Ab Initio Simulation of the Absorption Spectra of Photoexcited Carriers

Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States. J. Phys. Chem. Lett. , 2016, 7 (18), pp 3597–3602. DOI: 1...
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Ab Initio Simulation of the Absorption Spectra of Photoexcited Carriers in TiO2 Nanoparticles Francesca Nunzi,*,†,‡ Filippo De Angelis,†,§ and Annabella Selloni*,∥ †

Computational Laboratory of Hybrid/Organic Photovoltaics (CLHYO), CNR-ISTM, via Elce di Sotto 8, I-06123 Perugia, Italy Department of Chemistry, Biology and Biotechnologies, Universitá degli Studi di Perugia, via Elce di Sotto 8, I-06123 Perugia, Italy § CompuNet, Istituto Italiano di Tecnologia, Via Morego 30, 16163 Genova, Italy ∥ Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States ‡

S Supporting Information *

ABSTRACT: We investigate the absorption spectra of photoexcited carriers in a prototypical anatase TiO2 nanoparticle using hybrid time dependent density functional theory calculations in water solution. Our results agree well with experimental transient absorption spectroscopy data and shed light on the character of the transitions. The trapped state is always involved, so that the SOMO/SUMO is the initial/final state for the photoexcited electron/hole absorption. For a trapped electron, final states in the low energy tail of the conduction band correspond to optical transitions in the IR, while final states at higher energy correspond to optical transitions in the visible. For a trapped hole, the absorption band is slightly blue-shifted and narrower in comparison to that of the electron, consistent with its deeper energy level in the band gap. Our calculations also show that electrons in shallow traps exhibit a broad absorption in the IR, resembling the feature attributed to conductive electrons in experimental spectra.

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to assign the TAS optical transitions to individual electronic excited states, it is possible to infer the characteristic features of photogenerated carriers from the position in energy and the shape of the TAS bands. The position in energy of the peaks reflects the trap depth of the charge carriers, so that a higher (lower) energy excitation corresponds to a deeper (shallower) trapped charge carrier. Moreover, the presence of a narrow band indicates charge carriers with a locally trapped character, whereas a broad band suggests more delocalized electronic states. In the visible region, the TAS traces of photogenerated electrons generally show a maximum at about 650 nm in TiO2 colloidal solutions13 and at slightly longer wavelength (770 nm)5 in TiO2 NPs. This absorption peak is attributed to trapped electrons and is associated with the excitation from trap sites to higher energy levels in the CB. For trapped holes, there are some differences between the TAS spectra reported by different research groups. By laser flash photolysis measurements on colloidal TiO2 suspensions, Bahnemann et al.13 identified two different types of trapped holes, namely, deep and shallow holes, associated with transient absorption peaks at 450 and 600 nm, respectively. Though deeply trapped holes are long-lived and unreactive, shallow holes are reactive and have a

emiconductor photocatalysis is a promising approach to solar energy conversion and environmental remediation. Because of their low cost and high stability, TiO2 nanoparticles (NPs), typically in the anatase form, are widely used for these applications. Photocatalysis is based on the generation of charge carriers by the absorption of UV−visible light, followed by their diffusion to the surface and their transfer to adsorbed species. Photogenerated carriers in TiO2 NPs have been studied by various experimental techniques, including electron spin resonance, laser-induced fluorescence, time-resolved second harmonic generation,1,2 scanning tunneling microscopy,3,4 and transient absorption spectroscopy (TAS).5−12 In particular, TAS measurements show that both “conductive” and trapped carriers are present in photoexcited TiO2 NPs. In the near-IR range (1000−2500 nm), the absorbance (A) increases at longer wavelengths (λ).5 This behavior can be reproduced using the Drude-Lorentz model (A ∝ λn), characteristic of free electrons. Thus, the absorption in the IR is assigned to intraband transitions from the bottom of the conduction band (CB) to higher levels in the same band. In the visible range, a broad absorption band is observed and attributed to trapped carriers.5,6,9−11 Because the TAS spectra of trapped electrons and holes overlap in the visible region, suitable scavengers are employed to distinguish their individual contributions.5−12 By this procedure, the TAS signals have been separated into contributions from trapped electrons at longer wavelengths and trapped holes at shorter wavelengths. Though it is difficult © XXXX American Chemical Society

Received: July 12, 2016 Accepted: August 29, 2016

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Figure 1. From left to right: frontier MOs energy levels for the (TiO2)38 NP in the ground state S0 (gray), individual electron (e−, green) and hole (h+, pink) polaronic states both in the unrelaxed S0 (dark) and relaxed D1,e/ D1,h (light) geometries, calculated at the B3LYP/6-31G* level in water solution. At the bottom, the frontier MOs energies (in electronvolts) are shown.

containing a fraction of exact Hartree−Fock exchange) are essential to properly describe the self-trapping of charge carriers in TiO2 NPs,16 whereas TDDFT offers a rigorous framework for the description of excited states and optical transitions in fairly large systems such as the TiO2 NPs studied here. As a model of a TiO2 NP, we consider a stoichiometric (TiO2)38 cluster exposing majority (101) surfaces.17 This cluster has been extensively characterized in previous studies18−21 and shown to have electronic and optical properties comparable to those of periodic TiO2 models.22 As in previous work,16 we examine the properties of a single photoexcited electron (e−)/ hole (h+) by considering the negatively/positively charged (TiO2)38−/(TiO2)38+ cluster, respectively. Starting from the equilibrium geometry of the neutral (TiO2)38 NP (hereafter S0 geometry), we allow the atomic positions of (TiO2)38− and (TiO2)38+ to fully relax in the corresponding open-shell doublet states. We then compute the electronic excitations of the (TiO2)38− and (TiO2)38+ clusters in both the initial S0 and fully relaxed geometries (D1,e and D1,h hereafter) within TDDFT using the B3LYP functional.23,24 The effect of water has been included by means of a polarizable continuum solvation model,25 rather than by explicitly considering the addition of water molecules on the cluster’s surface. Accordingly, the present simulation does not include the electronic transitions of holes trapped at terminal OH groups, as described in ref 15. The results of these studies allow us to make direct contact with experimental TAS spectra and provide insights into the nature of the excited states involved in photocatalytic processes. It is worth noting that the (TiO2)38 cluster employed in this work is very small in comparison to the typical anatase nanoparticles used in experiments (∼20 nm) and is structurally quite

high oxidation potential. On the basis of TAS measurements on TiO2 nanocrystalline films over a wide spectral range (400− 2500 nm), Yoshishara et al.5 assigned a peak at 520 nm to trapped holes, whereas a low-intensity band in the near IR at ca. 1200 nm was also generically attributed to holes. Despite the interest in photocatalysis, only a few theoretical studies on the absorption spectra of photoexcited TiO2 have been reported, due to significant modeling difficulties. The absorption of trapped holes in the bulk and at the (001) and (101) surfaces of anatase was studied by Zawadki.14 This author assigned the broad band from 300 to 800 nm to interpolaron transitions, from a hole state localized on an O− site to an adjacent localized state, the excitation energy increasing with increasing distance between neighboring O sites. Cheng et al.15 investigated the nature of trapped holes at the rutile (110)−water interface by ab initio molecular dynamics simulations. They concluded that holes can be trapped at the terminal TiOH• and TiO•− groups, for which they computed vertical transition energies (from the valence band (VB) maximum) of 2.40 eV (517 nm) and 2.76 eV (449 nm), respectively, consistent with the experimental TAS peaks at 2.4 and 2.8 eV (520 and 450 nm).5,7,12,13 However, a detailed computational spectroscopy study of photogenerated carriers in TiO2 NPs models including electron/hole interaction and solvation effects is still missing. In this work, we investigate the absorption spectra of a single excess electron and a single photoexcited hole in a prototypical anatase TiO2 NP, using hybrid time dependent density functional theory (TDDFT) calculations. This approach represents an optimal compromise between accuracy and computational cost: hybrid functionals (i.e., DFT functionals 3598

DOI: 10.1021/acs.jpclett.6b01517 J. Phys. Chem. Lett. 2016, 7, 3597−3602

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Figure 2. DOS profile of the top VB and bottom CB of the (TiO2)38 NP in the e− and h+ polaronic states both in the unrelaxed S0 (a, b, respectively) and relaxed D1,e/D1,h (c/d) geometries, calculated at the B3LYP/6-31G* level in water solution. A Gaussian broadening σ = 0.18 eV was used. The insets show the electron densities (isovalue = 0.01 e/au3) of the SOMO and SUMO of e− and h+, respectively.

highlight not only the localization of the SOMO/SUMO in the band gap but also a change in the distribution of the states in the tail of the CB/VB upon relaxation. In the unrelaxed S0 geometry, the SOMO/SUMO (Figure 2 a/b) are essentially part of the CB/VB tails of the DOS, which appear constituted by a set of relatively well-spaced and localized states. Conversely, in the relaxed D1,e and D1,h geometries (Figure 2 c,d) the SOMO and SUMO lie deep in the band gap and become more localized, as clearly shown by the insets. At the same time, the states constituting the CB and VB tails of the DOS become closer in energy, showing also a less localized character with respect to the unrelaxed geometry. Our results for the optical spectra of excess electrons and holes are summarized in Figure 3. Here, we compare the computed spectra of the (TiO2)38− and (TiO2)38+ clusters in the unrelaxed S0 and relaxed D1,e/ D1,h geometries (b) to experimental TAS spectra of Furube and co-workers (a).6,9,25,30 As a reference, the absorption spectrum of the neutral (TiO2)38 NP is presented in Figure S1 of the Supporting Information. We can see clear differences between the computed spectra of the charged clusters in the unrelaxed and relaxed structures. The latter exhibit quite narrow absorption bands centered in the visible, whereas the (TiO2)38−/(TiO2)38+ clusters in the S0 geometry give rise to broad and red-shifted bands, with a continuous increase of the intensity up to the IR region. In particular, the absorption spectrum of a trapped electron consists of a relatively large band extending from 400 to 1200 nm, while that of trapped holes exhibits a narrower band between 300 and 600 nm, slightly blue-shifted and with higher intensity with respect to the electron band. By contrast, the spectra of the unrelaxed carriers show a low-intensity shoulder between 600 and 800 nm that evolves in a broad band whose intensity increases with wavelength from 800 nm up to IR region. In addition, analysis of the composition of the

distorted in comparison to crystalline anatase. As a result, it has only deep trap states, whereas real nanoparticles have both shallow and deep trap states. In particular, it is now widely accepted that bulk-like polaronic states are very shallow in crystalline anatase.26 Therefore, the computed spectra of (TiO2)38−/(TiO2)38+ clusters in the unrelaxed S0 geometry are meant to mimic the experimental transient absorption spectra of charge carriers in shallow traps, which are absent in our reduced model. Figure 1 shows the frontier MOs’ energy levels of the neutral (TiO2)38 cluster in its S0 equilibrium geometry and the charged (TiO2)38− and (TiO2)38+ clusters in both the unrelaxed S0 and relaxed D1,e/ D1,h geometries. We find a HOMO−LUMO gap of 4.53 eV for the neutral NP, a value much larger than the experimental band gap (3.2 eV) of anatase.27 Overestimation of band gaps is a typical drawback of the B3LYP functional;28,29 for this reason, our focus will be on the electronic structure changes upon the addition of an e− and h+, rather than on the absolute value of the energy gap. For the (TiO2)38− and (TiO2)38+ clusters, the excess electron and hole states are associated with the highest singly occupied MO (SOMO) and lowest singly unoccupied MO (SUMO), respectively. In the S0 geometry, the SOMO (SUMO) of the anionic (cationic) cluster lies only 0.30 eV below the LUMO (0.20 eV above the HOMO) in the NP band gap. Upon structural relaxation, these SOMO and SUMO shift dramatically, resulting in deep energy levels at 1.94 eV below the LUMO and 2.59 eV above the HOMO, respectively. The hole SUMO state is deeper in energy than the electron SOMO, Figure 1, suggesting that the corresponding hole state is more localized than that of the electron. The density of states (DOS) of the top of the VB and bottom of the CB for (TiO2)38−/ (TiO2)38+ in the S0 and D1,e/ D1,h geometries are reported in Figure 2. The DOS profiles 3599

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relative to experiment, our computed absorption spectra for the relaxed D1,e/ D1,h geometries agree quite well with the TAS spectra6,7,25,30 attributed to trapped carriers. In particular, the computed absorption band of trapped electrons is broader and red-shifted by ca. 0.40 eV with respect to that of trapped holes, consistent with the differences in line-shape and the relative energy shift of 0.70 eV observed in experiment.6,10,30 The relative shift between electron and hole absorption bands can be understood by considering the energy levels of the trapped states; because trapped holes give rise to deeper levels in comparison to trapped electrons (Figure 1), the optical excitations involving excess electrons occur at larger wavelengths with respect to those involving excess holes. As for the relative intensities of the electron and hole contributions, the computed excitations of trapped electrons are weaker than those of trapped holes, indicating a less effective spatial overlap for the electron’s Ti 3d states than for the hole’s O 2p orbitals. As mentioned above, the computed spectra of unrelaxed electrons, representing shallow traps in our study, exhibit two contributions: a shoulder with low intensity in the visible around 600−800 nm, and a broad absorption band with intensity increasing with increasing wavelength up to the IR (Figure 3b). The latter is clearly reminiscent of the spectrum experimentally assigned to conductive electrons,6,10,30 but its intensity is significantly higher than the experimental one, suggesting that partial relaxation of the “conductive electrons” is actually present in the experiment. The blue shift of the absorption band assigned to trapped carriers with respect to unrelaxed carriers can be related to the deeper energy levels of the SOMO and SUMO in the relaxed D1,e/ D1,h geometry vs those in the unrelaxed S0 one. To obtain further insights into the nature of the electronic excitations, we computed the electron density difference between excited and ground states for selected excitations of the anionic (TiO2)38− and cationic (TiO2)38+ clusters in the unrelaxed and relaxed geometries, Figure 4. For the electron, the excitations in the relaxed D1,e geometry (Figure 4c) are strongly localized in the IR (excitation D3), with the excited electron and hole in close proximity, whereas the electron density progressively spreads to the entire TiO2 NP at higher energy in the visible (excitation D17). The excitations in the unrelaxed S0 geometry (Figure 4a) show some delocalization of the electron density both in the IR and visible. Similarly, the excitations of the (TiO2)38+ cluster in the D1,h geometry (Figure 4d) are well localized in the IR (excitation D1), and spread to the entire TiO2 NP at higher energy (excitation D44), whereas they are always partially delocalized in the S0 geometry (Figure 4a). These results can be rationalized on the basis of the MOs composition of the initial and final states (see Supporting Information). In summary, the assignment of the optical transitions derived by our TDDFT calculations sheds light on the character of the TAS spectra of photoexcited charge carriers. Our results show that the trapped state is always involved in the absorption, that is, the SOMO is the initial state for the photoexcited electron absorption, whereas the SUMO is the final state for the photoexcited hole. For a trapped electron, optical transitions in the IR range correspond to final states in the low energy tail of the CB, whereas optical transitions in the visible correspond to final states at higher energy in the CB. For the absorption spectrum of a trapped hole a similar picture holds, but because the SUMO lies quite high in energy wrt the VB maximum (deep trap), the optical transitions are blue-shifted with respect

Figure 3. (a) Experimental TAS spectra after high intensity excitation, reprinted from ref 6 with permission from Elsevier, copyright 2010. (b) Computed absorption spectra of the (TiO2)38− and (TiO2)38+ clusters, representing an excess electron and excess hole, respectively, in the relaxed D1,e/ D1,h (triangle-shaped orange solid/green dashed curve) and unrelaxed S0 geometries (blue dashed/green dotted curves). The solid blue line is the sum of the trapped electron, trapped hole, and conductive electron contributions.

computed excitations shows that for the electron the initial state is always the SOMO, whereas the final states are among the unoccupied MOs above the LUMO, formally constituting the CB (see Figure 2). Similarly, for the hole, the final state is always the SUMO, whereas the initial state is one of the occupied MOs below the HOMO, formally constituting the VB. Energies, oscillator strengths and compositions of selected excitations of the trapped electron and trapped hole are reported in the Supporting Information (Figures S2 and S3 and Tables S1 and S2). Experimentally, the TAS spectra of nanocrystalline TiO2 films5,6,10,30 have been deconvoluted into three contributions: trapped electrons in the visible and near IR (400−1200 nm, with a maximum at ca. 770 nm), conductive electrons in the far IR (1200−2500 nm), and trapped holes in the visible, giving rise to a narrow band centered at ca. 520 nm with a low intensity shoulder at ca. 1200 nm. The relative intensities of these components depend significantly on the excitation intensity, the spectral contribution of trapped electrons becoming more pronounced and of similar intensity to that of trapped holes at high excitation; this effect was attributed to a change of the structure of the trapped electron due to the interaction with other photoexcited electron hole pairs under high excitation conditions. Although slightly blue-shifted 3600

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Figure 4. Top and side views of the electron density difference (isovalue = 0.002 e/au3) between excited and ground states for selected excitations of an excess electron/hole in the S0 (a/b) and D1,e/D1,h (c/d) geometries, computed at the TD-B3LYP/3-21G* level of theory in water solvent. Blue/ yellow indicates an electron density increase/decrease upon excitation.

Notes

to those of a trapped electron and occur mostly in the visible. Our results further show a strong dependence of the computed spectra on the carrier relaxation. The computed absorption of unrelaxed carriers in the ground state geometry of the neutral NP has a broad tail whose intensity increases with increasing wavelength. The line-shape is qualitatively similar to the spectrum experimentally assigned to conductive electrons, but the intensity is higher than the experimental one, suggesting that partial relaxation of the “conductive electrons” is actually present in the experiment.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.S. thanks the support of DoE-BES, Chemical Sciences, Geosciences and Biosciences Division, Contract No. DE-FG0212ER16286. F.N. thanks MIUR-PRIN 2010-2011 65 Project No. 20104XET32 “DSSCX”.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b01517. Computational methods; absorption spectrum of (TiO2)38 neutral NP; absorption spectra (different basis sets), energies, oscillator strengths and MOs compositions of selected excitations for an excess electron/hole in the S0 and D1,e/D1,h. (PDF)

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REFERENCES

(1) Lantz, J. M.; Corn, R. M. Electrostatic-Field Measurements and Band Flattening During Electron-Transfer Processes at Single-Crystal TiO2 Electrodes by Electric-Field-Induced Optical 2nd-Harmonic Generation. J. Phys. Chem. 1994, 98, 4899−4905. (2) Lantz, J. M.; Corn, R. M. Time-Resolved Optical 2nd-Harmonic Generation Measurements of Picosecond Band Flattening Processes at Single-Crystal TiO2 Electrodes. J. Phys. Chem. 1994, 98, 9387−9390. (3) Komiyama, M.; Yin, D.; Li, Y. Electronic Structure Change on TiO2 Surface due to UV Light Irradiation. In Studies in Surface Science and Catalysis; Masakazu Anpo, M. O., Hiromi, Y., Eds.; Elsevier: Amsterdam, 2003; Vol. 145, pp 153−156. (4) Komiyama, M.; Li, Y. J.; Yin, D. H. Apparent Local Structural Change Caused by Ultraviolet Light on a TiO2 Surface Observed by Scanning Tunneling Microscopy. Jpn. J. Appl. Phys. 2002, 41, 4936− 4938. (5) 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 Wide-

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. 3601

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The Journal of Physical Chemistry Letters Wavelength-Range (400−2500 nm) Transient Absorption Spectroscopy. J. Phys. Chem. B 2004, 108, 3817−3823. (6) Katoh, R.; Murai, M.; Furube, A. Transient Absorption Spectra of Nanocrystalline TiO2 Films at High Excitation Density. Chem. Phys. Lett. 2010, 500, 309−312. (7) Jing, L. Q.; Zhou, J.; Durrant, J. R.; Tang, J. W.; Liu, D. N.; Fu, H. G. Dynamics of Photogenerated Charges in the Phosphate Modified TiO2 and the Enhanced Activity for Photoelectrochemical Water Splitting. Energy Environ. Sci. 2012, 5, 6552−6558. (8) Kafizas, A.; Wang, X. L.; Pendlebury, S. R.; Barnes, P.; Ling, M.; Sotelo-Vazquez, C.; Quesada-Cabrera, R.; Li, C.; Parkin, I. P.; Durrant, J. R. Where Do Photogenerated Holes Go in Anatase:Rutile TiO2? A Transient Absorption Spectroscopy Study of Charge Transfer and Lifetime. J. Phys. Chem. A 2016, 120, 715−723. (9) Yoshihara, T.; Tamaki, Y.; Furube, A.; Murai, M.; Hara, K.; Katoh, R. Effect of pH on Absorption Spectra of Photogenerated Holes in Nanocrystalline TiO2 Films. Chem. Phys. Lett. 2007, 438, 268−273. (10) 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. (11) Furube, A.; Katoh, R.; Hara, K. Electron Injection Dynamics in Dye-Sensitized Semiconductor Nanocrystalline Films. Surf. Sci. Rep. 2014, 69, 389−441. (12) Yang, X. J.; 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. (13) 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. (14) Zawadzki, P. Absorption Spectra of Trapped Holes in Anatase TiO2. J. Phys. Chem. C 2013, 117, 8647−8651. (15) Cheng, J.; VandeVondele, J.; Sprik, M. Identifying Trapped Electronic Holes at the Aqueous TiO2 Interface. J. Phys. Chem. C 2014, 118, 5437−5444. (16) Nunzi, F.; Agrawal, S.; Selloni, A.; De Angelis, F. Structural and Electronic Properties of Photoexcited TiO2 Nanoparticles from First Principles. J. Chem. Theory Comput. 2015, 11, 635−645. (17) Vittadini, A.; Selloni, A.; Rotzinger, F. P.; Gratzel, M. Structure and Energetics of Water Adsorbed at TiO2 Anatase (101) and (001) Surfaces. Phys. Rev. Lett. 1998, 81, 2954−2957. (18) Lundqvist, M. J.; Nilsing, M.; Persson, P.; Lunell, S. DFT Study of Bare and Dye-Sensitized TiO2 Clusters and Nanocrystals. Int. J. Quantum Chem. 2006, 106, 3214−3234. (19) De Angelis, F.; Tilocca, A.; Selloni, A. Time-Dependent DFT Study of Fe(CN)64‑ Sensitization of TiO2 Nanoparticles. J. Am. Chem. Soc. 2004, 126, 15024−15025. (20) Persson, P.; Bergstrom, R.; Lunell, S. Quantum Chemical Study of Photoinjection Processes in Dye-Sensitized TiO2 Nanoparticles. J. Phys. Chem. B 2000, 104, 10348−10351. (21) De Angelis, F.; Fantacci, S.; Selloni, A. Alignment of the Dye’s Molecular Levels with the TiO2 Band Edges in Dye-Sensitized Solar Cells: a DFT-TDDFT Study. Nanotechnology 2008, 19, 424002. (22) De Angelis, F.; Fantacci, S.; Mosconi, E.; Nazeeruddin, M. K.; Gratzel, M. Absorption Spectra and Excited State Energy Levels of the N719 Dye on TiO2 in Dye-Sensitized Solar Cell Models. J. Phys. Chem. C 2011, 115, 8825−8831. (23) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula Into a Functional of the ElectronDensity. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785. (24) Becke, A. D. Density-Functional Thermochemistry 3. The Role of Exaxct Exchange. J. Chem. Phys. 1993, 98, 5648−5652. (25) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comput. Chem. 2003, 24, 669−681.

(26) Selcuk, S.; Selloni, A. Facet-Dependent Trapping and Dynamics of Excess Electrons at Anatase TiO2 Surfaces and Aqueous Interfaces. Nat. Mater. 2016, 4672. (27) Diebold, U. The Surface Science of Titanium Dioxide. Surf. Sci. Rep. 2003, 48, 53−229. (28) Cramer, C. J.; Truhlar, D. G. Density Functional Theory for Transition Metals and Transition Metal Chemistry. Phys. Chem. Chem. Phys. 2009, 11, 10757−10816. (29) Bredas, J.-L. Mind the Gap! Mater. Horiz. 2014, 1, 17−19. (30) 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.

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