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Hydrogen-Bond Relations for Surface OH Species Getachew G. Kebede, Pavlin D. Mitev, Peter Broqvist, Jolla Kullgren, and Kersti Hermansson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b10981 • Publication Date (Web): 11 Jan 2018 Downloaded from http://pubs.acs.org on January 12, 2018

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The Journal of Physical Chemistry

Hydrogen-bond relations for surface OH species Getachew G. Kebede, Pavlin D. Mitev, Peter Broqvist, Jolla Kullgren and Kersti Hermansson* Department of Chemistry-Ångström, Uppsala University, Box 538, SE-751 21 Uppsala, Sweden

Abstract This paper concerns thin water films and their hydrogen-bond patterns on ionic surfaces. As far as we are aware, this is the first time H-bond correlations for surface water and hydroxide species are presented in the literature, while hydrogen-bond relations in the solid state have been scrutinized for at least five decades. Our data-set, which was derived using Density Functional Theory, consists of 116 unique surface OH groups – intact water molecules as well as hydroxides – on MgO(100), CaO(100) and NaCl(100), covering the whole range from strong to weak to no H-bonds. The intact surface water molecules are always redshifted with respect to the gas-phase water OH vibrational frequency, whereas the surface hydroxide groups are either redshifted (OsH) or blueshifted (OHf) compared to the gasphase OH– frequency. The surface H-bond relations are compared with the traditional relations for crystals. We find that the 'ν(OH) vs. R(H∙∙∙O)' correlation curve for surface water does not coincide with the solid state curve: it is redshifted by about 200 cm–1. The intact water molecules and hydroxide groups on the ionic surfaces essentially follow the same H-bond correlation curve.

Keywords: Metal oxide surface, hydrogen bond, hydroxide ion, water, anharmonic OH stretching frequency, DFT, H-bond correlation curves, electric field

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1. Introduction This paper concerns thin water films and their hydrogen-bond patterns on ionic surfaces, up to one water monolayer or just above, i.e. molecules at the very interface between the water/hydroxide species and the ionic materials. For thicker water films, the water phase will quickly approach bulk water behaviour1–3 and display the structural and spectroscopic signatures of bulk water. In the thin water films, however, the final overlayer structure is the result of a compromise between favourable Hbonding among the (intact or dissociated) water molecules and favourable water-surface bonding.4,5 Here our main question is whether the hydrogen bonds in such thin-film structures behave like traditional hydrogen bonds and demonstrate the common H-bond relations – or not. Our golden standard here for "normal H-bond behavior" will be the many experimentally derived hydrogen-bond relations known from the literature on bulk structures. Some prominent examples based on often large collections of structural and spectroscopic data for ionic crystalline hydrates and hydrogen-bonded crystals are contained in the following studies, Ferraris and Franchini-Angela6, Novak7, Olovsson and Jönsson8, Berglund et al.9, Mikenda10, Beckenkamp and Lutz11, Chiari and Ferraris12, Steiner and Saenger13, Lutz14, Libowitzky15, Gilli and Gilli16, Rozenberg et al.17,18 and Steiner19. The DFT-based correlation curves we present here constitute a first attempt to fill this gap and we present results from 140 unique surface OH groups and compare them with results for 80 unique OH groups from crystalline hydrates and hydroxides. As far as we are aware, no H-bond correlation curves have been presented for surface water molecules in the literature before. The surface OH data were collected from NaCl(001), MgO(001) and CaO(001) with different water coverages. Some of the adsorbed water molecules on MgO(001) and CaO(001) dissociate, and we present results for both the intact and dissociated water molecules. High-quality experimental vibrational spectroscopy data for thin water films on metal oxide surfaces have been published in the literature, such as the recent Infrared reflection-absorption spectroscopy (IRRAS) studies for deuterated water on CaO(100)20,21 and on MgO(001)22,23, at low temperature. For one monolayer coverage, the two systems display quite consistent spectra: two distinct high-frequency peaks and a broad band centered about 300-400 cm–1 further down in (OD) frequency with some faint structure. As for structural data, it is generally difficult to obtain direct and measures of the intermolecular distances for the H-bonded water network in thin water layers from experimental methods. However, with access to experimentally measured vibrational frequencies and access to frequency-distance correlation curves H-bond distances can be estimated. In this paper we provide the latter. One such example of a predictive use of correlation curves is that of Eriksson et al.24 who estimated the average R(O• • •O) H-bond distance between the first and second hydration shells around metal cations in aqueous solution based on the IR-measured OH vibrational spectral peak for the first hydration shells in those solutions and the classical frequency-distance H-bond correlation curves available in the literature for solid H-bonded crystals. 2 ACS Paragon Plus Environment

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In addition to local structure prediction, H-bond correlation curves present physical insight in terms of useful rules-of-thumb. They can also serve as reference relations for validation of new data and help to screen for errors in experimental or computational data. The paper is arranged as follows. The Method section describes the electronic structure calculations, geometric structure optimizations and the calculation of the OH vibrational frequencies. Our OH frequencies correspond to experimental isotope-isolated frequencies (had they been measured), i.e. they are uncoupled vibrations and therefore particularly sensitive probes of the environment and straightforward to interpret, and they are anharmonic. The Results chapter starts in Sction 3.1 by highlighting the importance of keeping track of the gas-phase reference values when different types of OH groups are compared, namely water and hydroxide in our case.. Section 3.2 discusses correlations involving the intramolcular r(OH) distance and proposes that calculations are more reliable than experiment in determining OH distance. In Section 3.3 we present the surface Hbond correlation curves and analyse the differences between bulk and surface. Section 3.4 reports the (large) anharmonicity constant found for many of the H-bond motifs on the surface and Section 3.5 introduces an untraditional, and successful, descriptor of the environment, namely the electric field at the OH vibrator.

2. Methods The structural and spectroscopic data were collected from the optimized geometry and subsequent onedimensional (1D) uncoupled OH stretching. In the following we will describe in detail our computational approaches.

2.1. Systems Interface systems. H2O/NaCl(001), H2O/MgO(001) and H2O/CaO(001) interfaces were modelled as 3-D periodic slabs, each system comprising 4 substrate layers and a 15 Å vacuum gap between the slabs. The optimized lattice parameters of 5.66 Å for NaCl(001) (experiment 5.64 Å25), 4.25 Å for MgO(001) (experiment 4.21 Å26) and 4.83 Å for CaO(001) (experiment 4.80 Å26) were used to build the slabs. Water coverages ranging from the water monomer to 1.5 monolayers (ML) were explored using slab supercells of different sizes. These slab cells and the total number of water molecules (intact and dissociated) contained in them are listed in Table 1. Here, 1 ML coverage means that one adsorbed water molecule (intact or dissociated) per surface ion-pair. In all interface calculations, the water molecules were adsorbed on one side of the slab. The starting geometries for the geometry optimizations were taken from the previously reported 1.5 ML overlayer structure on NaCl(001) by Yang et al. 27, and for the 1.0 ML and 1.25 ML overlayer structures on MgO(001) and CaO(001) from Włodarczyk et al.22 and Zhao et al.20, respectively. Two of these structures are shown in Figures 1a-b. 3 ACS Paragon Plus Environment


Two types of surface water species have been identified in small water clusters, and thin water layers on metal oxide surfaces, namely intact and dissociated water molecules. Dissociated water gives rise to hydroxide ions of the OsH or OHf kind (the negative charge is seldom written out in this notation). The s in Os stands for "surface" and the f in Hf stands for "free". They are schematically depicted in Figure 1c. The OsH surface hydroxide group typically either donates a hydrogen bond to an OHf ion or points into the free space above the surface. The OHf surface hydroxide group binds directly to a surface metal cation on its O side with the H side pointing away from the surface into the free space, although with a tilt from the surface normal; in our optimized structures up to 40°. An intact water molecule binding directly to a surface metal cation on its O side, typically donates two hydrogen bonds to water, OHf or surface oxide ions. Some of the water OH groups are non-H-bonded or "dangling". In our data collection, the interface data set contains 58 unique water molecules, 41 intact and 17 dissociated, i.e 116 unique OH groups. Bulk crystalline hydrates and hydroxides. We have selected four crystalline hydrates and four hydroxides as listed in Table 2. Their structural data are available from low (and room) temperature neutron diffraction measurements28–33 except Na2CO3∙10H2O, where as far as we know, only X-ray diffraction data is available34. For each structure, the space group, number of formula units per crystallographic unit cell (Z), and the structural references that we used for the starting geometries, are collected in Table 2. Geometry optimizations were performed without imposing any symmetries or cell shape constraints. All water molecules in our dataset of crystalline hydrates have unique environments, and contain altogether 37 structurally different water molecules and 74 different OH groups. For our sample of solid hydroxides, the unit cells of Be(OH)2 and Zn(OH)2 contain two structurally unique hydroxide ions each whereas the other two hydroxides contain one unique hydroxide ion each, giving 6 independent OH groups. Gas-phase systems. The isolated gas-phase water molecule and hydroxide ion were optimized with the 3D periodic boundary conditions in 14 Å x 15 Å x 16 Å simulation boxes.

2.2 Electronic structure calculations Our DFT calculations were performed with the VASP program35–38 using the optPBE-vdW functional39. In a recent paper5, we examined eight dispersion-corrected DFT methods and compared them with the PBE functional, and showed that inclusion of dispersion interactions at the optPBE-vdW level leads to good agreement with experimental adsorption energies for H2O/NaCl(001) and H2O/MgO(001); this is the method chosen here. The electron-core interactions were described using the PAW formalism.40,41 For H, O, Li, Na, Be, Mg, Ca, Al, Zn, C, N, S and Cl, the 1s1, 2s22p4, 2s1, 2p63s1, 2s2, 2p63s2, 3p64s2, 3s23p1, 3d104s2, 2s22p4, 2s22p5, 3s23p4 and 3s23p5 electrons, respectively, were treated as valence electrons. All 4 ACS Paragon Plus Environment

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calculations were performed with a plane-wave kinetic energy cutoff of 400 eV. All the interface calculations were performed with a 4 x 4 x 1 Monkhost-Pack k-point mesh and for the crystalline hydrates and hydroxides were chosen as required by the length proportions of the lattice parameters a, b and c. Thus, a 2 x 3 x 2 grid was chosen for Na2CO3∙10H2O, 4 x 4 x 1 for MgSO4∙11H2O, 2 x 2 x 4 for MgSO4∙7H2O and LiOH∙H2O, 2 x 3 x 3 for Al(NO3)3∙9H2O, 3 x 3 x 2 for Be(OH)2 and Zn(OH)2 and 5 x 5 x 5 for Mg(OH)2. We used Gaussian smearing with a width of 0.1 eV in all cases. All structures were optimized until the forces on each atom was less than 0.002 eV/Å.

2.3 Calculation of anharmonic OH frequencies We have calculated all OH stretching vibrational frequencies using a 1-dimensional uncoupled OH vibrational model. In this model, each OH potential energy curve was constructed by allowing the vibrating OH bond (in a H2O molecule or OH– group) to contract and stretch around its centre of mass while the remaining parts of the system were kept fixed. We used a reduced mass of 0.94808 amu for the vibrating OH oscillator and 19 energy points were generated along the potential energy curve with a step size of 0.06 Å; more precisely we used 12 energy points above and 7 below the equilibrium OH distance, re. The 1D vibrational Schrödinger equation was then solved for the vibrational energy levels using the discrete variable basis-set representation (DVR) approach of Light et al.42,43 The anharmonic stretching frequencies were calculated from the energy difference between the ground and first vibrationally excited state. This computational approach has previously been used by us to calculate OH frequencies of water44,45 and hydroxides46 in solid H-bonded systems as well as in liquid water and ionic aqueous solutions.47

3. Results and Discussions 3.1 Intramolecular H-bond correlations on the surface All systems studied in this report are incuded in Figure 2, i.e. intact and dissociated surface water molecules as well as the water molecules and hydroxide ions in the ionic bulk crystals. The plot comprises contributions from 74 OHcrystal water + 82 OHintact surf water groups and in Figure 3b from 6 OHcrystal hydroxides + 17 OsH + 17 OHf groups. The figure displays the calculated uncoupled ("isotopeisolated") anharmonic OH stretching vibrational frequency, ν(OH), on the y-axis and the corresponding optimized equilibrium intramolecular OH distance, re (OH), on the x-axis. In the following, we will often drop the subscript e, but it is worth noting that all intra- and intermolecular distances reported in this study correspond to optimized values. r(OH) and ν(OH) are both intramolecular properties and both are sensitive probes of the molecular surroundings and we observe an excellent correlation between the two. This tight correlation between r(OH) and ν(OH) for bulk water molecules is well known from the theoretical literature45,48, 5 ACS Paragon Plus Environment


and Figure 2 confirms that this relation also holds for water molecules bound on ionicsurfaces. The hydroxide ions, in the bulk as well as on the ionic surfaces, essentially follow the same correlation as the water molecules. The points in the Figure 2 represent an extraordinarily large variety of different surroundings: the OH frequencies cover a range of almost 1600 cm–1 and the r(OH) distances a range of about 0.07 Å. The re (OH) distances for the bulk crystalline hydrates in our sample lie in the range 0.98–1.01 Å. The smaller value is typical for moderately strong hydrogen bonds and the larger for strong hydrogen bonds. The points at the extremes in the graph originate from surface species, yet they nicely adhere to the same correlation curve. Almost all of the surface OH species in the figure are elongated with respect to the OH distance in the gas-phase water molecule, which is 0.972 Å with the DFT method used here. Likewise, and consistently, the OH frequencies of all the OH oscillators lie below the gas-phase value for the water molecule, which is 3580 cm–1 with our DFT method. This similarity between the water and hydroxide groups is only a chimera, however. Figures 3a and b display the surface-induced changes in OH frequency and OH distance for the surface water molecules and surface hydroxide ions, i.e. Δν = νbound – νgas and Δre = r e, bound – r e, gas; we will often drop the subscript e in the following. From these two figures it is clear that the water and hydroxides OH groups are qualitatively different. The calculated gas-phase values are the dashed lines in the two figures, for water and the hydroxide ion, respectively, and now it is clear that, when bound, the water OH bonds are always elongated and down-shifted (redshifted) in frequency with respect to the isolated molecular value, the OH bond in the hydroxide ions become either shorter or longer than the gas-phase hydroxide ion and either upshifted (blueshifted) or downshifted (redshifted) in frequency. The hydroxide ion in the Mg(OH)2 crystal ("brucite") is one of the crystals in the blue-shifted crowd in Figure 3b, and indeed it is known from experiment that the OH groups in this and many other hydroxides lie at 3650 cm–1 or higher, i.e. the crystalline environment induces a blueshift compared to the experimental gas-phase value at 3556 cm–1.49 Bulk hydroxides have been amply investigated in the literature, for example by Lutz and co-workers.11,14,50 We conclude that the bound water molecule and hydroxide ion are indeed different, despite their apparent similarities in Figure 2. The clue lies in the circumstance that the uncoupled anharmonic OH frequency of the gas-phase hydroxide ion lies more than 100 cm–1 below that of the gas-phase water molecule (120 cm–1 in our calculations, 150 cm–1 in experiment). Correlation curves were derived by fitting the Δν(OH) vs. Δr(OH) data points to the functional form Δν(OH) = b • Δr(OH). The resulting curves are the solid lines in Figures 3a and b. As we want b to go through zero when there is no interaction at all, the fitted curves were constrained to pass through zero at Δr(OH) = 0. Results from fittings for the individual systems (except solid hydroxides) as well as of the concatenated data-sets are listed in Table 3. 6 ACS Paragon Plus Environment

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3.2 r(OH) vs. R(O • • • O) for surface H-bonds . The r(OH) vs. R(O • • • O) correlations for our intact surface water molecules are presented in Figure 4a (red rings) The bulk crystal hydrate results are given for comparison (small black rings). The surface and bulk results partly overlap but the surface data-set is on average shifted towards larger r(OH) values. Figure 4b displays the H-bond correlation plot for surface hydroxide species, again compared with bulk hydroxide groups. All surface hydroxide groups here are of the OsH type, as these are the only hydroxides that donate hydrogen bonds. The OHf hydroxide groups form the blue-coloured rings to the very right in the figure; all of them are shorter than the reference gas-phase r(OH–) distance. We have marked their R(O

• • • O)

distance as ∞ along the abscissa to indicate that they are not H-bond

donors (although all of them accept H-bonds). These are the same OHf groups that were highlighted in Figure 3b, i.e. the blueshifted ones. We find that for the hydroxides, the bulk and surface species essentially follow one and the same r(OH) vs. R(O

•••

O) correlation, although our data here is too

scarce to draw precise conclusions. Next we compare our calculated correlation curve for water in crystalline hydrates with experiment. The experimentally determined r(OH) and R(O • • • O) distances for three of the four crystalline hydrates discussed in this paper are shown as green diamonds in Figure 4c, namely those three for which neutron diffraction data are available in the literature.28,29,31 Many of their OH distances are seen to be significantly shorter than the experimental gas-phase value; this is unphysical as the intramolecular water OH distances are known to always elongatewhen H-bonded. The situation is not always as bad as in the examples shown in Figure 4c, but there are abundant examples in the literature of intramolecular r(OH) distances that come out foreshortened compared to the gas-phase value, even in the case of high-quality neutron diffraction studies. In contrast, our DFT-calculated r(OH) vs. R(O •••

O) relation for all water molecules from crystalline hydrates displays a strong correlation and the

OH bond distances are in all cases longer than in the reference gas-phase molecule. The reason for the rather unpredictable neutron diffraction result is the following. Even in “wellbehaved” solid crystals at low temperature, neutron diffraction investigations yield OH distances with uncertainties of some 0.02 Å or larger due to systematic errors in the model used in the analysis, or, differently put, due to a mismatch between the model used in the structure refinement procedure and the experimental reality.51,52 The effects are mainly a result of shortcomings in the simple vibrational models used in standard refinement procedure, namely neglect of anharmonicity and librational motion; the former makes the refined O-H bond too long, the latter too short. Calculations (see e.g. Figure 4) tell us that an error of 0.02 Å is similar in magnitude to the effects of a typical crystalline environment on the OH bond length, hence the problem of using neutron diffraction data to determine OH distances. In summary, knowing the locations of the hydrogen atoms in a structure gives important clues to the properties of H-containing materials (not least in geochemistry and geology), and is a 7 ACS Paragon Plus Environment


prerequisite for the formulation of distance relations involving H. Consequently, there are many ongoing efforts in the scientific community to improve procedures and experimental techniques in this direction. The recent electron diffraction study to determine H positions in single nanocrystals using electron diffraction53 is an example. In our opinion, to reveal structural trends involving H-bond positions in moderately complicated crystals, the best technique today appears to be theoretical calculations.

3.3 ν(OH) vs. R(H • • • O) for surface H-bonds Another of the most useful H-bond relations, is 'ν(OH) vs. R(H • • • O)'. Here our focus will be on surface water and comparisons with the bulk correlation curve. On the MgO(100) and CaO(100) surfaces with their various water coverages (up to 1.25 ML) examined here, the water molecules that remain intact all reside on a surface metal cation with O towards the cation and typically donate their two hydrogen bonds to the following types of surface acceptors: water, OHf or surface oxide ions (Os2– ). The ν(OH) vs. R(H∙∙∙O) curve for all these intact surface water molecules are shown in Figure 5a. In the figure we have colour-coded the H-bonds donated by surface water molecules according to the type of acceptor. In some cases, a water OH group is non-H-bonded or "dangling"; this is also indicated. Different types of acceptors are seen to fall in different distance-frequency regions of the correlation. The most strongly redshifted OH groups are those involved in Ow-Hw∙∙∙OHf hydrogen bonds, followed by the Ow-Hw∙∙∙Os2– and lastly the Ow-Hw∙∙∙Ow hydrogen bonds. Inspection of the coordination number of each surface water molecule was made (not shown here), and revealed that 3- and 4coordination was predominant in all three acceptor classes (some 2-coordinated water molecules also occur in the Ow-Hw∙∙∙ OHf class); this suggests that the coordination number is not an important factor in determining the position of a data point in the correlation plot. The position should be the result of a balance related to the effective charge and size of the acceptor and perhaps also of the screening from other neighbours nearby. The ν(OH) vs. R(H∙∙∙O) curve for the intact water molecules on the MgO and CaO surfaces (red rings in Figure 5b) is distinct from water in the crystalline compounds (black rings) in two aspects, although the general appearances of the curves are the same. First, the surface water curve is shifted (a bit) "down" or "to the right" with respect to the crystalline compounds. This is already evident for medium-strong H-bonds, i.e., around R(H • • • O) ≈ 1.8 Å. Second, the regions covered by the data points are different. Libowitzky noted that all frequencies in his ample bulk crystal data-set lay above 2650 cm‒1 (except for a few scarce cases below 1500 cm‒1, not shown here), i.e. there was an empty data region between 2650 and 1500 cm‒1.15 In fact, in experimental studies this region is difficult or impossible to analyze as combination bands between the redshifted OH bands and bending overtone tend to populate this region [E. Libowitzky, private communication]. This is what we, too, find for the calculated crystalline hydrates. But this gap is filled by the surface water molecules (Figure 5b).


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There is some scatter around the calculated least-squares correlation curves from the DFT data in Figure 5b (and in the other panels of Figure 5 as well), and the scatter is even more prominent when one uses R(O∙∙∙O) as the distance variable. The numerical errors in our calculated frequency and distance data are much smaller than our marks (the rings), namely just a few cm–1 and much less than 0.01 Å, so the scatter originates solely from structural effects, not captured when using the intermolecular H-bond distance as a descriptor. The ν(OH) vs. R (H∙∙∙O) data were fitted to a function of the form ν(OH) = ν0 + b • exp[‒k • R(H∙∙∙O)], where ν0, b and k are the fitting parameters expressed in cm‒1, cm‒1 and Å‒1 and the resulting values are listed in Table 3. We chose the ν0 value to be the stretching frequencies of the gas-phase reference systems, namely ν0 = 3582 cm‒1 for the H2O(g) and 3464 cm‒1 for the OH‒(g), with the method used here. The same functional form was used for ν(OH) vs. R (O∙∙∙O). Figure 5c compares our theoretical calculations with experiment, and as for the r vs R correlation in the previous section, only bulk correlation curves are available from experiment. Two sets of experimental data are included in the figure: those presented by Berglund et al. for many crystalline hydrate compounds (green rings)9 and those by Libowitzky (green diamonds)15 for an even larger number of minerals. The line is our fitted line for the crystals from Figure 5b. For a proper comparison one may want to take into account that our DFT-calculated OH frequencies are systematically lower than the experimental frequencies due to shortcomings in the GGA functional.44 This is well demonstrated by the mismatch between the experimental and calculated gas-phase frequencies (horizontal lines in the plot). The experimental value for the uncoupled ν(OH) frequency of the gas-phase water molecule54 is at 3707 cm–1, i.e it lies 125 cm–1 above the value calculated with the DFT method used here which is 3582 cm–1. Such a systematic downshift of about 100–125 cm–1 pertains to all functionals of the "PBE family". If we take this systematic error into account by shifting all our theoretical frequencies in Figure 5c upwards by approximately 125 cm–1, it will make the agreement between experiment and theory very good. This is equivalent to plotting 'Δνgas=>crystal vs R(H • • • O)' instead of the absolute frequencies. We note that that the systematic mismatch between experiment and calculation is not exactly a constant shift but rather increases somewhat with H-bond strength. Nevertheless the conclusion remains: the agreement between experiment and calculation in Figure 5c is very good. This lends credibility to our surface results as well. For completeness, Figure 5d shows the ν(OH) vs. R(H∙∙∙O) correlation for the dissociated molecules. Again we conclude that OsH and OHf hydroxide ions display a very similar behaviour to the water molecules. Another geometrical parameter of interest is the Ow-Hw∙∙∙Oacceptor hydrogen-bond angle, which expresses the directionality of the hydrogen bond and connects the R(H∙∙∙O) and R(O∙∙∙O) distances. The DFT-calculated H-bond geometries for our crystal water molecules (black rings in Figure 6) are all > 150°, and the R(O∙∙∙O) are all < 3.2 Å and conform well with the H-bond statistics presented in, for example, the neutron-diffraction based survey by Jönsson&Olovsson8 and Ferraris&Franchini9 ACS Paragon Plus Environment


Angela6. The surface water molecules display a different H-bond angle distribution from that of the bulk crystals (insets in Figure 6). The angle range here is very large, namely approximately 130–175°, which is without doubt a consequence of unsymmetrical surroundings offered by the solid-overlayer interface and the simultaneous drive for the water molecules to optimize their O-cation and various Ow-Hw∙∙∙O contacts. In the crystals, on the other hand, the water molecules generally have a much isotropic surroundings. The broadest angle range is exhibited by the surface Ow-Hw∙∙∙Ow bonds, i.e. with water as an acceptor. Do all the highly bent Ow-Hw∙∙∙O bonds in Figure 6 deserve to be called hydrogen bonds? Certainly not, if one follows the traditional geometrical criteria given in many well-known text books and review papers on hydrogen bonding, which typically quote the upper R(O∙∙∙O) distance limit to be 3.2–3.4 Å and the lower angle limit as 150o. Counting the entries with angle 1) and the first overtone (ν0‒>2) using the expression: ωeχe = ½ (2ν0‒>1 – ν0‒ 50,56 >2).

Figure 7 presents the anharmonicity as a function of R(H∙∙∙O) for water on the surfaces and in the crystals and we find that (i) the H-bonded surface OH groups are generally considerably more 10 ACS Paragon Plus Environment

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anharmonic than the bulk OH groups, and (ii) there exists a strong correlation between the anharmonic constant and R(H∙∙∙O), where the anharmonicity drastically increases towards shorter H-bonds for both types of system, and (iii) in the weakly H-bond region and for the dangling OH bond, the anharmonicity constant is close to the gas-phase value (79 cm‒1 in our calculations, 91.5 cm–1 experimentally for the HDO(g) molecule54). In conclusion, the anharmonicity constant for the strongly bound surface water oscillators is more than 4 times that of the weakly bound ones; this effect contributes to the shape of the correlation curve.

4. Summary and concluding remarks Hydroxylation changes the properties and reactivities of solid surfaces, not least metal oxides, and often with far-reaching consequences. Consequently there is an ongoing quest to characterize the structure and bond strengths of the OH groups in a thin water film at a solid surface. Here vibrational spectroscopy is one of the most common and powerful tools to probe the nature of the OH group and its surroundings. However, the assignment of the frequencies to the correct structural motifs is much less straightforward on a surface than for a periodic bulk structure, which limits the full characterization. In this report we have presented theoretical data for OH groups adsorbed on MgO, CaO and NaCl, in all cases on the stable (001) surface. Both intact and dissociated water molecules and different coverages constitute our data-set. We find that there is a strong relationship between the OH frequency and intermolecular H-bond distances on the ionic surfaces but the correlation curve is different from the bulk curve, namely shifted towards longer H-bond distances. The surface data points represent a larger variety of different environments than the bulk cases, some with quite extreme bonding situations since this is an interface with very non-uniform surroundings. At the surface, different types of H-bond acceptors make up different (overlapping) parts of the correlation curve, where the Ow-Hw∙∙∙OHf motifs are the most redshifted. The frequency-distance correlation curves for the surface hydroxide ions and the intact water molecules are essentially the same. Furthermore, we noticed that the H-bond angular distribution of surface water molecules in our surface OH data-set is different from thosein our bulk crystals dataset. While the maximum in H-bond angle distribution for bulk hydrates lies in the range 170–175°, our surface H-bonds are often appreciably bent, namely 155–165° (Figure 6). The H-bond relations that are well known for bulk systems thus cannot automatically be transferred to the interface systems. Moreover, we noticed that the choice of H-bond definition (we made use of two well-known ones) has a larger impact on the classification of surface hydrogen bonds than in the bulk as there exist considerably bent H-bonds on the surface. Thus, using only a geometric criterion for H-bonding can altogether be questioned for the surfaces: in many cases the geometric criterion is not fulfilled because the angle is small but the OH groups are nevertheless very strongly redshifted. 11 ACS Paragon Plus Environment


We also showed that the surface water OH groups involved in Ow-Hw∙∙∙OHf are particularly anharmonic. This effect contributes to making the surface ν(OH) vs. R(H∙∙∙O) correlation curve steeper than the bulk curve. In conclusion, our theoretical correlation curves – adjusted for the systematic mismatch in the gas-phase frequency between calculation and experiment – offers the possibility to estimate experimentally inaccessible surface hydrogen bond distances from the OH vibrational spectra, and vice versa, although the latter situation may be more rare. In any case, these correlation curves provide new insights about hydrogen bonds on ionic surfaces.

Acknowledgments This work is supported by the Swedish Research Council (Vetenskapsrådet). Funding from the National Strategic e-Science program eSSENCE is greatfully acknowledged. The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at UPPMAX and NSC.


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Table 1. System set-ups for the H2O/solid systems explored by DFT in this study, namely three types of isolated water islands (water monomer, dimer and trimer), and a number of overlayer structures (1.0, 1.25 and/or 1.5 ML H2O) on MgO(001), CaO(001) and NaCl(001). The table lists the periodic surface cells used in the calculations and the number of water molecules (intact or dissociated) contained in them.

MgO(001)

NaCl(001) Systems

a

Surface cell

No. of H2O per surface cell a

Surface cell

CaO(001)

No. of H2O per surface cell a Intact

Dissociated

No. of H2O per surface cell a Surface cell Intact

Dissociated

1-mer

p(2√2 x 2√2)

1 (1)

p(2√2 x 2√2)

1 (1)

0

p(2√2 x 2√2)

0

1 (1)

2-mer

p(2√2 x 2√2)

2 (2)

p(2√2 x 2√2)

2 (2)

0

p(2√2 x 2√2)

0

2 (2)

3-mer

p(2√2 x 2√2)

3 (3)

p(2√2 x 2√2)

2 (2)

1 (1)

p(2√2 x 2√2)

1 (1)

2 (2)

1 ML

p(2√2 x 2√2)

8 (1)

p(3 x 2)

4 (2)

2 (1)

p(4 x 3)

8 (8)

4 (4)

1.25 ML

–

–

c(4 x 2)

8 (2)

2 (1)

p(4 x 3)

10 (10)

5 (5)

1.5 ML

c(4 x 2)

12 (6)

–

–

–

–

–

–

The value in parenthesis denotes the number of structurally unique water molecules (intact or dissociated) in

the surface cell.

Table 2. The crystalline ionic hydrates and hydroxides included in this study, together with their space groups, number of formula units per crystallographic unit cells and the experimental references from which our starting structures were taken. These were neutron diffraction data for LiOH∙H2O, MgSO4∙7D2O, MgSO4∙11D2O, Al(NO3)3∙9D2O, Mg(OH)2, Be(OD)2 and Zn(OD)2, and X-ray diffraction data for Na2CO3∙10H2O. Single crystals were used for LiOH∙H2O, Na2CO3∙10H2O and Al(NO3)3∙9H2O, and powder samples for the others. Hydrates

Hydroxides

Space group

Z

References

Space group

Z

References

Na2CO3∙10H2O

Cc

4

Libowitzky(2003)34

Mg(OH)2

P-3m1

1

Catti (1995)32

MgSO4∙7H2O

P212121

4

Fortes (2006)28

LiOH∙H2O

C2/m

4

Hermansson (1982)30

MgSO4∙11H2O

P1–

4

Fortes (2008)29

Be(OH)2

P212121

4

Jacobs (2005)33

Al(NO3)3∙9H2O

P21/c

4

Hermansson(1983)31

Zn(OH)2

P212121

4

Jacobs (2005)33


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Table 3. Results of least-squares fitting of simple functions to the correlations discussed in this paper. The functional forms are given in the left column and the fitted parameters and the goodness of fit in the four rightmost columns.

+Figure

ν0

b

c

R2

Water: Surfaces

Figure 3a

0

‒24519

‒

0.998

Water: Crystals

Figure 3a

0

‒25626

‒

0.998

Δν(OH) = ν0 +

Water: Crystals + Surfaces

Figure 3a

0

‒24855

‒

0.997

b • Δr(OH)

Hydroxides: Surfaces

Figure 3b

0

‒26774

‒

0.995

Hydroxide: Crystals + Surfaces

Figure 3b

0

‒26893

‒

0.993

ν(OH) vs. R (H∙∙∙O)

Water: Surfaces

Figure 5b

3582

‒7.19E5

3.9

0.936

Function:

Water: Crystals

Figure 5b

3582

‒3.96E5

3.7

0.866

ν(OH) = ν0 +


Figure 5b

3582

‒2.13E5

4.6

0.839

b • exp[‒c • R


Figure 5d

3464

‒4.16E5

3.7

0.950

(H∙∙∙O)]


Figure 5d

3464

‒5.22E5

3.8

0.952

ν(OH) vs. R (O∙∙∙O)

Water: Surfaces

-

3582

‒5.06E8

4.9

0.883

Function:

Water: Crystals

-

3582

‒3.52E7

4.0

0.805

ν(OH) = ν0 +


-

3582

‒7.75E11

7.7

0.688

b • exp[‒c • R


-

3464

‒1.19E8

4.6

0.852

(O∙∙∙O)


-

3464

‒7.56E7

4.4

0.855

Correlation Δν(OH) vs. Δr(OH) Function:

Dataset(s)

0



Figure 1. Top and side views of two of the many interface structures examined in this study. (a) H 2O monomer/MgO(100), (b) 1ML H2O/MgO(100).The atomic positions shown are from the optPBE-vdW optimized structures. In (b), there are three inequivalent water molecules W1, W2 and W3, where W1 is dissociated and W2 and W3 intact. The two types of hydroxide groups originating from W1are labelled OsH (burgundy red) and OHf (orange). The colour scheme is yellow atoms = Mg, burgundy red atoms = O (surface lattice oxide), light red atoms are = O (intact adsorbed water molecules), orange atoms = O (OHf), white atoms = H. The cartoons in (c) defines the hydrogen-bond distances in focus in this paper (using a water molecule as an example) and the OHf and OsH hydroxide groups.

Figure 2. Our calculated 'ν(OH) vs. r(OH)' correlation curves for the intact water molecules (on the ionic surfaces and in the bulk structures; red rings) and hydroxides (dissociated water molecules on the ionic surfaces and in bulk ionic hydroxides; blue rings).


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(b)

(a)

Figure 3. Same as Figure 2 but here the gas-to-surface and gas-to-crystal frequency shifts for the surface and bulk OH species, respectively, are plotted on the y-axis against the corresponding shifts of the intramolecular equilibrium bond distance. The solid line is the resulting fitted line through the concatenated surfaces + solids data-sets, constrained to pass through the gas-phase, i.e. (0,0), point. The resulting functions are given in Table 3. Unless otherwise mentioned, here and in the following figures, red open rings = intact surface water molecules, red bottom half filled rings = OsH, and blue upper half filled rings = OHf and small open black rings are bulk crystal reference data.

Figure 4. 'r(OH) vs. R(O···O)' correlations from experiment and calculation for bulk water and hydroxides and from calculation for the surface water and hydroxide species. The experiments are low temperature neutron diffraction experiments as listed in Table 2 and the calculations are our optPBEvdW calculations. (a) intact surface water molecules compared to crystalline hydrates, (b) surface hydroxide ions compared to crystalline hydroxides, (c) calculated crystalline hydrates compared to experimental.



(a)

Page 20 of 22

(b)

(c)

(d)

Figure 5. 'ν(OH) vs. R(H···O)' correlations. In (a) we have colour-coded the H-bonds donated by surface water molecules according to the type of acceptor; see text. The black rings in (b) and (c) represent our data points for the crystalline hydrates and the red rings in (b) represent intact surface water molecules. Experimental data from two different sources are included in (c) namely those of Berglund et al. 9 for many crystalline hydrate compounds (green rings) and those of Libowitzky 15 (green diamonds) for many minerals. The uncoupled OH frequency for the gas-phase water molecule and hydroxide ion calculated with the optPBE-vdW method is 3582 cm–1 which is indicated by the dashed line in (a - c) (the experimental value is 3707 cm–1 (Ref. 54)). The dashed line at 3464 cm–1 in (d) indicates the OH frequency for the gas-phase hydroxide ion calculated with the optPBE-vdW method (the experimental value is 3556 cm–1 (Ref. 49)).


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Calc H2O(g)

Figure 6. 'ν(OH) vs. O-H···O angle' ) for bulk (black) and surface (red) water molecules. The histograms in the inset display the normalized H-bond angles distributions for the surface OH groups (upper inset) and for the bulk crystals (lower inset).

Calc H2O(g)

Figure 7. Anharmonicity as a function of R(H···O) distance for intact surface water molecules (red rings) and bulk water molecules (black rings).



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Hydrogen-Bond Relations for Surface OH Species - The Journal of

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