Mechanisms of Visible Light Photocatalysis in N-Doped Anatase TiO 2 with Oxygen Vacancies from GGA + U Calculations

We have systematically studied the photocatalyticmechanisms of nitrogen doping in anatase TiO 2 using first-principles calculations based on density functional theory, employing Hubbard U (8.47 eV) on-site correction. The impurity formation energy, charge density, and electronic structure properties of TiO 2 supercells containing substitutional nitrogen, interstitial nitrogen, or oxygen vacancies were evaluated to clarify the mechanisms under visible light. According to the formation energy, a substitutional N atom is better formed than an interstitial N atom, and the formation of an oxygen vacancy in N-doped TiO 2 is easier than that in pure TiO 2 . The calculated results have shown that a significant band gap narrowing may only occur in heavy nitrogen doping. With light nitrogen doping, the photocatalysis under visible light relies on N-isolated impurity states. Oxygen vacancies existence in Ndoped TiO 2 can improve the photocatalysis in visible light because of a band gap narrowing and n-type donor states.These findings provide a reasonable explanation of the mechanisms of visible light photocatalysis in N-doped TiO 2 .


Introduction
Photocatalytic mechanisms are created with an electron-hole pair by exciting an electron from the valence band to the conduction band through absorption of the electromagnetic radiation.Since the pioneering work of Fujishima and Honda in 1972 [1], titanium dioxide (TiO 2 ) has attracted attention as a photocatalytic material due to nontoxicity, low cost, and chemical stability.However, anatase TiO 2 has a wide band gap (3.2 eV) and only absorbs ultraviolet (UV) light at wavelengths shorter than 387 nm.UV light accounts for a small fraction (∼5%) of solar energy impinging on the surface of the Earth; that is, solar energy utilization is low.Limitations due to the wide band gap make TiO 2 ineffective for many potential applications.Because visible light (400-700 nm) accounts for a large fraction (∼45%), the modification of TiO 2 for extending optical absorption to the visible light region has become a thoroughly researched topic.
Since Asahi et al. [2] reported in 2001 that nitrogen doping enhances photocatalytic activity under visible light, TiO 2 has been doped with a variety of elements, such as N [3][4][5][6][7][8][9][10], C [11], B [12], P [13], Fe [14,15], and La [16] to study photocatalytic activity under visible light with nitrogen doping proving effectiveness.Although the nitrogen doping is considered more effective and widely studied, the photocatalytic mechanisms under visible light are still debatable.Asahi et al. [2] indicated that the N 2p states hybridize with O 2p states that result in a narrowing of the band gap with the material becoming photoactive in the visible light region.However, other studies have supported the notion that Ndoping does not cause a narrowing of the band gap of TiO 2 [3,4].For example, Irie et al. [4] considered that an isolated N 2p band above the valence band was responsible for the response to visible light.Oxygen vacancies induced by N-doping contributed to the absorption as well as photoactivity in the visible light region were also reported [17][18][19].Valentin et al. [20] employed theoretical calculations to show that nitrogen doping led to a substantial reduction of energy costs to form oxygen vacancies in TiO 2 .This suggested that nitrogen doping was likely to be accompanied by the formation of oxygen vacancies.Rumaiz et al. [21] indicated that the related defect level of oxygen vacancies was approximately 1 eV above the valence band maximum (VBM) and explained the knee formation in the optical absorbance spectra of N-doped TiO 2 .Lee et al. [22] suggested that the interstitial N-doping states with the oxygen deficiency were more effective for photocatalysis than the substitutional N-doping states with the oxygen deficiency.Zhao and Liu [23] have employed density functional theory (DFT) and adopted a 2 × 1 × 1 supercell model to investigate the modification mechanism of N-doped anatase TiO 2 .The calculated band gap of pure anatase TiO 2 was 2.68 eV, which was smaller than the experimental value of 3.2 eV, due to the limitation of DFT.The results have shown that except for oxygen deficient model, the band gaps of N-doped TiO 2 , including substitutional and interstitial Ndoping models, were narrowed between 0.03 and 0.23 eV.The fundamental absorption edges extended to the visible light region.
As mentioned above, the mechanisms of N-doping in TiO 2 under visible light region have three views: (1) band gap narrowing, (2) impurity energy levels, and (3) oxygen vacancies.Although theoretical calculations have been investigated for the mechanisms, most of them greatly underestimated the band gap of TiO 2 due to the adoption of conventional DFT method.In this paper, first-principles calculations employing the generalized gradient approximation (GGA) and Hubbard U approach are performed to investigate the formation energy, charge density, and electronic structure of N-doped anatase TiO 2 with oxygen vacancies systematically to comprehend the mechanisms of N-doped anatase TiO 2 .The calculated results were analyzed and compared with the previous literature.

Calculation Models and Methods
A 2 × 2 × 1 supercell of a pure anatase TiO 2 containing 16 Ti atoms and 32 O atoms was considered in this study as shown in Figure 1(a).To investigate the effect of the N-doping and oxygen vacancy in TiO 2 on the electronic structure, five defect types were modeled as shown in Figures 1(b)-1(f).The substitutional N-doping supercell (Figure 1 First-principles calculations were performed using the CASTEP module [24] in Materials Studio 5.0 developed by Accelrys Software Inc. Electron-ion interactions were modeled using ultrasoft pseudopotentials in the Vanderbilt form [25].The valence atomic configurations were 2s 2 2p 4 for O, 2s 2 2p 3 for N, and 3s 2 3p 6 3d 2 4s 2 for Ti.The wave functions of the valence electrons were expanded through a plane wave basis set, and the cutoff energy was selected as 400 eV.The Monkhorst-Pack scheme [26] K-points grid sampling was set at 4 × 4 × 3 (less than 0.04 Å−1 ) in the supercells.The convergence threshold for self-consistent iterations was set at 5 × 10 −6 eV.In the optimization process, the energy change, maximum force, maximum stress, and maximum displacement tolerances were set at 9 × 10 −5 eV/atom, 0.09 eV/ Å, 0.09 GPa, and 0.009 Å, respectively.
The spin-polarized GGA+U approach introduced an intra-atomic electron-electron interaction as an on-site correction to describe systems with localized d and f electrons capable of producing a more optimal band gap.Determination of an appropriate effective Hubbard  eff parameter is necessary in GGA+U calculations to interpret the intraatomic electron correlation correctly.As shown in Figure 2, for anatase TiO 2 , the band gap widens when the effective Hubbard  eff was increased.The band gap was effectively widened by increasing  eff from 2 to 8 eV.Here, the effective on-site Coulomb interaction was  eff = 8.47 eV for Ti 3d in the GGA+U approach and the calculated band gap of pure anatase is 3.21 eV, similar to the experimental value.

Formation Energy.
To examine the relative stability of Ndoped TiO 2 for various defective models, the defect formation energies (  ) were calculated according to the following formula: tot (defect) and  tot (pure) are the total energies of defective models and pure TiO It should be noted that the formation energy of a defective system depends on the selected U value.The U value of 8.47 eV was fixed to qualitatively examine the relative stability of N-doped TiO 2 for various defective models in this study.Table 1 summarizes the calculated formation energies for different defective models in TiO 2 .The smaller   value represents that a defective system is more stable.The   (N s ) (formation energy of N s model) is smaller under the Ti-rich condition than that under O-rich condition, indicating that the incorporation of N into TiO 2 at the O site is thermodynamically favorable.At the Ti-rich condition, the   (N s ) is smaller than   (N i ), indicating that substitutional N atoms are more probable to be formed.This result is opposite with Zhao's calculated result (interstitial N atoms are favored) [23], but is consistent with Lee's calculated result [22].It can be found that the formation energy of an oxygen vacancy from pure TiO 2 is 1.0 eV (  (O v ) = 1.0) and that from N doped TiO 2 is 0.26   the formation of oxygen vacancies with N existence in TiO 2 is easier than pure TiO 2 and is in agreement with the previous literature [21,23].

Electronic Density.
Table 1 summarizes Mulliken populations.Figure 3 indicates the charge distribution of each  1 shows that the Mulliken population of N s (−0.62) is larger than that of O (−0.737) and leads to an unfilled 2p orbital in the N atom because the electronegativity of N is lower than that of O as shown in Figure 3(a).For N i model, the Mulliken population of N i is −0.27, indicating that the N i atom obtains fewer electrons from Ti atoms.3.3.Electronic Structure.Figure 4 indicates the total density of states (TDOS), and the projected density of states (PDOS) of various defective models was calculated to investigate the electronic properties of N-doped anatase TiO 2 .Other related values that were calculated include the band gap (  ), the width of the valence band ( VB ), and the maximum absorption wavelength ( max = 1240/  ) that Table 2 summarizes.The band gap (  ) of pure anatase TiO 2 is 3.21 eV as shown in Figure 4(a) and is consistent with the experimental value of  6 International Journal of Photoenergy As a result, the electron transition energy from the valence band to the conduction band decreased by approximately 0.88 eV because of the heavy nitrogen doping and, thus, may induce a red shift (extending to 532 nm) at the edge of the optical absorption range.Both the narrowing of the band gap and the increased mobility of photo-generated carriers in heavy nitrogen doping concentrations improve the photocatalytic activity under visible light, as illustrated in recent experimental results [6,7].

Conclusions
Using the GGA+U method, this study calculated impurity formation energy, charge density, and electronic properties of an N-doped anatase TiO 2 with oxygen vacancies system to investigate the photocatalytic mechanisms of N-doped TiO 2 under visible light.An effective Hubbard U of 8.47 eV was adopted to determine the experimental band gap correctly.The formation energy calculated results have shown that the substitutional N atom was easier to be formed than the interstitial one and the formation of oxygen vacancies under nitrogen existence in TiO 2 was easier to be formed than pure TiO 2 .The calculated results have shown that the mechanisms of photocatalytic activity under visible light are concluded as the following: (1) the significant band gap narrowing may occur in heavy nitrogen doping; (2) with light nitrogen doping, the mechanism is the result of N-isolated impurity states; and (3) oxygen vacancies existence in N-doped TiO 2 improves the photocatalysis in visible light because of a band gap narrowing and n-type donor states.
(b)) was labeled N s and constructed by substituting one oxygen atom with one nitrogen atom (2.1 at.%) and the interstitial N-doping supercell (Figure 1(c)) being labeled N i , with one N atom was embedded into the interspace.In oxygen vacancy systems, one O atom was removed and were labeled O v (Figure 1(d)), N s O v (Figure 1(e), with one O atom being substituted by N atom), and N i O v (Figure 1(f), with one N atom being embedded into the interspace).

2 ;
N and  O represent the chemical potentials of the N and O atoms;  and  are the numbers of doped nitrogen and removed oxygen atoms;  = 1 and  = 1 for N s model, and  = 1,  = 0 for N i model,  = 0,  = 1 for O v model,  = 1,  = 2 for N s O v model,  = 1,  = 1 for N i O v model.The formation energy depends on growth conditions and can be Ti-rich or O-rich.For TiO 2 ,  Ti and  O satisfy the relationship  Ti + 2 O =  TiO 2 .Under the Orich growth condition,  O is determined by the total energy of an O 2 molecule ( O =  O 2 /2) and  Ti is determined by the formula  Ti =  TiO 2 − 2 O .Under the Ti-rich growth condition,  Ti is the energy of one Ti atom in bulk Ti and  O is determined by  O = ( TiO 2 −  Ti )/2.

Figure 2 :
Figure 2: Relationship between the effective Hubbard parameter ( eff ) and the band gap (  ) of anatase TiO 2 .

Figure 3 (NFigure 3 :
Figure 3: Charge distribution of various defective models in N-doped TiO 2 : (a) N s , (b) N i , (c) O v , (d) N s O v , and (e) N i O v .

Figure 3 (
c) shows that the electrons are remained in a Ti atom near the oxygen vacancy.Comparing the N s with N s O v models, the Mulliken population of N atom decreases from −0.62 to −0.75, indicating that there are more electrons that transfer from oxygen vacancy to the N atom, and the N 2p orbital is filled as shown in Figure 3(d).For N i O v model, the electron clouds are shared between N i and the adjacent O atoms.They increase the population values in N i and O atoms.

Table 1 :
Formation energy and average Mulliken population of various defective models of N-doped TiO 2 .
s model, Table

Table 2 :
[2]] gap, maximum absorption, wavelength, and width of valence band for various defective models of N-doped TiO 2 .The valence band of TiO 2 has a large bandwidth ( VB ) of approximately 4.63 eV, showing a strong delocalization among the O 2p electrons.For N  model from Figure4(b), the   gap is 3.17 eV and the  VB is 4.68 eV, implying that   and  VB are not changed obviously compared with the pure TiO 2 .It is demonstrated from Figure4(b) that one isolated N 2p state is localized above the top of the VB of the host TiO 2 and is consistent with the calculations of Long[27].The electron in the VB is excited to localized impurity states in the band gap and subsequently to the CB through absorption of visible light.For N i model from Figure4(c), the   is narrowed to 3.08 eV and the  VB is broadened to 4.86 eV.It was observed that the N 2p states primarily contributed to three energy ranges: −7.5 to −6.1, −0.6 to 0, and 1.8 to 2 eV.For O v model from Figure4(d), the   (3.18 eV) is not changed obviously and the  VB is broadened to 5.12 eV.The two extra electrons resulted from removing an oxygen atom lead to an occupied state near Fermi energy level and are localized at 1.0 eV above the top of VB and consistent with the experimental results[21].Comparing with the N  and N  models, both band gaps of the N s O v and N i O v (2.95 and 3.06 eV) became smaller and extended optical absorption into the visible region (420 and 405 nm).Figures 4(e)-4(f) show that the  VB became broader.Therefore, the existence of oxygen vacancies in N-doped anatase TiO 2 improves the photocatalysis under visible light.Our previous work regarding DOS for heavy nitrogen doping in the N-doped anatase TiO 2 are shown in Figures4(g)-4(h)[8].It can be observed that a significant narrowing of the band gap of Ndoped TiO 2 occurs only for heavy nitrogen doping (≥8.3 at.%) and is in agreement with Ashai calculated results[2].