Absorption Spectra of Trapped Holes in Anatase TiO2 - The Journal of

Article pubs.acs.org/JPCC

Absorption Spectra of Trapped Holes in Anatase TiO2 Paweł Zawadzki*,‡ Department of Physics, Center for Atomic-Scale Materials Design, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark ABSTRACT: Charge transport to surface reactive sites is a crucial step in any photocatalytic process. In the most popular photocatalystthe anatase TiO2−this step is complicated by the fact that photogenerated carriers can trap. Studies of charge trapping and transfer in anatase often employ transient absorption spectroscopy (TAS), but the understanding of the optical absorption due to trapped carriers in TiO2 is incomplete. On the basis of the generalized Δ selfconsistent field density functional theory (Δ-SCF DFT) calculations, we attribute the experimentally observed absorption band at 430−550 nm to the interpolaron transitions of the stable surface and subsurface O− centers and associate the blue shift of the spectra after the photoexcitation with holes migration to surfaces. We also suggest that subsurface hole trapping may contribute to generally lower photocatalytic performance of the anatase (101) surface compared to the (001) surface.

■

generated holes at 430−550 nm4,10,10,12,18,23−25 and a blue shift of the spectra within picoseconds after excitation.4,13,18,18,20,23,25,26

INTRODUCTION TiO2, while a chemically inert material in the dark, in the UV light becomes a strongly oxidizing photocatalyst. This property of TiO2 has been known for almost 100 years1 and has been extensively researched over the last four decades leading to a number of applications such as water and air purification systems or self-cleansing surfaces.2 The oxidative properties of TiO2 are delivered through photogenerated holes which are predominately trapped3,4they form O− small polarons localized on the oxygen p-like orbital perpendicular to the OTi3 building blocks of TiO2 (p⊥).5−7 Since hole trapping can have significant effects on photocatalytic performance (for instance, it may lead to morphology-dependent photocatalytic activity),8,9 understanding of the dynamics of trapped holes is necessary to assess the performance of TiO2 in various photocatalytic processes. Transient absorption spectroscopy (TAS)4,10−13 and electron paramagnetic resonance (EPR)3,14,15 are two techniques commonly used to study the charge trapping in TiO2. Only TAS, however, provides a subpicoseconds temporal resolution16,17 necessary to study processes such as ∼100 fs carrier trapping or picosecond carrier transport to surfaces.18−21 TAS spectra of photoexcited TiO2 samples reveal that both free and trapped carriers are present.4 The free carrier absorption is due to photogenerated electrons and can be explained with the Drude-Lorentz model (follows the λn power law).4,22 The absorption range attributed to trapped carriers has been deconvolved (by application of carrier scavenging agents such as CH3OH, Ag+, or Pt) into contributions from holes, 430−550 nm, and electrons, 700− 1000 nm.11,12,23 Here, we calculate optical interpolaron transition energies of holes trapped on oxygen lattice sites (O− centers) in bulk anatase TiO2 and in surface layers of the (101) and the (001) facades. The calculated optical absorption bands explain the experimentally observed strong optical absorption of photo© 2013 American Chemical Society

■

METHOD We performed DFT calculations with the revised Perdew− Burke−Ernzerhof (RPBE)27 exchange-correlation functional within the projector-augmented wave formalism implemented in the GPAW code.28 The wave functions/densities and potentials were described on a grid with a spacing of 0.2 Å. Atomic structures were defined by lattice vectors a⃗′ = 3a⃗, b⃗′ = 3b⃗, c′⃗ = 2c,⃗ for the bulk and for the (001) surface (eight-layer slab), and a⃗′ = (−a⃗ + c)⃗ , b⃗′ = −3b⃗, and c′⃗ = 3(a⃗ + c)⃗ for the (101) surface (six-layer slab), a⃗, b⃗, and c ⃗ being the vectors of the respective tetragonal crystallographic cells. All cells contain 216 atoms. The lattice constants were optimized: |a|⃗ = |b⃗| = 3.829, |c|⃗ = 9.744 Å.5 For surface slabs no periodic boundary condition in the direction normal to the surface and a vacuum layer of 5 Å were applied. The Brillouin zone was sampled with a 2 × 2 × 1 Monkhorst−Pack mesh which was found sufficient to converge absorption energies within 10 meV. To calculate optical transition energies of the O− centers, we employed Δ-SCF DFT.29 This simple extension of the conventional DFT can be used to calculate the total energy of a system with the electron density constrained to occupy a localized state, thus allows to circumvent the known failure of (semi)local DFT to describe O− small polarons.30,31 We previously applied this method to study O− states in the bulk5,32 and in surface layers8 of anatase and rutile TiO2. To form O− centers we removed the electron density of the oxygen Received: January 3, 2013 Revised: April 8, 2013 Published: April 10, 2013 8647

dx.doi.org/10.1021/jp400082u | J. Phys. Chem. C 2013, 117, 8647−8651

The Journal of Physical Chemistry C

Article

in the bulk anatase. The transition energy from the p⊥ to s state equals 15.4 eV, whereas to the two other p states equal 0.65− 1.61 eV. Thus, intrapolaron transitions, even if allowed, cannot account for the experimentally observed absorption of trapped holes in the range of 2.9−2.3 eV (430−550 nm). Therefore, in the remaining part of the article we focus on the interpolaron mechanism. Interpolaron Transitions. We consider interpolaron transitions from O− centers located in the bulk and in surfaces layers (the initial states I, see Figure 1) to neighboring oxygen lattice sites (the final states F). For the TiO2 bulk all oxygen lattice sites are equivalent; therefore, it is sufficient to consider transitions from one trapping site (I = X). Anatase has several stable surface terminations, and each surface layer contains up to two nonequivalent oxygen lattice sites. Since the trapping strength varies in surface layers and between different surface terminations,8 the number of possible transitions is large. Therefore, we limit our analysis to the most stable, the (101), and often reported as the most photocatalytically active, the (001), anatase surfaces. For these surfaces we consider the most stable trapping sites (see Figure 2): O, P, Q in (101) surface

p⊥ orbital expanded in Kohn−Sham states below the Fermi level occ

|ψ ⟩ =

∑ ⟨ψiKS|p⊥⟩|ψiKS⟩ i

(1)

from the total electron density n(r) =

∑ fN + 1 |ψiKS(r)|2 − |ψ (r)|2 i

(2)

where f N+1 is the Fermi−Dirac distribution with an electron added to the bottom of the conduction band to keep the systems neutral. The Kohn−Sham equations were then solved until self-consistency is achieved. The added electron remained delocalized over all Ti atoms and over two spin channels, thus its interaction with the O− states localized on different sites should be similar and thus should cancel in the calculated interpolaron absorption energies (the energy differences between neighboring O− states). The atomic structures with O− states were then relaxed until each force component of each atom decreases below 0.05 eV/Å. During geometry optimization, two bottom layers of the slabs were kept fixed. Optical transition energies were calculated as the total energy differences between the energies of the excited states and the ground state of the O− center calculated at the ground state atomic structure.

■

OPTICAL TRANSITIONS OF O− CENTERS O− centers in metal oxides absorb visible light according to two mechanisms: (a) an interpolaron transitionan optical charge transfer from a small polaron state localized on one site to a state localized on a neighboring site33,34 (see Figure 1)and Figure 2. Locations of the most stable O− centers X, O, P, Q, and R in anatase TiO2. Arrows indicate the strongest optical charge transfer paths (oscillator strength f > 10−3) to neighboring oxygen lattice sites A−E.

layers, positioned 0.5, 0.5, and 0.4 eV above the bulk valence band edge, respectively,8 and R on the (001) surface, positioned 1.3 eV above the bulk valence band edge. (The subsurface trapping centers in the (001) surface layers are much less stable compared to the R centerthe trapping energies are smaller by ≈1.0 eV.8) To denote optical charge transfer paths to the neighboring oxygen lattice sites F in the bulk, we use letters A−E, and paths that are nonequivalent in surface layers are supplemented with a number; e.g., A1 and A2 are equivalent in the bulk but are nonequivalent in surface layers. The transition energy ℏωIF is obtained as the total energy difference between systems with an electron hole confined to sites I and F at the equilibrium distortion associated with the site I (ρI) (see Figure 1)

Figure 1. Schematic energy diagram for an optical charge transfer transition between two O− states |I⟩ and |F⟩ localized on distinct sites I and F, respectively. Potential energy surfaces are displaced along the lattice coordinate ρ due to electron−lattice interaction. The interpolaron absorption bands arise due to optical transitions between vibrational states associated with |I⟩ and |F⟩; ℏωIF denotes zero phonon transition energy. ΔIF is the difference between hole trapping strengths on oxygen lattice sites I and F. In TiO2 bulk all oxygen lattice sites are equivalent, and therefore ΔIF = 0; in surface layers an increase in ΔIF increases absorption energies and barriers Eb for small-polaron hopping.

(b) an intrapolaron transitiona transition between crystal field split p orbitals associated with the same trapping center. While interpolaron transitions of O− centers lead to strong optical absorption features, intrapolaron transitions are largely forbidden due to symmetry rules, and their strength is determined by the s−p hybridization of oxygen orbitals.35,36 In TiO2, the s orbital of the oxygen contributes only weakly to the valence band, formed from the oxygen p states,5 as it lays ≈13 eV below the center of the valence band. Using Δ-SCF we calculated the intrapolaron transition energies of the O− center

ℏωIF = E F(ρI ) − E I(ρI )

(3)

The relative shift of potential energy surfaces (PESs) ΔIF is the energy difference between states |F⟩ and |I⟩ calculated at their equilibrium distortions ρF and ρI, respectively ΔIF = E F(ρF ) − E I(ρI )

(4)

To calculate absorption bands we assume harmonic approximation for PESs: EI(ρ) = 1/2ℏΩ(ρ + s/2)2 and EF(ρ) = 1/ 2ℏΩ(ρ + s/2)2 + ΔIF, where reduced coordinates ρ = (mΩ/ 8648

dx.doi.org/10.1021/jp400082u | J. Phys. Chem. C 2013, 117, 8647−8651

The Journal of Physical Chemistry C

Article

ℏ)1/2q apply (m and Ω are the mass and the angular frequency, respectively, along the effective mode q). At large relative displacement of the two PESs, s ≫ 1, EF can be treated classically, and the band shape GIF is a Gaussian centered at ℏωIF37 1/2

G IF(ω) = [wIF/π ]

2

1/2

exp[(ℏω − ℏωIF) wIF]

Table 1. Calculated Parameters for the Strongest (Oscillator Strength f > 10−3) Optical Charge Transfer Transitions from Sites I ∈ {X, O, P, R} to Neighboring Sites Fa

(5)

2

with wIF(T) = tanh(ℏΩ/2kT)/(sℏΩ) and ℏωIF = ℏΩs 2 /2 + ΔIF

(6)

The total absorption cross-section due to the small polaron center at I is a sum over possible charge transfer paths F weighted by their oscillator strength f IF σI(ω) ∝

∑ G IF(ω)fIF F

(7)

where f IF = [(2meωIF)/(3ℏ)]|μIF|2. The electronic transition moment between states |I⟩ and |F⟩, |μIF| = |⟨I|(−er)|F⟩|, can be approximated in the first order by35 |μIF | ≈ (et IFdIF)/(ℏωIF)

(8)

where dIF and tIF are the distance and the electronic coupling element, respectively, between sites I and F. To obtain the electron coupling tIF we construct the bonding and the antibonding combinations of hole orbitals p⊥ associated with sites I and F, (|+⟩ = (|I⟩ + |F⟩)/√2 and |−⟩ = (|I⟩ + |F⟩)/√2), and calculate the energy gap between systems with the hole density constrained to these orbitals (see eqs 1 and 2) at a nondistorted structure: tIF = |E+ − E−|/2. Table 1 summarizes the calculated transition energies for the strongest (f IF > 10−3) interpolaron transitions. The shortest paths A and B dominate optical absorption as the oscillator strength f IF is proportional to the electronic coupling tIF (eq 8) and electronic couplings increase exponentially with decreasing distance between interacting orbitals. For the same reason the A and B paths also dominate hole hopping transport in the anatase bulk.32,38 The symmetry of the interacting orbitals, however, also affects the electronic couplings, and therefore the decrease in values of the oscillator strength f IF with the increase in the distance dIF is not monotonic; e.g., transition A ← X is stronger than B ← X because the electronic coupling tXA > tXB despite the distance dXA > dXB. We note that the A and B paths are not possible for the R trapping center at the (001) surface, and therefore transitions from this surface are much weaker. As expected from eq 6 and Figure 1 the transition energies ℏωIF increase with the separation of trapping sites dIF and the relative trapping strengths ΔIF.

F←I

nF

dIF [Å]

ℏωIF [eV]

A←X B←X E←X

2 4 2

2.81 2.56 3.88

1.96 1.85 2.53

A1 ← O C1 ← O A1 ← P B1 ← P B2 ← P E1 ← P A1 ← Q A2 ← Q B1 ← Q B2 ← Q E1 ← Q E2 ← Q

1 2 1 2 2 1 1 1 2 2 1 1

2.62 3.01 2.63 2.85 2.81 3.96 2.48 2.49 2.84 2.84 3.85 3.81

3.11 3.04 2.70 2.61 2.67 3.08 2.52 2.35 2.40 2.50 2.78 2.95

E1 ← R E2 ← R

1 1

4.80 3.26

3.74 3.15

ΔIF [eV] Bulk 0.00 0.00 0.00 (101) Surface 0.92 0.72 0.50 0.26 0.45 0.16 0.34 0.20 0.11 0.12 −0.16 0.10 (001) Surface 0.00 0.00

tIF [eV]

f IF

0.41 0.29 0.11

3.8 × 10−1 1.7 × 10−1 4.5 × 10−2

0.32 0.04 0.32 0.21 0.16 0.09 0.30 0.32 0.19 0.20 0.09 0.10

1.3 2.7 1.5 7.7 4.4 2.4 1.2 1.6 6.8 7.2 2.6 3.1

0.04 0.04

5.0 × 10−3 2.7 × 10−3

× × × × × × × × × × × ×

10−1 10−3 10−1 10−2 10−2 10−2 10−1 10−1 10−2 10−2 10−2 10−2

a nF denotes the number of equivalent sites F; dIF is the distance between I and F; ℏωIF is the transitions energy; ΔIF is the displacement of the potential energy surfaces EF relative to EI on the energy scale; tIF is the electronic coupling; and f IF is the oscillator strength.

Figure 3. Calculated and experimental optical absorption spectra of the self-trapped holes in anatase TiO2. Absorption bands due to the X, O, P, Q, and R trapping centers (see Figure 2) are marked by shaded curves. The experimental spectra are marked with lines: solid, ref 10 (time resolution 50 ns); dashed, ref 11 (measured after 5 ms); dashdotted, ref 11 (measured after 20 ns); dotted, ref 12 (measured after 20 ms).

■

ABSORPTION SPECTRA Figure 3 shows the shapes of the absorption bands for holes trapped in the bulk and in surface layers of anatase TiO2 calculated at T = 300 K and with ℏΩ = 40 meV32 according to eq 3−7. The condition that is necessary to treat excited state PESs classically (eq 5) is met for all the transitions: s ∈ [10,14] ≫ 1. Since the total absorption spectra will depend on a particular sample morphology and the distribution of holes among available sites at a given time after the photogeneration, Figure 3 shows the positions of the bands on the energy scale rather than their relative intensities, and the bands’ maxima are aligned. Bulk centers (X) absorb at 550−800 nm and subsurface centers (P, Q) at 430−550 nm, whereas surface centers (O, R) absorb below 450 nm. This progression of the

absorption band energies is largely a consequence of the oscillatory behavior of the trapping strengths in surface layers.8 Differences between the trapping strengths at neighboring oxygen lattice sites increase from ΔIF = 0 in the anatase bulk, where all oxygen sites are equivalent, to ΔIF ≈ 0.5−1.0 eV in top surfaces layers (see Table 1 and ref 8). The increase in ΔIF increases absorption energies since ℏωIF = ℏΩs2/2 + ΔIF. Thus, hole migration toward the surface can be associated with a blue shift in transition energies. This result agrees with experimental observations: After hole trapping (50−200 fs after excitation18−21) the absorption spectra change within 1−3 ps from a 8649

dx.doi.org/10.1021/jp400082u | J. Phys. Chem. C 2013, 117, 8647−8651

The Journal of Physical Chemistry C

Article

wide featureless band to a broad peak at 550 nm18,20,25,26 and then shift to 450 nm within the next 20−100 ps.4,13,18,23,25 The shape then remains unchanged on a nanosecond time scale.4,13,18,23−25,39 Comparison of the calculated and the experimental data in Figure 3 indicates that nanoseconds to microseconds after the excitation holes occupy the surface/subsurface sites rather than the bulk sites. This explains the large sensitivity of the TAS and EPR spectra14,15,20 to sample morphology. Furthermore, a long absorption tail below 450 nm in experimental spectra suggests significant occupation of the subsurface trapping sites. Hole trapping in subsurface layers of TiO2 has also been observed in EPR measurements. Howe et al. pointed out that the EPR spectra change only slightly between deuterated and hydrated anatase samples14 and suggested the presence of subsurface hole trapping sites. This has important implications for the efficiency of photocatalytic processes on anatase, as holes trapped in subsurface layers are nonreactive. Such immobilization of holes can be caused by the increase in barrier heights for hole transfer due to differences in the trapping strength ΔIF in surface layers. For the anatase (101) surface, variations of the trapping strength are large,8 and for instance for the P subsurface site, barriers along paths A2 and B2 increase by ≈0.50 and 0.45 eV (see ΔIF in Table 1 and Figure 1) on top of the bulk values of 0.14 and 0.15 eV in ref 32 (or 0.14 and 0.59 eV in ref 38), respectively. For a barrier height Eb = 0.15 eV and an effective mode quantum ℏΩ = 40 meV,32 a single smallpolaron hop at T = 300 K occurs on average every τ ∼ (2π/ Ω)exp(Eb/kT) = 70 ps. However, for a barrier height of 0.60 eV such a transfer would take 20 mssignificantly longer than the typically femtosecond to picosecond electron transfer to reactants adsorbed on a semiconductor surface. We suggest that charge trapping in subsurface layers of anatase (101) can contribute to generally lower oxidative activity of this surface compared to the (001) surface.40 In the case of the (001) surface, the trapping strength profile is much smoother,8 thus no large barrier heights are expected for holes transport to reactive sites. Furthermore, the (001) surface offers the strongest hole trapping centers among anatase surfaces, thus it will serve as a sink for photogenerated holes.8 In fact, larger concentrations of trapped holes on the (001) surface compared to the (101) have been detected in EPR measurements.9 Holes on the (001) surface, however, are less oxidative, and an increase in their concentration may not always translate into an improvement in photocatalytic performance.

Present Address ‡

National Renewable Laboratory, Golden, Colorado 80401, USA. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The author wishes to thank Dr. Jun Yan and Dr. Georgios Tritsaris for proofreading of the manuscript. This work was supported by the Danish Center for Scientific Computing. Support from the Danish Council for Technology and Innovation’s FTP program and the Danish Council for Strategic Research though the HyCycle Center (No. 2104-070041) is acknowledged.

■

■

CONCLUSION In conclusion, interpolaron transitions of the O− centers in anatase TiO2 explain experimentally observed absorption of trapped holes: bulk centers absorb at 550−800 nm, subsurface centers at 430−550 nm, and surface centers below 450 nm. A picosecond blue shift of the anatase TAS spectra4,13,18,23,25 can be associated with migration of photogenerated holes to surface and subsurface sites. On the basis of the comparison between the calculated and the experimental optical absorption spectra, we suggest that trapping of holes in subsurface layers of the anatase (101) surface is a contributing factor to a generally lower photocatalytic activity of this surface compared to the (001) surface.

■

REFERENCES

(1) Goodeve, C. F.; Kitchener, J. A. The Mechanism of Photosensitisation by Solids. Trans. Faraday Soc. 1938, 34, 902−908. (2) Fujishima, A.; Zhang, X.; Tryk, D. A. TiO2 Photocatalysis and Related Surface Phenomena. Surf. Sci. Rep. 2008, 63, 515−582. (3) Berger, T.; Sterrer, M.; Diwald, O.; Knozinger, E.; Panayotov, D.; Thompson, T.; Yates, J. Light-Induced Charge Separation in Anatase TiO2 Particles. J. Phys. Chem. B 2005, 109, 6061−6068. (4) Tamaki, Y.; Furube, A.; Murai, M.; Hara, K.; Katoh, R.; Tachiya, M. Dynamics of Efficient Electron-Hole Separation in TiO2 Nanoparticles Revealed by Femtosecond Transient Absorption Spectroscopy Under the Weak-Excitation Condition. Phys. Chem. Chem. Phys. 2007, 9, 1453−1460. (5) Zawadzki, P.; Jacobsen, K. W.; Rossmeisl, J. Electronic Hole Localization in Rutile and Anatase TiO2 - Self-Interaction Correction in Delta-SCF DFT. Chem. Phys. Lett. 2011, 506, 42−45. (6) Di Valentin, C.; Selloni, A. Bulk and Surface Polarons in Photoexcited Anatase TiO2. J. Phys. Chem. Lett. 2011, 2, 2223−2228. (7) Yang, S.; Brant, A. T.; Halliburton, L. E. Photoinduced SelfTapped Hole Center in TiO2 Crystals. Phys. Rev. B 2010, 82, 035209− 035214. (8) Zawadzki, P.; Laursen, A. B.; Jacobsen, K. W.; Dahl, S.; Rossmeisl, J. Oxidative Trends of TiO2-Hole Trapping at Anatase and Rutile Surfaces. Energy Environ. Sci. 2012, 5, 9866−9869. (9) D’Arienzo, M.; Carbajo, J.; Bahamonde, A.; Crippa, M.; Polizzi, S.; Scotti, R.; Wahba, L.; Morazzoni, F. Photogenerated Defects in Shape Controlled TiO2 Anatase Nanocrystals: A Probe to Evaluate the Role of Crystals Facets in the Photocatalytic Processes. J. Am. Chem. Soc. 2011, 133, 17652−17611. (10) Yoshihara, T.; Katoh, R.; Furube, A.; Tamaki, Y.; Murai, M.; Hara, K.; Murata, S.; Arakawa, H.; Tachiya, M. Identification of Reactive Species in Photoexcited Nanocrystalline TiO2 Films by WideWavelength-Range (400−2500 nm) Transient Absorption Spectroscopy. J. Phys. Chem. B 2004, 108, 3817−3823. (11) Bahnemann, D. W.; Hilgendorff, M.; Memming, R. Charge Carrier Dynamics at TiO2 Particles: Reactivity of Free and Trapped Holes. J. Phys. Chem. B 1997, 101, 4265−4275. (12) Tang, J.; Durrant, J. R.; Klug, D. R. Mechanism of Photocatalytic Water Splitting in TiO2. Reaction of Water with Photoholes, Importance of Charge Carrier Dynamics, and Evidence for FourHole Chemistry. J. Am. Chem. Soc. 2008, 130, 13885−13891. (13) Furube, A.; Asahi, T.; Masuhara, H.; Yamashita, H.; Anpo, M. Direct Observation of a Picosecond Charge Separation Process in Photoexcited Platinum-Loaded TiO2 Particles by Femtosecond Diffuse Reflectance Spectroscopy. Chem. Phys. Lett. 2001, 336, 424−430. (14) Howe, R. F.; Gratzel, M. EPR Study of Hydrated Anatase Under UV Irradiation. J. Phys. Chem. 1987, 91, 3906−3909. (15) Dimitrijevic, N. M.; Saponjic, Z. V.; Rabatic, B. M.; Poluektov, O. G.; Rajh, T. Effect of Size and Shape of Nanocrystalline TiO2 on Photogenerated Charges. An EPR Study. J. Phys. Chem. C 2007, 111, 14597−14601.

AUTHOR INFORMATION

Corresponding Author

*Phone: +1 (303) 384 6444. E-mail: [email protected]. 8650

dx.doi.org/10.1021/jp400082u | J. Phys. Chem. C 2013, 117, 8647−8651

The Journal of Physical Chemistry C

Article

(37) Keil, T. Shapes of Impurity Absorption Bands in Solids. Phys. Rev. 1965, 140, A601−A617. (38) Deskins, N. A.; Dupuis, M. Intrinsic Hole Migration Rates in TiO2 from Density Functional Theory. J. Phys. Chem. C 2009, 113, 346−358. (39) Furube, A.; Asahi, T.; Masuhara, H.; Yamashita, H.; Anpo, M. Charge Carrier Dynamics of Standard TiO2 Catalysts Revealed by Femtosecond Diffuse Reflectance Spectroscopy. J. Phys. Chem. B 1999, 103, 3120−3127. (40) Liu, S.; Yu, J.; Jaroniec, M. Anatase TiO2 with Dominant HighEnergy 001 Facets: Synthesis, Properties, and Applications. Chem. Mater. 2011, 23, 4085−4093.

(16) Berera, R.; van Grondelle, R.; Kennis, J. Ultrafast Transient Absorption Spectroscopy: Principles and Application to Photosynthetic Systems. Photosynth. Res. 2009, 101, 105−118. (17) Zhang, J. Z. Interfacial Charge Carrier Dynamics of Colloidal Semiconductor Nanoparticles. J. Phys. Chem. B 2000, 104, 7239−7253. (18) Tamaki, Y.; Furube, A.; Katoh, R.; Murai, M.; Hara, K.; Arakawa, H.; Tachiya, M. Trapping Dynamics of Electrons and Holes in a Nanocrystalline TiO2 Film Revealed by Femtosecond Visible/NearInfrared Transient Absorption Spectroscopy. C. R. Chim. 2006, 9, 268−274. (19) Skinner, D. E.; Colombo, D. P.; Cavaleri, J. J.; Bowman, R. M. Femtosecond Investigation of Electron Trapping in Semiconductor Nanoclusters. J. Phys. Chem. 1995, 99, 7853−7856. (20) Murakami, Y.; Nishino, J.; Mesaki, T.; Nosaka, Y. Femtosecond Diffuse-Reflectance Spectroscopy of Various Commercially Available TiO2 Powders. Spectrosc. Lett. 2011, 44, 88−94. (21) Philip Colombo, D.; Roussel, K. A.; Saeh, J.; Skinner, D. E.; Cavaleri, J. J.; Bowman, R. M. Femtosecond Study of the Intensity Dependence of Electron-Hole Dynamics in TiO2 Nanoclusters. Chem. Phys. Lett. 1995, 232, 207−214. (22) Fox, M. Optical Properties of solids, 2nd ed.; Oxford Master Series in Condensed Matter Physics; Oxford Univ. Press: Oxford, 2010. (23) Tamaki, Y.; Furube, A.; Murai, M.; Hara, K.; Katoh, R.; Tachiya, M. Direct Observation of Reactive Trapped Holes in TiO 2 Undergoing Photocatalytic Oxidation of Adsorbed Alcohols: Evaluation of the Reaction Rates and Yields. J. Am. Chem. Soc. 2006, 128, 416−417. (24) Shkrob, I.; Sauer, M. Hole Scavenging and Photo-Stimulated Recombination of Electron−Hole Pairs in Aqueous TiO2 Nanoparticles. J. Phys. Chem. B 2004, 108, 12497−12511. (25) Tamaki, Y.; Hara, K.; Katoh, R.; Tachiya, M.; Furube, A. Femtosecond Visible-to-IR Spectroscopy of TiO2 Nanocrystalline Films: Elucidation of the Electron Mobility before Deep Trapping. J. Phys. Chem. C 2009, 113, 11741−11746. (26) Yang, X.; Tamai, N. How Fast is Interfacial Hole Transfer? In Situ Monitoring of Carrier Dynamics in Anatase TiO2 Nanoparticles by Femtosecond Laser Spectroscopy. Phys. Chem. Chem. Phys. 2001, 3, 3393−3398. (27) Hammer, B.; Hansen, L. B.; Norskov, J. K. Improved Adsorption Energetics Within Density Functional Theory Using Revised Perdew-Burke-Ernzerhof Functionals. Phys. Rev. B 1999, 59, 7413−7421. (28) Enkovaara, J.; et al. Electronic Structure Calculations with GPAW: A Real-Space Implementation of the Projector AugmentedWave Method. J. Phys.: Condens. Matter 2010, 22, 253202−253226. (29) Gavnholt, J.; Olsen, T.; Engelund, M.; Schiotz, J. Delta SelfConsistent Field Method to Obtain Potential Energy Surfaces of Excited Molecules on Surfaces. Phys. Rev. B 2008, 78, 075441−075451. (30) Laegsgaard, J.; Stokbro, K. Hole Trapping at Al Impurities in Silica: A Challenge For Density Functional Theories. Phys. Rev. Lett. 2001, 86, 2834−2837. (31) Lany, S.; Zunger, A. Polaronic Hole Localization and Multiple Hole Binding of Acceptors in Oxide Wide-Gap Semiconductors. Phys. Rev. B 2009, 80, 085202−085207. (32) Zawadzki, P.; Rossmeisl, J.; Jacobsen, K. W. Electronic Hole Transfer in Rutile and Anatase TiO2: Effect of a Delocalization Error in the Density Functional Theory on the Charge Transfer Barrier Height. Phys. Rev. B 2011, 84, 121203−121207. (33) Marcus, R. A. Electron Transfer Reactions in Chemistry. Theory and Experiment. Rev. Mod. Phys. 1993, 65, 599−610. (34) Emin, D. Optical Properties of Large and Small Polarons and Bipolarons. Phys. Rev. B 1993, 48, 13691−13702. (35) Schirmer, O. F. O-Bound Small Polarons in Oxide Materials. J. Phys.: Condens. Matter 2006, 18, R667−R704. (36) Schirmer, O. F. Holes Bound as Small Polarons to Acceptor Defects in Oxide Materials: Why Are Their Thermal Ionization Energies So High? J. Phys.: Condens. Matter 2011, 23, 334218−334225. 8651

dx.doi.org/10.1021/jp400082u | J. Phys. Chem. C 2013, 117, 8647−8651