Microscopic structure of water at elevated pressuresand temperaturesChristoph J. Sahlea,b,1, Christian Sternemanna, Christian Schmidtc, Susi Lehtolab, Sandro Jahnc, Laura Simonellid,Simo Huotarib, Mikko Hakalab, Tuomas Pylkkänenb, Alexander Nyrowa, Kolja Mendea, Metin Tolana,Keijo Hämäläinenb, and Max Wilkec

aFakultät Physik/Dortmund Electron Accelerator, Technische Universität Dortmund, Dortmund, Germany; bDepartment of Physics, University of Helsinki,Fi-00014, Helsinki, Finland; cDeutsches GeoForschungsZentrum, Section 3.3, Telegrafenberg, 14473 Potsdam, Germany; and dEuropean Synchrotron RadiationFacility, F-38043 Grenoble Cedex 9, France

Edited by Alan K. Soper, Sciences and Technology Facilities Council Rutherford Appleton Laboratory, Didcot, United Kingdom, and accepted by the EditorialBoard February 12, 2013 (received for review November 27, 2012)

We report on the microscopic structure of water at sub- and super-critical conditions studied using X-ray Raman spectroscopy, ab initiomolecular dynamics simulations, and density functional theory.Systematic changes in the X-ray Raman spectra with increasingpressure and temperature are observed. Throughout the studiedthermodynamic range, the experimental spectra can be interpretedwith a structural model obtained from the molecular dynamicssimulations. A spatial statistical analysis using Ripley’s K-functionshows that this model is homogeneous on the nanometer lengthscale. According to the simulations, distortions of the hydrogen-bond network increase dramatically when temperature and pres-sure increase to the supercritical regime. In particular, the averagenumber of hydrogen bonds permolecule decreases to≈0.6 at 600 °Cand p = 134 MPa.

supercritical water | water structure | X-ray scattering | X-ray scatteringspectroscopy

Water is one of the most fascinating and controversially dis-cussed substances in condensedmatter research (1). Several

experimental investigations have been carried out to decipher thelocal structure of water at various thermodynamic conditions.However, there is still no consensus on how to describe the mi-croscopic structure of this elusive liquid (2–4). The most prominentmethods of study are the determination of site-site correlationfunctions using neutron or X-ray diffraction (5–8), the analysis ofdensity fluctuations by small angle X-ray and neutron scattering (9–11), and the investigation of the oxygen’s local environment byspectroscopic methods (2, 3, 10, 12, 13) providing controversialinterpretations of the local atomic structure of water. This hasresulted in an intense discussion of whether the microscopicstructure of ambient water can be described as a liquid with ho-mogeneous density (e.g., refs. 4, 11, 14) or as an inhomogeneousmixture of two types of structural states with a hydrogen-bond(H-bond) distorted structure surrounding less dense, tetrahedrally-like coordinated patches (e.g., refs. 7, 10, 12). In this article, wepresent significant information obtained by an in situ study ofchanges of the water structure at high pressure and temperatureconditions up to the supercritical state.Due to experimental difficulties, water under supercritical con-

ditions has only rarely been the subject of detailed in situ spec-troscopic investigations to date (12, 15). The pressure (p) and tem-perature (T) regime of supercritical water, however, is especiallyinteresting for geoscientists because water plays a key role in heatand mass transfer as well as element fractionation processes in theEarth’s lithosphere, such as volcanism and ore deposit formation(16, 17). Geochemical processes and reactions, such as the forma-tion of petroleum (18) and even contributions to the origin of life(19), have been linked to the high-temperature and high-pressureproperties of water. The polar character of the H2O molecule andthe tendency to dissociate makes it a more powerful solvent thanother volatiles. This is also taken advantage of in chemical pro-

cessing, where supercritical water is used as a reaction medium forchemical andmaterial synthesis, waste destruction, plastics recycling,and biomass processing (20). These solvent properties of H2O de-pend not only on density and dissociation but on structural param-eters, which are poorly understood, particularly at the supercriticalconditions prevalent in the Earth’s upper mantle and crust.A large degree of disorder with an essentially broken H-bond

network in supercritical water was reported by Postorino et al. (9)using neutron scattering data. Although this conclusion was soft-ened later, newly derived site-site pair correlation functions(PCRs) from the old data still suggest a highly distorted arrange-ment of water molecules with a largely reduced degree ofH-bonding compared with water at ambient conditions (5, 21). Op-tical Raman spectra of water indicate that a significant fraction ofnetwork water is still present even at high temperatures, pressures,and solute concentrations (22–24). Likewise, NMR studies ofwater up to 600 °C and 400 bar suggest a significant amount ofH-bonding up to the highest temperatures and pressures studied(25). Sit et al. (15) used Compton scattering to measure thebonding and coordination in water up to supercritical conditionsand found a large increase in the number of water monomers ontransition to the supercritical regime, but they also reporta remaining number of higher coordinations, such as dimers andtrimers. Based on X-ray Raman spectroscopy (XRS) measure-ments, Wernet et al. (12) proposed that supercritical water con-sists of small H-bonded patches surrounded by less dense non–H-bonded regions in line with local density inhomogeneitiesrevealed by small angle neutron scattering (26) but reported arelatively small proportion of non–H-bonded H2O species.However, Clark et al. (27) and Sedlmeier et al. (28) have shownthat the interpretation of small angle scattering data is notstraightforward. They found no strong spatial correlation be-tween structure and density fluctuations even in ambient waterand affirmed these claims by reproducing all features of measuredsmall angle scattering spectra using the tip4p/2005 and extendedsimple point charge models, respectively. On the other hand,analyses of tip4p/2005 water models using tetrahedral orderparameters imply tendencies toward clustering of low- and high-tetrahedrality regions (29, 30). Heterogeneity has also been

Author contributions: C.J.S., C. Sternemann, C. Schmidt, L.S., M.T., K.H., and M.W. de-signed research; C.J.S., C. Sternemann, C. Schmidt, L.S., A.N., K.M., and M.W. performedresearch; C.J.S., J.L., and S.J. contributed new reagents/analytic tools; C.J.S., C. Sternemann,J.L., S.J., S.H., M.H., T.P., and M.W. analyzed data; and C.J.S., C. Sternemann, J.L., S.J., S.H.,M.H., T.P., M.T., K.H., and M.W. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. A.K.S. is a guest editor invited by the EditorialBoard.

See Commentary on page 6250.1To whom correspondence should be addressed. E-mail: christoph.sahle@helsinki.fi.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1220301110/-/DCSupplemental.

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reported, for example, in terms of nucleation of small molecularclusters (31) or tetrahedrally coordinated patches connected byless ordered nets, building up a gel-like network that persists inpressurized high-temperature water up to T = 473 K and ρ = 0.88g/cm3 (32). However, the occurrence of these structural speciesmight be transient (4). More distorted H-bonded networks werefound when using new van der Waals functionals (33).In the current work, we use XRS as a probe of the local water

structure over a large temperature and pressure range. The ex-perimental results are compared with spectra calculated from abinitio molecular dynamics (MD) simulations. These spectra givea good description of the changes of the experimental spectra withtemperature and pressure in the sub- and supercritical regimes. Onthis resemblance of the experimental data and the simulationresults, more detailed information on the microscopic local struc-ture of water is extracted from the underlying MD simulations.In the ab initio MD structures, the water molecules at ambient

conditions have, on average, a near-tetrahedral coordinationwith a considerable number of water molecules having fivenearest oxygen neighbors. With increasing temperature andpressure along the liquid-vapor equilibrium, the extended H-bonded network is strongly distorted and broken. However, H-bonded species are found even for the highest temperatures andpressures investigated. From a detailed analysis of the MDmodel, we find that the spectra are most sensitive to the directlocal environment (i.e., the number of formed H-bonds andnearest oxygen neighbors) but even reflect the influence of theintermediate range order. Based on a spatial statistical analysis,we find the MD simulations to predict structures that are ho-mogeneous on the length scale of the simulation boxes. Theexperimental spectra are in good agreement with those derivedfrom the simulations using density-functional theory (DFT).

Results and DiscussionXRS spectra of the oxygen K-edge were measured along thevapor pressure curve and in the supercritical regime for con-ditions as indicated in the H2O phase diagram in Fig. 1. Highpressures and high temperatures were reached using a hydro-thermal diamond anvil cell (HDAC; Fig. 1, Inset). Temperaturecalibration was achieved using type-K thermocouples, and thepressure/density was obtained by measuring the liquid-vaporhomogenization temperature using visual observation of a vaporbubble in the sample volume as shown in Fig. 1 (Lower) (detailsare provided in Materials and Methods).The measured XRS oxygen K-edge spectra are shown in Fig. 2.

Spectra taken along the vapor pressure curve are presented in Fig.2A. The spectrum of water at ambient conditions agrees well withother oxygen K-edge spectra reported earlier (e.g., ref. 34),showing a pronounced pre-edge shoulder at 535 eV of energy loss(feature A in Fig. 2), a dominating main-edge at 538 eV (feature Bin Fig. 2), and a post-edge (feature C in Fig. 2) with significantspectral weight up to energy losses of 546 eV. With increasingpressure and temperature, spectral weight is transferred from thepost-edge region into the pre- and main-edge regimes. Moreover,a shift of the energy loss position of both the pre-edge and main-edge toward the position of the O-H anti-bonding 4a1 and 2b1orbitals of a free water molecule at 534 and 536 eV, respectively,can be observed. The interpretation of K-edge X-ray absorption(XAS) or XRS spectra of water is neither unambiguous norstraightforward (3, 35–37). As temperature and pressure increasealong the vapor pressure curve, a gradual transition from a water-like spectrum to a more gas-phase–like spectrum can be observed.However, a clear difference between the gas-phase spectrum andthe experimental data at supercritical conditions remains.Fig. 2C shows the influence of pressure, and thus density, on the

K-edge spectrum of water at T = 400 °C. A clear drop of intensityin the pre-edge regime is visible for the spectrum measured at 371MPa (0.86 g/cm3) compared with the spectrum measured at 48

MPa (0.54 g/cm3). The spectrum at ambient temperature andpressure is also shown as a reference. The structural origin ofspectral changes similar to the ones observed here has been dis-cussed extensively in the literature. For instance, the role of dis-torted or broken H-bonds and the influence of the non–H-bondedmolecules in liquid water and ice polymorphs were recently ad-dressed (36). In those cases, broken or highly distorted H-bondswere shown to increase spectral weight in the pre-edge and non–H-bonded molecules approaching the first coordination shell wereshown to increase intensity in the main-edge region. Pylkkänenet al. (38) also pointed out that the non–H-bonded neighboringmolecular fraction has a significant influence on the shape of thespectra in high-pressure ice phases. Furthermore, the H-bondnetwork order has been shown to influence the spectra in liquidwater and ice phases (39, 40). These observations clarify the diffi-culty of assigning changes of certain features in the oxygen K-edgespectra to particular structural changes related to, for example,H-bond breaking, density changes, or single structural motifs.To gain deeper insight into the interpretation of the experi-

mental spectra, we performed DFT calculations from ab initioMDsimulation snapshots. We calculated spectra from geometries di-rectly extracted from MD snapshots with no restraints on themolecular configurations, such as including or excluding structuressubject to specific H-bond statistics (details are provided in Mate-rials and Methods). Calculated spectra for temperature and pres-sure values similar to the experimental parameters are shown inFig. 2 B and D. All calculated spectra were shifted on the energyloss scale so that the main edge feature B of the experimental andcalculated spectra coincide. Although the pre- and post-edge fea-tures of the calculations are underestimated for the highest densityspectra (0.99 and 0.86 g/cm3), the overall agreement between theexperimental data and the calculated spectra is good. This is validespecially if we consider the systematic evolution of both experi-mental and theoretical spectra as a function of temperature and

Fig. 1. Phase diagram of water shows the numerous ice phases at highpressures and low temperatures and the region of interest for this study (i.e.,high temperatures and high pressures). Oxygen XRS K-edge spectra wererecorded at the pressure and temperature values indicated by colored stars.(Inset) Schematic drawing of the HDAC. (Lower) Photographs of the watersample in the HDAC at different temperatures and pressures are shown todemonstrate the visual control of the sample, exemplified by a measure-ment of the homogenization temperature of a vapor bubble and liquid,which is used to determine the density and pressure.

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pressure. For ambient water, the deviations between experimentand theory are similar to what has been reported earlier (42).For a quantitative comparison of the experimental and cal-

culated spectra, the integral over the post-edge and the energyloss position of the pre-edge were determined and are presentedin Fig. 2 E and F, respectively. Compared with the values derivedfrom the experimental data, the integrated post-edge intensitiesof the simulated spectra show the same dependence on the waterdensity with only a slight constant offset, which is due to a sys-tematic underestimation of the post-edge intensity by the theory.This is caused by the theoretical approach used to calculatethe spectra. As suggested by Chen et al. (36), the energy-in-dependent exchange potential in DFT calculations is toostrong close to the ionization threshold, and thus results in a post-edge feature that is too narrow. Almost quantitative agreementbetween experimental XAS and XRS spectra of ambient waterand ice was recently achieved by the use of path integral ab initio

MD simulations in conjunction with a Bethe–Salpeter equation(BSE)-based approach for the spectrum calculation (43). Mostnotably, the BSE benefits from accounting for the electron-holeinteraction, which ensures a better representation of the pre-edge feature in the calculated spectra (36, 43). The computa-tional cost of such methods, however, forbids this approach in thecurrent case. Using a real-space multiple scattering approach tocalculate the oxygen K-edge in different ice phases results ina post-edge feature that closely resembles the experimentalfindings but fails to reproduce the pre- and near-edge (44). In ourresults, good quantitative agreement is achieved when comparingthe energy loss position of the pre-edge for all p, T conditions(Fig. 2F). It should be noted that both our theoretical and ex-perimental spectra at T = 400 °C and p = 48 MPa, correspondingto ρ = 0.54 g/cm3, differ from those reported by Wernet et al. (12)for similar conditions. However, the overall systematic agreementbetween the theoretical and experimental spectra, consideringboth the overall spectral features and their dependence onthermodynamic conditions, gives confidence to the quality ofour data. The theoretical results describe both the overall ex-perimental spectra and their systematic spectral changes withvarying thermodynamic conditions to a very high degree, especiallyin the unprecedented supercritical regime. This gives con-fidence that the underlying structural model can now be used toextract detailed information on the local atomic structure of water.The O-H, H-H, and O-O PCFs extracted from the MD trajec-

tories are shown in Fig. 3 A–C, respectively. For each set of PCFs,the room temperature (RT) PCF is compared directly with PCFstaken from Soper (45) and shows good agreement with these. ThePCFs extracted from simulations at higher temperature andpressure also follow the trends reported by Soper (5) and Ikedaet al. (46), but they cannot be compared directly with the presentedresults because the exact temperature and pressure conditionsdiffer. With increasing p and T, the second peak in the O-O PCFloses intensity and disappears at supercritical conditions. The firstintermolecular peaks in the O-H and H-H correlation functionalso weaken with increasing p and T. Similar behavior was recentlyobserved in MD simulations of water along different isochoresusing theMatsuoka-Clementi-Yoshimine with nonadditives model(47). These results were interpreted as a transition of a tetrahedralstructure at ambient temperature to a more disordered medium-density fluid at elevated temperatures. Nevertheless, simple H-bonding between two water molecules was found to persist evenbeyond the critical point.As ameasure of the local structure in water, the average number

of H-bonds per molecule (nHB) and nearest neighboring oxygenatoms (nOO) were calculated from the MD snapshots. Thus, nHBwas determined using geometric criteria of Marti et al. (48), andnOO is simply the number of oxygens within a sphere with a radiusof 3.6 Å from the central oxygen atom. The results are depicted inFig. 3 D and E. Both nHB and nOO increase with density and differonly slightly for equal density but different temperature [i.e., 0.45g/cm3 (370 °C and 600 °C) and 0.86 g/cm3 (200 °C and 400 °C)]. Fora density of 0.86 g/cm3, nHB is found to be above the percolationthreshold of npHB ≈ 1:6 (31) for both studied temperatures, whichsuggests a strongly distorted H-bonded, tetrahedral, percolatingnetwork. This is reflected in the experimental spectra by similarpre- and main-edge structures in both measurements at this den-sity. An average number of nearest neighbors nOO ≈ 5, as well asthe increase in nOO with increasing density, is in good accordancewith findings from X-ray diffraction (49, 50) and other MD sim-ulation data (36, 47). The average number of H-bonds as a func-tion of density is also in line with previously reported experimentaland theoretical values (48).A more detailed analysis of the local arrangements around the

scattering oxygen atoms is achieved by a classification of the MDgeometries used for the XRS spectra calculations for sub- andsupercritical conditions with respect to nHB and nOO. The resulting

Fig. 2. (A) Spectra of the oxygen K-edge of water at different temperaturesand pressures along the liquid-gas coexistence curve. The pre-, main-, andpost-edge are indicated by A, B, and C, respectively. (B) Calculated spectrafor similar temperatures and densities as in A, as well as a water monomerspectrum. The densities are indicated in the figure, and the color code cor-responds to the color of the respective spectrum. (C) Effect of pressure onthe spectra measured at T = 400 °C in comparison to the ambient-waterspectrum. (D) Calculated spectra for temperatures and densities corre-sponding to the experiments presented in C. (E) Comparison of the in-tegrated post-edge intensities between 537 and 544 eV of energy lossobtained from experiment (exp.) and theory (theo.). Here, “high” refers tomeasurements at a similar density but higher temperature than indicated inA. (F) Energy loss position of the pre-edges for the different densities de-termined from theory and experiment. arb., arbitrary.

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histograms for each p and T are shown in Fig. 4. For ambientwater, the distributions of nHB and nOO are clearly peaked at fourH-bonds per water molecule and five nearest oxygen neighbors(denoted H4O5). At all other state points, both distributions aremuch broader, indicating more distorted local arrangements. Al-though the average number of H-bonded molecules decreasesquickly with increasing temperature, H-bonded species can befound even at the highest temperature probed, where simple H-bonding between two water molecules (one H-bond) dominates.The fact that at elevated temperatures, the average number ofnearest neighbors exceeds the average number of H-bonds permolecule can be interpreted as a sign of a more gas-like behaviorat these temperatures and densities in line with the X-ray andneutron data and MD simulations.A spatial statistical analysis using Ripley’s K-function of the

different structural motifs supports the assumption of a morehomogeneous structure because no heterogeneities beyond thefirst coordination shell (r ) 5 Å) could be identified. Using thelocal structure index (LSI) (7, 51) to identify high (I > 0.03) andlow (I < 0.03) structured local coordinations results in an amountof high-LSI molecules of ∼50% at ambient conditions and a rapiddecrease of this number with increasing p, T. However, a spatialstatistical analysis of these subpopulations also shows no spatialcorrelations beyond r ) 5 Å even for the high-LSI molecules (SIText), which indicates that molecules with different local envi-ronments are present at all simulated temperatures and pressures

but are not spatially correlated beyond their characteristic dis-tances (i.e., the second coordination shell). This is in line with thefindings of English et al. (4).The calculated XRS spectra resulting from averaging over

clusters resembling the most frequently occurring structural con-figuration (with respect to nHB and nOO) at each p, T condition areshown in the third column of Fig. 4. The positions of the pre-edgeand main-edge, the intensity of the pre-edge feature, and theoverall shape of the spectrum change systematically for differentdistributions of H-bonds and number of nearest oxygen neighbors(Fig. 4, columns 1 and 2). It is noticeable that smaller numbers ofH-bonds and nearest oxygen neighbors result in distinct pre- andmain-edge features (H1O1 and H1O3), whereas distributions withhigher nHB and nOO result in smaller pre-edges and more spectralweight in the post-edge region (H2O5 and H4O5). In this respect,the spectral changes observed for constant temperature and dif-ferent density (Fig. 2C) are caused by a different microscopic to-pology (i.e., a change from mainly one H-bond and three nearestoxygen neighbors to predominantly two H-bonds and five oxygensin the first coordination shell).The sensitivity of the XRS spectra on the local structure is

illustrated in Fig. 4 (Upper) by a comparison of similar local

Fig. 3. (Upper, A–C) O-H, H-H, and O-O PCFs, respectively, as derived fromthe MD trajectories and in comparison to the two experimental results froma study by Soper (45). (Lower, D and E) Number of H-bonds per molecule andnumber of nearest neighbors as a function of density extracted from the MDsimulation snapshots. (Lower) Term “high T” refers to values determined forequal density but higher temperature conditions, as indicated in the otherpart of the figure (Upper). arb., arbitrary.

Fig. 4. (Lower Left) Distribution of the number of H-bonds of the centralwater molecule in the clusters extracted from the different MD snapshots forall pressure and temperature conditions estimated by geometric criteria(details are provided in main text). (Lower Center) Same except for thenumber of oxygen neighbors within 3.6 Å from the central oxygen atom.(Lower Right) Averages over XRS spectra calculated for snapshots resemblingthe most frequently occurring subset of configurations from the histograms(Lower Left) as well as representative stick and ball plots of these motifs.arb., arbitrary. (Upper) Comparison of calculated XRS spectra of similar localmotifs for different p, T conditions (details are provided in main text).

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configurations for different thermodynamic conditions. In Fig. 4(Upper Left), spectra from local environments having four H-bondsand five oxygen neighbors at ambient conditions (1.00 g/cm3),200 °C (0.86 g/cm3), and 400 °C (0.86 g/cm3) are compared andshow significant spectral weight in the post-edge region and onlyminor intensity in the pre-edge region. In Fig. 4 (Upper Right),spectra from local environments having one H-bond and threenearest oxygen neighbors at 370 °C (0.45 g/cm3), 400 °C (0.54 g/cm3),and 600 °C (0.45 g/cm3) are shown. Here, independent of the statepoint, pronounced pre- and main-edges are visible. Obviously,XRS spectra related to distinct structural motifs conserve theirspectral shape for similar densities at different temperatures. Theremaining differences systematically depend on temperature,which stresses the effect of increasing disorder even in the firstcoordination shell with increasing temperature, along with theinfluence of non–H-bonded molecules in the immediate and in-termediate local environments.

ConclusionThe microscopic structure of water under high pressure and hightemperature conditions, as prevailing, for example, in the deepEarth, was investigated using XRS as well as ab initio MD sim-ulations. The XRS spectra show a continuous evolution froma water-like spectrum at RT and atmospheric pressure to a moregas-like spectrum at the highest temperatures and pressures in-vestigated. Comparison with spectra calculated from ab initioMD snapshots demonstrates that the spectral features and sys-tematic changes in the spectral shape over the entire pressureand temperature regime probed can be understood in terms ofa homogeneous microscopic structure.Based on the close resemblance of the calculated spectra and

the measured data, as well as the accordance of PCFs extractedfrom the MD runs and published data, more detailed informationon the local structural environment of the scattering oxygen atoms,such as the number of H-bonds and nearest oxygen neighbors, wasextracted from our MD model. At ambient conditions, specieswith four H-bonds and five oxygen neighbors within a distance of3.6 Å dominate. With temperature and pressure increasing alongthe vapor pressure curve, the number of H-bonds per moleculedecreases to 0.6 at T = 600 °C and p = 134 MPa. Typical localstructural environments, with specific spectral fingerprints, couldbe identified to describe water at different pressure/temperatureconditions. However, no clustering of these motifs could be foundby a spatial statistical analysis of theMD simulation boxes. Hence,the present study implies a homogeneous spatial distribution ofthese motifs. By comparing simulated spectra from specific localenvironments at different temperatures and pressures, the sensi-tivity to and systematic dependence of the shape of the oxygenK-edge spectrum on the direct local environment of the oxygenatoms in water over a wide range of temperatures and pressures isstressed. The presented experimental spectra provide a bench-mark for further theoretical investigations using other means tosimulate the atomic structure and other approaches to calculateXRS spectra from the models, such as BSE-based methods.

Materials and MethodsA resistively heated HDAC (52, 53) with a rhenium gasket was used to pro-duce high-pressure, high-temperature conditions. The X-rays penetrated thesample, Milli-Q (Millipore) water, contained in a recess hole with a diameterof 500 μm and a depth of 120 μm in the culet of the lower diamond rightbelow the rhenium gasket. Thus, the pathway of the X-ray through the di-amond was optimized, together with an increase of probed sample volume.The temperature was measured by a type-K thermocouple on each of thetwo diamonds (Fig. 2, Inset). The HDAC was loaded before measuring ateach state point, and pressures were calculated from the liquid-vapor ho-mogenization temperature, which was determined by visual observation ofa vapor bubble contained in the sample volume, before and after each ex-periment. The equation of state according to the method of Wagner andPruss (54) was used. XRS (55) was used to measure the oxygen K-edge

spectra in situ at high-pressure and high-temperature conditions. The XRSexperiment was conducted at the inelastic X-ray scattering beamline ID16 ofthe European Synchrotron Radiation Facility in Grenoble, France. A detaileddescription of the instrument can be found elsewhere (56). Using the 1-mRowland geometry spectrometer, XRS spectra were collected by scanningthe incident energy at a fixed analyzer energy of 9.69 keV, such that theenergy loss was scanned across the oxygen K-edge at 535 eV. Scatteringfrom nine bent (R = 1 m) Si(660) crystals was focused onto a photon-counting pixel detector. Using the imaging properties of the analyzer crys-tals in combination with the 2D detector (57), scattering from the samplecould conveniently be discriminated against parasitic scattering from theHDAC. Using a Si(220) channel-cut monochromator in succession to a Si(111)high-heat-load double-crystal monochromator, an overall energy resolutionof 0.7 eV was obtained. The incoming X-ray beam was focused to ∼50 × 130μm2 (vertical × horizontal) on the sample. For the RT spectrum, count ratesfor one analyzer were ca. 40 counts per second at the maximum of theoxygen K-edge on top of a background of ∼90 counts per second. At thelowest density of 0.45 g/cm3 and 600 °C, we could measure 20 counts persecond at the maximum of the oxygen K-edge on top of a background of120 counts per second per analyzer crystal. For the final spectra, the signalsfrom all nine analyzer crystals and multiple individual scans were checkedfor consistency and summed up taking the statistical weight into account,such that an average momentum transfer of q = (1.6 ± 0.2) atomic units (a.u.)was achieved. A linear background was subtracted from the summed data.Typical counting times were 4–5 h per state point. Final XRS spectra werenormalized to the integral intensity between 531 eV and 555 eV. Details ofthe data processing and analysis can be found in a study by Sternemannet al. (58). Because we could observe the sample during the experimentthrough a microscope, we can exclude any sample damage due to the X-rayexposure. The structure of liquid and supercritical water was modeled by abinitio MD simulations using the Car–Parrinello method (59) as implementedin the CPMD code (60). The simulation cells contained 64 H2O molecules, andsimulations were performed at a constant volume and temperature (i.e., inthe NVT ensemble). Densities were adjusted to those of the experiments.Temperature was controlled by a Nosé–Hoover thermostat (61, 62). For theelectronic structure calculations, plane-wave basis sets, the Becke–Lee–Yang–Parr exchange correlation functional (63, 64), and Goedecker-type pseudo-potentials (65) were used. The Kohn–Sham orbitals were expanded up to anenergy of 70 Ry. For the Car–Parrinello dynamics, a fictitious electron mass of600 a.u. was used. The equations of motion were integrated with a time stepof 0.12 fs. The initial water structure was modified from a previous simulationstudy of supercritical aqueous solutions (66). After equilibration at each statepoint, production runs of 5–10 ps were performed. From the recorded tra-jectories, partial radial distribution functions were computed. CPMD has beenshown to give a representative measure of the local atomic environment insupercritical water despite the limited simulation box size (67). With the lim-ited MD simulation box size used, large-scale fluctuations are not taken intoaccount. However, in our experiment, there was no indication from the liquid-vapor homogenization behavior that any of our spectra were significantlyaffected by density fluctuations and no critical phenomenon, such as criticalopalescence, was observed. The XRS spectra of the individual MD snapshotswere calculated with ERKALE (68) in the transition-potential approximation(69) within DFT, using the revised Perdew–Burke–Ernzerhof functional (70–72).The IGLO-III basis set (73) was used for the excited oxygen site, whereasDunning’s augmented correlation consistent polarized valence double zetabasis set (74) was used for all other atoms. The localization of the core holewas enforced by freezing the other oxygen core orbitals in the system (68).Broyden mixing (75) of the Kohn–Sham–Fock matrix was used in solving theself consistent field (SCF) equations. To improve the description of the virtualorbitals, a large set of diffuse functions was added on the excited site after SCFconvergence was attained. For each p, T condition, spectra of 128 sphericalclusters of ∼90 atoms each were calculated and averaged over. For the XRSspectra of the most frequently occurring motifs, calculated spectra of 120clusters, extracted from the MD trajectories, were averaged over. The calcu-lations were converged with respect to the basis set.

ACKNOWLEDGMENTS. We thank the European Synchrotron Radiation Facilityfor providing synchrotron radiation. We acknowledge C. Henriquet (EuropeanSynchrotron Radiation Facility), M. Kreplin (Deutsches GeoForschungsZen-trum), and J. Schüssler (Deutsches GeoForschungsZentrum) for technical sup-port. This work was supported by the Deutsche Forschungsgemeinschaft(Grants TO 169/14-1 and JA1469/4-1), the Academy of Finland (Grants 1256211,1127462, and 1259526), the University of Helsinki Research Funds (Grants490076 and 490064), the Bundesministerium für Bildung und Forschung (Grant05K10PEC), and the Jenny and Antti Wihuri Foundation. We also acknowledgesupport by the Juelich Supercomputing Centre under Project ID HPO15.

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