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. 2023 Oct 2;127(40):20128–20136. doi: 10.1021/acs.jpcc.3c04665

Role of N Doping in the Reduction of Titania Nanostructures

Elena R Remesal 1, Ángel Morales-García 1,*, Francesc Illas 1
PMCID: PMC10578348  PMID: 37850083

Abstract

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The effect of N-doping of titania (TiO2) nanoparticles (NPs) on their reduction through neutral O vacancy (Ovac) formation is investigated using all electron density functional theory-based calculations, including hybrid density functionals, and taking the bipyramidal anatase (TiO2)84 NP as a realistic model. The location of the N dopant is systematically analyzed, including O substitution in the (TiO2)84 structure and N occupying interstitial regions. Our computational study concludes that interstitial N doping is more favorable than N substituting O atoms and confirms that the presence of N reduces the energy gap. In the N-doped NP, Ovac formation is more favored than in undoped NP but less than in the N-doped bulk, which has important consequences.

Introduction

During the last decades, an intense research activity has been carried out around semiconducting transition metal oxides (i.e., TiO2, ZnO, WO3) and their possible heterostructures formed by mixing configurations.1 These materials constitute the leading families of photocatalytic materials with implications in energy and environmental science.2,3 Since the pioneering works by Fujishima and Honda4 and Schrauzer and Guth,5 TiO2 has become one of the most promising photoactive materials, especially when nanostructured, due to its intrinsic electronic properties attributed to a plentiful availability, nontoxicity, chemical stability, and high reactivity.6 Nevertheless, TiO2 exhibits important limitations such as a wide energy gap and fast recombination of photogenerated electrons and holes, which cause a restrictive light absorption.7,8 These drawbacks have greatly motivated further research aimed at developing and designing TiO2-derived materials active in the visible-light region of the electromagnetic spectrum with low recombination.9−11

In the last years, numerous theoretical and experimental studies on TiO2 have been published following different strategies to overcome these drawbacks, aiming at improving the photocatalytic performance.12−16 One of these strategies is doping stoichiometric TiO2 polymorphs with nonmetals such as C, N, or S.17−20 Nonmetal doping in the main has been found to be more favorable than doping with the metal counterpart due to the low rate of recombination center formation, where the photogenerated species are annihilated. Furthermore, electronic analysis confirms the presence of additional electronic states in between the valence and conduction bands of doped TiO2 promoting the reduction of the energy gap and, consequently, the activation under visible-light illumination.10

Most of these investigations focused on the structural and electronic properties, and just a few of them paid attention to how nonmetal doping affects the TiO2 reducibility through the formation of oxygen vacancies (Ovac). In this context, Di Valentin et al.21 have investigated the effect of carbon impurities on the electronic band structure of bulk titania polymorphs (i.e., anatase and rutile) with respect to the oxygen partial pressure. Those results reported that the oxygen vacancy formation energy decreases up to 20% in the presence of interstitial carbon and more than 50% in the presence of substitutional carbon. This effect might be ascribed to the tendency of substitutional C atoms to accept the excess electrons generated from oxygen vacancy formation. These authors also investigated the electronic and optical properties of bulk TiO2 modified by substitutional N.22 From first-principles calculations, they concluded that N-doping leads to different behaviors depending on the crystalline structure. For instance, N-doping promotes red and blue shifts of the absorption edge in anatase and rutile, respectively, thus inducing different levels of photoactivity. A subsequent study aimed at characterizing the nature of paramagnetic species in N-doped TiO2 polymorphs23 concluded that one of the consequences of nitrogen doping is the reduction in the formation energy of an oxygen vacancy, in some cases by up to 80%. The energetically favorable charge transfer from Ti3+ ions to N results in a lower formation of the oxygen vacancy compared to the undoped counterpart.24 This finding is puzzling because, as oxygen vacancy sites are efficient electron traps, it seems to indicate that N-doped titania, even exhibiting a reduced gap, will easily form electron traps that are detrimental to the photocatalytic activity.

Several additional publications have characterized the effect of the dopant location on TiO2 surfaces and nanostructures. Recently, Di Liberto et al.25 investigated the N-doping of the exposed (001)/(101) surfaces of anatase TiO2 heterostructures. They found that N at the (001) side of the interface constitutes the most stable doping arrangement. On the other hand, Kakil et al.26 demonstrated that subsurface N doping in TiO2 anatase is depth-dependent for both substitutional and interstitial N, and that N location depends on the nanocrystal facet. Moreover, they investigated N-doping of Ti9O18 and Ti28O56 nanoclusters and found that the interstitial N formation energy is lower than that of substitutional N. Additional theoretical calculations predicted a decreasing of the band gap due to the presence of nitrogen, in agreement with results from UV–vis spectroscopy.27 Combining the density functional theory (DFT) calculations and extended X-ray absorption fine structure (EXAFS) techniques, Ceotto et al.28 studied the nitrogen location in nanocrystalline N-doped TiO2 and concluded that, at a low concentration of N-doping, N atoms substitute O atoms, whereas at higher N-doping concentrations, oxygen vacancies appear.

A common feature of most of the previous computational studies is the use of bulk or extended surface models. However, in real nanostructured finite systems, exhibiting a variety of morphologies,29 extended surface models represent solely their facet regions, but cannot provide information regarding other regions such as edges, corners, or apical sites, which can actively participate in the formation of the N-doped titania nanostructures as well as in the vacancy formation thereon.30 Hence, the use of realistic nanostructure models appears necessary to account for the chemistry of these systems. The goal of the present study is precisely to analyze N-doping in TiO2 NPs and its effect on the oxygen vacancy formation.

Computational Strategy and Titania Models

The realistic bipyramidal (TiO2)84 anatase nanoparticle (NP), well-defined in the scalable regime30 with a Wulff-like equilibrium geometry31 (Figure 1), has been selected to carry out a systematic exploration on N-doping and its effect on its reducibility. This NP model is representative of those found in most photocatalytic oriented experiments29,32 that do not rely on the use of single-crystal samples with well-defined surfaces. This (TiO2)84 bipyramidal model exposes the most stable (101) facets, only conferring it a high structural stability. On this model, different regions are selected to generate the N-doped nanostructures. The investigated regions are located in apical (labeled as T), edge (E), facet (F), and inside (I) portions, as shown in Figure 2. Here, one needs to distinguish different O atoms as there are different atomic environments. In particular, O atoms with 2-fold (O2c) and 3-fold (O3c) coordination; the former are located at the shell of the bipyramid (i.e., apical, edges, and facets), while the latter are mainly located at the core of the nanoparticle. On the other hand, the interstitial dopant is located inside the channel of the structure visualized in the side view (Figures 1 and 3). Further details regarding the notations used to describe the relevant atomic environment are introduced later and clearly explained for each particular case. To inspect the stability and electronic structure of the N-doped (TiO2)84 NP, we perform density functional theory (DFT)-based calculations by explicitly including all electrons with the electron density described through a numerical atom-centered orbital (NAO) basis set as implemented in the Fritz Haber Institute ab initio molecular simulations (FHI-aims) code.33 The Perdew–Burke–Ernzerhof (PBE)34 density functional within the generalized gradient approximation (GGA) was selected to describe the thermodynamic stability of N-doped titania nanostructures. Calculations were carried out using the tier-1/light grid basis set. For TiO2 systems, this setting leads to results of Gaussian type orbital (GTO) valence triple-ζ plus polarization basis set quality.35 The convergence threshold for atomic forces in relaxation of all atoms in the N-doped and pristine (TiO2)84 nanostructures was set to 10–3 eV Å–1. Due to the presence of relatively heavy Ti atoms, relativistic effects were explicitly included through the zero-order regular approach (ZORA).36,37

Figure 1.

Figure 1

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Side and top views of (TiO2)84 NP. This nanostructure exhibits a bipyramidal morphology with (101) surfaces in the eight facets. Red and cyan spheres correspond to oxygen and titanium atoms.

Figure 2.

Figure 2

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Side and top views of the representative optimized Ns-doped (TiO2)84 NPs. Cyan, red, and blue spheres denote titanium, oxygen, and nitrogen atoms, respectively. Note that the N atom has been represented by a double radius to better visualize the doping site.

Figure 3.

Figure 3

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Side and top views of the representative optimized Ni-doped (TiO2)84 NPs. Note that N atoms have been represented with a double radius to better visualize the doping site. The color scheme is similar to that in Figure 2.

To examine the stability of N-doped TiO2 NPs, we consider the formation energy of substitutional (Ns) and interstitial (Ni). The formation energy labeled as Ef is defined as

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where EN@Ti84O167 and EN@Ti84O168 correspond to the total energies of substitutional and interstitial doped NPs, respectively; ETi84O168 is the total energy of the undoped NP; and EN2 and EO2 are the total energies of the N2 and O2 molecules in their electronic ground state, which for the O2 molecule is a triplet state. This definition of reference state of element is consistent with previous studies.19,26,35 Consequently, the nitrogen molecule is taken as a convenient reference, and from the energy balance in eqs 1 and 2, we do not expect any difference when employing a different source of nitrogen. In fact, different nitrogen precursors are used in experimental studies such as ammonium hydroxide or ammonia. However, these lead to additional products, thus complicating the underlying basic chemistry, and, therefore, are not considered in the present work.

On the other hand, the oxygen vacancy formation energy Ef,vO in doped titania nanostructures is defined as

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where ED@Ti84O168 and ED@Ti84O167 are the total energies of a doped (TiO2)84 NP, with either substitutional or interstitial N, and its reduced counterpart, respectively. In all cases, the titania nanostructures are fully relaxed. According to eq 3, Ef,vO > 0 corresponds to the extra energy required for removing a neutral single oxygen relative to the O2 molecule; in other words, the energy required to reduce the N-doped (TiO2)84 NP.38

To analyze the electronic structure, it is necessary to recall that generalized density functionals such as PBE systematically underestimate the energy gap of semiconducting materials.39 To overcome this deficiency, we rely on the PBEx hybrid density functional containing 12.5% of Fock exchange, which accurately reproduces the structural and electronic properties on anatase and rutile bulk titania phases.40 Since the PBE structures for these systems are generally accurate,41 single-point calculations with the PBEx functional are carried out at the PBE geometry. Analysis of the effect of the N atom on the energy gap relies on the Kohn–Sham energy levels of the frontier orbitals instead of density of states (DOS) plots. This is because the scrutinized systems are finite and, hence, exhibit discrete levels, and because a DOS analysis includes an artificial broadening that can somehow bias the results.

Results and Discussion

Formation of N-Doped (TiO2)84 Nanostructures

The formation of N-doped titania nanostructures is investigated using the (TiO2)84 NP depicted in Figure 1 as a suitable model and analyzing O substitution by N (Ns) and interstitial N (Ni). In each case, various configurations exist, which are analyzed systematically following that recently published by some of us investigating C-doped TiO2 NPs.19 For Ns, six different positions in the apical (T), facet (F), edges (E), and inside (I) of the NP are investigated as highlighted in Figure 2. The formation energy of the corresponding N-doped NPs is reported in Table 1, where values are in the 4.70–5.44 eV range. Thermodynamically speaking, the I-3-1 N-doped configuration is the one most favorable, while T-1 is the less one. These results are consistent with a previous analysis of C-doped (TiO2)84 NPs,19 where the I-3-1 C-doped NP is the most stable regardless of the oxygen chemical potential.

Table 1. Formation Energy of N-Doped (TiO2)84 NPs Calculated Following Equations 1 and 2 a.

doping site Ef (eV) doping site Ef (eV)
Ns-E-2 5.05 Ni-I-1 4.09
Ns-F-2 5.16 Ni-I-1b 2.35
Ns-F-3 4.90 Ni-I-2-1 3.20
Ns-I-3-1 4.70 Ni-I-2-2 2.62
Ns-I-3-2 5.06 Ni-I-2-1b 2.96
Ns-T-1 5.44 Ni-I-3-1-1 5.36
    Ni-I-3-1-2 3.59
    Ni-I-3-1-3 4.20
    Ni-I-3-2-1 4.15
    Ni-I-3-2-2 2.76
    Ni-I-3-2-3 4.08
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a

Ns and Ni denote substituting O by N atom and interstitial positions, respectively.

At this point, it is interesting to compare the cases of N- and C-doping. The formation of Ns-doped titania nanostructures is energetically more favorable than the formation of C-doped ones (CO).19 Although there is no clear correlation between the formation energies of N- and C-doped (TiO2)84 NPs, the N-doped titania formation energy range is almost twice lower than that corresponding to C-doped NPs. Moreover, it is also of interest to compare our results with those involving N-doping of bulk and extended surface models. For the anatase phase, the reported Ns formation energy is ∼5 eV, independently of nitrogen concentration.42 For the (001) and (101) anatase surfaces, the most stable position is located near the interface region, although the location on the (101) surface is thermodynamically preferred than on the (001) one.25 In general, the present results for finite titania NPs show similar Ns formation energies to those in bulk and surface models, with values of ∼5 eV. This seems to indicate that the (TiO2)84 NP is large enough to mimic the facet sites of extended surfaces.

We now focus on N-doping at interstitial regions (Ni) as depicted in Figure 3. Here, the N atom localizes in one of the existing four channels (see Figure 1, side view) moving from the apical to the equatorial region. The number of sites able to accommodate the N atoms increases in the same direction, as expected from the increasing thickness at the equatorial region where the N atom finds a larger space. This is the reason why there is only one site in the apical region labeled as Ni-I-1, and three sites in the equatorial channel (Ni-I-3-2-3). All of these sites are located inside the nanoparticle and thus, only the I capital letter is used to denote them, with the three digits indicating the position with respect to the apical region in terms of proximity, the interstitial channel, and the position inside the channel, respectively. In some cases, the b letter is included in the notation to indicate that the N is near the surface of the (TiO2)84 NP. Table 1 lists the formation energies of N-doped titania nanostructures in the interstitial region ranking between 2.35 and 5.36 eV. The structures I-1b, I-2-2, and I-3-2-2 are the most favorable situations showing the lowest formation energies of 2.35, 2.62, and 2.76 eV, respectively. From these results, one may conclude that the Ni is energetically more favorable than Ns. Compared to a similar case of C-doping (Ci), it is clear that Ni is by far more favorable and the Ci formation energies are around 8.5 eV.19 The comparison to the results from extended models is also interesting. There, Ni doping of the anatase bulk phase requires 4.3 eV, whereas a lower value of 3.7 eV is required to insert Ni at surface sites. Clearly, the formation of Ni-doped titania nanostructures is more favorable than either the bulk or the extended surface site, although for such extended systems Ni is also preferred to Ns.42

Once we have discussed the formation of N-doped (TiO2)84 NPs, it is important to analyze the effect that N doping has on the resulting electronic structure. To this end, we focus on the electronic structure arising from the hybrid PBEx density functional. As expected, the presence of N in the (TiO2)84 NP results in addition of energy levels with concomitant electronic modifications that decrease the energy gap with respect to the undoped (TiO2)84 NPs (see Table S1 of Supporting Information, SI). This effect has also been reported for the C-doped (TiO2)84 NP, but with significant differences. In general, C doping leads to a larger reduction of the energy gap. In the N-doped structures, Ns promotes a stabilization of the Kohn–Sham LUMO orbital energy relative to that of the undoped NP, resulting in the reduction of the energy gap at 1.9 eV, almost half of the value corresponding to the undoped nanostructure (3.60 eV). This trend is systematically observed except for the T-1 site, as shown in Figure 4. On the other hand, in most of the Ni-doped (TiO2)84 NPs, the energy gap decreases due to the addition of extra electrons, which raises the HOMO levels (Figure 5). The lowest energy gap is found for I-3-1-1 and I-3-1-2 in the equatorial cases (0.41 and 1.68 eV), whereas it is larger for the edge E-2 (1.78 eV) and inside I-3-1 and I-3-2 regions (1.88 and 1.83 eV).

Figure 4.

Figure 4

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Kohn–Sham orbital energy level diagram of Ns-doped (TiO2)84 NPs obtained from DFT based calculations through the hybrid PBEx functional. The dotted lines correspond to Kohn–Sham orbital energy levels of bare (TiO2)84 NP.

Figure 5.

Figure 5

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Kohn–Sham orbital energy level diagram of Ni-doped (TiO2)84 NPs obtained from DFT based calculations through the hybrid PBEx functional. The dotted lines correspond to Kohn–Sham orbital energy levels of bare (TiO2)84 NP.

Here, one may wonder whether the effect of the N doping is analogous (or not) to the effect of another nonmetal doping such as C. To answer this question, we extend our previous analysis19 to investigate how doping affects the electronic structure and to make systematically the comparison between these two cases. The calculations of C-doped titania nanostructures were carried out without using spin-polarized calculations because C has an even number of electrons different from N that exposes an unpaired number as mentioned earlier. This extended analysis includes the formation of titania-doped structures by substitutional C atoms replacing O atoms, CO, and interstitial C atoms, Ci, both having similar effects (see Figures S1 and S2). For instance, consider CO for the I-3-2 inside, T-1 apical, and F-3 facet together with the I-1, I-2-1, I-2-2, I-3-1-1, I-3-1-3, I-3-2-1, and I-3-2-2 interstitial sites. This notation follows the same sequence described earlier when discussing N-doping at interstitial regions. In general, the LUMO energy orbital is unaltered by the presence of the C doping, but in most of the cases, the HOMO energy rises due to localized occupied states in the energy gap. These impurity states modify the absorption range, which is consistent with the experimental absorption edge shift toward the visible up to almost 1.7 eV.43 In general, the energy gap decreases more than 2 eV with respect to (TiO2)84 NP by the presence of the C-doping agent. The face and apical position of CO, F-2 and T-1, have the lowest energy gap of 0.88 and 0.83 eV, respectively, followed by the internal position, I-3-2, with 1.13 eV. This is the only case where the LUMO energy orbital is stabilized. Finally, it is necessary to point out that the largest reduction of the energy gap is observed when the C atom locates in the interstitial regions close to the equatorial area, like I-3-1-1, I-3-1-2, I-3-1-3, and I-3-2-2, whose formation energy ranges between 0.22 and 0.31 eV.

Formation of Reduced N-Doped (TiO2)84 Nanostructures: Formation of Oxygen Vacancies

It has been well established that the presence of certain dopants on semiconducting oxide materials favors somehow their reducibility by facilitating the generation of oxygen vacancies.22−24 It has previously been shown that the formation of oxygen vacancies (Ovac) in undoped (TiO2)84 NP requires energies between 3.63 and 4.54 eV.38 In that study, the NP region where vacancy creation is the most favorable is in the subsurface region. Taking advantage of our previous analysis on the bare system, we investigate here the influence of N-doping on the reducibility of the N-doped (TiO2)84 NP. For completeness, we also comment on the influence of C-doping on the NP reducibility.

Studying the effect of Ns doping on Ovac formation required fixing the N atom in one of the following sites: T-1, E-2, F-2, F-3, I-3-1, and I-3-2; then, the octahedral O atom was removed from the other sites. Therefore, for each N-doped (TiO2)84 NP, one has five different sites to create Ovac. For example, one can locate the N atom in the E-2 site and the Ovac can be generated in T-1, F-2, F-3, I-3-1, or I-3-2 site. An analogous strategy is followed in case of Ni doping here, fixing the N position and considering Ovac formation on the possible symmetry distinct sites. The results of the corresponding series of calculations are listed in Tables 2 and 3. Starting with the Ns case (Table 2), the Ovac formation energy ranges between 1.81 and 5.15 eV, with most cases exhibiting formation energies below 3.80 eV, thus confirming that the presence of N in the structural framework of the (TiO2)84 NP favors its reducibility, as found for periodic models.22−24 More importantly, by comparing the Ovac formation energies of the titania nanostructures,38 it turns out that this reduction is larger in the case of the TiO2 NPs. To rationalize somehow this low Ovac energy formation in the N-doped NP, we consider the distance between the vacancy and the N dopant atom, denoted as dN-Vo, which is also listed in Table 2. Unfortunately, there is no systematic correlation of all cases investigated, but interesting information emerges when analyzing each case individually. There are six cases in which the lowest Ef,vO correlates with the shortest dN-Vo distance. Using a Ovac/N-atom notation to define simultaneously the position of Ovac and N atom, the six cases above are E-2/I-3-2, F-2/I-3-2, F-3/I-3-2, E-2/I-3-2, I-3-2/F-2, and T-1/I-3-1. In this shortlist, the Ef,vO is between 1.81 and 2.71 eV. Interestingly, the inside regions are consistently involved in all of these cases. The I-3-2 site is able to hold the doping of N atom by substituting the O atom. If we spotlight on the oxygen vacancy energy formation on face (F-2, F-3) and apical (T-1) regions, we can observe a correlation between the vacancy energy formation and dN-Vo distance, which grows consistently as dN-Vo grows (see Figure 6). Compared to the undoped nanostructures, Ovac formation (solid lines in Figure 6) is energetically more favorable in N-doped titania nanostructures by ∼1 eV. Finally, for the Ni-doped (TiO2)84 NPs, Table 3 indicates a vacancy formation energy between 2.11 and 4.91 eV. As mentioned earlier, the presence of Ns favors the NP reducibility, but its presence in the interstitial region has a less effect. The most favorable situation gives formation energies of 2.11 and 2.86 eV, when the vacancy locates at the internal position (I-3-2) or apical (T-1) area. Also, the I-3-1 vacancy position is the only one that is practically unaffected by the dopant agent. Finally compared with previous studies, for the Ni cases, the presence of the dopant has less effect on reducibility than reported for the bulk, where the oxygen vacancy formation energy in the presence of Ni was around 0.6 eV.24

Table 2. Formation Energy of the Oxygen Vacancy (Ef,vO, in eV) of Ns-Doped (TiO2)84 NPa.

Ovac N site dN-Vo Ef,vO Ovac N site dN-Vo Ef,vO
E-2 F-2 11.50 2.85 I-3-1 E-2 13.16 4.33
F-3 9.00 2.76 F-2 7.59 3.76
I-3-1 13.06 2.93 F-3 15.42 3.84
I-3-2 8.26 2.71 I-3-2 9.46 3.73
        T-1 3.16 5.15
F-2 E-2 11.50 3.16 I-3-2 E-2 8.33 2.24
F-3 9.33 2.75 F-2 6.73 1.86
I-3-1 7.47 2.73 F-3 7.92 1.96
I-3-2 6.75 2.50 I-3-1 9.39 1.90
        T-1 12.15 3.76
F-3 E-2 9.03 3.03 T-1 E-2 14.75 3.25
F-2 9.24 2.72 F-2 9.12 2.68
I-3-1 15.32 2.76 F-3 17.30 2.76
I-3-2 7.84 2.49 I-3-1 3.03 1.81
        I-3-2 12.16 2.65
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The Ovac and N notation indicates the sites in the nanoparticle where the oxygen vacancy and the N doping locates, respectively. The dN-Vo (in Å) corresponds to the distance between Ovac and N atom.

Table 3. Formation Energy of the Oxygen Vacancy (Ef,vO, in eV) of Ni-doped (TiO2)84 NPa.

Ovac N site dN-Vo Ef,vO Ovac N site dN-Vo Ef,vO
E-2 I-1 10.60 3.33 I-3-2 I-1 6.78 2.25
I-1b 9.95 3.82 I-1b 6.99 2.86
I-2-1 8.03 3.22 I-2-1 5.74 2.40
I-2-1b 5.22 3.66 I-2-1b 5.17 2.85
I-2-2 4.59 3.23 I-2-2 5.97 2.11
I-3-1-2 8.94 4.12 I-3-1-2 2.74 3.33
I-3-2-2 3.14 4.08 I-3-2-2 6.41 2.97
F-2 I-1 6.94 3.19 I-3-1 I-1 3.15 3.63
I-1b 4.95 3.63 I-1b 3.70 4.91
I-2-1 5.96 3.10 I-2-1 5.10 4.30
I-2-1b 6.26 3.61 I-2-1b 8.67 4.73
I-2-2 10.90 3.13 I-2-2 6.98 4.09
I-3-1-2 5.63 3.36 I-3-1-2 10.45 4.78
I-3-2-2 11.99 3.73 I-3-2-2 11.58 4.72
F-3 I-1 13.28 3.17 T-1 I-1 5.90 2.76
I-1b 11.97 3.65 I-1b 5.71 3.54
I-2-1 11.04 3.13 I-2-1 7.42 2.81
I-2-1b 7.96 3.62 I-2-1b 10.41 3.73
I-2-2 12.26 3.08 I-2-2 9.27 3.09
I-3-1-2 5.88 3.97 I-3-1-2 12.86 4.16
I-3-2-2 10.07 3.73 I-3-2-2 13.66 3.76
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The Ovac and N notation indicates the sites in the nanoparticle where the oxygen vacancy and the N doping locate, respectively. The dN-Vo (in Å) corresponds to the distance between Ovac and the N atom.

Figure 6.

Figure 6

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Trends between Ef,vO and dN-Vo. The solid lines correspond to Ef,vO in bare (TiO2)84 NP. (See ref (38).).

To get further insight into the nonmetal doping of TiO2 NPs, we also performed an analogous analysis for the Ovac formation on the CO and Ci doped (TiO2)84 NP. For this purpose, we have selected the E-2, F-2, and I-3-1 sites because these are the most stable sites for CO doping. In addition, we also consider the I-3-2 site to directly compare with previous surface and bulk models.17,24,26 Concerning Ci doping, we considered the I-1, I-2-2, I-3-1-2, and I-3-2-3 positions, as these are the most stable ones. For the CO-doped NPs, we found the Ovac formation energy values in the 2.30–5.12 eV range (Table S2). All cases where the dopant species or oxygen vacancy is located at the I-3-2 site show an Ovac formation energy below 3.85 eV. This indicates that sites located in the subsurface as I-3-2 play a key role in the formation of reduced titania nanoparticles, in agreement with previous results for the undoped (TiO2)84 NP.38 On the other hand, for Ci doping there is almost no effect in the oxygen vacancy energy formation, with values between 3.7 and 5.0 eV. Despite this unfavorable situation, the Ovac in the I-3-2 site emerges again as the most favorable thermodynamically, in consistency with the cases of CO doping and undoped (TiO2)84 NPs.

Once the thermodynamic aspects have been discussed, it is necessary to describe the effect of Ovac on the electronic structure of the N-doped (TiO2)84 NP. To make this discussion easy to follow, we focus on the cases where reducibility is facilitated in terms of lowest formation energies. At the same time, we select representative positions from the apical to the equatorial region for substituting oxygen models. For completeness, we comment on both N and C doping. We selected positions labeled as E-2, F-2, F-3, I-3-1, and I-3-2 for Ns, and E-2, F-2, I-3-1, and I-3-2 for CO, and at least one of each channel at the interstitial models for Ni and Ci with positions I-1, I-2-2, I-3-1-2, and I-3-2-2, and I-1, I-2-2, I-3-1-2, and I-3-2-3, for Ni and Ci, respectively (see Tables S3–S6). In a previous study on the stoichiometric (TiO2)84 NP, it was reported that the presence of Ovac reduced dramatically the energy gap at ∼0.5 eV, as reproduced in Figure S3.38 The resulting energy gap for the reduced doped (TiO2)84 NP is sensitive to the Ovac and dopant positions. When Ovac locates at the edges (E-2, Figure S4), the resulting energy gap of the N-doped titania nanostructure decreases by 2 eV with respect to that of undoped (TiO2)84 NP. This reduction is systematically observed regardless of the N position. This situation is even more pronounced in the case of C-doped (TiO2)84 NP, where the energy gap is reduced by 3 eV with respect to the undoped NP. Thus, C doping has a larger impact on the electronic structure of reduced/doped (TiO2)84 NP. A similar situation is observed when Ovac locates at the face (F-2, Figure S5). Here, C-doped nanostructures expose similar energy gaps (see Figure S3 for comparison). However, for the N-doped nanostructures, the energy gap decrease is larger than in the former case (Figure S5). More interesting is the case where Ovac locates in another facet region, labeled as F-3 (Figure S6). The energy gap decrease is analogous regardless of whether the dopant is a C or N atom and of the position they occupy. This result is similar to that where the Ovac is in the subsurface region (I-3-2, Figure S8). The energy gap of doped titania nanostructures shows a higher variation when creating an Ovac in the presence of the C atom; meanwhile, such variation is less pronounced when the titania nanostructure is N-doped.

Conclusions

The formation of N-doped titania NPs and the impact of such doping on their reducibility through a neutral oxygen vacancy formation have been computationally studied thoroughly using the bipyramidal (TiO2)84 NP as a realistic, representative model. For these NPs, N-doping takes place by either substituting one O atom by one N atom, or adding a N atom to the interstitial region. The former requires energies in the 4.70–5.44 eV range, with doping in the inside region being the most favored. However, interstitial doping is even more favorable as it involves formation energies in the 2.35–5.36 eV range. Interstitial N-doping is also preferred in anatase bulk but at a higher cost of 4.3 eV, and this is also the case for the anatase most stable surface, where the predicted cost is of 3.7 eV. From the electronic viewpoint, substitutional N largely stabilizes the LUMO orbital energy with a concomitant reduction of the energy gap of about 2.0 eV. Meanwhile, the most stable interstitial N doping leads to a somewhat small reduction of the energy gap going from 0.41 to 1.88 eV.

Concerning the NPs’ reducibility, substitutional N leads to an oxygen vacancy formation energy in the 1.81–5.15 eV range, and in the 2.11–4.91 eV range for interstitial N. These values are sensibly larger than the 0.6 eV reported for N-doped anatase bulk. A result questioned the efficiency of N-doped titania in photocatalysis because oxygen vacancies act as efficient electron traps. Now, the fact that N doping of anatase titania nanostructures is more favorable than for anatase bulk together with the more difficult reducibility of the N-doped structure, and an additional decrease of the energy gap in the reduced N-doped (TiO2)84, offers a sound explanation for the observed photocatalytic efficiency of N-doped titania while showing the need for realistic models of these systems.

Acknowledgments

The authors wish to thank Prof. Gianfranco Pacchioni for fruitful discussions relating to titania doping and reducibility. This work has benefited from the financial support from the Spanish Ministerio de Ciencia e Innovación and Agencia Estatal de Investigación (AEI) MCIN/AEI/10.13039/501100011033 through grants PID2020-115293RJ-I00, PID2021-126076NB-I00, TED2021-129506B-C22, la Unidad de Excelencia María de Maeztu CEX2021-001202-M granted to the ITQCUB, and, in part, from COST Action CA18234 and Generalitat de Catalunya 2021SGR00079 grant. The authors are indebted to the Red Española de Supercomputación (RES) for the generous allocation of computational resources.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcc.3c04665.

  • Listed the energy gap of (N, C)-doped (TiO2)84 NP using PBE and PBEx functionals (Table S1); compiles the formation energy of Ovac of CO-doped and Ci-doped (TiO2)84 NP (Table S2); energy gap of all reduced and Ns-doped (TiO2)84 NPs investigated including PBE and PBEx results (Table S3); compiles the energy gap of all reduced and Ni-doped (TiO2)84 NPs investigated including PBE and PBEx results (Table S4); energy gap of reduced and CO-doped (TiO2)84 and Ci-doped (TiO2)84 NPs respectively, using PBE and PBEx functionals (Tables S5 and S6); Kohn–Sham orbital energy level diagram of doped (TiO2)84 NPs including interstitial and substitution N or C as doped element (Figures S1–S9) (PDF)

Author Contributions

E.R.Remesal carried out the calculations, formal analysis, data curation, and writing of a first draft. Á.M.-G. contributed to the conceptualization, supervision, funding acquisition, and writing-reviewing and editing. F.I. contributed to the funding acquisition, scientific discussion, and writing-reviewing and editing.

The authors declare no competing financial interest.

Supplementary Material

jp3c04665_si_001.pdf (853.4KB, pdf)

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