Fast Interconversion of Hydrogen Bonding at the Hematite (001

Publication Date (Web): March 8, 2016. Copyright ... The lifetimes of all hydrogen bonds formed at the interface are shorter than those in pure liquid...
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Fast Interconversion of Hydrogen Bonding at the Hematite (001)− Liquid Water Interface Guido Falk von Rudorff,† Rasmus Jakobsen,† Kevin M. Rosso,*,‡ and Jochen Blumberger*,† †

Department of Physics and Astronomy, University College London, London WC1E 6BT, U.K. Pacific Northwest National Laboratory, Richland, Washington 99352, United States

‡

S Supporting Information *

ABSTRACT: The interface between transition-metal oxides and aqueous solutions plays an important role in biogeochemistry and photoelectrochemistry, but the atomistic structure is often elusive. Here we report on the surface geometry, solvation structure, and thermal fluctuations of the hydrogen bonding network at the hematite (001)−water interface as obtained from hybrid density functional theory-based molecular dynamics. We find that the protons terminating the surface form binary patterns by either pointing in-plane or out-of-plane. The patterns exist for about 1 ps and spontaneously interconvert in an ultrafast, solvent-driven process within 50 fs. This results in only about half of the terminating protons pointing toward the solvent and being acidic. The lifetimes of all hydrogen bonds formed at the interface are shorter than those in pure liquid water. The solvation structure reported herein forms the basis for a better fundamental understanding of electron transfer coupled to proton transfer reactions at this important interface. Here we report on the structure and thermal fluctuations of the hydrogen bond network at the neutral hematite (001)− liquid water interface obtained by first-principles molecular dynamics simulation using a validated hybrid density functional. We focused on the oxygen termination because it is generally considered the most prevalent. While our simulated structure is in fair agreement with the CTR data, we find that the protons terminating the surface are highly dynamic, frequently switching between out-of plane and in-plane positions. At any instant of time only about half of the surface protons are in out-ofplane positions from where deprotonation is possible, although this process is not observed in our simulation. As a consequence of the strong thermal fluctuations at the interface, the lifetimes of all hydrogen bonds formed within the surface layer and between hematite and water are significantly shorter than those in liquid water. The simulated system is shown in Figure 1. It consists of a 2 × 2 × 1 supercell of hematite with an additional oxygen layer added to terminate the (001) plane. This gives a symmetric slab of about 14 Å thickness. All hematite terminal oxygen atoms were protonated,29 which yields a charge neutral termination, corresponding to the experimental point of zero charge at about pH 8.4 (this number is still uncertain, see ref 27). The protonated slab was solvated with a water layer of about 33 Å thickness consisting of about 90 water molecules, and the hematite−water system is periodically replicated in all three directions. We found this system, containing about 2000 explicitly treated electrons, to be close to the minimum system

H

ematite is one of the most abundant metal oxide minerals on Earth1 and takes a prominent role in many different areas of research ranging from mineralogy,2 colloid chemistry,3 catalysis,4 and atmospheric science5 to energy harvesting6,7 and storage,8 bioenergetics,9−12 and even archeology.13 It is a cheap mineral, is stable under aqueous conditions, and has a favorable band gap for photo-oxidation catalysis.14 On this account, hematite has gained attention for use in photoelectrochemical applications, and much effort is currently being invested to improve its properties in this respect via nanostructuring6,15 and doping.16−21 Given the significance of hematite as metal oxide mineral and material in chemical research, it is surprising that many of its properties are still not well understood. One of them is the atomistic structure of its interface with liquid water,2,22−24 which is of fundamental importance for our understanding of crystal growth and dissolution phenomena,2 bacterial extracellular electron transfer, 9 − 1 1 and (photo)electrochemistry.6,15,25,26 Much of our current knowledge on the hematite−water interface comes from the interpretation of crystal truncation rod (CTR) experiments.22 Using the CTR technique, it has been shown that there can be two stable terminations denoted oxygen and iron termination of the hematite (001) surface (which is the dominant crystal face together with the (012) and (113) orientations27). CTR data gave also insight into the changes of the layer structure of hematite at the interface with liquid water.22,28 However, this technique does not give information on the protons that terminate the surface and the hydrogen bonding interactions with the solvent. These are important properties that determine, for example, the reactivity of hematite toward electron- and proton-transfer reactions. © XXXX American Chemical Society

Received: January 25, 2016 Accepted: March 8, 2016

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Figure 1. Snapshot of the hematite (001)−liquid water interface taken from the first-principles molecular dynamics simulation reported in this work. Fe atoms and oxygen atoms of hematite are drawn in green and red spheres, respectively, and water molecules are shown in licorice representation. The dimension of the hematite slab and of the supercell in the direction perpendicular to the (001) surface is indicated.

size that is required to obtain bulk-like properties both in the middle of the water layer as well as in the middle of the hematite layer. We have checked for finite size effects by comparing the internal geometry of bulk hematite cells (1 × 1 × 1 to 3 × 3 × 1) to the experimental bulk structure30 and found that neither geometric nor electronic properties like the iron spin charge to change by more than 0.3% for systems larger than the 2 × 2 × 1 supercell employed in this work. A similar setup has been used31−35 to simulate the aqueous interface of early transition-metal oxides like TiO2. In the case of hematite, an additional challenge for density functional theory (DFT) is the complex antiferromagnetic spin pattern, which has a strong influence on electron mobility.36 As for electronic structure, a modified HSE06 hybrid functional was used with the Hartree−Fock exchange reduced from 25% to 12%.37 This functional was shown to reproduce a wide range of experimental properties of bulk hematite such as crystal structure, band gap, antiferromagnetic ordering, and spin density distribution, clearly outperforming generalized gradient approximation (GGA) and GGA+U functionals.37 With regard to the latter functional, the U parameter can be optimized either for the band gap of hematite or the spin population of the iron atoms but not for both. Besides, the U parameter has a strong impact on the relative surface termination stability.38 All simulations were carried out at 1 bar and 330 K in the NPT ensemble using the CP2k program package.39 We have chosen the NPT ensemble to obtain the proper thermal average of the solvation structures of the interface. Hence, care must be taken when interpreting the dynamics of our trajectories, which may differ from the ones obtained in the NVE ensemble. The temperature was chosen to be slightly higher than room temperature to account for the underestimation of the selfdiffusion constant of liquid water in DFT-based MD.40 Further simulation details can be found in the Supporting Information. To the best of our knowledge, our setup constitutes the highest-quality molecular dynamics simulations that has been performed to date for the hematite−water interface. Recent advances in computational methods like the auxiliary density matrix method (ADMM) approximation41 rendered this simulation feasible. However, the computational cost is still large and limited the accessible time scale to about 15 ps of surface solvation dynamics. All properties reported have been averaged over this window of time. Figure 2 shows the shift in position of each layer in a cross section through hematite, i.e., along the normal of the (001) surface, relative to the position in the experimental crystal

Figure 2. Shift of layer positions relative to the experimental (exp) position in single crystalline hematite.30 The data are obtained from energy minimization of the hematite crystal using the HSE06 functional with 12% HFX (blue), from first-principles MD simulation for the hematite−water interface (green), and from CTR data for the same interface (orange).22 The middle oxygen layer (solid horizontal line) has been used as the reference point for all systems; the proton termination layer is not observed in the CTR experiment. Distances in Angstroms give absolute layer separations. The outermost layer is composed of the oxygen atoms of the first solvation layer. Color coding is the same as in Figure 1.

structure.30 One can clearly see that the computed layer spacing for the hematite crystal (blue) is in excellent agreement with the experimental structure.30 Upon solvation of the (001) surface, the terminating oxygen layer shifts toward the solvent by about 0.1 Å, which induces a similar shift of the proximate layers with alternating sign (green). The net effect of solvation is a slight expansion of the hematite slab by 1%. The computed layer structure is in fair agreement with the CTR data from Trainor et al.22 (orange) with the exception of the outermost iron sublayer. Most likely, this is due to a specific assumption made by Trainor et al. in their CTR analysis, that the in-plane positions of the iron atoms in the (001) plane remain unchanged upon solvation. We observe a small but significant relaxation of these positions. An additional discrepancy is the distance between the terminating oxygen atoms and the water oxygen atoms of the first solvation shell, reported to be 1.9 Å in ref 22, compared to 2.6 Å in our simulated structure. We note that the 1.9 Å interpreted from the CTR data is significantly below the usual oxygen−oxygen contact distance. This has been pointed out also by the authors in a later publications,42 but no potential reasons for the discrepancy were discussed. Because the analysis of CTR data is a complex task that involves optimization over a large number of variables, our calculated structure may aid the interpretation of these existing data or of future measurements. Figure 3 shows the location of the protons terminating the surface and the solvation structure of the interface. The density of terminating protons (green), water oxygen (blue), and water 1156

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Figure 3. Atom number density per unit cell versus distance relative to the topmost hematite oxygen layer for protons terminating the hematite surface (green), water oxygen (blue), and water hydrogen atoms (orange). Dashed lines denote the integral of the solid lines. The dotted line is twice the hydrogen water atom count (dashed blue). Note the close correspondence of the dotted line with the oxygen water atom count (orange dashed) at distances larger than 5 Å, indicative of bulk water structure.

Figure 4. (A) Top view on the two most stable surface termination patterns, present over 1.8 and 1.2 ps. Circles are protonated surface oxygen sites. Those with a strike-through bar are periodic images. Red circles: OH bond perpendicular to the surface (out-of-plane) with probability of donating a HB to water indicated in percent. Blue circles: OH bond parallel to the surface (in-plane) with probability of accepting a HB from water indicated in percent. Solid arrows: hydrogen bond from donor to acceptor with formation probability given in percnet. Dashed arrows: periodic images of solid arrows. (B) Circles with numbers are protonated surface oxygen sites. Labels enumerate all oxygen sites and illustrate periodic images (gray). Red bars: HB formation suppressed by iron atom close to surface. Green bars: Remaining possibilities for HB formation. Black lines: HBs actually observed. (C) Illustration of the geometry of two hypothetical HB chains 1−3−4 and 9−8−6, see text for details.

hydrogen atoms (orange) are plotted as a function of the distance relative to the topmost hematite oxygen layer. We

observe two well-separated features for the terminal protons (green): a peak at 0 Å corresponding to protons that are in1157

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see Figure 4 B. However, in both cases, the lone pair of the middle oxygen atom (3 and 8, respectively) would be above the surface oxygen layer pointing toward water, as indicated in Figure 4 C. This is highly unfavorable because the Hartree potential steeply decreases when crossing from the hematite to the water phase (see Figure S1). In the case of the two-site and three-site HBs described above, the lone pair is located below the oxygen layer and therefore is not affected by the energy penalty due to the Hartree potential. For a lifetime analysis of the HBs, we have calibrated the HB criterion to match reference data for bulk water45 (see Supporting Information). While the average lifetime is 150 fs for bulk water, we observe reduced lifetimes at the interface: 140 fs for HBs from surface terminating protons to water, 120 fs for HBs from water hydrogens to surface oxygens, and 80 fs for HBs across the surface. This suggests that the energy barrier for break of HBs at the hematite surface is reduced compared with bulk water, in particular for in-plane HBs. The lifetimes correlate with the average number of hydrogen bonds formed per unit cell: 1.7 from hematite to water, 1.4 from water to hematite, and 1.2 across the surface. In conclusion, we have presented a detailed, atom-scale picture of the solvation structure and dynamics at the hematite−water interface as obtained from first-principles molecular dynamics simulation. The interface structure and in particular the terminating protons are found to be highly dynamic at room temperature, with only about half of the protons being acidic (out-of-plane) at any given instant in time. Our predictions are in fair agreement with the CTR data of Trainor et al., though some discrepancies exist, in particular relating to the distance between the oxygen atoms of terminating layer and water molecules. New CTR measurements are planned in the future to verify the DFT-based MD simulation results reported herein. It would be of interest to study solvent reorganization and mobility at the surface in a next step. Such studies would strongly benefit from longer simulations times, possibly with classical force fields parametrized to reproduce the picosecond dynamics reported herein. Moreover, the present work forms a solid basis for a theoretical investigation of holes and electrons at hematite−water interfaces relevant for our fundamental understanding of biogeochemical transformations and watersplitting catalysis. Work along these lines is currently underway in our laboratory.

plane and a second peak at 0.95 Å corresponding to protons pointing in perpendicular direction (out-of-plane) toward the first water layer. The two peaks integrate to approximately the same value (see Table S1). Most of the classical force fields available for this interface do not reproduce the atom number density of the surface protons.23 Only one force field23 captures the two-peak structure in Figure 3, but the in-plane component is underestimated and the peak width of the out-of-plane component is overestimated. The ClayFF force field appears to be reasonably accurate when compared to ab initio calculations for some systems like the quartz−water interface.23,43 However, for the hematite−water system, it significantly underestimates the fraction of protons forming in-plane hydrogen bonds in the topmost oxygen layer. Whereas the peak of the oxygen atom density at 2.6 Å (blue) is very well-defined, we observe few structural features at larger distances hinting toward a strong dielectric screening of the hematite interface. This is in contrast to the predictions of a range of classical models evaluated for this system,23 in which structural features were reported to persist over longer distances. Furthermore, we find that some of the water molecules in the first solvation layer are oriented with their hydrogen atoms toward hematite (peak at 1.7 Å) or in the opposite direction (peak at 2.9 Å). Although the peak at 2.9 Å is higher than that at 1.7 Å because of the onset of the second hydration layer, the water molecules in the first layer have a clear preference to orient their hydrogen atoms toward hematite. Besides the static properties discussed so far, our calculations give insight into the dynamical processes that occur at the hematite−water interface. Over the course of the simulation, we observe the formation of distinct patterns of terminal oxygen atoms binding protons either in-plane (blue circles in Figure 4 A, in the following denoted as “in-plane” sites) or out-of-plane (red circles, denoted as “out-of-plane” sites), with the protons corresponding to the two density peaks indicated in green in Figure 3. These patterns are stable on the time scale of 0.7−1.8 ps. Thermal fluctuations of the coordinating water molecules induce fast switches between different patterns within about 50 fs; see Figure 4 A for an example. Dissociation events of surface terminating protons are not observed within the present simulation time, unlike results reported for SnO2.35 Among the large number of possibilities for the formation of hydrogen bond (HB) chains and networks at the interface, only two are dominant in any of the patterns observed: a three-site chain where two in-plane sites donate a HB to an out-of-plane site that in turn donates a HB to a water molecule, and a twosite chain where an in-plane site accepts a HB from a water molecule and donates a HB to an out-of-plane site that in turn donates a HB to a water molecule. Interestingly, we do not observe the formation of longer HB chains within the (001) surface, which would require the formation of HBs between inplane sites (blue circles). Surprisingly, not a single such HB is observed, despite the distance between in-plane sites being favorable for HB formation.44 The absence of HBs between in-plane sites can be understood by geometric and electrostatic considerations: in each unit cell there is one iron atom in close proximity to the terminal oxygen layer so that HBs between the three oxygens nearest to the iron atom cannot be formed (connections in red in Figure 4 B). This leaves two remaining possibilities for HBs between in-plane sites, e.g., connections 1−3−4 and 9−8−6,

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b00165. Simulation details, coordinates and the HB detection method, the vibrational density of states, two figures showing the Hartree potential across the interface and the surface termination patterns as well as three tables summarizing the HB lifetime distribution and the conditional probabilities for finding a HB alongside the possible angles according to Figure 4 (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. 1158

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(17) Zhou, Z.; Huo, P.; Guo, L.; Prezhdo, O. V. Understanding Hematite Doping with Group IV Elements: A DFT+U Study. J. Phys. Chem. C 2015, 119, 26303−26310. (18) Engel, J.; Tuller, H. L. The Electrical Conductivity of Thin Film Donor Doped Hematite: From Insulator to Semiconductor by Defect Modulation. Phys. Chem. Chem. Phys. 2014, 16, 11374−11380. (19) Hu, Y.-S.; Kleiman-Shwarsctein, A.; Forman, A. J.; Hazen, D.; Park, J.-N.; McFarland, E. W. Pt-Doped α-Fe2O3 Thin Films Active for Photoelectrochemical Water Splitting. Chem. Mater. 2008, 20, 3803− 3805. (20) Ling, Y.; Wang, G.; Wheeler, D. A.; Zhang, J. Z.; Li, Y. SnDoped Hematite Nanostructures for Photoelectrochemical Water Splitting. Nano Lett. 2011, 11, 2119−2125. (21) Toroker, M. C. Theoretical Insights into the Mechanism of Water Oxidation on Nonstoichiometric and Titanium-Doped Fe2O3 (0001). J. Phys. Chem. C 2014, 118, 23162−23167. (22) Trainor, T. P.; Chaka, A. M.; Eng, P. J.; Newville, M.; Waychunas, G. A.; Catalano, J. G.; Brown, G. E. Structure and Reactivity of the Hydrated Hematite (0001) Surface. Surf. Sci. 2004, 573, 204−224. (23) Kerisit, S. Water Structure at Hematite-water Interfaces. Geochim. Cosmochim. Acta 2011, 75, 2043−2061. (24) Kerisit, S.; Rosso, K. M. Computer Simulation of Electron Transfer at Hematite Surfaces. Geochim. Cosmochim. Acta 2006, 70, 1888−1903. (25) Nguyen, M.-T.; Piccinin, S.; Seriani, N.; Gebauer, R. PhotoOxidation of Water on Defective Hematite(0001). ACS Catal. 2015, 5, 715−721. (26) Liao, P.; Keith, J. A.; Carter, E. A. Water Oxidation on Pure and Doped Hematite (0001) Surfaces: Prediction of Co and Ni as Effective Dopants for Electrocatalysis. J. Am. Chem. Soc. 2012, 134, 13296− 13309. (27) Chatman, S.; Zarzycki, P.; Rosso, K. M. Surface Potentials of (001), (012), (113) Hematite (α-Fe2O3) Crystal Faces in Aqueous Solution. Phys. Chem. Chem. Phys. 2013, 15, 13911−13921. (28) Tanwar, K. S.; Petitto, S. C.; Ghose, S. K.; Eng, P. J.; Trainor, T. P. Fe(II) Adsorption on Hematite (0001). Geochim. Cosmochim. Acta 2009, 73, 4346−4365. (29) Yamamoto, S.; Kendelewicz, T.; Newberg, J. T.; Ketteler, G.; Starr, D. E.; Mysak, E. R.; Andersson, K. J.; Ogasawara, H.; Bluhm, H.; Salmeron, M.; et al. Water Adsorption on α-Fe2O3 (0001) at Near Ambient Conditions. J. Phys. Chem. C 2010, 114, 2256−2266. (30) Blake, R. L.; Hessevick, R. E.; Zoltai, T.; Finger, L. W. Refinement of the Hematite Structure. Am. Mineral. 1966, 51, 123− 129. (31) Cheng, J.; Sulpizi, M.; VandeVondele, J.; Sprik, M. Hole Localization and Thermochemistry of Oxidative Dehydrogenation of Aqueous Rutile TiO2(110). ChemCatChem 2012, 4, 636−640. (32) Cheng, J.; Sprik, M. Acidity of the Aqueous Rutile TiO2(110) Surface from Density Functional Theory Based Molecular Dynamics. J. Chem. Theory Comput. 2010, 6, 880−889. (33) Cheng, J.; Sprik, M. The Electric Double Layer at a Rutile TiO2water Interface Modelled Using Density Functional Theory Based Molecular Dynamics Simulation. J. Phys.: Condens. Matter 2014, 26, 244108. (34) Ni, M.; Leung, M. K.; Leung, D. Y.; Sumathy, K. A Review and Recent Developments in Photocatalytic Water-splitting Using TiO2 for Hydrogen Production. Renewable Sustainable Energy Rev. 2007, 11, 401−425. (35) Kumar, N.; Kent, P. R. C.; Bandura, A. V.; Kubicki, J. D.; Wesolowski, D. J.; Cole, D. R.; Sofo, J. O. Faster Proton Transfer Dynamics of Water on SnO2 Compared to TiO2. J. Chem. Phys. 2011, 134, 044706. (36) Rosso, K. M.; Smith, D. M. A.; Dupuis, M. An Ab Initio Model of Electron Transport in Hematite (α-Fe2O3) Basal Planes. J. Chem. Phys. 2003, 118, 6455. (37) Pozun, Z. D.; Henkelman, G. Hybrid Density Functional Theory Band Structure Engineering in Hematite. J. Chem. Phys. 2011, 134, 224706.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS G.F.v.R. gratefully acknowledges a Ph.D. studentship cosponsored by University College London and Pacific Northwest National Laboratory (PNNL) through its BES Geosciences program supported by the U.S. Department of Energy’s Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences and Biosciences Division. MD simulations were carried out on ARCHER, the U.K. national HPC facility (Edinburgh), to which access was granted via the ARCHER Leadership pilot call and the Materials Chemistry Consortium (EPSRC Grant EP/L000202).

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REFERENCES

(1) Hamann, T. W. Splitting Water With Rust: Hematite Photoelectrochemistry. Dalton Trans. 2012, 41, 7830−7834. (2) Yanina, S. V.; Rosso, K. M. Linked Reactivity at Mineral-Water Interfaces Through Bulk Crystal Conduction. Science 2008, 320, 218− 222. (3) Philippe, A.; Schaumann, G. E. Interactions of Dissolved Organic Matter with Natural and Engineered Inorganic Colloids: A Review. Environ. Sci. Technol. 2014, 48, 8946−8962. (4) Kuhlenbeck, H.; Shaikhutdinov, S.; Freund, H.-J. Well-ordered Transition Metal Oxide Layers in Model Catalysis - a Series of Case Studies. Chem. Rev. 2013, 113, 3986−4034. (5) Ravishankara, A. R.; Rudich, Y.; Wuebbles, D. J. Physical Chemistry of Climate Metrics. Chem. Rev. 2015, 115, 3682−3703. (6) Sivula, K.; Le Formal, F.; Grätzel, M. Solar Water Splitting: Progress Using Hematite (α-Fe2O3) Photoelectrodes. ChemSusChem 2011, 4, 432−449. (7) Lützenkirchen, J.; Heberling, F.; Supljika, F.; Preocanin, T.; Kallay, N.; Johann, F.; Weisser, L.; Eng, P. J. Structure-Charge Relationship - the Case Of Hematite (001). Faraday Discuss. 2015, 180, 55−79. (8) Reddy, M. V.; Subba Rao, G. V.; Chowdari, B. V. R. Metal Oxides and Oxysalts as Anode Materials for Li Ion Batteries. Chem. Rev. 2013, 113, 5364−5457. (9) Shi, L.; Squier, T. C.; Zachara, J. M.; Fredrickson, J. K. Respiration of Metal (Hydr)Oxides by Shewanella and Geobacter: A Key Role for Multihaem C-type Cytochromes. Mol. Microbiol. 2007, 65, 12−20. (10) Breuer, M.; Zarzycki, P.; Blumberger, J.; Rosso, K. M. Thermodynamics of Electron Flow in the Bacterial Deca-heme Cytochrome MtrF. J. Am. Chem. Soc. 2012, 134, 9868−9871. (11) Breuer, M.; Rosso, K. M.; Blumberger, J.; Butt, J. N. Multi-heme Cytochromes in Shewanella Oneidensis Mr-1: Structures, Functions and Opportuntities. J. R. Soc., Interface 2015, 12, 20141117. (12) Blumberger, J. Recent Advances in the Theory and Molecular Simulation of Biological Electron Transfer Reactions. Chem. Rev. 2015, 115, 11191−11238. (13) Dallongeville, S.; Garnier, N.; Rolando, C.; Tokarski, C. Proteins in Art, Archaeology, and Paleontology: From Detection to Identification. Chem. Rev. 2016, 116, 2−79. (14) Gilbert, B.; Frandsen, C.; Maxey, E.; Sherman, D. Band-gap Measurements of Bulk and Nanoscale Hematite by Soft X-ray Spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 035108. (15) Cesar, I.; Sivula, K.; Kay, A.; Zboril, R.; Grätzel, M. Influence of Feature Size, Film Thickness, and Silicon Doping on the Performance of Nanostructured Hematite Photoanodes for Solar Water Splitting. J. Phys. Chem. C 2009, 113, 772−782. (16) Rettie, A. J. E.; Chemelewski, W. D.; Emin, D.; Mullins, C. B. Unravelling Small-polaron Transport in Metal Oxide Photoelectrodes. J. Phys. Chem. Lett. 2016, 7, 471−479. 1159

DOI: 10.1021/acs.jpclett.6b00165 J. Phys. Chem. Lett. 2016, 7, 1155−1160

Letter

The Journal of Physical Chemistry Letters (38) Hellman, A.; Pala, R. G. S. First-Principles Study of Photoinduced Water-Splitting on Fe2O3. J. Phys. Chem. C 2011, 115, 12901−12907. (39) CP2K developers group. CP2K, version 2.7 (Development Version). http://www.cp2k.org/, 2015. (40) VandeVondele, J.; Mohamed, F.; Krack, M.; Hutter, J.; Sprik, M.; Parrinello, M. The Influence of Temperature and Density Functional Models in Ab Initio Molecular Dynamics Simulation of Liquid Water. J. Chem. Phys. 2005, 122, 014515. (41) Guidon, M.; Hutter, J.; VandeVondele, J. Auxiliary Density Matrix Methods for Hartree-Fock Exchange Calculations. J. Chem. Theory Comput. 2010, 6, 2348−2364. (42) Catalano, J. G. Weak Interfacial Water Ordering on Isostructural Hematite and Corundum (001) Surfaces. Geochim. Cosmochim. Acta 2011, 75, 2062−2071. (43) Skelton, A. A.; Fenter, P.; Kubicki, J. D.; Wesolowski, D. J.; Cummings, P. T. Simulations of the Quartz(1011)/Water Interface: a Comparison of Classical Force Fields, Ab Initio Molecular Dynamics, and X-ray Reflectivity Experiments. J. Phys. Chem. C 2011, 115, 2076− 2088. (44) Steiner, T. The Hydrogen Bond in the Solid State. Angew. Chem., Int. Ed. 2002, 41, 48−76. (45) Luzar, A.; Chandler, D. Hydrogen-bond Kinetics in Liquid Water. Nature 1996, 379, 55−57.

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