000 cm-1 for the single-point models, while a negative peak is present at ~430 – 570 cm-1 for the three-point models. By including the cross-


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correlation terms in the SFG response calculations, a new resonance appears for the threepoint models (isotropic model 735 cm-1, anisotropic model 760 cm-1), whereas the SFG amplitude differs dramatically among these models. We can disentangle the impact of the different approaches for calculating the dipole moment and polarizability on the librational SFG spectra by comparing Figure 2(d) with Figure 2(e) and 2(f). The spectra in Figure 2(d) are very similar to those in Figure 2(f), despite different approaches having been used for calculating the dipole moment. This clearly demonstrates that the dipole moment modeling does not critically affect the librational mode SFG spectrum. In contrast, Figure 2(d) significantly differs from Figure 2(e). Since we used different models for calculating the polarizability, these different spectra indicate that the librational model SFG spectrum is very sensitive to the specific approach for inferring the polarizability. The same trend can be also seen by comparing Figure 2(a) with Figure 2(e) and 2(f). The high sensitivity of the librational mode of the SFG spectra to the details of the modeling of the polarizability can be explained as follows. At the water-air interface, the hydrogen-bond network is interrupted, creating e.g. dangling O-H groups.13 In such a heterogeneous environment the two O-H bonds of a water molecule can experience a very different local electric field depending on the librational motion of neighboring water molecules, which would be difficult to reproduce with a single-point polarizability model. Our results indicate that such heterogeneous local environment at the water-air interface can be evaluated by placing multiple point polarizability sites on the water molecule. In contrast, the librational mode SFG spectrum is insensitive to the dipole moment modeling, presumably


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because the librational mode does not change the relative distance between molecules and thus the electrostatic interactions are almost unchanged through the librational motion.

, , simulated with the SPC/E Figure 2: Imaginary part of the resonant susceptibilities, Im

MD trajectories for various cross-correlation cutoff rt. The optical responses were calculated

with (a) single-point isotropic, (b) single-point anisotropic, (c) three-point isotropic, and (d) three-point anisotropic dipole moment/polarizability models. (e) Spectra constructed with the dipole moment calculated with the three-point anisotropic model and the polarizability with the single-point isotropic model. (f) Spectra constructed with the dipole moment calculated with the single-point isotropic model and the polarizability with three-point anisotropic model.


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Spectra were normalized so that the negative peak height of the SFG spectrum with rt = 8 Å in (d) was -1.

In the following, we explore the effect of different force field models of water on the librational mode of the SFG spectra. To do so, we also calculated the librational SFG spectra from the TIP4P and iAMOEBA MD trajectories. In both cases, we used the single-point anisotropic model for the optical response calculation. The simulated SFG responses, displayed in Figure 3, show a very similar trend to the results obtained using the SPC/E MD trajectory (Figure 2(b)). This clearly indicates that the librational SFG features are quite insensitive to the force field models. As a further comparison, we calculated the spectra by using the (polarizable) POLI2VS MD trajectory and the POLI2VS model for the optical response calculation (Figure 4). The calculated spectra are again very similar to the spectra simulated with the SPC/E MD trajectory and the three-point anisotropic model (Figure 2(d)). This further corroborates the conclusion that the water force field model does not affect the shape of the SFG response for the librational mode. Our analysis leads to the conclusion that the dipole moment model and force field model do not affect the SFG libration feature. This is in contrast to the O-H stretch SFG feature at the water-air interface, where different force field models and ab initio simulations provide qualitatively different spectra.25–32


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Figure 3: SFG spectra simulated with (a) the TIP4P MD trajectory and (b) the iAMOEBA MD trajectory. The single-point anisotropic dipole moment/polarizability model was used for the optical response calculations.

Figure 4: (a) SFG spectra simulated with the POLI2VS MD trajectory and POLI2VS model for the optical response calculation with various correlation cutoff rt. (b) Comparison of the spectra with rt = 6 Å calculated using POLI2VS and SPC/E water models. The POLI2VS model is the same as in (a), while the single point isotropic, single point anisotropic, three-point isotropic, and


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three-point anisotropic models with the SPC/E water model are the same as in Figure 2(a), (b), (c), and (d), respectively.

B. Effects of Vibrational Coupling on SFG Libration Spectra We next discuss the effect of the cross-correlation on the simulated libration mode spectra. For all the spectra in Figures 2, 3, and 4, the spectra appear to converge as the cutoff radius reaches rt = 6 Å. In other words, the librational mode is not coupled between the water molecules which are distant beyond 6 Å. The intermolecular coupling of the water molecules within the first hydration shell (~3 Å) critically affects the librational mode in the SFG spectra and generates a new peak at 520 – 670 cm-1. By increasing rt from 4.5 to 6.0 Å the peak position is blue-shifted to 660 – 760 cm-1 (660 cm-1 for the POLI2VS model). No further dramatic changes were observed in the range rt = 6 to 8 Å, suggesting that no major contribution comes from water molecules beyond the second hydration shell. This result indicates that the librational band in the SFG spectrum arises from the cooperative molecular motion involving the water molecules within the second hydration shell. The delocalized nature of the librational mode had already been reported for (bulk) liquid water;6,63–65 the instantaneous normal mode analysis showed that the librational modes were strongly delocalized within a 5 - 8 Å cutoff sphere,6,66 which is in good agreement with our observation.

C. Comparison with Previous Simulations Here, we compare our results with the previous simulations.36,39 The peak frequencies of 660 – 760 cm-1 in our simulated spectra differs from the peak frequency of 870 cm-1 in


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Reference 39. In the previous computational works36,39, the induced dipole moment and induced polarizability were neglected for the SFG spectra calculation, based on the observation that the induced dipole moments do not change the peak frequency in bulk water, although the intensity is strongly affected.41,67 However, the induced dipole moments may affect the SFG peak frequency of the librational mode at the water-air interface in a different way from that in the bulk. Indeed, the different spectra reported in the current study and the previous study39 seem to indicate that the inclusion of the induced dipole moments causes a shift of the resonance of the librational mode in the SFG spectra. Furthermore, it should be pointed out that the half width of half maximum (HWHM) for the librational mode above the peak frequency side (>750 cm-1) in Figure 2(c), 2(d) and Figure 4 amounts to ~150 cm-1, which is substantially larger than the HWHM of ~60 cm-1 predicted in the previous simulation paper.39 The peak frequency of ~600 cm-1 predicted in our previous study,36 is below the frequency of 660 – 760 cm-1 predicted in this study. In Reference 36, we have focused on the SFG bending mode feature where the intermolecular coupling does not affect the SFG feature and thus we used the cross-correlation cutoff of 4 Å. As is shown in this paper, the 4 Å cutoff including couplings with the water molecules within the first hydration shell is not sufficient for capturing the librational mode and by including the second hydration shell water in the response functions, the SFG peak is blue-shifted. This demonstrates that the influence of the intermolecular couplings on the vibrational spectra may be different for each vibrational mode.

D. Comparison to Experiment


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, The peak of the librational mode in the simulated Im is located at ~660 – 750

cm-1 when using three-point models (Figure 2(c) and (d)) or POLI2VS model (Figure 4(a)). Note

that the comparison of the spectra with rt = 6 Å with various models is given in Figure 4(b). The peak frequencies in the simulated imaginary part spectra are red-shifted by over 100 cm-1 compared with the peak frequency of 875 cm-1 observed in the homodyne SFG experimental , and data.38 However, to allow for a meaningful comparison between the simulated Im

the experimentally measured SFG intensity data (ISSP(ω)), we need to take the non-resonant

signal68 and the Fresnel factors69,70 into account. To examine the consistency of the simulated , with the experimentally measured ISSP, we used the equation:

r, , l hiij ∝ lm ino m pqi m q +

where

r,

, ∝ lm q s tuv + l ,

(10)

denotes the non-resonant susceptibility, and mcc is the frequency-dependent

Fresnel factor.71 The Fresnel factors for the SFG and visible light are frequency-independent and

therefore we omit the terms m ino and m pqi . We use simulated with the ,

SPC/E MD trajectory, the three-point anisotropic model, and the cross-correlation cutoff of rt =

8 Å (blue line of Figure 2(d)). m is calculated with the equations given in Reference 69

using the refractive index of water for the interfacial layer70 and the refractive index of water

from Reference 72. The parameters s and wr are associated to the amplitude and the phase

of the non-resonant signal, respectively. We fit our simulated to the experimentally ,

measured intensity data (ISSP) in the frequency range from 720 to 1030 cm-1. The comparison

between the fits and experimental data for the two experimental setup geometries (geometry I


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Page 20 of 31

and II)38 are shown in Figure 5. From the fittings, we obtained the parameters sxy / lIm l ,

z{|

= 0.82 ± 0.09, wr,xy = 16 ± 5 °, sxyy /lIm l ,

z{|

= 0.97 ± 0.16 and wr,xyy = 20

± 5 °. The index gI (gII) stands for the setup geometry I (II),38 while lIm l ,

z{|

is the maximal

intensity of Im between 200 and 1200 cm-1. The difference of s/lIm l ,

,

z{|

and wr

between the parameters for setup geometry I and II are within the error bars, showing the consistency between the two data sets. The agreement between the fit and the experimental data demonstrates that for the broad librational mode the peak position in the imaginary resonant part of the SFG spectrum and the SFG intensity spectrum may differ by ~100 cm-1. This observation suggests that special care should be taken when the homodyne SFG librational mode spectra is analyzed. A previous study has concluded that the vibrational nature of the libration mode are similar between ice and interfacial water, based on the observation that the librational mode peak frequencies are similar for the IR spectra of ice and the SFG spectra of interfacial water.38 However, when only the resonant contribution from the calculation is taken into account, the frequency of the librational mode is 660 – 750 cm-1, which would rather indicate a liquid-like librational mode (the peak frequency of librational mode in the bulk water is ~700 cm-1). Further simulation work and/or heterodyne measurement would be very helpful to understand the nature of the librational mode of water at the water-air interface.


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Figure 5: (a) Imaginary and real parts of the spectrum simulated with the SPC/E MD ,

trajectory and three-point anisotropic dipole moment/polarizability model are shown in solid

, in this figure is the same as the blue line of Fig. 2(d). The dashed line. Note that Im

lines represent the non-resonant contributions obtained from our fitting (setup r,

geometry I of Reference 38). Experimentally measured ISSP(ω) vs. the fit of the SFG intensity

with the simulated }} spectrum for the (b) setup geometries I and (c) setup geometry II. ,

Experimentally measured spectra were normalized.

E. Temperature Dependence We further simulated the temperature dependence of the librational mode SFG responses. From the discussion above, it is apparent that the cross-correlation cutoff of rt = 6 Å is adequate to capture the librational mode of the SFG response. Thus, we used this cutoff. Furthermore, to accelerate the simulation, we used a smaller system of 500 POLI2VS water molecules contained in a 26.6 Å × 26.6 Å × 160 Å cell. The MD simulations were performed in the NVE ensemble and temperatures of 282, 293, 305, 318, and 331 K were used. The details of the simulation can be found elsewhere.73


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Page 22 of 31

The simulated spectra are shown in Figure 6. This figure indicates that with decreasing temperature, the peak position becomes increasingly blue-shifted. This trend is opposite to the O-H stretching mode, where the hydrogen-bond strength becomes stronger with decreasing temperature, making the O-H stretch frequency shift to the red side, while it is similar to the frequency shift of the IR librational mode of bulk water.8 Furthermore, the SFG amplitude increases with decreasing temperature. The IR librational mode spectrum of bulk liquid water also shows a similar trend.8 This indicates that the librational mode of interfacial water at the water-air interface is similar to that in bulk water. Finally, we comment on the NVT ensemble and NVE ensemble. The calculated spectra using the MD simulation in the NVT ensemble is also plotted in Fig. 6. This demonstrates that the calculated spectra are not sensitive to the ensemble used in the MD simulation.

Figure 6: Temperature dependence of the SFG spectra simulated with the POLI2VS MD trajectories. The spectra have been normalized so that the negative peak at 305 K has a minimal value of -1. The spectra calculated with the POLI2VS MD simulation at 300K in the NVT


22

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ensemble is also plotted. This data is the same as that shown in Figure 4(a). A scalling factor has been used in order to take into account the ratio between the cross-section of the NVE and NVT boxes.

IV.

Conclusions

We simulated the librational mode of the SFG spectra at the water-air interface with various force field models and dipole moment/polarizability models. The peak associated to the librational mode is surprisingly insensitive both to the details of the force field model and to the models for computing the dipole moment, whereas it is strongly affected by the polarizability modeling. In the SFG spectra at the water-air interface, the local environment is highly heterogeneous, so that the variation of the polarizability due to the librational motion is inadequately captured by using the single-point polarizability, unlike the depolarization Raman spectra in the bulk;42 the molecular polarizability can be well captured by placing the point polarizabilities at each atom site (three-point polarizability model). Since the O-H stretching mode SFG features are reported to be very sensitive to the force field model and/or the dipole moment modeling, the current results indicate that the level of theory required for calculating the vibrational spectra is clearly mode-dependent: different approaches are required for correctly describing the O-H stretching mode and librational mode of a water molecule. Our analyses using the truncated response function formalism indicate that the coupling to the first hydration shell water generates a peak in the imaginary part of the susceptibility at ~520 – 670 cm-1, while the coupling to the second hydration shell (~6 Å) shifts the peak to 660 – 760 cm-1. The coupling of a water molecule beyond the second hydration shell does not affect


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Page 24 of 31

the librational mode, which is in good agreement with a previous study for bulk water. Our simulated spectra indicate that the librational mode frequency is not so close to the frequency of bulk crystal ice (~840 cm-1), but rather in between the peak frequencies of crystal ice and liquid water (~670 cm-1) or even closer to the peak frequency of liquid water. This seems consistent with the previous conclusions drawn from the O-H stretch SFG spectra at the waterair interface that the interfacial water is not ice-like.16,18,20,22,23,74 Furthermore, the current study indicates that the librational mode vibrational spectra are sensitive to the polarizability modeling of a water molecule, in particular in a heterogeneous environment. This knowledge is crucial not only for simulating the SFG spectra but also for simulating the Raman, 2D-Raman,75–78 2D-Raman-THz spectra43,79,80 in bulk water as well as in ionic solutions.

Corresponding Author *Email: [email protected] (tel: +49 6131 379-380); [email protected] (tel: +49 6131 3923641)

Notes The authors declare no competing financial interests. ACKNOWLEDGMENTS We are grateful to Yujin Tong and Kramer Campen for sharing experimental data and their manuscript with us before publication. M.S. and Y.N. thank the German Science Foundation


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through the project of TRR 146. The simulations were performed on the Mogon ZDV cluster and on the Cray XC40 Hornet at the HLRS supercomputing center.

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Ito, H.; Hasegawa, T.; Tanimura, Y. Calculating Two-Dimensional THz-Raman-THz and Raman-THz-THz Signals for Various Molecular Liquids : The Samplers. J. Chem. Phys. 2015, 141, 124503.

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Molecular Dynamics Simulations of SFG Librational Modes Spectra of

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