Molecular dance: Water’s collective modes

Chemical Physics Letters 588 (2013) 1–10

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FRONTIERS ARTICLE

Molecular dance: Water’s collective modes Mary Jane Shultz ⇑, Patrick Bisson 1, Tuan Hoang Vu 2 Laboratory for Water and Surface Studies, Chemistry Department, Tufts University, Medford, MA 02155, USA

a r t i c l e

i n f o

Article history: Received 21 August 2013 In final form 20 September 2013 Available online 1 October 2013

a b s t r a c t Ice surfaces are used to assign five resonances in the hydrogen-bonded vibrational spectrum of water. Ice surface experiments are complemented with room temperature matrix isolation experiments providing compelling evidence that the OH vibration of the donor is affected by the environment around the lone pairs, i.e., compelling evidence for the importance of three-body interactions. In addition, longer-range, correlated motion produces a quadrupole at the ice surface. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Hydrogen bonding in aqueous systems is likely the most important, single interaction [1] directing biological [2–5], geological [6], and environmental [7–9] chemistry. Although this interaction has been scrutinized even before Linus Pauling’s famous book [10] on the subject, understanding the nature of the hydrogen bond still challenges theorists and experimentalists alike [1]. The perspective in this contribution is that the source of this challenge lies in the extended nature of the hydrogen bond, spreading its influence beyond the hydrogen-bonded pair due to longer-range, charge-density shifts accompanying formation of the bond. Recent theoretical developments [11–18] recognize the extended nature of the hydrogen bond, thus explicitly include both three-body interactions and quantum mechanical effects [11,16,18,19]. Experimentally, there are few probes that unambiguously show the nonlocal nature of the hydrogen bond to guide theoretical developments. One older technique, Compton profile anisotropy [20], is sensitive to the phase of the electronic wavefunction and shows that the hydrogen bond both spreads beyond the dimer pair and is partially covalent. This article presents experimental developments using two methods: polarization sensitive sum frequency generation (SFG) and room-temperature, matrix isolation spectroscopy (RT-MIS) that isolate vibrational resonances to reveal multibody effects on hydrogen-bonded resonances. Vibrational spectroscopy is, in principle, an excellent method for revealing hydrogen-bond interactions since the OH stretch frequency is quite sensitive to the local environment [21]. Short lifetimes [22] complicate the spectrum by broadening any given ⇑ Corresponding author. Fax: +1 617 627 3443. E-mail address: [email protected] (M.J. Shultz). Current address: Dartmouth College, Thayer School of Engineering at Dartmouth, 14 Engineering Drive, Hanover, NH 03755, USA. 2 Current address: Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA. 1

0009-2614/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cplett.2013.09.053

resonance. The combination of short lifetimes and multiple local environments leads to very broad, overlapping resonances. In the hydrogen-bonded region of liquid water, this combination results in an OH stretch spectrum that extends for 600–700 cm1: a significant fraction of the entire infrared! One approach to simplify the spectrum is to transform liquid water into ice. Under atmospheric pressure, ice crystalizes as hexagonal ice, Ih. If Ih ice were an extended, symmetric crystal the vibrational wavefunctions would couple forming Bloch functions with bands of states. Ice, however, is a proton-disordered solid [23]. That is, within the Bernal-Fowler ice rules [24] – every oxygen is covalently bonded to exactly two hydrogen atoms and precisely one hydrogen atom lies between every pair of oxygen atoms – the protons form a disordered array, hence the OH oscillators form a disordered array. Disorder breaks symmetry and localizes the wavefunction. Competition between proton disorder and vibrational coupling produces multifaceted spectra that have, so far, resisted agreed upon interpretation. The interfacial hydrogen-bonded spectrum introduces yet another symmetry breaking to the interpretation-resistant bulk spectrum. Nonetheless, there is significant motivation for developing a deeper understanding of surface spectra [25] since many biological and environmental reactions either occur at or are catalyzed by the aqueous surface [4]. Diagnosing interactions could provide key insight for goals such as structural modification of drugs to enhance efficacy [3,26,27] or guiding policy for emission regulation. For example, chelation of peptides to transition metals is strongly affected by protonation at the amine. Unfavorable equilibrium inhibits peptide formation in aqueous solution; shifted pKa [28] along with altered water and possibly proton activity at the surface promote bond formation rendering it observable [5]. Although proton activity is critical here, even the fundamental question of whether the neat water surface is acidic or basic remains a contentious debate [5,29–32] with proponents of a basic surface [33–36] competing with equally vociferous supporters of an acidic surface [37–40]. This controversy rests in part on lack of clarity concerning spectral signatures and structures [30] of the relevant ions – H3O+ and OH

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(and related hydrates) – as well as on interpretation of the hydrogen-bonded spectrum of water. There are two recent approaches using SFG to help unravel the interfacial hydrogen-bonded spectrum: phase measurements [41– 43] and polarization sensitive measurements with ice [44,45]. The latter is elaborated below. Phase measurements are described briefly here. SFG selectively probes the interfacial region due to nonlinear mixing of infrared and visible electromagnetic fields. The resulting nonlinear polarization has real and imaginary parts: that is, it has both a phase and an amplitude. In a conventional SFG experiment, the intensity – the square of the amplitude – is observed. Thus, overlapping resonances of amplitude A1 and A2 yield an intensity that is proportional to the square of the sum of these amplitudes: |A1 + A2|2. The sum, then square not only produces interference but also results in ambiguous deconvolution of the spectral contributions of the separate resonances. Water, with a plethora of overlapping, broad resonances, compounds the ambiguity. The motivation for phase measurements is that if one could measure the amplitude spectrum, then the response would be linear and deconvolution into separate resonances facilitated. Experimentally the amplitude spectrum is measured by combining the amplitude spectrum of the sample with a broad, nonresonant spectrum from a reference material. Interference between the sample and the known-phase reference yields the amplitude spectrum of the sample. Unfortunately, the amplitude spectrum of aqueous solutions is also very broad. Interpretation then relies on assuming a certain number of resonances, fitting the amplitude spectrum, and monitoring changes with experimental parameters such as solute addition. Once determined, connecting the measured amplitude spectrum with parameters such as molecular orientation hinges on knowledge of the resonant mode properties – properties that depend on the nature of the hydrogen bond. Simply stated: Does one start with the molecular normal modes that emphasize intramolecular coupling or with the OH oscillators emphasizing intermolecular coupling? Like the surface pH issue, the answer is not yet clear [46]. Polarization-sensitive SFG measurements on ice described below suggest that both couplings are important. Long-range intermolecular coupling manifests as a correlated OH stretching motion leaving the surface vibrating like a drum. Intramolecular coupling indicates an isolated, short-range symmetric configuration. Conceptually, the motivation for room temperature matrix isolation spectroscopy (RT-MIS) is similar to theory where a fully quantum mechanical treatment of a local cluster is embedded in a bath treated at a lower level [47]. Classical matrix isolation consists of the subject molecule(s) dispersed in a low-temperature, often solid matrix. Dispersing the subject molecules turns off longrange and resonant energy transfer, thereby simplifying the vibrational spectrum. Low temperature also diminishes thermal broadening, narrowing resonances and minimizing spectral overlap. RTMIS modifies classical matrix isolation by maintaining higher thermal energy. For vibrational spectroscopy, it is desirable to select a matrix that is liquid at the target temperature, is transparent in the region of interest and has low subject-molecule solubility. Results described below use carbon tetrachloride as the matrix. Manybody effects are shown for salt-water interactions. RT-MIS is also used to address the question of the expected frequency of OH in restricted water environments [48]. Measurements of the OH stretching frequency often depend on bandprofile analysis, separating the OH ion contribution from that of water with which it overlaps [49,50]. In bulk water, the OH ion is solvated by five water molecules: four in an axial ring around the oxygen and a fifth top molecule held in place via hydrogen bonds to the axial water molecules [51]. This hydration shell structure provides an intriguing model for the OH ion surface structure: loss of the top water molecule. Knowledge of the OH ion

stretching frequency would be very helpful for finding experimental evidence for its existence on the surface. RT-MIS provides an environment for determining the frequency under ambient energy conditions. The resonance is found 29 cm1 red of the free-OH peak. The remainder of this Letter discusses contribution of the above-mentioned polarization sensitive SFG and RT-MIS measurements to the on-going efforts to get water to reveal the secrets of its hydrogen-bond interactions. The next section contains a description of the two experimental techniques and a brief description of ice sample preparation. This is followed by presentation and analysis of the data in the context of normal modes versus many-body effects. Finally, this contribution concludes with an overview of the findings and thoughts about future directions. Jargon box a-face basal face blue shift c-axis d-O d-OH Ih input plane PAN RT-MIS red shift s (p) SFG ssp, ppp TMA-OH

surface cut perpendicular to a hexagonal a-axis hexagonal surface of an hexagonal prism a vibrational resonance that occurs at a higher frequency due to interaction the optical axis, also the hexagonal rotation axis of ice dangling O: unsatisfied coordination at the oxygen lone pair of water dangling OH: unsatisfied coordination at the H atom of water the hexagonal form of ice phase I (hexagonal cell) plane formed by the light-beam propagation vector and the surface normal polarization angle null room-temperature-matrix-isolation spectroscopy a vibrational resonance that occurs at a lower frequency due to interaction light polarization perpendicular to (parallel to) the input plane sum frequency generation polarization of the sum frequency, visible, and infrared beams tetramethylammonium hydroxide

2. Experimental methods 2.1. SFG The basic theory and experimental aspects of sum frequency generation (SFG) have been reviewed numerous times [52]; so only essential details are given here. Applied to vibrational spectroscopy, SFG combines an infrared and a visible light beam at the surface. The infrared frequency is either scanned (psec systems) or consists of a broad band (fsec.). In either case, the sum frequency intensity is enhanced when the infrared frequency is resonant with a surface vibration. In essence, the surface vibrational signature is mapped into the visible due to combining with the visible. This mapping enhances detection since sensitive photomultiplier tubes, CCD arrays or photon counting can be used rather than the less sensitive infrared detectors. Momentum matching at the surface results in a coherent SFG beam facilitating collection of the low number of photons generated by the nonlinear process. Polarizations of the two input beams are experimentally controlled. Polarization is measured relative to the input plane: the plane formed by the propagation direction and the surface normal.

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If the electric field vector is in the input plane, the beam is said to be p-polarized; if the electric field vector is perpendicular to the input plane, the beam is s-polarized. Polarization is used heavily for identification of the surface modes of ice. SFG spectra are labeled by the polarization of the generated sum frequency, the visible, and the infrared in that order. With three beams to specify, there are eight polarization combinations. Often symmetry reduces that number. Specifically, aqueous solutions are isotropic in the surface plane, so polarization combinations that contain an odd number of s polarizations are forbidden; ssp, ppp, pss and sps are allowed. (The intensity of the pss and sps combinations differ only in optical factors since for vibrational sum frequency the first two indices refer to a Raman process and the Raman tensor is symmetric.) Very often, the sps intensity is weak hence most SFG experiments collect only ssp and/or ppp data. In addition to vibrational frequency data, in some cases, the intensity of ppp relative to ssp can be used to deduce molecular orientation. The connection between relative intensity and orientation depends on the vibrational mode symmetry. For water, this connection is straightforward if the vibrational modes are the normal modes of water. Collective or intermolecular-coupled modes thus present a challenge. Despite the challenge, the SFG polarization data can be informative [53]. The information content can be appreciated by considering the following (Figure 1). With p-polarized infrared, p-polarized visible can only produce p polarized sum frequency. Similarly, ppolarized infrared and s-polarized visible can only produce s polarized sum frequency. Thus with p-polarized infrared and the visible polarization rotated 45° relative to the input plane, the sum frequency polarization angle is not restricted by symmetry. Instead, the sum frequency polarization is given by a superposition of pand s-polarized responses. The relative weighting depends on input angles, optical factors, and the surface longitudinal versus transverse polarization (see supplementary material):

  vZZZ 1 vis ¼  cos gr;SF LX K vis  X  tan Hnull LY K Y vXXZ sin gr;SF LZ K vis Z

ð1Þ

where vIJK is the surface hyperpolarizability and I,J,K references the surface Cartesian coordinates, gr is the reflected angle, vis (SF) references the visible (sum frequency) beam, L(K) is the nonlinear optical (linear Fresnel) factor, [84,85] and Hnull is the analyzer angle with minimal intensity. (Note that incoherent, unpolarized, background scattering is usually nonzero.) Due to measuring the null angle, this variation of SFG is called polarization angle null (PAN). vXXZ is the surface-plane or tangential hyperpolarizability while vZZZ is the longitudinal hyperpolarizability. Note that with the exception of Hnull, the parameters on the right side of Eq. (1) are either under

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experimental control (gr) or are properties of the bulk phases (L and K). Thus, PAN reveals the hyperpolarizability orientation. If neighboring resonances have distinct null angles (likely), then PAN can be used to deconvolute the spectrum into its components [54,55]. Thus PAN is generally applicable. Additionally, if the resonance is due to a cylindrical mode (having only three nonzero Raman polarizations: axx = ayy and azz) then the molecular orientation can be determined from the linear Raman depolarization ratio [53]. Again, for liquid water, the latter is problematic; both the mode and the depolarization ratio depend on the environment. Ice differs from liquid water due to the crystalline configuration of water molecules. As discussed below, the observed PAN and combined crystal orientation and polarization data enables assignment of five distinct resonances in the hydrogen-bonded region, demonstrating the power of SFG. 2.2. Ice sample preparation Ice is a relatively loosely bound solid since it is held together by relatively weak hydrogen bonds. Likely due to these weak bonds, ice shows no preferred cleavage planes. In addition, ice grows cryptomorphologically from its melt. Both make preparation of ice substrates difficult. Growing ice on a substrate raises significant issues concerning templating of the ice surface by the substrate, strain in the ice due to accommodating an imperfect lattice match, and submicroscopic holes in the ice structure. Ice was thus grown from the melt. Fortunately, differentiating single-crystal samples from their multiple-crystalline counterparts as well as identifying the crystal orientation can be accomplished using the birefringence of ice. Single crystal growth is critically dependent on maintaining equilibrium conditions for the advancing front and this appears to require slow growth [56–58]. The growth apparatus is based on a modified Stockbarger technique. The apparatus and protocol produce boules that are 2.5 cm diameter and up to 20 cm long with near 100% yield. Boules can be inspected for single crystal formation by placing the boule between crossed polarizers. Optical axis orientation is determined with a Rigsby [59] stage. Orientation parameters are transferred to a custom-built clamping device and the boule cut to expose the selected face. The cut face is made nearly smooth by shaving it in a microtome. An optically flat surface is produced by slow annealing of the sample at 253 K. The ice is mounted on a copper heat sink and cooled to the experimental temperature through a copper stem in contact with liquid nitrogen. The temperature of the ice surface is monitored with a thermocouple embedded in the surface. It should be noted that the H-bonded spectrum depends on the exposed face, so polycrystalline samples often produce inconsistent results. Similarly, strain in the ice sample appears to alter the molecular-level configuration on the surface and again produces inconsistent results. 2.3. RT-MIS

Figure 1. Beam polarization illustrated. With p-polarized infrared and 45° polarized visible, the sum frequency can have any polarization angle. Determining the angle reveals information about the surface longitudinal polarization relative to the transverse polarization.

There have been numerous reports of the structure of the hydration shell for a variety of ions in water. Most often, these studies treat the anion and cation as independent, uncorrelated species despite over 100 years since Arrhenius won the Noble prize for his work including ion-pair formation. Success in interpreting data, including very recent studies [60,61], seems to justify an independent-ion treatment. As experimental techniques probe more local, correlated dynamics effects of ion pairing are emerging. Relevant to this work, 15N NMR has been used to probe H-bond dynamics and finds evidence for an intramolecular contact-ion pair [62]. Ultrafast, 2D spectroscopy has found that rotational anisotropy of both water and SCN depends on the ion pair [63]. Very surface active anions [64–66] show distinct behavior with various cations including divalent cations that are normally thought to be

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inactive at the surface. Here, we report the results of RT-MIS showing that both members of the ion pair influence formation of a water–water H-bond. RT-MIS is based on isolating small water clusters in a medium that is infrared transparent in the region of interest: for water this is the H-bonded region. Ideally, the matrix isolation medium is a liquid at the temperature of interest, thus allowing molecular exchange rather than the caging effect seen in solid matrices. In this work, carbon tetrachloride is chosen. Neat water forms only monomers in carbon tetrachloride [67]; water spins freely about its molecular axis but has highly restricted rotation about the other two axes. Thus, the multi-featured, gas-phase water spectrum is greatly simplified and consists of a symmetric and asymmetric stretch. The latter is accompanied by a broadened molecular-axis rotational structure. Thus, interaction with the hydrogen atoms of water is identified by collapse of the rotational structure and by formation of red-shifted hydrogen-bonded structures [68]. Sample preparation consists of mixing carbon tetrachloride and the aqueous solution, waiting for stable phase separation, and collecting infrared data through the carbon tetrachloride layer. For some salts (those that form an outer sphere complex [69]), water interacts with the cation and is polarized by the interaction enabling formation of a water–water hydrogen bond [68]. Formation of the water–water hydrogen bond depends on both the anion and the cation of the salt demonstrating the importance of the larger environment, many-body interactions for hydrogen-bond interactions.

3. Results and discussion This work is motivated by the following. Water is an extremely important solvent in atmospheric, environmental, and biological systems. It can also play either a facilitating or an inhibiting role in catalysis. Thus, understanding molecular-level interactions that modify the properties of water is central to numerous fields. In principle, vibrational spectroscopy, specifically in the hydrogenbonded region, should be a powerful tool for building this understanding. The major problem has been that the H-bonded region is very broad and lacks distinct features. This combination makes it very challenging to identify and assign resonances, hence difficult to build a picture of molecular-level interactions. Theoretically, the problem is equally challenging: it is not yet clear whether condensed water should be treated by starting with the normal modes or with linked OH bonds that form a tetrahedral structure around the oxygen atom. Here we show experimental evidence that the H-bond strength as reflected in the OH stretch frequency, is affected by the configuration of the other H-bond acceptor as well as the configuration of donor molecules. Interpretation of the experimental spectra is consistent with recent theoretical treatments [11,14,16,70–72] but, in the case of the prism face of ice, shows exquisite molecular-level detail. A clear illustration showing that formation of a hydrogen bond between two water molecules is affected by interaction at the donating partner lone pair is the RT-MIS spectrum of salt-water [68,73]. In addition to the isolated water resonances, a feature appears at 3440 cm1 for some salts. The frequency of this feature is independent of both anion and cation of the salt, provided that the anion–cation interaction is not too strong [69]. Specifically, this feature is observed for NaBr, NaI, and KI solutions. For ions that interact more strongly (NaCl, KCl, KBr), the spectra resemble that of neat water with an altered intensity. Since the absorbance intensity reflects the amount of water in the matrix, and the salt concentration in the carbon tetrachloride layer exceeds that of water, it appears that salts do not enter the matrix with their solvent shells [74] but rather enter as associated ion clusters with water decorat-

ing the cluster. Lack of H-bonded resonances for the strongly interacting salts indicates that water associates with the cluster via a cation-oxygen attachment leaving water free to rotate about the molecular axis and presenting a spectrum similar to neat water. For salts with less strongly interacting ions, interaction with the cation polarizes the attached water molecule sufficiently that it forms an H-bond with an additional water molecule (Figure 2). In this case, the strength of the donor OH bond as reflected in the vibrational resonance is independent of the ions. It appears that the key lies in polarization of water; this polarization can extend beyond the immediate water molecule [75]. The salt RT-MIS results provide insight into requirements for observing the OH ion vibrational resonance. Like water, the OH ion resonance is often buried in the much more intense H-bonded spectrum of the aqueous solvent. Vibration of hydroxide groups on metal or metal oxide surfaces have been observed, but their frequencies are strongly affected by the solid substrate. Theoretical calculations report that the OH vibration should be between 3560 and 3610 cm1; experimental results show the resonance in a much larger range of 3080–3660 cm1 [51]. At aqueous solution interfaces, presence of OH is often deduced via its effect on water molecules and interpretation depends on a molecular water interpretation of the imaginary part of the spectrum [76]. To directly observe OH at the aqueous solution interface, it is helpful to know the expected frequency and dynamic dipole; RT-MIS contributes to the first, theory to the second. To observe OH in the RT-MIS system, OH should be partnered with a very large cation ensuring that the ion-ion interaction is sufficiently weak to support formation of a separated-ion pair. Several large cations were chosen; all show similar results [77]. The spectrum of (CH3)4NOH (TMA-OH) (Figure 3) is representative. In ordinary water, there are two resonances located between the symmetric and the asymmetric stretch of water. Discriminating between OH and a free- or dangling-OH of water relies on two observations: (1) the peak at 3634 cm1 tracks the concentration of TMA-OH in the aqueous solution and (2) the resonance at 3663 cm1 is greatly enhanced for a 1:1 mixture of H2O and D2O. Rapid exchange results in H2O, D2O and HDO in solution along with OH, OD, and (CH3)4N+ ions. (Vibrational resonances of the latter are outside the H-bonded window.) Comparison of TMA-H2O/D2O/ HOD solution spectrum with that of H2O/D2O/HOD reveals that the OH resonance is 29 cm1 to the red side of the free-OH resonance. The OH ion environment here likely consists of a weak interaction between the ion and the somewhat positively charged carbon of

Figure 2. The potential density plot of NaBr2H2O is similar to that between NaI, or KI and water. Note the contact between the Na+ ion and the oxygen atom of water. Contact polarizes water’s electrons facilitating interaction with a second water molecule. Note the lack of contact between water and the Br ion.

M.J. Shultz et al. / Chemical Physics Letters 588 (2013) 1–10

1M (CH3)4NOH + D2O

0.5

HOD Difference vs HOD

3663 cm-1

Absorbance

0.4 0.3

3634 cm-1

0.2 0.1 0.0 3200

3400

3600

3800

4000

Wavenumber (cm-1) Figure 3. The frequency of the OH ion vibrational resonance is identified with the aid of RT-MIS. The resonance at 3663 cm1 is identified as decoupled OH resonance due to its prominence in the HDO spectrum. The resonance at 3634 cm1 is distinct from the decoupled OH: the intensity of this peak is correlated to the concentration of (CH3)4NOH or CsOH in their respective solutions.

CCl4, similar to that between water and CCl4 [67]. (The OH resonance is independent of the cation and there is no evidence of a HOH. . .OH hydrogen bond.) This result provides guidance for the frequency of potential OH resonances at the aqueous surface. It is possible that a phase measurement with a well-chosen system would show this resonance since the OH transition dipole is negative, opposed to the static dipole [51]. On chemical grounds it is expected that the OH vector for OH will point out of the solution just as the free-OH vector does. Since the dynamic dipole for the OH oscillator of water is positive, the negative dynamic dipole of OH should destructively interfere with that of the dangling-OH. A sensitive, well resolved phase measurement might thus directly detect the OH resonance. 3.1. Ice As indicated above, the basic impetus for using ice is to minimize both the variety of local configurations and the thermal motion [78], thereby narrowing resonances. Note that solidifying water does not necessarily reduce the number of configurations; for

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example, ice produced by rapid freezing of supercooled water contains stacking faults and is neither cubic nor hexagonal [79]. Indeed, production of strain-free, single crystals is itself challenging, likely due to the small differences in face energies. Crystal growth is a large topic. Briefly, it is found that slow, seeded growth with tight control of the growth interface temperature can produce large single crystals [56–58]. High quality ice greatly facilitates resonance identification and assignment. At atmospheric pressure, the stable form of ice is Ih denoting the hexagonal variant of crystal form I (XIV phases are currently known [80]). A tube model of the hexagonal prism that gives hexagonal ice its name is shown in Figure 4A. Since ice grows cryptomorphologically, identifying the orientation relies on the birefringence of ice. Due to the different densities along and perpendicular to the hexagonal axis, called the optical- or c-axis, ice is birefringent. Placing the crystal between crossed polarizers enables identification of the optical axis. A Rigsby stage [59] uses crossed polarizers to identify the c-axis orientation; once the hexagonal prism orientation has been identified, the crystal can be cut to expose the hexagonal face, called the basal face. Etching the surface (the Shultz laboratory uses FormvarÒ) can verify the cut (Figure 5A). Selecting one of the sides, called the prism faces, is slightly more involved. The ice boule is cut parallel to the c-axis. The exposed prism face is determined by etching. The cut can be adjusted to expose the desired face. The prism-face results discussed here use an a-face cut; Figure 5B shows an initial a-face cut [56]. Each of these faces produces a distinct H-bonded vibrational spectrum. Correlating the orientation and polarization dependent Hbonded spectra with the molecular-level configuration of water molecules in the hexagonal structure enables identification and assignment of five resonances in the H-bonded spectrum. The most prominent feature in ice, particularly at low temperature, is the feature at 3098 cm1. This feature has been identified and discussed in the literature [53,55,73,81], so only aspects that enable assignment are discussed. PAN-SFG (Figure 6) identifies a significant quadrupole component to this resonance as follows. Within the dipole approximation, linearly polarized infrared and visible inputs generate a linearly polarized SF output. By the principle of superposition of plane waves [53], overlapping resonances also produce linearly polarized light with a polarization direction weighted by the strength of the contributing resonances. For linearly polarized light, intensity falls off as cos2h as the analyzer rotates from the polarization direction. Figure 6 is not a cos2h; a longitudinal quadrupole must be added to fit the data. Observation of the quadrupole raises two issues: what is the origin of the quadrupole and can a quadrupole be observed in SFG?

Figure 4. Two faces of ice are cut from the hexagonal prism crystal structure. The prism axis is the c, or optical axis. The a axes point to the hexagonal apices. Note that due to tetrahedral bonding, water molecules form a chair structure within the hexagonal prism – shown outlined in (A) above. (A) The basal face is the top bilayer of the hexagonal prism. Three-coordinate water molecules in the basal face – starred in the above – all have three-coordinations to four-coordinate water molecules in the lower half of the top bilayer (for clarity, coordinations to adjacent hexagonal prisms are not shown). (B) The prism a-face features dimers in the top half bilayer: pairs of hydrogen-bonded water molecules each of which has two coordinations to four-coordinate water molecules in the lower half bilayer. There are four distinct motifs among these pairs, numbered 1–4 as discussed in the text and shown in Figure 8.

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Figure 5. Ice faces are revealed via FormvarÒ etching. (A) The basal face forms hexagonal etch pits reflecting the hexagonal prism face structure. The etch-pit shape verifies that the c-axis is perpendicular to the face to within 0.5°. (B) The a-face forms v-groove etch pits. In this example, the cut has the c-axis tilted 3° with respect to the surface plane as reflected by the trapezoidal shape and the ‘hip’ on the right-hand end of the v apex. Asymmetry indicates that the a-axis 3.6° from the perpendicular. Scale bars are 100 lm.

0

0.35 315

0.00

45

270

90

225 0.35

135 180

Figure 6. Polarization analysis of the 3098 cm1 resonance of ice at 113 K. Linearly polarized light generates a cos2h plot; the 3098 cm1 peak has a significant quadrupole component. Filled squares are the experimental points; open circles a dipole:quadrupole ratio of 1:0.6.

The origin of the quadrupole can be envisioned by examining the model in Figure 4. The hydrogen bonds connecting the top bilayer to the one below it – termed bilayer stitching bonds – can originate either from a donor in the lower or the upper bilayer. These alternatives have oppositely directed dipoles; oppositely directed dipoles form a quadrupole. One question remains: How can a quadrupole, which has a center of inversion, be SF active? This question was answered by Morita et al. [82]: due to location within the field gradient of the surface, a surface quadrupole can be SF active. Furthermore, it is precisely bonding asymmetry at the surface and the extended H-bonded surface net that enhances the gradient due to stretching one O. . .HOH stitching bond pulling neighboring O. . .HOH stitching bonds. A quadrupole in the bulk lacks layer asymmetry, hence contributes only weakly to the intensity. All surface bonds are connected via the surface network and the surface layer asymmetry; it lacks a layer above it. 2Thus the very red, 3098 cm1 resonance is assigned to the bilayer stitching, donor bonds. Combined experimental and theoretical efforts have resulted in the first definitive assignment of a resonance in the H-bonded region of water. Note that the OH oscillators are not normal modes of water, but rather OH dipoles with correlated motion due to the H-bonded network. Correlated motion of oppositely oriented OH dipoles forms the observed quadrupole. The earliest theoretical attempt to calculate the SFG spectra of ice [83] accounted for several broad features, but was unable to

account for the weaker, bluer H-bonded features. In the reported work, SFG polarization analysis together with ice face orientation suggests assignment of four resonances in the weak hydrogenbonded region. The relevant spectra are shown in Figure 7. Four resonances are shown: 3372, 3385, 3397, and 3435 cm1. Each of these features is separated from the remainder of the H-bonded spectrum, facilitating identification of the peaks. These features appear relatively weak in the spectra shown; however, the intensity is comparable to the free-OH (not shown) resonance that occurs at the usual 3700 cm1. Early on, it was recognized that these features are likely associated with double-donor water molecules, i.e., those with a dangling lone pair; these are termed d-O water molecules. This recognition is consistent with the current view that the strongest hydrogen bonds, thus the reddest OH stretches, are associated with those water molecules with a larger number of acceptor bonds [11]. All top half bilayer water molecules are three-coordinate. These may thus have either one acceptor, two donors and hence is a d-O molecule, or may have two acceptors, one donor and hence is a d-OH molecule. With two acceptors, the d-OH water molecules have redder OH stretches than the one-acceptor d-O molecules. Thus the candidates for these bluer resonances are the d-O motifs. Mode assignments are based on a combination of SFG polarization and ice orientation (Figure 8) correlated with the d-O motifs. Observation of the unique molecular-level structure of the a-face is the key for making assignments. Figure 4 shows that the top half-bilayer of the a-face consists of pairs of water molecules mutually H-bonded, each of which is connected by two H-bonds to the lower half bilayer. Figure 8 shows details of these pairs. A d-O water molecule may either act as an acceptor from its dimer partner (top row) or donate to it (bottom row). In either case, the partner may have either a d-O (first column) or a d-OH (second column). Within the ice rules, these are the only allowed d-O configurations. Observe that the OH stretch for the pair-stitching H-bond is in the surface plane. Since these stitching OH bonds have no net orientation (they are randomly forward or backward as depicted in Figure 4B) they are SFG inactive. (Unlike the bilayer stitching bonds of the basal face, these H-bonds do not form a net and hence are uncorrelated.) The focus is therefore on the donor-to-four-coordinate OH stretches. (These are denoted with stripes on the left-hand molecule for each pair in Figure 8.) Column one pairs feature two sets of lone pairs oriented perpendicular to the surface. Since the dangling lone pairs are the most polarizable part of these pairs, these molecules can be characterized as having longitudinal polarization. Longitudinal polarization is associated with p-polarized

M.J. Shultz et al. / Chemical Physics Letters 588 (2013) 1–10

(A) SFG Intensity (a. u.)

0.20

ppp basal face 103 K

0.15 0.10 3385 cm-1

0.05 0.00

3000

3300

3600 -1

Wavenumber (cm )

(B)

p-prism 103 K

0.20

ssp ppp

Intensity (a. u.)

0.15 0.10 3385 cm-1

3435 cm-1

0.05 0.00 3000

3300

3600 -1

Wavenumber (cm )

7

can be viewed in molecular water terms: a symmetric and an asymmetric stretch. The asymmetric stretch dipole is in the surface plane, hence SFG inactive. The symmetric stretch dipole is in the plane formed by the surface normal and the c-axis. Since the IR is p-polarized, these two pairs are expected to be active when the c-axis is in the input plane; that is called p-oriented ice. Thus, pair 1 is assigned to the resonance that is observed with p-oriented ice and ppp SFG; this is the mode at 3385 cm1. Similarly, pair 3 is assigned to the resonance that is observed with p-oriented ice and ssp SFG; this is the mode at 3435 cm1. In similar fashion, pair 2 is associated with ppp SFG on s-oriented ice: the mode at 3397 cm1. Pair 4 is associated with ssp on s-oriented ice: the mode at 3372 cm1. The assignments in the preceding paragraph are consistent with observations on the basal face. Figure 4A shows that all d-O water molecules on the basal face are identical. All are marked by three coordinations to four-coordinate water molecules in the lower half bilayer. There is no orientation dependence since the basal face has a threefold rotation axis. The two covalent, donor OH bonds are in comparable environments. In water molecule terms, the asymmetric stretch is in the surface plane, hence SFG inactive. The symmetric stretch is similar to those in the top row of Figure 8. The difference between the basal face and the a-face hinges on the origin of the local polarization. On the basal face, the dangling valence is orthogonal to the face and the nearest neighbors are four-coordinate, thus lacking dangling valences. Accordingly, the local polarization is determined by the d-O molecules and is longitudinal. (On the a-face, the local polarization is determined by both molecules of the dimer pair.) As a result the d-O resonance on the basal face is observed in ppp polarization. The bluest resonance on the basal face is at 3385 cm1: the same frequency as pair 1. Since the basal face has threefold symmetry, the polarization orientation is measured with a PAN experiment. A purely longitudinal polarization has a null angle of 90°; the measured null angle is 84° [55]. 3.2. Emerging picture of surface water — remaining challenges

(C)

s prism 103 K ssp ppp

Intensity (a. u.)

0.10

0.05

3372 cm-1 3397 cm-1

0.00 3000

3300

3600 -1

Wavenumber (cm ) Figure 7. The basal and prism faces of ice show distinct features in the 3400 cm1 region (T=113 K). (A) The basal face shows a single peak at 3385 cm1. (B and C) The a-prism face shows four distinct resonances: (B) at 3385 cm1 and 3435 cm1 when oriented with the c-axis in the input plane (p-oriented) and (C) at 3372 cm1 and 3397 cm1 when oriented with the c-axis perpendicular to the input plane (soriented). These distinct features result for the distinct bonding motifs probed. (Free OH resonance, easily observed at 3710 cm1, is beyond the scanned range.)

sum frequency, p-polarized visible, requiring p-polarized infrared: i.e., ppp. Comparatively, the polarization of the pairs in the second column is more parallel to the interface: these have a larger transverse polarization, ssp. Pair 1 has both donor OH bonds in similar environments, as does pair 3. The like environment suggests that the OH stretches

Together the RT-MIS, SFG, and PAN-SFG experiments suggest a rich picture for the aqueous surface. Many features in the hydrogen-bonded spectrum are most consistent with an intermolecularly coupled OH-oscillator model; when the two dimer OH bonds are in very similar environments, intramolecular coupling is dominant. Hydrogen-bond formation as well as strength depends on molecular polarization. RT-MIS results show that water interacts with the cation of the salt; such interaction polarizes water sufficiently to form a water–water hydrogen bond if the cation–anion pair forms an outer sphere complex. Judicious choice of solutes can guide the search for important resonances. In the reported work, TMA-OH is used to find the vibrational resonance of hydroxide ion in a weakly interacting environment. The resonance is found 29 cm1 red of the free-OH resonance. The richest detail is provided by SFG experiments on the prism a-face of ice. The molecular configuration of the a-face features dimers: a pair of hydrogen bonded water molecules that sit on a lower half-bilayer of 4-coordinate water molecules. Due to the bonding, these pairs are physically decoupled from the remainder of the lattice and from other pairs. In addition, the weakest hydrogen bonds are formed by water molecules with a dangling lone pair; hence the bluest H-bond resonances are associated with double-donor water molecules in the dimers. These weak hydrogen bonds are also spectrally isolated. SFG probes these localized vibrations. There are four possible configurations for the pairs containing at least one double-donor water molecule; four resonances are observed. Matching resonances with a given dimer configuration relies on the twofold rotational symmetry of the a-face and on the polarization ability of SFG.

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M.J. Shultz et al. / Chemical Physics Letters 588 (2013) 1–10

longtudinal

transverse

1

3

3385 cm-1

3435 cm-1

2

4

3397 cm-1

3372 cm-1

p oriented

s oriented

Figure 8. Dimer motifs found in the a-prism face of ice. OH bond associated with the resonance is denoted with stripped hydrogen atom(s). Left-hand column: features d-O to d-O bonding. Adjacent uncoordinated lone pairs result in local polarizability perpendicular to the face. Right-hand column d-O to d-OH bonding results in a tangential polarizability. Top row: OH stretch dipole is in the c-axis, surface-normal plane, hence observable in p-orientation. Lower row: OH stretch is a local OH oscillator with a transition dipole nearly perpendicular to the c-axis, surface-normal plane, hence observable in s orientation. Mode assignments based on polarization and orientation observations. Numbers correspond to those in Figure 4.

Assignments of two of the four resonances on the a-face are consistent with an intramolecular-coupled or normal-mode interpretation; the other two are consistent with an intermolecular, coupled OH oscillator interpretation. In all four cases, the frequency of the donor OH stretch is affected by the bonding mode of its dimer partner – a clear demonstration of the need to include three-body effects in H-bonding. The picture that results from the a-face is consistent with the polarization and bonding for the weak H-bond resonance in the basal face. The basal face is much simpler, presents only one bonding motif for the d-O molecules and shows only one resonance. This resonance is a longitudinal mode, consistent with the polarization observed on the a-face. One resonance can be identified in the strong H-bond region of ice: the resonance at 3098 cm1. This feature has a significant quadrupole contribution; a contribution that enables assigning the resonance to the bilayer stitching bonds [55]. This assignment was subsequently verified by theoretical calculations [82]. The five assigned modes for the aqueous interface are a beginning. The remaining hydrogen-bonded region for ice clearly con-

tains rich detail, but the secrets have not yet been revealed. There are a number of techniques that might unlock the information. Two-D, pump–probe experiments can reveal coupling among modes. Well resolved phase measurements could separate resonances with distinctly oriented transition dipoles. Isotope substitution can decouple modes, thereby simplifying the spectra and guide interpretation. Judicious choice of dopants can probe specific surface-water configurations. Experimental efforts such as these can guide theoretical efforts. Given the importance of the aqueous interface, the challenge will likely be taken up by experimentalists and theoreticians alike.

Acknowledgements The authors gratefully acknowledge support from the United States National Science Foundation (Grant Nos. CHE1306933 and CHE0844986) and the Petroleum Research Fund (Grant No. 46671-AC6). THV acknowledges support from the U.S. Department of Education GAANN Fellowship.

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Mary Jane Shultz received her Ph.D. in theoretical chemistry from M.I.T. She conducted theoretical research at Berkeley and Harvard University, followed by experimental research at Brandeis and Boston College. She joined the faculty at Tufts University and served as Chair of the Department from 2000–2006. Professor Shultz’s research interests include everything associated with water: aqueous solution and ice interfaces, water quenching of photochemical reactions, and photochemical remediation of polluted water. She develops analytical techniques to probe these varied interfaces.

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M.J. Shultz et al. / Chemical Physics Letters 588 (2013) 1–10 Patrick Bisson received his BS in Electrical Engineering from U. Mass Amherst and his BS in Chemistry from U. Mass. Lowell. He received his Ph.D. from Tufts University and is currently a Postdoctoral Fellow at Dartmouth College. His research interests are centered on ice. He is presently investigating mechanical properties of ice.

Tuan Hoang Vu received his BS in Mathematics and Chemistry from Brooklyn College of the City University of New York. He received his Ph.D. from Tufts University and is currently a Postdoctoral Associate at the Jet Propulsion Laboratory in Pasadena, California. At this time he is focusing on planetary and interplanetary ices and clathrates.