Surface Polarons Reducing Overpotentials in the Oxygen Evolution

Letter Cite This: ACS Catal. 2018, 8, 5847−5851

pubs.acs.org/acscatalysis

Surface Polarons Reducing Overpotentials in the Oxygen Evolution Reaction Patrick Gono,* Julia Wiktor, Francesco Ambrosio, and Alfredo Pasquarello Chaire de Simulation à l’Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland S Supporting Information *

ABSTRACT: We investigate the stability of hole polarons at the rutile surface induced by electronegative adsorbates in the intermediate steps of the oxygen evolution reaction through hybrid density functional calculations. Applying the computational hydrogen electrode method, we find that hole polarons reduce the overpotential of the reaction-determining step leading to good agreement with experiment. The stability of the polarons is confirmed at the hydrated surface through a free energy study involving the explicit solvent. The occurrence of surface hole polarons is unrelated to the scaling relationships and offers an additional handle in the search for improved catalysts. KEYWORDS: surface hole polarons, oxygen evolution reaction, overpotential, oxygen dimer, rutile, TiO2 fficient photocatalytic water splitting remains elusive even after decades of research.1 The process can be split into two simultaneous reactions: the hydrogen evolution reaction, which takes place at the cathode, and the oxygen evolution reaction (OER) at the anode. While the former routinely reaches very high efficiencies,2 water splitting is limited by the kinetics of the latter.3 Various restrictions apply to the catalyst in order to facilitate the OER, most notably the size of the band gap, the band alignment with respect to the redox levels, and the chemical stability in aqueous environment.4−7 From a theoretical point of view, a common approach to describe the reaction is the computational hydrogen electrode (CHE) method developed by Norskøv, Rossmeisl et al.8 It allows one to calculate the Gibbs free energy differences corresponding to the reaction intermediates. The OER is split into four steps, each involving a proton-coupled electron transfer:

E

Titanium dioxide has been found to be a promising OER catalyst,12 attracting a vast body of research.13−18 Rutile TiO2 (r-TiO2), and especially its (110) facet, has been extensively studied as a benchmark system to understand the reaction.19−28 Using the CHE approach at the semilocal level of density functional theory (DFT), the first step of eq 1 was found to be the reaction-determining step with an overpotential of 0.8 eV.29 Cheng et al. calculated a similar value for this step using the thermodynamic integration method at the same level of theory.30 However, the application of hybrid functionals, a more advanced electronic structure method, results in an overpotential for the first step that is too high to be in accord with experiment.31 The mechanism behind the OER at the rutile surface is assumed to be as follows:32 a photon is captured in the material and an electron−hole pair is created consequently. The electron is conducted away from the anode. It has been shown that the holes form polarons that travel to the surface.33 The trapped hole then drives water dissociation, the initial step of the OER.34 Hole trapping (i.e., localization of hole states) in TiO2 has been studied previously.30,35−38 Wang et al.39 considered that OH species adsorbed on the surface were at the origin of hole generation. The OH covered surface is one of the intermediates in the proton-coupled electron transfer model of the OER. Strongly electronegative species such as these may take an electron from the slab, thereby effectively generating a

* + H 2O → OHads + H+ + e−, OHads → Oads + H+ + e−, Oads + H 2O → OOHads + H+ + e−, OOHads → * + O2g + H+ + e−,

(1)

where the asterisk (*) refers to an active surface site. Highthroughput screenings of potential catalysts have identified an interdependence of the free energy differences corresponding to the above reaction steps.9,10 This is referred to as the linear scaling relationship, which determines a restriction on the maximum efficiency of possible catalysts.11 © XXXX American Chemical Society

Received: March 21, 2018 Revised: May 23, 2018

5847

DOI: 10.1021/acscatal.8b01120 ACS Catal. 2018, 8, 5847−5851

Letter

ACS Catalysis hole. In turn, the hole could then lead to the formation of a polaron at the surface. In this Letter, we study the stability of surface hole polarons in the intermediates of the OER using hybrid functional theory. We assess the effect of these polarons on the free energies calculated via the computational hydrogen electrode method. Furthermore, we investigate the stability of these polarons at the hydrated surface adopting a free energy analysis and an explicit solvent. We first study the stability of polarons at OH, O, and OOH covered surfaces in vacuum. The simulation cells contain five layer slabs of the 4 × 2 (110) rutile surface, with adsorbates on the 5-fold coordinated titanium atoms on both sides of the slab,40 and a coverage of 0.25. We model the proton-coupled electron transfer steps through intermediates in globally neutral charge states. The use of symmetric configurations prevents the buildup of electric fields in the simulation cell. A hybrid functional, which partially corrects the self-interaction error, is employed to better describe the localization of the polaronic states.25,39,41 The hybrid functional simulations are carried out with the PBE042 functional, in which the fraction of Fock exchange is set to 16%, in order to reproduce the experimental band gap of 3.0 eV of r-TiO2.43 This setting is supported by a recent study in which it is shown that a hybrid functional reproducing the correct band gap generally also gives an accurate energetic description of polarons.44 Surface polarons consisting of O dimers are created by manually moving a surface plane oxygen and a neighboring bridge oxygen to a relative distance of 1.46 Å. Each polaron draws two positive charges, effectively leaving the adsorbates in a negatively charged state. The thermodynamic stability of the O−O dimer in the +2 charge state stems from the fact that this state is composed of two 3-fold coordinated O atoms in the charge state +1, which satisfy the octet rule. Hole O−O bipolarons have already been proposed in various bulk transition metal oxides, such as anatase TiO2, V2O5, and MoO3,45 but also in amorphous Al2O3.46,47 In our calculations, two polarons are created on each side of the slab in a symmetric manner. A detailed description of the DFT geometry optimization can be found in the Supporting Information (SI). For comparison, we also consider the case of •OH radicals on the surface. This can be realized by starting the relaxation from a configuration in which the Ti−O bonds between the surface and the adsorbates have slightly been elongated following ref 39. However, we find that this configuration is higher in energy by 0.29 eV per unit of trapped charge with respect to the O−O dimer polaron configuration. This implies that our hybrid functional scheme favors the occurrence of OH− rather than •OH. In comparison, the experimental characterization has so far been inconclusive in determining the relevant reaction intermediates,24,32,48 even though •OH radicals have been observed upon illumination.49,50 Figure 1 illustrates the relaxed surfaces with and without polarons. The figure also gives the DFT energy difference between the slab with polarons and the corresponding structure without polarons for the three intermediates (i.e., with OH, O, and OOH adsorbates). For both the OH and OOH covered surfaces, the structures with polarons are energetically more favorable, by as much as 1.58 eV per polaron in the case of OHads. For the oxygen covered surface, the adsorbed oxygen atom itself relaxes toward a position in which it forms a dimer with a surface plane oxygen.

Figure 1. Top view of the relaxed surface layer of the OER intermediates without polarons (top) and with polarons (bottom). Ti atoms are shown in gray, H atoms in white, and O atoms in red. The total energy differences per polaron (ΔEpol) of the OH, O, and OOH covered slabs with and without polarons are shown. A negative sign indicates that the polaron formation leads to a lower total energy.

To understand the effect of polaron formation on the electronic structure, we study projected densities of states (PDOS) for the relaxed structures with and without polarons. Figure 2 shows the density of states of the OH covered slab

Figure 2. Projected density of states (PDOS) calculated for the OH covered rutile slab without (blue) and with (red) polarons. The density is projected on surface plane oxygen atoms. The projected densities are normalized with respect to the number of surface oxygen atoms. The energies are referred to the highest occupied state.

projected on surface O atoms. In the absence of the polarons, we observe unoccupied levels inside the band gap localized on surface plane oxygen atoms, as well as on subsurface oxygen atoms. Upon the formation of the polarons, a sharp peak appears below the Fermi level (occupied levels). Likewise, we observe a relative increase in the PDOS at the bottom of the conduction band. The unoccupied states in the gap vanish. Hence, the creation of polarons stabilizes the system and pushes the unoccupied levels into the conduction band. A similar behavior is observed for the OOH covered surface. By taking into account surface polarons, we can quantify their effect on the energetics of the oxygen evolution reaction. Using the CHE approach, we calculate the free energy differences, ΔG1 through ΔG4, corresponding to the four proton-coupled electron transfer steps of water splitting given in eq 1. A detailed description of the method can be found in the Supporting Information. Our results are given in Table 1 and are illustrated in Figure 3. Nozik et al. estimated the experimental overpotential of the OER on TiO2 to lie between 0.9 and 1.1 eV.51 As seen in the work of Valdés et al.,29 calculations based on the RPBE functional52 result in overpotentials that agree with the experimental findings. Our 5848

DOI: 10.1021/acscatal.8b01120 ACS Catal. 2018, 8, 5847−5851

Letter

ACS Catalysis

where the reaction coordinate varies from ξ0 = 2.75 Å for the pristine structure to ξ1 = 1.46 Å corresponding to polaron formation. We perform MD runs for seven values of the constraint. A duration of 0.75 ps is sufficient for each of these runs to reach convergence. Figure 4 shows the free energy

Table 1. Free Energy Differences Corresponding to the Four Steps of the OERa previous (ref 29) present present present a

functional

polarons

ΔG1

ΔG2

ΔG3

ΔG4

RPBE RPBE PBE0 PBE0

no no no yes

2.20 2.09 2.75 1.96

1.47 1.31 1.01 1.80

1.55 1.63 2.22 1.84

−0.30 −0.18 −1.46 −1.09

Energies are given per active site and are in eV.

Figure 4. Free energy profile calculated by integrating the average forces for various fixed O−O distances.

curve obtained from the integral of the average forces (see Figure S2 in the SI). The free energy of the structure with the polaron is indeed lower, following the same trend observed for the total energies. We find a free energy difference of 1.29 ± 0.04 eV, to be compared with the value of 1.58 eV obtained above for the surface in vacuum within the CHE approach. The effect of the water solvent can thus be estimated to be about 0.3 eV. The calculated free energy profile also reveals that there is a barrier of 0.21 ± 0.03 eV for polaron formation at the hydrated surface. This free energy barrier makes spontaneous polaron formation improbable in MD evolutions lasting only a few picoseconds, consistent with our observations. However, this barrier is sufficiently low to allow for the thermal generation of surface polarons at room temperature. In summary, we demonstrated that the intermediates of the oxygen evolution reaction stabilize hole polarons at the rutile TiO2 surface. When polarons are considered, the calculated overpotential of the reaction-determining step is found to be lowered and to agree with experiment. The occurrence of polarons is material specific and affects the binding energies of the adsorbates. This effect is not considered in the linear scaling relationships, which limit the efficiency of the oxygen evolution reaction. Hence, polaron formation could partially overcome such limitations and should be systematically addressed in materials searches for the optimal catalyst.

Figure 3. Gibbs free energy steps corresponding to the intermediates of the OER on r-TiO2. The gray line indicates the standard potential of water splitting.

results at the RPBE level are consistent with this previous work,29 demonstrating the reliability of our setup. Next, we recalculate the free energies at the more advanced PBE0 level. As with the RPBE functional, the first step of the OER is the reaction-determining step. With the PBE0 functional, the overpotential of this step increases to 1.52 eV, well above the experimental range (0.9−1.1 eV).51 A similar discrepancy between measured and hybrid-functional overpotentials had been found previously and was attributed to localized charges associated with unidentified defects.31 Our calculations demonstrate that surface polaron formation indeed reduces the overpotential of the reaction-determining step to 0.73 eV, bringing the calculated result back in agreement with experimental observations.51 We now address the stability of surface polarons at the hydrated surface. To this end, we first carry out two molecular dynamics (MD) simulations at the hybrid functional level with explicit water solvent starting from different initial configurations with the OH adsorbate. In the first one the structure does not show any polaron, whereas four of them are present in the second one. More simulation details are given in the SI. Although the total energy of the structure with polarons is lower by about 1 eV per polaron, we do not observe spontaneous polaron formation over a MD duration of 3.5 ps (see SI). To properly assess the relative stability of the two structures, we hence perform a free energy analysis via the Blue Moon sampling scheme.53 We carry out a series of constrained MD simulations, in which the distance between two relevant surface oxygen atoms is varied. The reaction coordinate ξ thus corresponds to an O−O distance and the Lagrange multipliers λ associated with the constraint can be directly identified with the forces.53 The averages of the forces are used to calculate the free energy curve via54 ΔF =

∫ξ

ξ1

0

dξ⟨λ⟩ξ

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acscatal.8b01120. Computational parameters of the setups, description of the computational hydrogen electrode method and details on the study of the hydrated TiO2 surface (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: patrick.gono@epfl.ch. ORCID

Patrick Gono: 0000-0001-7451-0482 Julia Wiktor: 0000-0003-3395-1104

(2) 5849

DOI: 10.1021/acscatal.8b01120 ACS Catal. 2018, 8, 5847−5851

Letter

ACS Catalysis

(17) Di Valentin, C.; Fittipaldi, D. Hole Scavenging by Organic Adsorbates on the TiO2 Surface: A DFT Model Study. J. Phys. Chem. Lett. 2013, 4, 1901−1906. (18) Li, Y.-F.; Liu, Z.-P.; Liu, L.; Gao, W. Mechanism and Activity of Photocatalytic Oxygen Evolution on Titania Anatase in Aqueous Surroundings. J. Am. Chem. Soc. 2010, 132, 13008−13015. (19) Stecher, T.; Reuter, K.; Oberhofer, H. First-Principles FreeEnergy Barriers for Photoelectrochemical Surface Reactions: Proton Abstraction at TiO2(110). Phys. Rev. Lett. 2016, 117, 276001. (20) Zhang, D.; Yang, M.; Dong, S. Hydroxylation of the Rutile TiO2 (110) Surface Enhancing Its Reducing Power for Photocatalysis. J. Phys. Chem. C 2015, 119, 1451−1456. (21) Deskins, N. A.; Rousseau, R.; Dupuis, M. Localized Electronic States from Surface Hydroxyls and Polarons in TiO2(110). J. Phys. Chem. C 2009, 113, 14583−14586. (22) Deskins, N. A.; Rousseau, R.; Dupuis, M. Defining the Role of Excess Electrons in the Surface Chemistry of TiO2. J. Phys. Chem. C 2010, 114, 5891−5897. (23) Deskins, N. A.; Rousseau, R.; Dupuis, M. Distribution of Ti3+ Surface Sites in Reduced TiO2. J. Phys. Chem. C 2011, 115, 7562− 7572. (24) Nakamura, R.; Nakato, Y. Primary Intermediates of Oxygen Photoevolution Reaction on TiO2 (Rutile) Particles, Revealed by in Situ FTIR Absorption and Photoluminescence Measurements. J. Am. Chem. Soc. 2004, 126, 1290−1298. (25) Di Valentin, C.; Pacchioni, G.; Selloni, A. Electronic Structure of Defect States in Hydroxylated and Reduced Rutile TiO2 (110) Surfaces. Phys. Rev. Lett. 2006, 97, 166803. (26) Shibuya, T.; Yasuoka, K.; Mirbt, S.; Sanyal, B. A Systematic Study of Polarons Due to Oxygen Vacancy Formation at the Rutile TiO2 (110) Surface by GGA + U and HSE06 Methods. J. Phys.: Condens. Matter 2012, 24, 435504. (27) Chrétien, S.; Metiu, H. Electronic Structure of Partially Reduced Rutile TiO2(110) Surface: Where Are the Unpaired Electrons Located? J. Phys. Chem. C 2011, 115, 4696−4705. (28) Cheng, J.; Sprik, M. Aligning Electronic Energy Levels at the TiO2/H2O Interface. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 081406. (29) Valdés, Á .; Qu, Z.-W.; Kroes, G.-J.; Rossmeisl, J.; Nørskov, J. K. Oxidation and Photo-Oxidation of Water on TiO2 Surface. J. Phys. Chem. C 2008, 112, 9872−9879. (30) Cheng, J.; Liu, X.; Kattirtzi, J. A.; VandeVondele, J.; Sprik, M. Aligning Electronic and Protonic Energy Levels of Proton-Coupled Electron Transfer in Water Oxidation on Aqueous TiO2. Angew. Chem., Int. Ed. 2014, 53, 12046−12050. (31) Oberhofer, H.; Reuter, K. First-Principles Thermodynamic Screening Approach to Photo-Catalytic Water Splitting with CoCatalysts. J. Chem. Phys. 2013, 139, 044710. (32) Imanishi, A.; Okamura, T.; Ohashi, N.; Nakamura, R.; Nakato, Y. Mechanism of Water Photooxidation Reaction at Atomically Flat TiO2 (Rutile) (110) and (100) Surfaces: Dependence on Solution PH. J. Am. Chem. Soc. 2007, 129, 11569−11578. (33) Di Valentin, C.; Selloni, A. Bulk and Surface Polarons in Photoexcited Anatase TiO2. J. Phys. Chem. Lett. 2011, 2, 2223−2228. (34) Di Valentin, C. A Mechanism for the Hole-Mediated Water Photooxidation on TiO2 (101) Surfaces. J. Phys.: Condens. Matter 2016, 28, 074002. (35) 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. (36) Ji, Y.; Wang, B.; Luo, Y. Location of Trapped Hole on RutileTiO2 (110) Surface and Its Role in Water Oxidation. J. Phys. Chem. C 2012, 116, 7863−7866. (37) Varley, J. B.; Janotti, A.; Franchini, C.; Van de Walle, C. G. Role of Self-Trapping in Luminescence and p-Type Conductivity of WideBand-Gap Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2012, 85, 081109. (38) Salvador, P. On the Nature of Photogenerated Radical Species Active in the Oxidative Degradation of Dissolved Pollutants with TiO2

Francesco Ambrosio: 0000-0002-6388-9586 Alfredo Pasquarello: 0000-0002-9142-2799 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank A. Bouzid and Z. Guo for useful interactions. This work has been realized in relation to the National Center of Competence in Research (NCCR) “Materials’ Revolution: Computational Design and Discovery of Novel Materials (MARVEL)” of the SNSF. We used computational resources of the Swiss National Supercomputing Centre (CSCS) and of the Scientific IT and Application Support Center (SCITAS) of Ecole Polytechnique Fédérale de Lausanne.

■

REFERENCES

(1) McCrory, C. C. L.; Jung, S.; Peters, J. C.; Jaramillo, T. F. Benchmarking Heterogeneous Electrocatalysts for the Oxygen Evolution Reaction. J. Am. Chem. Soc. 2013, 135, 16977−16987. (2) Seh, Z. W.; Kibsgaard, J.; Dickens, C. F.; Chorkendorff, I.; Nørskov, J. K.; Jaramillo, T. F. Combining Theory and Experiment in Electrocatalysis: Insights into Materials Design. Science 2017, 355, eaad4998. (3) Walter, M. G.; Warren, E. L.; McKone, J. R.; Boettcher, S. W.; Mi, Q.; Santori, E. A.; Lewis, N. S. Solar Water Splitting Cells. Chem. Rev. 2010, 110, 6446−6473. (4) Guo, Z.; Ambrosio, F.; Chen, W.; Gono, P.; Pasquarello, A. Alignment of Redox Levels at Semiconductor-Water Interfaces. Chem. Mater. 2018, 30, 94−111. (5) Tentu, R. D.; Basu, S. Photocatalytic Water Splitting for Hydrogen Production. Curr. Opin. Electrochem. 2017, 5, 56−62. (6) Suen, N.-T.; Hung, S.-F.; Quan, Q.; Zhang, N.; Xu, Y.-J.; Ming Chen, H. Electrocatalysis for the Oxygen Evolution Reaction: Recent Development and Future Perspectives. Chem. Soc. Rev. 2017, 46, 337− 365. (7) Montoya, J. H.; Seitz, L. C.; Chakthranont, P.; Vojvodic, A.; Jaramillo, T. F.; Nørskov, J. K. Materials for Solar Fuels and Chemicals. Nat. Mater. 2017, 16, 70−81. (8) Nørskov, J. K.; Rossmeisl, J.; Logadottir, A.; Lindqvist, L.; Kitchin, J. R.; Bligaard, T.; Jónsson, H. Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode. J. Phys. Chem. B 2004, 108, 17886−17892. (9) Rossmeisl, J.; Qu, Z. W.; Zhu, H.; Kroes, G. J.; Nørskov, J. K. Electrolysis of Water on Oxide Surfaces. J. Electroanal. Chem. 2007, 607, 83−89. (10) Christensen, R.; Hansen, H. A.; Dickens, C. F.; Nørskov, J. K.; Vegge, T. Functional Independent Scaling Relation for ORR/OER Catalysts. J. Phys. Chem. C 2016, 120, 24910−24916. (11) Man, I. C.; Su, H.-Y.; Calle-Vallejo, F.; Hansen, H. A.; Martínez, J. I.; Inoglu, N. G.; Kitchin, J.; Jaramillo, T. F.; Nørskov, J. K.; Rossmeisl, J. Universality in Oxygen Evolution Electrocatalysis on Oxide Surfaces. ChemCatChem 2011, 3, 1159−1165. (12) Fujishima, A.; Honda, K. Electrochemical Photolysis of Water at a Semiconductor Electrode. Nature 1972, 238, 37. (13) Hashimoto, K.; Irie, H.; Fujishima, A. TiO2 Photocatalysis: A Historical Overview and Future Prospects. J. Appl. Phys. 2005, 44, 8269. (14) Chen, J.; Li, Y.-F.; Sit, P.; Selloni, A. Chemical Dynamics of the First Proton-Coupled Electron Transfer of Water Oxidation on TiO2 Anatase. J. Am. Chem. Soc. 2013, 135, 18774−18777. (15) Selcuk, S.; Selloni, A. Facet-Dependent Trapping and Dynamics of Excess Electrons at Anatase TiO2 Surfaces and Aqueous Interfaces. Nat. Mater. 2016, 15, 1107−1112. (16) Savory, D. M.; McQuillan, A. J. IR Spectroscopic Behavior of Polaronic Trapped Electrons in TiO2 Under Aqueous Photocatalytic Conditions. J. Phys. Chem. C 2014, 118, 13680−13692. 5850

DOI: 10.1021/acscatal.8b01120 ACS Catal. 2018, 8, 5847−5851

Letter

ACS Catalysis Aqueous Suspensions: A Revision in the Light of the Electronic Structure of Adsorbed Water. J. Phys. Chem. C 2007, 111, 17038− 17043. (39) Wang, D.; Wang, H.; Hu, P. Identifying the Distinct Features of Geometric Structures for Hole Trapping to Generate Radicals on Rutile TiO2 (110) in Photooxidation Using Density Functional Theory Calculations with Hybrid Functional. Phys. Chem. Chem. Phys. 2015, 17, 1549−1555. (40) Mom, R. V.; Cheng, J.; Koper, M. T. M.; Sprik, M. Modeling the Oxygen Evolution Reaction on Metal Oxides: The Infuence of Unrestricted DFT Calculations. J. Phys. Chem. C 2014, 118, 4095− 4102. (41) Spreafico, C.; VandeVondele, J. The Nature of Excess Electrons in Anatase and Rutile from Hybrid DFT and RPA. Phys. Chem. Chem. Phys. 2014, 16, 26144−26152. (42) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods Without Adjustable Parameters: The PBE0Model. J. Chem. Phys. 1999, 110, 6158−6170. (43) Kavan, L.; Grätzel, M.; Gilbert, S. E.; Klemenz, C.; Scheel, H. J. Electrochemical and Photoelectrochemical Investigation of SingleCrystal Anatase. J. Am. Chem. Soc. 1996, 118, 6716−6723. (44) Miceli, G.; Chen, W.; Reshetnyak, I.; Pasquarello, A. Nonempirical Hybrid Functionals for Band Gaps and Polaronic Distortions in Solids. Phys. Rev. B: Condens. Matter Mater. Phys. 2018, 97, 121112. (45) Chen, S.; Wang, L.-W. Double-Hole-Induced Oxygen Dimerization in Transition Metal Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 014109. (46) Århammar, C.; Pietzsch, A.; Bock, N.; Holmström, E.; Araujo, C. M.; Gråsjö, J.; Zhao, S.; Green, S.; Peery, T.; Hennies, F.; Amerioun, S.; Föhlisch, A.; Schlappa, J.; Schmitt, T.; Strocov, V. N.; Niklasson, G. A.; Wallace, D. C.; Rubensson, J.-E.; Johansson, B.; Ahuja, R. Unveiling the Complex Electronic Structure of Amorphous Metal Oxides. Proc. Natl. Acad. Sci. U. S. A. 2011, 108, 6355−6360. (47) Guo, Z.; Ambrosio, F.; Pasquarello, A. Oxygen Defects in Amorphous Al2O3: A Hybrid Functional Study. Appl. Phys. Lett. 2016, 109, 062903. (48) Nakabayashi, Y.; Nosaka, Y. OH Radical Formation at Distinct Faces of Rutile TiO2 Crystal in the Procedure of Photoelectrochemical Water Oxidation. J. Phys. Chem. C 2013, 117, 23832−23839. (49) Anpo, M.; Shima, T.; Kubokawa, Y. ESR and Photoluminiscence Evidence for the Photocatalytic Formation of Hydroxyl Radicals on Small TiO2 Particles. Chem. Lett. 1985, 14, 1799−1802. (50) Murakami, Y.; Kenji, E.; Nosaka, A. Y.; Nosaka, Y. Direct Detection of OH Radicals Diffused to the Gas Phase from the UVIrradiated Photocatalytic TiO2 Surfaces by Means of Laser-Induced Fluorescence Spectroscopy. J. Phys. Chem. B 2006, 110, 16808−16811. (51) Nozik, A. J. Photoelectrolysis of Water Using Semiconducting TiO2 Crystals. Nature 1975, 257, 383−386. (52) Hammer, B.; Hansen, L. B.; Nørskov, J. K. Improved Adsorption Energetics Within Density-Functional Theory Using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 7413−7421. (53) Sprik, M.; Ciccotti, G. Free Energy from Constrained Molecular Dynamics. J. Chem. Phys. 1998, 109, 7737−7744. (54) Ciccotti, G.; Ferrario, M. Rare Events by Constrained Molecular Dynamics. J. Mol. Liq. 2000, 89, 1−18.

5851

DOI: 10.1021/acscatal.8b01120 ACS Catal. 2018, 8, 5847−5851