Abstract. In order to understand the photocatalytic mechanisms of N-doped TiO2 with
different doping positions of N, this research performed ab-initio calculations based on
density functional theory (DFT) without and with Hubbard U correction, concentrate on
the electronic structure of the materials. The adopted value of effective Hubbard U for Ti
3d is 8.18 eV; the corresponding calculated band-gap value of TiO2 with this value of U
is 3.201 eV, in a good agreement with experiment value. The calculated results show that
substitutional doping is easier to form than interstitial doping in the N-doped TiO2 material.
Band-gap of defective models are decreasing, lead to the shifting of edges of absorption to
the visible light region.

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JOURNAL OF SCIENCE OF HNUE DOI: 10.18173/2354-1059.2016-0045
Mathematical and Physical Sci., 2016, Vol. 61, No. 7, pp. 157-164
This paper is available online at
A DFT STUDY ON N-DOPED TiO2 ANATASE
Duong Quoc Van, Le Minh Thu, Nguyen Manh Nghia and Nguyen Minh Thuy
Faculty of Physics, Hanoi National University of Education
Abstract. In order to understand the photocatalytic mechanisms of N-doped TiO2 with
different doping positions of N, this research performed ab-initio calculations based on
density functional theory (DFT) without and with Hubbard U correction, concentrate on
the electronic structure of the materials. The adopted value of effective Hubbard U for Ti
3d is 8.18 eV; the corresponding calculated band-gap value of TiO2 with this value of U
is 3.201 eV, in a good agreement with experiment value. The calculated results show that
substitutional doping is easier to form than interstitial doping in the N-dopedTiO2 material.
Band-gap of defective models are decreasing, lead to the shifting of edges of absorption to
the visible light region.
Keywords: N-doped TiO2, substitutional, interstitial, oxygen vacancy, DFT and DFT + U.
1. Introduction
Since the first demonstration of Fujishima and Honda in 1972 [1], TiO2 has been considered
as one of most important material due to nontoxic, chemical and physical stability, low cost and
photocatalytic activity. However, band-gap value of pure anatase TiO2 is approximates 3.2 eV and
only absorbs ultraviolet light with wavelengths shorter than 387 nm. The limitation due to wide
band-gap lead to the ineffective of TiO2 photocatalytic activity in the region of visible light. To
reduce this limitation, modified TiO2 has been studied for the extending of optical absorption to
the visible light region.
After Asahi et al. [2] reported that doping N into TiO2 lead the optical absorption extends
to the visible region, N-doped TiO2 has been studied widely all over the world. N-doped TiO2 has
been prepared in different shapes such as powders [3], films [4-7] and studied for photocatalytic
activity in visible light region. The shifting of absorption edge of N-doped TiO2 to the visible
region was hypothesized by Asahi et al. [2] from the hybrid of N 2p and O 2p and narrowed
band-gap of N-doped TiO2 whereas Irie et al. [3] considered the reason from the appearance of
N 2p doped level above the valence band. Effects of oxygen vacancies and its contribution to the
absorption spectra of N-doped TiO2 were reported [8-10]. Theoretical calculations of Valentin
et al. [11] showed that the energy costs to form oxygen vacancies in TiO2 reduced when nitrogen
is doped. Rumaiz et al. [12] indicated that the defect level of oxygen vacancies above the valence
band maximum is the reason for the knee formation in the optical absorbance spectra of N-doped
TiO2. Effects of interstitial and substitutional N-doping states were reported by Lee et al. [13],
Received September 30, 2016. Accepted October 27, 2016.
Contact Duong Quoc Van, e-mail address: vandq@hnue.edu.vn
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Duong Quoc Van, Le Minh Thu, Nguyen Manh Nghia and Nguyen Minh Thuy
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. All of these
theoretical calculations have been investigated for the mechanisms of photocatalytic activity of
N-doped TiO2, most of them greatly underestimated the band gap of TiO2 due to the adoption of
conventional density functional theory (DFT) method. Wu et al. [14] used Generalized Gradient
Approximation (GGA) with Hubbard [15] parameter (GGA+U) to investigate the mechanism of
photocatalytic activity in N-doped TiO2.
In this research, we both use GGA and GGA+U approaches to investigate electronic
structure of the N-doped anatase TiO2 with oxygen vacancies systematically to comprehend the
mechanisms of photocatalytic activities of materials.
2. Content
2.1. Computational methods
In this research, a 2 × 2 × 1 supercell of pure anatase TiO2 containing 16 Ti atoms and
32 O atoms (labeled as TOO) was used to studied (Figure 1a). The effects of N doping or O
removing in TiO2 on structural and electronic properties were investigated using the modified
supercells as shown in the Figure 1 (b-f). The substitutional N-doping supercell (labeled as TON-s)
was constructed by substituting one O atom with one N atom, the interstitial N-doping supercell
(labeled as TON-i) was constructed by embedding one N atom into the interspace and the oxygen
vacancy TiO2 supercell (labeled as TOO-v) was constructed by remove one O atom. The supercell
of both interstitial doping and oxygen vacancy was labeled as TON-iv while the supercell of both
substitutional doping and oxygen vacancy was labeled as TON-sv.
Calculations based on first principles were performed using the CASTEP [16] modules in
Materials Studio 6.0. The interactions of electron-ion were modeled using the Vanderbilt ultrasoft
pseudopotentials [17] with the valence atomic configurations for Ti is 3s23p63d24s2, for O is
2s22p4 and for N is 2s22p3. The wave functions was expanded through a plane wave basis set
with cutoff energy is 380 eV. The Monkhorst-Pack scheme [18] k-points grid sampling was set
at 7 × 7 × 3 in the supercells. The convergence threshold for self-consistent iterations was set at
5× 10−7 eV. In the geometry optimization process, the energy change, maximum force, maximum
stress and maximum displacement tolerances were set at 5 × 10−6 eV/atom, 0.01 eV/A˚, 0.02 GPa
and 5.10−4 A˚, respectively.
For the spin-polarized GGA+U approach, the increasing of appropriate effective Hubbard
U for anatase TiO2 lead to increase the band-gap of materials. This increment of band-gap value
was studied by increasing U from 0.5 to 9.5 eV in order to find the consistent value of U. The
adopted value for effective Hubbard parameter was U = 8.18 eV for Ti 3d in the GGA+U approach.
Calculated band gap of pure TiO2 anatase with this Hubbard parameter is 3.201 eV, similar to the
experimental value.
2.2. Results and discussion
2.2.1. Formation Energy
To determine the relative stability of defective TiO2 models, their formation energies
(∆Emod) were calculated according to the following formula:
∆Emod = Etot(models) − Etot(pure) −mµN + nµO
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A DFT study on N-doped TiO2 anatase
Etot (models) and Etot (pure) are the total energies of N-doped models and pure TiO2; µ N
and µ O represent the chemical potentials of the N and O atoms and can be determined from the
total energy of N2 and O2 free molecules; m and n are the numbers of doped nitrogen and removed
oxygen atoms in the models (listed in Table 1).
Figure 1. The 2 × 2 × 1 supercell of pure and defective TiO2 models
An important note is the formation energy of a doped model depends on the Hubbard
parameter U used for calculation. A systematic calculation has been done to investigate the
Hubbard U dependence of pure TiO2 band-gap. The relationship between Hubbard parameter U
and band-gap of TiO2 is shown in the Figure 2. The adopted value for U is 8.18 eV and will be
used for latter calculations.
Table 1. Values of doped nitrogen atoms (m) and removed oxygen atom (n)
for pure and defective TiO2 models
Models TOO TOO-v TON-i TON-iv TON-s TON-sv
m 0 0 1 1 1 1
n 0 1 0 1 1 2
Calculated results for formation energies of models are listed in Table 2. The model with
smaller formation energy is more stable than the model with larger value. The formation energy
of TON-s model (labeled as Es) is smaller than formation energy of TON-i model (Ei), indicating
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Duong Quoc Van, Le Minh Thu, Nguyen Manh Nghia and Nguyen Minh Thuy
that substitutional N atoms are formed easier than N interstitial atoms. This result is consistent
with results from Wu et al. [14], Lee et al. [13].
Figure 2. The relationship of pure TiO2 band-gap Eg and Hubbard parameter U
Table 2. Formation energies of defective TiO2 models
Models Formation Energy (eV)
TOO-v ∆Ev = 1.064
TON-i ∆Ei = 6.218
TON-iv ∆Eiv = 7.353
TON-s ∆Es = 2.863
TON-sv ∆Esv = 3.733
The formation energy of oxygen vacancy from pure TiO2 is ∆Ev = 1.064 eV while the
corresponding value for Ns-doped is ∆Evfs = ∆Esv - ∆Es = 0.870 eV. It is easy to see that
∆Evfs < ∆Ev, which mean that the oxygen vacancy is easier to form with the existence of N
atoms, in a good agreement with previous results [12, 13].
2.2.2. Density of states
To have a detail view on electronic properties of N-doped TiO2, total density of states
(DOS) and projected density of states (PDOS) of defect models were calculated and showed in
Figure 3. The band-gap values (Eg), the maximum absorption wavelengths (λmax = 1240/Eg) and
the width of valence band (WVB) of defect models were calculated and summarized in Table 3.
The calculated band-gap of pure TiO2 anatase is 3.201 eV, in a good agreement with
experimental result (3.2 eV). All calculated band-gap of defect models is smaller than pure value,
which mean that N doping lead to the shifting of absorption edge to the visible light region. Figure
3 shows the appearance of N 2p state over the valence band, which play an important role in the
narrowing band-gap of N-doped TiO2. For TOO-v model, the widening of the O 2p valence band
lead to the narrowing of band-gap of the model.
The width of valence band of pure TiO2 model is 4.90 eV (see Figure 3a) showing a strong
delocalization between O 2p state electrons. For defective models, the widths of valence bands
are increase, which mean that doped N atom or oxygen vacancies can increase the mobility of
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A DFT study on N-doped TiO2 anatase
electrons in the valence bands. This can be explained by the appearance of O 2p or N 2p states,
increasing the delocalization of electrons in the valence bands.
Figure 3. Density of states (DOS) of pure and defective TiO2 models
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Duong Quoc Van, Le Minh Thu, Nguyen Manh Nghia and Nguyen Minh Thuy
2.2.3. Electron density differences
Table 3. Band gap, maximum absorption wavelength, width of valence band and Hirshfeld [19]
population of pure and defective TiO2 models
Models Eg (eV) λmax (nm) WVB (eV) Hirshfeld Charge |e|
Ti O N
TOO 3.20 387 4.90 0.680 -0.340
TOO-v 3.05 406 4.75 0.601 -0.311
TON-i 3.02 410 5.45 0.609 -0.303 -0.04
TON-iv 2.83 438 5.05 0.602 -0.305 -0.15
TON-s 3.13 396 4.95 0.610 -0.307 -0.24
TON-sv 2.75 450 5.25 0.601 -0.307 -0.36
Figure 4. Charge distribution of defective TiO2 models
(the dotted circle represent for oxygen vacancy)
The Hirshfeld population [19] of all models were calculated and listed in Table 3.
Figure 4 shows the charge distributions of pure and defective TiO2 models. The average Hirshfeld
population values of pure TiO2 are 0.680 |e| and -0.340 |e|. The much higher population value of
Ti atom indicates that a large oxidation occurred in the TiO2 bulk materials. For TON-s model, the
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A DFT study on N-doped TiO2 anatase
Hirshfeld population of N atom (-0.24 |e|) is larger than that of O atom (-0.307 |e|), meaning that
the 2p orbitals of substitutional N atom is unfilled. For TON-i model, the Hirshfeld population of
N atom is -0.04 |e|, indicating that the interstitial N atom is obtains fewer electrons from Ti atoms
than O atoms in TOO model. Figure 4c and 4d show that the charge is shared between interstitial
N atom and its neighbor O atoms, similar with the results of Rumaiz et al. [12] and Wu et al. [14].
For TON-iv model, the sharing of electrons between N and its neighbor atom lead to increase the
Hirshfeld population for both of them. For TOO-v model, the Hirshfeld population of Ti is smaller
(the charge difference is -0.079 |e| - see Table 3) while that of O is larger (the charge deference is
0.029 |e|). This mean that the extra electrons in this model concentrate around Ti atom near the
oxygen vacancy. The populations of Ti and N atoms in TON-s and TON-sv models show that more
electrons move from the oxygen vacancy to its neighbor Ti atom and to the N atom.
3. Conclusion
The GGA and GGA+U methods have been used to calculate the formation energy,
electronic structure and charge density of N-doped TiO2 models with oxygen vacancies. To correct
the band-gap value of pure TiO2, an effective Hubbard parameter U = 8.18 eV has been adopted for
all calculations. We built 6 different models in order to investigate their stability and properties.
Calculated results show that the substitutional N-doped TiO2 is easier to form than interstitial
N-doped TiO2 and the oxygen vacancy is easier to form in the present of doped N atoms. The
calculated results also show that the photocatalytic mechanisms in the visible light region of
N-doped TiO2 can be explained through following reasons: (i) the narrowing of band-gap caused
by N doping; (ii) the appearance of N 2p states above the top of valence bands and (iii) the
narrowing of band-gap caused by the widening of valence bands caused by O 2p states.
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