Vibrational Sum Frequency Generation Spectroscopy of the Water

Letter pubs.acs.org/JPCL

Vibrational Sum Frequency Generation Spectroscopy of the Water Liquid−Vapor Interface from Density Functional Theory-Based Molecular Dynamics Simulations Marialore Sulpizi,*,† Mathieu Salanne,‡ Michiel Sprik,§ and Marie-Pierre Gaigeot*,∥,⊥ †

Department of Physics, Johannes Gutenberg Universitat, Staudingerweg 7, 55099, Mainz, Germany UPMC Université Paris 06, CNRS, ESPCI, UMR 7195, PECSA, F-75005 Paris, France § Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom ∥ LAMBE CNRS UMR8587, Université d’Evry val d’Essonne, Boulevard F. Mitterrand, Bât Maupertuis, 91025 Evry, France ⊥ Institut Universitaire de France, 103 Boulevard St. Michel, 75005 Paris, France ‡

S Supporting Information *

ABSTRACT: The vibrational sum frequency generation (VSFG) spectrum of the water liquid−vapor (LV) interface is calculated using density functional theory-based molecular dynamics simulations. The real and imaginary parts of the spectrum are in good agreement with the experimental data, and we provide an assignment of the SFG bands according to the dipole orientation of the interfacial water molecules. We use an instantaneous definition of the surface, which is more adapted to the study of interfacial phenomena than the Gibbs dividing surface. By calculating the vibrational (infrared, Raman) properties for interfaces of varying thickness, we show that the bulk spectra signatures appear after a thin layer of 2−3 Å only. We therefore use this value as a criterion for calculating the VSFG spectrum.

SECTION: Spectroscopy, Photochemistry, and Excited States nterfaces play key roles in diverse fields, including heterogeneous catalysis, electrochemistry, transport across biological membranes, growth of aerosols and nanoparticles, and nanotechnologies. The water liquid−vapor (LV) interface is especially interesting since it is involved in a wide range of phenomena of atmospheric and geochemical relevance, ultimately also connected to global climate changes.1 A complete understanding of the structural and chemical organization of the water molecules at the interface as well as their dynamics is still lacking, despite several experimental2−7 and theoretical8−13 investigations. One key goal is to elucidate the detailed molecular structure at the LV boundary as an essential step for the understanding of the reactivity and functionality of this interface. Vibrational sum frequency generation (VSFG) has contributed to provide such microscopic knowledge.14,15 The first VSFG spectrum of the neat water LV interface in the O−H stretch region was reported in 1993.2 The main features include a sharp peak at 3700 cm−1, readily assigned to the dangling OH bonds protruding into the vapor, and a very broad band for the hydrogen bonded OH groups whose interpretation remains controversial. In the original interpretation of Shen and coworkers2,3 the broad band is decomposed into two sub-bands located around 3400 and 3200 cm−1. They were respectively labeled “liquid-like” and “ice-like” bands, since they were

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assigned to water molecules being weakly and strongly hydrogen bonded, as would be the case in liquid water and ice, respectively. Alternatively, the double peaks have been assigned to the symmetric and antisymmetric modes arising from the intramolecular vibrational couplings between O−H oscillators.6,16 Supplementary inhomogeneities coming from intermolecular hydrogen bond (Hbond) strengths have also been envisaged.6,16 Bonn et al.7 have furthermore argued that the double-peaked structure originates from vibrational coupling between the stretch and bending overtone. Recently Ishiyama and Morita17 have pointed out the effect of anisotropic local fields. All the proposed interpretations were either based on fits of the experimental data or on (at least partially) classical simulations. Here, we propose an entirely first-principles method employing density functional theory-based molecular dynamics simulations (DFT-MD) in order to unravel the VSFG signal. A fully consistent approach is applied where the dynamics of the water molecules at the interface as well as their individual molecular dipoles and polarizability tensors are all extracted from the DFT-MD trajectory. Received: November 14, 2012 Accepted: December 13, 2012

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systems). Due to computational costs, the calculation of interfacial VSFG spectra has been achieved on a 3 ps portion of the trajectory, and for statistical needs, both interfaces within the periodically repeated cell have been taken into account for χ2(ω) calculation as well as each time-step of the 3 ps trajectory. We limit our analysis to the self-correlation part of the VSFG signal according to

Our sample of the water LV interface is composed of 128 water molecules in a box of (15.64, 15.64, 31.00) Å3, periodically repeated in the (x,y) directions and separated by a vacuum layer of 15 Å in the z direction, as illustrated in Figure 1. Simulations are carried out with the CP2K package,18

(2),self (ω) = χpqr

iω kBT

N

∑∫ i=1

0

∞

i dt exp(iωt )⟨αpq (t )pri (0)⟩

(2)

This is necessitated by the slow convergence of the crosscorrelation contribution,28,34 which brings such calculation at the limit of what is currently affordable in DFT-MD. We discuss here the real and imaginary parts of χ(2) ssp (ω) signal, where s = x,y and p = z, to be compared to phase sensitive VSFG experiments from Shen et al.35 Using the knowledge of dipole moments and polarizability tensors of the individual water molecules, we also extract IR and Raman spectra of the interfacial region, through time-dependent correlation functions.36 The inclusion of dispersion corrections provides a bulk density of 1.06 g/cm3, very close to the experimental value of 1.00 g/cm3, whereas the simple GGA functionals are known to produce a too low equilibrium density.37 As can be seen in Figure 1S (Supporting Information), the density profiles of the 128 and 256 LV interfaces are identical, the larger system providing a slightly lower 1.02 g/cm3 bulk density. The degree of water ordering at the interface can first be analyzed by calculating the electrical potential arising from the individual water dipoles, which includes both orientational and polarization effects. It is calculated from the individual water dipoles, periodicity being explicitly taken into account by including the first two periodic images of the cell (which was found sufficient to get a converged profile), and it is referred to the asymptotic value in vacuum, which in practice is set equal to the “plateau” value in the vacuum part of the periodic cell. The dipole potential is found to be positive in the water slab and negative on the vacuum side. The overall interface potential is 0.47 V, close to the experimental surface dipole (0.13−0.17 V38). If we can reproduce the correct sign of the dipole potential, the absolute value is somewhat overestimated, possibly due to the DFT level employed in the calculation. For the definition of the interface, we innovate by using the instantaneous liquid interface recently defined by Willard and Chandler,39 rather than the most commonly used Gibbs dividing surface criterium. As shown in refs 39−41, a local definition preserves the layering of the atomistic solvent, which is otherwise washed out when using the mean Gibbs dividing surface. Using 2, 3, and 7 Å thicknesses, we have hence defined three different interfacial regions, comprised of respectively 18, 37, and 103 water molecules. A pictorial view of the two instantaneous interfaces in the slab is reported in Figure 1. Reχ(2)(ω) and Imχ(2)(ω) signals are presented in Figure 2 for the 2 Å thickness (the choice of this thickness is demonstrated later in the paper). They compare very well with the experimental phase sensitive VSFG experiments from Shen et al.35 Although more noisy than the experiment, our spectra reproduce the three changes in signs recorded experimentally. Our calculated Imχ(2) presents a well-defined positive peak at 3700 cm−1 (free O−H stretch from the dangling waters at the interface), a negative band between 3500 and 3050 cm−1 and a slightly positive band below 3000 cm−1 (H-bonded OH

Figure 1. Simulated water LV interface. The instantaneous surface is reported as a blue grid. A pictorial representation of incident/resultant probes (IR, visible, VSFG) is presented. Right panel: three most favorable orientations for the water molecules at the interface, revealed by our structural analyses. d stands for vector dipole, and z stands for the normal to the surface.

consisting in Born−Oppenheimer MD, BLYP19,20 electronic representation including Grimme (D2) correction for dispersion,21 GTH pseudopotentials,22,23 a combined Plane-Wave (280 Ry density cutoff), and TZV2P basis sets. The system has been equilibrated with a 10 ps NVT simulation, followed by a 20 ps dynamics in the NVE ensemble for data analysis. The time step is 0.4 fs, and the average temperature is 330 K. Recent theory of the SFG signal by Morita24 and Shen25 have shown that the resonant electric dipole susceptibility (χ(2)) is the origin of the surface SFG signal, although higher order quadrupolar terms arising from the bulk should also participate. However, no MD-derived SFG spectrum of the LV interface has yet been obtained including these quadrupolar terms. Our modeling of VSFG was performed following the methods introduced by Morita et al.11,16,26,27 The classical expression for resonant χ(2) is ∞ iω (2) (ω) = dt exp(iωt )⟨A pq(t )Mr (0)⟩ χpqr kBT 0 (1)

∫

where Apq and Mr are, respectively, the components of the polarizability tensor and dipole moment of the whole modeled system, (p,q,r) any direction among (x,y,z), kB and T are the Boltzmann constant and temperature, and ⟨...⟩ denotes an average over the trajectory. The total dipole Mr(t) and polarizability Apq(t) components can be decomposed into individual molecular contributions (pir(t), αipq(t)), which are calculated from the position of the nuclei and Wannier centers.28,29 Calculations involving finite electric fields of 0.0001 au intensity were performed independently along the x, y, and z directions at each time step to extract the individual molecular polarizabilities. Note that these calculations were performed using the plane-wave DFT code CPMD,30,31 following the procedure detailed in ref 29 (see also refs 32 and 33 for checks on the accuracy of the method on various 84

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average angle between the normal to the surface and the dipole of 60−80°: one O−H points toward the vacuum and one O−H points toward the liquid. Each of these water molecules forms 1−3 Hbonds, mainly with other molecules below the 2 Å surface layer. Six water molecules have their dipole parallel to the surface (dz = 0): one O−H points toward the vacuum and one O−H toward the liquid. Four of these molecules are not involved in Hbonds, while two of them are, forming 2−3 Hbonds with the water molecules located below the thin 2 Å interface. Four other molecules have their dipole directed toward the liquid (dz < 0), with an average angle between the dipole and the normal to the surface within 110−156°: one O− H points to the liquid, while the other is roughly located within the surface or slightly pointing toward the vacuum. All of these water molecules are strongly involved in Hbonds, displaying 1− 4 Hbonds with the water molecules located below the thin 2 Å interface. Decomposing the Imχ(2)(ω) signal in terms of the orientation of the dipole of the interfacial water molecules (along the normal to the surface dz > 0, opposite dz < 0, and perpendicular dz = 0), we find that all interfacial water molecules participate to the 3700 cm−1 positive band because of at least one O−H pointing toward the vacuum. Water molecules with dipole components dz < 0 or dz = 0 provide a negative contribution to Imχ(2)(ω) in the 3500−3050 cm−1 domain, while water molecules with dz > 0 have a contribution positive or close to zero within 3500−3250 cm−1, and a negative contribution below 3250 cm−1. The positive peak in Imχ(2)(ω) below 3000 cm−1 is due to the water molecules whose dipoles point toward the liquid (dz < 0). In our calculation of the VSFG signal, we have considered a water layer of 2 Å thickness. Our choice is motivated by a close analysis of the IR and Raman signals (both have to be active for SFG activity), keeping in mind that once the bulk properties are recovered, the SFG signal is inactive. Our guide in the separation between surface and bulk is the appearance of the vibrational IR and Raman spectra of bulk water as a function of increasing thickness of the interface. IR and Raman spectra of the 2, 3, and 7 Å interfacial thicknesses are reported in Figure 3. The IR spectrum of liquid water44 is also reported, in excellent agreement with experiment,15 showing a red-shift of 40 cm−1 from the experiment (main peak at 3400 cm−1), and displaying the asymmetry of the IR

Figure 2. Calculated Reχ(2) (blue) and Imχ(2) (red) spectra for a 2 Å thick interface.

groups). Similarly, the Reχ(2) signal displays three changes in sign: a negative band peaked at 3740 cm−1, a positive band between 3700 and 3280 cm−1, and a negative band below 3280 cm−1. The noise in our calculations, seen as small oscillations and bumps, is certainly due to the relatively small size of the simulated sample (128 waters) and to the short 3 ps trajectory. The use of a larger system size, as recommended by Baer et al.42 was rendered difficult by the increased computational cost associated with the calculation of individual molecular polarizabilities. The short time-scale and the lack of crosscorrelations in Figure 2 will certainly affect convergence of the band intensities, and therefore impede a complete comparison to experimental data in terms of band intensities (note also the current debate on consistency of VSFG experiments43). This being noted, it is remarkable that all relevant peaks, signs, and change of signs are correctly reproduced by the calculated signals even if only a small sizescale and short time-scale are investigated. The values of ω where the changes in signs occur are different from the experiment though: for Imχ(2), we observe roughly a 100−200 cm−1 red-shift in the calculated frequencies with respect to the experiment. Such relatively small red-shifts in the frequencies can be attributed to the choice of the DFT functional and/or the lack of cross-correlations. Nonetheless, our calculation reproduces the broadness of the negative band, i.e., ∼ 460 cm−1 to be compared to 400 cm−1 in the experiment, where previous MD based on classical force fields or mixed ab initio and classical force fields underestimated the broadness of that band.26,27 This points to anharmonic vibrational couplings captured by the present DFT-MD as well as high reliability of the Hbond structure between the water molecules at the interface. Note here that the positive sign of Imχ(2) below 3000 cm−1 is highly debated in the theoretical community, and it has been suggested in the past that this positive sign could only be recovered when including cross-correlation terms in χ(2).11 In our case, however, only the self-correlation contribution is included in the signal, still providing a clear positive sign of Imχ(2). Ishiyama et al.27 have also obtained a positive sign of Imχ(2) in their very recent quantum mechanics-molecular mechanics (QM-MM) MD of the interface. We now describe the structural organization of the water in the thin 2 Å thick surface layer. We find that four waters have their dipole oriented toward the vacuum (dz > 0), with an

Figure 3. IR and Raman (polarized parallel) spectra of the three defined interfacial regions. Signals have been normalized to reflect the number of water molecules included in each interface. Signals are averaged over the two equivalent surfaces of the water slab. 85

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band including the shoulder at 3180 cm−1. The Raman spectrum for the thicker interfacial region of 7 Å is also similar to the experiment in bulk water,15 although the experimental signal provides one broad single band (main amplitude at 3400 cm−1 and a shoulder of lower amplitude at 3200 cm−1), while our calculated spectrum has two distinct peaks of the same amplitude (blue-shifted by 20−30 cm−1 from experiment). The crucial point we make here is that our calculated spectra for the 7 Å thick interface already closely resemble the liquid phase signals, so that this thickness can be considered as dominated by the bulk structure. The spectra for a 3 Å thick interface is very close to the latter, already possessing the main characteristics of the liquid in terms of both number and broadness of the active bands. However, the 3 Å thickness retains vibrational features of the thinner 2 Å interface, as can be seen by the presence of the two interfacial specific peaks at 3600−3700 cm−1 (free O−H stretch) and 3100 cm−1. We have shown that it is possible to calculate the VSFG spectrum of the water LV interface using an entirely firstprinciples approach (DFT-MD where individual molecular dipoles and polarizability tensors are extracted from Wannier centers at each time step). The calculation of the molecular polarizability tensors is challenging since it is based on the linear response of the electron density to an applied external field. Unlike previous works based on the Gibbs dividing surface, we have used the instantaneous liquid interface providing a local definition of the surface probed during a VSFG experiment. We have shown that the bulk signals for the IR and Raman spectra are recovered when using interface thicker than 3 Å, which led us to choose a thickness of 2 Å for the VSFG calculation. The obtained spectrum then presents a good agreement with the experiment, despite the short time and length-scales available in DFT-MD. We show that the broad 3500−3050 cm−1 negative band in Imχ(2)(ω) arises from interfacial waters which dipoles are pointing toward the liquid or laying within the plane of the interface (3500−3200 cm−1), and from waters in which dipoles are pointing toward the vacuum below 3250 cm−1: without this last contribution, the final Imχ(2)(ω) would not match the experimental broadness. All these water molecules are involved in Hbonds of different strengths with the subsequent bulk layer. The Imχ(2)(ω) positive band below 3000 cm−1 arises from waters pointing their dipoles toward the liquid. This distribution of molecular orientations also reflects in the dipolar contribution to the surface potential, which is found close to the experimental value.

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ACKNOWLEDGMENTS Financial support from EPSRC (M. Sulpizi) and computer time from CINES (Montpellier, France) within the “Grands Challenges” scheme (MPG, M. Sulpizi) are greatly acknowledged.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Density profiles of the 128 water LV interface and 256 water LV interface presented and compared in order to show that the smaller sample correctly represents the interface and subsequent bulk density properties. This material is available free of charge via the Internet at http://pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (M.S.); [email protected] (M.-P.G.). Notes

The authors declare no competing financial interest. 86

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