N-doped TiO2

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N-doped TiO

₂

: Theory and experiment

Cristiana Di Valentin

^a,*

, Emanuele Finazzi

^a

, Gianfranco Pacchioni

^a

, Annabella Selloni

^b

, Stefano Livraghi

^c

, Maria Cristina Paganini

^c

, Elio Giamello

^c

aDipartimento di Scienza dei Materiali, Universita` di Milano-Bicocca, Via R. Cozzi, 53, 20125 Milano, Italy

bDepartment of Chemistry, Princeton University, Princeton, NJ 08540, USA

cDipartimento di Chimica IFM, Universita` di Torino and NIS, Nanostructured Interfaces and Surfaces Centre of Excellence, Via P. Giuria 7, I-10125 Torino, Italy

Received 16 April 2007; accepted 10 July 2007 Available online 27 July 2007

Abstract

Nitrogen doped titanium dioxide is attracting a continuously increasing attention because of its potential as material for environmental photocatalysis. In this paper we review experimental and theoretical work done on this system in our groups in recent years. The analysis is largely based on electron paramagnetic resonance (EPR) spectra and on their interpretation based on high-level ab initio calculations. N-doped anatase TiO₂contains thermally stable single N-atom impurities either as charged diamagnetic N_b centers or as neutral paramagnetic N_bcenters (b stays for bulk). The N-atoms can occupy both interstitial or substitutional positions in the solid, with some evidence for a preference for interstitial sites. All types of N_bcenters give rise to localized states in the band-gap of the oxide, thus accounting for the related reduction of absorption band edge. The relative abundance of these species depends on the oxidation state of the solid. In fact, upon reduction, oxygen vacancies form and transfer electrons from Ti³⁺ions to the N_bwith formation of Ti⁴⁺and N_b. EPR spectra measured under irradiation show that the Nbcenters are responsible for visible light absorption with promotion of electrons from the localized N-impurity states to the conduction band or to electron scavengers like O₂adsorbed on the surface. These results provide an unambiguous characterization of the electronic states associated with N-impurities in TiO2and a realistic picture of the processes occurring in the solid under irradiation with visible light.

Keywords: TiO2; Doping; Nitrogen; EPR; Experiments; DFT; Theory; Oxygen vacancy; Photocatalysis; Vis-light

1. Introduction

Worldwide concerns with environmental and energy- related issues have prompted an enormous interest in semi- conductor-based heterogeneous photocatalysis over the last decade. Photocatalysis allows the use of sunlight for the destruction of highly toxic molecules and remediation of pollutants; for the selective, synthetically useful redox transformations in speciﬁc organic compounds; for the production of hydrogen, and the conversion of solar energy to electric power[1–6].

The most widely used material in heterogeneous photocatalysis is titanium dioxide (TiO2). It is inexpensive, non- toxic, resistant to photo-corrosion, and has high oxidative power. However, an important drawback of TiO2for photocatalysis is that its band-gap is rather large, 3.0–3.2 eV, and thus only a small fraction of the solar spectrum (k < 380 nm, corresponding to the UV region) is absorbed.

To lower the threshold energy for photoexcitation, a great deal of research has focused on doping TiO2 with both transition metal and non-metal impurities. Doping with transition metals has shown both positive and negative eﬀects. Indeed, several authors have reported that although metal ion doping decreases the photothreshold energy of TiO2, the metal ions may also serve as recombination

doi:10.1016/j.chemphys.2007.07.020

* Corresponding author. Tel.: +39 0264485235.

E-mail address:cristiana.divalentin@mater.unimib.it(C. Di Valentin).

www.elsevier.com/locate/chemphys

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centers for electrons and holes, thus reducing the overall activity of the photocatalyst.

Stimulated by the report of Asahi et al. in 2001 [7], recently there has been an explosion of interest in TiO2

doping with non-metal ions, especially with nitrogen (see Fig. 1, from ISI). New papers on this topic appear every week, showing the importance of the subject but also mak- ing it diﬃcult to keep track of the rapid developments.

Unfortunately, not all these studies are as innovative and original as one would like to see, sometimes contributing to the confusion more than to the understanding of the problem. Many authors have reported that N-doped titanium dioxide, hereafter N-TiO2, shows a signiﬁcant catalytic activity in various reactions performed under visible light irradiation[8–19]. However, as summarized in a number of very recent reviews [4–6] (to which we refer for a more exhaustive account), there is also an open debate on how doping achieves this, as well as disagreements in many of the conclusions drawn from the results. One of the reasons for this may be that, to incorporate nitrogen in titanium dioxide, diﬀerent strategies are used, either based on chemical reactivity (sol–gel synthesis[8,9,13–15], chemical treatments of the bare oxide[7,10,11,18], oxidation of titanium nitride[20], etc.) or on physical methods (ion implantation [21–23], magnetron sputtering [24,25]).

These diﬀerent procedures probably lead, at least in some cases, to materials with somewhat diﬀerent properties.

Independent of the preparation procedure, there are a number of key questions which need to be answered to characterize the properties and behavior of N-TiO2. The first and most basic question concerns the chemical nature, the location in the solid, and the involvement in photoactivity of the nitrogen species. Different chemical species like NOx [8,9,15,26–28] substitutional N [7,12,14,21], or NHx [11] have been proposed. It is essential to know whether the species are primarily interstitial or substitutional, because the behavior of these two species is very different and will affect the material properties accordingly. It is also important to determine whether the species tend to

segregate at the surface of the material or are preferentially incorporated in sub-surface or bulk sites, because this can strongly inﬂuence the surface reactivity and photocatalytic properties.

A second key issue concerns the electronic structure of the doped material and the change of the optical gap [4,7,29]. Many studies have addressed the question of the character, localized or delocalized, of the electronic states associated to the N-impurities, but no general consensus has been reached yet. While some authors claim that the band gap of the solid is reduced due to a rigid valence band shift upon doping [7,20,25], others attribute the observed absorption of visible light by N-TiO2 to the excitation of electrons from localized impurity states in the band-gap [9,10,12,15,16]. Interestingly, it appears that the N-doping induced modiﬁcations of the electronic structure may be slightly diﬀerent for the anatase and rutile polymorphs of TiO₂. In fact, while it is well established that N-doping low- ers the onset of optical absorption to the visible in anatase, a slight increase of the optical gap has been in some cases observed for rutile [21].

Another crucial question concerns the interaction between N-impurities and oxygen vacancies. Density functional theory (DFT) calculations by our group [28] have shown a large decrease in the formation energy for oxygen vacancies as a result of the presence of nitrogen atoms in the lattice. This decrease can be attributed to a ‘compensa- tion’ eﬀect: electrons in vacancy related states near the bot- tom of the conduction band can be transferred to empty nitrogen impurity states near the top of the valence band, leading to a considerable energy gain. The large decrease in the oxygen vacancy formation energy also suggests that oxygen vacancies are most probably induced by N-doping of TiO2. Recent STM [22] and UPS [30] data appear to support these predictions, but a detailed understanding of the structure and electronic characteristics of the vacancy–impurity complex is still missing. It is important to determine the energetics and the character of the electronic states of these complexes, e.g. how the occupied states of the vacancy–impurity complex are distributed, whether they are spread throughout the complex, and how close should the vacancy and the impurities be in order to form such a charge transfer complex.

The last and probably most important question for photocatalysis is the eﬀect of N-doping on the photocatalytic activity of TiO2. A large part of the existing literature on N-doped TiO₂materials agrees that the addition of nitrogen results in an improvement in visible light photocatalytic activity, but contrasting ﬁndings have also been reported [4]. For instance, in a recent study on N-TiO2

ﬁlms obtained by the addition of ammonia during chemical vapor deposition growth of TiO2[5], no evidence of photocatalytic activity in the visible was found, in spite of clear evidence of the presence of N impurities at substitutional sites.

Significant advances towards a clarification of the above issues can only be achieved via multi-pronged efforts based

Fig. 1. Number of published articles on X-doped TiO2(X = N, C, S, F).

From ISI (February 26, 2007).

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on the use of diﬀerent experimental techniques together with theoretical calculations. Our group has used a combination of electron paramagnetic resonance (EPR), X ray photoelectron spectroscopy (XPS), and DFT calculations to characterize the paramagnetic species in N-doped anatase TiO2powders obtained by sol–gel synthesis. The pur- pose of this paper is to present a critical review of this work together and some recent new results, such as the analysis of the EPR feature intensity during some red–ox cycles performed on the samples and the theoretical simulation of the N-doped anatase (1 0 1) surface.

2. Experimental and computational details 2.1. Sample preparation

N-TiO2 samples have been prepared via the sol–gel method using several nitrogen containing inorganic compound (NH4Cl, NH3, N2H4, NH4NO3 and HNO3) as nitrogen source. When necessary¹⁵N enriched compounds were employed. A solution of titanium (IV) isopropoxide in isopropylic alcohol was mixed with an aqueous solution of a nitrogen compound and kept upon constant stirring at room temperature (RT). The gel so obtained has been left ageing overnight at RT to ensure the completion of the hydrolysis and subsequently dried at 343 K. The dried compound was heated at 773 K in air for 1 h. The best results were obtained using ammonium chloride as nitrogen source.

The calcination influences the final properties of the material depending on the temperature and heating rate employed in the treatment. After heating in air at 773 K and at a relatively slow heating rate (5 K/min) the final material exhibits a pale yellow colour and has the anatase structure. We will hereafter report results concerning this material which has shown the best catalytic performance among all materials examined.

2.2. Computational set-up

The computations have been done at the DFT level using the plane-wave-pseudopotential approach, together with the Perdew–Burke–Ernzerhof (PBE) [31] exchange- correlation functional, and ultrasoft pseudopotentials [32]

(with kinetic energy cut-oﬀs of 25 ad 200 Ry for the smooth part of the electron wavefunctions and augmented electron density, respectively). We considered nearly cubic 2p

2· 2p

2· 1 and 2 · 2 · 3 supercells to model anatase and rutile, respectively. The optimized bulk lattice parameters, taken from previous calculations [33], are a = 3.786 A˚ , and c = 9.737 A˚ for anatase, and a = 4.634 A˚, and c = 2.963 A˚ for rutile. Two diﬀerent codes within the Quantum ESPRESSO package [34]were employed: CP90, based on the Car-Parrinello (CP) approach [35,36], which allows for eﬃcient structural optimizations with k-point sampling restricted to C, and PWscf, which was used for electronic structure calculations at a low-symmetry special k point

(hereafter denoted Kls). With CP90, all atoms of the supercells were relaxed using a damped second-order dynamics until all components of the residual forces were less than 0.025 eV/A˚ . In the case of rutile, optimizations at Klshave been performed with the Broyden–Fletcher–Goldfarb–

Shanno technique.

Substitutional N-species (N_s) were modelled by replac- ing 1, 2, or 3 oxygen atoms in the 96-atoms anatase supercell and 1 or 2 oxygens in the 72-atoms rutile supercell. The resulting stoichiometry is TiO_2xNxwith 0.031 < x < 0.094 for anatase and 0.042 < x < 0.084 for rutile. These N concentrations are comparable to those used in experiments.

The procedure of including more N-atoms in the same supercell is more accurate than using diﬀerent smaller supercells as it allows a direct comparison of the various levels of doping on the band structure of the material.

Interstitial N-species (N_i) were modeled by adding one N-atom in the supercell. In the following, the paramagnetic species will be denoted as N_b, where b stands for bulk, when the distinction between N_i and N_s is irrelevant for the discussion. To study oxygen vacancy formation in presence of N-impurities in anatase, one oxygen atom was removed while either two other oxygens were replaced with N-atoms or two N-atoms were added in interstitial positions. The resulting stoichiometry is TiO_23xN2x or TiO_2xN2x, respectively, with x = 0.031. The supercell models are overall neutral despite the fact that the isolated defects may be charged (as described below) in order to reﬂect the experimental situation.

In order to compute atomic spin properties, such as hyperﬁne coupling constants of the electron spin with the nuclear spin of ¹⁴N and atomic spin densities, we used the CRYSTAL03 package[37], based on an atomic orbital basis set, together with the Becke-3 [38] and Lee–Yang–

Parr [39] (B3LYP) exchange and correlation functional.

Hybrid functionals are indeed known to give more accurate descriptions of spin-polarized systems [40,41]. We performed single point B3LYP calculations using the C point and the geometries given by the PBE calculations. The atoms were described with the following basis sets: Ti 86411(d41)[42], O 8411(d1) [43], N 7311(d1) [44], respectively. The hyperﬁne spin-Hamiltonian, Hhfc= S Æ A Æ I, is given in terms of the hyperﬁne matrix A which describes the coupling of the electron with the nuclear spin [45].

The A matrix can be decomposed in two parts: Aiso(isotro- pic component of the hyperﬁne coupling constants) and B (dipolar component of the hyperﬁne coupling constants).

3. Results and discussion

3.1. Catalytic and spectroscopic characterization

The anatase N-TiO2materials were compared with bare TiO2materials prepared and treated with the same procedure. The photocatalytic activity of N-TiO2in the reference reaction of methylene blue degradation performed under visible light (wavelength 437 nm) is deﬁnitely (though not

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largely) higher than that of the bare oxide in the same conditions. This enhanced photocatalytic activity is in agreement with results previously reported in the literature.

N-TiO2were examined with a variety of spectroscopic techniques including infra-red spectroscopy, MAS-NMR, DR-UV–Vis spectroscopy, XPS and EPR. The most significant results are those obtained by the latter three techniques and in particular by EPR.

The optical absorption of N-TiO2 materials is that of bare TiO2modiﬁed by an absorption in the visible region centred at about 430–450 nm. The intensity and width of this absorption depends on the preparation history of the material. In particular, for the N-TiO2material here considered, the DR-UV–Vis spectrum,Fig. 2, is close to that ﬁrst published by Sato[8]in 1986 and explains the pale yellow colour of the solid.

3.1.1. EPR spectroscopy

An important turning point of our investigation on N- TiO2 is related to the observation that the sample is rich of paramagnetic centers [8,46]clearly detectable by EPR.

Due to its high sensitivity and to its capability of an accurate description of paramagnetic centers this latter technique is particularly suited for the investigation of defects in the solid state. The analysis of a long series of EPR spectra performed on samples of N-TiO2prepared and treated in diﬀerent ways has allowed us to identify two types of paramagnetic species, denoted as I and II. Type I consists of molecular nitrogen oxide species, NO and NO2, trapped in microvoids of the solid, provided the solid itself has a porous texture[47],Fig. 3.

Nitric oxide (NO) species is a product of the complex oxidation process of ammonium salts occurring upon calci- nations of the solid. NO2, on the contrary, is formed only when nitrates or nitric acid are used as nitrogen source and can be thus considered to derive from their decomposition.

The experimental and simulated EPR spectra of NO species are shown in Fig. 4, respectively obtained with

14NO and with a ¹⁵NO enriched (70%) mixture at 77 K.

At RT the EPR spectrum of this species is not observed.

The isotopic substitution was performed to unambiguously assign the EPR spectrum whose parameters are those expected for a NO molecule adsorbed on a positively charged site. The numerical values of the parameters are reported inTable 1.

The nitric oxide molecule is observed by EPR in the region of the free electron g value only when adsorbed on a surface[48,49]. When NO is in the adsorbed state, in fact, two eﬀects allow the observation of an EPR spectrum. The former one is the orbital momentum quenching by the electric ﬁeld of the adsorption site which causes the²P1/2state of the gaseous molecule (complete coupling between the electron spin S and the angular momentum L) to become a paramagnetic, pure spin state. The second is the lifting of the degeneracy of the two p* orbitals producing an energy splitting which determines the gzz value of the adsorbed species. Since the NO spectrum is observed at low temperature only it was concluded that it must be a

300 450 600 750

Green

Blue

Reflectance %

b a

λ (nm)

Fig. 2. UV–Vis spectra of (a) bare TiO2, (b) N-TiO2.

Fig. 3. Schematic representation of NO molecules trapped in microvoids of N-TiO2crystal.

3300 3375 3450 3525

b a'

15N (70%)

14N

g₃ g₂

g₁

b' a

B/Gauss

Fig. 4. EPR spectra of NO species: (a, a⁰) experimental and simulated spectra obtained with¹⁴N compounds, (b, b⁰) experimental and simulated spectra obtained with¹⁵N enriched (70%) compounds.

Table 1

EPR parameters of the three diﬀerent paramagnetic species identiﬁed in N-TiO2

Species g1 g2 g3 A1(G) A2(G) A3(G)

NO 2.001 1.998 1.927 < 1 32.2 9.6

NO2 2.004 2.001 1.990 53.3 66.3 50.1

N_b 2.005 2.004 2.003 2.3 4.4 32.3

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weakly adsorbed species, easily desorbed by raising the temperature. Since the EPR spectrum reversibly shows up upon lowering the temperature and the species is not removed upon pumping oﬀ up to 773 K, it was concluded that the species itself is trapped in a cavity of the bulk, adsorbed at low temperature on the walls of the microvoids,Fig. 3.

A similar eﬀect was observed for trapped NO2, see the spectrum ofFig. 5.

The highest concentration of NO2 was observed when nitric acid is used as a source of nitrogen but the lines of this species also appear in the case of samples prepared by NH4Cl and reoxidized at high temperature (773 K). In this case NO2lines are overlapped with those of NO. The generation of NO2and its segregation in bulk microvoids like for the NO molecule, is a result of the decomposition of HNO3during calcination:

2HNO3! 2NO2þ H2Oþ 1=2O2 ð1Þ

When NO and NO2species are simultaneously present in the system they are not independent as NO2concentration increases, upon thermal treatment, with decreasing that of NO. However, as the respective amounts of the two species are diﬀerent (NO2concentration is two order of magnitude lower than that of NO) the reaction occurring is somehow complex and likely involves the formation of diamagnetic intermediates like nitrites and nitrates formed via reaction with oxygen ions of the solid. Due to their nature of trapped species, it is easy to conclude that both NO and NO2are by products of the nitrogen incorporation in the solid and do not directly inﬂuence the electronic structure of the system.

Much more interesting is the paramagnetic nitrogen species of type II, which always forms upon calcination of the system after geliﬁcation. The EPR signal of such N_bspecies is characterized by an orthorhombic g tensor whose main values are, however, very close one to the other [28]. For this reason the species has been investigated by a multifre- quency approach. InFig. 6the EPR spectra of N_b species measured at 9.5 GHz (X-band) and 35 GHz (Q-band), respectively are shown.

Both the g tensor and the hyperfine tensor are reported inTable 1. The hyperfine tensor is based on a quite large coupling constant (±32.3 G) in the direction of the g3ele- ment and two smaller constants in the other directions (A1= ±2.3 G and A2= ±4.4 G). The same set of spin Hamiltonian parameters was used to simulate both the X-band and the Q-band spectra obtaining a satisfactory fit between experimental and simulated traces in the two cases (Fig. 6). N_bspecies contains one N-atom which bears a total spin density of about 0.54, the larger contribution being due to a single p orbital of the nitrogen atom in the centre. The previous analysis indicates that the hyperfine tensor does not account for the whole unpaired electron spin density. In most cases of molecular radical centres the unaccounted spin density is usually localized on other atoms of the species having zero nuclear spin.

On the basis of the EPR spectra recorded in various conditions it was possible to understand, ﬁrst of all, that N_bis a monomeric nitrogen species incorporated in the bulk of N- TiO2 as the species does not undergo dipolar broadening when oxygen is adsorbed at low temperature on the surface. The species is stable even at rather high temperature and, as shown in the following, sensitive to visible light irradiation.

3.1.2. X ray photoelectron spectroscopy (XPS)

InFig. 7the XPS spectrum of N-TiO2(in the region of binding energy typical of N(1s)) is reported. The signal deconvolution allows the identiﬁcation of two peaks at 399.2 eV and 400.7 eV.

After a careful washing of the material in ultrasonic, the XPS peaks tend to decrease in intensity or in some cases disappear. XPS peaks in the range (396–404 eV) were observed by several authors and are typical of nitrogen

3250 3300 3350 3400 3450 3500 3550 a'

a

B/Gauss

Fig. 5. (a) EPR spectrum of NO2species and (a⁰) its simulation.

3320 3340 3360 3380

12040 12060 12080 12100

c' c b' b a'

a ¹⁴N + ¹⁵N

14N

(X-Band) B/Gauss

(Q-B and) B/Gauss

Fig. 6. EPR spectra and related simulations of species N_b: (a) X-band spectrum of the species containing ¹⁵N (70%) and ¹⁴N, (b) X-band spectrum of the species containing¹⁴N, (c) Q-band spectrum of the species containing¹⁴N. a⁰, b⁰ and c⁰ are the related simulations (ﬁgure adapted from Ref.[46]).

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doped titanium dioxide [16,26]. The assignment of XPS features in N-TiO2, however is still under debate and con- troversial hypotheses are found in the literature. Peaks at 396–397 eV were attributed to substitutional nitrogen because of the proximity to the typical binding energy of 396 eV observed for N in TiN, while peaks at higher binding energies (400 eV like those found in our case) were observed and usually ascribed to a generic interstitial site.

In the case of the sample here described and prepared via sol–gel, peaks at 396 eV were never observed.

The abovementioned reduction or elimination of the XPS peaks observed after a careful washing of the material suggests a relation between the peak at 400 eV and the residual ammonium ions which are indeed easily removed from the surface by washing. Being N_b species unambiguously located in bulk a doubt arises regarding a clear-cut correlation of the XPS nitrogen peaks in N-TiO2with this species. A variety of species including N_b, and not a unique one, is probably responsible for the XPS features.

3.2. Theoretical models of N-TiO2

We have used DFT calculations to study two models capable of explaining the observed properties of the nitrogen species, namely substitutional (Ns) and interstitial (Ni) nitrogen impurities in the anatase bulk structure,Fig. 8. In the substitutional model, the nitrogen atom is bound to three Ti atoms and replaces a lattice oxygen in TiO2. The Ti–N bond lengths, 1.964 and 2.081 A˚ , are only slightly longer than the Ti–O ones, 1.942 and 2.002 A˚ . This nitrogen atom is in a negative oxidation state. In the lowest energy interstitial model, the nitrogen atom is bound to one lattice oxygen and therefore is in a positive oxidation state. The resulting NO species (d(N–O) = 1.36 A˚ ) interacts with the lattice Ti atoms through its p bonding states (Fig. 8).

Electronic structure calculations indicate that for both Nsand Nithere is virtually no shift of the upper and lower edges of the O 2p valence band, as well as of the conduc-

tion band, with respect to the undoped material. For substitutional N, a few occupied N 2p localized states appear slightly above the valence band edge (Fig. 9). For interstitial N, the NO bond generates localized states with p character (Fig. 9). The two bonding states are deep in energy and lie below the top of O 2p band. The two antibonding (but still occupied) states lie above the O 2p band and are higher in the gap than the N 2p states generated by substitutional nitrogen: the highest localized state for the interstitial species is 0.73 eV above the top of the valence band, while for the substitutional species it is 0.14 eV above it, Fig. 9. The computed band-gap for these systems is 2.6 eV, obtained as the diﬀerence between conduction and valence band energy eigenvalues (band gaps are noto- riously underestimated by standard DFT methods, such as the present PBE functional) [28]. Thus, the conclusion is that both Nsand Niinduce formation of localized occupied states in the gap, accounting for the visible light activity of N-doped samples. The localized nature of the N-induced states has the consequence that the hole generated by

Fig. 7. Deconvolution of the N-TiO2XPS spectrum. A and B indicate the two peaks used to convolute the spectrum.

Fig. 8. Model structures for substitutional and interstitial N-dopants in anatase TiO2phase (ﬁgure adapted from Ref.[28]).

VB CB

N 2p

VB CB

π* N-O

π N-O SUBSTITUTIONAL

0.14 eV 0.73 eV

2.6 eV 2.6 eV

INTERSTITIAL

Fig. 9. Electronic structure computed with PBE density functional for substitutional and interstitial models (ﬁgure adapted from Ref.[28]).

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vis-irradiation is less mobile than that generated by UV irradiation in the O 2p band and has also a lower direct oxidation potential for photocatalytic applications[50,51].

Even though core level binding energy values for the N 1s state, computed within the initial state approximation, cannot be directly compared to experimental XPS data because of the absence of final state relaxation effects, the relative values of substitutional vs interstitial configurations are qualitatively relevant. The calculated values for these two species differ by 1.6 eV, with higher core level binding energy for the interstitial configuration. This result qualitatively correctly correlates with the two experimentally observed peaks for N-doped TiO2, one at 397 eV (attributed to substitutional N) and the other at >399 eV (interstitial N).

A more detailed analysis can be performed for the spin properties, by comparing the computed and measured hyperﬁne coupling constants (A matrix in Table 1). The agreement can be considered satisfactory for both Ns and Nispecies, even though in the latter case it is slightly better.

In the Ns case, the unpaired electron is almost entirely (0.87) localized on the substitutional N-atom, more pre- cisely on the p state perpendicular to the plane deﬁned by the three Ti atoms to which nitrogen is bound (Fig. 10).

In the case of interstitial nitrogen, the unpaired electron is shared between the N and O atoms of the NO species and the localization on N is reduced to 0.67. Here the spin density is localized on the p system of the NO species (Fig. 10) involving only N-atomic p states. Despite the different calculated spin densities on Nsand Ni(0.87 and 0.67, respectively), the hyperﬁne coupling constants are quite similar in the two cases, and rather close to the experimental values as well (see Table 1). As mentioned above, the experimental estimate of the spin density on N, 0.54, obtained as the ratio of the experimentally measured B values with tabulated atomic B, might not be strictly correct, so that it cannot be used to discriminate between the two model species under investigation. Therefore, the above comparative experimental–computational EPR analysis indicates that both proposed models, Ns and Ni, may account for the paramagnetic species observed in the TiO2powders.

To summarize, stable bulk N-species can be obtained by sol–gel synthesis. They give rise to localized states in the gap with paramagnetic character. Identiﬁcation of the location of the N-impurities is not straightforward, but the results are more in favor of interstitial nitrogen species.

3.3. Anatase versus rutile: diﬀerences and similarities For the rutile TiO2polymorph, the structural variations following O replacement with N in the 72-atom supercell are found to be slightly more pronounced than for anatase.

The equatorial Tieq–N bonds are asymmetrically stretched, from 1.956 to 1.988 and 2.036 A˚ , with respect to the corresponding bonds in undoped rutile, while the axial Tiax–N bond is slightly stretched, from 1.999 to 2.021 A˚ (see Fig. 11). As for anatase, the spin density is largely localized on the N-atom. The electronic structure shows both analo- gies and diﬀerences with respect to anatase. Not only the top of the valence band, Ev, is lowered by 0.4 eV with respect to the undoped case (seeFig. 12), but also the N 2p localized states are slightly lower in energy (by E3= 0.05 eV) than Evin pure rutile,Fig. 12. Thus N-doped rutile is predicted to show a small blue-shift of 0.1 eV in the optical absorption rather than a red-shift, as observed for anatase. This conclusion is consistent with measurements by Diwald et al.[21]on N-doped rutile TiO2single crystals.

As discussed in detail in Ref.[52], the different behavior of rutile and anatase can be rationalized on the basis of their different structures and densities and of their different O 2p band width.

3.4. Role of other defects: O vacancies 3.4.1. Thermodynamic aspects

An unexpected but relevant aspect of the interaction between N-centers and oxygen vacancies (VO) is that the cost of VO formation in bulk anatase TiO2 is drastically reduced in the presence of N-impurities, from 4.2 eV in

O N O

O T i O T i

T i

O T i O T i O O

O

O N O

O T i O T i

T i

O O

T i T i O O

SUBSTITUTIONAL INTERSTITIAL

Fig. 10. Electron spin density contour lines for substitutional and interstitial N-dopants (ﬁgure adapted from Ref.[28]).

Fig. 11. Supercell models for anatase and rutile N-doped TiO2 (ﬁgure adapted from Ref.[52]).

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pure TiO2to 0.6 eV in N-doped TiO2, as indicated by the computed energetics for the following processes[28]:

TiO2! TiO2xþ xVOþ 1=2xO2 DE¼ 4:2 eV ð2Þ TiO_22xN2x! TiO23xN2xþ xVOþ 1=2xO2 DE¼ 0:6 eV

ð3Þ This result is very important and explains why in oxygen poor conditions (low values of the oxygen chemical potential) substitutional N impurities in the presence of VO

become very favorable, as clearly indicated by the stability diagram inFig. 13 [53]. By contrast, under oxygen-rich conditions (higher values of the oxygen chemical potential), interstitial nitrogen species (Ni) become favored.

The energies of formation are evaluated according to the formula:

E_form ¼ 1=nEtot ðN-dopedÞ 1=n½Etot ðpureÞ þ nl_N ml_O ð4Þ

where n is the number of N-atoms and m is the number of oxygen vacancies per supercell in the model considered. We use a ﬁxed value of the nitrogen chemical potential, l_N= 1/2 lN2, while for oxygen we take l_O¼ 1=2l_O₂þ l⁰_O (l_N₂ and l_O₂ are the total energies of N2 and O2, respectively).

3.4.2. Electronic aspects

Experiments show that O vacancies in undoped TiO2

introduce defect states in the band-gap at energy of about 0.8 eV below the conduction band; these are assigned to Ti³⁺ 3d [1] states on the basis of EPR experiments [54–

56]. The theoretical description of these states is a delicate issue which we have analyzed in detail in a recent paper [41]. In particular we have shown that the electronic structures of hydroxylated and reduced TiO2 are very similar and, in both systems, the localized defect states on Ti³⁺ions can be well described only by use of hybrid functionals.

In Fig. 14we compare the total and projected (on two selected Ti ions) density of states (DOS) for the hydroxylated system calculated using (a) the B3LYP functional for both geometry optimization and DOS calculations; (b) the B3LYP functional for geometry optimization and the PBE functional for the DOS calculation; (c) the PBE functional for geometry and B3LYP for DOS calculation; (d) the PBE functional for both geometry and DOS calculations. It is clear from this picture that the PBE functional (d) underes- timates the band-gap and leads to a very delocalized solution for the defects states. The band-gap problem is amended by use of the B3LYP functional with the PBE geometry, but the defect state is still delocalized (c). In order to achieve the correct structural deformation (pola- ronic distortion) for the electron localized on the Ti³⁺ions it is necessary to perform the atomic relaxation with the hybrid functional, as it is clear from Fig. 14a and b. In Fig. 14b, however, the band-gap description by PBE functional is still poor and thus, although the states are rather localized (because of the proper structural relaxation with B3LYP), they are still too close to the conduction band.

Only the full B3LYP calculation correctly describes the localization and energy position of the impurity states in the band-gap, Fig. 14a.

Unlike the case of undoped TiO2, in N-TiO2 oxygen vacancies can be satisfactorily described even without using hybrid functionals. There are two main reasons for this: (1) the position of the N-impurity states is not altered when computed with the B3LYP hybrid functional [28] which correctly describes the band-gap of TiO₂; (2) when consid- ering the concomitant presence of N-impurities and oxygen vacancies, there are no excess electrons in Ti³⁺ states (poorly described by standard DFT), as they are transferred to the empty N-states (see below). Even if the original position of the Ti³⁺states is not accurately predicted by standard DFT, there is no doubt that these states are higher in energy than those associated with the N-impurities. Thus, internal charge transfer occurs independently of the exchange-correlation functional used.

Fig. 13. Stability diagram for the various bulk N-doped anatase models considered.

Fig. 12. Schematic electronic structure for pure and N-doped anatase and rutile TiO2 polymorphs (substitutional N) computed with the PBE functional (ﬁgure adapted from Ref.[52]).

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To study N-doping in presence of oxygen vacancies, DFT calculations have been performed on a bulk anatase supercell of 96-atoms containing either two N_i or two N_s paramagnetic species plus one oxygen vacancy located as far as possible from the N-centers, so as to avoid any direct defect-impurity interaction. Due to the presence of unpaired spins at various sites, various spin configurations were considered. In particular, the high-spin configuration corresponds to four unpaired electrons (quintet state), two on the two N-impurities and two on two Ti³⁺ions, while a low-spin closed shell configuration (singlet state) results from the charge transfer of the two unpaired electrons occupying the high lying Ti³⁺ states to the low lying N_i and/or N_s singly occupied levels, just above the top of the valence band (Fig. 5). This process leads to the formation of charged diamagnetic N_i and N_s defects and reoxidized Ti⁴⁺ions. The latter low-spin configuration is found to be about 3 eV more stable than the high-spin quintet one. The formation of charged defects in the material is

accompanied by a local distortion: the N_s center is characterized by shorter N–Ti bond lengths than N_s; N_i by a longer NO bond length than N_i.

Similar to their neutral counterparts, the diamagnetic N_i and N_s charged defects give rise to localized levels in the gap of the material which lie few tenths of an eV above the valence band edge. Because of the increased Coulomb repulsion, the N-induced defect states for the diamagnetic charged species are slightly higher in energy than the corresponding singly occupied levels for the paramagnetic neutral species: 0.59 eV for N_s and 0.75 eV for N_i ðDEd in Fig. 15), to be compared to 0.14 eV for N_s and 0.73 eV for N_i (DEp in Fig. 15). The N_s N_s shift of about 0.4 eV for substitutional nitrogen is caused by the fact that in this case the orbital where the extra electron is accom- modated is a localized atomic-like orbital; instead the shift is almost negligible for interstitial nitrogen because the added electron occupies a more extended p molecular orbital. On the basis of these data, no signiﬁcant variations in the absorption spectrum of the doped material are expected as a consequence of the internal charge transfer from the oxygen vacancies derived states to the N-impurity states, in particular if the species present are interstitial N-atoms, N_ior N_i.

Our finding that N-doping favors O vacancy formation is fully supported by real-time transmission electron microscopy (TEM) experiments [57]. Similarly, recent experiments have found that N-implantation reduces the features associated to Ti³⁺ions[22]. All these data suggest that N-TiO2contains, besides a given number of paramagnetic N_b centers, a fraction of diamagnetic N_b impurities, which depends on the level of oxygen deficiency in the sample. A particularly clear proof of this dependence comes from the observation that the intensity of N_b is deeply affected by the redox state of the solid.Fig. 16shows the intensity variation of the EPR spectrum upon reductive and oxidative cycles of the solid. After the very first cycle which is affected by the presence of surface hydroxyl groups, the successive cycles show that the N_b EPR intensity vanishes in parallel with thermovacuum reductive treatments at 773 K (in such conditions O2 depletion occurs in parallel with formation of anion vacancies and enrichment of the electron population of the solid). Restor- ing the initial situation by reoxidation at the same temperature, the EPR intensity is fully recovered, thus confirming the predicted connection between the presence of N_b and the redox state of the solid.

Fig. 14. Total and projected (on relevant Ti atoms) density of states for the hydroxylated TiO2(1 1 0) rutile surface obtained with B3LYP and PBE density functionals. (a) B3LYP functional for both geometry and DOS calculations; (b) B3LYP functional for geometry and PBE functional for the DOS calculation; (c) the PBE functional for geometry and B3LYP for DOS calculation; (d) the PBE functional for both geometry and DOS calculations. Vertical dashed lines indicate the highest occupied level.

Nb

.

3d Ti³⁺

VB CB

Nb

- 3d Ti⁴⁺

VB CB

ΔEp ΔEd

Fig. 15. Electronic band structure modiﬁcations resulting from the interactions between N_b (N_s or N_i) and Ti³⁺ (oxygen vacancy) defects (ﬁgure adapted from Ref.[59]).

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3.5. From bulk to surface: anatase (1 0 1)

Doping of the surface layers may induce new and/or special features in the geometry and electronic structure of TiO2 not present in the bulk. Therefore, it is relevant to determine whether the nitrogen species is on the surface, either in bridging or in a three-coordinated position, or prefers to lie in the second layer of TiO₂ (sub-surface).

We have studied this issue in the case of the anatase (1 0 1) surface,Fig. 17.

InFig. 18, we report the total and projected (on the N- atoms) DOS for the most stable substitutional and interstitial conﬁgurations. From the comparison of the DOS, we can see the occurrence of the N-impurity states near the edge of the valence band for Ns and higher in energy for the Nispecies. The projection onto the N 2p states provides evidence for the localized character of these states. There- fore, N-doping induces a reduction of some tenths of eV of the energy gap between highest occupied and lowest unoccupied states which is not due to a real shift of the valence band edge, but to the appearance of localized states

in the gap, in complete analogy with the bulk case. The presence of an empty spin-down state in the middle of the gap is also evident for both conﬁgurations. These states can act as a deep electron trap in the material.

The stability diagram of some of the investigated surface species as a function of the oxygen chemical potential, Fig. 19, is qualitatively similar to that obtained for the bulk species in Fig. 13. However, after careful inspection, one can note that the stability range for the N-atom bound to a lattice O in a surface position is larger than that of the typical interstitial species in the bulk (Fig. 13).

For both surface and sub-surface doping, it is found that at low oxygen concentrations substitutional N-impurities accompanied by oxygen vacancies are favored. The substitutional N-impurities are found to be more stable in the sub-surface layers while only surface bridging oxygen vacancies have been considered. The stabilization eﬀect associated to the simultaneous presence of oxygen vacancies and nitrogen impurities is a consequence of the electron transfer from the reduced Ti³⁺ atoms to states deriving from the N substitutional impurities, as observed in the bulk. This stabilization almost cancels the energy cost to form surface bridging O vacancies (from 4.6 to 0.3 eV). Thus, N-doping is expected to introduce many more oxygen vacancies on the surface than commonly observed for the anatase (1 0 1) surface and therefore to largely increase adsorption and reaction properties, commonly associated to the presence of such defects. Some

as produced

red 1 ox 1 red 2 ox 2 red 3 ox 3 red 4 ox 4

cycle 4 cycle 3

cycle 2 cycle 1

I (a.u.)

Thermal treatment

N_b

.

Fig. 16. EPR intensity of species N_b upon diﬀerent thermal treatments (intensity in arbitrary units).

Fig. 17. Model of anatase (1 0 1) TiO2surface.

-60 -40 -20 0 20 40 60

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

DOS

E-E_V (eV)

Total DOS PDOS, N 2p Total DOS, pure

-60 -40 -20 0 20 40 60

-1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5

DOS

E-E_V (eV)

Total DOS PDOS, N 2p Total DOS, pure

Fig. 18. Total (continuous line) and projected (ﬁlled line) DOS of (a) Ns- doped and (b) Ni-doped (bound to a surface bridging O atom) anatase (1 0 1) TiO2 surface. The DOS of the undoped system is reported as a reference (dotted line). The origin is set at the top of the valence band of the undoped system. The vertical dotted line deﬁnes the uppermost occupied state energy. DFT results with PBE functional.

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experimental evidences of this eﬀect have already been reported in the literature[58].

3.6. Dynamics of N-TiO2under irradiation

Conclusive evidence of the crucial role of N_b in the photoactivity of N-TiO2 in visible light was obtained by irradiating the material with visible light having wavelength corresponding to the absorption maximum [59]

(437 nm, seeFig. 2).

Fig. 20 reports the EPR signals of N_b observed under various conditions.

The ﬁrst spectrum,Fig. 20a was recorded at room temperature using a N-TiO₂sample kept in the dark. The second one, Fig. 20b, was recorded during irradiation of the same sample in visible light (437 nm, blue). The concentration of N_b increases in these conditions but the intensity

immediately recovers the initial value as soon as the light is switched off. The irradiation cycles in vacuo can be repeated indefinitely. The phenomenon is not observed if a different wavelength is used (es. 500 nm, green). The increase of N_b intensity is even higher in the presence of oxygen in the gas phase,Fig. 20c. In such condition, however, a second paramagnetic species is formed which can be best observed at 77 K and which is visible in the EPR spectrum at room temperature, though overlapped with the signal of N_b, provided that excess oxygen is removed from the atmosphere,Fig. 20d. This species is the well known superoxide O₂ anion, whose formation is due to a photoinduced electron transfer from the solid to the surface adsorbed oxygen molecule.

The formation of superoxide is irreversible at RT. Upon turning the lamp oﬀ the intensity value of species N_b remains higher than the initial value recorded in the dark prior to oxygen adsorption.

The experimental results discussed above allowed us to draw a schematic picture of the mechanism connected to the interaction of N-TiO2 with visible light [59]. Indepen- dently of its speciﬁc lattice position (interstitial or substitutional species), the N_bcenter introduces localized electronic states in the gap which can be either doubly occupied (diamagnetic N_b) or singly occupied (paramagnetic N_b).

Irradiation under vacuo with visible light 437 nm (2.84 eV) selectively promotes electrons from these states to the conduction band according to the following process:

N_b !^hm N_bþ e N_b!^hmN^þ_b þ e

ð5Þ

The energy of the visible light in fact is not suﬃcient to ex- cite electrons from the valence band, as the TiO2anatase band-gap is 3.2 eV. Diamagnetic N_b species at equilibrium are expected to be deﬁnitely more abundant than N_b because, under irradiation, an increase of the concentration of the paramagnetic centres N_b is observed, Fig. 20. The equilibrium conditions in the dark are recovered instanta- neously when irradiation is stopped.

The presence of oxygen in the gas phase modiﬁes the situation as a fraction of photoexcited electrons is scavenged by O2producing adsorbed O₂:

N_b þ O2ðgasÞ!^hm N_bþ O_2ðsurfÞ N_bþ O2ðgasÞ!^hm N^þ_b þ O_2ðsurfÞ

ð6Þ

This interaction shifts the equilibrium with formation of a higher amount of paramagnetic N_b centres with respect to simple irradiation in vacuo. In other words, photoinduced charge separation has occurred. The generation of surface adsorbed O₂ causes the formation of a negative layer at the interface. This, in turn, is expected to cause band bending which limits further electron transfer. Stopping irradiation, the electrons scavenged by oxygen remain in the ad-layer so that the initial concentration of N_b centers

3350 3375 3400 3425

d

c

b

a

B/Gauss

Fig. 20. EPR spectra of species N_b (a) as synthesized in dark, (b) under irradiation in vacuo with visible light of 437 nm (c) under irradiation with visible light of 437 nm in the presence of oxygen (d) after removal of the excess of oxygen.

Fig. 19. Stability diagram for the various N-doped models considered for the anatase (1 0 1) TiO2surface.

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is not recovered. Fig. 21 schematically describes the two processes.

4. Summary and conclusions

In this paper we have reviewed recent work of our group, based on a combination of electron paramagnetic resonance (EPR), X ray photoelectron spectroscopy (XPS), and DFT calculations to characterize the paramagnetic species in N-doped anatase TiO2powders obtained by sol–gel synthesis. EPR measurements have provided evidence for the existence of a paramagnetic nitrogen species intimately interacting with the TiO2lattice. The spin-Ham- iltonian parameters of the observed species are found to be consistent with calculations for both substitutional (Ns) and interstitial (Ni) N-impurities. Calculations also show that the electronic states of these species are localized, and their energies are just and somewhat above the top of the valence band for Nsand Ni,respectively[52]. Anal- ysis of the interaction between nitrogen impurities and oxygen vacancies and of the relative stability of the diﬀerent species as a function of the oxygen chemical potential (oxygen partial pressure) shows that under oxygen-rich (poor) conditions Ni (Ns accompanied by oxygen vacancies) is most stable. Finally, by investigating the behavior of the sol–gel N-TiO2samples under irradiation with photons of diﬀerent energy and in the presence of adsorbates, we show that the EPR-active N-species is responsible for the absorption of visible radiation and for the photo-induced electron transfer from the solid to a surface adsorbed electron scav- enger as molecular oxygen. In conclusion, with the present study we have been able to identify the role played by impurities (dopants, oxygen vacancies, hydroxyl groups) in the photo-activity of N-doped TiO2 samples. On the basis of this work we believe that the photocatalytic properties of TiO2, both in UV and Vis-regions, can be largely improved by tailoring the number and type of defect present in the photocatalyst.

Acknowledgements

This work is supported by the Italian MIUR through a Coﬁn2005 Project. A.S. acknowledges the Department of Energy for ﬁnancial support (DE-FG02-05ER15702).

References

[1] K. Hashimoto, H. Irie, A. Fujishima, Japanese J. Appl. Phys. 44 (2005) 8269.

[2] M. Anpo, Bull. Chem. Soc. Jpn. 77 (2004) 1427.

[3] A. Kudo, H. Kato, I. Tsuji, Chem. Lett. 33 (2004) 1534.

[4] T.L. Thompson, J.T. Yates Jr., Chem. Rev. 106 (2006) 4428.

[5] H.M. Yates, M.G. Nolan, D.W. Sheel, M.E. Pemble, J. Photochem.

Photobiol. A 179 (2006) 213.

[6] M. Ni, M.K.H. Leung, D.Y.C. Leung, K. Sumathy, Renew. Sustain.

Energy Rev. 11 (2007) 401.

[7] R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, Y. Taga, Science 293 (2001) 269.

[8] S. Sato, Chem. Phys. Lett. 123 (1986) 126.

[9] S. Sakthivel, M. Janczarek, H. Kisch, J. Phys. Chem. B 108 (2004) 19384.

[10] H. Irie, Y. Watanabe, K. Hashimoto, J. Phys. Chem. B 107 (2003) 5483.

[11] O. Diwald, T.L. Thompson, T. Zubkov, E.G. Goralski, S.D. Walck, J.T. Yates Jr., J. Phys. Chem. B 108 (2004) 6004.

[12] M. Miyauchi, A. Ikezawa, H. Tobimatsu, H. Irie, K. Hashimoto, Phys. Chem. Chem. Phys. 6 (2004) 865.

[13] J.L. Gole, J.D. Stout, C. Burda, Y. Lou, X. Chen, J. Phys. Chem. B 108 (2004) 1230.

[14] Z. Lin, A. Orlov, R.M. Lambert, M.C. Payne, J. Phys. Chem. B 109 (2005) 20948.

[15] S. Sato, R. Nakamura, S. Abe, Appl. Catal. B 284 (2005) 131.

[16] M. Sathish, B. Viswanathan, R.P. Viswanath, C.S. Gopinath, Chem.

Mater. 17 (2005) 6349.

[17] M. Alvaro, E. Carbonell, V. Forne´s, H. Garcia, ChemPhysChem 7 (2006) 200.

[18] Y. Nosaka, M. Matsushita, J. Nasino, A.Y. Nosaka, Sci. Technol.

Adv. Mat. 6 (2005) 143.

[19] Y. Irokawa, T. Morikawa, K. Aoki, S. Kosaka, T. Ohwaki, Y. Taga, Phys. Chem. Chem. Phys. 8 (2006) 1116.

[20] T. Morikawa, R. Asahi, T. Ohwaki, K. Aoki, Y. Taga, Jpn. J. Appl.

Phys. 40 (2001) L561.

[21] O. Diwald, T.L. Thompson, E.G. Goralski, S.D. Walck, J.T. Yates Jr., J. Phys. Chem. B 108 (2004) 52.

[22] M. Batzill, E.H. Morales, U. Diebold, Phys. Rev. Lett. 96 (2006) 026103.

[23] A. Ghicov, J.M. Macak, H. Tsuchiya, J. Kunze, V. Haeublein, L.

Frey, P. Schmuki, Nano Lett. 6 (2006) 1080.

[24] J.M. Mwabora, T. Lindgren, E. Avendano, T.F. Jaramillo, J. Lu, S.E.

Lindquist, C.G. Granqvist, J. Phys. Chem. B 108 (2004) 20193.

[25] Y. Nakano, T. Morikawa, T. Ohwaki, Y. Taga, Appl. Phys. Lett. 86 (2005) 132104.

[26] X. Chen, C. Burda, J. Phys. Chem. B 108 (2004) 15446.

[27] Y. Sakatani, J. Nunoshige, H. Ando, K. Okusako, H. Koike, T.

Takata, J.N. Kondo, M. Hara, K. Domen, Chem. Lett. 32 (2003) 1156.

[28] C. Di Valentin, G. Pacchioni, A. Selloni, S. Livraghi, E. Giamello, J.

Phys. Chem. B 109 (2005) 11414.

[29] N. Serpone, J. Phys. Chem. B 110 (2006) 24287.

[30] A. Nambu, J. Graciani, J.A. Rodriguez, Q. Wu, E. Fujita, Sanz J.

Fdez, J. Chem. Phys. 125 (2006) 094706.

[31] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.

[32] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.

[33] M. Lazzeri, A. Vittadini, A. Selloni, Phys. Rev. B 63 (2001) 155409.

[34] S. Baroni, et al.<http://www.democritos.it>.

C.B.

V.B.

E_f

C.B.

V.B.

E_f Lamp ON

e^-

Lamp Off

C.B.

V.B.

E_f

C.B.

V.B.

E_f Lamp ON

e

Lamp Off O2

.

-

Fig. 21. Energy states involved during N-TiO2 visible irradiation. (a) Vacuum condition. (b) O2atmosphere.

(13)

[35] R. Car, M. Parinello, Phys. Rev. Lett. 55 (1985) 2471.

[36] K. Laasonen et al., Phys. Rev. B 47 (1993) 10142.

[37] V.R. Saunders, R. Dovesi, C. Roetti, R. Orlando, C.M. Zicovich- Wison, N.M. Harrison, K. Doll, B. Civalleri, I.J. Bush, P.h. D’Arco, M. Llunell, CRYSTAL03.

[38] A.D. Becke, J. Chem. Phys. 98 (1993) 5648.

[39] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785.

[40] G. Pacchioni, F. Frigoli, D. Ricci, J.A. Weil, Phys. Rev. B 63 (2001) 054102.

[41] C. Di Valentin, G. Pacchioni, A. Selloni, Phys. Rev. Lett. 97 (2006) 166803.

[42] C.M. Zicovich-Wilson, R. Dovesi, J. Phys. Chem. B 102 (1998) 1411.

[43] E. Ruiz, M. Llunlell, P. Alemany, J. Solid State Chem. 176 (2003) 400.

[44] R. Pandey, J.E. Jaﬀe, N.M. Harrison, J. Phys. Chem. Solids 55 (1994) 1357.

[45] J.A. Weil, J.R. Bolton, J.E. Wertz, Electron Paramagnetic Reso- nance, Wiley, New York, 1994.

[46] S. Livraghi, A. Votta, M.C. Paganini, E. Giamello, Chem. Commun.

4 (2005) 498.

[47] S. Livraghi, M.C. Paganini, M. Chiesa, E. Giamello, Res. Chem.

Intermed. (in press).

[48] J.H. Lundsford, J. Chem. Phys. 72 (1968) 2141.

[49] M.C. Paganini, M. Chiesa, P. Martino, E. Giamello, J. Phys. Chem. B 106 (2002) 12531.

[50] R. Nakamura, T. Tanaka, Y. Nakato, J. Phys. Chem. B 108 (2004) 10617.

[51] M. Mrowetz, W. Balcerski, A.J. Colussi, M.R. Hoﬀmann, J. Phys.

Chem. B 108 (2004) 17269.

[52] C. Di Valentin, G. Pacchioni, A. Selloni, Phys. Rev. B 70 (2004) 085116.

[53] C. Di Valentin, G. Pacchioni, A. Selloni, Chem. Mater. 17 (2005) 6656.

[54] E. Serwicka, M.W. Schlierkamp, R.N.Z. Schindler, Naturforsch. 36a (1981) 226.

[55] T. Berger, M. Sterrer, O. Diwald, E. Kno¨zinger, D. Panayotov, T.L.

Thompson, J.T. Yates Jr., J. Phys. Chem. B 109 (2005) 6061.

[56] D.C. Hurum, A.G. Agrios, K.A. Gray, T. Rajh, M.C. Thurnauer, J. Phys. Chem. B 107 (2003) 4545.

[57] E. Sutter, P. Sutter, E. Fujita, J. Muckerman, Abstracts of the European Materials Research Society Spring Meeting, Nice, France, 2006, p. M-14.

[58] T. Tachikawa, Y. Takai, S. Tojo, M. Fujitsuka, H. Irie, K.

Hashomoto, T. Majima, J. Phys. Chem. B 110 (2006) 13158.

[59] S. Livraghi, M.C. Paganini, E. Giamello, A. Selloni, C. Di Valentin, G. Pacchioni, J. Am. Chem. Soc. 128 (2006) 15666.