Theoretical Studies on Anatase and Less Common TiO2 Phases: Bulk

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Theoretical Studies on Anatase and Less Common TiO2 Phases: Bulk, Surfaces, and Nanomaterials Filippo De Angelis,† Cristiana Di Valentin,‡ Simona Fantacci,† Andrea Vittadini,§ and Annabella Selloni*,∥ †

Computational Laboratory for Hybrid Organic Photovoltaics (CLHYO), Istituto CNR di Scienze e Tecnologie Molecolari, Via Elce di Sotto 8, I-06123 Perugia, Italy ‡ Dipartimento di Scienza dei Materiali, Università di Milano-Bicocca, I-20125 Milano, Italy § Istituto CNR per l’Energetica e le Interfasi (IENI), c/o Dipartimento di Scienze Chimiche, Universita’ di Padova, I-35131 Padova, Italy ∥ Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States 4.3. Polymers’ Morphology on TiO2 4.4. Quantum Dots on TiO2 5. Modeling TiO2 Nanoparticles 5.1. Shape, Size, and Phase Stability of TiO2 Nanocrystals 5.2. Molecular Dynamics of TiO2 Nanoparticles 5.3. Electronic Structure of TiO2 Nanocrystals 6. Less Common TiO2 Phases 6.1. Three-Dimensional Systems 6.1.1. Point Defects and Doping 6.2. Surfaces 6.3. Two-Dimensional Systems: Nanolayers, Nanosheets, and Films 6.3.1. Nanosheets 6.3.2. Adsorption 6.3.3. Point Defects and Doping 6.3.4. Supported Films 6.4. One-Dimensional Systems: Nanotubes 7. Concluding Remarks Author Information Corresponding Author Author Contributions Notes Biographies Acknowledgments References

CONTENTS 1. Introduction 2. Anatase Bulk: Electronic Properties 2.1. Remarks on Theoretical Methods 2.2. Band Structure 2.3. Polaronic States 2.3.1. Photoinduced Excitons and Intrinsic Polarons 2.3.2. Dopants Induced Polarons 2.3.3. Donors Induced Polarons (H and Li) 2.3.4. Surface Self-Trapped Polarons 2.4. Intrinsic Defects States 2.4.1. Oxygen Vacancies 2.4.2. Titanium Interstitials 2.4.3. Defect-Induced Ferromagnetism 2.4.4. Oxygen Interstitials 3. Anatase Surfaces: Energetics, Structure, and Reactivity 3.1. Clean Surfaces 3.1.1. Surface Energies 3.1.2. Surface Structure 3.1.3. Surface Defects 3.2. Adsorption of Small Molecules 3.2.1. Water 3.2.2. Molecular Oxygen 3.2.3. Methanol and Formic Acid 3.2.4. Water, Methanol, and Formic Acid at Step Edges on Anatase (101) 4. TIO2 Sensitization and Applications to Hybrid and Organic Photovoltaics 4.1. Dye and Coadsorbent Effects on TiO2 4.2. Insulating Metal Oxide Monolayers © XXXX American Chemical Society

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1. INTRODUCTION Driven by growing concerns for environmental and energy issues, interest in semiconductor-based heterogeneous photocatalysis has increased considerably over the last decades. Photocatalysis allows the use of sunlight for the destruction of highly toxic molecules and remediation of pollutants; for the selective, synthetically useful redox transformation of specific organic compounds; for the production of hydrogen, and the conversion of solar energy to electric power.1−12 Due to its abundance, nontoxicity, and high stability under a variety of conditions, the most widely used material in heterogeneous photocatalysis is titanium dioxide (TiO2).3,5,6,13,14 Accordingly,

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measurements that are not fully understood. Theoretically, the answer to the above question depends critically on the electronic structure method used for the calculations, and the question is not completely settled yet. Polaronic states have been obtained using “non-standard” DFT methods, but the degree of localization of the polaronic state depends on many details and is difficult to determine. Surfaces have a prominent role in nanomaterials, where a large fraction of atoms is at surface sites, and are also essential for understanding the material’s reactivity. In section 3 we thus review studies on the structure and reactivity of extended anatase surfaces, focusing on the (101), (001), and, to a lesser extent, (100) surfaces. These are the crystal faces that are most frequently exposed by anatase (nano)crystals, including natural anatase samples, and are also the surfaces for which the larger amount of theoretical studies is available. Similarly, in reviewing studies of the surface reactivity, we have chosen to focus on only a few representative probe molecules, which are important in photocatalysis and/or photovoltaics, notably water, oxygen, methanol, and formic acid. Of these, water is of particular interest because of its central role not only in photocatalysis but also in a variety of other fields, ranging from the synthesis of TiO2 nanomaterials and biomaterials to geochemistry and environmental chemistry.32−34 Surface functionalization/modification is widely used to induce new material’s properties that can be exploited for technological applications. In this review we focus on TiO2 surfaces’ modifications relevant to hybrid photovoltaics and dye-sensitized solar cells (DSCs). In hybrid photovoltaic devices a film of sintered TiO2 nanoparticles behaves as electron acceptor and transporter, to convey the photoexcited electrons from an electron donor. In DSCs the TiO2 surface is functionalized (sensitized) by a dye (or in general a light absorbing material) that is adsorbed on the TiO2 surface. Many theoretical investigations on the interaction of dyes with TiO2 have focused mainly on the properties of the adsorbate. In section 4 we review computational studies where the focus is rather on the modification of the TiO2 properties (notably the conduction band energies) upon functionalization with dyes, oxide overlayers, polymers, and quantum dots. Reviewed work ranges from studies exploring the correlation between the open circuit voltage Voc, a fundamental parameter of DSC devices, and the dipole moment of adsorbed species or electrolyte additives, to molecular dynamics studies addressing the relationship between the morphology of polymer-functionalized TiO2 and the improvement of the device efficiency. In many technological applications, TiO2 is present in the form of nanoparticles/nanocrystals. In section 5, we present an overview of computational studies of the properties of TiO2 nanoparticles in relation to these applications, particularly photocatalysis and hybrid/organic solar cells. The shape, size and crystal phase markedly influence the stability of TiO2 nanoparticles. Studies addressing these issues are reviewed in section 5.1. In particular, there have been several studies on the phase transitions between the anatase and rutile polymorphs, including the effects of aqueous environments with different pHs. Molecular dynamics simulations based on force field potentials have opened the possibility to model the sintering of TiO2 nanoparticles; these studies are reviewed in section 5.2. The evolution of modern parallel computers and computational algorithms have further expanded the scope of first-principles electronic structure simulations, allowing an accurate picture of the interplay between the structural and electronic factors

there has been a tremendous amount of studies on widely diverse aspects of TiO2 (nano)materials, ranging from their synthesis and characterization to atomic scale experimental and theoretical investigations of their fundamental physical and chemical properties.13,15−20 Even restricting to theoretical/ computational studies, it would be hard to provide an exhaustive overview of all the available work on TiO2. For this reason, in this manuscript we almost completely ignore the work on rutile TiO 2 , for which recent reviews are available,13,14,17,20 and focus mainly on theoretical/computational studies of anatase TiO2, and other phases relevant to TiO2 nanomaterials. As the majority of the available studies, most of the work described in this review is based on density functional theory (DFT) calculations,21,22 which have generally proven quite successful at both predicting TiO2 properties and explaining experimental observations on TiO2 systems over the last 20 years. DFT has also several difficulties22 and limitations,23 however, and theoretical studies of TiO2 materials based on a variety of more advanced techniques are reviewed in the following. To treat systems of large sizes, e.g., nanoparticles and interfaces, atomistic simulations based on classical interatomic potentials are often performed. These studies are reviewed only partially, focusing on work particularly relevant to photocalysis and photovoltaics. Of the three natural polymorphs of TiO2, rutile, anatase, and brookite, rutile is the thermodynamically most stable bulk phase, while anatase is very common and stable in nanomaterials.24,25 Interestingly, for a long time it has been challenging for first-principles electronic structure calculations to describe correctly the relative stabilities of the rutile and anatase bulk phases,26−29 and only recently the inclusion of dispersion interactions, not present in usual DFT calculations, has been shown to be essential for reproducing the observed greater stability of rutile with respect to anatase.30 Besides being stable in nanoparticles, the anatase phase shows also the highest photocatalytic activity,31 making it the most interesting phase for use in high surface area photocatalytic and photovoltaic devices.4 A key role in all these applications is played by the electronic properties. For instance, the positions of the conduction and valence band edges relative to the potentials of relevant redox couples determine whether a photocatalytic reaction can occur or not; the band gap determines the optical absorption, which has an essential role in the performance of photocatalytic devices; the states near the valence and conduction band edges have a major influence on the electrical conductivity and chemical reactivity. For these reasons, we start this review with a survey of the electronic properties of bulk anatase (section 2). We first review some of the issues and recent progress in the study of the band structure of pure anatase, focusing on the description of the band gap. An accurate theoretical description of the band gap is indeed important because it would allow quantitative prediction of the energies of trap states, defect, and impurity levels, as well as the influence of doping on optical absorption; all these quantities are crucial for the design of TiO2 materials with improved properties. Also in section 2, we discuss the character of electron and hole states in anatase, i.e. whether charge carriers (originating from photoexcitation, doping or intrinsic reducing defects) are in delocalized band states or are coupled to the lattice polarization to form more or less localized polaronic states. The polaronic picture is supported by various experimental observations, but there are also significant differences between the results of spectroscopic and transport B


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underlying the properties of realistic TiO2 nanocrystals of few nm size. We discuss these results with emphasis on the role of electron/hole traps in photoelectrochemical and photocatalytic processes. The role of surface passivation and sintering of TiO2 nanocrystals on the electronic properties of model systems is also discussed. Finally, section 6 presents an overview of less common TiO2 polymorphs, including brookite (the third natural form of TiO2), TiO2(B) (also observed in nature but only in trace amounts), the so-called “high-pressure TiO2 phases”, and the lepidocrocite-like polymorph, which forms 2D sheets. In section 6.1, we review studies on the bulk and surface properties of these polymorphs, including defects, doping, and the adsorption of small molecules. Section 6.2 focuses on 2D nanomaterials, notably nanosheets and supported films, while section 6.3 discusses 1D nanomaterials, with particular focus on the mechanism of formation of nanotubes.

sufficient. There are two main approaches to go beyond DFT in these cases,23 notably: (i) many-body perturbation theory (MBPT) in the GW approximation and the Bethe-Salpeter equation; (ii) time-dependent DFT (TD-DFT). The latter approach is appealing for being simpler and computationally more affordable than MBPT, but the typical approximations that are used for the exchange-correlation kernel of TD-DFT fail to reproduce the optical absorption spectra of extended systems, which are instead well described by solving the BetheSalpeter equation of MBPT.47 For solid materials, MBPT methods are used to describe both the optical spectra and, more frequently, the single particle excitations by the GW approximation, with increasing applications to large and more realistic models.48 The situation is different for finite systems, e.g. molecules and clusters, for which TD-DFT methods are widely used and work quite well in most cases.49,50

2. ANATASE BULK: ELECTRONIC PROPERTIES

Anatase has a tetragonal lattice (P42/mnm) with four TiO2 units per unit cell forming chains of slightly elongated TiO6 octahedra. The Ti−O bonding is largely ionic with some covalent contribution.51 The dielectric properties show a significant anisotropy with static (optical) dielectric constants of 22.7 (5.41) and 45.1 (5.82) for polarization parallel and perpendicular to the c axis, respectively.52 The large difference between static and optical dielectric constants is already an indication of the importance of lattice relaxation effects in this material. The electronic structure of semiconducting oxides is challenging to describe even for state-of-the-art computational methods. The two most critical quantities to be accurately reproduced are the band gap and the band edge positions with respect to the vacuum reference level. For anatase, the minimum fundamental band gap is indirect, with the bottom of the conduction band (CB) at Γ and the top of the valence band (VB) close to the X point, along the Δ (or Γ-X) direction. Two relevant gaps should be considered: the fundamental or electronic band gap and the optical band gap. Experimentally, the fundamental band gap was determined to be 3.2 eV with electrochemical measurements at room temperature (RT),31 while for the optical band gap a value of ∼3.4 eV was obtained with optical absorption measurements at 4 K.53 Theoretically, the band gap is generally determined from the difference of the lowest unoccupied and highest occupied Kohn−Sham eigenvalues. As mentioned in the previous section, this is significantly underestimated by DFT-LDA and DFT-GGA. On the contrary, hybrid functionals, with a typical 20−25% contribution of exact exchange, overestimate the anatase band gap.54 A reduction of this contribution to 12−15% makes the Kohn−Sham gap match the experimental fundamental gap of TiO2.54 For the screened hybrid functional HSE different values have been reported, ranging from 3.58 to 3.89 eV.55,56 With the DFT+U method, very large and unphysical U values (U = 6 eV) for the on-site correction on Ti 3d states are required to reproduce the experimental band gap, whereas the use of the self-consistent linear response derived U value (U = 3.23 eV) improves only slightly the band gap given by GGA.56 Interestingly, the situation highly improves when an additional on-site correction on the O 2p states is introduced, and in this case the computed band gap matches the experimental one.56 For bulk stoichiometric anatase, given the limited size of the system, quasiparticle calculations with the GW approximation

2.2. Band Structure

2.1. Remarks on Theoretical Methods

As pointed out in the introduction, most of the calculations discussed in this review are based on DFT.21 This approach has gained a prominent position in the general scenario of computational materials science thanks to its rather high accuracy at a relatively low cost. In most cases, the local density approximation (LDA) or the generalized gradient approximation (GGA)35,36 is used for the exchange correlation functional. Because of these approximations, however, DFT suffers of a residual electron self-interaction and an improper description of electronic correlations,22,37 causing a number of problems, such as the underestimation of band gap values and the overdelocalization of electrons in defects or impurity states, which are commonly predicted to be shallower than they should be. Another major issue is the fact that, being a ground-state theory, DFT is intrinsically not suitable to describe excited systems. Viable approaches for the correction of the electronic selfinteraction are DFT+U,38,39 where an on-site Hubbard U repulsion is added on selected localized orbitals, and hybrid density functional methods,40,41 which include a fraction of exact Hartree−Fock exchange in the DFT exchange-correlation functional. These approaches generally provide an improved description of the one electron spectrum (e.g., the fundamental gap and photoemission energies), but a limitation is that they depend on the chosen value of U or the percentage contribution of exact exchange in the case of hybrid functionals. The U term can be derived from first-principles,39 but it is often empirically set to the value that correctly reproduces the experimental fundamental band gap. Unfortunately, this practice can have severe consequences on the description of other properties,42 for example of defects states in the gap, as it will be discussed later in this review. As for hybrid functionals, recently a new generation of screened hybrid density functionals (also named short-range hybrid functionals) has been developed which neglect the long-range Hartree−Focklike exchange,43 and better reproduce the band gaps and other properties of solid state materials.44−46 However, DFT+U methods have a much lower computational cost in comparison to hybrid functionals, and therefore are often preferred to the latter in many studies of oxide materials. To calculate excitation energies (e.g., the optical spectrum), the knowledge of the static ground-state density is not C


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Figure 1. (a) Electronic band structure of anatase bulk along the high symmetry directions of the first Brillouin zone. Black lines indicate the GGA calculation, yellow dots indicate the values obtained after G0W0 corrections. (b) Imaginary part of the dielectric constant for anatase, in-plane polarization xy left and out-of-plane polarization z right, calculated by GGA random-phase approximation (RPA@PBE, dashed blue line) using G0W0 on top of GGA (RPA@GW, dotted light green) and via Bethe-Salpeter equation (BSE@GW, black solid line). The experimental spectrum solid dotted black is also shown for comparison purposes (Cardona, M.; Harbeke, G. Phys. Rev. 1965, 137, A1467). Insets: BSE spectrum (BSE2, red solid line) calculated by including in the screening calculation the proper G0W0 electronic gap. Reproduced with permission from ref 59. Copyright 2010 American Physical Society.

have recently become available (Figure 1a).57−59 Both G0W058,59 and self-consistent GW (scGW)57 calculations are reported in the literature, but they all appear to overestimate the band gap. G0W0 results are dependent on the starting point, while scGW calculations are known to give too large band gaps, especially for polar materials.57 The causes for this error have been discussed in the literature.57 Better starting points for the G0W0 approach are provided by calculations based on hybrid functionals (HSE)60 or the DFT+U.61 UV light absorption causes electrons to be excited in the conduction band with holes left in the valence band. Thus, to correctly reproduce the optical band gap associated with this event, the inclusion of two-particle interactions, i.e., the interaction between the photoinduced CB electron and VB hole, is necessary. Bethe-Salpeter equations have been used to simulate the experimental optical spectra of bulk anatase TiO2 in several studies.58,59,62 In particular, so-called BSE@GW curves match nicely the experimental spectral shape59,63 of anatase for both xy and z polarizations, radically improving the poor description obtained with an independent particle approach (RPA; Figure 1b). It should be noted, however, that even these sophisticated BSE@GW calculations do not take into account important effects such as electron−phonon coupling (indirect processes) and self-trapping phenomena, whereby exciton creation induces a local ionic relaxation which traps the exciton (see section 2.3). As mentioned above, the second critical issue is the correct alignment of the anatase valence and conduction bands with respect to the vacuum. Two quantities need to be accurately computed: the workfunction or ionization potential (IP), and the electron affinity (EA) of the stoichiometric material. Recently the IP of bulk anatase was estimated considering a QM/MM cluster model,64 and employing a hybrid meta-GGA method.65 The authors noticed that the difference between their computed value of the IP (8.3 eV) and the commonly accepted band gap value for anatase (3.2 eV), corresponds to

an estimated EA of 5.1 eV, in good agreement with the experimental result of 5.1 eV.66 2.3. Polaronic States

The question whether charge carriers in TiO2 behave as quasifree electrons and holes or are coupled to the lattice polarization to form polarons has been the subject of longlasting debates. The electron transport, which is a key aspect of most applications of TiO2 (e.g., photocatalysis, new generation photovoltaics, etc.), depends strongly on the nature of the electronic states. Charge carriers can originate from photoexcitation, reduction, or doping. We discuss these different cases separately in the following sections. 2.3.1. Photoinduced Excitons and Intrinsic Polarons. Ultraviolet photoexcitation of anatase TiO2 causes the creation of excitons which can become self-trapped. The existence of self-trapped excitons in bulk anatase is proven by the large Stoke-shift of the photoluminescence emission peak, centered at 2.3 eV,67,68 and is also indicated by the Urbach tail dependence of the absorption peak edge with temperature.53 In order to be able to describe the self-trapping process of excitons and polarons within density functional model calculations, it is necessary to introduce some correction to the self-interaction error. As mentioned in the previous section, this can be done by replacing part of the semi(local) exchange with the exact Hartree−Fock exchange or by introducing a Hubbard U term which penalizes the delocalized solutions. For example, the triplet exciton has been modeled in a periodically repeated bulk anatase supercell (96-atoms) with the hybrid functional B3LYP, first in the singlet (S0) ground state relaxed atomic structure and then, through internal coordinates optimization, in the triplet (T1) relaxed (self-trapped) atomic structure.69 (As the triplet state of lowest energy, the triplet exciton can be determined by standard DFT minimization techniques with the constraint S = 1 for the total spin.) The reorganization energy associated with the exciton self-trapping is estimated to be about 0.6 eV, while the computed T1-S0 photoluminescence D


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temperature which can be self-trapped through lattice reorganization. The application of polaron theory to transition metal oxides, including TiO2, has been discussed by Austin and Mott75 in terms of effective mass, mobility and hopping. The activation barrier for electron transport via polaron hopping has been estimated within the Marcus-Emin-Holstein-Austin-Mott theory using the DFT+U method and found to be ∼0.3 eV along both the [100] and [201] directions in bulk anatase76 (Figure 3). Electron polarons in anatase are usually identified as Ti3+ species where the electron is largely trapped at one Ti lattice site which is characterized by elongated Ti−O bonds. The size of the polaron cannot be easily established and is still under debate. From a theoretical point of view, the polaronic nature of extra electrons in the perfect anatase lattice has been described using either hybrid functionals69 or DFT+U.76,77 The size and degree of localization of the electron polaron can be affected by the fraction of exact exchange or the value of U. HSE06 calculations with 25% of exact exchange did not find electron self-trapping at regular Ti lattice sites in anatase,78,79 at odds with the rutile bulk case where Ti3+ species were identified with the same functional.78,80 With the hybrid functional B3LYP, instead, it is found that a fraction of about 0.76 electron is localized on a single Ti ion and the remaining 0.22 electron is shared by the four next-nearest Ti ions.69 As a result, ∼0.98 of the electron charge is confined within a sphere of about 6 Å in radius, even though the polaron lattice reorganization has a longer range. The corresponding electron polaron self-trapping energy is estimated to be 230 meV with B3LYP,69 suggesting that electron polarons in bulk anatase are rather weakly bound. This picture has been confirmed and reinforced by recent experimental studies on anatase samples heavily doped with Ovacancies.81,82 Here the radius of the electron polaron states was estimated to be ∼20 Å and the corresponding energy 10 to 100 meV below the bottom of the CB (Figure 4). Hole self-trapping has been obtained with different hybrid functionals and with DFT+U,69,77−79 even though the value of

emission peak is at 2.6 eV. Given the approximations of the model and the approach used, the agreement with experiment can be considered excellent (see Figure 2). The triplet exciton is highly localized on two nearest-neighbor Ti6c3+ and O3c− ions, although lattice relaxation effects extend to larger distances.

Figure 2. Schematic representation of the S0-T1 excitation, exciton self-trapping and emission energies for bulk anatase TiO2 as computed with spin polarized B3LYP calculations on a 96-atoms supercell model. Experimental emission energy from refs 67 and 68.

Electrons and holes that do not undergo radiative recombination can follow different paths and thus separate. Transient photoconductance measurements indicate that the recombination rate in anatase is much lower than in rutile,70 probably as a consequence of the indirect minimum band gap. Photogenerated charges in TiO2 have been probed also by electron paramagnetic resonance71,72 and by infrared spectroscopy73,74 and found to form localized polaronic states at low

Figure 3. (a) Schematic diagram of polaron e− transfer. In the initial state A, with structure qA, the electron is localized on the left Ti ion, while in the final state B, with structure qB, the electron is localized on the right Ti ion. At the transition state C, with structure qC, a thermal transfer regime, the electron is shared between the two Ti ions. (b) General features of Marcus-Emin-Holstein-Austin-Mott theory for symmetric polaron transfer. The potential-energy surfaces of the initial state A and final state B are shown with equilibrium structures qA and qB. The initial state is Ti3+−Ti4+ and the final state is Ti4+−Ti3+. The coincidence state, or transition state, between the two states is shown as qC. The reorganization energy corresponds to the energy of the final state B at the geometric configuration qA. The diabatic activation energy is shown as ΔG*. The adiabatic energy curves are shown as dashed lines, with the electronic coupling matrix element VAB given as twice the energy difference between the two adiabatic states. Reproduced with permission from ref 76. Copyright 2007 American Physical Society. E


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Figure 4. (a) An as-grown anatase single crystal. (b) The BZ of anatase. (c),(d) constant energy maps at EF (T = 20 K, hν = 85 eV) of electrondoped anatase (001) in the kxky (c) and kxkz (d) planes, respectively. The blue lines outline the boundaries of the 3D BZs. (e) E vs k dispersion of the bottom of the conduction band for a sample with ne ≈ 3:5 1019 cm−3. (f) ARPES intensity measured at k = kF for a sample with ne ≈ 5 × 1018 cm3. The solid line is a Franck−Condon line shape. Voigt peaks of width E = 90 meV (fwhm) are separated by 108 meV, while intensities follow a Poisson distribution. (g−i) Cartoon of the polaron formation induced by the photoemission process, showing the solid in its ground state (g) and two possible final states (h and i) of ARPES. Reproduced with permission from ref 82. Copyright 2013 American Physical Society.

site, see, e.g., refs 83, 84. Transparent Ti1−xNbxO2 films with x ≥ 0.01 have been found to exhibit metallic behavior.83 The existence of electron polarons in niobium, antimonium and fluorine doped anatase was probed by EPR measurements.85,86 Several computational studies have also been reported. Typical substitutional dopants used to create electron polarons in anatase are Nb, Sb, V, Ta, and F,18,55,87−90 while Al, Sc, Ga, and In are used to create hole polarons.55,91 Analogously to what described in the previous section, the character of the impurity states depends critically on the density functional method used for the calculations. If (semi)local functionals are used,87,90 a V, Nb, or Ta impurity gives rise to a broad resonance in the conduction band, and therefore the extra electron coming from this impurity is in a delocalized CB state. On the contrary, GGA +U88 and B3LYP18 calculations indicate the formation of a localized polaron. At odds with these findings, but in line with what reported above for intrinsic self-trapped polarons, the HSE functional predicts that the electron from a Nb impurity is in a completely delocalized state,55 a result that can more directly explain the metallic behavior of Nb-doped anatase observed experimentally. Results similar to the HSE ones were obtained also with another screened exchange (sX) hybrid functional,92 whereas highly localized Ti3+ polarons were found for Nb-doped rutile.55,92 Hole polarons deriving from substitutional doping in bulk anatase have been systematically studied by Deak et al. by means of the HSE hybrid functional.55 They considered Al, Ga, In, Sc, and Y substitutional doping. For the Al case, they computed the photoluminescence emission peak from the hole trapping state at 1.4 eV, which compares well with the experimental value of 1.7 eV. Al incorporation into the anatase structure was also investigated with a semiempirical approach.91 Other computational studies examined Al-doping in the rutile phase.93,94 2.3.3. Donors Induced Polarons (H and Li). Hydrogen95 and lithium96,97 are particularly interesting donor dopants (Figure 5). Hydrogen atoms donate the valence electron and form O−H bonds with the lattice oxygens, as probed by various

the self-trapping energy at a fully coordinated bulk anatase O site depends significantly on the method used, as it varies from 0.2 eV with HSE (estimated from the adiabatic transition level) to 0.74 eV with B3LYP (determined as a difference of total energies). Hole-associated acceptor states in anatase are generally found to be deeper in the gap than electronassociated donor states.55,69 Such traps have been experimentally proved to exist by EPR studies with 17O labeling.71 The comparison of measured hyperfine coupling constants with computed ones is fairly satisfactory.69 2.3.2. Dopants Induced Polarons. The formation of electron and hole polarons in anatase TiO2 can be also induced by substitutional nonisovalent dopants (Figure 5). A number of experimental studies have analyzed the electronic properties of n-type Nb-doped anatase, where niobium is substituted at a Ti

Figure 5. Ball and stick representation of pure and stoichiometric anatase TiO2 bulk structure. On the left top side, spin density plot associated with Ti3+ centers deriving from one lattice oxygen vacancy. On the left bottom side, spin density plot associated with an interstitial Ti3+ ion. On the right top side spin density plot of Ti3+ species deriving from n-type dopants (e.g., F). On the right bottom side spin density plot of Ti3+ species from donor dopants (e.g., H). B3LYP calculations on a 96-atoms supercell. From ref 18. Copyright 2009 American Chemical Society. F


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2.4.1. Oxygen Vacancies. The removal of a neutral oxygen atom from stoichiometric bulk anatase leaves two excess electrons in the lattice which becomes reduced. This process can be easily observed after thermal annealing treatments. For this reason TiO2 is known as a reducible semiconducting oxide. It is also generally recognized that partial reduction of TiO2 is associated with the formation of Ti3+ species. For example, it is observed that, following the creation of O vacancies, a small peak in the photoemission spectrum of anatase single crystals appears at around 1 eV binding energy, which is assigned to Ti3+ species.102,103 Very recently it was shown that anatase TiO2 can be tuned from an insulator to a polaron gas to a weakly correlated metal as a function of the electron doping by UV photon irradiation creating oxygen vacancies in the bulk of the material.82 In particular, the single polaron picture valid at low density of defects is found to break down as charges added to the conduction band progressively screen the electron−phonon interaction at the basis of the polaron self-trapping. The electronic model of an oxygen vacancy defect in anatase has evolved significantly during the past decade. Before 2008, it was usually accepted that oxygen vacancies in anatase do not produce levels in the band gap but rather give rise to delocalized resonant states at the bottom of the conduction band.104 Following the pioneering work on rutile,105−108 several studies showed that if some self-interaction correction is introduced in the calculations, either in terms of exact exchange in hybrid functionals or in terms of a Hubbard U correction in DFT+U, the oxygen vacancy states become localized on few Ti lattice sites with an associated polaronic distortion98,109(Figure 5). At the same time, defect levels appear in the band gap at about 1 eV below the bottom of the conduction band, consistent with experiment.102,103 This general picture of the electronic structure for oxygen deficient anatase has been confirmed by many studies.56,77−80,110 However, depending on the computational method and setup, the details of the electronic states associated with the VO defect are different. (i) In DFT+U studies there is a significant dependence of the defect state energy levels in the band gap on the value of U applied on the Ti 3d states. Values of U between 3 and 4 eV are often considered most appropriate since they give rise to defect state level positions consistent with experiment (∼1 eV below the bottom of the conduction band), even though they do not properly reproduce the band gap of anatase. In particular, the U value determined by the self-consistent linear response approach,39 U ≈ 3.2−3.3 eV for Ti atoms in the anatase lattice, fits well in this range of values. On the other hand, larger U values that better reproduce the band gap (U > 5 eV) lead to very undesirable effects such as defect levels inside the valence band. Hybrid functional calculations show also a dependence of the position of the defect states on the fraction of exact exchange in the functional. For hybrid functionals, however, values which provide a reasonable band gap (20−25% as in B3LYP or HSE), also give reasonable positions of the defect states in the gap. (ii) The two excess electrons deriving from the removal of the oxygen atom may prefer to be spin paired (close-shell solution)78 or spin parallel (open-shell solution).77,98,56,109 (iii) The two excess electrons can be trapped at different Ti ions: either on the two undercoordinated Ti ions56,77,78 or on one undercoordinated Ti ion and on a neighboring 6-fold Ti ion,56,98 or even, as found in some studies, only one electron is trapped at a Ti3+ site, while the second remains delocalized in a resonant conduction band state.56,98,109 From a more technical point of view, we note that

Infrared studies for mixed anatase/rutile (Degussa) and pure rutile nanoparticles.73,95 In GGA+U and B3LYP calculations two types of solutions exist where the electron is either delocalized or almost entirely transferred to the Ti ion bound to the newly formed hydroxyl species,98 while only a totally delocalized solution is obtained with the HSE functional.55 Lithium atoms intercalate in the lattice interstices and also donate the extra electron to form lattice Ti3+ species.96 The GGA+U picture of the Li-induced states is a strongly localized polaron at a Ti3+ site, associated with the appearance of a defect state about 1 eV below the conduction band.99 As usual, local and semilocal DFT calculations describe the excess electronic charge as distributed over all the Ti atoms in the supercell, giving a metallic system with partial occupation of the bottom of the conduction band (see references in ref 99). Core level and valence photoemission measurements on LixTiO296 indicate an electronic charge transfer to the Ti 3d level of about 0.85 ± 0.10 as well as the formation of a localized defect state about 1 eV below the conduction band, in very good agreement with the GGA+U calculations. 2.3.4. Surface Self-Trapped Polarons. Electrons and holes that do not recombine may diffuse from the bulk to the surface, where they can trigger redox transformations of adsorbed species.100 The polaron self-trapping energy is larger at the surface, thus making the electron and hole diffusion from the bulk to the surface energetically favorable, according to B3LYP calculations on anatase (101) slab models.69 Note that electrostatic interactions between electrons (or holes), as well as surface charging and band bending effects are not included in these simplified models. Electrons are trapped at surface undercoordinated Ti sites with an energy gain of 0.6 eV, while holes are trapped at bridging (2-fold coordinated) Oxygen surface sites with an even larger gain of 1.4 eV.69 Holes can be trapped also by surface hydroxyls. These species are often invoked when discussing surface reactivity. Surface hydroxyls are considered to be excellent hole traps since hydroxyl radicals have been often observed through EPR spectroscopy. Recently, it has been possible to prove by means of a hybrid density functional study that hydroxyl groups on the anatase (101) surface are truly capable of hosting a hole.69 However, it was also shown that this is only possible when they are not involved in hydrogen bonding with other hydroxyl species on the surface because the interaction with a proton through hydrogen bonding inhibits the hole trapping by the hydroxyl, preferring other surface low coordinated oxygen species (bridging oxygens), as trapping sites. Subsurface layer ions could also trap electrons or holes, as found for the rutile (110) surface where the most stable Ti trapping site is in the first subsurface layer (0.15 eV better than a Ti5c surface trap), according to a PBE+U study.101 It should be kept in mind, however, that polarons will hop from one site to the next at finite temperature and will thus visit many surface and subsurface sites in a relatively short time scale.76 2.4. Intrinsic Defects States

Intrinsic defects are extremely important since they determine the electrical conductivity and optical properties of TiO2. Slightly reduced anatase samples, resulting from common thermal treatments, are electrically conductive. Further reduction induces the characteristic blue color observed in many samples. Understanding the electronic structure modifications induced by these types of defects is thus crucial in order to be able to tailor and control the material properties. G


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reduced anatase can also explain spectroscopic features and transport properties in a way analogous to the oxygen vacancy model. 2.4.3. Defect-Induced Ferromagnetism. Undoped anatase TiO2 thin films have been found to have room-temperature ferromagnetic behavior,120 and experimental evidence exist that the magnetic properties are related to the presence of oxygen vacancies.120 Similar results have been obtained also on single crystals of rutile which are supposed to be free from any unwanted impurity. These findings triggered a lot of computational work aimed at rationalizing the observed behavior. Nonmagnetic, ferromagnetic and antiferromagnetic solutions for the two extra electrons left by the removal of a neutral oxygen atom have been investigated and compared in a number of studies, leading to contrasting solutions. According to LSDA,121 GGA,122 and GGA+U (U = 4 eV)123 studies, oxygen vacancies in anatase are not related to the so-called d0 ferromagnetism since they do not induce any appreciable magnetic moment, even at a rather high concentration (TiO1.75 in ref 123). On the contrary, GGA+U calculations with both U = 3.5 and 5.8 eV124 show that the extra electrons, in a 48-atoms anatase bulk supercell model (TiO∼1.95), convert two Ti4+ into two Ti3+ ions resulting in a local magnetic moment of about 1.0 μB per Ti3+ ion. The antiferromagnetic solution is found to be lower in energy than the ferromagnetic one with both the U values considered.124 In summary, there is no unifying and conclusive outcome from the existing studies, so that the origin of the magnetic properties of undoped TiO2 is still an open question. 2.4.4. Oxygen Interstitials. Only few studies of interstitial oxygen species are available. These show that an additional neutral oxygen atom prefers to bind to a lattice oxygen atom forming an O−O bond,104,125 instead of being stabilized as a charged species in the middle of an interstice. Interestingly, oxygen interstitials are predicted to be good electron traps by GGA+U calculations.125 The extra electron occupies a σ* state, which leads to a significant elongation of the O−O bond from 1.484 to 1.970 Å.

it is often important to introduce a small local lattice distortion of the initial atomic configuration in order to converge to a localized electronic state. Different choices of the initial lattice distortion generally lead to different localized solutions and many different initial configurations should thus be sampled in order to identify the most stable localized solution. A thorough study of this type was carried out by Deskins et al.111 for an Ovacancy on the rutile TiO2(110) surface. This variety of possible solutions is an indication that at finite temperature the electron polarons associated with an oxygen deficiency are likely to hop from one cationic site to the next, with some preference for the ones adjacent to the defect. This picture is also supported by an ab initio molecular dynamics study on the rutile polymorph.112 The polaronic nature of oxygen vacancy states is also crucial for understanding the dual character of these defects: on the one hand their behavior is that of deep traps, as probed by photoemission measurements, on the other hand they induce an n-type conductivity.56 In fact, the large energy gain associated with the polaronic relaxation or reorganization effectively drops the energy cost of adiabatic or thermodynamic electronic transitions (involved in the electron transport) with respect to that of vertical electronic transitions (probed by the spectroscopic techniques).56 2.4.2. Titanium Interstitials. Reduced titania can be represented by two chemical formulas, TiO2‑x and Ti1+xO2. The former corresponds to the situation where there is a deficiency of oxygen atoms (as discussed in the previous paragraphs), while the latter represents the situation where there is an excess of titanium atoms. The true nature of reduced anatase and rutile TiO2 has been debated for a long time,113 and it is possible that both type of defects, oxygen vacancies and Ti interstitials, coexist in nonstoichiometric TiO2 in different concentrations, depending on the sample preparation and treatment. Experimental evidence of the existence and role played by Ti interstitials have been reported in the literature, especially for rutile,114,115 but more recently also for anatase.116 The Ti interstitial species, which is highly symmetric in an octahedral (Oh) coordination in bulk rutile,117,118 is a low symmetry species in anatase (C2v).104,117,119 It is relevant to note that it is actually such low symmetry and the large distortion caused by the insertion of a Ti atom in the lattice interstice that makes this defect a good electron trapping site (Figure 5), even at the GGA level of theory. The introduction of some exact exchange or of a Hubbard U parameter enhances the trapping ability, producing lower defect states in the gap. Differently from the case of oxygen vacancies, however, for a Ti interstitial a state in the band gap is predicted also by PBE calculations;110,117 a similar result is found also in the case of rutile.115 Depending on the method used, there will be a larger portion of electron trapped at the interstitial Ti ion; this fraction is 0.61 in PBE but becomes 0.86 in B3LYP (Tii3+). The other three electrons introduced by the addition of one Ti atom (for the overall neutrality) are donated to the lattice and they are found to be distributed on the next shell of lattice Ti ions, forming other Ti3+ species. There are many analogies between the vertical and adiabatic transition energy levels of the interstitial Ti species and those of the oxygen vacancies in anatase.56 Thermodynamic transition levels are much shallower than vertical transition levels, as observed for oxygen vacancies. The barycenter of the transition levels is about the same for the oxygen vacancy transitions (+1/ 0 and +2/+1) and for the Ti interstitial transitions (from +1/0 to +4/+3). Thus, the model of interstitial titanium species for

3. ANATASE SURFACES: ENERGETICS, STRUCTURE, AND REACTIVITY Because of difficulties in growing sufficiently large single crystals, for many years most of the available experimental information on the surface chemistry of anatase has been based on studies of disperse samples. Over the past decade, however, the situation has changed significantly with the development of various growth techniques, and currently large anatase samples in the form of epitaxial thin films126 and bulk material82 are available. This has led to a considerable increase in the number of experimental studies on anatase surfaces, including several atomic scale surface science studies, which, in turn, have motivated a large amount of theoretical studies. 3.1. Clean Surfaces

3.1.1. Surface Energies. Surface energies have a central role in the thermodynamic, structural, and chemical properties of TiO2 surfaces. Besides determining the relative stabilities of different structures and terminations and thus the crystal shape, surface energies are essential for understanding the phase stability of different TiO2 polymorphs, notably the phase transformation from anatase to rutile in nanocrystalline TiO2. In addition, surface energies are related to the surface reactivity, as a low surface energy generally corresponds to a low H


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Table 1. Surface Energies (in J/m2) of Selected Low Index Anatase Surfaces, As Obtained in Different DFT Studies surface

LDA, refs 26 and 129

PBE, refs 26 and 129

PW91, ref 131

PW91, ref 132

PBE, ref 134

PBE0, ref 136

PW1PW, ref 135

(101) (100) (001) (110)

0.84 0.96 1.38

0.44 0.53 0.90 1.09

0.435 0.533 0.984 1.024

0.35 0.39 0.51 0.81

0.609 0.712 1.082

0.65 0.79 1.27 1.34

0.64 0.81 1.36 1.38

reactivity. These reasons, coupled with the fact that surface energies are difficult to measure experimentally, explain why anatase surface energies have been the subject of numerous theoretical studies. In the work reviewed in this section, surface energies and corresponding equilibrium crystal shape are calculated assuming perfectly clean, stoichiometric and defectfree bulk-terminated surfaces. As defects, steps, and adsorbates are generally present on the surfaces of real materials, the crystal shape calculated under the above assumptions should in principle be very different from the shapes observed in experiment. Interestingly enough, however, this “ideal” anatase crystal shape is rather common in colloidal particles as well as in natural anatase samples. The structure and stability of anatase surfaces were first studied by Oliver et al.,127 who performed atomistic simulations based on classical interatomic potentials128 and compared the surface energies and equilibrium shapes of anatase and rutile TiO2. For anatase, they found that the (101) and (001) surfaces dominate the morphology, as observed experimentally for natural anatase crystals, with the (001) surface slightly more stable than the (101) one. The latter result does not agree with the observed predominance of (101) facets in the morphology of most anatase samples. Based on the computed surface energies of Oliver et al.,127 Zhang and Banfield24 performed a thermodynamic analysis of the phase stability of nanocrystalline anatase and rutile. Their study predicts that anatase becomes more stable than rutile when the particle size is smaller than ∼14 nm, consistent with the observation that nanomaterials grow preferentially in the anatase phase and transform to rutile when the particle size increases.24 First-principles calculations of the energetics of anatase surfaces have been reported by several groups.26,129−136 In these studies, surfaces are usually modeled as slabs of finite thickness with periodic boundary conditions in the surface plane, and surface energies are determined from the difference between the total energy of the slab and the total energy of an equal number of TiO2 units in the bulk phase, divided by the total exposed area. Computed surface energies for a few low index bulk-terminated surfaces of anatase are presented in Table 1. By hybrid functional B3LYP calculations on unrelaxed or partially relaxed surface models, Beltràn et al130 found that the relative energies of low Miller index surfaces follow the sequence (001) < (101) < (100) < (110). As shown by other DFT studies,26,129,134 however, relaxation has a major effect on the surface energetics, e.g. it can reduce the surface energy by more than 50%. For the relaxed surfaces, the relative energies follow the sequence (101) < (100) < (001) < (110), which can be related to the density of undercoordinated Ti surface atoms on the different surfaces.26 The same sequence is obtained with a variety of DFT functionals, including LDA, GGA, and different types of hybrid functionals.26,131,132,134−136 Once the surface energies are known, the equilibrium shape of a macroscopic crystal can be determined via the Wulff construction. The computed Wulff shape for anatase is shown in Figure 6. As typically found for natural samples, it consists of

Figure 6. Equilibrium shape of a TiO2 crystal in the anatase phase, according to the Wulff construction and the calculated surface energies of refs 26 and 129. Reprinted with permission from ref 26. Copyright 2001 American Physical Society.

a truncated tetragonal bipyramid exposing majority (101) and minority (001) facets.26,129,131,132 The most stable (101) facets dominate the crystal surface, e.g. constituting more than 94% of the exposed surface according to ref.26,129 Using DFT surface energies for anatase and rutile, thermodynamic studies of the anatase vs rutile phase stability as a function of nanoparticle size predicted that at low temperature a phase transition occurs at an average anatase diameter of about 9.3−9.4 nm.132 The equilibrium shape of anatase is further discussed in section 5.1, where the influence of different adsorbed species is considered. 3.1.2. Surface Structure. 3.1.2.1. Anatase (101). It is known from LEED experiments137 that clean anatase (101) has the same (1 × 1) periodicity of the bulk-terminated surface, consistent with the low formation energy of this surface (see Table 1). Figure 7 shows the characteristic sawtooth profile of

Figure 7. Side view of the anatase (101) surface. Relevant structural parameters are given in Table 2 I


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Table 2. Bond Distances (Å) on the Relaxed (101) Surface and Their Deviations from the Unrelaxed Value (in Parentheses), from DFT-PBE Calculations26a Ti1 Ti2 Ti3 a

O1

O2

O3

O4

O5

O6

1.83 (−8.6%) 1.84 (−5.0%)

1.98 (+2.0%) 2.01 (+0.3%)

2.07 (+3.3%) 1.94 (−0.3%)

1.78 (−8.4%) 2.10 (+5.1%) 2.04 (+5.2%)

2.11 (+8.7%) 1.98 (−1.2%)

1.94 (0.0%)

Atom labels are as in Figure 7.

Figure 8. Ball and stick models of (a) unreconstructed anatase (001); (b) ADM model of reconstructed anatase (001)-(1 × 4), showing ridges running along the [100] direction; (c) unreconstructed anatase (100) surface.

between the two surfaces to be always small (≤0.1 J/m2) except with B3LYP, which predicted the rutile (110) surface more stable by ∼0.15 J/m2. Using the hybrid PW1PW functional, Esch et al.135 studied the dependence of the computed surface energies on the slab thickness. For well converged calculations, their results finally show that the surface energies of rutile (110) and anatase (101) are essentially identical. 3.1.2.2. Anatase (001). The bulk-terminated TiO2(001) exposes coordinatively unsaturated Ti5c and O2c atoms, as well as fully coordinated O3c, see Figure 8a. In DFT calculations, the two bonds formed by each bridging O2c with its neighboring Ti5c become strongly inequivalent upon relaxation,26 with bond lengths of ∼2.2 and 1.8 Å. The surface energy, however, does not change significantly and remains large in comparison to the (101) surface (see Table 1), suggesting that an energetically more favorable surface structure might exist. In fact, experimental studies on anatase (001) films grown epitaxially on SrTiO3 revealed that the surface is reconstructed, with a (1 × 4) periodicity with respect to the bulk.138−140 To explain this structure, Herman et al.139 suggested a model with (103) and (−103) microfacets that was subsequently shown to be inconsistent with STM data.140 Liang et al. proposed an

anatase (101) viewed along the [010] direction. The surface exposes both 5-fold (Ti5c) and 6-fold (Ti6c) coordinated Ti atoms, as well as 2-fold (O2c) and 3-fold (O3c) oxygens. The surface atoms undergo significant displacements from the ideal bulk-like positions upon relaxation.26,131,132,134 This is particularly evident for the surface O3c and Ti5c atoms, which relax outward and inward, respectively, thus causing a small ripple on the sawtooth profile. Computed bond distances on the relaxed surface and their deviations from the ideal values are reported in Table 2. An important feature is that the Ti−O bonds formed by the bridging oxygens with their neighboring Ti atoms are ∼5−10% shorter than average. As a result, the relaxed surface is predicted to be quite rigid. Given that anatase (101) and rutile (110) are the most stable surfaces of anatase and rutile, respectively, it may be interesting to ask which of the two surfaces has lower surface energy. Lazzeri et al.26,129 found the two surfaces to have nearly the same energy at the LDA level, whereas rutile (110) has a significantly (0.13 J/m2) lower surface energy using the PBE functional. Labat et al.133 computed the anatase (101) and rutile (110) surface energies using Hartree−Fock, DFT-LDA, DFT-PBE, B3LYP, and PBE0. They found the differences J


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“added-and-missing row” (AMR) model,140 but also in this case the computed STM image141 turned out to be very different from the experimental one. Based on DFT calculations, Lazzeri and Selloni141 proposed the “ad-molecule” (ADM) model, see Figure 8b, for which the theoretical STM image agrees nicely with the experiment.140,142 The ADM model is constructed by periodically replacing [100] rows of bridging O2c atoms of the unreconstructed 1 × 1 surface with rows of TiO3 species. This results in “ridges” on which the Ti atoms are 4-fold coordinated. The computed surface energy of the 1 × 4 ADM structure is 0.48 Jm−2, nearly half that of the unreconstructed surface, indicating that this reconstruction stabilizes the surface quite effectively. The primary mechanism of this stabilization is the relief of the surface stress.141 On the bulk-terminated surface, the large Ti5c−O2c−Ti5c bond angles (∼156°) and Ti5c−O2c bond lengths (1.96 Å) give rise to a significant tensile surface stress. In the 1 × 4 ADM structure, the insertion of an extra TiO2 row causes a compression which makes the surface bonds shorter, 1.80−1.85 Å, and the bond angles smaller, ∼120°; as a result, the tensile stress is also strongly reduced.141 An alternative “ad-molecule” model was suggested by Ignatchenko et al.,143 in which water was added instead of TiO2 to the original unreconstructed (0 0 1) surface in periodic (1 × n) rows. Different supercells with n original unit cells were constructed and their energy was minimized with and without water. The surface energy of the hydrated periodic model of the (0 0 1) anatase surface was found to go through a minimum at n = 3, i.e. for a (1 × 3) periodicity, rather than the (1 × 4) periodicity observed in experiment. Based on these results, it was suggested that water, and perhaps some other molecules, could play a similar stabilization role for the (0 0 1) anatase surface as the TiO2 ad-molecule in the ADM model,141 depending on the environment. The ADM model of anatase TiO2(001)-(1 × 4) has been recently questioned on the basis of microscopic and spectroscopic experiments indicating that this surface, when oxidized, is essentially inert with respect to water adsorption.144 In the ADM model, instead, water dissociates on the ridges due to the presence of reactive 4-fold Ti sites, see section 3.2.1.2. To explain their findings, the authors proposed a modified ADM model where the Ti atoms on the ridges are 6-fold (rather than 4-fold) coordinated due to the presence of oxygen adatoms, and suggested that the reconstructed (001) surface is reactive only when reduced.144 Another modified ADM model has been recently proposed by Xia et al.145 on the basis of high resolution STM measurements. This model includes 3-fold coordinated bridging oxygen atoms beneath some of the added TiO3 rows of the ADM model. 3.1.2.3. Anatase (100). Although not present in the Wulff shape of anatase, the (100) surface is very frequent in the nanoparticles used for photocatalysis and has been recently reported to have a higher photocatalytic activity than both the (101) and (001) surfaces.146,147 The bulk-truncated (100) surface, Figure 8(c), shows flat regions separated by narrow channels running along the [010] direction. The outermost layer exposes Ti5c, O2c and O3c atoms, while the second layer at the bottom of the channels exposes fully coordinated Ti and O atoms. For this surface, the effects of relaxation are qualitatively similar to those found on the (101) surface. In particular, the surface O3c and Ti5c atoms are predicted to relax outward and inward, respectively, resulting in a small (∼0.35 Å) corrugation of the first layer.26,131,132,148

According to the low surface energy predicted by DFT calculations (Table 1), the relaxed bulk-truncated (100) surface should be quite stable. On the sputtered and annealed (100) surface, however, LEED and STM experiments have detected a (1 × n) reconstruction characterized by bright ridges running along the [010] direction.149,150 This structure has been qualitatively explained in terms of a (101)-microfaceted model,149 but so far no detailed computational study has been reported. 3.1.3. Surface Defects. The most common defects on TiO2 surfaces are oxygen vacancies and steps, with the concentration of surface oxygen vacancies being very sensitive to the oxygen pressure, temperature and duration of the annealing used to prepare the surface. Under the typical preparation conditions used for surface science experiments, a large (5−10%) concentration of surface oxygen vacancies is present on the most stable (110) surface of rutile. For a long time it was assumed that the same would hold also for the surfaces of anatase, but recent experimental and theoretical work has shown that this is actually not true. In this section we review this work and further discuss step edges, which have also a strong influence on the surface reactivity. 3.1.3.1. Oxygen Vacancies and Ti Interstitials. Due to their strong influence on the reactivity, defects on TiO2 surfaces have been extensively investigated for many years.13 In particular, a wealth of experimental13,151−155 and theoretical156−159,101,105−108,112,113,160,161 studies have focused on surface oxygen vacancies (VO’s) on rutile (110), for which a concentration of the order 5−10% is typically observed in surface science experiments. For anatase (101), on the other hand, the concentration of surface VO’s was much lower under similar preparation conditions.13,162,163 To rationalize this difference, it was suggested that the formation energy of surface O-vacancies may be larger on anatase than on rutile because the removal of a surface O2c results in two Ti5c cations on rutile (110), whereas one Ti5c and one 4-fold Ti (Ti4c) are formed on the anatase (101) surface.16 To obtain more detailed insight, Cheng and Selloni performed DFT-GGA calculations of the formation energies of O-vacancies at several surface and subsurface sites of anatase (101), anatase (001)-(1 × 4), and rutile (110).119,164 Their results show a significant difference between the anatase and rutile surfaces, that is supported also by DFT+U calculations.119 On rutile (110) the formation energy of surface O2c vacancies is lower than that of subsurface VO’s, in agreement with other DFT studies.159,165 On anatase surfaces, instead, O-vacancies have lower formation energy in the subsurface and bulk than at the very surface (see Figure 9).119,164 The predominance of subsurface defects at the

Figure 9. Various surface and subsurface O vacancies (left) and their corresponding formation energies (right) at the anatase (101) surface. The ball and stick model on the left shows only part of the six-layerthick slab used for the calculations. Red and light blue spheres represent O and Ti atoms, respectively. Yellow spheres highlight the investigated oxygen vacancies sites. K


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Figure 10. The structures of the steps were constructed maintaining the TiO2 stoichiometry and for some steps different possible terminations were examined. To determine step formation energies, vicinal surfaces were considered; details of the procedure are given in ref 170. From the results, it was inferred that the preferred orientation of the islands is the one indicated by the full line in Figure 10. This assignment was supported by the agreement between the theoretical and experimental STM images for a step along the [11−1] direction.

anatase (101) surface was confirmed by STM measurements on a freshly cleaved anatase TiO2(101) sample, which showed an almost perfect surface with very few subsurface impurities and adsorbates.166 Surface oxygen vacancies were not present in this sample but could be induced by electron bombardment, and found to migrate to subsurface sites at temperature larger than 200 K.167 From time-lapse STM images, the activation energies for subsurface migration were estimated to lie in a rather wide range, between 0.6 and 1.2 eV,167 due to inhomogeneously distributed subsurface defects in the reduced sample. In comparison, DFT-GGA calculations of O-vacancy diffusion predict the barrier for subsurface-to-surface migration to be about 0.75 eV.119,167 The electronic structure of O-vacancies at anatase surfaces is not fully understood. A number of DFT(GGA)+U studies with various U values have been reported,119,168,169 but the extent of the analysis and the quality of the models is still insufficient to allow clear conclusions to be drawn on important aspects such as, e.g., the extent of the polaronic distortion and the preferred localization sites of the excess electrons. In ref 119, the binding sites and diffusion pathways for a Ti interstitial (Tiint) at the anatase (101) surface were also studied. The most stable surface binding site is between two adjacent O2c atoms along the [010] direction, where the interstitial is coordinated to four oxygens. In all the subsurface sites, Tiint is coordinated to five oxygen atoms, as in the bulk, and the defect formation energy decreases steadily as Tiint moves away from the surface to the bulk. Altogether the interstitial is predicted to be ∼1.2−1.3 eV more stable at a bulk site than at the surface and the highest barrier in the diffusion pathway from the surface to a deep subsurface site is less than 0.5 eV. 3.1.3.2. Steps. Steps are very common surface defects that have a strong influence on the reactivity of metal oxides. A detailed study of the structure and energetics of monatomic steps on anatase (101) was reported by Gong et al.170 On this surface steps occur along a few well-defined directions and give rise to characteristic trapezoidal islands (Figure 10). The

3.2. Adsorption of Small Molecules

3.2.1. Water. Due its relevance to photocatalysis, water splitting, and other important applications,171 the interaction of water with TiO2 surfaces has been the subject of countless investigations over the last decades. Several reviews articles are also available,3,7,8,13,172,173 including a recent review specifically focused on theoretical studies of titania-water interactions.174 Here we shall mainly consider work reported after that review (ca. 2009). 3.2.1.1. Anatase (101). The computed adsorption structure of water on undefected anatase (101) is shown in Figure 11.174,175 Water adsorbs in molecular form with the oxygen forming a dative bond with an undercoordinated surface Ti5c atom while the hydrogens form H-bonds with two bridging O2c atoms. This structure, first predicted theoretically,175 is supported by various experimental observations, including atomic-scale STM images.176,177 The influence of subsurface defects on water adsorption in the dilute limit was investigated by Aschauer et al.116 The calculations predict a strong preference for water to adsorb in the vicinity of the subsurface defects. The H2O adsorption energy at these sites is higher than on the stoichiometric surface, in agreement with the experimental finding that the water desorption temperature increases when the surface reduction increases.116 Molecular adsorption, strongly favored on the defect free surface, is preferred also in the presence of a subsurface oxygen vacancy, whereas dissociation becomes slightly favored in proximity of a Ti interstitial in the second layer. The barrier for a water molecule to dissociate is much smaller on the reduced surface (∼0.25 eV) than on the stoichiometric one (∼0.52 eV). More recently, Zhao et al. considered also the effect of doping by studying the adsorption and dissociation of a water molecule on p-type N-doped and n-type V-doped178 anatase (101). They found that water dissociation remains unfavorable on the V-doped surface, whereas it becomes favorable with respect to molecular adsorption on the N-doped surface. As the character of water adsorption in the dilute limit has been largely established, recently increasing attention has been devoted to the properties of adsorbed water layers and the anatase/water interface. Raju et al.179 studied the adsorption and dissociation of water at 300 K using ReaxFF reactive force field simulations. In these simulations, water dissociation was observed on the defect-free surface for water coverages of 0.75 ML and higher, indicating that the dissociation is assisted by the surrounding water molecules. The water dissociation percentage (WDP) was of ∼10% at 1 ML coverage, and showed only minor variations up to 3 ML water coverage, while the terminal WDP (TWDP) increased steadily up to ∼22% at 3 ML coverage. These findings, however, do not agree with firstprinciples molecular dynamics (FPMD) studies (see below) and temperature-programmed desorption (TPD) experi-

Figure 10. Left: STM image of anatase TiO2 (101) showing preferential orientations of monatomic steps; one isolated trapezoidal island is highlighted by a red circle. Right: Schematic plot of possible island shapes and orientations on anatase TiO2 (101); five different types of steps are identified and labeled as A−E. Adapted from ref 170. Copyright 2006 Nature Publishing Group.

parallel sides of all trapezoids are oriented along the [010] direction, and the two nonparallel sides are directed along [−111] and [11−1]. Due to the lack of mirror plane symmetry, the two parallel sides of the trapezoidal islands are nonequivalent and one of the two trapezoidal island orientations indicated in Figure 10 (right panel) is preferred. Step formation energies were calculated for the edges of the islands sketched in L


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Figure 11. Adsorption structures of (a) H2O, (b) CH3OH, and (c) HCOOH on anatase TiO2(101) terraces. C atoms are in deep gray and H in white. The dashed lines indicate H-bonds between molecules and surface O2c.

ments,176 in which no evidence for water dissociation on anatase (101) was obtained. The effect of a subsurface Ti interstitial on the structure and reactivity of thin water layers on anatase (101) was investigated by Tilocca and Selloni180 using DFT-GGA and DFT+U based FPMD simulations at 160 K (the temperature at which desorption starts to occur in TPD experiments149). Standard DFT-GGA and the DFT+U method were found to predict similar energetic and dissociation barrier for an isolated adsorbed water molecule, as well as very similar structural features for an adsorbed water monolayer on the reduced surface, thus justifying the use of simple DFT-GGA for the simulation of thicker water layers. Compared to the defect-free surface, the subsurface defect was found to enhance the surface reactivity and to lead to a more disordered structure of the first water layers adsorbed on the reduced surface. In particular, no water dissociation was observed in rather long simulations for a water monolayer (ML), bilayer (BL), and trilayer (TL) on the defect-free surface, whereas dissociated water was present on the defected surface. FPMD simulations of the interface between anatase (101) and liquid water have been reported by a few groups. Sumita et al.182 concluded that the structure of the interface is characterized by a first layer of water molecules adsorbed molecularly at Ti5c sites and a second layer forming strong Hbonds with the O2c surface atoms. These two layers form a stable bilayer at the interface due to the presence of short Hbonds between first and second layer water molecules (Figure 12), as first pointed out and analyzed in detail by Mattioli et al.181 Cheng et al.183 analyzed the number of surface sites coordinated to water molecules during a rather long (∼30 ps) FPMD simulation at 300 K. They found that on average about 75% of the Ti5c sites and ∼85% of the surface O2c atoms were bonded to water molecules during the simulation.183 The existence of a stable water bilayer at the interface was recently discussed also by Zhao et al.,184 who used static DFT calculations to study adsorbed water up to 8 ML coverage in combination with force field simulations of the anatase/liquid water interface. As a further advancement, recent theoretical studies have addressed the oxidation of water on various TiO2 surfaces.185−187 For anatase, in particular, Li et al.187 determined the mechanism and energetics of the oxygen evolution reaction (OER) on the (101), (001), and (101) surfaces in aqueous environment, described using a continuum solvation model.

Figure 12. (A) Structure and (B) charge density difference Δρ = ρ [2H2O/anatase] − (ρ[H2O](I) + ρ[H2O](II) + ρ [anatase]) for a pair of water molecules adsorbed on anatase (101). Red (blue) regions in (B) indicate an increase (decrease) of the charge density. The arrow highlights the charge transfer from Ti5c to O2c atoms via the adsorbed water molecules. From ref 181. Copyright 2008 American Chemical Society.

Their results show that the OER is not sensitive to the local surface structure, as very similar mechanisms are found on the different surfaces. Instead the overpotential is strongly influenced by the position of the valence band maximum. For all surfaces, the rate limiting step is the first proton removal leading to the formation of an OH radical. A detailed analysis of the kinetics of this step has been presented recently.188 In the latter study the liquid water environment is explicitly described and the energy profiles of the proton-coupled electron transfer (PCET) are determined by means of hybrid functional calculations. The results suggest that the first PCET is sequential, with the electron transfer (ET) following the proton transfer and occurring via an inner sphere process, M


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Figure 13. Adsorption structures of (a) H2O, (b) CH3OH, on anatase TiO2(001)-1 × 1. C atoms are in deep gray and H in white.

Figure 14. Optimized structure of one monolayer of water adsorbed on the unreconstructed (left) and (1 × 4) reconstructed (right) anatase (001) surface.

which were based on smaller unit cells. For the bulk terminated surface at 1 ML coverage, Selcuk et al.191 obtained a mixed dissociated-molecular structure where only 25% of the water molecules is dissociated, while the other molecules form Hbonds with the surface and between themselves (Figure 14). Interestingly, the surface structure formed by the dissociated water molecules is essentially identical to the model for the reconstructed (001) surface proposed by Ignatchenko et al.143 (see section 1.2.2), and is also similar to the ADM model in Figure 8, which may be the reason for its stability. The computed adsorption energy is 0.98 eV per molecule for the structure in Figure 14, against 2.38 eV at 0.25 ML coverage. Incidentally, we note that incomplete dissociation of the first layer of adsorbed water molecules was observed also in FPMD simulations of the anatase (001)/liquid water interface,182 but the authors attributed this effect to the use of a 3 × 3 supercell preventing full dissociation.182 Figure 14 shows also the structure of one water monolayer on reconstructed anatase (001)-(1 × 4). This surface is significantly less reactive than the unreconstructed one, consistent with the relative stabilities of the two surfaces.141 The site of highest reactivity for anatase (001)-1 × 4 is the ridge, where water adsorbs dissociatively with a computed energy of 1.54 eV, whereas water is only weakly adsorbed on the terraces.191,192

which is facilitated by a shared hole state shared between the two oxygen ions involved in the transfer. 3.2.1.2. Anatase (001). Vittadini et al.175 first reported that water adsorption on unreconstructed anatase (001) is strongly exothermic at low coverage and associated with a major restructuring of the surface: the water molecule dissociates, disrupting one of the bonds of the bridging oxygens, see Figure 13. This result was confirmed by several other studies,131,189,190 and can be related to the large surface energy and tensile strain of the clean unreconstructed (001) surface,141,173 which make adsorption extremely favorable. The structure of adsorbed water is not as clear at higher coverage, however. At 1 ML, in particular, different configurations have been proposed, such as a mixed molecular-dissociated monolayer where half of the H2O molecules are adsorbed dissociatively and form H-bonds with a “second layer” of intact molecules,131,175 or a fully dissociated monolayer with terminal/bridging OH groups at all Ti5c/O2c sites of the clean surface.190 The structure of an adsorbed water monolayer on anatase (001) has been recently revisited by Selcuk et al.,191 who optimized a very large number of structures in a 2 × 4 supercell in order to accurately determine the most stable configurations for water adsorbed on both the bulk terminated and (1 × 4) reconstructed (001) surfaces at different coverages up to 1 ML. Their results show some differences from previous studies, N


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Figure 15. Adsorption structures of (a) H2O, (b) CH3OH, and (c) HCOOH on anatase TiO2(100). C atoms are in deep gray and H in white.

It is interesting at this point to ask which of the two structures in Figure 14 is more stable. The computed free energy diagram for the anatase (001) surface in the presence of water vapor191 shows a close competition in the region of water chemical potential relevant to liquid water. While the reconstructed surface appears to remain energetically more stable also in the presence of water, additional studies, e.g., FPMD simulations in a full liquid environment, may be needed to completely sort out this issue. 3.2.1.3. Anatase (100). Despite recent experimental evidence that anatase (100) may be the low-index anatase surface with highest photocatalytic activity,146 studies of the (100) surface and its interaction with water are still relatively scarce. At low coverage, all available studies have consistently predicted that water adsorption in dissociative form is slightly more stable than molecular adsorption,131,143,190,193−195 see Figure 15. Zhao et al.195 determined also the water dissociation barrier and found it to be ∼0.34 eV. Dissociated and undissociated configurations were found to have very similar energies also at higher coverages. Arrouvel et al.131 found that mixed structures of dissociated and undissociated molecules are slightly more stable than fully dissociated structures, whereas a fully dissociated monolayer was slightly more stable according to Barnard et al.190 and Ignatchenko et al.143 In reactive force field simulations at 300 K,179 the fraction of first layer water molecules that were dissociated was ∼15% and ∼33% at 1 and 3 ML coverage, respectively, indicating that the dissociation is water-assisted. 3.2.2. Molecular Oxygen. Molecular oxygen plays a key role in many TiO2-based photocatalytic processes; in particular, O2 adsorbed on TiO2 surfaces is known to act as an electron scavenger and is often used to suppress electron−hole recombination, which increases the lifetime of the excited state and thus the yield of the photocatalytic reaction. Electron transfer from the surface to the O2 molecule is essential for oxygen adsorption. In fact, O 2 does not adsorb on stoichiometric TiO2; excess electrons are required. As titania samples are very often reduced,13 excess electrons originating from oxygen vacancies and titanium interstitials are typically present in the material. Theoretical studies of O2 adsorption on reduced anatase have mostly focused on the (101) surface. The structural, electronic, and vibrational properties of O2 adsorbed in superoxo (O2−) and peroxo (O22−) forms were investigated by Mattioli et al.196,197 As shown in Figure 16, both species adsorb in a sideon configuration and exhibit O−O bond lengths of ∼1.33 and 1.46 Å, respectively. The calculations further predicted peroxo species to be more stable than superoxo ones whenever the Fermi energy is above the middle of the gap, as it is always the case in reduced TiO2. The greater stability of the peroxide species was confirmed by Aschauer et al., who studied O2

Figure 16. Optimized geometries, desorption enthalpies, and O−O stretching frequencies of (A) a physisorbed O2 molecule, (B) an adsorbed superoxo (O2−) species, and (C) an adsorbed peroxo (O22−) species on anatase (101). From ref 196. Copyright 2006 American Chemical Society.

adsorption on a reduced surface with a subsurface oxygen vacancy198 or Ti interstitial.199 These authors also found that it is energetically favorable for O2 to adsorb in the vicinity of the defect, e.g., the adsorption energy at the Ti5c site closest to VO is ∼0.5 eV larger than at a site ∼5 Å farther away from it.198 Upon adsorption, the extra charge associated with the defect is transferred to the O2 molecule, converting it to an O22− species with electronic states in the anatase band gap. More recently, however, First-Principles Molecular Dynamics (FPMD) simulations at T ≈ 220 K showed that the configuration with O2 adsorbed atop a subsurface VO is only metastable.200 In the presence of adsorbed O2 the oxygen vacancy prefers indeed to migrate from subsurface to the surface, where it recombines with the adsorbed O2 to form a bridging dimer species (O2)O. This process is strongly exothermic, with an energy gain of about 1.6 eV from the state with O2 adsorbed atop a subsurface VO to the bridging dimer (O2)O state. This theoretical prediction has been verified experimentally by STM.200 The predicted stability of O22− species seems to contradict the experimental observation of stable O2− species by EPR.201,202 This difficulty has motivated recent hybrid functional calculations of the charge transfer reaction between O


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reduced anatase (101) and molecular O2 by Li et al.203 It was found that although the peroxo O22− species is energetically more stable than O2−, there is a significant barrier, ∼0.3−0.4 eV, that must be overcome to transfer an additional electron to *O2− and transform it to a peroxide, whose formation is instead barrierless. The existence of this barrier can thus explain why experimentally superoxo species are often observed. 3.2.3. Methanol and Formic Acid. Experimental investigations on the adsorption of organic molecules on anatase single crystal surfaces are scarce.204−206 Here we consider only methanol and formic acid, as an extensive review has recently been given by Thomas and Syres.207 Besides being a simple prototype for organic compounds as well as an important molecular probe for the investigation of surface properties, methanol is frequently used as a hole scavenger in photocatalysis. For these reasons, the interaction of methanol with anatase surfaces has been the subject of several studies. Experimentally, X-ray photoelectron spectroscopy (XPS) measurements on anatase (101) did not show any evidence of methanol dissociation, whereas features of methoxy groups were detected by TPD on the same surface and attributed to CH3OH dissociation at step edges.176 Similarly, sum-frequency generation (SFG) experiments on a nanoparticulate anatase film indicate that molecular adsorption dominates at regular surface sites, whereas chemisorption with methoxy formation is related to defects.208,209 In theoretical studies, trends in the adsorption structures of methanol on different anatase surfaces appear to be similar to those of water and reflect the relative energies of these surfaces. Molecular adsorption is preferred on undefected anatase (101), see Figure 11, and the adsorption energy is only slightly smaller than that of water.193,210 By contrast, dissociative adsorption was predicted to occur on both the (001)189 and (100)193 surfaces, Figures 13 and 15, respectively. The stability of the molecular adsorption state on the (101) surface has been confirmed by recent B3LYP hybrid functional calculations.211 The latter study further showed that methanol can trap holes only when it is dissociatively adsorbed on the surface. Carboxylic acids and carboxylates are widely used anchoring groups for the modification of TiO2 with functional molecules, notably dye sensitizers in dye sensitized solar cells.4,212 This has motivated several theoretical/computational studies of the adsorption properties of formic acid (HCCOH), which is the simplest species containing a carboxylic group. On anatase (101), GGA calculation indicate that the most stable HCOOH adsorption structure is a molecular monodentate configuration where the carbonyl oxygen binds to a surface Ti5c while the hydroxyl hydrogen forms a H-bond with a bridging O2c,193,213,214 see Figure 11. This finding has been confirmed by B3LYP hybrid functional calculations,211 but the difference between the undissociated monodentate and dissociated bridging bidentate forms is only 0.05 eV with B3LYP,211 against 0.24 eV with DFT-GGA.213 HCOOH adsorption in the bridging bidentate form was predicted to be favorable also on the (100)193 (Figure 15) and unreconstructed (001)192 surfaces. For the reconstructed (001)-(1 × 4) surface, calculations based on the ADM model192 indicate that formic acid adsorbs preferentially on the ridges where it has a bidentate chelating configuration. This assignment is supported not only by the computed total energies but also by the good agreement of the calculated STM image with experiment.142 3.2.4. Water, Methanol, and Formic Acid at Step Edges on Anatase (101). Gong and Selloni193 reported

extensive DFT calculations showing that the reactivity of step edges is very similar to that of the extended surfaces which are exposed at their facets. Adsorption of water and methanol at steps with (112) facets (denoted D-(112) in ref 193) is nondissociative even though stronger than at (101) terraces. By contrast, dissociative adsorption is preferred for water and methanol at steps with (100) facets (denoted B-(100) in ref 193). At both step D-(112) and B-(100) the adsorption energy of H2O is lower than that of CH3OH, even though the two molecules have very similar adsorption configurations. This can be attributed to the relatively higher acidity (weaker RO-H bond strength) of CH3OH with respect to H2O. On the flat TiO2(101) surface, instead, H2O has a slightly higher adsorption energy than CH3OH (0.78 vs 0.73), due to the fact that H2O can form two H-bonds with O2c, while CH3OH can form only one (see Figure 11). For HCOOH, while molecular adsorption is favored on (101) terraces (Figure 11), a dissociated bidentate adsorption geometry is favored at both D-(112) and B-(100) step edges. This can be attributed to the fact that the HCOO moiety in bidentate configuration can form two O−Ti5c bonds with reactive Ti5c atoms at the edges. This also suggests that the binding of HCOOH with stepped anatase TiO2(101) surfaces is more “robust” than that of H2O and CH3OH, consistent with various experimental evidence.

4. TIO2 SENSITIZATION AND APPLICATIONS TO HYBRID AND ORGANIC PHOTOVOLTAICS Due to its abundance and stability against photocorrosion, TiO2 is an interesting material for solar energy conversion, yet it is not very efficient. One of the most serious drawbacks of TiO2 is its large band gap, Eg∼ 3.2 eV, which results in the absorption of only a small portion of the solar spectrum in the UV region. A widely used strategy for overcoming this difficulty, is to “sensitize” TiO2 by attaching suitable molecules to its surface. A large body of theoretical/computational investigations on sensitized TiO2 surfaces has been reported, especially with reference to Dye-sensitized solar cells (DSCs),4,12,215−217 in which a dye molecule is covalently grafted to TiO2. Many theoretical studies have examined the electron injection step, which is the primary charge generation event in DSCs, and the dye adsorption mode on TiO2.218−268 Since various reviews dealing, in full or in part, with computational approaches to DSCs are available,249,260,269−273 including another contribution to this issue,274 in the present review we focus almost exclusively on the effect of the adsorbate on the underlying TiO2 electronic structure. 4.1. Dye and Coadsorbent Effects on TiO2

A crucial ingredient of the DSC efficiency is the open circuit voltage, VOC, which is essentially given by the difference between the TiO2 CB edge and the redox potential of the electrolyte. The energetic of the TiO2 CB in DSCs is known to depend on several factors, such as the local pH,215,275−278 the concentration of potential determining ions (e.g., Li+),276,279,280 and also on the nature of the electrolyte solvent.279,281 While the role of surface adsorbed molecules, including the dye, in determining the TiO2 CB energetics is generally less clear,282−289 an interesting correlation between the dipole moment of coadsorbing species, mainly substituted benzoic acids, and VOC was observed by Rühle et al.,284 who pointed out a linear relation between the dye coverage (N), the dipole (μ) component normal to the surface (θ is the molecule tilting P


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Figure 17. Adsorption geometries of two prototypical Ru(II)-complexes: (left) N719 with three anchoring points (one bidentate bridging and two monodentate) and (right) C106 with two monodentate anchoring points.

by the adsorbate dipole. When an adsorbate binds to a semiconductor surface, one should indeed consider also the effect of the charge transfer (CT) between the dye and the semiconductor which may accompany the adsorbate/semiconductor physisorption or chemisorption (bond formation). Both the EL and CT terms can vary with the surface coverage, so it is important to check also this quantity for meaningful comparisons with experiment. Ronca et al.292 used a charge displacement (CD) analysis293 to investigate the adsorption of several prototypical organic dyes and coadsorbents on a TiO2 cluster model, quantifying and rationalizing the separate effects of EL and CT contributions to the TiO2 CB energetics. These authors investigated a series of dyes with vastly varying dipole moment and electron donating properties considering both dissociative bridged bidentate (BB) and molecular monodentate (M), adsorption modes.292 Investigation of the charge displacement curves showed significant charge in the interface region, of the order of 0.3−0.4 electrons. Based on the CD analysis, they proposed a simple interpretative model by expressing the total TiO2 CB shift, ΔCBTOT, as the sum of the two main effects strictly related to the dye sensitizer: 292 ΔCB TOT = ΔCBEL+ΔCBCT.

angle) and the potential shift (ΔV) at the interface affecting the TiO2 CB energy: ΔV = (εε0)/(Nμ cos θ) De Angelis et al.290 proposed that the high VOC measured for DSCs sensitized by the prototypical N719 ruthenium dye originates from the special dye adsorption mode, involving two or three carboxylic anchoring groups residing on different bipyridines, see Figure 17, while most other ruthenium dyes have only two anchoring units. DFT calculations for the dye adsorbed on a model TiO2 cluster revealed also a dipoleinduced shift of the TiO2 CB, indicating that the sensitizer’s adsorption mode influences the position of the TiO2 CB. Kusama et al. reported a combined experimental and theoretical study which showed a clear correlation between the dipole moment of (liquid) electrolyte additives and the measured VOC in DSC devices.288 These authors investigated the adsorption of nitrogen-containing heterocycles such as pyrazole, imidazole, 1,2,4-triazole, pyridine, pyrimidine, pyrazine, and 4-t-butylpyridine (TBP) on TiO2 anatase (101), (100), and (001) surfaces, using periodic DFT calculations; optimized structures for the (101) surfaces are shown in Figure 18. All the investigated structures displayed a negative (i.e., upward) shift in the TiO2 Fermi level upon adsorption of Ncontaining heterocycles, that the authors correlated to the adsorbate dipole moment component normal to the TiO2 surface plane. Mattioli et al.291 investigated the interaction of a oxo-Tiphtalocyanine (TiOPc) with the anatase TiO2 (101) surface. The interaction was found to take place mainly through the Tioxo phtalocyanine group, with creation of a Ti-oxo-Ti (surface) bond. The equilibrium geometries and isosurfaces of difference electron densities for such system are reported in Figure 19. An electron density rearrangement accompanies the oxo-Ti (surface) bond formation, which was also found to lead to a negative TiO2 CB shift (i.e., the TiO2 CB was pushed at higher energies relative to the molecular HOMO). A much stronger interaction was observed when the molecule was interacting with the (101) anatase surface doped by a Ca2+ ion. In this case a pronounced charge density rearrangement involving also the TiOPc carbon atoms was found, leading to a substantial charge transfer from the TiOPc molecule to the TiO2 surface. Although the “dipole effect” can explain a number of results related to DSCs, the adsorbate/TiO2 interaction usually is more complicated than the simple electrostatic (EL) effect mediated

4.2. Insulating Metal Oxide Monolayers

An appealing strategy to reduce recombination losses in DSCs is to introduce an “insulating oxide” layer between the TiO2 surface and the sensitizing dye. Typically, these oxide layers are grown by atomic layer deposition (ALD), which is an ideal technique to deposit close to monolayer films. Terranova and Bowler investigated by periodic DFT calculations the interface between amorphous Al2O3 (a-Al2O3) and the TiO2 anatase (101) surface, and further studied the sensitization of the ensuing interface by a ruthenium dye.294 They considered two a-Al2O3 thicknesses, and relaxed the structure of the resulting aAl2O3/TiO2 interfaces, see Figure 20. The DOS of the bare TiO2 and of the two a-Al2O3/TiO2 interfaces are also reported in Figure 20. Although in the thick coating, a net dipole moment (0.67 eÅ) was present along the direction perpendicular to the interface, the authors considered it to be too small to significantly affect the TiO2 energy levels. The PDOS for the bare and a-Al2O3-coated TiO2 are indeed quite similar, even though some states appear close to the VB maximum, possibly reflecting hybridization with Al2O3 states. Q


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Figure 19. Equilibrium geometries and isosurfaces of difference electron densities of (A) a TiOPc molecule bonded to the (101) anatase surface and (B) a TiOPc molecule bonded to a p-doped anatase surface. Electron density difference maps show the displacements of electronic charge induced by the molecule−surface interaction. Red surfaces cover areas where the difference is positive, blue surfaces, where it is negative. From ref 291. Copyright 2009 American Chemical Society.

polymer−TiO2 hybrid solar cells was investigated by Canesi et al. in a combined experimental and computational investigation.296 These authors reported a step-change improvement in the solar cell device performance, which was enabled by engineering the hybrid interface by the insertion of an appropriate molecular interlayer between the polymer donor and the TiO2 semiconductor. By positron annihilation techniques, it was experimentally observed that the presence of a 4-mercaptopyridine (4-MP) interlayer led to better contact between the oxide and polymer phases and a closer polymer packing at the interface. Canesi et al. performed classical molecular dynamics simulations based on a model potential for the P3HT polymer/TiO2 interface with and without the presence of a 2-mercaptopyridine (2-MP) and 4-MP interlayer. 2-MP and 4-MP are both able to bind to TiO2 by virtue of the nitrogen lone pair and to possibly interact with the polymer by their S−H groups. In a subsequent study, Malloci et al.297 extended the study on the effect of interlayers on P3HT adhesion to TiO2 to 2-MP, PYR (pyridine), 4-MP, and TBP (tert-butylpyridine). A survey of the ensuing optimized structures is reported in Figure 21. Ordered monolayers were found for PYR and 4-MP, a partially ordered monolayer for TBP, and a disordered one for 2MP. Interestingly, these authors also found a correlation between the dipole moment of interlayer molecules and the Voc of the corresponding solar cells, in line with what discussed above for DSCs. When considering a polymer/metaloxide hybrid, usually the polymer does not form covalent bonds with the inorganic material, and therefore covalent bonds do not contribute to the adhesion. This is clearly at variance with dye-sensitized solar

Figure 18. Geometry-optimized structures of N-containing heterocycles adsorbed on a TiO2 anatase (101) surface: (a) pyrazole, (b) imidazole, (c) 1,2,4-triazole, (d) pyridine, (e) pyrimidine, (f) pyrazine, and (g) TBP. From ref 288. Copyright 2008 American Chemical Society.

The calculated DOS and energy level alignment were similar to the electronic structure for the same interface in the study by Wang et al. .295 The calculated interaction energies of a formic acid probe were found to increase on the a-Al2O3 overlayer with respect to TiO2, suggesting a stronger dye loading on the former oxide. This trend was confirmed also for the N3 dye binding to a-Al2O3, for which a largely increased binding energy was obtained compared to TiO2. 4.3. Polymers’ Morphology on TiO2

As an alternative to molecular dyes, donor polymers can be used as light-harvesters in hybrid solar cells based on TiO2 or ZnO. The effect of selective interactions at the interface of R


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to absorb light at any wavelength, by exploiting quantum size effects,299 have high extinction coefficients and large intrinsic dipole moments, and are photochemically robust. Long and Prezhdo258 investigated the interfacial properties of a PbSe QD adsorbed on a (110) rutile TiO2 surface. They found that thermal fluctuations, as evaluated by molecular dynamics simulations, may impact the system geometry, with the largest scale motion associated with QD displacements in the plane of the TiO2 surface. Figure 22 shows the electron densities of the interfacial donor and acceptor states. The density of the electron donor is delocalized over the whole QD, while the acceptor state is spread nearly uniformly across the TiO2 slab. A rather strong QD/TiO2 coupling was found even in the absence of a QD/surface linker molecule, producing the mixing of the donor and acceptor energy levels shown in Figure 22. As such, a substantial QD → TiO2 charge-transfer is expected to occur at the interface, similar to what discussed above for molecular dyes and for polymer donors. Patrick and Giustino300 simulated the interface between a 12 Å ultrathin stibnite Sb2S3 film and the (101) TiO2 anatase surface, see Figure 23, as representative of the quantum-dot sensitizer systems employed in solid-state solar cells.301 The stibnite LUMO was found to lie above the TiO2 CB edge, suggesting energetically favorable electron injection, and it was shown to extend into the TiO2 substrate through the coupling between the S 3p and Ti 3d orbitals at the interface, thereby providing a direct pathway for carrier injection. As such, the situation is rather similar to the PbSe-sensitized TiO2 discussed above. A key aspect shared by all the reviewed prototypical systems is the presence of strong electronic coupling, obtained through the formation of covalent and/or charge-transfer interaction between the electron donor and the TiO2 acceptor, as an essential prerequisite for efficient solar energy conversion.

Figure 20. Top: front view of the thin and thick overlayers relaxed onto the (101) anatase substrate. Bottom: PDOS of the two oxides for the three systems (coating 0, 3, and 9 Å). The highest occupied levels are indicated by the vertical dashed lines. From ref 294. Copyright 2012 American Chemical Society.

5. MODELING TIO2 NANOPARTICLES TiO2 nanoparticles or nanocrystals (here we use the two terms as synonyms) lie at the heart of many technological applications, notably photocatalysis and hybrid/organic solar cells. An advantage of TiO2 nanoparticles over conventional semiconductors is that their phase, size, and morphology can be widely tuned and tailored for specific target applications, thus providing an efficient strategy for engineering more efficient photoelectrochemical devices. The main property of TiO2 nanoparticles (and in general of nanostructured semiconductors) is their high surface to volume ratio. Since most photoelectrochemical reactions mediated by TiO2 are initiated by surface adsorption of a chemical species on TiO2, the high surface exposure ensures an overall high density of reactive centers. This feature is specifically exploited in dye-sensitized solar cells (DSCs), in which the core of the device is represented by a film of sintered TiO2 nanoparticles, so that the exposed surface is magnified by ca. a factor 1000 compared to a flat TiO2 surface. In turn, this allows a high dye loading, which ensures complete light absorption with films of just 10 μm thickness (using conventional dyes, characterized by a molar extinction coefficient of ∼10−20.000 M−1 cm−1). At the same time, the high number of reactive sites introduced by, e.g., the nanoparticles edges, ensures a high reactivity of the sintered films in photocatalytic applications. At ambient pressures and temperatures, the rutile TiO2 phase is more thermodynamically stable than the anatase phase,28 while the anatase phase is preferred for nanoparticles of dimension ∼20 nm or smaller.302 The size range of the anatase

cells, as discussed previously. Nevertheless, strong electrostatic interactions may occur between the ions of the surface and the partially charged atoms in the polymers due to the ionicity of the metal oxide.298 This is, for instance, the case of poly(3hexylthiophene) (P3HT), for which large atomic partial charges (up to 0.15e, where e is the electronic charge) are found. A second important issue to take into account is the effect of the morphology of the nanostructured substrate films conventionally used in hybrid devices. Since polymer/metal oxide adhesion may affect the overall efficiency of polymer-based solar cells, investigating the morphology of this interface is important for further optimization of the related solar cell devices. Melis et al. investigated P3HT adhesion to flat and nanostructured TiO2 by means of classical molecular dynamics based on a model potential.298 The surface morphology of the titania film, the local charge of the surface, or the presence of defects in the lattice can in principle strongly affect the polymer/TiO2 interaction. Melis et al. found that when P3HT interacts with TiO2 the adhesion energy is dominated by electrostatic contributions. In addition, the nanomorphology does not necessarily increase the polymer adhesion with respect to the planar case, due to the strain introduced in the polymer by the curvature radius. 4.4. Quantum Dots on TiO2

As a last example of TiO2 functionalization/sensitization for application to hybrid photovoltaics, we discuss the case of quantum dots (QD)/TiO2 interactions. QDs are easily tunable S


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Figure 21. Ternary systems formed by the 2-MP, PYR, 4-MP, and TBP interlayers for P3HT adhesion on TiO2. For clarity, all hydrogen atoms have been omitted and the carbon atoms of P3HT are marked in white to distinguish them from those of the interlayer. From ref 297. Copyright 2013 American Chemical Society.

factors affecting the anatase to rutile transformation is thus very important for the control of nanoparticle nucleation and growth processes, in relation to target technological applications. Despite the clear advantages in the use of sintered TiO2 nanoparticles, a significant drawback is represented by the slow electron mobility in such disordered mesoscopic materials. For nanostructured TiO2 films commonly employed in, e.g., DSCs, effective diffusion coefficient values in the range 10−8 to 10−4 cm2 s−1 have been measured, i.e. orders of magnitude smaller than those observed for TiO2 single crystals.304,305 This observation clearly suggests a high concentration of electrontrapping sites in the semiconductor film which slow down the electron transport. 306,307It has been suggested that in mesoporous TiO2 films made of sintered nanoparticles, the conduction band (CB) has a low energy tail of localized states below the energy characterizing the onset of fully delocalized conduction band states (also termed mobility edge). Kavan et al.308 and many others since then309−311 proposed the existence of deep, surface trap states in the band gap, below the most significant portion of the exponential tail of the DOS. Although the effect of trapping states on electron transport in mesoporous nanocrystalline TiO2 has been extensively investigated,312−314 it is still unclear whether these states originate from defects in the bulk and surface regions, from the grain boundaries of the particles, from Coulomb trapping due

Figure 22. Charge densities of (a) donor and (b) acceptor states at the PbSe QD/TiO2 interface. From ref 258. Copyright 2011 American Chemical Society.

to rutile phase transition for hydrothermal samples was however shown to be sensitive to a variety of factors, such as temperature, pH, presence of impurities, reaction conditions, etc. In particular, the pH value of the sol−gel was shown to crucially control, among other factors, the phase, size and shape of the synthesized nanoparticles.303 A detailed understanding of the thermodynamic phase stability of TiO2 nanocrystals and the T


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Figure 23. Left: Atomistic model of the TiO2/Sb2S3 interface. The colored atoms represent the periodic repeat unit, and the view is along the TiO2 [010] direction. Inset: Schematic representation of the stibnite-sensitized solar cell. Right: Isodensity plot of the Kohn−Sham LUMO state of Sb2S3 at the TiO2 /Sb2S3 interface. The charge density is plotted in a plane through the Ti−S bond. The coupling between the S 3p states of the sensitizer and the Ti 3d states of the substrate, which provides a pathway for electron injection, is highlighted. Reprinted with permission from ref 300. Copyright 2011 John Wiley and Sons.

yielding improved results for the energy level alignment at heterointerfaces compared to DFT.237,318

to interactions of electrons with the cations of the electrolyte, or from a combination of all these factors. Also, TiO2 nanocrystals of different shapes and sizes can have different types of defects and trap states, along with a different value of the fundamental band gap or distribution of unoccupied states. Understanding the subtle interplay between the nature of trap states in TiO2 nanocrystals and the size/shape/surface functionalization of these materials is thus essential for further optimization of their technological applications. Similarly, clear insight into the parameters ruling the sintering process and the possible consequences of sintering on the electronic properties of TiO2 nanoparticles is also crucial, since most technological applications require sintering of the TiO2 nanoparticles and sintering of the titania nanoparticles takes place in typical dry synthetic approaches requiring thermal annealing.315 In this section, we present an overview of computer simulations aimed at predicting, rationalizing and understanding the properties of TiO2 nanoparticles in relation to the technological issues mentioned above. Due to the complexity and large dimensions of the investigated systems, most computational investigations have been based on atomistic molecular dynamics based on a model potential, or on thermodynamic model approaches, possibly augmented by or with parameters derived from DFT calculations on reduced periodic surface slab models. Also, semiempirical tight-binding DFT calculations have been employed both for structural optimization and for gaining some insight into the electronic properties of the TiO2 nanoparticles. While various DFT studies have been performed on clusters made by to ∼10−50 TiO2 units, only recently first-principles DFT approaches have been employed to study realistic TiO2 nanoparticles of ∼3 nm size, made of several hundred TiO2 units.316,317 Recently, the study of small TiO2 nanocrystals has been approached also with post-DFT methods based on perturbation theory, i.e. GW,

5.1. Shape, Size, and Phase Stability of TiO2 Nanocrystals

As pointed out in section 3.1.1, the equilibrium shape of a crystal of an arbitrary material is given by the standard Wulff construction,319 which requires knowledge of the energies of the various exposed surfaces. The Wulff shape of anatase was first derived by Lazzeri et al.26 for the case of clean dry surfaces (see Figure 6). Results for hydrated and hydrogenated surfaces were later reported by Arrouvel et al.131 and Barnard et al.,320 who performed calculations also for rutile. In agreement with experimental observations for naturally occurring anatase, the Wulff construction shows that in anatase crystals the only two surfaces exposed to the vacuum are the (101) and (001) surfaces, while for rutile the most stable surfaces are the (110), (101), and (100). To evaluate the thermodynamic stability of TiO2 anatase and rutile nanoparticles as a function of the particle’s size and surface functionalization, Barnard and Zapol320 estimated the Gibbs free energy of formation of a nanocrystal of a material x, Gox, in terms of the surface energy γxi for each surface i, weighted by the factors f i, such that Σi f i = 1: Gxo = Δf Gxo +

M (1 − e)[q ∑ fi γxi] ρx i

(1)

ΔfG0x

where is the standard free energy of formation of the bulk (macroscopic) material, M is the molar mass, ρx is the density and e is the volume dilation induced by the surface tension. The latter term cannot be ignored at the nanoscale and may be approximated using the Laplace−Young equation321 for the effective pressure, which is defined in terms of the surface tension σ and is approximated by summing over the (weighted) surface tensions of the crystallographic surfaces present on the nanocrystal. The surface to volume ratio q and the weighting U


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Figure 24. Morphology predicted for anatase (top) with (a) hydrogenated surfaces (b) with hydrogen rich surface adsorbates, (c) hydrated surfaces, (d) hydrogen-poor adsorbates, and (e) oxygenated surfaces, and rutile (bottom) with (f) hydrogenated surfaces, (g) with hydrogen rich surface adsorbates, (h) hydrated surfaces, (i) hydrogen-poor adsorbates, and (j) oxygenated surfaces. From refs 323 and 324. Copyright 2005 American Chemical Society.

factors f i must be calculated explicitly for each shape and the facet therein. The effects of edges and corners were omitted in ref 320, since they were expected to be small for relatively large nanocrystals. As discussed in the following, these effects have been explicitly evaluated by Hummer et al.322 and found to be important for particles size below ∼3 nm. According to eq 1, one can predict the Gibbs free energy of formation of a nanocrystal by employing the experimental ΔfG0x and ρx, while explicitly calculating the surface energy and tension (γi and σi) for each surface, and the weighting factors f i. The surface tension can be calculated by applying a two-dimensional dilation to the slab in the plane of the surface and calculating the resulting free energy change. The results obtained by DFT calculations of γi and σi for each surface have been employed by Barnard and Zapol to construct phase diagrams for the faceted nanocrystals as a function of the nanocrystals size. Their results predict that the phase transition from anatase to rutile takes places at ∼12 300 TiO 2 units for the clean surface, corresponding to anatase particles of diameter of ∼9.3 nm. For the partially hydrogenated and fully hydrogenated surfaces the intersection points were found to occur at ∼10 800 and ∼196 900 TiO2 units, respectively, corresponding to anatase nanocrystals with average diameters of ∼8.9 and ∼23.1 nm, respectively. This dramatic change indicates that the termination of under-coordinated surface sites plays a major role in determining the stability of nanoscale TiO2. Full hydrogenation of the nanocrystal surfaces is predicted to promote stability of the anatase phase, whereas hydrogenation of only the bridging oxygens (partial hydrogenation) promotes stability of the rutile phase. These results are in agreement with the observed stabilization of anatase nanoparticles in acidic media.303 Barnard and Curtiss further investigated how the surface acid−base chemistry may influence the shape of the nanocrystals and the anatase-to-rutile transition size.323,324 They considered the surfaces to be water-terminated and simulated variations in the surface pH by varying the ratio of hydrogen and oxygen atoms on the surface. The final shapes predicted for each type of surface chemistry are shown in Figure 24. Anatase

nanocrystals with hydrogen-poor surfaces showed well developed facets (100) and (010) surfaces, which appear as the “belt” around the center of the nanoparticles. The effect of changing the surface chemistry upon the shape of the anatase and rutile nanoparticles is readily apparent. When hydrogen is dominant on the surface (or there is a greater fraction of hydrogen present in the adsorbates), there is little change in the shape of the nanocrystals with respect to the (neutral) water terminated nanoparticles; however, when oxygen is dominant on the surface, the nanoparticles of both polymorphs become elongated. The dependence of the anatase-to-rutile phase transition on the surface chemistry is illustrated in Figure 25. This also shows the possibility for phase transitions to be induced by a change in the absorbed groups on the surfaces. For instance, one can consider the vertical guideline at 45 000 TiO2 units. Beginning with hydrogen-rich surfaces (solid lines), anatase is thermodynamically stable. As the surface chemistry is neutralized to

Figure 25. Free energy as a function of the number of TiO2 units for anatase and rutile with hydrogen-rich, hydrated, and hydrogen poor surfaces. Vertical guidelines assist in the comparison of different stable phases at 45 000 and 75 000 TiO2 units during deprotonation (moving from the bottom upward). From refs 323 and 324. Copyright 2005 American Chemical Society. V


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peculiar reactive/electronic properties of nanoparticles, as discussed in section 5.3. The sintering of two spherical rutile nanoparticles was simulated by molecular dynamics by Collins et al.,327 who explored the collision of ∼3 nm size particles initially separated by ca. 4 nm in the 1200−2000 K temperature range. The dynamics simulation was conducted for up to 1 ns time. The nanoclusters were initially oriented so that the (100) direction of the underlying rutile phase was parallel to the direction of motion. The resulting collision could therefore be described as occurring between the (100) faces of the nanoclusters, though this picture is complicated by the roughness of the faces. Snapshots of a typical nanocluster collision at 1200 K are shown in Figure 26.

correspond with hydrated surface, the anatase phase remains stable. However, further deprotonation induces a phase transition to rutile, since with hydrogen-poor surface chemistry (dotted lines), rutile is thermodynamically preferred at a size of 45 000 TiO2 units. Then, one may consider the same procedure following the guideline at 75 000 TiO2 units. Beginning with hydrogen-rich surfaces, anatase is again thermodynamically stable. As the surface undergoes deprotonation, the anatase phase transforms to rutile, since for hydrated surfaces, rutile is thermodynamically preferred at a size of 75 000 TiO2 units. This phase transition for nanoparticles containing 75 000 TiO2 units occurs at an earlier stage of deprotonation than nanoparticles containing 45 000 TiO2 units. These results indicate not only that the opportunity exists for surface chemistry induced phase transitions to occur, but that these types of phase transitions are also size dependent. 5.2. Molecular Dynamics of TiO2 Nanoparticles

The main difference between the studies considered in this section and those based on a thermodynamic approach in the previous section is that in the latter an accurate electronic structure method, i.e., DFT, is used to calculate the surface energies in various conditions, which are then combined with a nonatomistic thermodynamic approach. In molecular dynamics simulations the structure of the nanoparticles retains its atomistic description, but the interatomic potential is described by a simple model force field. In these simulations, systems of several thousand atoms are typically considered, which prevents the use of electronic structure tools. All the MD simulations reviewed below employed the Matsui-Akaogi force field.128 In this force field, the potential is expressed as a combination of a repulsive exponential term, an attractive van der Waals term and an electrostatic contribution, for which partial charges q of +2.196 and −1.098 are assigned to titanium and oxygen, respectively. The main point of strength of this force field is its simplicity and the accuracy in reproducing the structural features and relative energies of various TiO2 polymorphs against experimental data. One of the earliest molecular dynamics simulation of TiO2 nanoparticles was reported by Collins et al.,325 who investigated an initially spherical rutile TiO2 nanocrystal made of 1245 atoms, i.e., with a radius of 1.4 nm. The authors investigated the system in the 1000−3000 K temperature range, for simulation times up to 600 ps. The temperature conditions are those typical of the so-called “chloride” synthesis of TiO2 nanoparticles. Interestingly, the initially spherical cluster structure evolved in time to a faceted arrangement, with microfacets corresponding to the (100), (110) and (101) planes of crystalline rutile. Furthermore, the rutile phase was retained throughout the simulation, up to the melting point. Naicker et al.326 performed molecular dynamics simulations of TiO2 nanoparticles in the anatase, brookite, and rutile phases, analyzing their structural features and surface energies. These authors investigated spherical nanoparticles of 2 to 6 nm size for 3 ns time, exploring 300−2000 K temperature range. Although anatase was predicted as the lowest energy phase for large surface areas, no phase transformation was observed during the simulation in the explored time/temperature regime. An interesting result of this study was the identification of fourand five-coordinated titanium ions at the nanoparticles surface, which showed shorter Ti−O bond lengths compared to sixcoordinated atoms. These surface sites are responsible of the

Figure 26. Time sequence of colliding TiO2 nanoparticles at (from left to right): (a) 0.3 ps, (b) 25.5 ps, (c) 27.0 ps, and (d) 288.3 ps. White and dark gray large spheres are oxygen, black and light gray small spheres are titanium. Reprinted with permission from ref 327. Copyright 1997 Royal Society of Chemistry.

The initially separated nanoparticles are mutually attracted by long-range intermolecular forces. Contact between the surfaces takes place after approximately 25−30 ps. The collision is mediated by surface roughness, and there is visual evidence of surface distortion when the surfaces are close. The collision takes place without sign of fracture or rebounding and the underlying phase remains rutile, although the former observation might be due to the initial preferential nanoparticle orientation. Following surface contact (third snapshot), there is an initial rapid reduction in configuration energy, which was associated with formation and widening of the “neck” between the two nanoparticles and the subsequent relaxation of the underlying lattice, particularly of the former surface layers, which occurs as a consequence of the nanoparticles contact. Along with the configuration energy decrease, a corresponding temperature increase was observed, which is due to energy conservation. Koparde and Cummings328 reported molecular dynamics simulations of TiO2 nanoparticles sintering, considering spherical anatase and rutile particles of 3 and 4 nm size, investigating various possible initial orientations. MD trajectories were propagated for 1 ns time, at temperature in the range 573−1473 K. We notice that such MD times are still short in comparison to the characteristic sintering time of ca. 12 μs observed for 3 nm TiO2 sintering at 1473 K.328 Nevertheless the investigated time span is likely sufficient to study the important initial stages of sintering, also considering that a plateau in the potential energy was reached after ca. 0.5 ns simulation. The early stages of these MD simulations resemble W


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Figure 27. Snapshots of the aggregation of two large (3774 atoms) symmetric nanocrystals. These figures are taken (a) at the beginning of the simulation, (b) after 100 ps, (c) after 160 ps, and (d) after 1.0 ns. Oxygen atoms are shown in red (dark) and titanium atoms are shown in white (light). From ref 330. Copyright 2009 American Chemical Society.

sintering nanoparticles is in the rutile phase. In case of the anatase + amorphous simulation, the simulated X-ray diffraction patterns revealed that phase transformation led to brookite, the third polymorph of titania. Notably, at initial temperature of 973 K no phase transformation was observed for any combination of particles over the simulated time scales, although the particles did undergo sintering. Altogether, these results indicate that enhanced ionic mobility in nanoparticles close to their melting points plays an important role in assisting phase transformations. Alimohammadi and Fichthorn330 reported classical MD simulations on faceted anatase nanocrystals. These authors considered charge-neutral anatase nanocrystals with variations of the truncated tetragonal bipyramidal Wulff shape, as predicted in refs 27 and 320 which contained both (101) and (001) facets. In addition to Wulff shapes, they considered also asymmetric nanocrystals, which mimicked possible off-Wulff shapes possibly occurring during crystal growth. These asymmetric nanoparticles had permanent dipole moments, while the symmetric nanocrystals did not. 50 different initial configurations were simulated for the symmetric nanoparticles and 40 for the asymmetric nanoparticles. The total simulation times in the two-particle runs ranged between 1.0 and 5.0 ns, which, as previously mentioned, is too short to study the entire sintering process, but is long enough to observe the approach, coalescence, and initial restructuring of the nanocrystals after coalescence. A survey of the structural evolution representative of the sintering dynamics of two symmetric nanoparticles is presented in Figure 27. Figure 27a shows the initial configuration, where the centerof-mass separation is ∼8.5 nm. After 100 ps (Figure 27b), the particles have already adopted the relative orientation that they assume upon aggregation. Aggregation begins when an (001) surface of one particle contacts the edge between two (101) surfaces of another particle (Figure 27c). The sintering is mediated by oxygen atoms on the edge between two (101) facets, which initially contacts one of the under-coordinated titanium atoms on the (001) surface of another particle, to form a “hinge” that joins the two nanoparticles at/near their

those of ref 327 and showed the nanoparticles contact to take place within 20−25 ps, followed by formation of a neck, with associated decrease of the configuration energy. Interestingly, the neck diameter was found to increase with temperature for 3 nm anatase nanoparticles, while it was almost independent of temperature in the case of 3 nm rutile nanoparticles. Also, no phase change was observed during the MD simulation. To study the effect of crystallographic orientation in the sintering of nanoparticles, the same authors328 rotated one of the two nanoparticles to ensure different crystallographic orientations along the axis the particles approach each other. MD simulations carried out for 3 nm anatase particles showed that neck formation occurred almost at the same time in all of the cases except the 180° rotation case, for which the particles moved away from each other. These simulations also indicated that a 90° orientation produced maximum interpenetration, suggesting that this initial configuration may be most favorable. This suggests that orientation of the nanoparticles is extremely important in the process of sintering, which the authors associated with the relevant role played by dipole−dipole interparticle interactions. Koparde and Cummings329 later extended their MD study to the sintering of 3 nm anatase nanoparticles with rutile and/or amorphous nanoparticles of the same size. The MD simulations were conducted at initial temperatures of 973 and 1473 K for 10 ns. Based on the calculation of the potential energy versus surface area of anatase and rutile nanoparticles at 1473 K, these authors predicted an anatase to rutile crossover at 1.65 nm, consistent with the results of Naicker et al.326 This crossover size is much smaller than that predicted for faceted nanocrystals. An interesting observation was that upon sintering of one anatase and one rutile nanoparticles, the sintered nanoparticles evolved toward the rutile phase, as inferred from the time evolution of the simulated X-ray diffraction patterns from the 1473 K simulation. Similar transformations to rutile are observed in simulations involving amorphous + rutile nanoparticles and those with anatase + amorphous + rutile nanoparticles. Thus, the authors concluded that the final agglomerate will be in the rutile phase whenever one of the X


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Figure 28. Left: Geometries of (TiO2)n cluster models, n = 16, 28, 38, 46, 60, and 68. The starting structure (left), the PW/VSZ optimized geometry (middle), and side and top view of the B3LYP/VDZ optimized geometry (right). Right: DOS plots including the top of the valence band, the fundamental bandgap, and the bottom of the conduction band regions for the (TiO2)n nanocrystals with n = 16, 28, 38, 46, 60, and 68. Results from B3LYP/VDZ//B3LYP/VDZ calculations. From ref 335. Copyright 2000 American Chemical Society.

edges, leading to the final arrangement, Figure 27d. In a few of the considered cases, interaction occurred by sintering via two (101) surfaces. The authors pointed at electrostatic interactions, generated by surface under-coordinated atoms at the nanoparticles edges, as being responsible of the observed directional preference for aggregation, while long-range interactions were considered negligible. Further simulations performed for the asymmetric nanoparticles revealed a similar aggregation mechanism as found for the symmetric nanoparticles, leading the authors to exclude a major role of dipole− dipole interparticle interactions in driving the sintering process, at variance with what reported in ref 328.

clusters is thus nowadays possible, while to our knowledge no ab initio MD simulation has been performed to extend the results of classical MD discussed in section 5.2. Also, only recently the study of sintered large nanocrystals has been approached by (semiempirical) electronic structure methods. Due to the large interest in TiO2 nanoparticles and nanocrystals several semiempirical and molecular orbital studies were reported starting in the early 1990s, see, e.g., refs 331−333. Here, we restrict to the most recent studies, with emphasis on those which seem more relevant to technological applications. Numerous studies on TiO2 nanocrystals have been reported by Persson, Lunell, and co-workers. These authors employed general bonding principles to predict the structure of individual anatase nanocrystals.334 Among the selected criteria, they considered that the semi-ionic character of the bonding in TiO2 requires high coordination, balanced charge (i.e., no or vanishingly small dipole moment), and charge neutrality distribution to be accomplished simultaneously, without resorting to artificial termination by embedding or saturation. Specifically, clusters with all oxygen atoms coordinated to at least two titanium atoms, and all titanium atoms coordinated to at least four oxygen atoms, were considered. After generating bare (TiO2) clusters with sizes of ca. 2 nm (n up to 68) based on these criteria, Persson, Lunell and co-workers335 investigated their structural and electronic properties by DFT calculations, Figure 28a. Despite these structures might not correspond to the global minima for a given n, they represent suitable models of extended TiO2 surfaces that have been used, e.g., to study

5.3. Electronic Structure of TiO2 Nanocrystals

While the thermodynamic approaches presented in section 5.1 introduce electronic degrees of freedom into nonatomistic simulations through the DFT-calculated surface and tension energies, and the MD results of section 5.2 have an atomistic resolution but are based on a model potential, it is only by an electronic structure, possibly first-principles, simulation of TiO2 nanocrystals that an accurate picture of the interplay between the structural and electronic factors underlying the nanocrystals properties can be derived. As previously mentioned, the main issue with electronic structure calculations is their unfavorable scaling (typically N3 or worse) with the number of electrons in the system, which substantially limits the size amenable to firstprinciples simulations. Ab initio molecular dynamics are also limited by the time span which can be simulated, typically of the order of 10−20 ps. A static description of relatively large Y


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Figure 29. Top: Energy minimized model TiO2 nanoparticles. (A) 1 nm anatase, (B) 2 nm anatase, (C) 3 nm anatase, (D) 1 nm rutile, (E) 2 nm rutile, (F) 3 nm rutile. (Blue) titanium; (red) oxygen. Retention of the apical, three-coordinated Ti atoms on the 1 nm anatase particle was necessary to preserve electrical neutrality. Bottom: Total DFT calculated surface energies of model 1, 2, and 3 nm anatase and rutile particles. Orange represents the contribution from the sum of the particle’s constituent crystallographic surfaces. Yellow represents the remainder, which is attributed to edges and defects. From ref 322. Copyright 2009 American Chemical Society.

dye-sensitized interfaces.226 The electronic structures of optimized 1−2 nm nanoparticles, showed well developed band structures with essentially no electronic bandgap defect states, Figure 28b. In all cases, the anatase crystal form was largely intact with at most a few Ti−O bonds broken and a few defect sites formed. Another interesting aspect concerns the convergence of the electronic properties with increasing cluster size.335 The calculated band edges were found to vary by less than 1 eV as a function of size, independent of the computational method. At the same time, the density of states (DOS) plots display gradually emerging quasi-continuous valence and conduction bands with no apparent defect states in the band gap. According to the B3LYP/VDZ calculations, the calculated band gap decreases monotonically from 5 to 4.6 eV when the

size is increased from n=16 to n=60, which roughly corresponds to a doubling of the nanocrystal size. The lowest calculated TDDFT excitations follow the trend in the HOMO−LUMO energy gaps but are consistently lower by ca. 1 eV. An extensive search for global minimum structures of small (n ≤ 15) TiO2 clusters was reported by Hamad et al.,336 who employed a combination of simulated annealing and Monte Carlo simulations, together with genetic algorithm techniques, with the energy calculated by means of an interatomic potential. A subsequent recalculation of selected structures by DFT allowed the authors to evaluate the accuracy of the model potential, which was found to provide results of increased similarity to DFT as n increased. The selected minimum structures did not retain the anatase structure and they showed Z


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Figure 30. Anatase decahedral nanoparticles models: (a) illustration of the sharp (left) and the flat (right) particles; (b) the geometrical parameters utilized in Wulff construction. The shape is determined by the ratio S = d[001]/d[101]. The calculated equilibrium S value in aqueous solution is 1.07, implying considerably flatter particles than those predicted in vacuo (S = 1.73), confirming that the shape of anatase nanoparticles could be sensitive to the synthetic conditions. From ref 316. Coyright 2011 American Chemical Society.

Interestingly, for the bare and hydrated nanocrystal, the LUMO was located on the central portion of the nanocrystal, similar to what was found later for larger systems.317 Hummer et al.322 used DFT calculations combined with in situ X-ray diffraction to analyze the factors contributing to the anatase to rutile phase conversion. They investigated stoichiometric anatase and rutile (TiO2)n nanoparticles with n up to 272 and 209, respectively, and compared the surface energies calculated for the whole nanoparticles to those calculated using their surface slab models, see Figure 29. These calculations revealed a significant difference between the total calculated particle surface energies and the summed energies of the constituent faces, which for small anatase particles amounted to 63% of the total surface energy. The differences were attributed to the contributions of the nanoparticle edges and corners, which led to an inversion of the relative stabilities of anatase and rutile when the surface contributions dominate, as is the case with nanoparticles. Including both surface and bulk terms, the transition from nanoanatase to nanorutile was predicted at particles size slightly larger than 3 nm, while without their inclusion a much slower convergence to phase equilibrium is predicted, in line with, e.g., ref 320. An important contribution to the atomic level understanding of the working mechanisms of TiO2 nanoparticles in photocatalysis was given by Li and Liu,316 who performed extensive DFT calculations on a series of TiO2 anatase nanoparticles with different sizes and shapes, and quantitatively correlated the particle size and shape with the photocatalytic activity of the oxygen evolution reaction. The authors focused their attention on the rate-determining first proton removal step in the oxygen evolution reaction on anatase particles, while simulating the surrounding water environment by a continuum solvation model. They considered 12 different (TiO2)n nanoparticles, of different size (n = 58−449) and different (flat or sharp) truncated-bipyramidal shape, with the under-coordinated surface atoms saturated by dissociated water molecules, see Figure 30. Their results show that the HOMOs of the nanoparticles are generally at lower energy compared to those of the extended surfaces, while the LUMOs are at similar energy for reasonably large particles. Importantly, the results of Li and Liu316 reveal that for nanoparticles larger than 2 nm, both the band gap and the HOMO/LUMO energies converge rapidly toward those of the extended (101) and (001) surfaces, implying that the quantum size effect may only be significant in very small TiO2 anatase particles, e.g., 0.75, which may have a role in electrode degradation. The same author investigated also a ramsdellite-structured LiTiO2 phase,356 and made a comparative study of Li intercalation in the rutile, anatase, brookite, hollandite, ramsdellite, and spinel (Li0.5TiO2) phases.357 In the latter work, it was found that intercalation properties are dominated by the strength of the coupling between the electronic and the structural degrees of freedom. In an earlier comparative study of the rutile, ramsdellite, orthorhombic (imma) and spinel-type LiTiO2 phases based on periodic Hartree−Fock calculations, Mackrodt358 predicted an orthorhombic > spinel > ramsdellite > rutile stability order. Spinel-type structures have been studied also by Wagemaker using GGA-DFT calculations and the cluster expansion method.359 Whereas for x < 0.5 the Li ions occupy tetrahedral 8a sites, for 0.5 < x < 1 the Li0.5TiO2 phase was found to coexist with a LiTiO2 phase where Li ions are at octahedral 16c sites. The diffusion barrier for Li in spinel-type LixTiO2 was recently estimated to be 0.68 eV by Liu et al.360 using the DFT+U approach. Most of the work on TiO2 lithiation has focused on the B phase. Due to the large channels in its structure, the B phase is indeed ideally suited as a host for interstitial doping. After early extended-Hückel calculations by Nuspl et al.,361 several GGADFT studies on LixTiO2(B) models have been reported, with rather conflicting results. The energetics of diluted Li atoms was studied Panduwinata and Gale,362 who predicted that Li prefers to bind in a 5-fold coordinated site close to the octahedral layer (A2 site, see Figure 37), while the most favorable diffusion path is along the open channels parallel to the b axis, and involves A2 → C→A2 jumps (C sites are located at the middle of the b-axis channels, and at the center of the square planar arrangement of O atoms, see Figure 37). A reversed stability order for the A2 and C sites was found by Arrouvel et al.,363 who predicted diffusion to occur along the b direction through C → C jumps. In a subsequent work, where DFT calculations were combined with powder neutron

ric units, and is characterized by the presence of layers linked by 2-fold coordinated oxygens. Recent first-principle calculations (using both PBE and B3LYP),346 have revealed that half of the Ti ions are not in a 6-fold, but rather in a 5-fold coordinated environment (see Figure 36), which makes them chemically

Figure 36. Local coordination around the Ti ions in TiO2(B). The “Ti1” ion is in a 5-fold coordination. Reproduced with permission from ref 346. Copyright 2009 American Institute of Physics.

nonequivalent. In tune with its open structure, the computed bulk modulus of TiO2(B) is lower than those of rutile and anatase, whereas the electronic bandgap (GGA, 2.68 eV; B3LYP, 4.28 eV) is predicted to be indirect and higher with respect to the other low-pressure TiO2 forms. On the other hand, the theoretical IR spectrum is very similar to that of anatase, which makes these phases difficult to distinguish with vibrational spectroscopy. Somewhat surprisingly, studies on the brookite and B phases were preceded by investigations on the more exotic highpressure TiO2 forms. Dewhurst and Lowther347 first explored the mechanical properties of some of these phases by LDA calculations. They found the sequence fluorite > baddeleyite (MI) ≈ columbite (II) > rutile > anatase for the bulk moduli, in line with the high-pressure nature of the first four phases. Different and conflicting results were reported in subsequent LDA calculations: Milman348 found a low bulk modulus for columbite, whereas a low B0 value was computed by Sasaki for baddeleyite.349 Dubrovinskaia et al.350 studied the stability of the various polymorphs as a function of pressure by linearized muffin tin LDA calculations. They found that the hypothetical pyrite structure is never stable, while rutile → columbite → baddeleyite transitions occur by raising the pressure. By further increasing the pressure, an orthorhombic structure (the socalled OI phase) becomes stable, and finally this converts to the cotunnite(OII) structure. Whereas the latter was already known, OI was a new structure, which was studied experimentally and theoretically for the first time. The above results were largely confirmed by Harrison and co-workers,28 who examined the effects of pressure for a large number of polymorphs using both GGA and Hartree−Fock calculations. They predicted the sequence anatase < rutile < columbite < baddeleyite < fluorite < cotunnite for the bulk moduli (the OI phase was not considered). Furthermore, by examining enthalpy curves, they found that the anatase → columbite transition occurs at lower pressure (3.5 GPa) with respect to the rutile→ columbite one (21 GPa), while the columbite → baddeleyite → cotunnite transitions occur at 31 and 63 GPa, respectively. No stability range was found for the pyrite and fluorite cubic phases. However, these polymorphs AF


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Figure 37. Interstitial sites for Li interstitials in TiO2(B). Reprinted with permission from ref 354. Copyright 2012 American Chemical Society.

Figure 38. Equilibrium crystal shape of the brookite polymorphs as obtained through the Wulff construction. Reproduced with permission from ref 367. Copyright 2007 American Physical Society.

diffraction, Armstrong et al.364 identified three structures, viz. Li0.25TiO2, Li0.5TiO2, and LixTiO2 (x = 0.80.9). In the lowconcentration case, Li was confirmed to prefer C sites. For intermediate concentrations, the C site is unfavorable, and A1 sites are occupied. Finally, at the highest Li concentration, A1 and A2 sites turn out to be equally occupied. Different results were found by Dalton et al. using DFT calculations in conjunction with Monte Carlo simulations.354 As in ref 364, the site occupation changes with x, but in a different way: for x < 0.5, Li ions are predicted to occupy A1 sites on different planes along the c-axis direction. At x = 0.75, an inversion of the stability order occurs, that causes A2 and C sites to be preferred, so that, at x = 1.0, all the A2 and C sites are ultimately occupied. Lithium incorporation through the TiO2(B) (001) surface was investigated by Koudriachova.357 The (001) surface is the most stable one for TiO2(B) (see section 6.2), and is also exposed by nanowires, which have a cylindrical shape elongated along the b direction. Li ions are predicted to find a low-energy diffusion path bringing them from the A1 surface sites to bulktype A2 sites (assumed to be most stable). This mechanism implies that each Li has its own independent diffusion channel, which explains the good pseudocapacitive behavior of TiO2(B) nanowires with respect to Li ions. Site occupations were recently studied with DFT+U calculations by Dylla et al.365 For 3D systems the predicted stability sequence is A2 > C > A1 in the dilute limit, whereas an alternating A1/A2 occupation is favored at higher x. A stability sequence C > A2 > A1 was instead predicted for nanosheets, where the stability inversion of the A2 and C sites is related to a reduction of the Li+-Li+ interactions, due to lattice relaxations.

introduce specific reactions sites, which make the brookite (210) surface significantly more reactive than anatase (101).368 Classical molecular dynamics studies on the adsorption of several proteins found a weaker adsorption on brookite than on anatase.369 For CO2, the interaction with brookite (210) was found similar to that with anatase (101).370 The surface → CO2 electron transfer is negligible, indicating that brookite may not be a suitable photocatalyst for CO2 reduction. On the other hand, the brookite (210) surface is an interesting support for gold nanoparticles in CO oxidation catalysis.371 In fact, brookite favors a higher dispersion of gold clusters, which in turn have a peculiar ability to switch from 2D to 3D configurations. This reduces the coordination number of Au atoms, making them suitable for strong adsorption and activation of CO and O2 molecules. The structure and stability of the surfaces of the B polymorph were first investigated by Vittadini et al. using DFT-GGA calculations.372 Due to the presence of 2-fold O anions and 5-fold Ti cations already in the bulk phase, the structure of the TiO2−B surfaces is not straightforward to describe. The (001) surface is by far the most stable, in agreement with experimental results of TiO2 heteroepitaxy, showing that the TiO2(B) phase grows under the form of (001)-oriented flat islands.373,374 The (001) surface exhibits two kinds of 5-fold Ti ions, one of which is not undercoordinated with respect to the bulk structure, while no true undercoordinated O ion is exposed. This makes the surface particularly stable. On the (100) surface, instead, there are one undercoordinated Ti-5c ion and two O-2c ions, of which only one is genuinely undercoordinated. A similar situation is found also on the (110) surface. The equilibrium shape of TiO2(B)was computed under both dry and wet conditions.372,375 As shown in Figure 39, the shape is more elongated in the latter case. On the (001) surface, water stabilizes the type-II termination, which is metastable in a dry environment, by converting the oxo ions into hydroxyls. Water adsorbs dissociatively on the (100) surface,375,376 whereas the nature of the interaction with water is less definite for the other surfaces, where a coverage-dependent behavior or a mixed molecular/dissociative adsorption is generally found.375 The high reactivity of the (100) surface toward water dissociation has stimulated a number of studies aimed at clarifying the fate of prototypical molecules interacting with this surface. Methanol was found to dissociate on both the clean and the hydroxylated surface.377 Most interestingly, terminal OH groups present on the hydroxylated (100) surface are able to extract protons from methanol. Adsorption structures and

6.2. Surfaces

The (010) and (001) surfaces of the brookite polymorph were first investigated with molecular dynamics simulations,366 which revealed that on both surfaces Ti ions in tetrahedral coordination are present. In a subsequent, more detailed, DFT study,367 numerous surfaces were investigated, specifically (001), (111), (121), (011), (101), (210), (010), and (100), and the relationships with the surfaces of rutile and anatase were discussed. On the basis of the stability of all the examined surfaces, the equilibrium shape of a brookite crystal was determined through the Wulff construction (see Figure 38), from which the authors concluded that the average surface energy of brookite is higher than that of anatase. The (210) surface, which is the most exposed one for brookite, is made of the same building blocks of the anatase (101) surface. Comparative investigations of the two surfaces indicate that the differences in the arrangement of the structural units AG


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6.3. Two-Dimensional Systems: Nanolayers, Nanosheets, and Films

In most of the current literature, “nanolayer” (NL), “nanosheet” (NS), and film are used as interchangeable terms. In this review we use the term film to indicate supported layers, while the term nanosheet is used to indicate nanolayers of intrinsic high thermodynamic stability. While nanosheets can be in some cases synthesized by a bottom-up approach, mostly as supported films, they are usually obtained by exfoliation of layered titanates. Similarly to the more famous graphene, TiO2 nanosheets are not only interesting for fundamental reasons, but also because they are ideally suited as building blocks for the fabrication of nanoarchitectures with a wide range of applications.383 6.3.1. Nanosheets. We have already mentioned that the lepidocrocite-like phase tends to form highly stable nanosheets. Lepidocrocite-like NSs are formed by a core of four atomic layers of alternating 4-fold coordinated O atoms and 6-fold coordinated Ti atoms. This core layer is terminated at both surfaces by an atomic layer of 2-fold coordinated oxygens. As shown in the following, lepidocrocite-like NSs are structurally related to anatase (001) nanolayers. The first theoretical investigation on lepidocrocite-TiO2 was performed by Sato et al. using DFT-GGA calculations.384 A stoichiometric unit of an isolated NS was found to be only 0.4 eV less stable than the anatase polymorph, whereas an hypothetical 3D stack was found to be 0.053 eV higher in energy, and thus unstable. The possible role of dispersion forces in stabilizing lepidocrocite-like stacks was later investigated by Forrer and Vittadini.385 The stacking energy was found to be ∼9 kJ/mol, which is considerably lower than in typical layered oxides such as V2O5. This explains why lepidocrocite-TiO2 stacks are not easily obtained as V2O5 ones are. The GGA study of Sato et al.384 predicted also a band gap of 3.15 eV, to be compared to band gap values of 2.28 eV for rutile and 2.67 eV for anatase obtained with the same approach. The wider band gap of the lepidocrocite-like phase should be attributed to the low dimensionality of the system. No dispersion was observed in the band structure along the stacking direction, while very small differences occurred between the DOS of single- and stacked lepidcrocite NSs (see Figure 41), in agreement with the computed energetics. Recently, GW calculations have shown the excitonic nature of optical transitions in the lepidocrocitelike phase, with a small blue shift when going from single NSs to NS stacks.386 While investigating the properties of Pt-supported TiO2 nanolayers, Orzali et al.387 realized that 2 ML anatase (001) systems are unstable and spontaneously interconvert to lepidocrocite NS by a barrierless mechanism which involves

Figure 39. Equilibrium crystal shapes of the B polymorphs as obtained through the Wulff construction: (a) dry conditions; (b) wet conditions. Reproduced with permission from ref 375. Copyright 2010 The Royal Society of Chemistry.

energies for CO on the (100) hydroxylated surface were found to be similar to those computed for other TiO2 surfaces.378 Surprisingly, while a CO → surface charge donation was predicted to occur, the authors claimed that the interaction mainly involves the 5π* state. The interaction of formaldehyde with the clean and partially hydroxylated (100) surfaces was studied by Liu et al.379 Three main adsorption configurations were identified, see Figure 40. Two of these are dioxomethylene-like structures, where a true undercoordinated O (a) and an intrinsic O-2c ion (b) is involved, respectively. The third case is a configuration where the adsorbate is singly coordinated to Ti-5c ion (c). The low reactivity of the type-I termination of the (001) surface375 was confirmed in a comparative study of the adsorption of NH3 on the (001) and (100) surfaces.380 Stimulated by the observation that the TiO2(B) phase is selectively formed when the synthesis is carried out using ethylene glycol (EG) as solvent, Xiang et al.381 studied the adsorption of EG on the high-energy (010) surface.372 They found that EG interacts strongly with TiO2− B(010), forming a dissociatively adsorbed bidentate structure. As a consequence, the stability of the TiO2−B(010) surface is drastically lowered, which explains the stabilization of the B polymorph in EG. The low-index surfaces of the columbite phase have been investigated by Kuo et al. with LDA calculations.382 The surface energy decreases in the order (100) > (001) > (110) > (010). This trend has been explained on the basis of the nature and density of undercoordinated Ti ion on the different surfaces. In particular, the (010) surface has the lowest surface energy, due to the exposure of highly symmetrical TiO4 species.

Figure 40. Possible adsorption configurations for CH2O on TiO2-B(100). Reproduced with permission from ref 379. Copyright 2013 the PCCP Owner Societies. AH


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Figure 43. Total energy curve, showing the activated conversion of a 4 ML TiO2-anatase (101) nanolayer to a 2 ML TiO2-B (001) nanosheet. Replotted from the original data of ref 173.

Figure 41. Density of states of lepidocrocite-like single and stacked nanosheets. Reproduced with permission from ref 384. Copyright 2003 American Chemical Society.

In the above investigation, Vittadini and Casarin389 did not consider 1 ML (101) layers, whose unrelaxed structure consists of noninterconnected clusters. Evarestov et al.390 showed however that, when optimized, a (101) layer gives rise to a denser and remarkably stable film of hexagonal symmetry, consisting of one layer of 6-fold coordinated Ti ions sandwiched between two layers of 3-fold coordinated oxygens (see Figure 44). As pointed out by Evarestov et al., this NS can be considered as originating from the fluorite (111) surface.390 6.3.2. Adsorption. Adsorption of water on lepidocrocitelike NSs was studied by Casarin et al.391 Here, we examine only the results of symmetric adsorption at both NS surfaces, since asymmetric adsorption leads to the formation of nanotubes, which will be examined in section 6.4. For 1/3 ML and 1/2 ML water coverage, only molecular adsorption occurs when the lepidocrocite-type structure is maintained. Increasing the coverage has the effect of strengthening intermolecular interactions. By forcing water dissociation, thermodynamically favored stepped tri- and dititanates are formed, which eventually form ABA-type stacks. The adsorption and diffusion of gold atoms on 2 ML TiO2− B NSs, used as models of films grown on Pt(110), were studied in ref 373. Gold atoms prefer to adsorb on top of the oxygens, but binding energies are weak (0.30 eV) and diffusion barriers very low (0.050.06 eV). By contrast, binding energies and diffusion barriers are large, 2.96 and 2.4 eV, respectively, on the “kagomé” reduced phase, which explains why experimentally clusters are more easily formed on reduced films. 6.3.3. Point Defects and Doping. Experimentally lepidocrocite-like NSs are obtained by delamination of alkali titanates, so they can easily incorporate metal dopants. Codoped lepidocrocite NSs were studied by Osada et al. with LSDA calculations in conjunction with X-ray adsorption fine structure spectra and magnetic circular dichroism measurements.392 Their calculations show that substitutional Co ions give rise to a ferromagnetic electronic structure, characterized by electron transfer to the Co 3d states. Titanium vacancies in lepidocrocite NSs were investigated by Ohwada et al. by transmission electron microscopy (TEM) and DFT calculations.393 These authors found that Ti vacancies are likely to give rise to larger defects, where two neighboring bridging oxygens are also missing. The energetics of oxygen vacancies was studied by Vittadini et al.394 Their computed formation energy of a neutral vacancy is in the range 5.05.5 eV, which is

the relative sliding of the upper and lower half of the NS, see Figure 42. Interestingly, similar transformations were observed

Figure 42. Total energy curve, showing the barrierless conversion of a 2 ML anatase nanolayer to lepidocrocite-like nanosheet. Replotted from the original data of ref 173.

in simulations starting from anatase-derived nanoribbon models of various size.388 Motivated by the close relationship between the anatase and lepidocrocite nanolayers, Vittadini and Casarin systematically investigated the energetics of anatase nanolayers of increasing thickness oriented along the main low-index directions.389 They found that for 2D nanosystems the most stable polymorph is not anatase, as commonly assumed for nanoscale TiO2, but lepidocrocite-like TiO2. Furthermore, the lepidocrocite/anatase interconversion is not the only spontaneous transformation occurring for TiO2 nanolayers. While there is a general and expected tendency toward higher stability with increasing thickness, several irregularities are present. In particular, 4 ML-thick layers oriented along (101) and (100) show an anomalous stability. For 2 ML (001) layers relaxation leads to a completely different structure where all the Ti ions are 5-fold coordinated (see Figure 43). This structure, which was originally called “pentacoordinated nanosheet” in ref 173, was later identified as a TiO2−B (001) 2 ML system.374 AI


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Figure 44. Structure (left) and PBE0 density of states (right) of 1 ML fluorite-type nanosheets. Reproduced with permission from ref 390. Copyright 2011 Elsevier Science.

unstrained lepidocrocite TiO2, interrupted by small patches where the oxide layer matches the periodicity of the substrate. Due to their multilayer nature, TiO2(B) films grown on a Pt substrate were simply modeled as unsupported TiO2(B) films.373 Hexagonal, fluorite-type films were grown on Cu(100) by Atrei et al.407 DFT calculations indicate that the film strain due to the c(2 × 6) coincidence is more than compensated by the interaction with the substrate. Furthermore, analysis of the DFT results shows that the TiO2 film loses its insulator character and the electron states close to the Fermi level are dominated by the contribution from the Ti 3d orbitals.

slightly larger than the values found for the rutile and anatase bulk phases. 6.3.4. Supported Films. The first theoretical study of a supported-TiO2 film, by Jennison et al.,395 concerned a Pt(111)-supported film of TiO composition, which was taken as a model for TiOx-encapsulated Pt clusters observed on TiO2(110). One of the main results of that investigation was that metal−supported reduced films of TiO composition prefer to arrange with Ti atoms at the metal/film interface.395 Zigzag features experimentally observed by STM were attributed to the O-layer strain, which induces an abrupt change from hcp to fcc arrangements of Ti atoms. More reduced TiOx phases were subsequently obtained and theoretically investigated in a series of papers by Granozzi, Fortunelli and co-workers396−403 (see ref 404 for a recent review). In contrast to reduced films, oxygen atoms are present at the interface of metal−supported TiO2 stoichiometric films. Studies of stoichiometric 2 ML-thick TiO2 films grown on (1 × 2)-Pt(110)387,388 show that the experimental structure can be reproduced by assuming a slightly distorted lepidocrocite sheet. Experimentally, a (14 × 4) reconstruction is observed, which is dominated by dark stripes. Calculations show that these stripes are related to the presence of an almost perfect coincidence between 14 substrate cells and 13 lepidocrocite overlayer units along the lepidocrocite short b-direction. This leads to differences in the local coordination of oxygens at the interface, which gradually change from on-top to bridging along the b direction. Oxygens occupying bridge positions have a lower height with respect to O atoms at on-top sites, and this difference leads to the corrugation shown by the STM images. Similar lepidocrocite-type films on Pt(111) were found to be characterized by a low surface-overlayer interaction, which is in agreement with the absence of features in the STM images of the film.405 A third type of supported lepidocrocite film was observed by Atrei et al.406 on the Ag(100) surface. In this case, a (5 × 1) reconstruction occurs along the long a-direction of the lepidocrocite-like film. However, a coincidence between the substrate and the overlayer along the short lepidocrocite b-axis was found to be unlikely by comparing the energy required for the film deformation with the adhesion energy. Thus, it was concluded that the film is composed by large patches of

6.4. One-Dimensional Systems: Nanotubes

The first theoretical investigation on TiO2 nanotubes was carried out with DFTB, a DFT tight binding method, by Enyashin and Seifert.408 Nanotubes were constructed either from bilayers with the lepidocrocite-like structure (i) or from monolayers of hexagonal structure (ii), which were defined as anatase-type, but were actually (111)-oriented monolayers of fluorite-type TiO2, since monolayers of (101)-oriented anataseTiO2 have been shown to convert spontaneously to (111)oriented fluorite-TiO12.390 For (ii), both single-wall nanotubes and nanorolls were examined (see Figure 45a,b), while for (i) single-wall structures made of the (n,0) and (0,n) type were considered (see Figure 45c,d). The lepidocrocite-like nanotubes, and in particular those of the (n,0) type, were found to be unfavorable, due to their thickness. By contrast, nanotubes made of the hexagonal monolayers were computed to be stable against nanostrips of the same size, suggesting that they could represent viable models for real TiO2 nanotubes. As far as the electronic structure is concerned, all the lepidocrocite nanotubes were found to have a ∼4.5 eV indirect band gap, whereas for those made of the hexagonal monolayer the gap is direct and slightly smaller (4.2 eV). As previously pointed out, lepidocrocite-like and (001)oriented anatase bilayers are closely related, as the former is obtained from the latter through a nonactivated transformation, whereas dissociative adsorption of water inverts the process391 (see below). Given the large difference between the a lattice constants of anatase and lepidocrocite, it was suggested that asymmetric water adsorption could give rise to a spontaneous curvature of the film, with the consequent formation of a AJ


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is studied with conventional periodic boundary conditions.389 As a consequence of the above-described structural strains on the top and bottom surfaces, (n,0) nanotubes made of 3 ML of anatase (001) have a negative strain (see Figure 46), i.e., their formation is thermodynamically favored.

Figure 46. Strain energy (Es) of TiO2 anatase(001) 3 ML nanotubes versus the nanotube diameter D [Å]. Reproduced with permission from ref 415. Copyright 2011 American Chemical Society.

Figure 45. Structures of some TiO2 nanotubes: (a) a (20,0) NT and (b) a (16,16) NT, both obtained from fluorite-type nanosheets; (c) a (0,28) NT and (d) a (28,0) NT, both obtained from lepidocrocite-like nanosheets. Adapted with permission from ref 411. Copyright 2011 The Royal Chemical Society.

In another study, Ferrari and co-workers re-examined the case of dititanate nanotubes.413 Several geometries were taken into consideration i.e., DT1, where the NT derives from the plain rollup of a stepped H2Ti2O5 NS; DT2A, where water is desorbed from the internal surface, while the external one is similar to that of DT1; DT2B, which differs from DT2A because the external OH groups interact via H-bonds; DT2C, where the structure is turned to an asymmetrically hydroxylated anatase/lepidocrocite one, similar to the one examined in ref 391. Calculations indicate that asymmetric DT2X NTs (particularly those of DT2A type) have a lower strain, while their strain vs diameter curve has a minimum, i.e., they spontaneously tend to assume a curved shape. However, DT1 NTs are thermodynamically more stable, and this is true also when they are compared to lepidocrocite NTs. As for the electronic properties, the band gap of dititanate NTs are predicted to be larger (by ∼1 eV) with respect to lepidocrocite/ anatase NTs. NTs based on 1-ML hexagonal fluorite (111) sheets have been studied by Evarestov and co-workers.390,412 These authors performed a comparative study of SW NTs obtained from 1ML fluorite with NTs obtained from 2-ML anatase (101) films, which are the thinnest sheets maintaining the rectangular structure of anatase (101).389 Although the 1 ML fluorite sheets are more stable than the 2 ML anatase sheets by 0.25 eV/TiO2 unit, the NTs obtained from the latter are generally more stable, and have lower strain energies, at least for diameters smaller than ∼25 Å. On the other hand, NTs made of thicker anatase sheets are found to be unstable. Concerning the electronic structure, the band gaps of anatase-type NTs are larger (up to 0.5 eV) with respect to the fluorite-type ones. Fluorite-based double-wall (DW) NTs (NTin@NTout)with (n,n) “armchair” and (n,0) “zigzag” structures were also studied.416 The stability of the DW NTs was found to depend on the difference between the NT radii (ΔRNT), which fixes the interwall distance, and on the diameters of the internal (Din) and external (Dout) NTs. The optimal configurations are (6,6) @(12,12) and (10,0)@(20,0), which correspond to ΔRNT values in the 4.55.0 Å range. Systems with smaller values for ΔRNT or Din are unstable, whereas systems with larger

nanotube. This possibility was proven using ribbon models, i.e., models where the periodic boundary conditions are suppressed along two directions. By extrapolating the results from such models, nanotubes with an average diameter of 27 Å carrying hydroxyls only on the external surface were predicted to form.391 Interestingly, spontaneous partial dehydration of the internal surface was observed to take place in DFTB simulations of the structure of single wall NTs made of trititanic acids by Enyashin and Ivanovskii.409 The same authors extended their study to NTs formed by another family of protonated TiO2 films, i.e., metatitanic acid.410 Recently, the implementation of rotohelical symmetry conditions in the CRYSTAL code has finally offered the possibility to carry out accurate density functional calculations on realistic nanotube models. Using this approach, Bandura et al.412 studied single wall (SW) nanotubes based on an anatase (101) ML (note that a TiO2 ML is made of three atomic layers). With the same approach, Szieberth et al. studied SW nanotubes made of two lepidocrocite MLs.413 Their results confirm that the (0,n) chirality is favored over the (n,0) one because of the lower strain. Furthermore, for diameters up to 25 Å, a substantial reconstruction is observed both for the (0,n) and for the (n,0) nanotubes. The hyperpolarizabilities of the above-described NTs were recently studied with the coupled perturbed Kohn−Sham approach.414 The strain properties of lepidocrocite NTs change drastically when the thickness increases from 2 to 3 ML.415 If the third TiO2 ML is added on top of the film, a more anatase-like surface is formed, while the structure of the bottom surface still resembles the lepidocrocite structure. Furthermore, the Obridges, which determine the direction of the surface stress, are mutually perpendicular on the top and bottom surfaces. Because of these structural differences, the bottom surface is subject to a large stress along , while the top layer is subject to a lower strain along . This effect, which is similar to that predicted for asymmetrically hydroxylated lepidocrocite bilayers,391 does not show up when the nanolayer AK


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values for ΔRNT or Dout correspond to quasi-independent pairs of NTs. Furthermore, zigzag configurations, and in particular those with an inverse-stacking structures are most stable. In the electronic structure, the strong interwall interactions cause the bandgaps of DW NTs to be considerably smaller than those of SW NTs. In comparison to nanotubes, very little work has been done on other 1D forms of less-common TiO2 polymorphs, such as nanoribbons (NRs). He et al.415 reported GGA calculations of the energetics and electronic properties of hexagonal fluoritetype NRs. Both armchair- (AR) and zigzag-terminated (ZZ) NRs were considered, and in the ZZ case both O- and Titerminated structures were included. As expected, Titerminated NRs are unstable, and reconstruct to an Oterminated superstructure where short and long O-bridges are present. Among O-terminated NRs, ZZ structures, particularly those with an even number of Ti cations, are most stable (see Figure 47). Band gaps for fluorite-type NRs, estimated from

nation of the band gap would also provide the basis for quantitatively predicting the energies of trap states, defect and impurity levels, which are crucial for the design of TiO2 materials with improved properties. Therefore, it is important to clearly identify which are the aspects that are not taken into account with satisfactory accuracy by the current theoretical approaches. Also not fully understood are the electron−phonon coupling and self-trapping phenomena. The characteristics of the electron and hole polaronic states (i.e., energy levels, radii, and effective masses), and how these change going, e.g., from photoexcited TiO2 to doped or reduced TiO2, are still under debate. In the current theoretical studies a major problem is that the size and degree of localization of the electron polaron depends critically on the fraction of exact exchange in hybrid functional calculations or the value of U in DFT+U studies. The situation is less critical for the hole states, which are generally found to be strongly localized. In any case, additional work would be desirable, also from the experimental side, in order to better understand the characteristics of electron and hole states as well as the connection between transport and spectroscopic measurements. This is especially important for polaronic states at surfaces, because the energies of these states can affect the reducing and oxidizing powers of electrons and holes in photocatalysis.69,417 There has been a lot of interest in assessing the relative photocatalytic activities of different anatase surfaces in the last several years. The expectation that the (001) surface could be extremely reactive stimulated intense experimental efforts aimed at synthesizing particles exposing a substantial amount of (001) facets.418,419 Recent reports, however, have been more contradictory,146,420,421 pointing to the need for more comprehensive fundamental investigations where both the surface structure, including surface and subsurface defects, as well as the interface with water (or, possibly, aqueous solution), are correctly taken into account. In this context, an important fundamental problem is the description of the level alignment between the TiO2 band edges and the relevant energy levels, e.g., the HOMO and the LUMO, of the adsorbate, notably water, see, e.g., ref 278 and references therein. Also in this case, approaches beyond standard local and semilocal DFT, particularly hybrid functionals, have proven essential for a correct description.188,278,417 Overall, the main issue to be addressed in the computational characterization of TiO2-adsorbate interfaces, as used, e.g., in hybrid photovoltaics, is the ability to couple the accuracy of typical quantum chemical methods for ground and excited state properties, with the large dimensions and complexity of the investigated systems. Most hybrid DFT methods seem to accommodate such challenging accuracy issue, but at the cost of a higher computational overhead. Furthermore, the inclusion of solvation effects is also important and is usually accounted in a simple and effective way by means of continuum solvation models. These approaches, however, are missing some of the relevant specific solute/solvent information, especially when the solvent is also a reactant, as it is the case in the water splitting reaction. In these cases ab initio molecular dynamics can offer an important simulation tool but its application is limited in both space and time scales. It seems likely that the future, grand-challenges in the simulations of TiO2 nanomaterials and their interfaces will be dominated by multiscale approaches, combining various levels of accuracy on different space/time scales. In this respect, the use of DFT-based tight-binging

Figure 47. Cleavage energies for fluorite-type nanoribbons with armchair and zigzag configuration as a function of the NR width. Numbers are the lines of Ti ions present in the structure. Reproduced with permission from ref 415. Copyright 2010 American Chemical Society.

GGA+U calculations, range from 2.93 to 4.04 eV, and are direct (indirect) for AR (ZZ) configurations. Furthermore, band gaps are higher for even NRs. Reduced ZZ NRs were studied, and O ions close to the edges were found to be most easily removed. Complete removal of one line of Ti ions brings to the formation of ferromagnetic NR.

7. CONCLUDING REMARKS Intense experimental and theoretical research efforts have led to considerable progress in the understanding of the bulk and surface properties of anatase TiO2 crystals and nanocrystals over the past decade. Nevertheless, there remain areas of considerable debate, even at the very fundamental level, as well as areas that are still largely unexplored. Starting from the bulk, the description of the bulk electronic structure and optical properties of anatase is still unsettled since even advanced theoretical techniques often tend to overestimate the fundamental band gap (e.g., hybrid functionals and GW methods) or underestimate the optical one (e.g., the BSE method). As pointed out in the Introduction, knowing accurately the band gap is important because this determines the optical absorption, which has an essential role in the performance of photocatalytic devices. An accurate determiAL


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schemes may offer a reasonable alternative to conventional DFT algorithms in terms of price/performance and encouraging results have been obtained in the specific simulation of TiO2 structures. Finally, much needs still to be done for better characterizing and understanding less common TiO2 phases. The available theoretical studies on these phases have focused almost exclusively on the bulk electronic properties, whereas their surface properties remain largely unexplored. Low-dimensional forms like lepidocrocite-like TiO2, on the other hand, have been mostly investigated for their intrinsic structural and electronic aspects, but little insight has been obtained on their catalytic activity. Further fundamental insights are clearly desirable, both for the intrinsic scientific interest of these materials, and for their potential to lead to new or improved technological applications.

Cristiana Di Valentin received her Master’s degree in Chemistry from the University of Pavia in 1997, and her Ph.D. degree jointly from the University of Pavia and the Technische Universität München in 2000.

AUTHOR INFORMATION

She was appointed as Assistant Professor at the University of Milano

Corresponding Author

Bicocca in 2002, and as Associate Professor of General and Inorganic

*E-mail: [email protected].

Chemistry in 2012. She has been a visiting scientist at Technische

Author Contributions

Universität München, Princeton University, Universitat de Barcelona,

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. All authors contributed equally to this manuscript.

and Ecole Nationale Superieure de Paris. Her research interests range from ab initio computational study of reaction mechanisms in organic chemistry and homogeneous catalysis to heterogeneous catalysis,

Notes

photocatalysis, doped and defective semiconducting oxides, chemically

The authors declare no competing financial interest.

modified graphene, and carbon based materials for fuel cells.

Biographies

Simona Fantacci is research scientist at the CNR Institute of Molecular Sciences and Technology, in Perugia, Italy. She is cofounder of the

Filippo De Angelis is senior research scientist and deputy director at the CNR Institute of Molecular Sciences and Technology, in Perugia, Italy. He is the founder and coleader of the Computational Laboratory for Hybrid/Organic Photovoltaics in Perugia. He earned a B.S. in Chemistry 1996 and a Ph.D. in Theoretical Inorganic Chemistry in 1999, both from the University of Perugia, Italy. He is an expert in the development and application of quantum chemical methods to the study of the structural, electronic, and optical properties of complex systems including transition metals. His main research interest are in the field of dye-sensitized and perovskite solar cells, employing firstprinciples computational methods to predict and interpret the properties of new and existing materials. First-principles simulations are also employed to investigate the active heterointerfaces constituting hybrid/organic photovoltaic devices. He is the 2007 recipient of the Raffaello Nasini Gold Medal of the Inorganic Chemistry Division of the Italian Chemical Society.

Computational Laboratory for Hybrid/Organic Photovoltaics (CLHYO) in Perugia. She received a Ph.D. in Theoretical Inorganic Chemistry from the University of Perugia in 1999 and was research associate at Princeton University (USA) in 2002−2003. Her research activity concerns the theoretical investigation of excited state properties of transition metal complexes by means of DFT and TDDFT methods, with focus on the linear and nonlinear optical properties of polypiridyl complexes of Ru(II) and Ir(III) employed in the fields of dye-sensitized solar cells, OLED devices and NLO materials. Recently, she has worked on the modeling of the photophysical properties and degradation processes of materials relevant to the Cultural Heritage. AM


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CARTES, of the Italian Ministry of the University and Research, for A.V.; DoE-BES, Division of Chemical Sciences, Geosciences and Biosciences under Award DE-FG0212ER16286, for A.S.

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Andrea Vittadini received his “laurea” degree (cum laude) in Chemistry from the University of Padua in 1983. After a period of training as a Research Fellow of the Italian National Research Council (CNR), in 1988 he joined the CNR Istituto di Chimica e Tecnologie Inorganiche e dei Materiali Avanzati as a Research Scientist. In 1998 he was appointed Senior Research Scientist, and moved to the University of Padova unit of the CNR Institute of Molecular Sciences and Technologies (now a part of the Institute for Energetics and Interphases). His expertise concerns the modeling of complex chemical systems by both quantum chemical and solid-state theoretical techniques. His current research interests include metal oxide surfaces, nanostructures metal oxides, functionalization of metal and metal oxide surfaces, and molecular self-assembly.

Annabella Selloni graduated in physics at the University “La Sapienza” (Roma, Italy), and received her Ph.D. degree from the Swiss Federal Institute of Technology (Lausanne, Switzerland) in 1979. After a postdoc at the IBM- T.J. Watson research center in Yorktown Heights, she held positions at the University “La Sapienza”, at the International School for Advanced Studies (Trieste, Italy), and at the University of Geneva (Switzerland). In 1999 she joined the Department of Chemistry of Princeton University, where in 2008 she became the David B. Jones Professor of Chemistry. She has coauthored ∼250 publications, mostly in the fields of surface physics and chemistry. Her current research interests are mainly focused on metal oxide materials, surfaces and interfaces, photocatalysis, and photovoltaics.

ACKNOWLEDGMENTS We are pleased to thank Ulrike Diebold, Francesca Nunzi, and Gianfranco Pacchioni for many helpful discussions. We acknowledge support from the following agencies: FP7 project ESCORT, for F.D.A. and S.F.; FIRB Project RBAP115AYN of Italian MIUR, and LISA Project LI01p_VISFOTOCAT of CINECA, for C.D.V.; PRIN-2010BNZ3F2, project DESAN


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