Origin of the Enhanced Visible-Light Absorption in N-Doped Bulk

ARTICLE pubs.acs.org/JPCC

Origin of the Enhanced Visible-Light Absorption in N-Doped Bulk Anatase TiO2 from First-Principles Calculations M. Harb,† P. Sautet,‡ and P. Raybaud*,† † ‡

IFP Energies Nouvelles, Rond-point de l'
echangeur de Solaize, BP 3-69360 Solaize, France Universit
e de Lyon, CNRS, Laboratoire de Chimie, Ecole Normale Sup
erieure de Lyon, 46 all
ee d'Italie, 69364 Lyon Cedex 07, France

bS Supporting Information ABSTRACT: Extension of the absorption properties of TiO2 photocatalytic materials to the visible part of the solar spectrum is of major importance for energy and cleaning up applications. We carry out a systematic study of the N-doped anatase TiO2 material using spin-polarized density functional theory (DFT) and the rangeseparated hybrid HSE06 functional. The thermodynamic stability of competitive N-doped TiO2 structural configurations is studied as a function of the oxygen chemical potential and of various chemical doping agents: N2, (N2 + H2), NH3, N2H4. We show that the diamagnetic TiO(2
3x)N2x system corresponding to a separated substitutional N species (with 2
4% N impurities) and formation of one-half concentration of O vacancies (1
2 atom %) is an optimal configuration thermodynamically favored by NH3, N2H4, and (N2 + H2) chemical doping agents presenting a dual nitrating
reducing character. The simulated UV
vis absorption spectra using the perturbation theory (DFPT) approach demonstrates unambiguously that the diamagnetic TiO(2
3x)N2x system exhibits the enhanced optical absorption in N-doped TiO2 under visible-light irradiation. Electronic analysis further reveals a band gap narrowing of 0.6 eV induced by delocalized impurity states located at the top of the valence band of TiO2. A fruitful comparison with experimental data is furnished.

1. INTRODUCTION Control of the electronic band gap in semiconducting compounds such as titanium dioxide (TiO2) is of utmost importance for optical and photocatalytic applications. Extensive efforts are currently devoted to the optimized preparation and characterization of TiO2-based materials for their potential application in the challenging photoelectrochemical or photochemical water splitting reaction for hydrogen production using sunlight.1
6 However, the relatively large band gap of TiO2 (3.2 eV for anatase and 3.0 eV for rutile) requires UV light (290
400 nm) for electronic excitation from the valence band to the conduction band, which only corresponds to 3
5% of the solar energy. It is hence of great importance to develop an active photocatalyst working under both UV (290
400 nm) and visible (400
800 nm) light in order to benefit more effectively from the solar energy. Two strategies are generally used to modify the optical response of TiO2 in the visible region, both based on the narrowing of the optical band gap of TiO2. One strategy is to dope TiO2 with various transition-metal cations,7
11 while the other one is to use doping anionic elements (such as N, S,...).12
15 N-Doped TiO2 is one of the most promising and widely investigated systems. Several experimental and theoretical studies have been devoted to investigation of various forms of N-doped TiO2 materials.12
37 Experimentally, various r 2011 American Chemical Society

nitrogen-containing molecules in the gas phase or in solution such as N2,13,21 NH3,30,32
34,37 N2H4,33 NH4Cl, 27,31,33,35 NH4NO3,33 HNO3,30,33 NH4OH,35 or C6H15N35,36 have been used as chemical nitration agents. The intrinsic characteristics of obtained N-doped TiO2 samples with different reaction conditions were analyzed using different techniques such as electron paramagnetic resonance (EPR),27,31,33,37 X-ray photoelectron spectroscopy (XPS),13,17,21,27,30,32
34,37 X-ray diffraction (XRD),13,17,21,30
32,34
37 transmission electron microscopy (TEM)32,36,37 and UV
vis diffuse reflectance spectra (DRS)17,30
37 techniques. The optical properties of these samples have revealed an experimental shift of the optical absorption edge and an improvement of the photocatalytic activity of N-doped TiO2 samples in the visible region with respect to undoped TiO2. However, the origin of the enhanced optical properties remains the subject of key open questions. The first important question concerns the chemical nature and structural location (substitutional, interstitial,...) of the bulk doping species responsible for the enhanced photoactivity of N-doped TiO2 in the visible region. Species like NOx,12,14,22,24,27 Received: May 2, 2011 Revised: August 2, 2011 Published: August 17, 2011 19394

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√ √ Figure 1. (a) (2  2  1) and (b) (2 2  2 2  1) undoped anatase supercells containing 48 atoms (16 TiO2 units) and 96 atoms (32 TiO2 units), respectively. Color legend: Ti atoms in gray, O atoms in red. The same color legend is used for all figures.

substitutional N,13,19,23 or NHx18 have been proposed so far without unambiguous assignment. In addition, EPR experiments revealed the existence of paramagnetic and diamagnetic bulk N species.31 However, the direct link between the bulk doping species and the resulting optical spectra remains difficult to be established by experiments because of the heterogeneous distribution of species. The second issue concerns the effect of the nitrogen source on the thermodynamic stability of various N-doped systems. For experimental applications, it is mandatory to optimize the choice of the nitration agent in order to stabilize the right N species. The third issue related to methodological aspects concerns accurate prediction of the electronic structure and optical properties of N-doped TiO2 materials as a function of the N-doping species. This requires beyond density functional theory (DFT) approaches. Very few theoretical studies have proposed direct and accurate simulation of absorption spectra of N-doped TiO213,23 because only recently the level of theory permits a direct comparison with experimental data. Moreover, no systematic simulation of the optical spectra as a function of the different doping configurations was achieved. Using non-spin-polarized density functional theory (DFT) within the local density approximation (LDA) the pioneering work by Asahi et al.13 reported the calculated UV
vis absorption response of N-doped bulk anatase TiO2 by considering either one substitutional or one interstitial N atom at 4 and 8 atom % N. They suggested that the observed red shift of the absorption edge in N-doped TiO2 is due to a band-gap narrowing induced by the substitutional N-atom configuration. Although forthcoming studies have confirmed that the band gap of TiO2 is reduced due to a rigid valence band shift upon doping,38,39 others have attributed the observed absorption of visible light by N-doped TiO2 to excitation from the localized impurity states in the band gap.14,16,19,24,25 Using the spin-polarized DFT method within the generalized gradient approximation (GGA) and with the hybrid B3LYP functional, Di Valentin et al. calculated the formation energy and electronic structure of N-doped bulk anatase TiO2 by considering one substitutional N atom at 1% N impurities as well as two substitutional N atoms with formation of one oxygen vacancy (i.e., 2% N impurities and 1% O vacancies).27,31,33 Substitutional nitrogen doping leads to a substantial reduction of the energy cost to form oxygen vacancies in bulk TiO227 and was suggested as playing a role

in visible-light absorption.31 However, in the absence of accurate first-principles simulation, the stability of the N-doping centers as a function of preparation conditions and their effects on the electronic and optical properties of TiO2 still remain to be clarified for solving the origin of enhanced optical properties. This step is mandatory for further improvement of photocatalytic materials. In this paper, we focus on the bulk properties of the anatase phase of TiO2 with a photocatalytic activity known to be higher than that of the rutile phase.40 Investigating the surface properties of this material is beyond the scope of this work, and we aim here at benchmarking the impact of the bulk doping species on the optical properties of the material. For that spin-polarized density functional theory (DFT) and the screened hybrid Heyd
Scuseria
Ernzehof (HSE06)50 exchange-correlation formalism (as described in the Methods section) are applied to determine the structural, thermodynamic, and electronic properties. For the optical properties spin-polarized density functional perturbation theory (DFPT) and the HSE06 exchange-correlation formalism are applied with an accuracy improved with respect to standard DFT calculations, commonly used to date. Substitutional, interstitial, and mixed N-doping species are considered as a function of N-impurity concentration together with possible formation of O vacancies. We will pay particular attention to optimal separation between isolated N-doping species and possible dimerized N
N species not investigated in the literature. Then, considering various possible chemical agents, such as N2, NH3, and N2H4, as the nitrogen source, we determine the stability of various N-doped systems as a function of the oxidizing/reducing/nitrating environment. Finally, we analyze the effects of incorporation of N impurities on the electronic structure and optical absorption edge of bulk anatase TiO2. Analysis of the impurity states in terms of the electron density is also given to understand their localized or delocalized nature.

2. METHODS 2.1. Total Energy Calculations. Total energy calculations were performed in the framework of the spin-polarized density functional theory (DFT) within the periodic planewave (PW) approach implemented in VASP 4.6.41
45 We employ the 19395

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Table 1. Configurations, Stoichiometries, and Corresponding Atomic or Vacancy Concentrations (including x, m, p values) of the various N-Doped TiO2 Systems doping

TiO(2
mx)Npx

TinO(2n
m)Np

(configurations)

stoichiometry

supercell

x

N impurities [O vacancy] in atom %

substitutional (isolated)

TiO(2
x)Nx, m = p = 1

n = 16 n = 32

0.125 0.0625

2 [0] 1 [0]

substitutional (dimerized or dispersed)

TiO(2
2x)N2x, m = p = 2

n = 16

0.125

4 [0]

n = 32

0.0625

2 [0]

interstitial (isolated)

TiO2Nx, m = 0, p = 1

n = 16

0.125

2 [0]

interstitial (dimerized or dispersed)

TiO2N2x, m = 0, p = 2

n = 16

0.125

4 [0]

n = 32

0.0625

2 [0]

mixed interstitial/substitutional (dimerized or dispersed)

TiO(2
x)N2x, m = 1, p = 2

n = 16

0.125

4 [0]

substitutional and O vacancy (dimerized or dispersed)

TiO(2
3x)N2x, m = 3, p = 2

n = 32 n = 16

0.0625 0.125

2 [0] 4 [2]

n = 32

0.0625

2 [1]

generalized gradient approximation (GGA) within the Perdew
Burke
Ernzerhof (PBE) exchange-correlation functional.46 The convergence criterion for the electronic SCF (self-consistent field) was fixed at 10
5 eV per cell. The core electrons for each atom were described with the projector-augmented planewave (PAW) approach.45,47 The valence atomic configurations used for the PAW potentials are 3d34s1 for Ti, 2s22p4 for O, and 2s22p3 for N. A cutoff energy of 400 eV is used. Full optimization of the atomic geometry was performed until all components of the residual forces were less than 0.01 eV/Å. As the magnetic state depends on the type of N-doping species, several spin multiplicities were tested for each N-impurity bulk configuration in order to identify the most stable spin electronic state. √ √ 2.2. Supercell Models. Both (2  2  1) and (2 2  2 2  1) anatase supercells were considered to simulate N-doped bulk anatase TiO2 structures at different N-impurity levels (Figure 1). The (2  2  1) supercell 16 TiO2 functional units √ contains √ (Ti16O32), while the (2 2  2 2  1) one contains 32 TiO2 functional units (Ti32O64). A 3  3  3 k-point mesh was used for the electronic energy calculations of both supercells. Substitutional, interstitial N-doping species as well as formation of O vacancies in the presence of N impurities were considered. In particular, we studied the stability of the doped structures as a function of N
N distance, hence distinguishing dispersed and dimerized N-impurity configurations. For the generic supercell of doped anatase with formula TinO(2n-m)Np, containing n Ti atoms, p N atoms, and m O vacancies, the atomic concentrations of N impurity and O missing atoms are defined as p/3n and m/3n, respectively. This supercell model leads to the corresponding stoichiometry TiO(2
mx)Npx with x = 1/n, notation used throughout this manuscript. For example, Table 1 indicates that the isolated substitutional N-doping species was modeled by replacing one neutral O atom with one neutral N atom (i.e., m = p = 1) in the 48-atom anatase supercell (n = 16). This leads to the stoichiometry TiO(2
x)Nx with x = 0.0625 (or 1/48
2 atom % N impurities). For dimerized or dispersed substitutional N-doping species, two neutral O atoms were replaced by two neutral N atoms (i.e., m = p = 2) in both 48-atom (n = 16) and 96-atom (n = 32) anatase supercells. The isolated interstitial N-doping species was modeled by adding one neutral N atom. Dimerized or dispersed interstitial N-doping species were modeled by adding two neutral

N atoms. Formation of O vacancies in the presence of substitutional N-doping species was modeled by replacing two neutral O atoms with two N atoms and removing one additional neutral O atom. The supercell models remain overall neutral, while N centers induce local charge redistribution. Construction of the various supercells was performed using the Materials Studio graphical interface.48 2.3. Formation Energy Calculations. Formation energy calculations of N-doped bulk anatase TiO2 were performed using three doping chemical agents as gas-phase nitrogen sources: dinitrogen, N2, ammonia, NH3, and hydrazine, N2H4. For each TinO(2n-m)Np supercell model we define the three following chemical reactions, expressing their formation from TiO2 and the considered N source Tin O2n



 p m þ N2 f Tin Oð2n
mÞ Np þ O2 2 2

Tin O2n þ pNH3 f Tin Oð2n
mÞ Np þ mH2 O
 3p
2m þ H2 2
 p N2 H4 f Tin Oð2n
mÞ Np þ mH2 O 2
 2p
2m þ H2 2

ð1Þ

ð2Þ

Tin O2n þ

ð3Þ

Note that eqs 2 and 3 are chemically valid for 3p g 2m and 2p g 2m, respectively. Thus, some specific cases must be underlined at this stage. The formation of titanium nitride TiN (also discussed later) together with H2O release using either NH3 or N2H4 implies m = 2p = 2n and would require to consider hydrogen as a coreactant. The same requirement is expected for formation of O vacancies with N impurities (2m = 3p) from N2H4. In the thermodynamic diagrams, we considered this pathway. However, it is also possible to consider the case where hydrogen is released together with O2 (instead of H2O). In these cases, eqs 2 and 3 are adapted to fit with these two chemical scenarios. For chemical reaction 1 using N2 and releasing O2, the (T, p) formation energy of each N-doped system normalized by n Ti 19396

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√ √ Figure 2. (a
d) Most stable structures and (e
h) metastable structures of various N-doped systems for two N atoms in the (2 2  2 2  1) supercell (x = 0.0625, 2% N impurities): (a,e) TiO(2
2x)N2x, (b,f) TiO2N2x, (c,g) TiO(2
x)N2x, and (d,h) TiO(2
3x)N2x.

atoms was calculated according to Ef orm ð1Þ ¼ E0K form ð1Þ þ

where

1 ½mμO
pμN  n

where E0K form(1) represents the electronic formation energy at 0 K and is defined by

   1 m p E E E N2 E0K ð1Þ ¼ ðdopedÞ
E ðpureÞ þ
tot tot O2 f orm n 2 2

ð5Þ It contains the total energies of TinO2n, TinO(2n-m)Np supercells and O2, N2 isolated molecules. The second term in eq 4 includes the oxygen and nitrogen chemical potentials depending on the pressure (p) and temperature (T) through the enthalpy (h) and entropy (s) of each molecule " !# 1 p O2 ð6Þ μO ¼ hO2 ðTÞ
TsO2 ðTÞ þ RT ln 2 p0 " μN ¼

!#

1 pN2 hN2 ðTÞ
TsN2 ðTÞ þ RT ln 2 p0

ð7Þ

The zero-point vibrational energy, enthalpy (h), and entropy (s) of each molecule as a function of temperature (T) were calculated using DMol3 with the PBE functional and the DNP basis set.48,49 The entropy and thermal contribution of the TiO2 systems were neglected. All electronic energies (for TiO2 systems and molecules) were calculated with VASP. For chemical reaction 2 using gas-phase NH3, the formation energy is expressed as follows Ef orm ð2Þ ¼ E0K form ð1Þ þ

ΔE1 ¼ EH2 þ

ð4Þ

1 ½mðμO
ΔE1 Þ
pðμN
ΔE2 Þ n ð8Þ

ΔE2 ¼

1 EO
EH2 O 2 2

ð9Þ

1 3 EN2 þ EH2
ENH3 2 2

ð10Þ

ΔE1 (ΔE2) represents the electronic energy variation calculated at 0 K for the chemical reaction H2O f H2 + 1/2O2 (NH3 f 1/ 2N2 + 3/2H2, respectively). Equation 8 shows that the stability of each N-doped system depends on the nature of the doping agent according to the value of 1/n[pΔE2
mΔE2]. It must be recalled that μN and μNH3 are also related by the following equilibrium μNH3 ¼ μN þ 3μH where μNH3

ð11Þ !

pNH3 ¼ hNH3 ðTÞ
TsNH3 ðTÞ þ RT ln p0

ð12Þ

In what follows, μH was assumed to be fixed at pH2 = 10
5 atm since the experimental pressure is usually negligible (although the thermodynamic model allows one to include this effect as discussed later). For a given experimental pNH3, we deduce the equivalent value of μN. For chemical reaction 3 using N2H4 in the gas phase as the doping agent the formation energies of each N-doped system were calculated according to a similar formula (see SI1, Supporting Information). 2.4. Electronic and Optical Spectra Analysis. Density of states (DOS) and band structure calculations of undoped and N-doped anatase models were investigated for the geometries optimized with the PBE functional by employing the rangeseparated hybrid Heyd
Scuseria
Ernzehof (HSE06)50 exchange-correlation functional, implemented in VASP 5.2.41
45 The correlation part is defined by PBE, whereas a range-separation approach is used for the exchange part. At short range a mixing of 19397

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Table 2. Relative Energies (eV) Calculated with PBE and HSE06 (in brackets) Formalisms Corresponding to the Configurations Reported in Figure 2 (x = 0.0625 or 2% N impurities), Spin Multiplicities, And Local Distances (Å) stoichiometry

configuration

relative energy PBE (HSE06)

spin multiplicity

N
N

TiO(2
2x)N2x

dispersed (2f)

1.56 (1.85)

3

3.83

TiO2N2x

dimerized (2e) dispersed (2f)

0.00 (0.00) 2.70 (3.14)

1 3

1.33 2.59

TiO(2
x)N2x TiO(2
3x)N2x

N
O

N
Ti 1.96/2.06

1.34

1.96/2.06 2.07

1.28

1.93/2.26

dimerized (2b)

0.00 (0.00)

1

1.13

dispersed (2g)

2.42 (2.55)

3

3.02

dimerized (2c)

0.00 (0.00)

1

1.21

dimerized (2h)

1.35 (1.63)

3

1.34

1.94/2.07

dispersed (2d)

0.00 (0.00)

1

3.84

1.89/1.91

25% of exact HF and 75% of PBE exchange is used, while at long range the standard PBE exchange is maintained. The rangeseparation parameter is fixed at 0.2 Å. The commonly underestimated band gap (a well-known limitation of GGA functionals) is expected to be corrected by use of the HSE06 formalism as it has been shown on reference systems.51 To reduce the HSE06 computational time as also suggested in ref 51, DOS and band structures have been calculated using a reduced subgrid of 11 k points for the exact-exchange HF kernel. UV
vis optical absorption calculations of undoped and N-doped anatase models were performed in the framework of the spin-polarized density functional perturbation theory (PT) implemented in VASP 5.241
45 by employing the HSE0650 exchange-correlation functional. We also use the geometry obtained with the PBE functional. The optical properties were calculated through the frequency-dependent dielectric function ε(ω) = ε1(ω) + iε2(ω) following a methodology described in ref 52. We plot the imaginary part ε2(ω) which represents the electronic transitions between the occupied and the unoccupied electronic states.53,54 Pre- and postprocessing operations of the optical response were performed with the graphical interface MedeA.55

3. RESULTS AND DISCUSSION 3.1. Optimized Structures and Relative Energies. We first calculate the total energies of all configurations of N-impurity atoms in anatase TiO2 as presented in the Methods section. Figure 2 shows the most relevant structures √for the√various N-doped systems with 2% N impurities for the (2 2  2 2  1) supercell. Relative energies, structural parameters, as well as spin multiplicities are reported in Table 2. Substitutional N-Doping Species. For the TiO(2
2x)N2x system (x = 0.0625 and 2 atom % N impurities) where two neutral atoms are substituting two neutral O atoms in the √ N√ (2 2  2 2  1) supercell, the lowest-energy structure reveals formation of a N2 dimer with a short N
N distance (1.33 Å) while the configuration with two separated substitutional N atoms at longer N
N distances (3.83 Å) is found to exhibit a much higher energy: 1.56 eV with PBE and 1.85 eV with HSE06 (Figure 2a and Table 2). Another configuration with two separated substitutional N atoms at a N
N distance of 2.58 Å was also found at 1.56 eV with PBE (1.85 eV with HSE06), higher than the most stable one. Similar results are obtained with higher (4%) N impurities, where strongly dimerized species are stabilized. This result highlights a strong stabilization for the substitutional dimer N2-doped system over the dispersed substitutional one.

2.22 2.09

In the case of one (or two dispersed) substitutional N atom in the supercell the most stable spin configuration is found to be an open-shell doublet (or triplet) state in which the unpaired electron is almost entirely localized on the N atoms, leading formally to charged paramagnetic N2
defects. Each N-impurity atom in the supercell carries one unpaired electron. In contrast, formation of a N2 dimer in the supercell is stabilized with a closed-shell singlet state in which the two unpaired electrons are paired up together in the N
N bonds, leading to a formal charged diamagnetic (N2)4
defect. Interstitial N-Doping Species. The most stable structure of TiO2N2x systems (with x = 0.0625 or 2% N impurities) is also characterized by formation of a N2 dimer with a short N
N distance (1.13 Å). The configuration with two separated interstitial N atoms at a longer N
N distance (2.59 Å) forming two NO species is found to exhibit a higher energy: 2.70 eV with PBE and 3.14 eV with HSE06 (Figure 2b and Table 2). Another configuration with two separated interstitial N atoms at a longer N
N distance (3.87 Å) is found at 3.08 eV with PBE (3.17 eV with HSE06) higher than the most stable one. A strong stabilization of dimerized species is also found for TiO2N2x systems (with x = 0.125) corresponding to 4% N impurities. Hence, similarly to the substitutional case, the dimerization process of the interstitial species is energetically favored. Again, to our knowledge, this formation of dimer species has never been reported in previous studies, which mainly invokes formation of dispersed or isolated NO species. For one (or two dispersed) interstitial N atom in the supercell, the most stable spin configuration is found to be an open-shell doublet (or triplet, respectively) state in which the unpaired electron is shared between the N and the O atoms of the NO bonds, leading to paramagnetic defects. Mixed Substitutional and Interstitial N-Doping Species. Analysis of the TiO(2
x)N2x system resulting from combination of the two previous configurations is reported in SI2, Supporting Information, for sake of clarity. In summary, for the most stable spin configuration, an open-shell triplet state is found for two separated mixed substitutional
interstitial N atoms (one substitutional N atom and one NO bond) in the supercell (paramagnetic defects), whereas a closed-shell singlet state is found for one mixed substitutional
interstitial N2 dimer in the supercell (diamagnetic defect). The latter case is energetically preferred as shown in Table 2. Substitutional N-Doping Species with One Extra Oxygen Vacancy. Contrasting with all previous cases, the most stable structure of the TiO(2
3x)N2x system (with x = 0.0625 or 2% N impurities and 1% O vacancies) exhibits two separated substitutional N centers with a large N
N distance (3.84 Å). 19398

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Figure 3. Stability diagram calculated with HSE06 as a function of oxygen atom chemical potential μO and p(O2) for the formation of N-doped TiO2 using N2 for μN =
0.6 eV ((p(N2) = 1 atm, T = 700 K). Solid lines represent the lowest energy N-doped systems obtained for 2 atom % N impurities. Large dashed lines represent the metastable species. Short dashed lines correspond to N-doped systems with 4% N impurities. The black solid line represents TiN (see text for complete definition).

The calculated energy is 1.35 eV with PBE (1.63 eV with HSE06) more stable than the configuration involving N2 dimer with a short N
N distance (1.34 Å) as shown in Figure 2d and Table 2. Hence, simultaneous formation of one oxygen vacancy induces stabilization of dispersed substitutional N-doping species with respect to dimerized species. The structure of TiO(2
3x)N2x with x = 0.125 corresponding to 4% N impurities and 2% O vacancies leads to a similar result. Removal of one neutral lattice oxygen atom leaves two extra unpaired electrons (assuming a formal
2 oxidation degree of O in TiO2). Due to the possible presence of unpaired electrons at various sites, several spin configurations were tested. First, a highspin open-shell configuration corresponding to four unpaired electrons (quintet state) in which two unpaired electrons are localized on the two N impurities and two other unpaired electrons on the two Ti3+ ions. Then, a low-spin closed-shell configuration (singlet state) resulting from localization of the an extra unpaired electrons on the two initially paramagnetic substitutional N2
species is formed. This process leads formally to charged diamagnetic substitutional N3
defects and fully oxidized Ti4+ ions. The singlet configuration is 3.74 (with PBE) and 4.16 eV (with HSE06) more stable than the quintet state. Note that formation of the N3
center in the material is accompanied by a local distortion characterized by shorter N
Ti bond lengths than for the N2
center (Table 1). 3.2. Thermodynamic Equilibrium Stability. In this section, we investigate the thermodynamic stability of the N-doped systems using three doping chemical agents as N2, NH3, and N2H4 in the gas phase. The stability diagram using N2 in the gas phase as the N-doping agent will be considered as the reference one. Our goal is to evaluate the impact of the reducing character of doping agents such as NH3 and N2H4 with respect to the reference N2. Each thermodynamic diagram is defined by the formation energies of the various N-doped bulk systems as a function of the oxygen chemical potential μO, which represents a

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more (high p(O2), low T) or less (low p(O2), high T) oxidizing environment. The range of μO is given as a function of p(O2) through eq 6 for 700 K, which is the typical annealing temperature of the N-doped anatase system. Using N2 as a Doping Agent. Following chemical reaction 1, Figure 3 shows the formation energy diagram given by eqs 4 and 5 for a fixed μN =
0.62 eV (p(N2) = 1 atm and 700 K, i.e., close to reasonable experimental conditions). The HSE06 functional is used, while a similar diagram obtained with PBE is reported in SI3, Supporting Information: the main trends are consistent with PBE and HSE06. The formation energies of the different studied N-doping species are all positive throughout the oxygen chemical potential range. Chemical reaction 1 remains endothermic with respect to undoped anatase, which may explain some experimental limitations encountered during synthesis of doped systems (metastable) using N2 doping agent. Among the doped systems, the diamagnetic TiO2N2x system corresponding to dimerized N
N species (with 2% interstitial N impurities) is found to be the most favorable only for ultrahigh p(O2) (>1010 atm). The diamagnetic TiO(2
x)N2x system associated to dimerized N
N species (with 2% N impurities) is found to be stabilized for a large range of μO, including p(O2) close to 1 atm. The diamagnetic TiO(2
3x)N2x system with 2% dispersed N impurities and 1% O vacancies becomes stable for ultralow p(O2) (