Water Interface Revealed by

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Temperature Dependence of the Air/Water Interface Revealed by Polarization Sensitive Sum-Frequency Generation Spectroscopy Daniel R. Moberg, Shelby C Straight, and Francesco Paesani J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b01726 • Publication Date (Web): 03 Apr 2018 Downloaded from http://pubs.acs.org on April 4, 2018

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The Journal of Physical Chemistry

Temperature Dependence of the Air/Water Interface Revealed by Polarization Sensitive Sum-Frequency Generation Spectroscopy Daniel R. Moberg, Shelby C. Straight, and Francesco Paesani∗ Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, United States E-mail: [email protected]

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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The temperature dependence of the vibrational sum-frequency generation (vSFG) spectra of the air/water interface is investigated using many-body molecular dynamics (MB-MD) simulations performed with the MB-pol potential energy function. The vSFG spectra calculated for different polarization combinations are then analyzed in terms of molecular auto-correlation and cross-correlation contributions. To provide molecular-level insights into interfacial hydrogen-bonding topologies, which give rise to specific spectroscopic features, the vSFG spectra are further investigated by separating contributions associated with water molecules donating 0, 1, or 2 hydrogen bonds to neighboring water molecules. This analysis suggests that the low frequency shoulder of the free OH peak which appears at ∼3600 cm−1 is primarily due to intermolecular couplings between both singly and doubly hydrogen-bonded molecules.

Introduction Aqueous interfaces play a key role in several processes relevant to biological, physical, earth, and atmospheric sciences. 1–4 Electrochemical systems can display different surface arrangements of water molecules depending on the electrode, 5–7 and many geophysical processes such as rock weathering, erosion, and glacial flow can be understood in terms of aqueous interfaces. 8,9 The structure and function of DNA is greatly influenced by the presence of interfacial water molecules in the major and minor grooves of the strands. 10–12 The structure and dynamics of molecular systems at the interface are generally different from the bulk region. While techniques such as photoelectron spectroscopy, 13 surface enhanced Raman spectroscopy, 14,15 and the BOXCAR and attenuated total reflection versions of two-dimensional (2D) infrared spectroscopy 16 are capable of providing information on the near-surface environment, they do not provide true surface specificity, with depths ranging from 1 to 100 nm below the surface, depending on system and specific experimental setup. 17 Vibrational sum-frequency generation (vSFG) spectroscopy 18–20 is an experimental 2


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technique that takes advantage of the non-centrosymmetric character of molecular interfaces to probe the second-order nonlinear susceptibility and recover a surface-specific signal. In these experiments, visible and tunable infrared lasers are overlapped in space and time, resulting in a reflected signal with the combined sum frequency. 21 The most common polarization combination is the SSP combination, where the letters specify the polarization of the vSFG, visible, and infrared beams, respectively, with S and P referring to beams parallel and perpendicular to the surface, respectively. 17,22 Among various aqueous interfaces, the air/water interface holds a special place, as it serves as a reference for understanding the behavior of more complex aqueous interfacial systems. Early vSFG experiments on the air/water interface were limited to measuring a signal proportional to the absolute square of the second-order nonlinear susceptibility, (2)

|χSSP |2 . 18–20,23 These spectra allowed for the identification of three main features corresponding to the stretching mode of free OH bonds at ∼3700 cm−1 , as well as two peaks attributed to hydrogen-bonded molecules, both weakly bound as in bulk water at ∼3400 cm−1 and strongly bound as in bulk ice around 3200 cm−1 . 18 An unambiguous interpretation (2)

of |χSSP |2 is, however, difficult to derive due to the interference between real and imaginary components of the second-order nonlinear susceptibility, and contributions from the nonresonant background. Without knowledge of the relative phase, there are multiple combinations (2)

of real and imaginary components that give rise to the same |χSSP |2 spectrum. 24 (2)

Before experimental measurements of the purely absorptive Im[χSSP (ω)] were available, theoretical methods were critical in interpreting the experimental spectrum. Molecular dynamics (MD) simulations provided the earliest predictions of the phase separated real and imaginary parts of the vSFG signal. 25,26 Normal mode-based methods also provided more granular details on the spectroscopic contributions in a system at different polarization combinations. 27,28 While different methods varied in the spectral details, there was general agreement on two main features in the OH stretching region: a positive high frequency free OH stretch peak and a broad negative band from hydrogen-bonded stretch modes at lower fre-

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quencies. 29–31 Advances in phase-sensitive vSFG experiments have allowed for the experimental de(2)

termination of the relative phase between real and imaginary components of χSSP . 32–34 Heterodyne-detected vSFG (HD-vSFG) both amplifies the vSFG signal and provides the phase through interference with a high energy local oscillator reference beam. 33 Measurements of the imaginary component of the air/water interface display the free OH peak at 3700 cm−1 as well as the negative hydrogen-bonded region between ∼3200 cm−1 and ∼3600 cm−1 , in good agreement with theoretical predictions. What was unexpected, however, was the presence of a positive feature near ∼3100 cm−1 , referred to as OH(x) and initially attributed to strongly hydrogen-bonded water molecules oriented towards the interface in a tetrahedral ice-like configuration. 35,36 After the first experimental measurements were reported, theoretical models struggled to explain and replicate the OH(x) feature. Several interpretations were proposed, including the effect of anisotropic local electric fields at the water surface 37 and the interplay of different contributions from various hydrogen-bonding environments. 38,39 MD simulations based on density functional theory (DFT) have also provided conflicting results, with an initial study displaying the OH(x) peak 40 which, however, is absent from vSFG spectra calculated more recently using similar theoretical/computational (2)

approaches. 41,42 New experimental measurements of Im[χSSP (ω)] performed with a picosecond heterodyne setup 43 have provided evidence for the absence of the OH(x) peak from the actual vSFG spectrum of the air/water interface, suggesting that initial measurements were affected by artifacts associated with the reference material. Recent MD simulations 44–47 agree with the new experimental data and show that, while the vSFG spectrum of the air/water interface in the low frequency OH stretching region is strongly influenced by intermolecular coupling, it remains negative. 45 Most experimental and theoretical studies of the air/water interface have focused on the OH stretch lineshape, and only in recent years has the bending region attracted interest, both experimentally and theoretically. 48–51 The bending mode of water is key to determining

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vibrational energy relaxation in liquid water. It also provides additional information on the surface structure due to both the absence of intramolecular coupling (since there is only one bending mode per molecule) and weaker intermolecular coupling (given the more localized nature of the bending mode compared with the stretching mode). 50,52 While studies using different polarization combinations have been previously conducted, 23,27–29,53,54 no temperature dependent analysis has been reported for the imaginary components of the (2)

different vSFG spectra. The temperature dependence of |χSSP |2 for the air/water 44 and air/ice 55,56 interfaces has been studied by combining experimental measurements with MD (2)

simulations. The difference spectrum for the imaginary component of χSSP at 300-303 K was also calculated from MD simulations, 57 showing three distinct temperature dependent features corresponding to a blue shift of the broad hydrogen-bonded negative band and a broadening of the free OH peak. In Ref. 44, the comparison between experimental and the(2)

oretical Im[χSSP ] at various temperatures showed that the free OH stretch peak is temperature independent, while the negative band associated with hydrogen-bonded water molecules in the interfacial region varies with temperature. This dependence was attributed to the variation of the optical activity of water with temperature and not to structural changes of the hydrogen-bond network at the interface. Building upon the accuracy of many-body molecular dynamics (MB-MD) simulations with the MB-pol potential energy function reported in Ref. 47, the present study investigates the temperature dependence of the vSFG spectra of the air/water interface calculated with different polarization combinations in the bending and stretching regions with the goal of providing a fully, self-consistent interpretation of the molecular structure at the air/water interface.

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Theory and Methods Since the theory of vSFG spectroscopy 22,24,58–61 along with specific applications to the air/water interface 44,45,62–64 has already been reported in the literature, only details relevant to the present study will be discussed here. Considering a slab that extends along the x and y directions, with the surface located at z = 0, the general expression of the resonant vSFG polarization, Pp , is given by 21,65–70

Pp =

(ef f ) vis IR Eq Er χpqr

(2)

=

vis IR χ(2) pqr Eq Er

κ

+p

κ2

vis IR eiϕ χ(3) pqrz Eq Er 2

+ (∆kz )

Z

0

Ezdc ei∆kz z dz. (1)

−∞

(3)

Here, χpqr and χpqrz are the resonant second-order and third-order susceptibilities of the material, respectively, where the indexes p, q, and r run over the Cartesian components x, y, and z, and Einstein’s notation is used in the summation of the tensor product. In Eq. 1, Eqvis and ErIR are the electric fields of the incident visible and infrared lasers, respectively, 1/κ is the Debye screening length, ϕ is the χ(3) phase angle, Ezdc is the static electric field generated by interfacial charges and/or net polarized dipoles, and ∆kz is the inverse of the coherence (3)

length of the vSFG process. To good approximation, the χpqrz term on the right-hand side of Eq. 1 can be neglected for interfaces with small interfacial electric potentials, such as the air/water interface. 70–72 It thus follows that, within the dipole moment approximation, the (2)

resonant vSFG polarization for these interfaces only depends on χpqr , which is represented by a time correlation function of the system dipole moment and polarizability operators. Replacing the quantum mechanical expression with its classical counterpart and including a (2)

quantum correction prefactor allows χpqr to be expressed with the time-dependent formalism as 26,73

χ(2) pqr (ω)

ω =i kB T

Z

∞

dt eiωt hµr (0)αpq (t)i

0

6


(2)

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Here, ω is the vibrational frequency, kB is Boltzmann’s constant, µ and α are the system dipole moment vector and polarizability tensor, respectively, and the angle brackets indicate an ensemble average. In order to account for the lack of nuclear quantum effects and decreased anharmonicity in the classical MD simulations, the spectra are redshifted to align their features with a linear fit to the difference between infrared spectra calculated with centroid molecular dynamics (CMD) and classical MD simulations. 74 From 238 K to 368 K, the redshift ranges from 59.4 cm−1 to 50.2 cm−1 in the bending region and 156.0 cm−1 to 166.7 cm−1 in the stretching region. The full list of redshift values used are listed in Table S1 in the Supporting Information. It is important to note that, beyond the frequency redshift, the actual vSFG spectral lineshape remain effectively unchanged upon inclusion of nuclear quantum effects. 47 By separating molecular auto-correlation from cross-correlation contributions, the total correlation function of the dipole moment and polarizability tensor can be rewritten as X XX hµr (0)αpq (t)i = h µi,r (0)αi,pq (t)i − h µi,r (0)αj,pq (t)i. i

i

(3)

j6=i

where the two sums run over all water molecules, and the first and second terms are the molecular auto-correlation (ACF) and cross-correlation (CCF) functions, respectively. Following Ref. 62, Eq. 3 can be further simplified as X XX 3 3 hµr (0)αpq (t)i = h µi,r (0)αj,pq (t)gsc (zi )gt (rij , rt )i µi,r (0)αi,pq (t)gsc (zi )i + h i

i

(4)

j6=i

where gt (rij , rt ) is a stepwise function that enforces cross-correlations only between molecules i and j that are within a predefined cutoff distance rt (in this study, rt = 4.0 ˚ A), and gsc (zi )

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is the screening function     0 if |z| ≤ zcl     gsc (zi ) = sign(z) × cos2 π(|z|−zc2 ) if zc1 < |z| ≤ zc2 2(zc1 +zc2 )       1 if zc2 < |z|

(5)

gsc (zi ) is designed to smoothly transition from including molecules with full contribution to (2)

χpqr (above zc2 from the center of mass of the slab) to eliminating contributions from the bulk (below zc1 from the center of mass of the slab). h i (2) In this study, Im χpqr (ω) was calculated from Eqs. 2 and 4 using classical MB-MD simulations 75 carried out with the MB-pol potential energy function. 76–78 MB-pol has been shown to correctly predict the properties of water across different phases, 79 reproducing the vibration-rotation tunneling spectrum of the water dimer, 76 the energetics, quantum equilibria, and infrared spectra of small clusters, 77,80–82 the structural, thermodynamic, and dynamical properties of liquid water, 78,83 the energetics of the ice phases, 84 the infrared and Raman spectra of liquid water, 74,75,85 the sum-frequency generation spectrum of the air/water interface at ambient conditions, 47 and the infrared and Raman spectra of ice Ih , 86 and the electronic band gap of liquid water, both in the bulk and at the air/water interface. 87 The MB-MD simulations were performed at seven temperatures (238 K, 258 K, 278 K, 298 K, 318 K, 338 K, 368 K) for a water slab containing 512 molecules centered along the z direction in a rectangular box of dimensions 26 × 26 × 100 ˚ A3 in periodic boundary conditions. The simulations were carried out using in-house software based on the DL POLY 2 MD software, 88 modified to include MB-pol. Starting from initial configurations taken from Ref. 47, the system was equilibrated at each temperature in the canonical (NVT = constant number of molecules - constant volume - constant temperature) ensemble. The equations of motion were propagated using the velocity-Verlet algorithm with a time step of 0.2 fs and the temperature was controlled via Nosé-Hoover chains of four thermostats coupled to each

8


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degree of freedom. 89–91 A cutoff of 9 ˚ A was used to calculate the short-range interactions, while the long-range electrostatic interactions were evaluated in reciprocal space using the Ewald summation technique. Starting from the equilibrated configurations extracted from the NVT simulations, 40 independent trajectories of 50 ps each were then simulated at each temperature in the microcanonical (NVE = constant number of molecules, constant volume, h i (2) constant energy) ensemble. These trajectories were used to calculate Im χpqr (ω) according to Eqs. 2 and 4, using “1B+NB” (“one-body + N-body”) dipole moments and “1B” (“onebody”) polarizability tensors as described in Ref. 47. The angles of the visible and infrared beams were set to 67◦ and 63◦ , respectively, with the visible laser wavelength set to 800 nm, corresponding to the experimental setup used in Ref. 48. (2)

(2)

(2)

(2)

Of the 27 tensor elements of χpqr (ω), only 4 are nonzero: χzzz (ω), χzxx (ω), χxzx (ω), and (2)

(2)

(2)

(2)

(2)

(2)

(2)

χxxz (ω), with χzxx (ω) = χzyy (ω), χxzx (ω) = χyzy (ω), and χxxz (ω) = χyyz (ω) due to the x-y plane being isotropic. Upon multiplication of the appropriate Fresnel factors and transformation from the molecular-frame to the lab-frame, 53 the 4 nonzero elements transform into (2)

(2)

(2)

(2)

χP P P (ω), χP SS (ω), χSP S (ω), and χSSP (ω), representing different experimental polarization combinations. It is important to note that the correspondence is not one-to-one. For ex(2)

ample, χP P P (ω) contains contributions from the zzz, zxx, xzx, and xxz tensor elements (2)

(2)

(2)

of χijk (ω). Furthermore, while χzxx (ω) = χxzx (ω) from the symmetry of the polarizability (2)

(2)

tensor, in general, χP SS (ω) 6= χSP S (ω) due to differences in Fresnel factor contributions. 92 Finally, it should be emphasized that Eq. 2 is strictly valid only within the dipole approximation, 93 which has been called into question for both the stretching and bending regions of the vSFG spectrum of the air/water interface. 51,60 However, considering the previously demonstrated accuracy of MB-MD simulations carried out within the dipole approximation for the air/water interface at ambient conditions, 47 the present study does not implement the transition quadrupole moments in the calculation of the spectra. 47 Further molecular insights into the structure and mobility of interfacial water molecules

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are gained from the analysis of the orientational autocorrelation function

C2 (t) = hP2 [e(0) · e(t)]i

(6)

which provides direct information on the time scales associated with the reorientation dynamics of water molecules within the hydrogen-bond network. In Eq. 6, P2 [e(0) · e(t)] is the second Legendre polynomial of the angle spanned over time by a unit vector e(t) along the OH bond vector, and the angle brackets indicate an ensemble average. The C2 (t) correlation function was then fitted to a decaying exponential of the form e−t/τ2 in order to estimate the τ2 orientational relaxation time.

Results and Discussion Stretching Region (2)

The variation of χSSP (ω) as a function of increasing distance from the center of mass of the water slab is shown in Figure 1. From this analysis, it is found that the optimum values for zc1 and zc2 in Eq. 5 are 4 ˚ A and 6 ˚ A, respectively, which guarantee convergence of the vSFG spectra at all temperatures. These values, which correspond to considering all water molecules within ∼6 ˚ A from the surface, were then used in all calculations of the vSFG spectra presented in this study. It should be noted, however, that the three main spectral features (3700 cm−1 , 3600 cm−1 , and 3200-3550 cm−1 ), clearly visible at low temperature, do not converge at the same distance from the surface. The 3700 cm−1 peak, associated with the stretching motions of free OH bonds directed away from the bulk, converges first, as it is associated entirely with molecules that reside at the surface. The spectral feature at 3600 cm−1 converges somewhat more slowly than the free OH peak, which suggests that, at least at low temperature, this feature is primarily due to hydrogen-bonded OH stretches of molecules that lie at or only slightly below the surface, such as single donor / double

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0.8 0.4 0.0 -0.4 -0.8

Im[χSSP(ω)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.8 0.4 0.0 -0.4 -0.8 0.8 0.4 0.0 -0.4 -0.8 0.8 0.4 0.0 -0.4 -0.8

zc1, zc2

238 K

10, 12 9, 11 8, 10 7, 9

258 K

318 K

278 K

338 K

298 K

368 K

3150 3300 3450 3600 3750

6, 8 5, 7 4, 6

3150 3300 3450 3600 3750 -1

ω (cm ) (2)

Figure 1: Depth dependence of the imaginary part of χSSP spectra of the OH stretching region at the air/water interface at various temperatures. The legend indicates values of zc1 and zc2 used in Eq. 5, respectively. The Gibbs dividing surfaces for each temperature are (2) included in the SI, however, all spectra are converged for zc2 values below 8 ˚ A. All χpqr (ω) were calculated according to Eq. 2, including Fresnel factor corrections, and normalized relative to kB T298 . Spectra were redshifted before applying Fresnel factors to account for nuclear quantum effects (see Table S1). acceptor (DAA) 17,23,94 and double donor / single acceptor (DDA) 44,95 molecules. Finally, the broad, negative band between 3200 and 3550 cm−1 , assigned to hydrogen-bonded OH stretches of molecules pointing towards the bulk, requires more layers of water to be included

11



before the signal is converged. This is necessary in order to capture the contributions from water molecules that simultaneously donate and accept two hydrogen-bonds (referred to as DDAA molecules).

SSP 1.0 0.5

SPS

PPP

(a)

(b)

x5

(c)

(d)

(e)

x5

(f)

(g)

(h)

x5

(i)

TCF

0.0 -0.5

(2)

Im[χ (ω)]

-1.0 1.0 0.5

ACF

0.0 -0.5 -1.0 1.0 0.5

CCF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.0 -0.5 -1.0

3200 3400 3600 3800 3200 3400 3600 3800 3200 3400 3600 3800 -1

ω (cm ) 238 K 258 K

278 K 298 K

318 K 338 K

368 K

Figure 2: Polarization and temperature dependent vSFG spectra of the OH stretching region at the air/water interface. From top-to-bottom: total contribution (TCF, a-c), autocorrelation contribution (ACF, d-f), and cross-correlation contribution only (CCF, g-i) to the vSFG spectra with intermolecular cut-off of 4.0 ˚ A. From left to right: imaginary components (2) (2) (2) (2) of χSSP (ω), χSP S (ω), and χP P P (ω). All χpqr (ω) were calculated according to Eq. 2, including Fresnel factor corrections, and normalized relative to kB T298 . Spectra were redshifted before applying Fresnel factors to account for nuclear quantum effects (see Table S1). Figure 2 shows the temperature dependence of the total vSFG spectra (TCF) of the air/water interface calculated in the OH stretching region for different polarization com12


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binations (top row), along with the decomposed contributions from auto-correlation (ACF, middle row), and cross-correlation (CCF, bottom row) functions defined in Eq. 3. The intensities of the calculated vSFG spectra in the OH stretching regions depend sensitively upon the polarization combination, with both SSP and PPP probing dipole moment changes perpendicular to the surface, and SPS probing dipole moment changes parallel to the surface. This trend is mirrored by the experimental measurements showing that the SPS spectra are roughly an order of magnitude smaller than the SSP and PPP spectra. 54 This is a direct result of both the SPS polarization probing the off-diagonal elements of the polarizability tensor (which are significantly smaller than the diagonal elements probed by the SSP and PPP spectra), and the x and y components of the dipole moment being equivalent due to their parallel orientation to the interface, which results in an averaging out of the signal for the SPS polarization. 23,54 It should be noted that, although the PPP polarization contains (2)

(2)

(2)

(2)

contributions from the χxxz (ω), χxzx (ω), χzxx (ω), and χzzz (ω) elements of the nonlinear susceptibility, the zzz contribution dominates with the laser geometry used in this study (see (2)

(2)

Supporting Information for the temperature dependence of the individual χxxz (ω), χxzx (ω), (2)

and χzzz (ω) spectra). (2)

(2)

The major differences between the χSSP (ω) and χP P P (ω) spectra are the absence of the positive feature at ∼3600 cm−1 from the latter, and the different temperature dependence displayed by the intensity of the free OH peak at ∼3700 cm−1 , with the SSP spectra showing no temperature dependence, in agreement with the results in Refs. 44 and 57 and contrary to the PPP spectra. As shown in the Supporting Information, the temperature dependence (2)

of the PPP free OH peak is entirely due to χzzz (ω) contributions, which suggests that it may arise from concerted interactions between the transition dipole moment and polarizability tensor perpendicular to the interface. While the spectral intensities display different temperature dependences from 238 K to 368 K, the position of the 3700 cm−1 feature in both the SSP and PPP spectra shows a similar redshift of ∼25 cm−1 and ∼20 cm−1 , respectively, in agreement with previous results. 44,96 In the SSP spectrum, the rate of change of the redshift

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due to the inclusion of nuclear quantum effects is almost 3 times smaller in magnitude than the redshift due to the temperature increase (∼4.7 cm−1 /K vs ∼12.8 cm−1 /K). Therefore, the linear trend observed in Fig. 2a is not influenced significantly by the accuracy of the redshift applied to the spectra for approximately accounting for nuclear quantum effects. It is important to note that a comparison between the temperature dependence of the free OH peak calculated here for the air/water interface with the analogous analysis carried out in Ref. 56 for the air/ice interface indicates qualitatively different trends. Specifically, as the temperature increases, the peak position of the free OH redshifts at the air/water interface but blueshifts at the air/ice interface. This difference provides further support for different structural arrangements and dynamics at the topmost layer of water and ice surfaces. In the SPS spectra, the highest frequency peak at 3700 cm−1 is associated with the inplane components of free OH stretching vibrations and is essentially temperature independent. By contrast, the spectral feature at 3550 cm−1 shows a strong temperature dependence. This feature has been assigned to either hydrogen-bonded stretches of DAA molecules 17,23,94 or intramolecular couplings associated with antisymmetric stretches of DDA molecules. 44,95 As the temperature increases and intramolecular couplings decrease, this spectral feature becomes progressively less pronounced and effectively disappears at temperatures higher than 318 K. While some of this temperature dependence is possibly due to the inherent decrease in optical activity with increasing temperature as demonstrated in Ref. 44 for a narrower temperature range, the sharp increase below 258 K also reflects the increased interfacial structural ordering as shown by the temperature-dependent analysis of the water density across the slab reported in the Supporting Information. The general trends seen in the difference spectrum of Ref. 57 are also reproduced in Fig. 2 as the temperature increases. The free OH peak is broadened and the negative hydrogen-bonded band is blueshifted. As mentioned above, the SPS spectra shown in Fig. 2 display three peaks at low temperature with negative, positive, and positive signs from low to high frequencies. The calculated SPS spectra are in good agreement with the corresponding experimental measurements 94

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above 3550 cm−1 . Both the two high frequency features are positive, reinforcing the hypothesis that the 3600 cm−1 peak can not be due to the antisymmetric stretching mode of DDA water, as this peak is positive in both the SSP and SPS spectra. 54,94 However, the calculated and experimental SPS spectra differ below ∼3550 cm−1 , with the latter being positive over the entire frequency range and the former displaying a broad, negative band. In this context, it should be noted that the SPS spectra calculated previously in Refs. 73 and 97 also disagree with each other, with the older study predicting only a positive signal as in the experimental spectrum and the more recent study predicting three peaks, alternating from positive to negative to positive. Furthermore, it should also be noted that, while the calculated 73 and experimental 94 spectra agree qualitatively, the sharp features found in the former are not observed in the latter. To date, the origin of these differences between different theoretical predictions and experimental measurements is unclear and certainly merits further investigation. 14 238 K 258 K 278 K 298 K 318 K 338 K 368 K

12

z - zcm (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


10

T

8

6 0

1

2

3

Lifetime (e

-t/τ2

4

5

6

) (ps)

Figure 3: Temperature and depth dependence of the C2 orientational autocorrelation function τ2 lifetimes according to an exponential decay fit. Distance is relative to center of mass of the slab in z direction (zcm ). C2 (t) is provided in Eq. 6. The second and third rows of Figure 2 display the molecular auto-correlation (ACF) 15



and cross-correlation (CCF) contributions to the water vSFG response in the OH stretching region. Comparison with the corresponding total vSFG (TCF) spectra in the first row further serves to highlight cross-coupling effects, particularly at low temperature. For example, the negative hydrogen-bonded region of the TCF SSP spectrum at 238 K is redshifted by 25 cm−1 (from 3420 cm−1 to 3395 cm−1 ) relative to the corresponding ACF vSFG spectrum. This follows from the fact that cross-couplings emphasize contributions from the more strongly hydrogen-bonded molecules, as shown by the more pronounced negative peak of the CCF spectrum at ∼3380 cm−1 . Both ACF and TCF SSP spectra display temperature-dependent frequency shifts resulting in isosbestic points at 3500 cm−1 and 3470 cm−1 , respectively, in agreement with previous theoretical estimates. 44 Regardless of the OH frequency and polarization combination, cross-couplings decrease in magnitude as the temperature increases. This can be readily explained by the increased reorientation mobility of the water molecules at higher temperature as demonstrated by the decrease in the reorientation relaxation time (τ2 ) shown in Fig. 3 as a function of temperature and distance from the interface. As expected, the weakening of cross-couplings correlates with the weakening of hydrogen-bond strength as the temperature increases, with τ2 decreasing from 5.9 ps at 238 K and 5 ˚ A from the center of the slab to 0.18 ps at 368 K and 13 ˚ A from the center of the slab. Clear similarities exist between the CCF spectra calculated for the SSP and PPP polarization combinations. Both spectra display four distinct, temperature-dependent features, with alternate signs from low to high frequency, reflecting the decreasing hydrogen-bond strength as a function of molecular orientation and depth. The inclusion of cross-couplings contributes to the reduction of the intensity of the positive shoulder at ∼3600 cm−1 in the SSP polarization spectra, indicating that the local-field effects induced by cross-couplings point down with respect to the Gibbs dividing surface. Since the CCF contributions of the SPS spectra point up regardless of frequency, the directions of the cross-correlated induced dipole and permanent dipole moments are always in the same direction. As the free

16


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OH stretch has relatively little intermolecular coupling, its CCF contribution is small in all polarizations. The strong contribution from intermolecular coupling as shown in the CCF spectra demonstrates that the hydrogen-bonding network plays an outsize role in the shape of the spectra, particularly for the positive shoulder. (2)

Fig. 4 shows the decomposition of the TCF, ACF, and CCF χSSP (ω) spectra into contributions associated with water molecules donating 0, 1, or 2 hydrogen bonds. 38,49 In this analysis, a common geometric definition of hydrogen bonds is employed, according to which a hydrogen-bond is established between two water molecules when the distance (ROD OA ) between the donor (OD ) and acceptor (OA ) oxygen atoms is less than 3.5 ˚ A and the HD OD · ··OA angle is less than 30◦ . 98 According to this definition, it follows that molecules donating 0 or 1 hydrogen bonds have at least one free OH bond. These are primarily DAA and AA molecules, which are collectively referred to as 0/1DH molecules. As shown in (2)

Fig. 4a, χSSP (ω) associated with 0/1DH molecules displays the expected features of the free OH stretching mode at 3700 cm−1 . While the free OH peak is particularly broad at high temperature, mirroring the behavior seen in Fig. 2a, at low temperature there remains a distinct contribution near 3600 cm−1 . By construction, this small but noticeable feature must arise from hydrogen-bonded DAA molecules. 17,23 It should also be noted that, as proposed in Ref. 94, this feature may also be due to Fermi resonances between OH stretches of DAA molecules and low frequency vibrations, which borrow intensity from the free OH peak. Since a quantitative description of Fermi resonances in liquid water through classical MD (2)

simulations is difficult, this interpretation remains a possibility. χSSP (ω) associated with 0/1DH molecules also displays a broad and highly temperature dependent negative band, which progressively blueshifts from 3350 cm−1 at 238 K to 3500 cm−1 at 368 K. The 2DH (2)

χSSP (ω), shown in Fig. 4b, also displays a small positive feature at high frequencies and a negative band between 3250 cm−1 and 3550 cm−1 , which decrease in intensity and slightly blueshift with increasing temperature. The analysis of the corresponding ACF and CCF spectra shown in the middle and bottom

17



0/1DH

2DH

1.0 0.5

(a)

(b)

(c)

(d)

(e)

(f)

TCF

0.0

Im[χSSP(ω)]

-0.5 -1.0 1.0 0.5

ACF

0.0 -0.5 -1.0 1.0 0.5

CCF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 38

0.0 -0.5 -1.0 3200

3400

3600

3800

3200

3400

3600

3800

-1

ω (cm ) 238 K 258 K

278 K 298 K

318 K 338 K

368 K

(2)

Figure 4: Temperature dependence of decomposition of stretching region of χSSP signal based on contributions from waters with (a, c, e) zero or one donating hydrogens (0/1DH) or (b, d, f) two donating hydrogens (2DH). The top row contains the total correlation function, the second row contains only auto-correlation function contributions, and the third row contains (2) only cross-correlation function contributions.All χpqr (ω) were calculated according to Eq. 2, including Fresnel factor corrections, and normalized relative to kB T298 . Spectra were shifted before applying Fresnel factors to account for nuclear quantum effects (see Table S1).

18


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rows of Fig. 4, respectively, provides further insights into the origin of the shoulder at 3600 cm−1 . In particular, only small contributions to this spectral feature are present in the ACF spectra associated with 0/1DH molecules (Fig. 4c). On the other hand, both ACF and CCF spectra of 2DH molecules (Figs. 4d and 4f) display distinct features, with opposite sign, in this frequency region. The presence of a strong negative peak in the CCF spectra of 2DH molecules indicates that the shoulder seen at 3600 cm−1 in the TCF spectra is not solely intramolecular in origin as proposed in Ref. 95 but contain significant contributions from intermolecular coupling, which are masked total vSFG spectrum by the net cancellation with positive ACF contributions. As both 0/1DH and 2DH spectra display intensity in the shoulder region, this suggests that both the intermolecular coupling of DAA molecules 23,94 and the intramolecular coupling of DDA molecules 44,95 are contributing to the shoulder region (2)

of the χSSP spectra in Fig. 2a. However, the presence of intermolecular cross-couplings of 2DH molecules that negates much of the intensity from the other contributions was not reported in previous studies and provides additional complexity to the interpretation of the shoulder.

Bending Region The total vSFG spectra (TCF, top row) of the air/water interface calculated for the three polarization combinations in the bending frequency region are shown in Fig. 5 as a function of temperature. Also shown in the same figure are the corresponding spectra obtained by considering only molecular auto-correlation (ACF, middle row) and cross-correlation (CCF, bottom row) contributions. Unlike the stretching region in Fig. 2, where the SPS signal is roughly an order of magnitude smaller than the SSP and PPP signals, all three polarization combinations have similar intensities in the bending region, with the TCF spectra displaying a pronounced temperature dependence. Since both infrared and Raman spectra of bulk water are effectively temperature independent in the bending region, 74 the temperature dependence displayed by the vSFG spectra must be associated with the presence of the interface, and can 19



SSP 0.14 0.07

SPS

PPP

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

TCF

0.00 -0.07

(2)

Im[χ (ω)]

-0.14 0.14 0.07

ACF

0.00 -0.07 -0.14 0.14 0.07

CCF

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.00 -0.07 -0.14 1500 1575 1650 1725 1500 1575 1650 1725 1500 1575 1650 1725 -1

ω (cm ) 238 K 258 K

278 K 298 K

318 K 338 K

368 K

Figure 5: Polarization and temperature dependent vSFG spectra of the HOH bending region at the air/water interface. From top-to-bottom: total contribution (TCF, a-c), autocorrelation contribution (ACF, d-f), and cross-correlation contribution only (CCF, g-i) to the vSFG spectra with intermolecular cut-off of 4.0 ˚ A. From left to right: imaginary components (2) (2) (2) (2) of χSSP (ω), χSP S (ω), and χP P P (ω). All χpqr (ω) were calculated according to Eq. 2, including Fresnel factor corrections, and normalized relative to kB T298 . Spectra were redshifted before applying Fresnel factors to account for nuclear quantum effects (see Table S1). be attributed to the fact that water molecules at the surface reorient more rapidly than in the bulk (see Figure 3) due to fewer and relatively weaker hydrogen bonds. This is particularly evident at low temperature (e.g., 238 K) where τ2 at the surface is ∼4 times smaller than the corresponding value calculated in the bulk. The dynamical heterogeneity across the slab decreases with increasing temperature and τ2 at the surface becomes only ∼1.6 times smaller

20


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than in the bulk at 368 K. Since the bending mode is less restricted by the hydrogen-bond network at the surface than in the bulk, the temperature dependence of the bending motions become more pronounced. As shown in Fig. 5, different polarization combinations result in qualitatively different vSFG spectra in the bending region. At all temperatures, the total SSP spectrum displays two peaks, one negative at ∼1580 cm−1 and one positive at ∼1640 cm−1 . These features have previously been assigned to molecules with (bending) transition dipole moments oriented towards the surface and the bulk, respectively. 48,49 By contrast, the total SPS and PPP spectra display a single negative peak. Besides these differences, the PPP spectra are redshifted by ∼20 cm−1 relative to both SSP and SPS spectra, suggesting that the PPP polarization combination is sensitive to bending vibrations with different hydrogen-bonding topologies than those probed by the other two polarization combinations. 48,49 It should be noted that recent HD-vSFG experiments have shown a potentially large electric quadrupole contribution from the bulk which results in only a single positive band in the bending region. 51 To date, no quantitative molecular model of the electric quadrupole for simulations of liquid water has been reported and this will be the subject of future developments within the MB-MD framework. Due to the more localized character of the bending vibrations, the ACF contributions effectively determine the total vSFG spectra for all polarization combinations, as demonstrated by the close similarity between ACF and TCF spectra over the entire temperature range examined in this study. It should, however, be noted, that, contrary to the corresponding TCF spectra, both ACF and CCF spectra in the the SPS polarization combination display isosbestic points and, particularly at low temperature, appear to be sensitive to different hydrogen-bonding topologies, as shown by the ∼35 cm−1 redshift in peak positions. While no contribution to the SSP spectrum was found from cross-correlation in Ref. 49, the present CCF spectra shown in Fig. 5g indicate the presence of nonnegligible cross-coupling contributions, which increase as the temperature decreases. Since these contributions add (remove)

21



intensity to (from) the positive (negative) peak of ACF spectrum, this result in the TCF spectrum displaying relatively larger positive intensity. For a given polarization, cross-coupling contributions are predominantly either positive or negative. This can be rationalized by considering the physical contributions to the correlation functions from which the spectra are derived. For both PPP and SSP polarization combinations, the correlation function is a measure of the coupling between the z component of the total dipole moment and either the zz or xx components of the total polarizability tensor, respectively. For these polarization combinations, the dipole moment induced on each water molecule by the surrounding environment points primarily up during the bending vibration and thus gives rise to the overall positive intensity in the corresponding CCF spectra, which is particularly pronounced in the SSP spectrum. On the other hand, autocorrelation contributions lead to a negative intensity in the ACF PPP polarization spectrum, indicating that the transition (permanent) dipole moment responsible for this signal points down, and to both positive and negative features in the ACF SSP spectrum, depending on the frequency. Like the PPP spectrum, the SPS spectrum in the bending region point downward. However, in this case, cross-coupling effects also contribute to negative intensity. Considering the transition dipole moments and polarizabilities from a molecular perspective, this analysis indicates that electrostatic coupling through bending vibrations between interfacial water molecules arises primarily from different orientational arrangements. (2)

Figures 6a and 6b show the decomposition of χSSP in the bending region into contributions from molecules donating 0 or 1 hydrogen bonds and at least 2 hydrogen bonds, respectively. At all temperatures, 0/1DH molecules contribute exclusively to the negative peak while 2DH molecules contribute exclusively to the positive peak. This agrees with previous studies 48,49 and confirms the assignment of the negative peak originating from water molecules with the HOH bisector pointing up and the positive peak due to molecules with the bisector oriented down. Although small, the temperature dependence can be seen to have opposite trends in the two groups. As the temperature increases, the intensity of

22


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Page 23 of 38

0.2

(a) 0/1DH

0.1 0.0

Im[χSSP(ω)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-0.1

238 K 258 K 278 K 298 K 318 K 338 K 368 K

-0.2 0.2

(b) 2DH

0.1 0.0 -0.1

-0.2 1500

1550

1600

1650

1700

1750

-1

ω (cm ) (2)

Figure 6: Temperature dependence of decomposition of bending region of χSSP signal based on contributions from waters with (a) zero or one donating hydrogens (0/1DH) or (b) two (2) donating hydrogens (2DH). All χpqr (ω) were calculated according to Eq. 2, including Fresnel factor corrections, and normalized relative to kB T298 . Spectra were shifted before applying Fresnel factors to account for nuclear quantum effects (see Table S1). the 0/1DH spectrum becomes larger, and, thus, more negative up to ∼318 K, after which it remains effectively unchanged, while the intensity of the 2DH spectrum decreases. The trend is reflected in the total vSFG spectrum (panel a of Fig. 5), where the presence of the negative peak corresponding to dipole moments pointing towards the air is nearly absent at 238 K, since the much broader 2DH component tends to overshadow the narrower 0/1DH contribution.

23



Conclusions The vSFG spectra of the air/water interface as a function of temperature for three distinct polarization combinations were calculated through the use of many-body molecular dynamics with the MB-pol potential energy function. Using the truncated cross-correlation function formalism, the vSFG spectra were decomposed into molecular auto- and cross-correlation contributions. Inclusion of cross-coupling effects is shown to be necessary to correctly describe both temperature dependence and lineshape. In both OH stretching and HOH bending regions, the magnitude of cross-couplings was shown to vary as a function of frequency and be dependent on the polarization combination. The SSP spectra were further broken down into contributions from molecules with free OH bonds (identified by molecules donating zero or one hydrogen bond) and doubly hydrogen-bonded species (molecules donating two hydrogen bonds). In the bending region, the positive and negative peaks are well defined by the 2DH and 0/1DH molecules, respectively. These are attributed to water molecules with the HOH bisector oriented towards the bulk and toward the surface, agreeing with previous studies. 48,49 More complicated is the stretching region, as while the highest frequency peak found at 3700 cm−1 in the vSFG spectra is shown to be entirely due to 0/1DH molecules, the ∼3600 cm−1 shoulder and the broad, negative band between ∼3200 cm−1 and ∼3550 cm−1 have contributions from both 0/1DH and 2DH molecules, especially at low temperature. Since the 2DH SSP spectra display strong contributions from intermolecular couplings in addition to the predicted intramolecular coupling, it follows that contributions from double donor / single acceptor molecules to the shoulder of the free OH peak at ∼3600 cm−1 are non-negligible. While a further breakdown of the contributions to this spectral feature could be investigated through normal mode analysis, 27,86 the present results suggest that previous assignments of the positive shoulder to hydrogen-bonded OH stretches of single donor / double acceptor molecules 23,94 and intramolecular coupling from the antisymmetric stretch of double donor / single acceptor molecules 95 are both potentially valid. 24


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Supporting Information Additional figures presenting the density profiles and Gibbs dividing surfaces of the water (2)

(2)

(2)

slabs used for each temperature, as well as the χxxz , χxzx , and χzzz spectra for the OH stretching and HOH bending regions. Also included are the average OH bond angles relative to the surface normal as a function of distance from the center of mass of the simulation slab for each temperature. A table containing the values for each temperature the spectra were redshifted to account for nuclear quantum effects is also provided.

Acknowledgements This research was supported by the National Science Foundation through Grant No. CHE1453204. This research used resources of the Extreme Science and Engineering Discovery Environment (XSEDE) 99 through allocation TG-CHE110009. XSEDE is supported by National Science Foundation grant number ACI-1548562.

25



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TOC Graphic

1.0 0.5

(a)

Donating 0 or 1 Hydrogen Bonds

0.0

Im[χSSP(ω)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 38

-0.5 -1.0 1.0 0.5

(b)

Donating 2 Hydrogen Bonds

0.0 -0.5 -1.0 3100 3200 3300 3400 3500 3600 3700 3800 -1

ω (cm )

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238 K 258 K 278 K 298 K 318 K 338 K 368 K

Water Interface Revealed by

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