Anatase TiO2(101) Interface: Structure

May 18, 2010 - Hydroxide Ions at the Water/Anatase TiO2(101) Interface: Structure and Electronic States from First Principles Molecular Dynamics. Hong...
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Hydroxide Ions at the Water/Anatase TiO2(101) Interface: Structure and Electronic States from First Principles Molecular Dynamics Hongzhi Cheng and Annabella Selloni* Department of Chemistry, Princeton University, Princeton, New Jersey 08544 Received February 15, 2010. Revised Manuscript Received April 14, 2010 Hydroxide (OH-) ions at or near the interface between water and titanium dioxide (TiO2) have an important role in many surface photocatalytic reactions, possibly including the photo-oxidation of water. Using first principles molecular dynamics (FPMD) simulations on the time scale of 30-40 ps, we have investigated the structure and electronic properties of a solvated or adsorbed OH- at the interface between liquid water and a stoichiometric anatase TiO2(101) slab. We observed that a solvated hydroxide ion diffuses spontaneously from bulk water toward the anatase surface, a result consistent with the known point of zero charge for TiO2 in water. The O atom of the adsorbed OH- forms two H-bonds with nearby water molecules, whereas three to four bonds are typically found for OH- solvated in bulk water. Analysis of the interface electronic structure along the FPMD trajectories shows significant differences in the densities of states of different atomic configurations, indicating that thermal fluctuations have an important effect on the electronic energy levels. In particular, while the topmost occupied levels of OH- (water) typically lie below (well below) the TiO2 valence band edge (VBE), thermal fluctuations can lead to special, poorly solvated configurations where the topmost OH- energy levels are above the TiO2 VBE. In these configurations, holes generated by UV light absorption can be transferred from the anatase surface to the adsorbed hydroxide ion, though such transfer is usually forbidden.

1. Introduction Solvated hydroxide anions (OH-) in aqueous solutions have a key role in many chemical and biochemical reactions.1,2 Hydroxide ions at the interface of water with metal oxide materials are similarly important in a wide variety of phenomena in geochemistry, (photo)electrochemistry, catalysis, and so on.3-5 In particular, the discovery of the photolysis of water on titanium dioxide (TiO2) surfaces6 has attracted broad interest and prompted intensive studies of the water/TiO2 interface for over 30 years.3,5,7-12 It is widely accepted that OH- ions at this interface have an essential role in many TiO2-based photocatalytic processes, possibly including the photo-oxidation of water.3,9,11,13 Specifically, photogenerated holes in TiO2 react with surface OH- groups to produce hydroxyl radicals (OH•), which then act as very efficient oxidating species. Understanding the detailed mechanism of this interfacial charge transfer process is not straightforward, however. Experiments show that the valence band edge (VBE) of TiO2 in contact with an aqueous solution lies at ∼ -7.6 eV relative to the vacuum level9,12,14 (always taken as the zero of energy in this work). In comparison, the redox potential of OH•(aq)/OH-(aq) is 6.3 eV and that of OH•(aq)/H2O is 7.3 eV (see, e.g., ref 9). From a thermodynamic point of view, a hole from the VBE of TiO2 has (1) Tuckerman, M. E.; Chandra, A.; Marx, D. Acc. Chem. Res. 2006, 39, 151. (2) Palascak, M. W.; Shields, G. C. J. Phys. Chem. A 2004, 108, 3692. (3) Hoffmann, M. R.; Martin, S. T.; Choi, W. Y.; Bahnemann, D. W. Chem. Rev. 1995, 95, 69. (4) Brown, G. E.; Henrich, V. E.; Casey, W. H.; Clark, D. L.; Eggleston, C.; Felmy, A.; Goodman, D. W.; Gratzel, M.; Maciel, G.; McCarthy, M. I.; Nealson, K. H.; Sverjensky, D. A.; Toney, M. F.; Zachara, J. M. Chem. Rev. 1999, 99, 77. (5) Henderson, M. A. Surf. Sci. Rep. 2002, 46, 1. (6) Fujishima, A.; Honda, K. Nature 1972, 238, 37. (7) Diebold, U. Surf. Sci. Rep. 2003, 48, 53. (8) Linsebigler, A. L.; Lu, G.; Yates, J. T., Jr. Chem. Rev. 1995, 95, 735. (9) Fujishima, A.; Zhang, X. T.; Tryk, D. A. Surf. Sci. Rep. 2008, 63, 515. (10) Carp, O.; Huisman, C. L.; Reller, A. Prog. Solid State Chem. 2004, 32, 33. (11) Mills, A.; Le Hunte, S. J. Photochem. Photobiol, A 1997, 108, 1. (12) Gr€atzel, M. Nature 2001, 414, 338. (13) Salvador, P. J. Phys. Chem. C 2007, 111, 17038. (14) Xu, Y.; Schoonen, M. A. A. Am. Mineral. 2000, 85, 543.

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thus enough free energy to oxidize an OH-(aq) or even H2O to produce OH•(aq). For the dynamics of the charge transfer process, however, the vertical ionization energies (VIE) of adsorbed OHand H2O species are more relevant quantities.15-17 Photoemission spectroscopy gives an ionization threshold of 9.9 eV for pure (bulk) water, and measurements for aq NaOH show an ∼1 eV wide OHpeak centered at 9.2 eV.18 These levels shift and broaden when water is in contact with the TiO2 surface. However, from analysis of UPS and MIES spectra of water on rutile TiO2(110), it was estimated that the highest energy levels of adsorbed water species are still ∼1.5 eV below the TiO2 VBE,13 which seems to exclude the possibility that a photogenerated hole is directly transferred from TiO2 to these adsorbed species. The aim of this paper is to contribute to the understanding of the water/TiO2 interface, and especially the properties of hydroxide ions at this interface, by reporting the results of extensive first principles molecular dynamics (FPMD)19 simulations for a hydrated OH- ion on anatase (101), the most abundant surface of anatase TiO2. Available experimental and theoretical studies of water on TiO2 surfaces have focused mostly on the (110) surface of the most stable TiO2 polymorph, rutile,7,20-22 whereas it is the (15) Blumberger, J.; Tavernelli, I.; Klein, M. L.; Sprik, M. J. Chem. Phys. 2006, 124. (16) Adriaanse, C.; Sulpizi, M.; VandeVondele, J.; Sprik, M. J. Am. Chem. Soc. 2009, 131, 6046. (17) For TiO2, there is no significant difference between the valence band edge energy obtained from electrochemical measurements and the VIE from photoemission experiments. (18) Winter, B.; Faubel, M.; Hertel, I. V.; Pettenkofer, C.; Bradforth, S. E.; Jagoda-Cwiklik, B.; Cwiklik, L.; Jungwirth, P. J. Am. Chem. Soc. 2006, 128, 3864. (19) Car, R.; Parrinello, M. Phys. Rev. Lett. 1985, 55, 2471. (20) Zhang, Z.; Fenter, P.; Cheng, L.; Sturchio, N. C.; Bedzyk, M. J.; Predota, M.; Bandura, A.; Kubicki, J. D.; Lvov, S. N.; Cummings, P. T.; Chialvo, A. A.; Ridley, M. K.; Benezeth, P.; Anovitz, L.; Palmer, D. A.; Machesky, M. L.; Wesolowski, D. J. Langmuir 2004, 20, 4954. (21) Predota, M.; Bandura, A. V.; Cummings, P. T.; Kubicki, J. D.; Wesolowski, D. J.; Chialvo, A. A.; Machesky, M. L. J. Phys. Chem. B 2004, 108, 12049. (22) Mamontov, E.; Wesolowski, D. J.; Vlcek, L.; Cummings, P. T.; Rosenqvist, J.; Wang, W.; Cole, D. R. J. Phys. Chem. C 2008, 112, 12334.

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interface of water with the metastable anatase TiO2 polymorph that is generally considered most relevant for photocatalytic applications.23 There are various structural differences between the rutile (110) and anatase (101) surfaces.24 In particular, surface science experiments have shown that oxygen vacancies reside predominantly in the subsurface region of anatase (101), whereas a large (5-10%) concentration of surface bridging oxygen vacancies is usually found on rutile (110).25,26 The subsurface defects enhance the adsorption energy of water molecules at selected anatase (101) surface sites and facilitate or even favor their dissociation,27 which is highly unfavored on the defect-free stoichiometric surface.24,27,28 While for simplicity we use a defectfree stoichiometric anatase (101) surface model in the present study, the adsorbed hydroxide ions that we are here considering could represent species resulting from water dissociative adsorption at defect sites not explicitly described in our simulations. We also note that these hydroxides are the only ions included in our model. Charge compensation is introduced through a uniform background of charge rather than with explicit dissolved counterions. A realistic description of the electric double layer that is present at real electrolyte/solid interfaces would indeed require simulation cells much larger (see, e.g., ref 21) than those currently accessible to first principles studies. Because of its relevance to the mechanism of photoexcited hole transfer to adsorbed water species, we have also computed the interface electronic structure, focusing on the electronic states around the TiO2 valence band edge. Due to the size of the systems of interest, the electronic structure method of choice for our calculations is density functional theory (DFT) in the generalized gradient approximation (GGA). This approach combines efficiency with an overall satisfactory accuracy, but it has also some inherent errors, in particular the so-called selfinteraction or delocalization error,29 whose influence on our computed electronic properties will be discussed in the following. Another limitation of the present electronic structure calculations is that they refer to the ground state in the absence of photogenerated holes, which are actually present both in a real photocatalytic reaction and in photoemission measurements, so that caution must be used in the comparison of our results with experiment. On the other hand, a distinctive characteristic of our approach with respect to available theoretical studies of the electronic structure of water on TiO2 surfaces is that the influence of thermal fluctuations is explicitly taken into account by calculations of the electronic properties of a large number of different configurations generated during our well equilibrated FPMD trajectories. This approach allows us to verify that the electronic structure does indeed depend significantly on the atomic configuration. In particular, while the alignment of the OH- energy levels relative to the TiO2 VBE does not usually allow the transfer of photoexcited holes from the surface to the adsorbed hydroxide, we found that thermal fluctuations can occasionally generate atomic configurations with a favorable level alignment for the charge transfer to occur. (23) Kavan, L.; Gratzel, M.; Gilbert, S. E.; Klemenz, C.; Scheel, H. J. J. Am. Chem. Soc. 1996, 118, 6716. (24) Diebold, U.; Ruzycki, N.; Herman, G. S.; Selloni, A. Catal. Today 2003, 85, 93. (25) He, Y.; Dulub, O.; Cheng, H.; Selloni, A.; Diebold, U. Phys. Rev. Lett. 2009, 102, 106105. (26) Cheng, H.; Selloni, A. Phys. Rev. B 2009, 79, 092101. (27) Aschauer, U.; He, Y.; Cheng, H.; Li, S.-C.; Diebold, U.; Selloni, A. J. Phys. Chem. C 2010, 114, 1278. (28) Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Gratzel, M. Phys. Rev. Lett. 1998, 81, 2954. (29) Cohen, A. J.; Mori-Sanchez, P.; Yang, W. T. Science 2008, 321, 792.

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2. Calculations Calculations were performed using the Car-Parrinello FPMD approach as implemented in the q-Espresso package.30 The electronic structure was treated within DFT-GGA, using the Perdew-Burke-Ernzerhof (PBE)31 exchange-correlation functional, which has proven to reliably describe the properties of anatase surfaces, including their interaction with water, in previous studies.28,32,33 The plane-wave-pseudopotential scheme was used, with ultrasoft pseudopotentials34 and a kinetic energy cutoff of 25 (200) Ry for the smooth part of the wave functions (augmented density). Valence states included the Ti 3s, 3p, 3d, and 4s states, the O 2s and 2p states, and the H 1s state. Due to the large sizes of the systems treated in this work, Γ only was used to sample k space. All the systems considered in this work are closedshell; as test calculations showed the effect of spin polarization to be irrelevant, non-spin-polarized calculations were performed in all our simulations. The TiO2/water interface was modeled using a periodic supercell approach. Each supercell contained an anatase (101)-1 3 slab consisting of two TiO2 layers (thickness of ∼7 A˚) in contact with a water environment filling the space between consecutive slabs. We verified that the thickness of the anatase slab is sufficient to avoid interactions between adsorbed water molecules on the two sides of the slab; we found indeed that the water adsorption energy is the same for the cases where one H2O molecule is adsorbed on both sides or on one side only of the slab. To check the influence of the water confinement on the results of the simulations, two different unit cells were considered, a smaller one of dimensions 10.26  11.31 17.06 A˚3 and a larger one of dimensions 10.26  11.31  27.10 A˚3. We used 38 H2O and 1 OH- or 39 water molecules (without OH-) in the smaller unit cell, and 77 water molecules plus 1 OH- in the larger one. In this way, the density of water is close to the experimental bulk density at normal conditions. A uniform background of charge was used to compensate the negative charge of the hydroxide ion. We explicitly verified that neither the clean slab nor the slab with an adsorbed OH- have a dipole moment (see Figure S1 of the Supporting Information). The FPMD equations of motion for the larger (smaller) system were integrated using a time step of 0.19 (0.12) fs, a fictitious electron mass of 700 (400) au, and a mass of 2 (1) AMU for hydrogen atoms. Canonical (NVT) simulations were carried out using a Nose-Hoover ionic thermostat, at T = 300 K. Usually, a Nose-Hoover thermostat was also applied to the electronic dynamics in order to maintain the adiabaticity of the motion over the relatively long duration of our simulations.

3. Results and Discussion Our simulations include three main trajectories: one for the surface in contact with a “thin” water overlayer formed by 38 H2O and 1 OH- (Run38a, of length 43.6 ps); another for the surface in contact with a “thick” water overlayer formed by 77 H2O molecules and 1 OH- (Run77, of length 30.8 ps); and a third one for a system with 39 water molecules and no hydroxide (Run39w, of length 32.8 ps). Run77 consists of two distinct sections (see below), which will be denoted as Run77b and Run77a in the following. Only the last part of each trajectory (30) Giannozzi, P..; et al. J. Phys.: Condens. Matter 2009, 21, 395502. (31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77. (32) Tilocca, A.; Selloni, A. Langmuir 2004, 20, 8379. (33) He, Y. B.; Tilocca, A.; Dulub, O.; Selloni, A.; Diebold, U. Nat. Mater. 2009, 8, 585. (34) Vanderbilt, D. Phys. Rev. B 1990, 41, 7892.

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Figure 1. Time evolution of (a) the shortest distance between the O atom of OH- and a surface Ti atom and (b) the total potential energy, Etot, during Run77 (see text). In (b), the zero of the energy has been rescaled so that Etot ∼ 0 at long times.

Figure 2. Water density profiles calculated by sampling the positions of the water oxygens in the z-direction for (a) system with 77 H2O and OH-; (b) systems with 38 H2O and OH- (Run38a) or 39 H2O molecules (Run39). The OH- is treated as a water molecule in all these plots. The positions of the outmost surface oxygens are at (a) z = 5.9 and 27.0 A˚; (b) z = 5.9 and 17.1 A˚. The OH- is adsorbed on the left surface in Run77a, panel (a), and on the right surface in Run38a, panel (b).

has been used for analysis, corresponding to about 14, 20, 6.5, and 10 ps for Run38a, Run39w, Run77b, and Run77a, respectively. To prepare the initial water configuration for Run38a, we took a configuration from a separate well-equilibrated FPMD trajectory for a bulk solution (represented by a system of 31 H2O þ 1 OH- in a periodically repeated 9.865 A˚ cubic cell1), added a few water molecules near the surfaces, and then relaxed the whole 11520 DOI: 10.1021/la100672f

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Figure 3. Fraction of surface (a) Ti5c and (b) O2c sites coordinated to a water molecule as a function of time during Run77. The bond length cutoffs are 2.5 and 2.3 A˚ for the Ow-Ti5c and Hw-O2c bonds, respectively. The Hw-O2c distance for an isolated H2O molecule adsorbed on anatase (101) is ∼2.2 A˚.27 (c) Average cosine of the angle between the water dipoles and the positive z-direction as a function of the z-coordinate of the water Ow atoms.

(slab þ solution) system. The OH- was initially in the middle of the water region between two TiO2 slabs, of thickness ∼10 A˚, and no dynamical constraint was used. After only 0.5 ps into the simulation, the OH- diffused rapidly to the TiO2 surface where it remained for the rest of the simulation, except for a few events in which a Hþ was briefly transferred from a neighboring H2O to the OH-, resulting in an adsorbed H2O and an OH- in water. To confirm this observation, we repeated our simulation using a thicker water overlayer (Run77). We generated the initial water configuration for this run in the following way: we “doubled” the water layer of a configuration taken from Run38a along the z direction, added a proton to one of the two resulting OH- so as to transform it into an H2O molecule while maintaining the other OH-, and finally relaxed the whole (slab þ solution) system. Again, the OH- was initially in the middle of the water region between two TiO2 slabs (∼20 A˚), but this time all the water molecules were kept rigid with the z-coordinate of the OH- ion also fixed during the first 5 ps of the simulation. This led to the formation of a well-defined solvation structure for OH-. Following this equilibration, the dynamical constraints were removed so that the OH- was free to diffuse. We observed that the OHremained solvated in water for about 15 ps, with its shortest distance from a Ti surface atom being larger than 6 A˚ (section Run77b of the Run77 trajectory). After this relatively long time, however, the OH- swiftly migrated via a Grotthus-like mechanism1 to the TiO2 surface and was adsorbed at a Ti5c site (Figure 1a). It then remained stably adsorbed for the rest of the simulation (section Run77a of the Run77 trajectory), except for a few “detachment” events similar to those described above for Run38a. The time dependence of the total electronic energy during the whole Run77 trajectory is shown in Figure 1b. Due to the large fluctuations, the effect of the sudden change in the OH- solvation state is hardly visible in this plot. However, the average energy after the jump is computed to be 0.12 eV lower than that in the first part of the run, consistent with the observed OH- diffusion toward the Langmuir 2010, 26(13), 11518–11525

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Figure 4. (a) Equilibrium configuration of an OH- adsorbed at the anatase-water interface, with two H-bonds between the O atom in the

OH- (O*) and nearby water molecules (from Run77a). (b) Configuration with only one H-bond between O* and the surrounding water molecules. Oxygen atoms are red, Ti atoms are gray, and H atoms are white. Dashed green lines indicate H-bonds. What seems to be an isolated proton on the left of (a) is actually an effect of the periodic boundary conditions used in the calculations.

surface during the simulation. These findings suggest that in aqueous solution the concentration of surface OH- should be higher than that of OH- in bulk water. Experimentally, the point of zero charge, pHZPC, for anatase TiO2 is found to be around 5.5,35 implying that in neutral water, pH = 7, an excess of negative charge is present on the TiO2 surface. Our results appear well consistent with these experimental observations, even though a complete description would include a study of the interaction of the anatase surface with hydronium ions in solution. 3.1. Structure of the Water/Anatase (101) Interface. The anatase TiO2(101) surface is characterized by a sawtooth-like structure with ridges of 2-fold coordinated (O2c) atoms along the [010] direction.24 Water adsorbs molecularly on the defect-free surface, with the water molecules in the first and second monolayer forming bonds with the undercoordinated 5-fold surface Ti atoms (Ti5c) and bridging surface O2c, respectively.28,32,33 The water density profiles determined from our FPMD trajectories are shown in Figure 2. The sharp outer peaks on the left- and right-hand sides correspond to the first water monolayer in contact with the TiO2 surface. These two peaks are not symmetrical in the presence of an OH- adsorbed on one side (only) of the anatase slab. From Figure 2, we can also see a significant layering of the water in both the smaller and larger confinement region, that is, at distances of more than 10 A˚ from the surface. Such a strong effect can be in part attributed to the fact that PBE-based FPMD simulations at 300 K underestimate the water diffusion by about an order of magnitude.36 A similar layering, however, was observed also in recent simulations of the interface between acetonitrile and the anatase (101) surface.37 Further information on the structure of the water/anatase interface is provided in Figure 3. The upper panels show how the water coordination to the surface Ti5c and O2c sites varies during the trajectory with 77 water molecules (Run77). We can see that about 25% of the Ti5c sites are not occupied by water during this (35) Kosmulski, M. Adv. Colloid Interface Sci. 2009, 152, 14. (36) Schwegler, E.; Grossman, J. C.; Gygi, F.; Galli, G. J. Chem. Phys. 2004, 121, 5400. (37) Schiffmann, F.; Hutter, J.; VandeVondele, J. J. Phys.: Condens. Matter 2008, 20.

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Figure 5. Radial O*H (upper panel) and O*O (lower panel) distribution functions for an adsorbed or solvated OH- at the water/anatase(101) interface. O* denotes the oxygen atom belonging to OH-. The solid black, dashed blue, and dotted red lines refer to Run77a, Run77b, and Run38a, respectively.

simulation, whereas ∼85% of the surface O2c atoms are involved in H-bonds with the water molecules. The average molecular orientation in the direction perpendicular to the surface, Figure 3c, confirms the layering effect observed in the water density profiles, with each successive layer having an alternate orientation of the molecular dipoles. The water molecules closer to the surface give rise to well-defined peaks which correspond to an angle of ∼60° formed by the molecular dipole with the direction perpendicular to the surface, an orientation quite different compared to that found in an isolated water monolayer on the anatase (101) surface.32 DOI: 10.1021/la100672f

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Figure 6. Partial densities of states for eight sequential snapshots from Run38a, each separated from the adjacent by 1.5 ps. The solid black (dashed red) curve is the PDOS for TiO2 (water). The PDOS for OH- (dotted blue line) is multiplied by a factor 10. The TiO2 valence band edge is set at -7.72 eV.

3.2. Adsorption and Solvation Structures of Hydroxide Ions. A typical configuration of the adsorbed OH- observed during our simulations is shown in Figure 4a. The oxygen (O*) of the adsorbed species is bound to a surface Ti5c atom with an average bond length of ∼2.03 A˚, while the H atom in the OHusually forms a H-bond with a surface O2c atom, as shown in the figure. Also, O* forms H-bonds with nearby water molecules, and in particular two such H-bonds are present for the configuration in Figure 4a. We observed that this is typically the case when the system is well equilibrated, that is, after long (∼20 ps) simulation times. We also observed, however, that one of the H-bonds can occasionally break due to thermal fluctuations (see Figure 4b); configurations where O* has only one H-bond generally show a slightly shorter O*-Ti5c bond length (∼1.98 A˚). The solvation structure of O* with only two H-bonds is obviously different from the solvation state of a hydroxide ion 11522 DOI: 10.1021/la100672f

in water, where the hydroxyl oxygen is coordinated on average by three or four water molecules.1 This difference is clearly shown by the radial distribution functions (rdfs) in Figure 5. Here the rdfs for the OH- in water were determined from Run 77b and agree well with those reported in other studies (see, e.g., ref 1 and references therein). The rdfs for the adsorbed OH- were calculated for both the larger (Run77a) and the smaller (Run38a) systems investigated in this work. We can see that the results for the two trajectories are quite similar up to distances of ∼2.5 A˚, suggesting that both systems are well equilibrated; differences at larger distances are clearly due to size effect, as the thickness of the water layer between two anatase slabs is only ∼10 A˚ in the smaller system. In all cases, the first peak of the O*O radial distribution function is located at ∼2.7 A˚, and its height is clearly much larger for OH- in water than for the adsorbed OH-. Similarly, also the height of the second peak of the O*-H radial distribution Langmuir 2010, 26(13), 11518–11525

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function, corresponding to the H-bonds with water molecules, is much larger for the OH- in water. This peak is also at larger distance, ∼1.7 A˚, for the adsorbed OH-, indicating that the TiO2 surface tends to keep water molecules away from the adsorbed hydroxide ion. Integration of the O*H radial distribution function from 1.2 to 2.5 A˚ yields a value close to 2 for both Run38a and Run77a, confirming that the average number of H-bonds for O* is 2. 3.3. Electronic Structure. In this section, we present our analysis of the electronic states at the water/anatase interface, with focus on the states with energies close to the TiO2 valence band edge. As mentioned in the Introduction, DFT-GGA electronic structure calculations, on which our analysis is based, have important limitations in the description of such energy levels. Specifically, while in exact DFT the highest occupied KohnSham (KS) energy level is equal to the ionization potential,38 this is not usually so in practical DFT calculations. The difference between the highest KS energy and the ionization energy originates mostly from the self-interaction error of the approximate DFT functional used, which is generally larger for more localized states.29 With our DFT-GGA approach, we found that the position of the valence band edge of the clean anatase TiO2(101) surface relative to the vacuum level is -7.72 eV. This value is well within the range of experimental values derived from measurements of the work function in ultrahigh vacuum.39,40 Similar values are also obtained from measurements of the flat band potential for TiO2 in contact with an aqueous solution at low pH.9,12,14 Thus, in this case, the DFT-GGA error is small. The error is more difficult to quantify for the adsorbed water species, in part because their levels are broadened by the interaction with the surface. However, the computed projected densities of states (PDOS) for the anatase (101) surface with an adsorbed H2O molecule and OH- ion in vacuo (Figure S2 of the Supporting Information) show that the topmost occupied energy levels of these species are ∼0.9 and 0.4 eV below the TiO2 VBE, respectively. Analysis of low temperature (120-160 K) photoemission data41,42 for water on rutile (110) indicates that the highest energy levels of the adsorbed water species are ∼1.5 eV below the TiO2 VBE.13 Thus, the error in the computed alignments can be approximately estimated to be in the range 0.6-1.1 eV, depending on whether the observed “highest energy levels of the adsorbed water species” are attributed to adsorbed water molecules or OHions. Since water prefers to adsorb in molecular form on rutile (110) at low temperature,5,7,41,42 an error of about 0.6 eV seems more likely. Projected densities of states of selected configurations generated during Run38a are reported in Figure 6. For each configuration, we show the PDOS for the TiO2 slab, for the adsorbed OH-, and for the water environment (38 H2O molecules). We can see that the PDOS change significantly from one configuration to the other, indicating that fluctuations have an important effect on the electronic structure. It is clear, however, that the uppermost peak in the PDOS for the adsorbed OH- is generally above the upper edge of the PDOS of water and below the VBE of the TiO2 surface, as found for adsorbed H2O and OH- in vacuo. Analysis of a small number of configurations, as presented in Figure 6, is only partially informative however. To gain more (38) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, NY, 1989. (39) Onda, K.; Li, B.; Petek, H. Phys. Rev. B 2004, 70, 045415. (40) Imanishi, A.; Tsuji, E.; Nakato, Y. J. Phys. Chem. C 2007, 111, 2128. (41) Kurtz, R. L.; Stock-Bauer, R.; Madey, T. E.; Roman, E.; De Segovia, J. Surf. Sci. 1989, 218, 178. (42) Krischok, S.; H€offt, O.; G€unster, J.; Stultz, J.; Goodman, D. W.; Kempter, V. Surf. Sci. 2001, 495, 8.

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Figure 7. (a) Trajectory-averaged density of states from Run38a (solid blue line) and Run39w (dotted red line). The DOS for Run38a (Run39w) is averaged over 11 248 (17 198) snapshots. The time step between adjacent snapshots is 50 au (0.0012 ps). (b) Difference between the two DOS curves in (a). The valence band edge of TiO2 is set at -7.72 eV.

insight, we calculated trajectory-averaged densities of states (DOS), with the average performed over a large number (>104) of configurations taken from the Run38a trajectory. For comparison, we examined also the pure water/TiO2 interface using configurations from Run39w, which has 39 water molecules and therefore the same number of electronic states as Run38a. Figure 7a shows the trajectory-averaged densities of states (DOS) for the two FPMD simulations. They are almost identical except for a few features which are shown more clearly by the difference curve in Figure 7b. Here, we can see a broad band centered at ∼ -7.9 eV, that is, about 0.2 eV below the computed valence band edge of anatase TiO2, which originates from the adsorbed hydroxide ion. To confirm this attribution, we also investigated how the electronic structure of the adsorbed hydroxide differs from that of an OHsolvated in water. Following the same procedure used for Figure 7, we computed the trajectory-averaged DOS along Run77a and Run77b for the system with 77 H2O þ OH- and then determined the difference between the two curves (Figure S3 of the Supporting Information). This difference exhibits a series of positive and negative peaks, which indicate shifts and rearrangements of the energy levels of the adsorbed OH- relative to those of OHsolvated in water. Most remarkably, the curve has a feature at ∼ -7.9 eV which is almost identical to the band in Figure 7b for the system with 38 H2O þ OH- (see Figure S4 of the Supporting Information). This band can be thus considered as a distinct characteristic of the adsorbed hydroxide ion. An important feature of this OH- band is that it extends above the VBE of the TiO2 surface. A configuration contributing to the high energy tail of this band is shown in Figure 8, together with its corresponding PDOS. This configuration is extracted from the last, well equilibrated, part of Run38a; for example, it shows two H-bonds for the O* of the adsorbed OH-, and its total energy is well within the standard fluctuation range. In this configuration, DOI: 10.1021/la100672f

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Figure 8. (a) Structure, (b) HOMO charge density (in yellow), and (c) PDOS for a partially unsolvated configuration from Run38a. The HOMO is mainly on OH-. The PDOS for OH- (dotted blue line) is multiplied by a factor 10.

Figure 9. Energy (EHOMO) of the HOMO of the adsorbed OH- as a function of time during the Run38a trajectory. EHOMO is defined as the energy from which the integral of the OH- PDOS up to the Fermi energy is equal to 1. The dotted horizontal line at -7.72 eV indicates the position of the TiO2 valence band edge (VBE). Only the last, well-equilibrated part of the trajectory is considered, for a total of 104 instantaneous configurations. Of these, the fraction of configurations with EHOMO above the TiO2 VBE is 3.23%. The occurrence frequency of such configurations is 6.5 ps-1 and their average lifetime is ∼5 fs.

however, the O*-Ti5c bond length is quite large, ∼2.2 A˚, as if the bond to the surface was nearly broken. We found that this was typical of other configurations contributing to the high energy tail of Figure 7b as well. These configurations can be characterized as “poorly solvated” (or “partially unsolvated”) ones. The connection between a large O*-Ti5c bond length and the presence of OH- states above the TiO2 VBE is illustrated by calculations for an adsorbed OH- in vacuo (Figure S2c-h in the Supporting Information). The computed equilibrium O*-Ti5c bond length at T = 0 K in vacuo is 1.82 A˚. In this situation, the highest occupied molecular orbital (HOMO) for the surface with an adsorbed OH- remains almost completely localized on the surface oxygen atoms, with only a small contribution from the lone pair on the adsorbed OH-. Accordingly, the PDOS shows that the topmost occupied energy levels for the adsorbed OH- are below the anatase VBE. When the O*-Ti5c bond length is increased to 1.9 A˚, however, the HOMO becomes almost completely localized on the OH- lone pair, while the PDOS shows a well-defined OH- peak at the upper edge of the valence band. This trend becomes even clearer when the O*-Ti5c bond length is further increased to 2 A˚. In fact, by increasing the O*-Ti5c bond length, the OH- states become more similar to those of an isolated OH-, whose ionization potential in vacuo is very low, only 1.8 eV experimentally. We estimated the occurrence frequency (ν) and average lifetime (τ) of the “poorly solvated” configurations by analyzing the OH- partial densities of states for as many as 104 configurations (cf. Figure 9). We obtained ν ∼ 6.5  1012 s-1 11524 DOI: 10.1021/la100672f

and τ ∼ 5 fs. Not surprisingly, ν is of the order of a typical thermal frequency (kbT/h ∼ 6  1012 s-1 at 300 K), confirming that the poorly solvated configurations are thermally activated. As for the lifetime, we notice that it is of the order of ultrafast electron injection times in dye sensitized solar cells.43,44 This suggests that, although short, τ should be sufficient to allow for photoinduced charge transfer. Summarizing, analysis of the electronic structure along the FPMD trajectories provides evidence that thermal fluctuations can lead to poorly solvated configurations of the OH- ion where the topmost energy levels of this species are above the TiO2 VBE. Thus, when the system is exposed to UV light irradiation, this fluctuation-induced favorable energy alignment can provide the driving force for the transfer of the photogenerated holes in TiO2 to the adsorbed OH-, consistent with Marcus theory’s picture of electron transfer at the liquid/semiconductor interface.45,46 On the other hand, analogous (partially unsolvated) configurations for molecularly adsorbed water are not clearly observed within the time scale of our simulations, suggesting that direct photooxidation of this species on the TiO2 surface is more unlikely. While our DFT-GGA approach may overestimate the number of configurations where hole transfer to OH- can occur, the basic picture that emerges from our simulations has a solid physical basis and should hold independent of the approximate electronic structure used for the calculations.

4. Conclusion In this work, we have investigated the structure and electronic properties of solvated and adsorbed OH- at the interface between water and the stoichiometric anatase TiO2(101) surface using first principles molecular dynamics simulations. Our results show that a hydrated OH- anion prefers to adsorb on the stoichiometric anatase (101) surface than to be solvated in bulk water, consistent with the known pHZPC ∼ 5.5 for the water/TiO2 interface. The O atom of the adsorbed OH- (O*) forms generally two H-bonds with nearby water molecules, and the average Ti5c-O* bond length, ∼2 A˚, is considerably larger than the corresponding distance in vacuo. Analysis of the electronic structure provides interesting hints on the charge transfers that can occur at the interface when holes generated by UV light absorption are present in TiO2. In particular, we have found that while hole transfer from the anatase TiO2(101) surface to an adsorbed hydroxide ion cannot usually take place due to the unfavorable alignment of the energy levels, this alignement can change significantly as a (43) Huber, R.; Moser, J.-E.; Gratzel, M.; Wachtveitl, J. J. Phys. Chem. B 2002, 106, 6494. (44) Duncan, W. R.; Prezhdo, O. V. Annu. Rev. Phys. Chem. 2007, 58, 143. (45) Anderson, N. A.; Lian, T. Q. Annu. Rev. Phys. Chem. 2005, 56, 491. (46) Gao, Y. Q.; Georgievskii, Y.; Marcus, R. A. J. Chem. Phys. 2000, 112, 3358.

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result of thermal fluctuations, thus making this transfer possible. After hole transfer, however, the generated hydroxyl radical should migrate away from the surface in order to act as a strong oxidant, otherwise it can gain back an electron and become again an OH- species. Finally, water molecules adsorbed in undissociated form cannot act as electron donors for the anatase surface. Acknowledgment. This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences (DE-FG02-05ER15702). We

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Article

acknowledge the Keck Computational Materials Science Laboratory in Princeton for computing time. Supporting Information Available: Additional figures showing the planar average of the electrostatic potential, the structure and HOMO charge density and partial densities of states of adsorbed H2O and OH- in vacuo, the trajectory averaged densities of states from Run77a and Run77b, and the comparison between the difference density of state curves in Figures 7b and S4b. This material is available free of charge via the Internet at http://pubs.acs.org.

DOI: 10.1021/la100672f

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