Origin of Vibrational Spectroscopic Response at Ice Surface - The

Letter pubs.acs.org/JPCL

Origin of Vibrational Spectroscopic Response at Ice Surface Tatsuya Ishiyama, Hideaki Takahashi, and Akihiro Morita* Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan S Supporting Information *

ABSTRACT: Since the basal plane surface of ice was first observed by sum frequency generation, an extraordinarily intense band for the hydrogen(H)bonded OH stretching vibration has been a matter of debate. We elucidate the remarkable spectral feature of the ice surface by quantum mechanics/molecular mechanics calculations. The intense H-bonded band is originated mostly from the “bilayer-stitching” modes of a few surface bilayers, through significant intermolecular charge transfer. The mechanism of enhanced signal is sensitive to the order of the tetrahedral ice structure, as the charge transfer is coupled to the vibrational delocalization.

SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis bands for the ice surfaces. One band at ∼3700 cm−1 is assigned to the dangling (free) OH, which is commonly observed for the water surface19,20 with comparable peak intensity. The other band at ∼3200 cm−1 is associated with the H-bonded OH. The intensity of the latter band is 10 times as large as that of the dangling band at 232 K,18 although the peak frequency is somewhat different among reported experiments so far: ∼ 3150 cm−1 (at 232 K)18 or ∼3097 cm−1 (at 113 to 178 K).21 Subsequently, several experimental and theoretical studies proposed some interpretations on this intense band.10−12,21−26 However, there has been no direct evidence to account for such intense signal and no molecular model that can reproduce the extraordinarily enhanced H-bonded band. The present study reproduces the intense H-bonded peak for the first time by theoretical calculation using quantum mechanics/molecular mechanics (QM/MM) method.27,28 The present analysis demonstrates the important role of intermolecular charge transfer accompanying the vibrationally delocalized OH stretching vibration. Remarkable temperature dependence of the spectrum, which was observed in the experiment,21 is well reproduced in the present MD system. We also argue that the enhanced intensity is a sensitive indicator of the order in the tetrahedral H-bond structure at the ice surface. The conventional SFG spectra mentioned above are represented with the square of the second-order nonlinear susceptibility, |χ|2.29 Recent phase-sensitive or heterodyne-

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ce surfaces are ubiquitous on the earth or in the universe and play important roles in atmospheric, planetary, interstellar physical, and chemical processes.1−3 Hydrogen(H)-bonding structure at ice surface exhibits several interesting phenomena such as surface melting of ice contacting with various phases,4−6 chemical reactions specific to the ice surface,7,8 brine rejection from freezing salt solutions,9 and so on. Observed phenomena associated with the ice surface may range spatially over several orders of magnitude from molecular level to macroscopic level,1 and it is a challenging issue to understand selectively the interfacial H-bonding network on a molecular level. Recently, a detailed structure of ice surface, particularly in relation to the proton ordering or disordering, has been argued with the help of molecular simulation.10−12 Whereas these studies have advanced our understandings of microscopic ice surface, we definitely need more experimental support to establish these theoretical findings, which were obtained from subtle energy differences and limited spatial and temporal scales. Nonlinear optical spectroscopy such as vibrational sum frequency generation (SFG) is quite appropriate for this purpose. In recent years, SFG spectroscopy elucidates the detailed structures of vapor/water and aqueous interfaces.13−16 Our knowledge on the ice surface via the SFG spectroscopy is still limited because of experimental difficulties compared with water surface (including laser heating, surface roughening, etc.17) as well as difficulties in interpreting the observed spectra. In this Letter, we elucidate the spectral features of the basal plane surface of hexagonal ice (ice Ih) by molecular dynamics (MD) simulation. The first SFG spectrum of the ice surface was reported in 2001 by Wei et al.18 Their spectra show two characteristic © 2012 American Chemical Society

Received: August 27, 2012 Accepted: October 2, 2012 Published: October 2, 2012 3001

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detected SFG measurements30,31 enable us to observe the χ itself. The direct observation of χ provides us with useful phase information on the orientational structure because the sign of Im[χ] reflects the polar orientation of the molecular transition dipole moment.32 The phase-sensitive SFG has been applied to the pure water or several aqueous surfaces.33−36 Unfortunately the phase of χ for the ice surface has not yet been reported experimentally. The present Letter reports Im[χ] of the ice surface and discusses it in relation to the surface structure. We carried out the MD simulation in the following way. The molecular model for generating trajectories is the flexible and polarizable water model developed by us.37,38 A rectangular simulation box with dimensions Lx × Ly × Lz = 31.44 Å × 31.11 Å × 150.00 Å contains an ice slab of 1120 H2O molecules. The ice forms a slab of ∼34 Å thickness, with two basal plane surfaces normal to the z axis. (See the configuration of Figure 1a.) The 3D periodic boundary conditions are imposed with

topmost bilayer B1 corresponds to a broader band of the density than the central (bulk) bilayers, which is indicative of surface melting of ice.3,4,41 The second and third bilayers, B2 and B3, are slightly disordered by the surface effect. To quantify the extent of disorder, we introduce an order parameter qi, called “tetrahedrality”, to each molecule i as 9 qi = 1 − 2Ni(Ni − 1)

Ni − 1

Ni

2 ⎛ 1⎞ ⎜cos ψ + ⎟ jk ⎝ 3⎠ k=j+1

∑ ∑ j=1

(for Ni ≥ 2)

(1)

where Ni is the coordination number of the ith molecule and ψjk is the angle among the oxygen site of the molecule i and the two adjacent oxygens of the H-bonded molecules j and k. We note that qi = 1 for complete tetrahedron, and qi = 0 for random structure. In panel c the average qi for each bilayer ⟨q⟩ is plotted as a function of temperature. One can see the phase transition occurs near 270 K, indicating that the present model can properly describe the surface melting. The bulk ice shows the tetrahedrality of ⟨q⟩ ≈ 0.95, as seen in the B5 bilayer below the transition temperature, whereas the liquid water shows ⟨q⟩ ≈ 0.60. The ⟨q⟩ value for the top bilayer (B1) gradually decreases with increasing temperature, which is qualitatively consistent with the recent SFG study by Groenzin et al.21 The ⟨q⟩ values also decrease with increasing temperature in the inner bilayers, B2∼B5, although the change become more abrupt in the inner region. At the temperature 230 K, the values of ⟨q⟩ are about 0.76 for B1 and 0.88 for B2 and converged to the bulk value 0.95 for B3 and inner bilayers. This behavior indicates that the quasi-liquid layer emerges in the top two bilayers of the ice surface. The QM/MM calculation of χ has been described in ref 28, and thus we outline the essential part of the calculation. The relevant component of Im[χ] is calculated by the following time correlation function formalism42 χxxz =

iωIR kBT

∫0

∞

dt exp(iωIR t )⟨Axx (t )Mz(0)⟩

(2)

where the z axis points upward along the surface normal. A and M are the polarizability and dipole moment of the surface system, respectively. kB and T are the Boltzmann constant and temperature, and ⟨...⟩ denotes thermal average. We calculated A and M at each time step in the following three cases. In Case 1, we define the QM region as one arbitrary molecule at the bilayer B1 or B2 and the surrounding molecules in its first solvation shell, whereas the rest of the system is treated as the MM region. In Case 2, we define the QM region as one surface water molecule only and the MM region as the other molecules. In Case 3, we define the QM region as one surface molecule as in Case 2, whereas the MM region is not considered. These definitions of Cases 1−3 are same as in ref 28. (See the illustration in S2 of the Supporting Information.) For all of the cases, A and M are calculated quantum chemically by Hartree−Fock/6-31+G(d),43 with the surrounding MM molecules represented by point charges. Note that all three cases share the same MD trajectories, and differences among the three cases are entirely attributed to the definition of the QM and MM regions for calculating A and M in eq 2. Case 1 allows for intermolecular charge transfer, in contrast with the other two cases. The difference between Case 2 and Case 3 enables us to examine the effects of polarization by the

Figure 1. (a) View of the initial configuration of the MD simulation box along the prism face (y−z plane), where the bilayers are labeled B1, B2, B3, ... from the topmost surface. (b) Density profile along the C (z) axis at 230 K. (c) Average tetrahedrality ⟨q⟩ of the bilayers B1− B5 as a function of temperature (150−300 K). The side views of the 3D plot in panel c are available in S1 in the Supporting Information.

the dipolar Ewald sum method for electrostatic interactions.37 The initial configuration of the ice slab is prepared according to the Bernal−Fowler ice rule39 as the proton disordered structure,40 and the configuration is equilibrated for 200 ps at a given temperature. The surface structure is examined with varying temperature from 150 to 300 K, and the SFG spectra of the ice slab are calculated at 230 and 130 K. The SFG calculations are carried out using 512 independent MD trajectories generated from different initial configurations by parallel computers. The structural and the spectroscopic data are obtained from a total of 200 ps and 100 ns (∼200 ps ×512 trajectories) ensemble averages, respectively, at each temperature. Figure 1b shows the density profile of the ice slab in the MD simulation. The bilayer structure of ice is clearly seen. The 3002

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The rest of this Letter focuses on the structural origin of the intense band and the charge transfer. To assign the structural origin of nonlinear susceptibility, we decomposed the calculated Im[χ] in Case 1 along the depth coordinate z, and the decomposed spectra are shown in the central panel of Figure 3. These results clearly indicate that the intense band is mainly attributed to the B1b and B2b regions. These regions correspond to the lower half of the surface bilayers. In the B1b and B2b layers, the OH bonds pointing vertically toward the bulk are the main source of the strongly negative Im[χ], whereas the OH bonds pointing toward the vapor side make a positive contribution to Im[χ]. The present interpretation of this negative intense band coincides with that of refs 25 and 26 in which the OH bonds toward the bulk are called “bilayer stitching” H-bonds. The right panel of Figure 3 displays the depth profile of Im[χ] in Case 3, where the intermolecular charge transfer is forbidden. In comparison with Case 1, one can see the following three interesting features in relation to the chargetransfer effect. First, the H-bonded frequency region generally shows enhanced amplitude in Case 1 compared with Case 3, consistent with the SFG spectra in Figure 2. Second, the sign of Im[χ] for the bilayer stitching regions is opposite in Cases 1 and 3. We found that the reverse sign is attributed to the fact that the two OH moieties of a single molecule, that is, the bilayer stitching O−H and its counterpart, have opposite influences on the Im[χ]. In Case 3, the counterpart OH is relatively significant, whereas in Case 1, the charge transfer emphasizes the bilayer stitching vibration and thereby reverses the sign of Im[χ]. Third, in Case 3, the positive and negative contributions of the different layers are almost equivalent and thus cancel each other, whereas in Case 1 the negative contribution overcomes the positive contribution. For example, the negative contribution from the B1b layer is larger than the positive contribution from the B2a layer. Such asymmetry is obviously attributed to the charge transfer because it does not appear in Case 3. The charge-transfer effect is sensitive to the tetrahedral ordering of surface layers, as we will argue below. The tetrahedral order gradually increases from surface to bulk, as shown in Figure 1c. Such asymmetric contributions of the charge transfer give rise to the net negative amplitude in the calculated Im[χ] of the ice surface. (See the left schematic of Figure 3.) We emphasize that the strong band of the SFG spectrum of ice is reproduced only in Case 1, where the effect of intermolecular charge transfer is incorporated. To examine further the charge-transfer effect, we carried out QM/MM calculations of the transition dipole and polarizability for the bilayer stitching OH vibration. The QM region consists of an arbitrarily selected H2O molecule in the B1b layer, which has a bilayer stitching OH (defined as W1 in Figure 4) and the four adjoining H2O molecules (W2−W5 in Figure 4) in an instantaneous configuration during the MD trajectories. The calculation was conducted with B3LYP/DZP+diffuse basis47 on Gaussian 03 program package48 by treating the W1−W5 molecules as QM region and the other H2O molecules as point charges. The partial charge of each atom is also calculated by the natural bond orbital analysis.49 The yellow numbers in Figure 4 denote ∂Qa/∂r, derivative of the partial charge Qa at each atom a with respect to the bond length r of the bilayer stitching OH of the W1 molecule. The derivative calculations were performed by moving the relevant hydrogen with the other atoms fixed. These values demonstrate

surrounding molecules. Further details in the QM/MM calculation are referred to in S2 of the Supporting Information. Figure 2 displays the calculated SFG spectra (∼|χ|2) in panel a and the imaginary susceptibility Im[χ] in panel b. The

Figure 2. (a) |χ|2 and (b) Im[χ] spectra calculated by the QM/MM simulations. The inset in panel a displays the experimental |χ|2 spectrum of ice (232 K, blue line) and water (298 K, red line).18 Blue, green, and purple lines denote the calculated results of ice surface in Cases 1, 2, and 3, respectively, and red lines denote the calculated results of water surface in Case 1.28 All spectra are normalized with the dangling peak intensity at ∼3700 cm−1. The nonresonant χ was set to zero in panel a.

experimental spectra are displayed in the inset of panel a. We find that Case 1 (blue line) can appropriately describe the remarkable enhancement of the H-bonded band, whereas Case 2 (green) and Case 3 (purple) fail to reproduce the intense band. The difference among these cases indicates that the intermolecular charge transfer plays a crucial role in the intensity of the H-bonded band of the ice surface. Panel b shows that the intense band has a main negative component of Im[χ], whereas both frequency sides of this intense band and the dangling OH band (at ∼3700 cm−1) have positive sign. Compared with the Im[χ] profile of water (red line), the intense negative Im[χ] band of the ice (blue) is red-shifted and narrower. This difference is more obvious in the Im[χ] spectra of panel b than in the intensity (|χ|2) spectra of panel a, implying that the H-bonds in ice are stronger and more homogeneous than those in the water. In the low-frequency tail at ∼3100 cm−1, the positive Im[χ] was also observed in the water surface,33,44,28 although the amplitude is enhanced in the ice surface. We notice in Figure 2a that the peak frequency in the present calculation (∼3300 cm−1) is somewhat higher than the corresponding experimental frequency (∼3150 cm−1). This may be attributed to inaccuracy of the present H2O model potential, as the calculated infrared and Raman spectra with the present H2O model for ice (not shown) also show the peak frequencies somewhat higher than the experimental ones45,46 by ∼100 cm−1. The essential conclusions about the origin of the intense band are nevertheless unaffected by this deficiency. 3003

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Figure 3. Decomposed Im[χ] spectra along the C axis into 1 Å layers in Case 1 (solid blue lines) and in Case 3 (dashed purple lines). The right panels show magnified Im[χ] spectra in Case 3. The left schematic illustrates the corresponding ice layers (see Figure 1), where the blue and red circles denote oxygen and hydrogen, respectively, and upper and lower halves of each bilayer are labeled with a and b, respectively (e.g., B1a, B1b, ...). The depth profiles are based on the center-of-mass position of the (core) QM molecule.

The charge transfer also affects the transition dipole and polarizability and thereby the nonlinear susceptibility. The χxxz component of eq 2 associated with the OH vibration of the bilayer stitching mode is proportional to the product of the transition polarizability and dipole as follows χxxz ∼

∂αxx ∂μz · ∂r ∂r

(3)

We calculated and compared the values of eq 3 in two cases: Case (i) treats W1−W5 as QM region and others are MM point charges, and Case (ii) treats only W1 as QM region and others including W2−W5 are MM point charges. Note that Case (ii) does not allow intermolecular charge transfer. The calculated results are (αxx/∂r)·(∂μz/∂r) = 3.29 × −5.403 = −17.77 D Å3/Å2 for Case (i), and (αxx/∂r)·(∂μz/∂r) = 1.47 × −1.83 = −2.69 D Å3/Å2 for Case (ii). The significant enhancement in Case (i) clearly evidence the importance of the charge transfer in the nonlinear susceptibility. Shown in Figure 5 are the calculated temperature dependence of |χ|2 and Im[χ] spectra of the ice surface. The intensity of the bilayer stitching mode in Figure 5a is strongly enhanced at the lower temperature, consistent with the experimental observation.21 The Im[χ] spectra in Figure 5b show that the intense negative band at 130 K becomes red-shifted and narrower compared with 230 K, indicating that the H-bonds become stronger and homogeneous at the lower temperature. The augmented intensity and amplitude at the lower temperature clearly imply the role of vibrational delocalization in the spectral intensity. When the delocalized vibrations are coupled to the charge transfer, the charge transfer also becomes

Figure 4. Results of natural bond orbital analysis at ice surface. The yellow colored numbers indicate ∂Q/∂r values (Q: charge, r: OH length) in unit e/Å.

that significant electron transfer occurs from the W2 (H-bond acceptor) molecule to the W1 (H-bond donor) with elongating OH bond. The charge transfer from the oxygen lone pairs of W2 (electron donor) to the OH antibonding orbital of W1 (electron acceptor) is of critical importance at the ice surface.49 The net amount of induced charge transfer is estimated by lumping the partial charge derivatives into a molecule, and the results are −0.2667e/Å for W1, 0.2816 for W2, −0.0024 for W3, −0.0013 for W4, and −0.0112 for W5, respectively. From these results, one can see that the charge transfer is mainly induced between W1 and W2 by the OH vibration, and the other molecules WX (X = 3−5) play a minor role. 3004

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ice surface may not be properly described by conventional water models. The intense band reflects the H-bond structure at a few top bilayers, which partially retain the tetrahedral ice structure.

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ASSOCIATED CONTENT

S Supporting Information *

Further information is provided regarding details of the tetrahedrality at ice surface and methodologies not covered in the main text. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +81 22 795 7717. Fax: +81 22 795 7716. Notes

The authors declare no competing financial interest.

■

Figure 5. (a) |χ|2 and (b) Im[χ] spectra of ice surfaces at 230 K (blue lines), and at 130 K (red lines) in Case 1 calculation. The blue lines are the same as those in Figure 2.

ACKNOWLEDGMENTS This work was supported by the Grants-in-Aid for the Scientific Research and the Next Generation Super Computing Project of MEXT, Japan.

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delocalized and cooperative, which in turn augments the induced transition dipole or polarizability. Considering the above mechanism of the temperature dependence of the SFG intensity observed both in the present calculation and in experiment,21 we also found that the enhancement of the χ amplitude is pertinent to the order of the local tetrahedral structure. In fact, the ice surface at 150 K keeps highly tetrahedral structure, as is indicated by the tetrahedrality parameter ⟨q⟩ in Figure 1c. At 230 K, the tetrahedrality parameter becomes lower at the top bilayers, where ⟨q⟩ = 0.76 for the B1 bilayer and 0.88 for B2. Whereas these values are smaller than that in the bulk ice, ∼0.95, they are significantly larger than the typical value in the liquid water ⟨q⟩ ≈ 0.6. The highly tetrahedral structure at the ice surface augments the delocalization of the OH vibrations. These features give rise to the intense SFG spectrum of the ice surface. To discuss the ice surface structure, we have debated possible proton ordering for a long time. Although a definite conclusion has not been established, it is widely believed that proton ordering is formed to some extent at low-temperature ice surface.11,12 It might be surprising in the present QM/MM calculations that the intense SFG band is well elucidated with the fully disordered proton structure. Whereas the proton ordering at the ice surface is a fascinating issue, the present Letter demonstrates that it is not a primary origin of the intense SFG spectra. Regarding the lattice disorder, realistic ice surface may involve large structural fluctuation with vacancies, akin to the amorphous ice.10 The present simulation reasonably captures the disordered structure of the ice surface, as shown in Figure 1, yet the present simulation shows that the bilayer feature of ice surface should largely survive, which is reflected in the SFG spectra. Detecting the vacancies would be challenging for the spectroscopic means, unless their surface concentration is large enough. In summary, the remarkably intense SFG band in the Hbond frequency region of the ice surface is accounted for by the bilayer stitching H-bond vibrations, which accompany the intermolecular charge transfer. This band characteristic to the

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dx.doi.org/10.1021/jz3012723 | J. Phys. Chem. Lett. 2012, 3, 3001−3006