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Ab-initio Simulation of the Effects of Hydrogen Concentration on Anatase TiO Samaneh Seyedeh Ataei, Mohammad Reza Mohammadizadeh, and Nicola Seriani J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b00019 • Publication Date (Web): 08 Apr 2016 Downloaded from http://pubs.acs.org on April 12, 2016

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The Journal of Physical Chemistry

Ab-initio Simulation of the Effects of Hydrogen Concentration on Anatase TiO2 S. Samaneh Ataei,†,‡ M. Reza Mohammadizadeh,† and Nicola Seriani∗,‡ †Superconductivity Research Laboratory (SRL), Department of Physics, University of Tehran, North Kargar Ave., P.O. Box 14395-547, Tehran, Iran ‡The Abdus Salam International Centre for Theoretical Physics, Condensed Matter and Statistical Physics Section, Strada Costiera 11, 34151 Trieste, Italy E-mail: [email protected]

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Abstract We have performed first-principles calculations of hydrogen doping in anatase TiO2 . Neutral and charged defects in interstitial and substitutional (for oxygen) positions have been considered, at concentrations between 0.125 and 0.03125

nH nTi .

A region of stabil-

ity has been found for positively charged interstitial hydrogen, at realistic conditions of temperature and pressure. For example, at a partial pressure of hydrogen of 0.01 atm and a Fermi energy 2.3 eV above the top of the valence band, this defect is stable up to ∼500 K. Remarkably, at the highest concentration, metastable ordered substitutional neutral hydrogen leads to the appearance of band-like states at the bottom of the conduction band, which lead to a band gap narrowing by 1 eV. On the contrary, in presence of disorder or at lower concentration the neutral defects yield only localized defect states, located 0.7-0.9 eV below the bottom of the conduction band. Finally, the electronic structure of charged defects is very similar to that of pure anatase. These results explain the discrepancies observed in experiments as due to different concentrations and charge states, and suggest that a high concentration of neutral hydrogen in oxygen vacancies could be of interest for photocatalytic applications.

INTRODUCTION Titanium dioxide (TiO2 ) became a promising material for photocatalytic applications after Fujishima and Honda used it for water splitting. 1 However, its large band gap of around 3 eV limits its absorption to the ultraviolet (UV) part of the solar spectrum. Among the three polymorphs of TiO2 in conventional conditions, rutile, anatase and brookite, the most promising efficiency for photocatalytic applications is achieved by anatase. 2 In order to increase anatase’s efficiency, many strategies are under investigation, from the production of mixed oxides 3,4 to the study of the effects of defects (e.g. oxygen vacancies) and impurities. 5–7 In this context, a breakthrough was achieved by Chen et al. 5 in 2011, when they engineered black hydrogenated anatase with a narrow band gap of 1.54 eV, thanks to a blue2


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shifted valence band edge, and a good efficiency in photocatalytic splitting of water under solar irradiation. Their sample consisted of TiO2 nanocrystals with an average crystal size of 8 nm, a disordered layer at the surface with a thickness of 1 nm, and a hydrogen concentration of 0.25 wt%, corresponding roughly to 0.2

nH nTi

(one H atom per 5 Ti atoms). They

produced it by hydrogenating titania in a 20 bar H2 atmosphere at about 200 ◦ C for 5 days. Similar results were obtained also by Mo et al. 8 Photocatalytically active black hydrogenated titania was also produced by a hydrogen plasma treatment for 4-8 hours at 500 ◦ C, resulting in particles with a larger size of 20 nm and a 2 nm thick disordered layer at the surface. 9 In this case, however, no modifications of the valence band position of TiO2 were observed. 9 Instead, an increased carrier concentration (up to 7.8×1020 cm−3 ) was observed, implying that hydrogen doping increases the concentration of itinerant electrons in the conduction band. Assuming one electron per hydrogen atom, a carrier concentration of 7.8×1020 cm−3 corresponds to a concentration of 0.03125

nH . nTi

It is to be noted that this concentration is

one order of magnitude lower than in the experiment by Chen et al. 5 It thus seems that the two hydrogenated titania samples are quite different from each other in terms of hydrogen concentration and of electronic properties, and still both are active. Moreover, hydrogen doping in sputtered anatase films may result in other electronic properties, with a single impurity level located 0.5 eV below the conduction band minimum (CBM), as observed in deep level transient spectroscopy (DLTS) experiments. 10 In this case, the carrier concentration of 4.4×1015 cm−3 implies an even lower hydrogen concentration than in the other two cases (0.0156×10−5

nH ). nTi

These results point to a strong dependence of the electronic properties on

the details of the hydrogenation process, in particular on hydrogen concentration. However, a full understanding of these effects is currently lacking, in particular regarding how hydrogen concentration and electrostatics affect the nature of the doping species and the resulting electronic properties. Through density functional theory (DFT) simulations, Liu et al. have explained that hydrogen contributes to disordering of the surface by breaking up Ti-O bonds at the surface of anatase nanocrystals (Ti25 O50 H6 with the size of 1 nm) and thereby form-

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ing Ti-H and O-H bonds. 11 With this atomic structure, the edge of the valence band was extended into the gap. Ma et al. 12 have performed DFT simulations of hydrogen doping in interstitial positions (Hi ) and as substitution for lattice oxygen (HO ) in bulk anatase (with 0.028

nH ). nTi

Both dopants lead to shallow donor levels ǫ(+1/0), which, together with the cal-

culated high solubility, can explain the large n-type conductivity and carrier concentration observed in hydrogen plasma treatment experiment. 9 Thus, the theoretical calculations so far are able to explain the extension of the valence band into the gap at high concentration 11 through hydrogen-induced disorder and Ti-O bond breaking, and the presence of shallow donors at low concentration by single isolated point defects. 12 It is however unclear what the nature of the hydrogen-doped titania is in the case of a high concentration of point defects, in absence of complete disruption of the crystal lattice. It has been shown that plasma treatments can lead to hydrogen concentrations up to 0.25

nH 13 . nTi

An open question is how

the different properties of the electronic structure, with either localized defects levels in the gap, or band-like features at the edge of the valence or conduction band, depend on hydrogen concentration and configuration. In order to understand the mechanisms responsible for the different electronic structures observed in the experiments for hydrogenated titania, a deeper insight into the effect of different hydrogen concentrations is desirable. Moreover, recent experiments have questioned the stability of hydrogenated titania, showing a high bulk diffusivity of hydrogen in rutile and easy hydrogen loss into the vacuum at pressures of 10−9 to 10−7 Torr. 14 In this work, we study stability, electronic and structural properties of oxygen vacancies (VO ’s), interstitial hydrogen Hi , and substituted hydrogen at oxygen vacancy sites HO , using spin polarized DFT+U calculations. We found a region of stability for hydrogen in anatase at realistic conditions of temperature and pressure. We found that considering different hydrogen concentrations in bulk anatase may result in different electronic properties. At high concentration of ordered neutral HO (0.125

nH ), nTi

band-like

states appear that effectively extend the conduction band by 1 eV into the gap, while in presence of disorder or at low concentration (0.0625 and 0.03125

4


nH ) nTi

a defect level 0.69

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eV below the conduction band minimum (CBM) is recovered. These results rationalize the different experimental results, suggest that it is possible to stabilize hydrogenated anatase under appropriate conditions, and that anatase with a high amount of ordered neutral HO should display unique properties and possibly be interesting for photocatalytic applications.

COMPUTATIONAL METHODS We have performed spin-polarized density functional theory (DFT) calculations, as implemented in the Quantum-Espresso package. 15 Exchange and correlation were described with the functional by Perdew, Burke and Ernzerhof (PBE). 16 The Hubbard U correction 17 was included to take care of the self-interaction error in DFT, 18 with values of 3.5 eV for O 2p states and 3.5 eV for Ti 3d states. 19 The choice to apply the Hubbard correction to the 2p states of oxygen as well was taken because applying the correction only to the 3d states might have an influence over the Ti-O covalent bonding, since the Ti states are shifted while the 2p states of oxygen are not, as observed in the literature in oxides of transition metals. 19–21 However, we have checked in selected cases that omitting U(O-2p) does not change qualitatively the results (see the Supporting Information). Requiring a norm conserving Ti pseudopotential with semicore states (Ti(3s, 3d, 3p, 4s)) and a fast convergence in Fourier space, we generated and tested it following the Troullier-Martins (TM) method 22 using the atomic code. 15 Energy cutoff of 100 Ry for the wave function and a Monkhorst-Pack grid of (6 × 6 × 2) k-points were employed for the unit cell of anatase. The atomic positions and cell parameters were optimized until the forces were smaller than 10−3 a.u. The neutral + and charged defects VO , Hi , H+ i , HO and HO were considered. In order to calculate the

charged transition levels, we have considered the method proposed by Freysold et al. 23 for the electrostatic potential corrections, using the SPHInX package. 24 It is computationally efficient and overcomes the problem of calculating formation energies for a range of supercell sizes. Using this setup, for the pure anatase TiO2 bulk, the calculated lattice parameters

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and indirect band gap (near X-Γ) are obtained as a=3.78 Å, c=9.53 Å and Eg =3.27 eV, respectively. These data are in a good agreement with the experimental one (a=3.78 Å, c=9.51 Å, Eg =3.2 eV). 25,26 The reported data by using HSE06 method are a=3.76 (3.77) Å, c=9.56 (9.66) Å and Eg =3.58 (3.37) eV. 6,27 Yamamoto et al. 27 calculated the lattice parameters and band gap (a=3.86 Å, c=9.74 Å, Eg =2.72 eV) using PBE+U method with U(O-2p)=5.25 eV and U(Ti-3d)=4.2 eV. Ab-initio thermodynamics has been employed to extend the zero-temperature results of DFT to finite temperature and pressures of hydrogen and oxygen. The free energy of formation of a phase with respect to perfect anatase and gaseous H2 and O2 is accordingly calculated as 28,29

∆Gf (T, pH2 , pO2 ) = E(H − T iO2 ) − E(T iO2 ) − ∆nH µH (T, pH2 ) − ∆nO µO (T, pO2 )

(1)

where the chemical potentials for the gases are taken from thermodynamic tables. 30,31 The choice of the sign implies that the free energy of formation is negative for a stable phase.

RESULTS and DISCUSSION In Fig. 1 we report the formation energies of the neutral and charged VO , Hi and HO in anatase TiO2 bulk, together with the charge transition levels, as calculated with the method √ √ proposed by Freysold et al. 23 We performed these calculations in a ( 2 × 2 × 1) supercell, large enough for the calculation of charged defects, as shown in Ref., 7 corresponding to a concentration of 0.03125

nH . nTi

The calculated charge transition levels of VO in anatase

TiO2 bulk ǫ(+1/0), ǫ(+2/0) and ǫ(+2/+1), are 0.52 eV, 0.67 eV and 0.82 eV below the experimental CBM of 3.2 eV. The calculated transition level ǫ(+1/0) is close to the CBM, representing the shallow donor behaviour of the oxygen vacancies which may lead to the n-type conductivity. Our calculated adiabatic charge transition levels are in agreement with the deep-level transient spectroscopy (DLTS) measurements of anatase TiO2 films, which report values of 0.47 eV and 0.92 eV. 32 The transition level (ǫ(+1/0)) was calculated to 6


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6 VO

4 Ef (eV)

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HO

2 VO

1+

VO HO

+

2+

Hi

0 Hi

+

-2 0

0.5

1

2 1.5 EF (eV)

2.5

3

Figure 1: Formation energy (Ef ) vs. the Fermi energy (EF ) for VO (violet line), VO 1+ + (orange), VO 2+ (brown), HO (green), H+ O (dark green), Hi (red), and Hi (magenta). be 0.91 eV with DFT+U and core-level alignment correction, 33 and 0.5 eV (0.03 eV) from the vertical (adiabatic) transition using the HSE06 functional. 7 Oxygen vacancies are the dominating intrinsic defect in anatase at room conditions, 34,35 therefore this is the only intrinsic defect we are considering in this work, mainly focused on hydrogen doping. It is however important to note that, under heavily reducing conditions, Ti interstitials might become prevalent. 34,35 In order to study Hi , we considered hydrogen to be perpendicular to the Ti-O-Ti plane (Fig. 2), because this configuration is more stable with respect to the parallel configuration. 36 As shown in Fig. 1, the neutral Hi and HO are more stable than the corresponding charged defects for Fermi energies higher than 2.97 eV and 2.96 eV above the maximum of the valence band, respectively, 0.23 eV and 0.24 eV from the experimental CBM of 3.2 eV. These are slightly shallower than the DLTS peak of 0.5 eV for hydrogenated TiO2 . 10 This difference might be due to our higher concentration in comparison with the DLTS measurements, where the carrier concentration corresponds to 0.0156×10−5

nH , nTi

orders

of magnitude lower than in our calculations. In fact, our transition levels are in agreement with the value of 0.2 eV below the CBM found by Deak et al. 6 with HSE06 calculations, at the same concentration we employ. Instead, at a lower concentration of 0.028

nH , nTi

Ma

et al. 12 found by HSE06 calculations that these transition levels are in resonance with the conduction band. 7



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Figure 2: Atomic structure of the (2×1×1) supercell of anatase TiO2 with Hi (left diagram) and HO (right diagram), where the grey, red and sky-blue balls represent Ti, O and H atoms, respectively. Since the original experiment on black hydrogenated titania employed a concentration of 0.25 wt% (0.2 nH ) nTi

nH ), nTi

we have considered a (2 × 1 × 1) supercell with one hydrogen atom (0.125

in interstitial and substitutional positions (Fig. 2). The calculated formation energies

of a neutral interstitial hydrogen and the substituted one at the VO site, and binding energy for HO , are 0.02 eV, 4.74 eV and −0.05 eV, respectively. Interstitial hydrogen is the stable defect. Therefore, in the limit of thermodynamic equilibrium at low temperatures, i.e. at a low concentration of VO ’s, the thermodynamically stable states will have hydrogen in interstitial position. However, the equilibrium concentrations of VO and HO , shown in Fig. 3, strongly depend on temperature and might become non-negligible even at thermodynamic equilibrium. At high hydrogen concentration, more complicated situations with coexistence of HO and Hi are in principle possible. To test this hypothesis, we have calculated a (2×2×1) cell with one HO and one Hi , set near and far from one another. The difference in energy between the near and the far configurations amounts to 0.02 eV. Thus, their interaction is weak and should not influence the concentration of each defect. Moreover, it is well possible to obtain higher concentrations of oxygen vacancies by quenching titania from high temperature or by modifying the synthesis procedure, and to keep this state as metastable state. In thise case, oxygen vacancies are kinetically stabilized due to their low mobility, and

8


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1E+24

-3

Concentration(cm )

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-10

1E+22

VO(PO2=10 atm)

1E+20

HO(PO2=10 atm-PH2=1atm)

1E+18

HO(PO2=PH2=10 atm)

-10

-10

1E+16 1E+14 1E+12 1E+10 1E+08

1E+00

500

750

1000

1250

1500

1750

2000

T(K)

Figure 3: Equilibrium concentrations of the defects VO and HO in anatase TiO2 , in dependence of temperature, for different conditions of pressure. only hydrogen is in thermodynamic equilibrium, thanks to its higher mobility. In this case, the relevant formation energies are those with respect to anatase with oxygen vacancies. At zero temperature, the formation energy of Hi is still 0.02 eV as in the previous case, but the formation energy of HO is much lower, −0.05 eV (i.e., the process is more exothermic) because it does not contain the energy necessary to produce an oxygen vacancy, which is assumed to be frozen in the anatase. In fact, high concentrations of oxygen vacancies have been experimentally observed. 37 In this second case, where we start with an anatase with oxygen vacancies, it is favorable for hydrogen to occupy the vacancies rather than to occupy interstitial sites. Given the importance of the HO in the subsequent discussion of the electronic structure, we have analyzed better this state. In particular, we have considered the possibility that the HO ’s might not be ordered as in our (2×1×1) supercell. To this aim, we have simulated also (2 × 2 × 1) supercells with two HO defects put in different positions. Indeed, configurations with the double periodicity are slightly more favourable energetically, with a formation energy of 4.59 eV vs. 4.74 eV for the singly periodic configuration. This is a sign that, thermodynamically, the defects will rather be disordered. Still, it could be possible to produce ordered arrays of oxygen vacancies that survive, thanks to their low mobility. It has been shown that, in vacuum conditions, hydrogenated rutile is short-lived due to high hydrogen mobility and fast desorption. 14 In Fig. 4 we show a portion of the phase diagram of

9



1000 800 600 400 200

T (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1000 800 600 400 200 1000 800 600 400 200 0

1

+

Hi -TiO2

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TiO2

+

Hi -TiO2

TiO2

+

TiO2

Hi -TiO2

1.5

2 EF(eV)

2.5

3

Figure 4: Phase diagram for the H-TiO2 system in dependence of temperature and Fermi energy. From above, the three insets show the results respectively for pO2 = pH2 = 1 atm; pO2 = 1 atm, pH2 = 0.01 atm; pO2 = pH2 = 10−10 atm. the hydrogen-anatase system by ab-initio thermodynamics and we show that hydrogenated titania is stable under certain realistic conditions. More results are shown in the Supporting Information. In all cases considered, the only defect that is more stable than pristine titania is the positively charged interstitial hydrogen. The stability of the H+ i depends on the partial pressure of hdyrogen, on temperature and on the position of the Fermi energy, i.e. on the electrostatic conditions. At a hydrogen partial pressure of 0.01 atm and a Fermi energy of 2.3 eV above the top of the valence band, this hydrogen defect is stable up to 500 K according to our calculations. At lower partial pressures, the hydrogenated phase becomes less stable with respect to pure titania. This is in agreement with the experiments of Ref., 14 performed in vacuum, but at the same time it suggests that hydrogenated titania might be thermodynamically stable under realistic conditions. It should be noted that here we are dealing with a system in full thermodynamic equilibrium, disregarding the possibility that kinetically stabilized oxygen vacancies might make the formation of HO defects possible. + The calculated DOS of Hi , H+ i , HO and HO for the two concentrations of 0.125 and 0.0625 nH , nTi

are plotted in Fig. 5. There is an occupied defect level for Hi at 0.91 eV below the

CBM, but this level disappears for the positively charged H+ i . According to the calculated PDOS, it is understood that the midgap level of Hi is related to the Ti3+ ion nearest to 10


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the hydrogen. This is confirmed also by its Bader effective charge, increased by 0.31 e, with a net magnetic polarization of 0.89 µB. On the contrary, the Bader effective charge of hydrogen in the structure with Hi is essentially zero. For neutral interstitial hydrogen, these results agree with previous calculations. 36,38 On the other side, hydrogen has a tendency to be accommodated in VO ’s. 39 As shown in Fig. 5, for the system with ordered HO defects the edge of the CBM is shifted to lower energies compared to the perfect bulk and, interestingly, there is a tail of defect states near the CBM, while this tail disappears in the DOS of H+ O . This CBM tail leads to a remarkable band gap narrowing of about 1 eV. Band gap DOS

(a)Hi

DOS

(c)Hi

(b)HO

+

(d)HO

DOS

(e)Hi

+

53

+

(f)HO

(g)Hi

DOS

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55

(h)HO

57

59

61

Energy (eV)

53

+

55

57

59

61

Energy (eV)

Figure 5: Calculated total density of states for anatase TiO2 with Hi ((a) and (e)) and H+ i ((d) and (h)) with different concentrations (1st and ((c) and (g)), HO ((b) and (f)) and H+ O nH nH 2nd rows for 0.125 nTi , 3rd and 4th for 0.0625 nTi ), where the zero of energy is set to the 3s state of titanium.The red dashed line is the Fermi energy. narrowing may result in the enhancement of photo-absorption under visible light irradiation. This band gap narrowing was not observed in previous calculations of HO in anatase 12,40,41 because of the lower hydrogen concentration they employed; indeed, also in our calculations the extended state is substituted by a localized defect state in presence of disorder or at lower concentrations (see below). Still, we cannot exclude that it could be possible to obtain such ordered arrays of HO ’s by careful defect engineering. To better characterize this state, we have calculated PDOS, the real-space charge density distribution of these states (Fig. 6) and the band structure (Fig. 7). The PDOS shows that these band tail states are related 11



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to the 3d states of the two Ti atoms nearest to the HO , and is confirmed by the charge density distribution. The states are delocalized over the two Ti atoms. Thus, the localized midgap states introduced by VO ’s are substituted by a tail of delocalized states when these defects are ordered. We notice that some experiments show an absence of localized Ti3+ signal in electron paramagnetic resonance (EPR) 9 and X-ray photoelectron spectroscopy (XPS) 5 in hydrogenated titania, also in presence of itinerant electrons at the CBM in the black hydrogenated TiO2 nanoparticles with high photocatalytic performance. 9 The band structure shows that the ordered array of defects creates band-like states with a non-negligible dispersion (Fig. 7). According to Bader analysis, the hydrogen atom has 1.55 electrons; the two nearest Ti atoms to the VO site have each a magnetic moment of −0.48µB and a charge increase of 0.21 e. The best description for this situation is that we have a H− ion and a triplet state for the two Ti atoms. To the best of our knowledge, there is no report of this triplet state for this case, so far. It should be stressed again that, thermodynamically, a disordered arrangement of the hydrogen defects is more stable. Remaining at the concentration of 0.125

Figure 6: The calculated density distribution of delocalized states in conduction band of HO nH , where the blue, red and pink balls represent doped TiO2 in the concentration of 0.125 nTi Ti, O and H atoms, respectively.

12


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nH , nTi

we have considered also the possibility of doping by molecular H2 , using a (2 × 2 × 1)

supercell with 16 formula units of titania. Its formation energy is high, 1.82 eV, and therefore 62 EFh

Energy (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


58 EFb 56 54 52 Γ

Z

T

Y

S

X

U

R

Figure 7: The band structure of HO -doped TiO2 (majority spin, blue lines) in the connH centration of 0.125 nTi and perfect TiO2 bulk (red lines), where EFh and EFb represent the Fermi energies of HO -doped TiO2 and perfect bulk.The zero of energy is set to the 3s state of titanium. this kind of defect is not very probable. Still, interestingly it leads to states located 0.2 eV above the valence band maximum, resulting from the hybridization between 1s orbitals of H2 and 2p orbitals of its neighboring oxygen atoms (not shown). These results are in line with a recent hybrid functional study. 11 So far we have considered a high concentration of 0.125

nH , nTi

comparable to the highest

concentrations obtained in photocatalytic experiments, like 0.25 wt%, corresponding roughly to 0.2

nH nTi

(one H atom per 5 Ti atoms). 5 It should be noted that, by applying a pressure

of 70 bar at 450◦ C, it was possible to reach concentrations of 1-1.4 wt%, 42 i.e. one H atom per Ti atom. Since, however, an improvement of the photocatalytic activity was observed also at lower concentrations, 9 we now show the results for a concentration of 0.0625

nH , nTi

corresponding to a single H atom in a (2 × 2 × 1) supercell, to understand the effect of the concentration. In this case, the calculated formation energies of Hi and HO are 0.2 eV and 4.59 eV, respectively. The dependence on concentration of the electronic properties of the two defects, Hi and HO , differs considerably. For Hi there is a defect level located at 0.71 eV below the CBM, that disappears in H+ i , similarly to what was shown above 13



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for high concentration. We checked that the same behaviour is found at an even lower concentration of 0.03125

nH . nTi

On the contrary, for HO the tail of the conduction band seen

at high concentration of ordered defects disappears already at the concentration of 0.0625 nH , nTi

substituted by a defect level located at 0.69 eV below the CBM, corresponding to a

Ti3+ ion (according to the calculated PDOS). Thus the delocalized state is a unique feature of the system at high hydrogen concentration, in presence of ordered oxygen vacancies. As a result, at lower concentration both Hi and HO behave like trap states with localized Ti3+ centers. Our results for lower concentrations explain the observed EPR signal of Ti3+ in the experiments with low hydrogen concentration. 43 We would like however point at the fact that the degree of localization of the additional electron on Ti3+ is a highly debated topic. 44–50 Still, in presence of defects like oxygen vacancies it seems that the electrons are localized at a Ti site in a neighbourhood of the defect, 34,35 and this effect is quite robust, as it is observed with DFT+U as well as with hybrid functionals. Refs. 34,35 also show that less localized states also exist and are near in energy, where the electron is shared among more Ti sites, even at low defect concentration. It might be that these states become even more delocalized at high defect concentrations, like those considered in our work. In conclusion, we have investigated hydrogen doping in anatase at concentrations of 0.125, 0.0625 and 0.03125

nH , nTi

observing three kinds of electronic structures: first, one with band-

like states extending the bottom of the conduction band into the gap, due to hydrogen occupying ordered oxygen vacancies at high concentration; second, localized defect states in the gap, mainly due to neutral hydrogen defects; third, barely modified electronic structure, associated with ionized hydrogen defects. We do not observe the extended edge of the valence band because this is due to Ti-O bond breaking and disorder, as pointed out in Ref. 11 These results help rationalizing the discrepancies among experiments performed under different conditions, such as the missing EPR signal from Ti3+ in some experiments.

14


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SUMMARY We have performed spin polarized DFT+U calculations to understand the effect of hydrogen doping at different concentrations in anatase TiO2 . Hydrogen was considered as interstitial defect Hi and as substitutional defect HO in oxygen vacancies, at concentrations of 0.125, 0.0625 and 0.03125

nH . nTi

The most stable defect is the interstitial hydrogen, neutral or

positively charged, depending on the position of the Fermi energy. However, in presence of oxygen vacancies there is a strong driving force for hydrogen to occupy those positions. At certain realistic values of partial pressures of hydrogen and oxygen, temperature and Fermi energy, the positively charged interstitial hydrogen is thermodynamically stable with respect to pure anatase. For example, at a partial pressure of hydrogen of 0.01 atm and a Fermi energy of 2.3 eV above the top of the valence band, this hydrogen defect is stable up to 500 K according to our calculations. The different kinds of defects correspond to different features of the electronic structure, also in dependence of the concentration. In particular, a high concentration of ordered neutral HO (0.125

nH ) nTi

shifts the edge of the conduction band

to lower energies with a band gap narrowing of about 1 eV, by introducing band-like states mainly contributed by Ti atoms near to the hydrogen site. At lower hydrogen concentration or in presence of disorder, this state disappears and is substituted by a localized defect level located 0.69 eV below the conduction band minimum (CBM). Also the neutral interstitial hydrogen leads to a localized defect level, located 0.7-0.9 eV below the CBM, depending on the concentration. The defect level disappears when the defect becomes positively charged, i.e. when the Fermi energy is lowered. These results explain discrepancies between different experiments as due to different concentrations of hydrogen and of oxygen vacancies, and point to a high concentration of neutral HO as a particularly promising system for photocatalytic applications, which deserves further investigation.

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ACKNOWLEDGMENTS S. Samaneh Ataei acknowledges partial financial support by the research council of the University of Tehran,“Center of Excellence on the Structure and Physical Properties of Matter”of the University of Tehran and the ICTP-IAEA Sandwich Training Educational Programme (STEP).

Supporting Information Supporting figures. This material is available free of charge via the Internet at http://pubs.acs.org.

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