C-, N-, S-, and F-Doped Anatase TiO 2 ( 101 ) with Oxygen Vacancies : Photocatalysts Active in the Visible Region

Anatase TiO2 presents a large bandgap of 3.2 eV, which inhibits the use of visible light radiation (λ> 387 nm) for generating charge carriers. We studied the activation of TiO2 (101) anatase with visible light by doping with C, N, S, and F atoms. For this purpose, density functional theory and the Hubbard U approach are used. We identify two ways for activating the TiO2 with visible light. The first mechanism is broadening the valence or conduction band; for example, in the S-doped TiO2 (101) system, the valence band is broadened. A similar process can occur in the conduction band when the undercoordinated Ti atoms are exposed on the TiO2 (101) surface. The second mechanism, and more efficient for activating the anatase, is to generate localized states in the gap: N-doping creates localized empty states in the bandgap. For C-doping, the surface TiO2 (101) presents a “cleaner” gap than the bulk TiO2, resulting in fewer recombination centers. The dopant valence electrons determine the number and position of the localized states in the bandgap. The formation of charge carriers with visible light is highly favored by the oxygen vacancies on TiO2 (101). The catalytic activity of C-doping using visible radiation can be explained by its high absorption intensity generated by oxygen vacancies on the surface. The intensity of the visible absorption spectrum of doped TiO2 (101) follows the order: C>N> F> S dopant.


Introduction
In the late '70s, photocatalysis took a turn when researchers discovered the TiO 2 ability to degrade stable organic compounds as they were studying the water photoelectrolysis [1][2][3].Since then, there has been a great interest to improve the degradation efficiency of organic pollutants using TiO 2 [4][5][6][7].
Atanelov et al. [15] theoretically studied TiO 2 doped with C and N atoms at two different concentrations.They found that dopants decrease the bandgap, which enhances the TiO 2 photocatalytic activity.It is crucial that states created by doping process localize close to the valence band maximum (VBM) or the conduction band minimum (CBM), since states spread along the bandgap may act as a recombination center [15,[30][31][32].Sakthivel and Kisch [33] found that C-doping TiO 2 is five times more efficient than N-doping in the degradation of 4-chlorophenol when artificial light (λ ≥ 455 nm) is used.Tian and Liu [34] showed that high S concentrations as a TiO 2 dopant induced a light absorption redshift.Whereas F-doped TiO 2 does not reduce the bandgap [16,35], Yu et al. [36] obtained a gap of 2.90 eV for an anatase and rutile mixture doped with F − ions, where the interface may reduce the recombination of photogenerated electrons and holes.Czoska et al. [16] reported that Ti 3+ states separate from the CBM when the local density approximation (LDA) + U parameter method is used, making this procedure suitable to describe the F-doping on the anatase TiO 2 .
TiO 2 usually presents oxygen vacancies; these defects can be controlled experimentally based on nonstoichiometric conditions of synthesis (Ti excess or oxygen deficiency) or by heating the sample in a vacuum at 900 K [37][38][39].Zhang et al. [40] showed that there is a synergistic effect of N dopant and oxygen vacancy in TiO 2 contributing to the significant enhancement of the visible light photoactivity.The synergy between species N-Ti and the oxygen vacancy also occurs in heterojunctions such as NiO/N-TiO 2 catalysts [41], but in general, doped TiO 2 and oxygen vacancies have been studied separately.For other dopants, it is not understood how the simultaneous interaction between dopants and vacancies affects the optical response of the TiO 2 (101) surface in the visible region.This knowledge will help optimize doped TiO 2 for the degradation of organic compounds.
This work aims to make a systematic study on C-, N-, S-, and F-doped TiO 2 (101) to obtain the most suitable element to reduce the bandgap or to generate localized states in the gap.Furthermore, the generalized gradient approximation (GGA) and the Hubbard U method are used to explain the intraband states' nature.Notably, this article focuses on the simultaneous interaction of oxygen vacancies and main group dopants to analyze and evaluate the anatase surface response to the visible radiation.
Standard DFT calculations underestimate the bandgap because of its difficulty in representing empty states [52].For recovering of the electron correlation effects-at least in pairs-and the Ti 3d orbitals additional repulsion, we use the Hubbard U parameter [53] as suggested by Morgade and Cabeza for TiO 2 [54].A value of U = 5 5 eV was considered only for Ti 3d electrons following the recommendation by Calzado et al. [55].
The projector augmented wave (PAW) approach is used for describing the ion-electron interactions [56,57].The plane-wave basis for all elements with an energy cutoff of 400 eV was employed throughout calculations.We used a k-point mesh of 3 × 3 × 3 for the bulk systems and 5 × 5 × 1 for the surface.The total energy convergence criterion was 1 × 10 −4 eV.
A 3 × 3 × 3 supercell was built for modeling the bulk.The (101) plane is the most stable for anatase TiO 2 [58,59].Then, the surface was represented by a 2 × 1 × 1 supercell considering four layers in the (101) direction; both the bulk and surface models contain 48 atoms (see Figure 1).A vacuum 2 International Journal of Photoenergy of 16 Å was included to ensure that the two adjacent surfaces do not interact.
For the bulk and surface models, the three-coordinated oxygen atom was substituted, yielding a doping concentration of 2.08% mole.On the surface, the second most exposed oxygen atom was replaced by the dopants (see Figure 1(b)).The bottom layer of the slab was constrained to simulate the bulk environment.
Three methodologies were used to study the electronic structure of doped TiO 2 .The first, an electronic and geometry relaxation using the PBE functional were performed (GGA); for the second approach, the relaxed geometry obtained by the first method was used to accomplish a single point calculation with the U parameter (GGA/GGAU).Finally, both geometry and electronic relaxation were determined with the U parameter (GGAU).For all calculations, spin polarization was considered.
For studying the simultaneous interaction between impurities and oxygen vacancies, we detach the nearest surface oxygen atom to the dopant on the doped TiO 2 (101); in the pristine TiO 2 surface, we removed the same oxygen for comparison (see Figure 1(b)).The absorption spectra were obtained with the VASPKIT program [60], using the real and imaginary parts of frequencydependent complex dielectric function [61], after the electronic ground state has been determined.The systems with oxygen vacancies were studied with the GGAU methodology, which represents the most reliable method of those tested in this work.

Results and Discussion
The optimized parameters for the bulk TiO 2 are a = 3 8248 Å, c = 9 6909 Å, and z = 0 2068, which agree with experimental values obtained by Horn et al. [62].For the GGA methodology in the bulk anatase, we obtain an energy bandgap (E g ) of 2.19 eV.For the GGA/GGAU and GGAU methodologies, the E g broadens to 2.81 and 2.76 eV, respectively, and there are no significant changes in the electronic structure for the bulk system (see Figure S1(a) in the Supplementary Materials).The main effect of the U parameter is to move the Ti 3d states toward more positive energies, which increases the bandgap because the CBM is displaced.From now on, every time the three bandgaps are mentioned, we are referring to the values obtained with the GGA, GGA/GGAU, and GGAU approaches.
For the TiO 2 (101) surface, the E g narrows to 1.85, 2.31, and 2.25 eV for each used methodology, respectively.We attribute this narrowness to the bond unsaturation at the material surface, corresponding to undercoordinated Ti species located at the beginning of the CB, which promotes a bandgap reduction.The density of states (DOS) for the surface depicts characteristic localized empty states below the CB, Figure S1(b).These states have a well-defined shape and are distinct from the occupied states created by the Ti 3+ species.at the end of these states.Furthermore, C-doping generates unoccupied states that lie in the bandgap region.The calculated bandgaps are 2.44, 2.66, and 2.66 eV (without considering the states introduced by dopants) for the three methodologies (see Figure 2(a) and S2(a)).
The O atoms in the anatase TiO 2 have an oxidation state of −2, which implies that O accepts two electrons in its 2p empty orbitals.Carbon has 2 electrons less than O, so its 2p orbitals are not going to be full by receiving 2 electrons like O atoms.This process will leave two unoccupied C 2p orbitals that are not in the same energy level that Ti 3d states therefore will appear below the CB.
When the U correlation is considered, the empty states introduced by C-doping are separated from the Ti 3d orbitals, and the extra repulsion pushes Ti 3d orbitals towards the CBM.This behavior also occurs on the TiO 2 (101) surface; the calculated bandgaps are 1.87, 2.36, and 2.30 eV, which are similar to the pristine system, but the C atom generates two empty states in the bandgap (see Figure 2 C-doped TiO 2 (101) presents a magnetic moment of 2 μ B per supercell, which has also been reported for both rutile and anatase phases [15,63].Our calculations confirm that one substitutional doping yields a paramagnetic material with a magnetic moment of 2 μ B , but only 0.70 μ B on the C atom was measured within the Wigner-Seitz radius of 1.0 Å.The experimental value observed by Ye et al. [64] was 0.0236 μ B per carbon in carbide state, that is, about 30 times less than the theoretical value.

N-Doped TiO 2 .
The N atom has one electron less than O, meaning that charge transfer by Ti will not fulfill all the N 2p orbitals, leaving one unpaired electron and also an empty spin-orbital.This process generates N 2p localized occupied states at the top of the VB and one empty state in the gap, near the VB (see Figure 3 and S3).
The empty states within the bandgap are not affected by the U correlation, which means that they are not hybridized with Ti 3d empty orbitals, neither the bulk nor the surface.These results agree with the data reported by Lin et al. [65] for anatase and Atanelov et al. [15] for rutile phase.For N-doped TiO 2 , it is easier to excite electrons from the surface (~0.4 eV) than from the bulk system (~1.0 eV), which are in agreement with previous results [66].
On the surface, there is a reduction of the energy bandgap to 2.30 eV (GGAU), whereas the reported experimental value is 2.5 eV [67].The substitution of O by N leaves an unpaired 4 International Journal of Photoenergy electron into the system, yielding a magnetic moment of 1 μ B per supercell, but only 0.503 μ B on the N atom was measured within the Wigner-Seitz radius of 0.979 Å.An experiment for rutile crystals reported a paramagnetic behavior for the N-doping [68]; our calculations also reproduced this result for the N-doped anatase surface and bulk.
The required energy to obtain charge carries is reduced regarding the pristine TiO 2 due to localized states within the bandgap generated by dopants.C-and N-doped TiO 2 have localized states within the bandgap, reducing the excitation energy, but it has been reported that there is not a direct correlation between the excitation energy to form charge carriers and the photocatalytic activity [69].The performance of the catalyst also depends on the recombination time, that is, the lifetime before holes and electrons are destroyed by mutual interaction.The position of the localized states within the bandgap affects the recombination time [32].

F-Doped TiO 2 .
The F atom has one electron more than oxygen.The substitution of F − instead of O 2− in the lattice leaves one unpaired electron; F can accept only one electron to acquire its closed shell configuration [36].There are three possible configurations for F-doped TiO 2 : (i) the unpaired electron locates in the surrounds of the fluorine; (ii) fluorine transfers the one electron excess to their neighbors, or (iii) the unpaired electron delocalizes within the CB.As Di Valentin et al. [70] have pointed out, the last two options have the same probability of occurrence.
Our results show that the Fermi level is displaced towards the CB, and for the bulk and surface, the GGA method delocalizes the electron in the conduction band.For the bulk system, adding the U correlation parameter to the bulk system localizes occupied states below the CB, separated by 0.6 and 1.31 eV for the GGA/GGAU and GGAU methods (see Figure 4(a) and S4(a)).These occupied states are Ti 3d orbitals, so it confirms the charge transfer and the reduction from Ti 4+ to Ti 3+ .The surface system, with the GGA/GGAU scheme, does not bring a clear picture of these Ti 3+ states; it seems these states are degenerated with the Ti surface states.Nonetheless, in the GGAU relaxation, the Ti 3+ states are separated from the CBM, so we can observe the different nature of the surface Ti and Ti 3+ states.The fluorine states, for the surface and bulk systems, are located at the VB bottom (see Figure S4).
Fluorine inhibits the full charge transfer from the Ti atoms, leading one Ti 3+ atom.These states are depicted on 5 International Journal of Photoenergy the DOS for the small dopant concentration using the GGAU scheme, which localizes an occupied state without F 2p orbital participation; this means the electron is in the Ti 3d orbital.
The F-doping TiO 2 system must be treated with caution because the F-doping creates Ti 3+ states, that is not adequately described by GGA functionals, as in the case of the oxygen vacancies [71], but hybrid functionals recover the physical picture [16].Here, it has been shown that the PBE functional gives delocalized solutions with the bulk and surface models, which is consistent with reports where F distributes its unpaired electron towards neighbors Ti atoms [16,35].The GGAU scheme recovers the localization of Ti 3+ with a lower computational cost compared with hybrid functionals.

S-Doped TiO 2 .
We have argued that the number of localized states-empty and occupied-and its electron distribution is directly related to the electron configuration of the dopant p orbitals; thus, we finally examined an element which is in the same oxygen group, the sulfur.
Sulfur has 16 electrons and presents a similar electron distribution and oxidation state like oxygen, which leads to an energy bandgap with no empty states as Figure 5 shows    1) is due to the occupied states that sulfur introduces at the top of the VB; it is important to note that spin-up and spin-down DOS are symmetrical (Figure S5) meaning all orbitals are fully occupied, confirming our configuration model.For the bulk system, these states are localized near the VB edge; this means there is some sulfur occupied states that show some repulsion from the occupied O 2p orbitals.This behavior is reflected in the high formation energy for S-doping (5.81 eV), as showed in Table 2. On the surface, in all cases, these states are closer to the VB than in the bulk.For the GGA/GGAU scheme, O 2p, S 3p, and Ti 3d occupied states are mixed just below the Fermi level.In the GGAU case, the occupied states under Fermi level present S 3p and Ti 3d character only.
The covalent radius of S (1.02 Å) differs considerably from the O atom (0.73 Å), and then the orbital O 2p and S 3p hybridization is inhibited as GGAU scheme shows.The S-doping generates some occupied localized states, mainly S 3p character, below the Fermi level.However, although these states are occupied, they do not overlap with the VB (see Figure 5(a)).This may explain why experimentally high concentrations of sulfur are needed to enhance the photoactivity in the pollutant degradation [34].If the sulfur substitution is located far from the surface, the charge carriers do not reach the surface, inhibiting the degradation activity.At high concentration, the probability that dopants reach the surface increases as well as the reactivity.This fact is carried out with large formation energies (5.81 eV, bulk) due to significant structural changes by S covalent radius.
The GGA/GGAU and GGAU methods give, for almost all cases, a good picture for the localized electronic states within the bandgap.However, the GGA/GGAU methodology has to be carefully treated because of the lack of ionic relaxation some states may not be well localized.It has been reported that the Hubbard U parameter depends heavily on the used geometry, so we encourage doing the full optimization GGAU methodology.
The Hubbard correction slightly widens the bandgap for all systems (see Table 1).U correlation is mandatory to describe TiO 2 systems if there is a hybridization between the dopant and Ti 3d orbitals.The Hubbard model is also necessary when unpaired electrons occupy Ti 3d states because the extra electron repulsion in the valence electrons localizes states below the CBM.

Oxygen Vacancies on Doped TiO 2 (101).
We also studied the effect on the electronic structure of oxygen vacancies on the doped TiO 2 (101) surface systems.The formation energy of one oxygen vacancy follows the order: F (5.740) > S (5.734) > C (4.084) > N (3.963 eV).Experimentally, the oxygen vacancies are promoted when the surface is doped with N and C, which is consistent with our theoretical results [72][73][74].
Removing one oxygen atom from the pure TiO 2 surface yields Ti 3+ states that are below the conduction band [71,75] (see Figure 6(e)).C-doping shows a different behavior, that is, the two electrons available after removing the neutral oxygen go to the C 2p orbital (empty states generated by C-doping), above the valence band (see Figure 6(a)).Since oxygen and sulfur are isoelectronic, the oxygen vacancy on the S-doped system generates Ti 3+ states just as with the pristine TiO 2 (101) (see Figure 6(d)).
For F-doping, there are three intrabandgap states, and one of them corresponds to the extra electron of fluorine compared to oxygen, which is in agreement with Czoska et al. [16] results.The other two states correspond to the ones generated by the oxygen vacancy.The electrons from the oxygen vacancies create Ti 3+ species near the Fermi level; the Ti 3+ state created by the F electron is the nearest to the valence band.
For N-doping, one electron from the oxygen vacancy locates at N 2p orbital; the other creates a Ti 3+ state near the CB (see Figure 6 7 International Journal of Photoenergy catalytic efficiency enhancement [74].Finazzi et al. [66] reported a similar behavior when substituting two O atoms by N; the unpaired electrons fill the dopant N 2p states giving a closed shell configuration.The synergy between the dopants and oxygen vacancies cleans the gap, but for nitrogen aside to clean the gap, these new states are well mixed with the O 2p states from the valence band, so it enhanced the charge mobility. For the C-doped TiO 2 bulk system, Kamisaka et al. [76] concluded that oxygen vacancies diminish the photocatalytic activity by filling the holes generated by the dopant, inhibiting the charge mobility.In our case, for the surface TiO 2 (101) anatase, C 2p states lie above the valence band, which is beneficial for the photocatalytic activity.Because the C dopant is localized near the surface, the generated charge carriers will already be at a reactive site, that is, these localized states may enhance the charge carrier lifetime.
3.6.Optical Response of Doped TiO 2 (101) with One Oxygen Vacancy.The optical absorption of the C-, N-, F-, and S-doped surface TiO 2 (101) was also determined (see Figure 7(a)).To correct the DFT gap underestimation, the optical absorption also includes the scissor operator (with a value of 0.44 eV).This method has been successfully applied to several materials [77][78][79].The same scissor operator is used for the doped surface with and without oxygen vacancies.
The UV-visible spectrum (Figure 7(a)) agrees with the experimental data reported by Chen et al. [80], where the C-doping shows the maximum absorbance.In our case, there is a shoulder at λ max = 500 nm (blue), which corresponds to transitions from valence band O 2p states to C 2p empty localized in the center of the bandgap (see Figures 3(b) and 6(a)).When the oxygen vacancy is considered, the optical activity in the visible region is significantly increased for doped TiO 2 , which favors the generation of charge carriers using visible light (see Figure 7(b)).
Due to that oxygen vacancies are present in almost all synthesized TiO 2 materials, the simultaneous presence of main group elements and one oxygen vacancy is frequent.According to experimental results [80], when the nitrogen concentration increases, it also rises the oxygen vacancies and Ti 3+ , leading to the enhancement of photocatalytic activity.From our theoretical results, N-doping presents the lowest formation energy of oxygen vacancies (3.963 eV).For the N-doped system with an oxygen vacancy, there are two shoulders at λ max ~550 and 750 nm, which correspond to transitions from Ti 3d occupied states to Ti 3d empty states (see Figure 6(b)).
The F atom hinders the formation of oxygen vacancy.These results contrast with Hattori et al. [81] results.They stated that F ion promotes the formation of oxygen vacancies.The partial DOS (Figure 6(c)) shows that the Fermi level is displaced about 0.2 eV from the conduction band when an oxygen vacancy is present, which does not reduce the TiO 2 chemical potential.The F-doping without oxygen vacancy presents a similar optical activity than TiO 2 with oxygen vacancies, which agrees with experimental evidence that F-TiO 2 can hardly displace the light absorption towards the visible region.In spite of this, it has been reported that F-doped TiO 2 has catalytic activity under visible light.It is speculated that this activity may be due to other species like F 2 or HF adsorbed on the surface [36,82].
For all the studied cases, oxygen vacancies on the TiO 2 (101) surface displace the light spectrum towards the visible region.A severe increase in the optical absorption intensity is obtained following the order C > N > F > S. The reason that F and S do not present a high photocatalytic efficiency is that they promote Ti 3+ states; the charge carriers have not the oxidation potential required to form the OH   International Journal of Photoenergy absorbance of C-doping in the visible light (Figure 7(b)) as well as the localized state above the bandgap explains why it is five times more efficient than N-doping in the degradation of 4-chlorophenol when it is used as an artificial light (λ ≥ 455 nm) [33].

Conclusions
The electronic structure of the bulk and surface (101) models of anatase TiO 2 doped with the main group elements C, N, F, and S, with and without oxygen vacancies, was studied using DFT and the Hubbard U approach.
The GGA approach alone underestimated the bandgap for all cases, with a systematic failure of the method.The best and simplest method for describing the doped TiO 2 electronic structure is the ionic relaxation of the TiO 2 models with the GGA + U scheme, which obtains localized solutions at the same computational cost of the GGA approach.
Two ways for reducing the TiO 2 bandgap were identified.The first mechanism is broadening the VB or CB.The presence of occupied states near the VBM reduces the bandgap, and then less energy is required to excite electrons from VB to CB.The S-doping TiO 2 (101) is an example of that mechanism.A similar process can occur, but in the CB when the TiO 2 (101) surface is formed, the exposed Ti atoms present undercoordination, giving rise to empty states very close the CBM.
The second mechanism for reducing the bandgap is to generate localized states in the gap.However, this process has the inconvenience that these states may act as recombination centers.For example, the C-and N-doping form localized empty states in the gap.For the C-doping, the surface TiO 2 (101) presents a "cleaner" gap than the bulk TiO 2 , which is favorable to eliminate recombination centers.Finally, the F-doping represents a similar case to oxygen vacancies, where the fluorine atom promotes the Ti 3+ species formation, which appears below the CBM.
The number of valence electrons of the dopant element determines the number of states and its position within the gap when the O atom is replaced.
Both doping and oxygen vacancies on TiO 2 (101) displace the light spectrum towards the visible region.A great increase in the optical absorption intensity is obtained with the following order C > N > F > S. Therefore, the high catalytic activity of C-doping using visible radiation is consistent with its high absorption intensity generated by oxygen vacancies on the surface.

Figure 1 :
Figure 1: Doping sites on anatase TiO 2 .(a) The 3 × 3 × 3 bulk supercell.(b) The 2 × 1 × 1 surface in the (101) direction with four layers.Both models constituted by 48 atoms.One three-coordinated O atom was replaced by C, N, S, or F atom.Red balls are O atoms; gray ones are Ti.Black balls indicate the substitution site, and green balls show the oxygen vacancy.

3. 1 .Figure 2 :
Figure 2: The total and partial density of states of the three relaxation methodologies for C-doped anatase TiO 2 .(a) The bulk supercell.(b) The TiO 2 (101) surface.The Fermi level corresponds to the zero energy.

Figure 3 :
Figure 3: The total and partial density of states of the three relaxation methodologies for N-doped anatase TiO 2 .(a) The bulk supercell.(b) The TiO 2 (101) surface.

Figure 4 :
Figure 4: The total and partial density of states of the three relaxation methodologies for F-doped anatase TiO 2 .(a) The bulk supercell.(b) The TiO 2 (101) surface.

Figure 5 :
Figure 5: The total and partial density of states of the three relaxation methodologies for S-doped anatase TiO 2 .(a) The bulk supercell.(b) The TiO 2 (101) surface.

Figure 6 :
Figure 6: The total and partial density of states for pure and C-, N-, S-, F-doped anatase TiO 2 (101) with one oxygen vacancy.Results obtained with the GGAU methodology.

Table 1 :
Summary of bandgaps (E g ) for the bulk and surface models for all doped and pristine TiO 2 .Energy units are in eV.

Table 2 :
Formation energy for anatase TiO 2 doped with the main group elements.Results obtained with the GGAU scheme.
g reduction (see Table