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Supporting Online Material The Structure of the First Coordination Shell in Liquid Water

Ph. Wernet, D. Nordlund, U. Bergmann, M. Cavalleri, M. Odelius, H. Ogasawara, L.Å.

Näslund, T. K. Hirsch, L. Ojamäe, P. Glatzel, L.G.M. Pettersson and A. Nilsson

Contents:

I. Materials and Methods a. X-ray absorption spectroscopy (XAS) and x-ray Raman scattering (XRS) b. Varying the probing depth c. Ice sample preparation d. Spectra calculations for H-bonded systems e. Molecular dynamics simulations

II. Supporting information

a. Q-transfer dependence and validity of the dipole approximation in XRS b. Determination of bulk and surface ice spectra in Figure 1 of the manuscript c. Quantification of species in the liquid from experimental ice spectra d. The 11-molecules cluster e. Geometric H-bond criterion and energetic vs. electronic structure f. Calculation of RDFs for small clusters in Figure 5B and C of the manuscript g. Influence of dynamics and vibrations on the theoretical analysis h. Changing the cut-off for H-bonding in the analysis of MD simulations

I. Materials and Methods a. X-ray absorption spectroscopy (XAS) and x-ray Raman scattering (XRS)

XAS and XRS at the O K-edge involve the excitation of an O 1s electron to the

unoccupied molecular orbitals. This occurs on a sub-fs timescale and determines the ultra-fast character of the probe [see (1), and II. g. Influence of dynamics and vibrations on the theoretical analysis]. In XAS the excitation occurs directly by absorption of a soft x-ray photon. The absorption cross section is measured here by detecting the fluorescence (Fluorescence Yield, FY), the electrons from Auger decay (Auger Electron Yield, AEY) or secondary electrons (Secondary Electron Yield, SEY). In XRS the equivalent of an x-ray absorption spectrum is measured by detecting inelastically scattered ~6.5 keV-photons. The abscissa in the XRS spectra corresponds to the energy transfer while for XAS the photon energy of the incident photons is given. The energy resolution is 0.1 eV (1 eV) for XAS (XRS). For XRS the momentum transfer q was chosen to ~4.2 Å-1 (for details see II. a. Q-transfer dependence and validity of the dipole approximation in XRS). Hence both excitations follow the dipole selection rule allowing for transitions from the O 1s level to

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orbitals with significant p contribution. The transition probability into an empty orbital is thus proportional to its amount of p character. This is determined by local structure and symmetry in, mainly, the first coordination shell of the excited molecule through orbital mixing (2, 3). Changes in the unoccupied orbital structure entail a redistribution of intensities leaving the integrated intensity approximately constant, which permits quantitative investigations of difference spectra. XAS and XRS provide ultra-fast, element-specific, symmetry-sensitive and local probes for the structure of water.

XAS of liquid water was performed at the Advanced Light Source, Berkeley (USA), on beamline 8.0 (4), and of ice at MAX-lab, Lund (Sweden), on beamline I511 using a Scienta SES-200 analyzer for electron detection. Details on the preparation of the ice samples can be found in I. c Ice sample preparation and in (5). XRS was carried out at the Advanced Photon Source, Argonne (USA), at the BioCAT beamline 18-ID. In contrast to our XRS study in (4) the XRS measurements presented here have been performed at a momentum transfer q of 4.2 Å-1. Further details can be found in II. a Q-transfer dependence and validity of the dipole approximation in XRS and in (4). Possible radiation damage was avoided in all experiments. For XAS small exit slits on the beamline monochromators were used to minimize the intensity of incident radiation. The ice samples were scanned and the water samples both for XAS and XRS were flowed during data acquisition to minimize exposure to radiation (2, 4, 5). Spectral features close to 531 eV that appeared in ice spectra when the sample was not scanned and that were avoided in the spectra shown here allowed for online control of beam damage during the measurements. b. Varying the probing depth

The probing depth, defined as the depth from where the signal drops to 1/e of the signal from the topmost layer of the sample, spans the range from 0.5 mm to 1 Å. Photons are detected to study the bulk of liquid water at 1 bar and 25 and 90(±2)°C. Electrons are detected to investigate ice samples in vacuum at low temperatures. Using ~6.5 keV incident photons the probing depth is ~0.5 mm for XRS (6). The probing depth of FY XAS is less than 0.5 µm, which follows from the penetration depth of soft x-rays at the O K-edge (~535-550 eV) in H2O (density 1 g/cm3) of ~0.5 µm (6). The spectrum in Fig. 1d in the manuscript is a FY XAS water spectrum [taken from (2)] corrected for saturation effects. Quantitative conclusions are drawn from the XRS and electron yield XAS spectra free from saturation (4). SEY and AEY XAS have been applied to ice Ih. By detecting secondary electrons with a kinetic energy of ~1-6 eV the SEY XAS ice spectrum in Fig. 1a has been recorded with a probing depth of ≥50 Å (7). Varying the take-off angle of the electrons changes the probing depth of AEY XAS. For normal emission with respect to the surface the probing depth is approximated by the inelastic mean free path λ of the Auger electrons [~20 Å for 510 eV kinetic energy Auger electrons in ice (8)]. Water molecules with saturated O-H groups dominate this spectrum. For grazing emission the probing depth is given by λ sin φ, where φ is the take-off angle relative to the surface. Here we used φ=4±0.5º to achieve a probing depth of 1±0.7 Å. These spectra correspond to the first bilayer of the ice surface. By subtracting appropriately scaled normal emission from grazing emission AEY spectra the signature from the molecules in the topmost surface

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layer (first half bilayer) with one free O-H as shown in Fig. 1b could be isolated (for details see below: II. b. Determination of bulk and surface ice spectra in Figure 1 of the manuscript). Adsorbing one monolayer of ammonia on the ice surface changes all relevant features in the subtracted spectrum (manuscript Fig. 1) confirming the analysis. Earlier AEY and H+-yield XAS studies of ice surfaces corroborate this result (9). c. Ice sample preparation

A Pt(111) single crystal, mounted on a rotatable sample rod in grazing angle (~5o) with the incoming light, was used as a substrate for the ice film. The Pt(111) single crystal, cleaned with repeated sputter-annealing cycles, showed a clear hexagonal LEED pattern and photoelectron spectroscopy verified that no contaminants were present. Using a pulsed gas delivery system, the ice film could be grown epitaxially in a controlled way. The 10 bilayer (BL) (~40 Å) thick ice film was deposited at 125 K at a speed of approximately one BL per minute, known to produce crystalline ice Ih (10) in a layer-by-layer mode (11). The NH3 termination was achieved by dosing on top of the ice film a saturated layer of NH3 above its multilayer desorption temperature. All ice measurements were performed at 90 K. For further details see (5). d. Spectra calculations for H-bonded systems

X-ray absorption spectra have been calculated using density functional theory (2). No significant change has been observed using different functionals. The oscillator strengths have been convoluted with Gaussians of linearly increasing Full Width at Half Maximum (FWHM). The parameters for this procedure (two energies and two widths) have been determined by fitting the calculated spectrum of a bulk molecule in the 44-molecules cluster with ice Ih structure (manuscript Fig. 2a, dashed line) to the corresponding experimental bulk ice spectrum (SEY XAS spectrum, manuscript Fig. 1a). Slightly different parameters (resulting in a larger broadening of the features) have been used for the 11-molecules cluster calculations used to characterize local configurations in the liquid to account for the larger vibrational motion of the molecules in the liquid. Figure 2 in the manuscript shows that this cluster is sufficiently large to give a reasonable approximation of the electronic structure of local configurations in water. Larger clusters, 27-44 molecules, give similar calculated spectra (manuscript Fig. 2) at a significantly increased computing time. All intramolecular O-H distances are 0.95 Å and all intramolecular H-O-H angles are 109.47º and changes of these parameters by about 3% had no significant influence on the spectra; vibrations do not need to be accounted for explicitly (see II. g. Influence of dynamics and vibrations on the theoretical analysis). Note that neutron diffraction shows that the intramolecular structure does not change with temperature and pressure (12). Starting with 2.75 Å for all O-O distances (12, 13) and linear H-bonds the groups of three molecules on both H-sides of the cluster have been moved systematically to study the effect of donor H-bond distortions on the central molecule.

The accuracy and reliability of our approach to use DFT to compute x-ray absorption spectra for H-bonded systems is best illustrated by recent results for H-bonded

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glycine on the copper (110) surface (14). For this system the structure is known (Fig. 1) and XA spectra have been measured resolving all p-components for both the N 1s (H-donor) and O 1s (H-acceptor) edges (Figs. 2 and 3). This is obtained through angular resolved measurements where the polarization vector of the incoming light is oriented with respect to the molecular axis on the surface.

In order to investigate the effects of H-bonding on the XA spectra we computed spectra for one, two and three glycine molecules on a large all-electron copper cluster (14). The spectrum for a single adsorbed molecule is shown in the left columns of Figs. 2 and 3. For the nitrogen the py spectrum shows a large discrepancy with experiment and we find a dramatic effect from introducing the first N-H…O H-bond bringing the computed spectrum into excellent agreement with experiment (Fig. 2, middle). No further changes are obtained in the absorption spectra from adding the third glycine; the amino group was already fully coordinated in the dimer model. In the oxygen pz XA spectrum there is an interesting development as the modeling is extended from one to three molecules (Fig. 3). Introducing the first H-bond (Fig. 3, middle column) we find that a feature at around 535 eV appears, also present in the experiment, which is interpreted as another sign of the hydrogen bond formation, but weaker than seen in the nitrogen spectrum. Analysis shows that this feature is dominated by contributions from the oxygen atom directly involved in the H-bond. In the computed H-bonded O pz spectrum, we find an extra peak at about 530 eV which is not present in the experiment. An analysis of the XA data shows that this feature is dominated by contributions from the oxygen atom, which is not involved in the H-bond to the amino end of the neighboring molecule. Finally, extending the model to include the third H-bonded glycine removes this feature leaving the final spectra in excellent agreement with experiment. It is thus clear that the present level of DFT treatment is capable of very accurately reproducing effects on the XA spectra from H-bonding between molecules. Further calibration calculations on single molecules may be found in (15) treating pyridine and in (3) dealing with water and methanol. e. Molecular Dynamics Simulations

The analytical-potential (“classical”) MD simulations employed non-rigid water molecule models as implemented in the flexible SPC (16) or MCYL (17) potential models and were performed in the NVE ensemble. The CPMD simulations were performed in the NVT ensemble using the CPMD code version 3.5. The parameters for the pseudopotential description of the core electrons were taken from (18) with the modification that the cut-off radius for the Trouiller-Martin type pseudopotential for oxygen was 1.05 a.u.. A 70 Ry kinetic energy cutoff for the plane-wave expansion was applied and the BLYP gradient-corrected exchange-correlation functional (19, 20) was used in the CPMD simulations. Nosé-Hoover thermostats (21-23) were used to regulate the ionic temperature in both the 25 and 90°C simulations. The CPMD simulations were started from equilibrated classical simulations at 25 and 90°C, using the SPC/E force field.

The number of water molecules in the cubic simulation boxes were 256 for the SPC, 216 for the MCYL and 64 for the CPMD simulation; periodic boundary conditions were applied in each case with box-sizes chosen in order to yield the experimental liquid water

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density. The analytical-potential simulations were equilibrated for at least 100 ps. The full RDFs for the SPC potential were evaluated from production runs of 10 ps duration with sampling at every 20th time step of 0.1 fs. A time step of 0.144 fs, together with a fictitious electronic mass of 700 a.u., was used in the CPMD algorithm and the trajectory was dumped every 10 time steps for structure analysis. The data was taken over the last 5 ps of the CPMD trajectories, after appropriate equilibration (4 ps). II. Supporting information a. Q-transfer dependence and validity of the dipole approximation in XRS

It is possible to select the q-transfer in the x-ray Raman scattering process and hence to vary the dipole and non-dipole contributions to the XRS spectrum. At low q-transfer (qr<<1, with the momentum transfer q and the radius of the O 1s shell r = 0.05 Å) the spectrum is dominated by dipolar transitions (s p) whereas at larger q-values transitions to s and d states also become possible. In contrast to our XRS study in ref. 11 of the manuscript the XRS experiments presented in Fig. 1e of the manuscript have been performed using two Si(440) analyzer crystals at a Bragg angle of 88º, at an energy of 6.46 keV and a q-value of 4.2 Å-1. Fig. 4 shows XRS spectra for different q-values (note the varying intensity in the pre-edge region at 535 eV) and Fig. 5 depicts the intensity ratios of the pre and main-edge peaks for the spectra in Fig. 4 as a measure of the deviation from the dipole approximation.

The spectra for 3.2 Å-1 and 4.2 Å-1 don’t show any significant differences and correspondingly the intensity ratio is approximately constant (~0.4). This demonstrates that the spectra taken at 4.2 Å-1 (manuscript Fig. 1e) can be interpreted within the dipole approximation (within the error bars in Fig. 5). Fig. 6 shows that an intensity ratio of ~0.4 is also consistent with the XAS measurement of ambient water using fluorescence yield (FY) and after correction for saturation effects as presented in the manuscript. XAS allows for dipolar transitions only. b. Determination of bulk and surface ice spectra in Figure 1 of the manuscript

Figure 7 shows the XA spectra as measured for the ice film without (a-c) and with (d, e) NH3 termination. The different detection modes translate to different probing depths: (a) Secondary Electron Yield (SEY) detection with a probing depth of ≥50 Å, (b, d) Auger Electron Yield (AEY) detection using normal emission with probing depth ~20 Å, and (c, e) Auger Electron Yield detection using 4±0.5° grazing angle emission (grazing AEY) with probing depth ~1-2 Å (details about the probing depths see I. b. Varying the probing depth). With the probing depth for each mode, we can calculate the contributions of the 1st, 2nd and 3rd-10th bilayers (BLs), as displayed in Table 1.

Here we have assumed each BL to be a slab of 3.7 Å thickness with homogeneous distribution of water molecules. Although all spectra in Fig. 7 are thus superpositions of 2 or more bilayers of the sample the effects discussed in the manuscript can be readily

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observed in the raw data. However, subtraction of appropriately normalized spectra isolates the spectra corresponding to more well defined H-bond situations. This is described in detail in the following and has been done to generate the spectra presented in Fig. 1 in the manuscript. A spectrum of the 1st BL (not shown) is generated from the grazing AEY and the AEY spectrum (Fig. 7b and c, respectively) by subtracting an appropriately normalized AEY from the grazing AEY spectrum to remove the 7%-contribution of the 2nd BL. Furthermore, to generate the spectra of the topmost molecules (topmost surface layer corresponding to the 1st half BL, Fig. 1b and 1c in the manuscript), another 50% of 4-coordinated water (AEY) is subtracted from this spectrum. This results in the spectrum of the topmost surface layer as shown in the manuscript. It is dominated by molecules with one free O-H [~80% of the molecules in the topmost surface layer have one free O-H bond, see (5, 24)]. To generate the bulk spectrum (Fig. 1a in the manuscript) the 1st-2nd BL contribution in the SEY spectrum is removed using the AEY spectrum. In conclusion, the expressions for the subtractions are as follows for the spectra corresponding to:

1) the topmost molecules (manuscript Fig. 1b, c) = grazing AEY - x1*AEY 2) the well-ordered bulk (manuscript Fig. 1a) = SEY - x2*AEY

The fractions x1 and x2 are rather insensitive to the experimental error bars and

uncertainties in the assumptions (including the inelastic electron mean free path for AEY and SEY, film thickness, presence of defects, grazing emission angle in the detection, internal arrangement within each bilayer, etc). We have used a conservative choice of x1=0.59 and x2 =0.5 so that the actual spectral differences for the various bonding situations in the pre, main and post edges as seen in Fig. 1 in the manuscript are – if anything – even larger. For further details see (5). c. Quantification of species in the liquid from experimental ice spectra Comparison of linear combinations of experimental ice surface and bulk spectra with the measured liquid water spectrum allows for an estimation of the contributions of SD (ice surface) and DD (ice bulk) configurations. As shown with Fig. 8, the ice surface spectrum without further bulk contribution (Fig. 8b) best fits the liquid spectrum at room temperature and a combination of 90% surface and 10% bulk spectra (Fig. 8c) is at the limit of being consistent with the spectral features of room temperature liquid water. More than 10% bulk contribution gives an inconsistently large post-edge intensity (Fig. 8d-g). With the amount of ~80% SD configurations in the ice surface spectrum (Fig. 8b) and taking into account the uncertainty of this value [II. b. Determination of bulk and surface ice spectra in Figure 1 of the manuscript and (5)] we estimate the contributions of the two different species at room temperature to 80±20% and 20±20% for species with only one strong H-bond and tetrahedrally coordinated, respectively; the corresponding numbers for 90°C are 85% (+15/-20%) and 15% (+20/-15%).

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d. The 11-molecules cluster

Spectra for Figs. 3 and 5 in the manuscript are calculated for the central molecule shown in green in Fig. 9 below. Asymmetric species with distorted H-bonds for Fig. 3 in the manuscript have been systematically generated by moving the groups of three molecules on the H-sides of the central molecule as indicated by the arrows for one of the two groups on one H-side (for details see manuscript). For the 14 configurations used for calculation of the XA spectra and RDFs in Fig. 5 in the manuscript the nearest neighbors and the attached molecules on the O-sides have been moved in addition.

e. Geometric H-bond criterion and energetic vs. electronic structure

Numerous calculated spectra show that distortions of donor H-bonds with nearest-neighbor O-O distances above 3.3 Å at θ=0º and above 2.5 Å at θ =45º are necessary to account for the experimentally observed strong pre and main-edge intensities at 535 and 537 eV, respectively. Taking into account uncertainties introduced by spectral changes due to varying a) the azimuthal angles, b) the cluster size, c) the remaining O-O distances and by combining different spectra we use the boundary between zones A and B highlighted as black line in Fig. 3B given by the relation r(θ) = -0.00044 θ2 +3.3 Å (θ in degree) as a cut-off for H-bonding. It should be noted that many different H-bond definitions can be found in the literature. Often the cut-off is based on the first minimum of the O-O RDF (the value of 3.36 Å for the O-O RDF from (12) which is shown in Fig. 5B is very similar to our value of 3.3 Å at θ=0°). The H-bond angle is often derived from theoretical considerations. The difference between this commonly used (constant r for all θ) and our approach is not significant as shows the fact that with our criterion an SPC simulation (16), e.g., at 25°C gives an average of 3.3 H-bonds per molecule, consistent with other studies reporting a value of 3.5 (25).

By simultaneously calculating the H-bond interaction energy and the area of the pre-edge peak for a molecule in a configuration undergoing a change from DD to SD character, we can correlate our geometric criterion with an energetic criterion and with the spectral changes as shown in Fig. 3 of the manuscript. Fig. 10 shows the H-bond energy and the integrated intensity of the pre-edge peak for a series of nearest-neighbor O-O distances between 2.5 and 10 Å. The similar slope of the two curves shows that the pre edge in the XA spectrum qualitatively reflects the strength in the H-bond interaction. In addition, Fig. 10 shows that the presence of a pre-edge peak corresponds to a loss of 40-70 % of the H-bond energy (compare the corresponding O-O distances in zone B at θ = 0° of 3.3-3.9 Å in Fig. 3B in the manuscript). This is a preliminary result since variations in second-neighbor interactions have not yet been accounted for. f. Calculation of RDFs for small clusters in Figure 5B and C of the manuscript

XA spectra and RDFs are calculated for the central molecule in clusters consisting of 11 molecules. A total of 14 clusters have been used. By varying the nearest neighbor environment of the central molecule a sampling of the different possible configurations in

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the liquid is guaranteed. For simplicity, the first coordination shell of this molecule is symmetric for each configuration: the bonding situation on the H-sides is the same as on the O-sides, i.e., the same O-O distances and angular deviations from tetrahedral arrangement have been used on both sides. Distortions on the O-side do not significantly affect the XA spectra consistent with the results in (2), but yield better agreement with the RDFs. For different weighted sums of these configurations the O-O and O-H RDFs have been generated accounting for the molecules in the first coordination sphere only: The number of molecules dN within a small distance dr at distance r from an atom is given by dN = 4π r2 g(r) dr, where g(r) is the RDF. dN has been determined by simply counting nearest neighbor atoms and accounting for the amount of the used configurations. For each O-O (O-H) distance a Gaussian profile has been calculated (area equal to the probability of finding an atom at the corresponding distance) and the sum of the Gaussians has been calculated (and scaled with 1/4π r2) in order to generate smooth g(r) curves. It has been checked that XA spectra do not significantly change for different O-O (O-H) distances within the width of the Gaussians. All RDFs are normalized to the number of nearest neighbors, which is equal to four in all configurations used here (∫ 4π r2 g(r) dr = 4). Therefore our approach gives reliable properly normalized intensities that can be compared to experiment directly. The validity of this approach for nearest neighbor distances is demonstrated for the SPC simulation in Fig. 5A and B, model c, by the close similarity of the model RDFs with the ones derived directly from the simulation. g. Influence of dynamics and vibrations on the theoretical analysis The excitation of an O 1s electron takes place on a time scale corresponding to the time that it takes the photon to travel the diameter of the O1s inner shell. With the proper parameters it can be estimated that the excitation takes place in about 10-17 to 10-18 s. The vibrational motions of the nuclei are much slower and typically occur in approximately 10-13 s. This allows for a separation of the electronic and nuclear degrees of freedom in the spectrum calculations. We can thereby use the Franck-Condon principle which states that the internuclear distance can be assumed to be constant during the fast electronic excitation process. During each absorption event the atoms can thus be assumed to be structurally frozen. This allows for the decomposition of the spectrum in terms of different configurations and spectra can be calculated for static structures. One simply needs to assure that enough inter- and intramolecular configurations have been taken into account to have a complete sampling of possible structures in the liquid present at all times.

We show representative spectra for different O-O distances r and O-H…O angles θ (Fig. 3 in the manuscript) and in this sense intermolecular vibrations are accounted for in our study. The spectra do show changes with these parameters but by classifying the configurations large intermolecular motions are accounted for. The spectra do change for atomic motions within each class but these changes are much smaller than the changes when changing classes. In addition, e.g., summing the spectra for different O-O distances yields a spectrum similar to the spectrum for a molecule with coordination that is well-centered within its class. Librational motions are included through the angular distortions

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discussed in the text. Intermolecular vibrations are thus accounted for indirectly for both the hindered translations and librational motion.

Similar arguments hold for intramolecular vibrations (for the symmetric and asymmetric stretch and the bend vibrations) as shown in the following with Fig. 11.

Figure 11 shows that the spectra do change for different O-H distances and H-O-H angles but the representative spectrum corresponding to the centered position in each case is very close to the spectrum composed of all different contributions superposing the configurations due to the oscillatory amplitudes from the O-H stretch and bend vibrations (Fig. 11b and f for a DD configuration and Fig. 11d and h for an SD configuration). The same holds for the case when both O-H distances are changed asymmetrically (asymmetric stretch vibration). This shows that intramolecular oscillations do not need to be accounted for explicitly.

Note that changing the intramolecular geometry by ~3% (from the values used in Figs. 2-5 in the manuscript for the H-O-H angle from 109.5° to 104.5°, e.g., and the O-H distances from 0.95 Å to 0.975 Å, e.g.) do not change the spectra significantly. In particular the estimation of the amounts of DD, SD and ND species from calculated spectra is not affected by this. In addition, it is important to note that the length of the O-H bond can depend on whether the H atom is H-bonded or not. Theoretical studies show that the O-H bond is elongated by up to 2% due to H-bond formation in liquid water (26). Test calculations show that the spectrum for an SD configuration with O-H bond lengths of 0.995 Å (0.975 Å +2%) and 0.955 Å (0.975 Å -2%) for the H bonded and non-H bonded O-H, respectively, is very similar to both the spectra where both O-H bonds have a length of 0.95 Å or 0.975 Å. Thus this doesn’t need to be accounted for explicitly. h. Changing the cut-off for H-bonding in the analysis of MD simulations Table 2 shows how the populations of the DD, SD and ND-configurations change for the SPC simulation at 25°C as a function of rmax, where r(θ) = -0.00044 θ2 + rmax (θ in degree, rmax in Å) is the cut-off for H-bonding (outer boundary of zone B, Fig. 3B in the manuscript). A copy of the program used for the analysis can be obtained by writing to L. Ojamäe (lars@ifm.liu.se).

Even reducing rmax to an unreasonable value of 3.0 Å does not yield satisfactory agreement with experiment (the even more extreme case of rmax=2.8, i.e. normal H-bond distance, is also included for clarity). An rmax of 3.0 Å is not reasonable for two reasons. Firstly, an elongation of the OO-distance on one H-side to 3.0 Å would not yield a pre-edge peak as observed experimentally (see, e.g., Fig. 3b in the manuscript, which shows a calculated spectrum for an OO-distance of 3.1 Å at θ=0°). Secondly, the criterion for H-bonding as used in the manuscript with rmax=3.3 Å is similar to conventional criteria typically applied to MD simulations. It therefore yields similar results for the number of H-bonds per molecule in our present analysis of the simulations (see manuscript).

Modifications of the cut-off in the definition of H-bonding presented in the manuscript cannot generate agreement between the presented MD simulations and experiment. We conclude that, although many aspects of liquid water are reproduced by the present MD simulations, further development is needed in order to bring these into

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agreement with experiment with respect to the new information on the local structure of the liquid that is the major result of the present work.

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Figures and Legends

Figure 1: Optimized (3x2) overlayer structure of glycine on Cu(110) (14).

Figure 2: Comparison of computed (upper curves, blue) and experimental (lower curves, red) X, Y, Z-resolved XA N 1s spectra of deprotonated glycine on Cu(110) for three different cluster models. From left to right: a single glycine molecule, two glycines interacting through a N-H.....O H-bond and three molecules with a fully coordinated carboxylic group (14).

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Figure 3: Comparison of computed (upper curves, blue) and experimental (lower curves, red) X, Y, Z-resolved XA O 1s spectra of deprotonated glycine on Cu(110) for three different cluster models. From left to right: a single glycine molecule, two glycines interacting through a N-H..... O H-bond and three molecules with a fully coordinated carboxylic group. Arrows indicate features discussed in the text (14).

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Figure 5: Full circles with error bars: Intensity ratios of the pre and main-edge peaks for the spectra in Fig. 4 as a measure of the deviation from the dipole approximation (the spectrum for q=3.2 Å-1 is not shown in Fig. 4). Solid line: Quadratic fit to the data points (a quadratic function is expected as follows from the scattering matrix element). Dashed line: Limit of 0.4 as consistent with the spectrum from XAS measured with fluorescence yield and corrected for saturation effects (see Fig. 6 below).

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Figure 6: Comparison of XRS (4.2 Å-1, open circles) and convoluted XAS (line) spectra. The XAS spectrum has been convoluted with a Gaussian with FWHM of 0.9 eV to account for the different energy resolutions.

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545540535Energy (eV)

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Figure 7: XA spectra of ice Ih (a) bulk (SEY), (b) surface and subsurface (AEY), (c) surface (grazing AEY), (d) NH3 terminated surface and subsurface (AEY) and (e) NH3 terminated surface (grazing AEY). For calculated contributions of the different bilayers see the Table above.

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convoluted surface (1 eV) and convoluted bulk (1 eV) summed

ice surface (0.8 SD) liquid

Figure 8: Comparison of (a) liquid water at room temperature (from manuscript Fig. 1d) and (b) convoluted experimental ice surface spectrum (from manuscript Fig. 1b and convoluted with a Gaussian of 1 eV FWHM) and (c-g) linear combinations of convoluted ice surface (b) and convoluted ice bulk spectra (the bulk spectrum as taken from manuscript Fig. 1a and convoluted with a 1 eV Gaussian is not shown). The ice surface and bulk spectra have been convoluted (broadened) to account for the larger vibrational motion of the molecules and the enhanced structural disorder in the liquid. Using other values for the FWHM in the convolution does not change the spectra significantly.

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Figure 9: The 11-molecules cluster used to calculate the spectra in Figs. 3 and 5 in the manuscript (here shown with bulk ice-like structure for manuscript Fig. 3a). O (H) atoms are depicted in red (white) and red dashed lines illustrate the hydrogen bonds.

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Figure 10: Solid line, left axis: H-bond interaction energy for one of the donor H-bonds of the central molecules in the 11-molecules cluster (see Fig. 9) as a function of the radial distortion (nearest neighbor O-O distances 2.5-10 Å) and dashed line, right axis: integrated area of the pre-edge peak in the corresponding calculated XA spectra. The solid line represents the BSSE (basis set superposition error) corrected total energy (relative to the energy at an O-O separation of 10 Å) as obtained from the Gaussian-03 program with the Becke-88 and Perdew-86 density functionals and a 6-311+G(d,p) basis set. The dashed line is the integrated pre-edge intensity in the calculated XA spectrum.

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bend

bend

Figure 11: Spectra are calculated as exemplary cases for the tetrahedral configuration in the bottom row (manuscript Fig. 3a) and the SD configuration in the top row (manuscript Fig. 3c) for different intramolecular O-H distances for the two O-H bonds in the left column (distances have been changed symmetrically on the two bonds thus simulating the symmetric stretch vibration) and different intramolecular H-O-H angles in the right column. The solid line in each panel is the spectrum shown in the manuscript and serves as a reference. The different panels show a (c): tetrahedral (SD) configuration with dotted: 0.975 Å, solid 0.95 Å, dashed 0.925 Å O-H distances. b (d): tetrahedral (SD) configuration with solid: 0.95 Å O-H distance and circles: sum of 7 spectra with different O-H distances where the different contributions have been weighted according to a Gaussian distribution of distances with 0.95 Å as the centre distance and a FWHM of 0.1 Å. e (g): tetrahedral (SD) configuration with dash-dotted: 99.5°, dotted: 104.5°, solid 109.5°, dashed 114.5°, short-dashed 119.5 ° H-O-H angles. f (h): tetrahedral (SD) configuration with solid: 109.5° H-O-H angle and circles: sum of 7 spectra with different H-O-H angles where the different contributions have been weighted according to a Gaussian distribution of angles with 109.5° as the centre angle and a FWHM of 20°.

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Tables and Legends Table 1: Contributions of the 1st, 2nd and 3rd-10th bilayers to the grazing AEY, AEY and SEY ice spectra (in percent).

Table 2: Change of the populations of the DD, SD and ND-configurations for the SPC simulation at 25°C as a function of rmax, where r(θ) = -0.00044 θ2 + rmax (θ in degree, rmax in Å) is the cut-off for H-bonding (outer boundary of zone B, Fig. 3B in the manuscript). References 1. J. Stöhr, NEXAFS Spectroscopy (Springer-Verlag, Berlin, 1992). 2. S. Myneni et al., J. Phys: Condens. Matter 14, L213 (2002). 3. M. Cavalleri, H. Ogasawara, L. G. M. Pettersson, A. Nilsson, Chem. Phys. Lett. 364, 363 (2002). 4. U. Bergmann et al., Phys. Rev. B 66, 092107 (2002). 5. D. Nordlund et al., unpublished results.

Probing depth

3rd-10th BL 2nd BL 1st BL

Grazing AEY ~ 1.5 Å 0 7 93

AEY ~ 20 Å 63 17 20

SEY ~ 50 Å 74 13 14

SPC 25°C EXP+FIT rmax (Å) 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.3

DD 9 24 39 52 63 70 76 81 15 2515+−

SD 42 50 47 40 33 27 22 18 80±20 ND 48 26 14 8 4 3 2 1 5±5

Total 99 100 100 100 100 100 100 100 100 Nb. Of

H-bonds 1.2 2.0 2.5 2.9 3.2 3.3 3.5 3.6 2.2±0.5

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