Photocatalytic and Photovoltaic Properties of TiO2 Nanoparticles

Article pubs.acs.org/JPCC

Photocatalytic and Photovoltaic Properties of TiO2 Nanoparticles Investigated by Ab Initio Simulations Giuseppe Mattioli,*,† Aldo Amore Bonapasta,† Daniele Bovi,‡ and Paolo Giannozzi¶,§ †

Istituto di Struttura della Materia del CNR, via Salaria Km 29,300 - C.P. 10 I-00015, Monterotondo Stazione (RM), Italy Dipartimento di Fisica, Sapienza-Università di Roma. P. le Aldo Moro 5, 00185 Rome, Italy ¶ Department of Chemistry, Physics, and Environment, University of Udine, via delle Scienze 208, I-33100 Udine, Italy § DEMOCRITOS CNR-IOM National Simulation Center, I-34014 Trieste, Italy ‡

S Supporting Information *

ABSTRACT: Titanium dioxide and TiO2-based materials are widely used in environmental- and energy-related applications like photocatalysis and photovoltaics, where they are usually employed as nanocrystals or nanostructures. The present contribution is aimed at filling the gap between the vast literature devoted to the simulation of electronic and photochemical properties of TiO2 crystals and surfaces, and the few theoretical studies of photoactivated processes involving instead TiO2 nanostructures. More specifically, photocatalytic and photovoltaic processes promoted by model TiO2 nanoparticles (NPs) have been investigated by using ab initio simulations based on the U-corrected density functional theory, and on the time-dependent density functional perturbation theory. We focus on well-investigated processes like the photogeneration of charge carriers in UV-irradiated NPs, the photoreduction of dioxygen and photooxidation of methanol catalyzed by NPs, and the splitting of photogenerated charge carriers occurring at a model NP-dye interface. Our results provide indications on some crucial points of such processes, showing that (i) excited charge carriers photogenerated within bare NPs are preferentially trapped as small polarons at surface undercoordinated Ti3+ and O−sites; (ii) dioxygen and methanol are efficient scavengers of such electrons and holes, respectively, and trigger surface redox processes likely involving proton coupled electron transfer (PCET) steps; (iii) dye-sensitized NPs are instead characterized by low-energy excited states in which electrons and holes photogenerated within the dye are efficiently split by the TiO2/dye junction, thus confirming the expected spontaneous formation of charge-separated states in TiO2-based photovoltaic devices; (iv) cost-effective theoretical tools can be fruitfully employed to obtain reliable predictions of the photocatalytic properties of nanostructured metal oxides and of the photovoltaic properties of hybrid organic photovoltaic devices.

1. INTRODUCTION There are nowadays countless reports of the properties and usage of titanium dioxide in several fields of chemistry and materials science. Well-investigated applications of TiO2 like photocatalysis1,2 and hybrid photovoltaics3−5 have been extensively reviewed, while possible applications in emerging fields, including but not limited to artificial photosynthesis6,7 and spintronics,8 have been often foreseen. Apart from fundamental investigations of the properties of well-defined surfaces, e.g., photoemission responses,9 surface defects,10,11 or sharp hybrid interfaces,12,13 where TiO2 single crystals are employed to reveal the basic features of surfaces and interfaces, a large majority of the above applications involving titanium dioxide is based on TiO2 nanocrystals or nanostructures. This is due to their large surface/volume ratio, favoring photocatalytic processes as well as increasing the loading of photoactive sensitizers in hybrid solar cells, and to the optimization at the nanoscale of the diffusion length of electron−hole pairs in hybrid-heterojunction solar devices.1−7,14 More specifically, photocatalytic and photovoltaic processes involving TiO2 © 2014 American Chemical Society

nanostructures are the result of a complex interplay between concurring phenomena taking place at the nanoscale, which include (i) the interaction of molecules (from small inorganic to large organic compounds) with the surface of nanocrystals and nanostructures, (ii) the absorption of light which raises such interacting systems up to high-energy excited states, and (iii) a series of charge-transfer or redox processes which lead the system to recover its ground state by accomplishing, at the same time, catalytic or photovoltaic tasks. Such phenomena have been often investigated by using ab initio theoretical simulations, and in this framework, TiO2 represents a longstanding benchmark for ab initio methods based on density functional theory (DFT). This is due to its interesting and technologically relevant applications but also to the challenging problems raised by the simulation of the molcule-surface Received: September 29, 2014 Revised: November 25, 2014 Published: December 4, 2014 29928

dx.doi.org/10.1021/jp509830w | J. Phys. Chem. C 2014, 118, 29928−29942

The Journal of Physical Chemistry C

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in a recent contribution,36 particularly aimed at clarifying the nature and spatial distribution of band-like conduction states within and across TiO2 NPs, carried out by means of conventional DFT-GGA ab initio calculations. However, the failures of DFT-GGA discussed above in the case of intrinsic defects prevented a suitable description of charge carriers selftrapped as small polarons. In this scenario, we present here the results of a beyondGGA theoretical study in which we investigate first the properties of charge carriers in anatase NPs, paying a special attention to the competition between polaronic trapping and bandlike conduction of both electrons and holes. Then, on the grounds of such results, we clarify at the atomistic scale the role played by anatase NPs in well investigated photocatalytic processes like dioxygen reduction37,38 and methanol oxidation,39 as well as in photovoltaic processes involving a model solar hybrid heterojunction formed by a NP sensitized by the prototypical donor-π-acceptor L0 dye.40,41 As major results of our study, we anticipate that the investigated anatase NPs: (i) favor the photoinduced oxidation and reduction of interacting molecules by enhancing the self-trapping of electron and holes at undercoordinated surface sites; (ii) are efficient acceptors of “hot” electrons photogenerated in chemically bound sensitizers, and promote the spontaneous formation of low-energy chargeseparated excited states, in agreement with their good efficiency when employed in hybrid organic photovoltaic devices.

interaction, as well as of the excitation and charge-transfer processes indicated above. It is impossible to cite but a minimal part of the theoretical investigations of the properties of intrinsic, doped, defective and dye-sensitized TiO2-based materials. Notwithstanding, some general trends and milestones of TiO2 simulations deserve to be addressed. DFT simulations performed at a conventional generalized gradient approximation (GGA) level suffer of well-known limitations, generally ascribed to the overestimate of the electron−electron repulsion (delocalization error),15 which is also responsible for the underestimation of semiconductor band gap.16 Moreover, DFT-GGA functionals tend to overcouple unpaired electrons (static correlation error),17 leading to the indication of low-spin configurations as wrong ground states for open-shell transition-metal compounds. DFT investigations of TiO2 have often focused on the electronic properties of bulk and surface defects like O vacancies and interstitial Ti atoms, because they are very common in TiO2 crystals and nanostructures and are responsible for their native n-type conductivity.18 Such studies can be considered as representative examples of the above DFT difficulties. Early investigations of intrinsic defects performed by using DFT approaches beyond the GGA level19−21 provided a first demonstration of the localization, as small polarons on paramagnetic Ti(3+) centers, of excess electrons accompanying the formation of defects in reduced TiO2. These findings were in close agreement with the results obtained by electronic paramagnetic resonance (EPR) measurements, showing a clear fingerprint of Ti3+ centers.22,23 They showed also a close correspondence with the presence of deep donor levels in the TiO2 band gap, found 0.8 (1.0) eV below the rutile (anatase) conduction band (CB) by, e.g., photoelectron spectroscopy (PES) measurements.9 These studies have stimulated further theoretical and experimental investigations, aimed at elucidating the properties of excess electrons and holes in TiO2, either photogenerated or connected to defects and dopants. A unifying picture has been proposed in the case of excess electrons, suggesting the close relationship between Ti3+ centers and deep levels as a general feature of TiO2 small polarons connected to all the point defects and dopants having a donor character.24 The same picture has been extended to photogenerated holes (p-type doping is very difficult to achieve in TiO2 due to its natural tendency to the formation of the intrinsic donor defects mentioned above), trapped at paramagnetic O− sites.25,26 This generalized picture of charge carriers “self-trapped” in deep levels clashes with their high mobility in UV-irradiated and reduced TiO2,27 not compatible with site-to-site hopping of small polarons. Further theoretical investigations have reconciled this apparent disagreement by indicating the coexistence of deep traps with shallow levels responsible for the high n-type conductivity of TiO2.28−30 However, it has to be stressed that all such theoretical results have been obtained by simulation of fully periodic bulk or surface models, and cannot be automatically applied to nanocrystals or nanostructures. A less abundant literature is available on theoretical simulations of TiO2 nanoparticles (NPs). Systematic studies of the energetics, of the wettability, and of the relationship between shape and band potentials of bottom-up clusters and NPs31−33 have been paralleled by pioneer investigations of the interaction between light-harvesting dyes and anatase nanostructures.34,35 The electronic properties of anatase NPs, commonly used in photocatalysis and hybrid photovoltaics, have been investigated

2. THEORETICAL METHODS The properties of anatase NPs have been investigated by using ab initio simulations based on the Hubbard U-corrected density functional theory (DFT+U),42 as implemented in the Quantum ESPRESSO package.43 Such an approach has proven successful in improving the DFT description of electron correlation in transition metal oxides and related compounds, in particular when the localization of charge carriers (e and h) is involved.28,44−46 As discussed in detail elsewhere,28 an “onsite” U correction for the 3d electrons of Ti atoms has been set to the value of 3.2 eV calculated by using the self-consistent linear response approach described in detail elsewhere.47,48 In addition to such Ti 3d correction, a further U correction, set to the value of 2.0 eV, has been applied to the 2p electrons of O atoms, since Coulomb interactions between p electrons of the oxo- ligands have to be considered comparable to those between the d electrons of the metals.49,50 Moreover, the strong coupling between Ti 3d and O 2p shells, contributing to the anatase valence as well as conduction bands, can induce a spurious charge transfer from O atoms to metal atoms when the U correction is applied to the metal d shell only.28 This approach has proven to be useful to correctly reproduce the strong p−d coupling reported on the ground of resonant photoemission measurements.51 DFT+U simulations have been performed by using the Γ point for the k-point sampling of the Brillouin zone, ultrasoft pseudopotentials,52 and the U-corrected PBE exchangecorrelation functional.53 Kohn−Sham orbitals have been expanded into plane waves up to energy cutoffs of 40 and 320 Ry for the wave functions and the charge density, respectively, in order to achieve satisfactorily converged results. Such strict convergence criteria on the plane wave basis set, as well as the inclusion of Ti semicore 3s and 3p shells among the valence electrons, have proven to be necessary in order to estimate with high accuracy the Ti−O interaction.28 All the NPs have been accommodated in large supercells to minimize 29929



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Figure 1. Equilibrium geometry of a 105-atom (A), a 246-atom (B), and a 465-atom (C) anatase TiO2 nanoparticle. The corresponding surface-tobulk ratio of the three NPs (defined as the fraction of undercoordinated atoms) is also indicated. The Wulff construction (see the text) of an ideal anatase nanocrystal exposing the (101) and (001) facets is shown in the figure inset D.

and referenced to εVBM, i. e., the maximum of the valence band (VBM) of the TiO2 host, taken as a reference for the oxidation potential. In the present case, we have considered dioxygen, methanol and dye molecules, as well as small polarons induced by excess charge carriers, as dopant agents of the anatase NPs. The calculation of formation energies permits, in turn, to estimate transition energy levels, εq/q+1, corresponding to the position of the Fermi level where the q and q + 1 charge states of the dopant agent have the same formation energy, that is, the species Mq and Mq+1 are in equilibrium. Transition energy levels have a broad field of applications, as they can be used as reliable estimates of optoelectronic transitions and charge-transfer processes, of doping levels, and of oxidation potentials.28,46,64,66,67 In the case of photogenerated charge carriers in anatase NPs, we distinguish between optical and thermodynamic transition energy levels. As discussed in detail in several previous contributions,28,64,66,67 εopt levels are theoretical estimates of the energy required to induce vertical electronic transitions in which the final state is not able to relax, while εtherm levels are complementary quantities related to the thermal ionization of defects and dopants, and can be used to provide reliable estimates of charge carrier concentrations, as well as of electronic transitions of deep levels (observed, e.g., in the case of deep level transient spectroscopy measurements) in which the final state can relax to its equilibrium configuration. As previously reported in the case of excess electrons in TiO2,28 the strong distortion of Ti3+ and O− sites which accompanies the localization of charge carriers in small polarons leads to marked differences between εopt and εtherm values calculated for the same electronic transition. Such a difference has been proposed to reconcile in a unified picture the quantitative ntype doping of reduced TiO2 with the strong optical fingerprint of excess electrons trapped in Ti3+ deep donor levels.28 Optical absorption spectra ranging from the near-IR to the near-UV regions have been calculated in the case of bare and dye-sensitized anatase NPs. The simulations have been performed in the plane-wave/pseudopotential framework discussed above by using a time-dependent density matrix perturbation theory (TDDFPT) approach at the adiabatic

the interaction between periodically repeated images. Energy barriers have been calculated by using a nudged elastic band (NEB) scheme54,55 at the DFT+U level of theory. A subset of the calculations involving anatase NPs has been performed at a Hybrid-DFT level of theory, as implemented in the CP2K package.56 Periodic simulations have been performed by using a mixed basis set: localized Gaussian-type orbitals (GTO) are employed to represent the molecular orbitals and charge densities in real space, while plane waves are used for the representation of charge densities in the reciprocal space. The B3LYP★ functional, that is, a modified B3LYP functional containing only 15% exact exchange,57−59 has been used, together with the DZVP-MOLOPT-SR-GTH Gaussian basis set (SZV-MOLOPT-SR-GTH for Ti), and with an auxiliary exchange-fitting basis set cFIT3.60 The electronic density has been expanded in plane waves up to an energy cutoff of 280 Ry. Goedecker−Teter−Hutter (GTH) pseudopotentials61−63 have been used to replace the nuclei and core electrons in the case of all elements. The photocatalytic and photovoltaic properties of anatase NPs have been simulated beyond the single-particle limit by using a robust technique, generally employed to estimate energy levels and optical properties of dopant and defects in semiconductors, including TiO2,28,64,65 which was already successfully extended to the investigation of photocatalytic processes occurring at the TiO2/water interface.38 In this approach, first, the formation energy Ωf of a q-charged species M, embedded in a semiconductor host matrix H, has to be estimated, which is defined as Ω f [M q] = E[M q] − E[H ] −

∑ nM μM

+ q(εF + εVBM) (1)

q

where E[H] and E[M ] are the total energies of supercells containing the undoped host matrix, and the dopant agent (adsorbed molecule, point defect) surrounded by the host, respectively; nM is the number of dopant agents inserted in (or subtracted by) the defected supercell and μM is the chemical potential of the same species. εF is the Fermi level of the system, corresponding to the chemical potential of electrons, 29930



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generalized gradient approximation (A-GGA) level.68,69 In detail, absorption frequencies and the corresponding oscillator strength are calculated as linear response of the whole charge density of the system to the oscillating electric perturbation. A Gaussian broadening of 0.2 eV has been applied to all the oscillators. Such an approach is expected to provide reliable results when applied to large systems, including sensitized metal oxides.70−72 Similar TDDFPT calculations have been carried out in the GTO/pseudopotential framework also introduced above.73 Both approaches converge to the same results in the case of all the systems investigated here.

3. RESULTS AND DISCUSSION 3.1. Structural and Electronic Properties of TiO2 Nanoparticles. Anatase NPs are synthesized by using different methods and, therefore, can be characterized by different sizes and shapes. An ideal growth yields truncated-bipyramidal NPs exposing a large majority of the most stable (101) surface termination on the side facets, with a minority contribution of the (001) surface on the top (bottom) facets.14,74 The corresponding Wulff construction,75,76 often observed in high resolution transmission electron microscopy images of anatase NPs,2 is shown in Figure 1 D. We have designed three anatase NPs in close agreement with such findings and with previous theoretical results,36 all shown in Figure 1 A-C. Our NPs span a size range going from 1 nm (the 105-atom A model, which can be considered as a large anatase cluster) to 3 nm (the 465-atom C model, having the size of the smallest real NPs). As discussed in detail elsewhere,36 4-fold coordinated Ti atoms placed at vertices where the side (101) facets join the top and bottom (001) facets are saturated by terminal hydroxyl groups to ensure the charge neutrality of the investigated models. This is particularly important when addressing the electronic properties of TiO2 because it permits to start the investigation from an “intrinsic” semiconductor model, which can be perturbed by light-induced excitation, doping or adsorbed molecules. Due to the high stability of the exposed facets, all the NPs retain a strong resemblance with the anatase crystal structure. The distributions of Ti−O (first shell only) and Ti−Ti distances in the A-C NPs are shown in Figure 2 as EXAFS simulations, obtained as normalized convolutions of Gaussian peaks (σ = 0.05 Å) centered on all the Ti−O and Ti−Ti distances. All the curves in the lower panel of Figure 2 show a series of peaks rapidly approaching the well-defined features of the anatase bulk (shown in the upper panel of Figure 2) in the case of the larger NPs. A similar convergence trend is also observed in the case of measured EXAFS spectra of anatase NPs.77−79 The additional features of the NP plots can be assigned to the characteristic relaxation of 2-fold-coordinated O atoms and 5fold-coordinated Ti atoms forming the topmost layers of the (101) facets. Such features dominate the Ti−O and Ti−Ti distance distributions in the case of the smaller 105-atom model, having a surface-to-bulk ratio larger than 50% (59.8%), while they are less prominent in the case of the largest 465atom model, where the fraction of surface atoms is smaller (37.4%), and therefore likely undetectable in the measured EXAFS spectra of larger NPs mentioned above. The achieved structural results indicates that even such small anatase NPs are characterized by a high crystallinity, fully compatible with that observed in the case of larger nanostructures.2,14 Regarding the electronic properties of the investigated NPs, the corresponding density-of-states plots are shown in Figure 3 and compared with those calculated in the case of a periodic

Figure 2. EXAFS simulations of Ti−O (first shell only) and Ti−Ti distances calculated in the cases of the A (green curve), B (blue curve), and C (red curve) anatase TiO2 nanoparticles shown in Figure 1. The simulations have been obtained as normalized convolutions of Gaussian peaks (σ = 0.05 Å) centered on all the Ti−O and Ti−Ti distances. The same distances, calculated in the case of the anatase bulk by using the same theoretical setup, are displayed as black bars in the upper panels and projected on the NP curves.

slab exposing the relaxed (101) plane on both sides.80 The vacuum level has been assigned in the case of all simulations to the asymptotic value reached by the Kohn−Sham potential, calculated as planar average, in the empty space between periodically repeated images of the NPs (or of the slab along the (101) direction in the case of the surface model). Further calculations have been performed in the case of the B model by using a mixed-basis/pseudopotential approach at the B3LYP★ level of theory, as detailed in Section 2, in order to compare the results of different beyond-GGA approaches. All the NPs are characterized by electronic properties quite similar to those calculated in the case of the surface model, with the band edge potentials of the larger B and C models in good agreement with previous calculations of large clusters and NPs,31,33 and with electrochemical measurements.6,81 As opposite to more conventional hybrid B3LYP and HSE calculations, reporting large overestimates of the measured optical anatase band gap (3.2 eV),18,24,28 the present DFT+U and B3LYP★ results provide values in a closer agreement with experimental measurements: the HOMO−LUMO gaps of the B and C models (DFT+U = 2.9 eV; B3LYP★ = 3.5 eV) nicely agree with that of the (101) slab (DFT+U = 3.1 eV) and with measurements. The structural and electronic properties of the investigated NPs indicate that the 246-atom B model can be already considered as a reasonably converged model of larger structures, and will be therefore used in the following to investigate the optoelectronic and photocatalytic properties of bare and sensitized anatase NPs. 3.2. Polaronic Trapping vs Band-Like States in Intrinsic TiO2 Nanoparticles. In spite of the wide usage of TiO2 and of the large amount of theoretical work on TiO2 doping, few contributions have been devoted to the ab initio investigation of the generation, localization and transport of charge carriers in TiO2, and most of them regard the bulk rutile, 29931



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to the system. This procedure, successfully employed in the case of the localization of excess electrons at the rutile surface,82 has been repeated for all the nonequivalent Ti (O) surface and “bulk” sites. Regarding electrons, it is worth noting first that if we do not break the NP symmetry we obtain a locally stable configuration with one excess electron accommodated in the band-like LUMO shown in Figure 4b. Moreover, irrespective of the initial position of the V atom, excess electrons are stable only when localized on undercoordinated Ti atoms placed at NP vertices. In detail, an excess electron occupies an atomic-like nonbonding 3d orbital belonging to a 4-fold coordinated Ti3+ ion, as shown in Figure 4d. The corresponding Kohn−Sham state is placed 1.1 eV below the cluster LUMO. Similar features have been also reported in several cases of excess electrons explicitly connected to donor defects and impurities.21,24,28 However, such a result is not strictly connected to the properties of the anatase lattice, but it is rather due to the features of the NP structure. In fact, we have performed the same kind of calculation in the cases of a 384-atom anatase bulk supercell as well as of a 384-atom (101) slab without observing any stable configuration of Ti3+ centers. The same behavior has been also observed in the case of anatase bulk on the grounds of previous DFT+U and hybrid HSE simulations: excess electrons, isolated or connected to interstitial H donor impurities, are accommodated in delocalized band-like states, as opposite to rutile, where similar conditions induce the formation of stable small polarons.83−85 The coexistence of band-like and trapped excess electrons in anatase NPs is also in agreement with the EPR measurements mentioned above.22 In order to gain more insight into the behavior of photogenerated electrons, we have calculated optical (εopt) and thermodynamic (εtherm) transition energy levels for the Ti(4+/3+) transition connected with the trapping of electrons at Ti3+ sites. The related values are displayed in the left part of Figure 4e. At thermal equilibrium the Ti3+ polarons require 0.2 eV for excitation of the electron into the delocalized NP LUMO (dashed yellow line in Figure 4e), in agreement with the shallow trap character (0.12−0.3 eV) detected by infrared spectroscopy measurements.27 The vertical excitation or ionization of the same electrons observed, e.g., in the case of PES, starts from a deep level placed 1.1 eV below the NP LUMO (solid yellow line in Figure 4e), in agreement with a similar determination made in the case of reduced anatase.9,28 The coexistence at low temperature of delocalized and trapped electrons in anatase NP is also supported by a nudged elastic band (NEB) estimate of the potential energy barrier which separates the two configurations. Delocalized electrons, which are expected to form after the thermalization of the first above-gap excitation, are separated from the more stable (by 0.3 eV) Ti3+ trapped configuration by a 0.03 eV barrier, corresponding to 350 K in kT units and, therefore, fully compatible with the quantitative detection of delocalized electrons at 90 K.22 A different behavior has been observed in the case of excess holes: when one electron is subtracted from the bulk anatase lattice, a small polaron forms as an atomic-like nonbonding 2p orbital belonging to one of the lattice O atoms.85 The same has been reported in the case of bulk rutile.26 Regarding the present anatase NPs, the hole is not stable in the delocalized HOMO shown in Figure 4a, but it spontaneously collapses into a polaron-like orbital, represented by an unoccupied paramagnetic Kohn−Sham state placed 1.1 eV above the cluster HOMO. More specifically, the hole is localized at a 2-fold-

Figure 3. Total density of states (DOS) of the A (green curve), B (blue curve), and C (red curve) anatase TiO2 nanoparticles (NPs) shown in Figure 1. A 0.01 Ry (0.136 eV) Gaussian broadening of Kohn−Sham eigenvalues has been applied to simulate the NP DOS. A zero energy value has been assigned to the vacuum level, calculated as the asymptotic value reached by the Kohn−Sham potential, calculated as planar average, in the empty space between periodically repeated images of the NPs (or of the slab along the (101) direction in the case of the surface model). The curves are compared with the blue one in the middle panel, obtained in the case of the B NP at the B3LYP★ level of theory, and with the black one in the upper panel, obtained in the case of the anatase (101) surface by using the same DFT+U approach employed in the case of the A, B and C NPs. The surface has been modeled by using a three-OTiO-layer 72-atom anatase slab exposing the relaxed (101) plane on both sides.

which is easier to obtain as a macroscopic single crystal.2,29 Experimental investigations report that the absorption of abovegap UV light by anatase NPs is followed by a fast phononassisted thermalization of the excited state, which results in the formation of an admixture of trapped and delocalized (or bandlike) electrons and holes.2 Low temperature EPR measurements22 indicate in particular that photogenerated holes are very efficiently trapped at paramagnetic O− sites, while electrons are distributed between band-like states and paramagnetic Ti3+ traps. At low temperature (90 K), the recombination rate is very slow, and all such excited charge carriers can be detected hours after their generation. To shed light on the competition between band-like and trapped states, we have first investigated the stability of isolated charge carriers in the 246-atom B model. In order to break the NP symmetry and to favor the localization of electrons and holes at Ti3+ and O− sites, respectively, we performed a first group of calculations in which one Ti (O) atom was substituted by a V (N) atom. The geometry of the locally distorted NPs was then reoptimized by replacing the V (N) atom with the original Ti (O) atom and by adding one excess electron (hole) 29932



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Figure 4. |ψ|2 plots of: (a) HOMO, (b) LUMO, (c) trapped hole, and (d) trapped electron in the case of the 246-atom B model of anatase NP. Magnified representations of the hole and electron are shown in the two insets. Electronic densities are sampled at 0.003 au (0.0005 au) in the cases of localized (delocalized) electronic states. Optical and thermodynamic transition levels related to trapped electrons and holes (Ti(4+/3+) and O(2−/1−) transitions, respectively; see the text for details) are shown in panel e. The PL red arrow indicates a tentative assignment of the strong photoluminescence band measured in anatase nanostructures.

coordinated surface O− atom (with a minority contribution of its nearest neighbors), as shown in Figure 4c, in agreement again with EPR measurements.22 As mentioned above, stable positive charge carriers delocalized in the NP valence band are not observed, nor predicted by the present simulations. Again, to strengthen such findings we have calculated the εopt and εtherm values in the case of the O(2−/1−) transition, which describe the trapping of a hole in a specular way to the previous Ti(4+/ 3+) case. The results are shown in the right part of Figure 4 e. The optical signature of trapped holes at O− sites is found 1.4 eV above the NP HOMO (solid green line in Figure 4e), while at thermal equilibrium 0.3 eV are needed to the capture of one electron at the same sites from the NP valence band (dashed green line in Figure 4e). Both values are close to those reported in the case of anatase bulk.85 A comparison between electrons and holes at thermal equilibrium indicates that holes are spontaneously trapped at O− sites and induce deeper defects in the NP gap, in agreement with the fact that delocalized holes are not detected in UV irradiated anatase NPs, as opposite to electrons.22 Moreover, on the grounds of such results the radiative recombination of photogenerated charge carriers, observed by photoluminescence measurements in several nanostructured anatase samples as a temperature-dependent broad band falling at 1.8−2.2 eV, 2,86−88 can be tentatively assigned to the vertical recombination of delocalized electrons with trapped holes (1.5 eV in the case of the present estimate, indicated by a red

arrow in Figure 4e). Finally, and more significantly, both kinds of charge carrier are trapped at surface sites, in close agreement with the observed high photocatalytic activity of anatase NPs.2 We note that the presence of intrinsic defects like O vacancies and interstitial Ti atoms, not considered in our NPs but often observed in TiO2 crystals and nanostructures,18 would not affect the extent of our results. Bulk defects can be considered as an additional source of excess electrons, which can be trapped as small polarons at Ti3+ sites. A pre-existing small imbalance between positive and negative charge carriers does not substantially modify the Fermi quasi-levels of holes and electrons, sketched as transition levels in Figure 4e, when the NPs are irradiated, and is not expected to affect our findings. Subsurface defects have been observed in macroscopic anatase crystals,11,89 and have been suggested to play a role in the interaction of small molecules with the anatase (101) surface.90 However, such defects are expected to migrate to the surface during thermal treatments of the NPs which usually follow the synthesis,91 where they are healed or fully passivated by dioxygen or water molecules.11,92,93 As a final remark on the properties of the bare anatase NPs, our findings enrich and complement the results previously obtained by means of DFTGGA calculations.36 Such results suggested that the occurrence of low-energy, unoccupied trap states for excess electrons, localized on the NP belt and similar to the LUMO orbital shown in Figure 4 b, was an inerhent characteristic of anatase NPs. We stress the fact that the explicit simulation of excess 29933



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Figure 5. Different configurations of O2 and CH3OH adsorbed on the (101) facet of the 246-atom B model of anatase NP: (a) Ti···O02; (b) Ti(O2)1−; (c) Ti(O2)2−; (d) molecular adsorption of CH3OH; (e) Meth1 dissociative adsorption of CH3OH; (f) Meth2 dissociative adsorption of CH3OH. |ψ|2 plots: (g) electron trapped by the Ti(O2)1− adsorbate; (h) hole trapped by the Meth1 adsorbate. Electronic densities are sampled at 0.003 au Thermodynamic transition levels corresponding to the trapping of charge carriers promoted by adsorbed dioxygen and methanol are sketched in part i, together with the competitive Ti(4+/3+) and O(2−/1−) transitions introduced in Figure 4

formation of two symmetrical tight bonds (2.05 Å) with the underlying Ti4+ atom. One more electron can be accommodated in the double-degenerate O2 LUMO, leading to the formation of a diamagnetic Ti(O2)2− peroxo species (Figure 5c) characterized by even tighter Ti−O bonds (1.85 Å), leading to the outward bending of the 7-fold-coordinated Ti atom. The accuracy and usefulness of transition levels95 is fully acknowledged by comparing the position of the O2(−1/0) transition level with that of O2(−2/−1), both sketched in Figure 5i together with the Ti(4+/3+) transition level discussed above. A photogenerated electron will be preferentially stored in the Ti(O2)1− adsorbed species than trapped in a less stable Ti3+ small polaron, and this is perfectly consistent with the experimental observation of electrons trapped in O2-related paramagnetic centers mentioned above. On the contrary, the diamagnetic Ti(O2)2− surface adsorbate is not observed, in agreement with a position of the O2(−2/−1) transition level slightly above the NP band gap. However, we note that the Ti(O2)2− species has been well characterized on the grounds of IR spectroscopy measurements as first intermediate of the O2 photoreduction promoted by anatase NPs in contact with a water solution.37 Parallel theoretical calculations, performed in the case of an O2 molecule interacting with an anatase periodic (101) surface slab at a DFT-GGA level of theory, indicated a O2(−2/−1) transition level below the surface band gap, in agreement with the quantitative formation of a surface Ti(O2)2− species in UV irradiated NPs.38,94,96 We suggest that such an apparent inconsistency can be overcome by considering that the formation energies of both the Ti(O2)1− and Ti(O2)2− charged intermediates should be lowered when the anatase is surrounded by the highly dipolar water molecules, thus leading, in turn, to the lowering of the

electrons performed here at the DFT+U level of theory permits to go beyond this simplified picture and to shed light on the competition between band-like delocalization and polaronic trapping in the same NPs, thus achieving a better agreement between simulations and measurements. 3.3. Photocatalytic Properties of TiO2 Nanoparticles. In this section we show how photogenerated electrons and holes, whose properties have been discussed above, act as reducing and oxidizing agents, respectively. We have investigated to this purpose the interaction of the 246-atom B NP with typical carrier scavengers, namely dioxygen and methanol. O2 molecules play a crucial role in photocatalysis. They are very efficient scavengers of electrons photogenerated in TiO2, as well as primary intermediates in the formation of kinetically more active oxidizing species released in solution.1,2,14,91 Low temperature EPR measurements indicate that the paramagnetic signal of photogenerated electrons arising from Ti3+ traps in irradiated anatase NPs is quickly quenched in the presence of dioxygen, with the formation of paramagnetic long-lived O2− radicals in contact with cationic Ti4+ surface sites.22 Regarding our simulations, neutral O2 molecules interact weakly with the (101) facets of the anatase NP. We have calculated an adsorption energy of 0.2 eV for a molecule physisorbed above one of the 5-fold-coordinated surface Ti4+ sites (see Figure 5a), in agreement with the results of previous simulations of O2 molecules in contact with the (101) anatase TiO2 surface.94 One excess electron is captured by the O2 molecule which undergoes a dramatic geometry change, leading to the formation of the paramagnetic charged Ti(O2)1− peroxo species shown in Figure 5b. In detail, the photogenerated electron is basically stored in the antibonding π★ LUMO of the oxygen molecule (see Figure 5g), and is stabilized by the 29934



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Figure 6. Potential energy curves along the minimum energy path for methanol photooxidation, obtained by using eight replicas of the system for each branch of the reaction path in a nudged elastic band (NEB) approach. Blue branches: a single oxidizing hole has been injected in the TiO2/ CH3OH system. A lower 0.1 eV barrier has been calculated in the case of the formation of the CH3O• intermediate (steps 1−3a), as opposite to the higher 0.4 eV barrier which hinders the formation of the C•H2OH intermediate (steps 1−3b). Green branch: a further hole has been injected in the TiO2/CH3O• system, which must cross a 0.3 eV barrier to lead the system to the thermodynamically favored formation of formaldehyde (steps 3a− 5a). Figure insets schematically represent reaction intermediates; the oxidation state of the O and C atoms belonging to the stable intermediates of methanol oxidation is also indicated.

adsorption, possibly occurring at surface steps.97 We confirm such results: a CH3OH molecule is chemisorbed without dissociation on the (101) facet of the anatase NP, as shown in Figure 5d, with an adsorption energy of 1.0 eV. We note that a dissociative [CH3O−/H+] adsorption (Figure 5e) is only slightly unfavored with respect to the stable CH3OH ground state (+ 0.1 eV), while the alternative [CH2OH−/H+] dissociative adsorption configuration (Figure 5f) is almost metastable (+0.9 eV). The small difference between molecular and dissociative (CH3O−/H+) adsorption energy is compatible with a minority presence of methoxy species on the surface. However, a significant 0.5 eV barrier has been calculated for the transfer of a proton from methanol to surface, as detailed in the Supporting Information. Such a high barrier supports the preferred molecular adsorption of methanol on anatase, as well as the involvement of surface steps in CH3OH dissociation, suggested on the grounds of measurements.97 We go beyond such ground-state analysis by simulating the injection of a photogenerated hole in the TiO2/CH3OH system. Our calculations indicate that the hole is not trapped at the undissociated CH3OH adsorbate, as suggested also by previous DFT-GGA calculations:92 there is no occupied Kohn− Sham level in the NP HOMO−LUMO gap suitable for exchanging holes with the valence band. Both the CH3O− and CH2OH− fragments are instead able to capture the hole, showing in both cases a large energy gain for its localization on the O atom (−0.8 eV for the formation of CH3O•), or on the C atom (−1.1 eV for the formation of C•H2OH). As an example, the hole trapped at an antibonding O 2p orbital of the CH3O− fragment is shown in Figure 5h. In terms of transition levels we found a CH3O•/CH3O− transition level (Meth1(1+/0) in Figure 5i placed 0.9 eV above the NP HOMO, and a C•H2OH/ CH2OH− (Meth2(1+/0)) placed 1.2 eV above the NP HOMO. This implies that the trapping of a hole at both dissociated

O2(−2/−1) and O2(−1/0) transition levels. The presence of Ti(O2)2− species on the surface of solvated anatase NPs can therefore be compatible with the results of the present simulations. Light-induced methanol oxidation is one of the most investigated photocatalytic processes promoted by TiO2.1,2,18,39 From a mechanistic point of view, the reaction is supposed to start with the transfer of a photogenerated hole trapped at an O− surface site to a CH3OH molecule adsorbed on the NP surface, accompanied by the transfer of one proton from the molecule to a surface O2− site. Ti(4+)−O− + CH3OH(ads) → Ti(4+)−O2 − + [CH3OH(ads)]+

(2)

Ti(4+)−O2 − + [CH3OH(ads)]+ → Ti(4+)−OH− + [CH3O(ads)]•

(3)

Further oxidation of the radical intermediate leads to the formation of formate in the presence of dioxygen, while formaldehyde is the main product in absence of O2. Whether the reactions sketched in eq 2 and eq 3 occur in a concerted or sequential process is still unclear.2 In absence of UV photoexcitation, a previous theoretical investigation of the interaction of CH3OH with the (101) anatase surface suggested that molecular adsorption of methanol is thermodynamically favored on the anatase surface unless defects like O vacancies are present on the surface.92 This suggestion is in substantial agreement with the results of temperature-programmed desorption (TPD) and X-ray photoelectron spectroscopy (XPS) measurements, indicating a preferred molecular adsorption of methanol on the anatase (101) surface, accompanied by a minority contribution of dissociative 29935



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Figure 7. (a) Equilibrium geometry (the donor−π-acceptor architecture of the molecule is indicated) and |ψ|2 plots of HOMO and LUMO of the L0 dye. |ψ|2 plots of the HOMO (b) and LUMO (c) of the interacting system formed by an L0 molecule chemically bound to one of the NP (101) facets.

suggesting that the oxidizing hole is more likely trapped at the O atom belonging to the methoxy radical, as also observed in the case of the interaction of methanol with the UVirradiated (110) rutile surface.98 The participation of further external species (OH•, O2) to the second oxidizing process is often invoked, leading to the formation of the final formate or formaldehyde products. The investigation of such process goes beyond the purpose of the present contribution. Notwithstanding, we hypothesize that a second hole photogenerated in the NP can be able to induce a further proton transfer to the surface, and to lead to the formation of the formaldehyde product without the participation of an external oxidizing species:

methanol fragments is favored with respect to self-trapping at surface O− sites (0.3 eV above the NP HOMO). Notwithstanding, we point out a significant difference with the previous case of O2 photoreduction. In that case, no significant barriers hinder the transfer of electrons from the substrate to the adsorbed molecule. On the contrary, the transfer paths of protons from methanol to surface which accompany the localization of holes are kinetically relevant processes, whose barriers have to be evaluated in order to characterize the CH3OH photooxidation beyond the mere thermodynamic stability of oxidized fragments. In this regard, we have performed a series of NEB calculations to map the potential energy surface and to estimate the dissociation barriers of CH3OH under UV irradiation. The calculations have been performed by using a less expensive periodic 108-atom slab model in the same DFT+U framework of NP calculations, and are characterized by small quantitative discrepancies with the NP results in the case of stable intermediates, as discussed in the Supporting Information. The results of NEB calculations are shown in Figure 6. When a single oxidizing hole has been injected in the TiO2/CH3OH system (blue branches of the curve in Figure 6), a lower 0.1 eV barrier is found in the case of the formation of the CH3O• intermediate (steps 1−3a), as opposite to the higher 0.4 eV barrier which hinders the formation of the C•H2OH intermediate (steps 1−3b). Despite of the higher stability of the C•H2OH adsorbate, the formation of the CH3O• intermediate is kinetically favored, thus

• Ti(4+) − O− + CH3O(ads) → Ti(4+) − O2 − • + [CH3O(ads) ]+

(4)

• Ti(4+) − O2 − + [CH3O(ads) ]+ → Ti(4+) − OH−

+ CH 2O(ads)

(5)

Once again, the thermodynamic gain is very relevant (almost 4 eV), as shown by the green branch of the curve in Figure 6. The corresponding CH2O/CH2O+ transition level (Meth1(2+/ 1+)) is even higher than the Meth1(1+/0) one, falling above the NP LUMO: if we neglected the proton transfer barriers we could erroneously suppose that the adsorbed CH3OH molecule 29936



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Figure 8. |ψ|2 plots of single-occupied molecular orbitals containing photogenerated electrons and holes in (a) a 246-atom anatase NP; (b) the same NP sensitized by L0. (c) Measured and calculated oxidation potentials of a dye-sensitized solar cell based on a TiO2/L0/iodide−triiodide photoactive heterojunction. Measured data are taken from previous contributions.4,40 (d) TDDFPT absorption spectra of an isolated L0 molecule (curve 1), of a bare anatase NP (curve 2), of a noninteracting TiO2/L0 system (curve 3; sum of curves 1 and 2), and of the interacting TiO2/L0 system (curve 4).

is able to simultaneously capture the two holes and to release immediately the oxidized products. A 0.3 eV barrier (green branch in Figure 6) must be crossed instead to transfer a second proton and to dissociate the CH3O•, thus leading to the formation of the final formaldehyde product. Such a barrier, significant, even if not very high, suggests the likely involvement of an external oxidizing species in the reaction process. Finally, we remark that all of the investigated steps of methanol photooxidation suggest the occurrence of a simultaneous transfer of one electron from the molecule to the catalyst (with the localization of a hole on the absorbed molecule), and of one proton from the molecule to the catalyst. In fact, the transfer of one proton to the catalyst without the electron counterpart is not favored, due to the higher energy of both dissociated species, while the transfer of one electron not

accompanied by a proton is hindered by the lack of a suitable acceptor level for the hole. These findings suggest the occurrence of a typical proton-coupled electron transfer event (PCET), often proposed in the case of reactions involving biological and bioinspired metal-oxide catalysts,99,100 and recently supposed to play a crucial role also in the case of conventional (photo)catalytic processes.101 3.4. Optoelectronic Properties of a Nanoparticle/Dye Heterojunction. Hybrid-organic photovoltaic (HOPV) cells based on TiO2 are generally formed by a ternary photoelectrolytic heterojunction: a TiO2 nanostructured anode, covered by light-harvesting molecules chemically bound to the oxide surface, is in contact with an electrolytic (or a solidstate) solution containing a hole-transporter to the cathode.3−5 The functioning of such a photoactive junction, extensively 29937



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localization processes of a photogenerated e−h pair in the bare and dye sensitized NPs. Identical lowest-energy excited states of the bare NP have been obtained by starting either from the excess-hole configuration of Figure 4c or from the excesselectron configuration of Figure 4d. The result is shown in Figure 8a. The coupled charge-carriers are localized on nearestneighbor Ti and O atoms and, as expected, cannot be easily separated in a bare NP. The lowest-energy excited state is radically different in the case of the sensitized NP (Figure 8b): electron and hole are arranged in a basically charge-separated (CS) state,103 in which the hole is mainly confined in the L0 D termination, ready to accept one electron from the holetransporter medium, and the electron is well delocalized in the NP conduction state (with a minority spill out in the A part of L0). It is worth noting that any tentative trapping of the electron at a localized Ti3+ site is not stable in the excited TiO2/ L0 system, and evolves spontaneously toward the CS state. The broad delocalization of the “hot” electron across the belt of the anatase NP is also compatible with its tendency to leak into the electrolytic solution when the NP surface is not coated by a tight admixture of dye and other coadsorbed species, likely the most significant source of power loss in HOPV devices.3 The electronic properties of our model TiO2/L0 system have been also tested against the measured values of all of the oxidation potentials (V vs SHE) relevant for the functioning of the solar cell, taken from previous contributions.4,40 Calculated and measured values are compared in Figure 8 c. A same oxidation potential has been attributed to the Fermi quasi-level of electrons measured in TiO2 photoanodes4 and to the Ti(4+/ 3+) transition level calculated in the case of the anatase NP, which can be considered as closely related quantities. The oxidation potential of the L0+/L0 couple has been calculated by using the corresponding L0(+1/0) transition level. The calculated value is 0.2 eV higher than the measured value, confirming the reliability of transition levels in the description of several kinds of charge transfer process. A same procedure cannot be used in the case of the L0+/L0★ potential because the L0 LUMO cannt be occupied by an excess-electron injected in the system in the present DFT+U ground-state framework. Our estimate of such value has been obtained by subtracting the calculated formation energy of the L0★ species (2.6 eV, see the red curve in Figure 8 d) from the L0(+1/0) transition level.104 Apart from the iodide/triiodide potential in acetonitrile, which can be hardly estimated in a DFT framework, the calculated values provide a reliable representation of the electronic properties of the hybrid TiO2/L0 junction, The optical properties calculated at the TDDFPT level for the TiO2/L0 system and its separated components provide further insight into the sensitization of anatase NPs. The absorption spectrum of L0 in the visible/near UV region (curve 1 in Figure 8d) is characterized by a single feature peaked at 2.9 eV, appreciably lower than the measured value (3.32 eV in acetonitrile) due to the charge-separated nature of the excited state, not optimally described by TDDFT calculations.68,105 The NP absorption (curve 2 in Figure 8d) is characterized instead by a monotonically growing onset following the conduction band density of states, as reported in the case of comparably small anatase NPs.106 If we sum in a 1:1 ratio the L0 and NP absorption spectra (curve 3 in Figure 8d), we obtain a convolution quite different from the absorption spectrum calculated in the case of the interacting TiO2/L0 system (curve 4 in Figure 8d). Two new features appear in the absorption spectrum of the sensitized system: a marked (0.3 eV) red shift

reviewed in several previous contributions, can be basically divided in three processes: (i) One of the molecules absorbs one photon and is raised to a high-energy excited state, often described in a simplified, single-particle framework as the promotion of one electron to the LUMO, which lets back a hole in the HOMO. (ii) The “hot” electron is transferred to the TiO2 conduction band with a first intrinsic loss of the initial photon energy due to the potential drop between the molecular excited state and the conduction band. The electron diffuses through the semiconductor and can be collected at the anode. (iii) The hole let back in the molecule is exchanged with a hole transporter and delivered to the cathode through the electrolytic solution, with a second intrinsic loss of the photon energy due to the potential drop between the positive molecular ion and the redox potential of the hole transporter. The residual energy acquired by the system during the first excitation is reduced to an amount which represent the maximum theoretical energy gain of the photovoltaic device, substantially corresponding to the measured open-circuit potential (Voc) of the cell. All the processes which lead the system to the ground state without inducing a photocurrent in the external circuit (e.g., direct transfer of the excited electron from the TiO2 surface to the hole transporter in its higher oxidation state) are called recombination losses and decrease the overall performance of the solar cell. The metal-free L0 dye,40 sketched in Figure 7a, represents a prototypical example of the class of donor-π-acceptor molecules used as sensitizers in HOPV devices.3−5 The significant spatial separation between the L0 HOMO, mainly centered on the diphenyl-amino donor termination (D in Figure 7), and the LUMO, pushed toward the cyanoacetic acceptor termination (A in Figure 7) is supposed to be responsible for the formation of a highly dipolar excited L0★ state, characterized by a strong absorption of light peaking at 3.3 eV.40 Moreover, such a polarization of L0★ is compatible with an easier transfer of the excited electron from the molecule to the TiO2 conduction band, as well as of the hole to the widely employed iodide/ triiodide transporter. This is due to the fact that the molecule is chemically bound to the anatase surface through its A termination, while the D termination is positioned outward from the surface and well inside into the electrolytic solution which contains the hole transporter. Despite its main absorption in the near UV region, the TiO2/L0 system is able to provide an appreciable overall performance when used in HOPV devices (power conversion efficiency η = 1.55%) and can be considered as a simple but useful model to gain a deeper insight into the basic mechanisms of the HOPV functioning at the nanoscale. The L0 molecule is connected to the NP through a bidentate link of the −COO− group with two undercoordinated surface Ti atoms, as extensively detailed in a previous contribution.41 The interacting system is characterized by a HOMO mainly localized on the molecule (Figure 7b), while the LUMO (Figure 7c) is basically similar to the conduction state already shown in Figure 4. The lowest-energy excited state of the TiO2/L0 system has been investigated here by forcing the occupation of its lowest unoccupied orbital with one electron, thus letting back a hole in the highest occupied orbital in an open-shell Kohn−Sham framework. Such an approach represent a robust, albeit rough, method which allows one to investigate the properties of excited states in large systems beyond the simple analysis of ground-state occupied and unoccupied eigenstates.102 It has been used here in order to gain a first insight into the 29938


The Journal of Physical Chemistry C of the main absorption peak, in agreement with a similar 0.12 eV shift measured in the case of L0 adsorbed onto TiO2, and a weak band at lower frequency (1.5 eV). The latter feature is almost entirely constituted by a direct excitation of one electron from the HOMO (Figure 7b) to the LUMO (Figure 7c) of the TiO2/L0 system. Even if the corresponding absorption frequency is likely underestimated, due to the known limits of TDDFT in the description of CS excitations mentioned above, such a direct transition between interfacial electronic states may contribute to the generation of photocurrent in a TiO2/L0 HOPV device.

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REFERENCES

(1) Fujishima, A.; Zhang, X.; Tryk, D. A. TiO2 Photocatalysis and Related Surface Phenomena. Surf. Sci. Rep. 2008, 63, 515−582. (2) Henderson, M. A. A Surface Science Perspective on TiO2 Photocatalysis. Surf. Sci. Rep. 2011, 66, 185−297. (3) Grätzel, M. Recent Advances in Sensitized Mesoscopic Solar Cells. Acc. Chem. Res. 2009, 42, 1788−1798. (4) Hagfeldt, A.; Boschloo, G.; Sun, L.; Kloo, L.; Pettersson, H. DyeSensitized Solar Cells. Chem. Rev. 2010, 110, 6595−6663. (5) Bouclè, J.; Ackermann, J. Solid State Dye-sensitized and Bulk Heterojunction Solar Cells Using TiO2 and ZnO Nanostructures: Recent Progress and New Concepts at the Borderline. Polym. Int. 2012, 61, 355−373. (6) Chen, X.; Shen, S.; Guo, L.; Mao, S. S. Semiconductor-based Photocatalytic Hydrogen Generation. Chem. Rev. 2010, 110, 6503− 6570. (7) Tachibana, Y.; Vayssieres, L.; Durrant, J. R. Artificial Photosynthesis for Solar Water-splitting. Nat. Photonics 2012, 6, 511−518. (8) Chambers, S. A. Ferromagnetism in Doped Thin-film Oxide and Nitride Semiconductors and Dielectrics. Surf. Sci. Rep. 2006, 61, 345− 381. (9) Thomas, A. G.; Flavell, W. R.; Mallick, A. K.; Kumarasinghe, A. R.; Tsoutsou, D.; Khan, N.; Stockbauer, R. L.; Warren, S.; Johal, T. K.; Patel, S.; Holland, D.; Taleb, A.; Wiame, F. Comparison of the Electronic Structure of Anatase and Rutile TiO2 Single-crystal Surfaces Using Resonant Photoemission and X-ray Absorption Spectroscopy. Phys. Rev. B 2007, 75, 035105. (10) Bikondoa, O.; Pang, C. L.; Ithnin, R.; Muryn, C. A.; Onishi, H.; Thornton, G. Direct Visualization of Defect-mediated Dissociation of Water on TiO2(110). Nat. Mater. 2006, 5, 189−192. (11) Martin Setvín, M.; Aschauer, U.; Scheiber, P.; Li, Y.-F.; Hou, W.; Schmid, M.; Selloni, A.; Diebold, U. Reaction of O2 with Subsurface Oxygen Vacancies on TiO2 Anatase (101). Science 2013, 341, 988− 991. (12) Yu, S.; Ahmadi, S.; Sun, C.; Adibi, P. T. Z.; Chow, W.; Pietzsch, A.; Göthelid, M. Inhomogeneous Charge Transfer within Monolayer Zinc Phthalocyanine Absorbed on TiO2(110). J. Chem. Phys. 2012, 136, 154703. (13) Kley, C. S.; Dette, C.; Rinke, G.; Patrick, C. E.; Cechal, J.; Jung, S. J.; Baur, M.; Dürr, M.; Rauschenbach, S.; Giustino, F.; Stepanow, S.; Kern, K. Atomic-Scale Observation of Multiconformational Binding and Energy Level Alignment of Ruthenium-Based Photosensitizers on TiO2 Anatase. Nano Lett. 2014, 14, 563−569. (14) Chen, X.; Mao, S. S. Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications. Chem. Rev. 2007, 107, 2891−2959. (15) Cohen, A. J.; Mori-Sànchez, P.; Yang, W. Insights into Current Limitations of Density Functional Theory. Science 2008, 321, 792− 794. (16) Mori-Sànchez, P.; Cohen, A. J.; Yang, W. Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction. Phys. Rev. Lett. 2008, 100, 146401. (17) Mori-Sànchez, P.; Cohen, A. J.; Yang, W. Discontinuous Nature of the Exchange-Correlation Functional in Strongly Correlated Systems. Phys. Rev. Lett. 2009, 102, 066403. (18) Diebold, U. The Surface Science of Titanium Dioxide. Surf. Sci. Rep. 2003, 48, 53−229. (19) 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. (20) Mattioli, G.; Filippone, F.; Alippi, P.; Amore Bonapasta, A. Ab Initio Study of the Electronic States Induced by Oxygen Vacancies in Rutile and Anatase TiO2. Phys. Rev. B 2008, 78, 241201.

ASSOCIATED CONTENT

S Supporting Information *

Interaction of methanol with periodic slabs and isolated nanoparticles. This material is available free of charge via the Internet at http://pubs.acs.org.

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ACKNOWLEDGMENTS

We acknowledge computational resources provided by the CINECA consortium (Grant ISCRA 2014 “BEAST”).

4. CONCLUSIONS Model TiO2 nanoparticles have been investigated in a theoretical framework based on the Hubbard-U corrected density functional theory and on the time-dependent density functional perturbation theory. Special care has been devoted to the accurate description of photocatalytic and photovoltaic processes involving the generation, localization and transfer of charge carriers in the NPs, as well as at selected molecule/NP interfaces. Our simulations support the reliability of the present theoretical approach and confirm its potentialities in the predictive investigation of complex catalytic environments and hybrid systems. Our results clarify several key points related to the role of TiO2 NPs involved in photocatalysis and photovoltaics, and provide useful information for the assessment of open questions as well as for the new interpretation of previous measurements. They indicate, in particular, that • Positive and negative charge carriers are preferentially trapped at undercoordinated surface sites. Holes are only found as small polarons trapped at 2-fold-coordinated O− sites, while electrons coexist as small polarons trapped at Ti3+ sites and band-like carriers. • Photogenerated electrons are efficiently scavenged by O2 molecules, whose reduction leads to the formation of stable, paramagnetic Ti(O2)1− adsorbates on the NP surface. • Photogenerated holes are captured by CH3OH molecules, likely through a proton-coupled electron transfer mechanism, leading to the formation of an adsorbed CH3O• species, first intermediate of methanol photooxidation. • The investigation of a model hybrid TiO2/L0 junction confirms the expected spontaneous formation of chargeseparated states and suggest that cost-effective theoretical tools can be fruitfully employed to obtain reliable prediction of the photovoltaic properties of hybrid organic photovoltaic devices.

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AUTHOR INFORMATION

Corresponding Author

*(G.M.) E-mail: [email protected]. Notes

The authors declare no competing financial interest. 29939



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Photocatalytic and Photovoltaic Properties of TiO2 Nanoparticles

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