Solvation structures of protons and hydroxide ions in ...

Solvation structures of protons and hydroxide ions in water Chen Chen, Congcong Huang, Iradwikanari Waluyo, Dennis Nordlund, Tsu-Chien Weng et al. Citation: J. Chem. Phys. 138, 154506 (2013); doi: 10.1063/1.4801512 View online: http://dx.doi.org/10.1063/1.4801512 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v138/i15 Published by the AIP Publishing LLC.

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THE JOURNAL OF CHEMICAL PHYSICS 138, 154506 (2013)

Solvation structures of protons and hydroxide ions in water Chen Chen,1,2 Congcong Huang,2 Iradwikanari Waluyo,1,2 Dennis Nordlund,2 Tsu-Chien Weng,2 Dimosthenis Sokaras,2 Thomas Weiss,2 Uwe Bergmann,3 Lars G. M. Pettersson,4 and Anders Nilsson2,4,a) 1

Department of Chemistry, Stanford University, Stanford, California 94305, USA Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, 2575 Sand Hill Rd., Menlo Park, California 94025, USA 3 Linac Coherent Light Source, SLAC National Accelerator Laboratory, 2575 Sand Hill Rd., Menlo Park, California 94025, USA 4 Department of Physics, AlbaNova University Center, Stockholm University, SE-106 91 Stockholm, Sweden 2

(Received 17 January 2013; accepted 28 March 2013; published online 19 April 2013) X-ray Raman spectroscopy (XRS) combined with small-angle x-ray scattering (SAXS) were used to study aqueous solutions of HCl and NaOH. Hydrated structures of H+ and OH− are not simple mirror images of each other. While both ions have been shown to strengthen local hydrogen bonds in the hydration shell as indicated by XRS, SAXS suggests that H+ and OH− have qualitatively different long-range effects. The SAXS structure factor of HCl (aq) closely resembles that of pure water, while NaOH (aq) behaves similar to NaF (aq). We propose that protons only locally enhance hydrogen bonds while hydroxide ions induce tetrahedrality in the overall hydrogen bond network of water. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4801512] I. INTRODUCTION

Water exhibits many anomalous properties as a result of intermolecular hydrogen (H-) bonding1–3 that constantly evolves through breaking and reforming H-bonds. The extended H-bond network also provides the pathway for proton displacements along the H-bonds, efficiently interconverting a hydrogen bond and a covalent bond, leading to high mobilities of protons and hydroxide ions in water.4–7 The mechanism of this structural diffusion process – H-bond network reorganization rather than Stokes mass diffusion – was first proposed by Eigen and de Maeyer8 and further advanced by both experimental9–14 and theoretical5, 6, 15–17 studies attempting to elucidate microscopic details of the dominant solvation structures of H+ and OH− . H+ and OH− are both the products of water autodissociation. In pure water, H-bond formation is symmetric, i.e., there are on average the same numbers of donated and accepted H-bonds. Excess amounts of H+ or OH− break the symmetry of H-bond coordination of water molecules. A protonated water molecule H3 O+ tends to form more and stronger donating H-bonds, whereas a negatively charged OH− tends to form more and stronger accepting Hbonds. Despite the symmetry argument, recent studies have reported that H+ (aq) and OH− (aq) have distinctly different local solvation patterns and cannot be modeled as mirror systems of each other.18–21 The local structure of a hydrated proton is generally described by the dynamic interconversion between the localized Eigen form H3 O+ 9 and the shared Zundel form [H2 O. . . H. . . OH2 ]+ 22 through fluctuations in the local Hbonds.4, 5, 7, 23–26 It has also been proposed that the presence of a) Author to whom correspondence should be addressed. Electronic mail:

[email protected]

0021-9606/2013/138(15)/154506/7/$30.00

excess protons affects the H-bond network in water well beyond its first solvation shell and involves up to 20 surrounding water molecules.14, 27 Size-selected H+ (H2 O)n clusters have been studied using vibrational spectroscopy28, 29 and infrared signature bands of both Eigen and Zundel ions were identified. Delocalization of the positive H+ (aq) and formation of an H(H2 O)6 + complex were observed in an IR spectroscopy study30 of bulk carborane acid H(CHB11 Cl11 ). Analysis of neutron diffraction data based on Empirical Potential Structure Refinement (EPSR) simulations suggested that the distinction between the Zundel and Eigen forms is sensitive to how these ions are defined, and a higher fraction of distorted Zundel ions was concluded in 1:9 HCl in water.31, 32 In contrast, based on ab initio molecular dynamics (AIMD) simulations, the dominating local solvation structure of OH− (aq) was proposed to be hypercoordinated in the first hydration shell (H9 O5 − ), forming four accepting Hbonds in a square-planar arrangement.18, 33, 34 This hypercoordination model is supported by a series of neutron scattering experiments35–38 and an x-ray diffraction study,39 but the structure of hydrated OH− has also been suggested to be cupshaped rather than planar, with an angle between the OH− axis and the accepting H-bonds that is larger than 90◦ .35, 36 The solvation structures of OH− (aq) resulting from AIMD studies have, however, been shown to be highly sensitive to the functional employed.18, 40 Another AIMD study41 and a recent empirical model based on explicit valency42 both support the view of OH− (H2 O)3 being the dominant form of OH− solutions and that OH− can indeed be viewed as the mirror image of the Eigen form. Application of recently developed ultrafast infrared spectroscopies to water in alkaline environments suggests that only water molecules that are tightly bound in the first hydration shell are involved in proton transfer and exchange with OH− ,21 implying that OH− ions have a

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short-ranged effect on the H-bond network in water. The situation regarding the structure of hydrated OH− is thus far from clear. The goal of the present study is to perform an experimental investigation, not only on the local hydration structure, but also to obtain a direct comparison between the effects of protons and hydroxide ions on the overall water structure. We have combined x-ray Raman scattering (XRS) and small angle x-ray scattering (SAXS) to study aqueous solutions of HCl and NaOH over a range of concentrations. XRS probes the unoccupied density of states through core-level excitations induced by the energy transfer of inelastically scattered highenergy photons (∼7 keV). When XRS is monitored along the low-momentum transfer regime, it indirectly yields O 1s x-ray absorption spectra (XAS) through the energy loss of the hard x-rays43 and thus provides a probe of the local electronic structure at the excited molecules. XRS is sensitive to changes in H-bonding in water and aqueous solutions, as the intensity of the transition is directly related to the density of states in the unoccupied molecular orbitals that are subject to interaction and rehybridization with orbitals of the nearby molecules. More importantly, using hard x-rays, XRS has a deep penetration length into the sample and is free from saturation effects. These are particular advantages compared to other XAS measurement techniques based on fluorescence yield (FY) or total electron yield (TEY).43–48 SAXS, on the other hand, measures the intensity, as function of momentum transfer Q, of x-ray photons that are elastically scattered at small angles by inhomogeneities in the electron density in the solution. It is highly sensitive to the presence of density inhomogeneities in the sample – the presence of density fluctuations is reflected by an increase in the scattering intensity at low Q.49–53 Such low-Q enhancement was observed in SAXS measurements on liquid water at various temperatures.53–57 SAXS has also been used to study the hydration structure of cations and it was found that multivalent cations such as Mg2+ and Al3+ form ordered hydration structures giving rise to a large density contrast compared to bulk water and to the development of a small discrete diffraction peak in the intermediate Q region.47 In contrast to Mg2+ and Al3+ , F− induces the formation of low-density, tetrahedral structures, which result in a strong low-Q enhancement in SAXS without a well-developed diffraction peak. The sensitivity of SAXS to the formation of ordered structures in solutions makes it a viable tool for the purpose of the present study.

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(SSRL) using a Si(311) double-crystal monochromator. The experimental end-station is described in detail in Refs. 47 and 58. Briefly, the incident x-ray beam hits the sample at ∼10◦ grazing angle whereas the x-ray Raman scattering is detected using a high-resolution 1 m Johann-type multicrystal spectrometer consisting of 40 spherically diced bent Si(110) analyzer crystals (26 of which were aligned for this measurement) in a Rowland geometry of 1 m radius. In the present study, the Si(440) diffraction order of the spectrometer was used; the overall energy resolution of the instrument was measured to be 0.297 ± 0.005 eV through the full width at half maximum (FWHM) of the elastic peak at 6462.2 eV (the elastic peak scan was recorded every five XRS scans to precisely monitor any changes during the experiment). The average momentum transfer is about 2.3 Å−1 which allows treating the transitions within the dipole approximation (see the supplementary material to Ref. 59). The oxygen K-edge XRS spectra were obtained by scanning the monochromator energy from 6980 to 7032 eV (thus measuring the energy transfer in the range of 520–572 eV). The sample was placed in a polyethylene bottle with a Si3 N4 membrane window (5 × 5 mm2 area and 1 μm thickness) to allow efficient x-ray penetration. The sample was stirred by placing a Tefloncoated magnetic stirring bar inside the bottle and the bottle on a magnetic stir plate in order to avoid beam damage and beaminduced air bubbles. The x-ray path from the beam pipe to the sample and the detector was kept in 1 atm He to minimize background scattering and x-ray attenuation from air. SAXS measurements were performed at BL 4-2 at SSRL using a photon energy of 11 keV and an optical fiber coupled CCD detector (MarCCD165). The experimental setup was also described in Refs. 47 and 60. A quartz capillary with an inner diameter of about 1.5 mm was inserted in an aluminum sample holder that was connected to a constant temperature water bath. The sample holder, detector, and the path in between were placed in a vacuum of 1 × 10−3 Torr in order to reduce background scattering. To avoid radiation damage, SAXS data were collected with 30 s exposure time for 15 frames, and all frames were averaged after discarding the ones that deviated significantly from the first frame. The scattering curves were corrected for the primary beam intensity, absorption, and detector readout noise. The scattering of the empty capillary, which contributes ∼20% of the total scattering at Q > 0.05 Å−1 , was measured separately and subtracted from the total scattering intensity. III. RESULTS

II. EXPERIMENTAL METHODS

0.5, 1, 2, 4, 6 M hydrochloric acid (HCl) aqueous solutions were prepared using 37% in weight stock solution from Sigma-Aldrich, and diluted with Millipore-purified H2 O (18.2 M cm). 0.5, 1, 2, 4, 6 M sodium hydroxide (NaOH) aqueous solutions were prepared by dissolving reagent grade pellets from Sigma Chemical Corp in Millipore-purified H2 O (18.2 M cm). All measurements were performed at a temperature of 298 K. O 1s XRS measurements were performed at beamline (BL) 6-2 at the Stanford Synchrotron Radiation Lightsource

The measured XRS spectra of 0.5, 1, 2, 4, and 6 M HCl and NaOH solutions compared to that of pure water are displayed in Fig. 1. Difference spectra of pure water subtracted from solution are displayed on top to aid in inspection of spectral changes. In the case of aqueous solutions of HCl (Fig. 1(a)), contrary to the findings based on FY-XAS measurements61 suggesting a qualitative transition from mostly distorted Zundeltype species at low concentrations to a higher fraction of the Eigen form at higher concentrations, we did not observe an abrupt change in spectral features between 1 and 4 M aqueous


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FIG. 1. (a) O 1s XRS spectra of 0.5, 1, 2, 4, and 6 M HCl (aq). Dotted black lines indicate the spectrum of pure water for comparison, with difference spectra between water and HCl solutions enlarged and displayed in the top panel. All spectra are normalized by area from 533 to 550 eV; (b) O 1s XRS spectra of 0.5, 1, 2, 4, and 6 M NaOH (aq). Dotted black lines indicate the spectrum of pure water for comparison, with difference spectra between water and NaOH solutions enlarged and displayed in the top panel. All spectra are normalized by area from 533 to 550 eV. (c) The region of the OH− absorption for 6 M NaOH (aq) is shown expanded in the inset figure.

solutions with the present, improved measuring technique. For the concentration series (0.5–6 M) measured, the spectra of HCl solution at lower concentrations (below 2 M) look almost identical to that of pure water, while at higher concentrations we observe a consistent trend of decreasing preand main-edge peak intensities. Moreover, particularly pronounced at higher concentrations, the post-edge shifts to a higher energy position, and so does the main-edge, although slightly. The peak position of the pre-edge in the XRS spectra of HCl (aq) remains the same as in the room temperature water spectrum, as opposed to the shift towards higher energy observed by Cavalleri et al.61 These discrepancies can be explained by a possible over-correction to compensate for saturation effects in FY-XAS in the earlier study, whereas the present XRS data are free from experimental artifacts.43 Since Cl− has minor effects on the H-bond network in water and on the XAS spectra,47 the spectral changes of HCl (aq) compared to pure water are almost entirely caused by the presence of excess protons. For aqueous solutions of NaOH (Fig. 1(b)), already observable at 1 M, the main-edge intensity decreases systematically with concentration. A new spectral feature appears as a shoulder at 532.9 eV (enlarged in Fig. 1(c)), whose intensity increases with NaOH (aq) concentration, which is attributed to the absorption of OH− .62 Another notable feature is the broadening of the pre-edge (Fig. 1(c)) which is not pronounced except at higher concentrations. These observations are consistent with the findings by Cappa et al.62 The post-

edge of the XRS spectra of NaOH (aq), on the other hand, matches the post-edge feature in the pure water spectrum almost exactly, both in terms of intensity and energy position. Unlike the case of HCl (aq), in which the Cl− ions fit almost perfectly in the H-bond network in water and thereby have minimal effect on the XRS spectra, NaOH is complicated not only by OH− absorption and perturbation of H-bonding in water, but also by the interaction between water molecules and Na+ . Based on a previous study, Na+ ions are structure breakers that weaken H-bonds in water, as evidenced by the O 1s XRS spectra showing an increase in the pre- and mainedge intensities and decrease in the post-edge.47 This cation effect has to be carefully taken into account when studying the spectroscopic response from the addition of OH− to water. SAXS data provide a unique perspective that adds information on the behavior of these ions. Scattering intensities I(Q) for the aqueous solutions of HCl and NaOH at concentrations of 0.1, 0.25, 0.5, 1, and 2 M are plotted as a function of momentum transfer Q, with the dashed curve of water scattering for comparison (Fig. 2). In the case of HCl (aq) (Fig. 2(a)), the scattering intensities at all concentrations are almost completely parallel to the scattering curve of water, with no distinct features in terms of the overall shape of the curves. SAXS data for NaOH (aq) (Fig. 2(b)), on the other hand, exhibit a clear enhancement at low Q, indicating the presence of structures that produce density inhomogeneities in the solution. The absence of such an enhancement in the


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FIG. 2. (a) SAXS scattering intensity I(Q) vs. momentum transfer Q for 0.1, 0.25, 0.5, 1 M HCl (aq); (b) SAXS scattering intensity I(Q) vs. momentum transfer Q for 0.1, 0.25, 0.5, 1 M NaOH (aq). Black dashed lines indicate the SAXS scattering curve for water.

scattering curves of NaCl (aq), as shown in a previous study,47 indicates that it is purely the effect of OH− (aq). IV. DISCUSSION

Both XRS and SAXS take place on an attosecond timescale, thereby capturing a statistical sampling of instantaneous configurations of molecules in the liquid. While SAXS is a sensitive probe of deviations from the average electronic density, the region of interest lies in low momentum transfer, which corresponds to nanometer length scales, i.e., at least a few hydration shells. XRS, on the other hand, probes the local environment of the atom of interest, and is only sensitive to effects caused by the neighboring molecules. It is thus useful to combine information from the two techniques to investigate both the short- and long-range effects of H+ and OH− on the H-bond network of water. In the XRS spectra of aqueous solutions, the peak intensities and energy positions are dictated by O–O bond lengths and the H-bonding environment in which the excited molecules are probed.43, 47, 48, 63 For HCl, the pre- (535 eV) and main-edge peaks (537–538 eV), which fingerprint distortion or weakening of H-bonds,48 both decrease in intensity. This is suggestive of an increase in the average number of donating H-bonds per water molecule, compared to pure water, and is consistent with the XAS measurements of Cavalleri et al.61 of HCl solution at higher concentrations. It reflects the local structure of protonated water, in which the hydrated proton with a positive charge has an enhanced H-bond donating strength; the post-edge is generally considered as a σ * shaperesonance that is localized along the H-bond,64 therefore its energy is sensitive to H-bond lengths (the “bond-length-witha-ruler” principle).43, 47, 61, 65, 66 By this reasoning, the significant shift of the post-edge towards a higher-energy position is an indication of shorter and stronger H-bonds in the first shell,63 which can be explained as a result of the positively charged, protonated water molecule enhancing its donating H-

bond to surrounding water molecules. In Ref. 31, the authors observed the downshift of the nearest-neighbor peak in the water-water gOO (r) pair-distribution function (PDF), which is consistent with our interpretation. They also found that the second peak in the water-water gOO (r) PDF shifts to 4 Å compared to 4.3 Å in bulk water, and interpreted this change as a pressure-like effect induced by HCl. The primary effect of pressure to water structure is to exert an inward pull of the second shell towards the central water molecule, causing Hbond distortions. In light of the observed trends in XRS, we interpret the downshift of the second peak in the diffraction as an indication of a decreasing second-shell distance as a result of shorter and stronger first-shell H-bonds around the excess protons. However, we do not rule out the possibility of a distortion similar to the effect exerted by pressure, as the local strong H-bond formed between the excess proton and surrounding water molecules break the tetrahedral symmetry, which may cause distortions in the extended H-bond network. As stated above, the case of NaOH is a bit more complicated. To first account for the effect of the Na+ counter ions, we turn to a previous XRS study47 and neutron diffraction measurements by Leberman and Soper,67 stating that the effect of adding NaCl salt to solutions in comparison to pure water is similar to increasing pressure. This is reflected in the XRS spectra through increasing pre-edge and main-edge intensity and decreasing post-edge intensities without any shifts in the energy positions of these features. Following a similar analysis as in Ref. 60, assuming that Na+ and OH− do not directly interact and that the total spectrum is a linear combination of the effects of the individual ions on water, we contend that after subtracting the effect of Na+ , OH− should have the effect of decreasing the pre- and main-edge intensities and increasing the post-edge, thus having similar effects as F− with respect to increasing the number of strong H-bonds in water.60 This is not surprising considering that OH− and F− are both small-sized, singly charged anionic species with strong Hbond accepting nature. The differences between these two


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FIG. 3. (a) Structure factor S(Q) derived from SAXS for 0.1, 0.25, 0.5, 1 M HCl (aq). Inset is an enlarged portion of Q = 0.04–0.5 Å−1 ; (b) structure factor S(Q) derived from SAXS for 0.1, 0.25, 0.5, 1 M NaOH (aq). Dotted black line is S(Q) for water.

Crystallography.70 For HCl, we assume that x-ray scattering is insensitive to the protons and that their contribution thus can be neglected. The form factor of OH− was taken from Ref. 71. After subtracting the independent scattering from the individual species, the structure factor of HCl (aq) at the concentrations measured almost exactly matches that of water (Fig. 3(a)). This suggests that density fluctuations in HCl (aq) closely resemble those in pure water. Figure 4 compares the SAXS structure factors for 1 M HCl (aq) and 1 m NaCl (aq) (molarity and molality are similar at such low concentrations). 0.15 0.14 NaCl 1m HCl 1M water

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species, as reflected in XRS studies, are the low-energy absorption at 532.9 eV, broadening of the pre-edge, and the much more significant decrease in the main-edge intensity compared to the pre-edge in the case of OH− . These observations are all related to the absorption of hydrated OH− that occurs in the low-energy region of the spectrum;62 particularly, the feature at 532.9 eV can be unambiguously assigned to the direct absorption of hydrated OH− . The reason that this feature occurs at such a low energy is likely the elongated H-bond donated by the OH− , where the fact that OH− is negatively charged makes it a very weak H-bond donor. The broadening of the pre-edge and its unaltered intensity may be the result of overlapping absorption of those water molecules in direct contact with OH− and those that are more bulk-like; the drastic decrease of the main-edge is an indication that the fraction of absorbing water molecules decreases in the presence of OH− , which is a mere result of normalization. Even with a reduced fraction of water molecules, the post-edge of the NaOH spectra still matches that of pure water almost perfectly. Conceivably, this is an indication that OH− contributes even more strongly to the formation of tetrahedrally coordinated water than F− . This effect of OH− on the structure of the H-bond network in water is consistent with a recent x-ray emission study,68 as manifested in the substantial increase in the peak relating to the 1b1 lone-pair peak of pure water, interpreted as a result of increased tetrahedrality. In order to extract structural information from the SAXS measurements, we obtained the experimental structure factor, S(Q), by subtracting the weighted sum of independent scattering of water molecules and the respective ions in HCl and NaOH solution from the scattering intensity I(Q), where Q = 4π sinθ /λ is the momentum transfer, 2θ the scattering angle, and λ the wavelength of the x-rays (Fig. 3). The H2 O molecular scattering factor used was obtained from quantum mechanical calculations69 while those of the monoatomic ions were taken from the International Tables for

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0.15 0.14

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We have previously demonstrated that the effect of Na+ (aq) is similar to increased pressure, indicated by a plateau at small angles in SAXS.47, 54 The resemblance of HCl (aq) and water suggests that solvated protons strengthen H-bonds locally, but the effect is short-ranged and does not extend beyond their neighboring water molecules and therefore causes minimal change in the overall structure of the H-bond network. The increase in local density does not lead to overall higher contrast of density inhomogeneities, probably due to rapid proton diffusion. The structure factor of NaOH (aq), on the other hand, is very similar to NaF (aq) – both showing a clear enhancement similar to the effect of decreasing temperature54, 60 (Fig. 5). This confirms the results from XRS that OH− (aq) and F− (aq) have similar effects on the structure of water. We interpret the low-Q enhancement as an indication of an anomalous contribution resulting from structural inhomogeneities in the liquid.48, 60 The presence of OH− not only strengthens Hbonds, but also restructures water molecules around it, having a long-ranged effect and causing enhanced density inhomogeneities in the solution. The differences in SAXS measurements between water in acidic and basic environments thus support the idea that solvated protons and hydroxide are not simple mirror images of each other. In the present work, we refrained from using the PercusYevick and Ornstein-Zernike (OZ) approximations as employed in our previous studies on pure water and salt solutions.54, 60 The addition of salts invariably induces concentration fluctuations in the solution, but the contribution to the SAXS intensity is small.61 The OZ approximation to the structure factor, valid for small Q, is in the form of a Lorentzian, S(Q) ∝1 /(Q2 + ζ −2 ), with ζ the correlation length. If there appears in aqueous solutions, due to ion-ion interactions, also significant pair-correlations at longer dis-

tances than typically seen for water72 this can lead to firstorder diffraction peaks at small Q which limits the range of validity of the OZ approximation. It was demonstrated in our previous study of strongly hydrated ions of Mg2+ and Al3+ ,47 that the cation hydration shells, with high density contrast to pure water, led to an additional first-order diffraction peak due to long-range ion-ion interactions (mostly through the hydration shells), which strongly limits the applicability of the OZ approximation in the case of strongly interacting ionic aqueous systems. In the current study, we observe that the low-Q enhancement in NaOH solutions is difficult to describe with a Lorentzian function from the OZ approximation and most likely this is a result of some ion-ion interactions. However, what is most dramatic is the overall difference in the intensity of the low-Q enhancement between the two solutions. We anticipate that in the case of the OH− hydration shell there is a much lower density due to strong tetrahedral ordering in contrast to pure water but similar to what has been observed for the F− ion.60 There is a clear asymmetry between OH− and H+ in terms of the local H-bonding network where in the case of OH− there is a much stronger tetrahedral ordering. V. CONCLUSIONS

Combined XRS and SAXS measurements of aqueous solutions of HCl and NaOH provide direct experimental evidence of the contrasting behaviors of hydrated H+ and OH− in water. Using XRS to examine the local chemical environment and SAXS to probe density inhomogeneities, we contrast the behaviors of protons and hydroxide ions. While both types of ions have strengthened H-bonds in their respective solutions compared to pure water, protons have minimal effects on the overall long-range packing of water molecules, whereas hydroxide ions enhance tetrahedrality in the overall H-bond network of water. The overlapping absorption of OH− and water in the x-ray spectroscopy measurements makes it challenging to separate the contribution from OH− and water molecules and derive the exact solvation structure of OH− ; however, a direct comparison between OH− and F− indicates that these two ions behave similarly in water. ACKNOWLEDGMENTS

This work was supported by the (U.S.) National Science Foundation (NSF) CHE-0809324, the Department of Energy through the SLAC Laboratory Directed Research and Development Program and the Swedish Research Council. Portions of this research were carried out at the Stanford Synchrotron Radiation Lightsource, a national user facility operated by Stanford University on behalf of the (U.S.) Department of Energy (DOE), Office of Basic Energy Sciences. The BioSAXS beamline 4-2 and the SSRL Structural Molecular Biology Program are supported by the Department of Energy, Office of Biological and Environmental Research, and by the National Institutes of Health (NIH), National Center for Research Resources, Biomedical Technology Program. 1 I. 2 P.

Ohmine and H. Tanaka, Chem. Rev. 93, 2545 (1993). G. Debenedetti, J. Phys.: Condens. Matter 15, R1669 (2003).


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