Electronic Structure and Reactivity of Ce- and Zr-Doped TiO2

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Electronic Structure and Reactivity of Ce- and Zr-Doped TiO2: Assessing the Reliability of Density Functional Theory Approaches Anna Iwaszuk and Michael Nolan* Tyndall National Institute, University College Cork, Lee Maltings, Prospect Row, Cork, Ireland

bS Supporting Information ABSTRACT: Substitutional cation doping of TiO2 is a topic of great interest, with many studies using first-principles modeling. However, the majority of studies uses standard approximate density functional theory (DFT) exchange-correlation functionals, which suffer from a severely underestimated band gap and the inability to describe localized defect states. DFT corrected for on-site Coulomb interactions (DFTþU) has been a popular choice for rectifying some of the issues with DFT but itself suffers from some important problems, namely, the dependence of material properties on U and the band gap underestimation. It is therefore important to be able to assess the performance of DFTþU against a higher level approach. Hybrid DFT provides such an approach. In this paper, we study Ce and Zr doped into bulk rutile and anatase TiO2, as well as oxygen vacancy formation in doped rutile, using DFTþU and the screened exchange HSE06 implementation of hybrid DFT. Both methods give a qualitatively similar description of a number of properties, such as the stability of the dopant in TiO2 and the effect of doping on the oxygen vacancy formation energies—indicating Ce doping to be effective in reducing the vacancy formation energy, but Zr increases the oxygen vacancy formation energy. However, DFTþU as used in this paper incorrectly predicts a reduced band gap for doped TiO2, which is not seen with HSE06. The band gap underestimation with DFT/ DFTþU means that the position of the defect states after oxygen vacancy formation cannot be correctly determined. The effect of these issues with DFTþU on important properties such as reactivity in catalytic reactions needs to be determined, and care must be taken in making any quantitative statements from DFTþU results.

1. INTRODUCTION TiO2 is a technologically important material with applications in numerous fields, including catalysis, electronics, coatings, photocatalysis, and pigments.14 In many of these applications, introduction of a dopant into the oxide is important, either intentionally, as is the case of recent work in photocatalysis,512 or unintentionally, e.g., through processing or through extraction of the oxide, e.g., Al in TiO2.4 First-principles modeling using density functional theory (DFT) has been widely used to study doped TiO2, e.g., refs 1317. Studies of doped TiO2 tend to focus on band gap modulation by doping with aliovalent cations, which presents issues with the reliability of DFT in describing the electronic structure of dopants in metal oxides.1822 A further issue is the severe underestimation of the band gap of a material with DFT. This can strongly influence interpretation of DFT results in regard to band gap changes upon doping. Doping of TiO2 with Zr and Ce has been shown to lead to potentially interesting photocatalytic properties.2234 In ref 22, it was found that up to 10% Ce could be accommodated, and a Ce concentration of 0.3 mol % gave the highest photocatalytic activity for degradation of methylene blue under UV illumination. Sidheswaran24 prepared Ce-doped TiO2 (mix of rutile and anatase), showing improved visible light photocatalytic activity to volatile organic compounds, and they claimed a lower band gap of Ce-doped TiO2, with improved visible light absorption. Zhu et al.25 prepared Ce/C-codoped TiO2 and found a reduced r 2011 American Chemical Society

band gap, with the incorporation of Ce reducing electronhole recombination. In ref 26, Ma et al. synthesized Ce-doped TiO2 and found enhanced adsorption in the visible light region. They also found improved photodegradation of Rhodamine B, as well as improved CO oxidation, over undoped TiO2. Silva et al.27 prepared Ce-doped TiO2. They found that low amounts of Ce extended light adsorption into the visible region but that only crystalline TiO2 showed any improvement with Ce doping, and the initial high photocatalytic activity decreases over time. Chen et al.28 measured the X-ray absorption spectrum and PL of Ce-doped TiO2. A red shift in the absorption edge was taken to mean a reduction in the band gap. Fu29 presented a DFTþU (although it is not clear on which species U is applied) study of Ce-doped TiO2 and claimed a red shift in the band gap of the doped oxide due to the conduction band moving to lower energy with increased Ce concentration. Liu et al.30 doped TiO2 nanotube arrays with Zr and found improved UV illuminated photocatalytic activity compared to undoped TiO2. Wang31 synthesized Zr-doped TiO2 and claimed that Zr doping expands the bad gap of TiO2, as well as retarding the transformation of anatase to rutile. Under UV illumination a mixed rutileanatase phase was optimum for benzene Received: April 4, 2011 Revised: May 26, 2011 Published: June 01, 2011 12995

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The Journal of Physical Chemistry C degradation. Luo32 prepared the Zr-doped TiO2 photocatalyst and claimed that the absorption edge of the doped material was shifted to the lower energy region. With 8% Zr doping, improved photocatalytic activity was found. Lippens et al.33 characterized Zr-doped TiO2 nanopowders with EXAFS and DFT. No indication of formation of defect states or a change in band gap was found. Long and English showed, using DFTþU calculations, that there is no band gap change upon Zr doping of TiO2.34 As well as photocatalytic properties arising from band gap modulation, doping of oxides is a potentially fruitful route to obtain new materials for catalysis. A good example of this is doping of CeO2 with metal cations, e.g., refs 3541. Regarding TiO2, a mixture of ZrO2/TiO2 is a known material in catalysis.4244 Given the relatively large oxygen vacancy formation of TiO2 when compared with, e.g., CeO2, it is reasonable to imagine that, in analogy with work on doped CeO2,3541 doping of TiO2 could also be used to devise candidate materials for catalysis. Chretien and Metiu have presented a study of rutile TiO2 doped with a number of metal cations45 and indicated that these would be better oxidation catalysts than undoped TiO2. Ce doping could enhance the oxidative power of TiO2, as measured by the oxygen vacancy formation energy, since oxygen vacancy formation could be made more favorable by lattice distortion upon substituting the larger Ce4þ cation for Ti4þ or by the reduction of Ce from Ce4þ to Ce3þ. Thus, in this paper we consider Zr and Ce substitutional doping of bulk rutile and anatase TiO2 and oxygen vacancy formation in doped rutile. Throughout, we are cognisant of the need to describe consistently reduced cation states and band gaps. To this end, the majority of our computations uses the wellknown DFTþU approach, which has been established as a reliable way of studying reduced Ti species.4649 DFTþU has also been widely used for CeO2,5053 but since we have only a single Ce ion, the possibility of a delocalized Ce3þ oxidation state should not be an issue; however, in some calculations, we apply the þU correction to the Ti 3d and Ce 4f states. While DFTþU goes beyond DFT in at least describing consistently different oxidation states of Ti in TiO2 and reduced TiO2, the band gap underestimation inherent in approximate DFT exchange-correlation functionals is still a key issue. Therefore, we also use hybrid DFT, in the shape of the screened exchange HSE06 hybrid exchange-correlation functional,54,55 to study doping of bulk anatase and rutile. HSE06 generally gives much better band gaps than DFTþU and also better positions of defect states.5660 A problem with DFTþU is that U is applied to a single angular momentum of one species, e.g., Ti 3d, which changes the energy separation between occupied states of that angular momentum on that species but leaves other electronic states described by DFT. This can potentially lead to incorrect interpretations of results, as we will highlight below. The comparison of DFTþU and HSE06 in two different environments will give a suitable assessment of the utility of DFTþU in describing doped metal oxides, highlighting potential pitfalls in applying this approach. We find: (i) the dopants do not lead to formation of states in the band gap of rutile or anatase, so that they are in their formal þ4 oxidation state; (ii) depending on the precise choice of U parameters, DFTþU can position the Ce 4f states above or below the TiO2 conduction band, but HSE06 positions the Ce 4f states above the TiO2 conduction band, so that a potentially incorrect conclusion of a reduced band gap with Ce doping could be reached; and (iii) there are quantitative differences in the oxygen vacancy formation energy when comparing HSE06 with DFTþU, although the qualitative trends are the same for both

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Table 1. Computed Lattice Constants of Bulk Rutile and Anatase TiO2 from DFTþU (See Section 2) and HSE06 rutile

anatase

phase

DFTþU

HSE06

DFTþU

HSE06

a, b/Å

4.638

4.593

4.172

3.822

c/Å

2.973

2.948

9.627

9.603

DFT approaches. We propose that when using DFTþU to study the positions of dopant-induced defect states in a metal oxide, extreme care must be taken when making even qualitative conclusions without reference to more accurate approaches or experiments.

2. METHODOLOGY To describe rutile and anatase TiO2, we use the VASP code61 and a three-dimensional periodic bulk model. A plane wave basis set is used to describe the valence electronic wave functions. The cutoff for the kinetic energy is 396 eV. For the corevalence interaction we apply Bl€ochl’s projector augmented wave (PAW) approach.62 For Ti, we use 4 valence electrons, and for O a [He] core is used. Ce is described with the 12 valence electron potential and Zr with a 4 valence electron potential. A small core Ti PAW potential, with 12 valence electrons, has been tested,63 and we find little change in the results; see, e.g., Figure S1 in the Supporting Information. We use the PerdewWang91 approximation to the exchange-correlation functional.64 For bulk rutile, a (2 2 3) supercell is used, and for bulk anatase, a (2 2 2) supercell is used. The k-point sampling grids are a Monkhorst-Pack (4 4 2) grid for both bulk polymorphs. The lattice constants for rutile and anatase from DFTþU and HSE06 are shown in Table 1. The rutile (110) surface cleaved from bulk rutile is made up of neutral OTiO trilayers along the slab with rows of 2-fold coordinated bridging oxygens terminating the slab, and in the next layer there are two types of Ti: 6-fold coordinated Ti and exposed 5-fold coordinated Ti. (2 2) and (2 4) surface cell expansions are employed, which allows for different doping and oxygen vacancy concentrations to be studied, while the slab is 6 OTiO layers thick (18 atomic layers) and the vacuum gap is 12 Å. The bottom trilayer of TiO2 is held fixed, and all other layers are allowed to relax. The convergence in the wave function relaxation is 0.0001 eV, while the ionic relaxation is converged when the forces on the atoms are less than 0.02 eV/ Å. Fermi level smearing with the Methfessel Paxton scheme is applied, with σ = 0.1 eV. All calculations are spin polarized. The dopant is substituted into a Ti site in TiO2 and fully relaxed with no constraints on atom positions, symmetry, or overall spin. Regarding oxygen vacancy formation, there are two types of bulk oxygen in rutile and anatase: four equatorial oxygens and two apical oxygens. In both doped polymorphs, a number of different oxygen vacancy sites have been investigated and have been ranked for stability according to their oxygen vacancy formation energy. The dopant incorporation energy is computed from Edope ¼ fEðMTiO2 Þ þ EðTiÞg fEðMÞ þ EðTiO2 Þg

ð1Þ

where E(M) and E(Ti) are the energy of one atom of the bulk metal (M = Ce, Zr) or Ti; E(TiO2) is the total energy of TiO2; 12996

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The Journal of Physical Chemistry C

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and E(MTiO2) is the total energy of TiO2 with the dopant on a Ti lattice site of the oxide. The oxygen vacancy formation energy is computed from EVac ¼ fEðMTiO2x Þ þ 1=2EðO2 Þg fEðMTiO2 Þg

Table 2. Formation Energy for Doping Bulk Rutile and Anatase TiO2 with Ce and Zr

ð2Þ

where E(MTiO2x) is the total energy of doped TiO2 with an oxygen vacancy and E(MTiO2) is the total energy of TiO2 with the dopant on a Ti lattice site of the oxide. The formation energy is referenced to half the total energy of molecular O2. A key question in studies such as that presented herein is describing the electronic structure, band gaps, and defect states correctly. We know that standard approximate DFT exchangecorrelation functionals strongly underestimate the band gap of metal oxides (which leads to incorrect positions of defect states) and will delocalize reduced cation states such as Ti3þ or Ce3þ over many atoms. Since we are investigating formation of oxygen vacancies in doped TiO2, this question is of key importance and requires an approach beyond the approximate exchange correlation functionals popularly used. We apply DFT corrected for onsite Coulomb interactions, i.e., DFTþU.65,66 DFTþU adds a Hubbard U correction to consistently describe the localized reduced cation states that result from formation of the vacancy. The ability of DFTþU to generally describe reduced Ti3þ and Ce3þ is well-known and has been the subject of a number of papers.4653 In this work, we apply DFTþU to the Ti 3d states and study two U parameters, namely, 3 and 4.5 eV on Ti. These choices of U are motivated by a number of papers that have applied DFTþU to the study of systems containing reduced Ti3þ species,4648 in which both values of U have been found to be suitable for recovering a consistent description of reduced Ti3þ and reaction energetics. For the dopants, we use standard DFT on Zr since there are no issues with describing the electronic structure. For Ce, we apply both standard DFT and DFTþU (with U = 5 eV50). Since there is only one Ce ion present, delocalization of charge upon oxygen vacancy formation should not occur, but using DFT and DFTþU allows us to investigate the importance of this issue. Despite the success of DFTþU, it still has issues: all material properties depend on U, and it is not possible to describe all properties to the same accuracy with the same value of U; for example, a value of U that recovers the bulk rutile band gap is so large that the Ti3þ states cannot be properly described, and U is applied only to one angular momentum of each species. Finally, the band gap underestimation with DFT is still present. Hybrid DFT, where a portion of HartreeFock exchange is mixed with local DFT exchange-correlation functionals, has proven to be a very good method for molecular systems and has recently been applied to a number of challenging oxide systems5660 HF exchange (25 %) is included in hybrid DFT; a contribution of 20% was originally determined from fitting to experimental molecular atomization energies;67 and Perdew and co-workers later showed that 25% exact exchange would be suitable.68 The exact exchange contribution is a universal parameter, applied to all species in the material system, which presents another advantage over the DFTþU approach. The HSE06 functional is a screened exchange functional,55,56 and we set the screening parameter set to 0.2/Å (0.11/Bohr). However, hybrid DFT is not free from adjustable parameters, namely, the exact exchange contribution and the screening length, both of which can be tuned to give, for example, the correct band gap. However, the deviations from the commonly used parameters in hybrid DFT

Edope/eV rutile TiO2

Edope/eV anatase TiO2

Ce

1.21 eV DFTþU

1.44 eV DFTþU

Zr

0.99 eV HSE06 0.25 eV DFTþU

0.32 eV HSE06 0.57 eV DFTþU

0.10 eV HSE06

1.24 eV HSE06

dopant

Figure 1. Atomic structure of bulk (a) rutile and (b) anatase TiO2, showing the dopant site. Ti is gray, oxygen red, and the dopant brown.

tend to be small for many oxides (see ref 69 for an exception), and the dependence of material properties on these parameters is much less severe than with DFTþU. Thus, one can use the default HSE06 parameters with some confidence. Given the heavy cost of hybrid DFT in a plane wave calculation, our strategy is to apply HSE06 to the bulk calculation and to a (2 2) surface supercell expansion of the rutile (110) surface, making direct comparison with DFTþU. We apply DFTþU to the (2 4) surface supercell calculations of the rutile (110) surface, allowing a study of the effect of the concentration of dopant and oxygen vacancies on the resulting properties.

3. RESULTS 3.1. Zr and Ce Doping of Bulk Rutile and Anatase TiO2. We first determine the energy associated with substituting the dopant for Ti in the bulk; these are presented in Table 2. For both TiO2 polymorphs and both DFT approaches, the energies are negative, favoring dopant incorporation. For rutile, Ce doping is more favorable than Zr doping, whereas for anatase, there appears to be a dependence on the precise calculation setup used. The HSE06 results for rutile indicate that dopant incorporation is less favorable than with DFTþU, but the differences are relatively small. However, for anatase, there appears to be a difference: first, the relative stability of Ce and Zr as dopants depends on the calculation method used, and second, the difference between the DFTþU and HSE06 energies is larger than for rutile. Figure 1 shows the structure of the bulk rutile and anatase supercells studied, with the dopant site indicated with a brown sphere. In Figure 2 we show the geometry around the dopant site in bulk rutile from DFTþU and HSE06. With DFTþU and HSE06, the CeO distances are lengthened compared to undoped TiO2. For Zr, the 6 ZrO distances are equal with DFTþU and almost equal with HSE06. When comparing Ce and Zr, the differences between the dopantO distances can be explained by the ionic radii of the dopants: Ce4þ has an ionic radius of 1.06 Å and Zr4þ an ionic radius of 0.72 Å, while the ionic radius of Ti4þ is 0.52 Å, so that both dopants should have longer cationO distances than Ti and those for Ce are longer than for Zr. For Zr, Lippens et al.33 found that ZrO distances are longer than 12997



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Figure 2. Structure around the dopant site for doped bulk rutile TiO2. (a) Ce DFTþU, (b) Zr DFTþU, (c) Ce HSE06, (d) Zr HSE06. All distances are in Å. Ti is gray, oxygen red, and the dopant brown.

Figure 3. Structure around the dopant site for doped bulk anatase TiO2. (a) Ce DFTþU, (b) Zr DFTþU, (c) Ce HSE06, (d) Zr HSE06. Ti is gray, oxygen red, and the dopant brown.

TiO distances. Comparing the DFT approaches, HSE06 gives dopantO distances no larger than 0.02 Å compared with DFTþU, showing that both approaches give a similar description of the energetics and structure of Ce and Zr doped into bulk rutile. Doped anatase is very similar to rutile, with the geometry around the dopant site shown in Figure 3. With Ce doping, the cationO distances are longer than both the TiO distances and the ZrO distances, which themselves are lengthened compared with undoped TiO2. The differences in cationO distances between DFTþU and HSE06 are no larger than 0.03 Å, so that DFTþU is reliable in this regard. Describing the electronic structure of doped TiO2 is where deficiencies in approximate DFT are most strongly manifested, as already discussed. Despite giving improvements over DFT, as demonstrated in refs 1820, 4653, 70, and 71, DFTþU still has issues with material properties such as band gaps showing a U dependence. Values of U that recover the correct band gap are so large as to degrade the description of other properties. Despite this, pragmatic choices of U in DFTþU for metal oxides have shown some success,4653 although for doping of TiO2 standard DFT exchange-correlation functionals are still widely used. The comparisons of DFTþU and HSE06 we present will allow us to examine this issue more deeply. Figures 4 and 5 show the Ti 3d and dopant (Ce 4f and Zr 5d) projected electronic density of states (PEDOS) for bulk rutile (Figure 4) and anatase (Figure 5) doped with Ce and Zr from DFTþU and HSE06. We recall that DFTþU is applied to Ti 3d states but not to the dopant, but see below. In all cases there are no obvious electronic states in the band gap that would correspond to reduced Ti species or to reduced species originating from the dopant. Therefore, Ti and the dopants are in their þ4 oxidation states, which is further confirmed by Bader72 charge analysis where Ti in rutile has a charge of ca. þ1.32 electrons, Ce a charge of þ2.27 electrons, and Zr a charge of þ2.57 electrons from DFTþU. With HSE06, the charge on Ti is ca. þ1.41 electrons, þ2.50 electrons on Ce, and þ2.74 electrons on Zr. Similar Bader charges are found in anatase and are typical of 4þ oxidation states for Ti, Ce, and Zr.

In both TiO2 polymorphs and with either DFT approach, the Zr 5d states are positioned well above the TiO2 conduction band edge with little interaction with the host electronic states, and the band gap is unchanged over undoped TiO2, consistent with a number of papers in the literature.3034 With the present DFTþU setup, the empty Ce 4f states are positioned below the bottom of the TiO2 conduction band, giving a small reduction in the energy gap of 0.1 eV in doped rutile. For anatase, there is no change in the energy gap—the Ce 4f and the bottom of the conduction band lie at the same energy. Thus, the present DFTþU setup predicts a small narrowing of the band gap in Ce-doped rutile, which is similar to the result of ref 29. However, when we examine the PEDOS for Ce-doped TiO2 from HSE06, it does not give the same result as DFTþU. For both rutile and anatase, the Ce 4f states appear above the CB edge. In addition, the Ce 4f peak is narrower with HSE06 than with DFTþU, indicating that there is less interaction between the Ce 4f states and the Ti 3d states from HSE06 compared with DFTþU. The DFTþU result in Figures 4 and 5 is for a particular setup, as discussed in Section 2. To examine the impact of the precise DFTþU setup on the position of the dopant and TiO2 electronic states, we have performed DFTþU calculations with the following combinations: (i) U = 4.5 eV on Ti 3d and U = 5 eV on Ce 4f, (ii) U = 3 eV on Ti 3d and U = 0 eV on Ce 4f, and (iii) U = 3 eV on Ti 3d and U = 5 eV on Ce 4f. The choice of U = 3 eV on Ti 3d states comes from a number of papers in the literature.47,73 In the Supporting Information, Figure S2(a)(c), we plot the PEDOS for Ti 3d and Ce 4f and see a significant dependence on the DFTþU setup used. If U = 5 eV on Ce 4f states, then the position of the Ce 4f and the Ti 3d conduction band states is consistent with HSE06; however, if U = 0 on the Ce 4f states, then the precise value of U on the Ti 3d states does not influence the position of the electronic states, and the result in Figure 4 is recovered. Under the reasonable assumption that the HSE06 description of the electronic states is more accurate than that from DFTþU, Ce doping of bulk rutile TiO2 should not lead to any notable 12998



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Figure 4. PEDOS for doped bulk rutile TiO2. (a) Ce-doped DFTþU, (b) Zr-doped DFTþU, (c) Ce-doped HSE06, (d) Zr-doped HSE06.

band gap narrowing. This finding is quite important, as it highlights that attempting to determine band gap changes, even qualitatively, in doped oxides with the DFTþU approach depends significantly on the choice of DFTþU setup, and caution must be urged in attempting such analyses without reference to more accurate calculations or high quality experimental data. 3.2. Zr and Ce Doping of the Rutile TiO2(110) Surface. We briefly consider Ce and Zr doping of the rutile (110) surface. In Figure 6 and Figure S3 in the Supporting Information we show the atomic structure of the rutile (110) surface with Zr and Ce dopants in their most stable lattice site, i.e., a 5-fold coordinated surface Ti site. We have used a (2 2) surface supercell (Figure 6) with DFTþU and HSE06 and a (2 4) surface supercell with DFTþU (Figure S3, Supporting Information); the latter surface supercell is too large to be treated with a plane wave hybrid DFT at present. For both dopants, the energy to incorporate the dopant is negative so that dopant incorporation is favored. The DFTþU energies are 0.5 eV for Zr substitution into both supercells of the (110) surface and 0.7 (2 2 supercell) and 0.8 eV (2 4 supercell) for Ce substitution, showing little dependence on the dopant concentration at the surface. With HSE06 in the (2 2) surface supercell, the incorporation energies are 1.70 eV for Zr and 1.90 eV for Ce doping. While the precise formation energies depend strongly on the DFT approach, as do all computed energies, it is reasonable to conclude that incorporation of both dopants into TiO2 is favorable. When Zr is incorporated into the rutile (110) surface, it leads to little distortion to the atomic structure, apart from a lengthening of the dopantO bonds around the dopant site, as shown in

Table 3, when compared to the undoped surface. There is a small Zr displacement of 0.06 Å out of the surface plane. When Ce is incorporated into the (110) surface, there is an obvious distortion to the structure around the site of the dopant compared to the undoped surface, and Table 3 shows the CeO distances. In both surface supercell modes, Ce is pushed out of the surface lattice site, due to the larger ionic radius of the Ce ion which is easily accommodated by the surface. The displacement perpendicular to the surface is 0.80 Å in the (2 2) surface supercell (with both DFT methods) and 0.75 Å in the (2 4) surface supercell. The displacement of Ce causes a strong elongation in distance to the subsurface oxygen. The plan view of both surfaces also shows that the local structure around the dopant is distorted, with in-plane oxygen atoms displaced away from their lattice sites, and the nearest bridging oxygen atoms also move. In Figure 7 we show the Ti and dopant PEDOS for Zr and Ce doping of the (2 2) TiO2(110) surface supercell with DFTþU and HSE06; the PEDOS for the (2 4) surface supercell with DFTþU is very similar to the smaller surface supercell with the same DFTþU setup and is not shown. The PEDOS from DFTþU and HSE06 both show no electronic states in the band gap of the TiO2 host, so that both dopants are in their þ4 oxidation states; computed Bader charges are þ2.37 and þ2.44 electrons with DFTþU and HSE06 for Ce. For Zr, the Bader charges are þ2.50 and þ2.63 electrons with DFTþU and HSE06. These are consistent with a formal þ4 oxidation state for Zr and Ce. Zr doping with both approaches shows no change in band gap of TiO2, with the unoccupied Zr states positioned well above the 12999



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Figure 5. PEDOS for doped bulk anatase TiO2. (a) Ce-doped DFTþU, (b) Zr-doped DFTþU, (c) Ce-doped HSE06, (d) Zr-doped HSE06.

bottom of the conduction band. Similar to bulk rutile, the position of the Ce 4f state depends on the DFTþU setup, and in Figure 7 the DFTþU setup (U = 4.5 eV on Ti U = 0 eV on Ce) predicts for the (110) surface a strong reduction in the band gap of TiO2. HSE06 positions the Ce 4f states around the conduction band edge essentially at the same energy as the Ti 3d conduction band states. Thus, in a real sample made up of nanocrystals and where surfaces dominate, it is possible that the precise effect of Ce doping and any band gap change will depend on the exact details of structure, processing, experimental conditions, etc., all of which could be the origin of apparent disagreements between some experimental studies.2234 3.3. Oxygen Vacancy Formation in Doped Rutile TiO2. We now investigate the effect of Zr and Ce doping on the reactivity of doped rutile TiO2, as characterized by the oxygen vacancy formation energy. To do this, we remove one oxygen atom from the doped structure and compute the oxygen vacancy formation energy from eq 2. In Table 4 we show the formation energy of the most stable oxygen vacancy site in undoped and doped bulk rutile TiO2 and the (110) surface from DFTþU and HSE06. The oxygen vacancy formation energy is always lower in the surface than in the bulk. When comparing the two surface supercells, the (2 4) surface has a smaller oxygen vacancy formation energy, arising from the smaller vacancy concentration. Comparing the two DFT approaches, HSE06 leads to a larger oxygen vacancy formation energy in the (110) surface compared with DFTþU. In the bulk, HSE06 gives a smaller oxygen vacancy formation energy. In attempting to compare the DFT approaches, we point out again that the precise results from

DFTþU will depend on the exact values of U used in the calculation; however, the DFTþU setup presented here is typical of DFTþU calculations in the literature. When comparing dopants, Zr doping of the bulk increases the oxygen vacancy formation energy, while Ce doping lowers the oxygen vacancy formation energy, although the reduction is not especially large. The lowering of the oxygen vacancy formation energy with Ce doping can be attributed to the ease with which Ce can be reduced from Ce4þ to Ce3þ upon formation of an oxygen vacancy as well as the larger ionic radius of Ce4þ compared to Ti4þ. The example of Zr doping suggests that although the structure around the dopant is distorted compared to TiO2 this does not necessarily guarantee that it will be easier to remove an oxygen atom. The fact that Zr is not a reducible cation also plays a role. In the (110) surface, both dopants usually reduce the oxygen vacancy formation energy compared to undoped TiO2, with Ce doping leading to quite a large reduction in the oxygen vacancy formation energy. Again, the ease of reduction of Ce compared with Ti and Zr must facilitate oxygen vacancy formation, and the lowered symmetry at the surface means that distortions due to dopant incorporation will be stronger also facilitating the formation of an oxygen vacancy. Figure 8 shows the atomic structure and excess spin density of the relaxed structures for oxygen vacancy formation in doped bulk rutile. Considering the geometry, Ce doping gives a distorted structure, in which Ce moves off its lattice site and the surrounding atoms are also distorted from their lattice sites. The dopantO distances most pertinent to the analysis are 13000


The Journal of Physical Chemistry C shown in Table 5. Comparing the CeO distances, the HSE06 distances are notably longer than those found with DFTþU. In

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both cases, Ce coordinates to four neighboring oxygen atoms and is not bonded to the fifth oxygen atom. The most stable oxygen vacancy site is an oxygen that was originally shared by the dopant and Ti, thus giving five oxygens surrounding the dopant after vacancy formation. Zr doping gives much smaller distortions: there is one short ZrO distance and four ZrO distances that are essentially uniform. For Zr doping, there are no electrons on the dopant after oxygen vacancy formation, so that the two electrons will be distributed on Ti ions. With DFTþU, there is one electron on a Ti ion (that is not a neighbor to the vacancy site), and with a computed spin magnetization of 0.90 electrons and a Bader charge of þ1.66, this is a Ti3þ ion. The second electron is shared by two partially reduced Ti ions, where each Ti has a spin magnetization of 0.37 electrons. With HSE06, a different solution is found, in which there are two fully reduced Ti3þ ions, with computed spin magnetizations of 0.75 and 0.77 electrons and Table 3. Dopant-O distances (in Å) in Ce and Zr doped rutile TiO2 (110) surface from DFTþU and HSE06

dopant Ce

Figure 6. Structure of Ce and Zr doped into the (2 2) surface supercell of the (110) rutile surface. (a) Ce DFTþU, (b) Ce HSE06, (c) Zr DFTþU, and (d) Zr HSE06. The gray spheres are Ti, the red spheres O, the white spheres Ce, and the blue spheres Zr.

Zr

dopantO

dopantO

dopantO

distance/Å

distance/Å

distance/Å

(110) (2 2)

(110) (2 2)

(110) (2 4)

DFTþU

HSE06

DFTþU

2.14 ( 2), 2.15 ( 2) 2.11 ( 1), 2.12 ( 3) 2.16 ( 4) 2.51 (to subsurface) 2.47 (to subsurface) 2.45 (to subsurface) 2.05 ( 4)

2.07 ( 4)

2.06 ( 4)

1.98 (to subsurface)



Figure 7. PEDOS plots for a (2 2) rutile surface supercell doped with Ce and Zr. (a) Ce DFTþU, (b) Zr DFTþU, (c) Ce HSE06, and (d) Zr HSE06. 13001



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Table 4. Oxygen Vacancy Formation Energies for the Most Stable Oxygen Vacancy Site in Bulk Rutile TiO2 and the Two Rutile (110) Surface Supercells from DFTþU and HSE06a bulk rutile TiO2 dopant

none

Zr

Ce

/eV DFTþU

4.97

5.19

4.06

4.32

4.76

3.93

Ovac

E

EOvac/eV HSE06

TiO2 rutile (110) (2 2) dopant

none

Zr

Ce

/eV DFTþU

3.68

3.48

2.38

3.79

4.01

3.30

Ovac

E

EOvac/eV HSE06

TiO2 rutile (110) (2 4) dopant

none

Zr

Ce

/eV DFTþU

3.08

2.88

1.92

Ovac

E a

The entry for “none” is undoped TiO2.

Bader charges of þ1.53 and þ1.52 electrons. These reduced Ti are not neighbors to the vacancy site. For Ce doping with DFTþU, one electron is found on a Ti that neighbors the vacancy site. This Ti3þ ion has a computed spin magnetization of 0.97 electrons and a Bader charge of þ1.72 electrons. Interestingly, with DFTþU, the second electron is shared by Ce and a neighboring Ti with spin magnetizations of 0.41 (Ce) and 0.34 (Ti), suggesting partial reduction of Ce and a second Ti, instead of full localization on two ions. With HSE06, there is again a difference to DFTþU, in which the two electrons released by formation of the oxygen vacancy are found on Ce and on one Ti ion, with computed spin magnetizations of 0.93 and 0.84 electrons and Bader charges of 2.19 electrons and 1.58 electrons, respectively. This gives a Ce3þ and a Ti3þ ion, which are separated due to the repulsion that arises between two metal 3þ cations. The localization of charge on Ti and Ce with HSE06 is consistent with the CeO distances in Table 5, where the significant elongation over the nondefective bulk is typical of a fully localized Ce3þ, rather than the partially localized reduced Ce ion found with DFTþU. To explore further differences between DFTþU and HSE06, we have used the DFTþU and HSE06 solutions as inputs to the other DFT approach to investigate if there are multiple solutions for the distribution of the electrons after oxygen vacancy formation.71,72 Table 6 gives the resulting oxygen vacancy formation energies and shows that using the DFTþU solution as a starting point for the HSE06 relaxation gives a solution that is less stable than the original HSE06 solution by ca. 0.3 eV. For a relaxation with DFTþU starting from the HSE06 solution, the final solution is less stable by 0.50.6 eV. Thus, the precise distribution of the electrons that result from oxygen vacancy formation depends sensitively on the DFT approach and starting structure. In the Supporting Information, Figure S4 and Table S1 show how the precise choice of U parameters on Ti and Ce affect oxygen vacancy formation. As expected, the precise energetics and the destinations of the released electrons depend on the DFTþU approach taken. However, we find that Ce doping will always reduce the formation energy of the oxygen vacancy compared with undoped TiO2 and result in formation of reduced Ce and Ti species.

Figure 8. Atomic structure and excess spin density for the most stable oxygen vacancy structure with Ce and Zr doping in bulk rutile TiO2. (a) Ce DFTþU, (b) Ce HSE06, (c) Zr DFTþU, and (d) Zr HSE06. The orange color indicates the spin density isosurface; Ce is white; and Zr is blue. V indicates the vacancy site.

Table 5. DopantO Distances in Ce- and Zr-Doped Bulk Rutile TiO2 with the Most Stable Oxygen Vacancy from DFTþU and HSE06 dopantO distance/Å dopant Ce Zr

dopantO distance/Å

DFTþU 2.13, 2.17 ( 2), 2.18

HSE06 2.21, 2.25, 2.26, 2.32

2.31

2.53

1.95, 2.04 ( 4)

1.91, 2.04 ( 2), 2.05, 2.06

This phenomenon is quite general, and recent work48,7376 has shown with reducible metal oxides that here can be solutions within a few tenths of an electronvolt of the most stable solution from a given method. This means that such solutions will be sampled in experimental time scales, giving an average of possible solutions accessible under those experimental conditions. In ref 48, Camellone et al. used CarParrinello molecular dynamics 13002



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to show that the distribution of Ti3þ in the (110) rutile TiO2 surface with a bridging oxygen vacancy changes over time—the system samples energetically accessible distributions of reduced Ti. Very recently, Chretien and Metiu73 and Deskins et al.74 have shown that a bridging oxygen vacancy can have many distributions of the Ti3þ ions that lie close in energy. Similarly, the adsorption of Au on the ceria (111)75 surface can result in different solutions for the oxidation state of Au, which is extremely sensitive to the method and starting structure used. We and others have also shown60,76 that for oxygen vacancies in ceria there can be multiple, energetically similar solutions to the distributions of the reduced Ce cations. Meredig et al. have demonstrated a controlled DFTþU approach to obtaining the most stable solution to a particular system within DFTþU and showed for an oxygen vacancy in the CeO2(111) surface that different solutions with respect to orbital occupations can give energy differences up to 0.25 eV. We have used this approach, for the oxygen vacancy in doped rutile, and have found that one can indeed obtain many solutions. The solution shown in Figure 8 persists as the lowest energy structure, with other solutions being 0.10.6 eV higher in energy, again highlighting the Table 6. Oxygen Vacancy Formation Energies (in eV) in Bulk Rutile from DFTþU and HSE06a dopant Ovac

most stable E

a

/eV with DFTþU

Zr

Ce

5.19

4.06

most stable EOvac/eV with HSE06

4.76

3.93

EOvac with DFTþU from HSE06

5.77

4.56

EOvac with HSE06 from DFTþU

5.07

4.30

The bottom two rows are the DFTþU and HSE06 results starting from the HSE06 and DFTþU solutions, respectively.

existence of multiple, low energy minima solutions to the problem of oxygen vacancy formation. Figure 9 shows the PEDOS projected on Ti and the dopant in doped bulk rutile to further highlight differences between DFTþU and HSE06. For both dopants, DFTþU shows two Ti 3d peaks in the band gap. The peak nearest the VB comes from the fully reduced Ti3þ. The partially reduced Ti ions are the source of the peaks close to the CB. For Ce as dopant, DFTþU shows a peak for partially reduced Ce3þ in the same position as the peak of the partially reduced Ti ion. For Zr doping with DFTþU, there are no states associated with the dopant. In contrast to DFTþU, the HSE06 PEDOS for Zr doping shows one broad peak that is made up of the two reduced Ti ions in the structure; their peak positions are slightly different, due to the different environment experienced by each Ti3þ ion. With Ce doping, we find two peaks, one derived from Ce3þ and one from Ti3þ, which happen to lie at the same position in the band gap. The peaks in the PEDOS associated with reduced Ti and Ce are consistent with the spin density plots in Figure 8. In the (110) surface, for which the geometry is given in Table 7, the most stable oxygen vacancy site is a bridging oxygen atom neighboring the dopant, as shown in Figure 10. With Ce doping, the reduced symmetry in the surface has a strong impact on the local structure around the dopant. Ce clearly moves off its original site in the surface, completely breaking the bond to the subsurface oxygen directly under it and making a new bond to a neighboring bridging oxygen atom, with a distance of 2.55 Å from DFTþU and of 2.65 Å from HSE06. The CeO distances are strongly elongated over the nondefective surface, consistent with formation of reduced Ce3þ. Both DFT approaches give similar geometry around the Ce site after the oxygen vacancy forms.

Figure 9. PEDOS projected onto Ti and dopant states for an oxygen vacancy in bulk doped TiO2. (a) Ce DFTþU, (b) Zr, DFTþU, (c) Ce HSE06, and (d) Zr HSE06. 13003



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Table 7. DopantO Distances (in Å) in the Ce- and Zr-Doped Rutile TiO2(110) Surface with the Most Stable Oxygen Vacancy dopantO distance/Å dopant Ce Zr

dopantO distance/Å

dopantO distance/Å

(110) (2 2) DFTþU

(110) (2 2) HSE06

(110) (2 4) DFTþU

2.24 ( 2), 2.34, 2.38

2.21, 2.22, 2.33, 2.34

2.25 ( 2), 2.38 ( 2)

2.55 (to bridging O)



2.04 ( 2), 2.09 ( 2)

2.06 ( 2), 2.08 ( 2)

2.04 ( 2), 2.09 ( 2)

1.94 (to subsurface O)



Figure 10. Atomic structure and excess spin density for an oxygen vacancy in the Ce-doped (110) rutile surface. (a) Oxygen vacancy in the Ce-doped (2 2) surface, (b) spin density with DFTþU, and (c) spin density with HSE06.

Figure 11. Atomic structure and excess spin density for an oxygen vacancy in the Zr-doped (110) rutile surface. (a) Oxygen vacancy in the Zr-doped (2 2) surface, (b) spin density with DFTþU, and (c) spin density with HSE06.

In contrast, with Zr doping with an oxygen vacancy, for which the structure is shown in Figure 11, changes to the structure are essentially limited to small changes in the ZrO distances around the dopant. The similarity between the DFT approaches and the surface supercells is encouraging. The reason for the limited changes in local structure around the dopant for Zr will be discussed in the following. Finally, with the larger surface supercell (see Supporting Information and Table 7), the geometry around the dopant is little changed compared with the smaller surface supercell. In all Ce-doped surfaces, an oxygen vacancy always results in formation of two reduced cations, namely, Ce3þ and Ti3þ. In the smaller surface supercell DFTþU and HSE06 both predict that a 6-fold coordinated Ti neighboring the vacancy site is reduced to Ti3þ. In the larger surface supercell, with DFTþU (Figure S5, Supporting Information), the structure around the dopant and Ce3þ formation are the same as the smaller supercell. However, in this surface model, a subsurface Ti3þ is formed. Subsurface Ti3þ is well-known for this particular surface supercell.48,73,74 The formation of localized Ce3þ is consistent with the very long CeO distances found after oxygen vacancy formation—the Ce3þ ion is larger than Ce4þ and Ti4þ. With Zr doping in the smaller surface supercell, DFTþU and HSE06 result in reduction of a surface 6-fold Ti and a subsurface Ti, while for the larger surface cell, it is two subsurface Ti atoms that are reduced. This is why the geometry around Zr is little affected by oxygen vacancy formation—it is Ti ions away from the dopant site that become Ti3þ. Since Zr is not reducible, only Ti ions from the oxide can be reduced, and we have not found any stable solutions in which Zr is reduced. Figure S6 (Supporting Information) shows the PEDOS for the doped (110) surfaces with an oxygen vacancy—the DOS shown are projected onto the dopant and Ti, and the PEDOS for both

surface supercells are similar. For Ce doping, two peaks are present in the PEDOS, one due to reduced Ti3þ and the other due to reduced Ce3þ. Both peaks lie at different energies in the band gap. Comparing DFTþU and HSE06, the latter positions the defect states well inside the gap, with Ti3þ found closer to the conduction band than Ce3þ. While DFTþU gives the same ordering of the peaks, both are positioned quite close to the valence band, particularly for Ce3þ. With Zr doping, the only peaks found arise from Ti3þ, and again similarities and differences between the DFTþU and HSE06 results are apparent.

4. DISCUSSION The DFTþU method is a popular pragmatic choice for modeling of reduced cations in metal oxides such as TiO2 and CeO2, where the addition of the Hubbard U parameter recovers a localized description. However, it does suffer from the problem of being empirical and does not repair the band gap underestimation that besets approximate DFT. To assess the applicability of DFTþU, one requires comparison either with experiment, which many DFTþU studies do, or with a more accurate modeling approach. In the absence of the necessary experimental data, hybrid DFT often serves as an excellent benchmark for DFTþU modeling. Unfortunately, hybrid DFT in a plane wave basis set is significantly more expensive than DFTþU, limiting the size of the system to which it can be applied. We take the approach of testing DFTþU against a well-studied implementation of hybrid DFT for tractable systems, and if it provides a consistent description of the system under examination, then we can use it for larger-scale simulations. For the particular examples in this paper, we are able to draw some conclusions regarding the performance of DFTþU, which helps shed some light on the strengths and weaknesses of DFTþU.77,78 13004


The Journal of Physical Chemistry C We find a consistent qualitative description of doped bulk rutile and its (110) surface and bulk anatase TiO2 with DFTþU and HSE06, which is encouraging. However, we also find quantitative differences. There is a notable difference in computed oxygen vacancy formation energies, which could be important in assessing the stability of defect structures. In the present case, where the oxygen vacancy results in formation of reduced cations, HSE06 stabilizes the bulk oxygen vacancy compared to DFTþU, but at the (110) surface, the HSE06 oxygen vacancy formation energy is larger than the DFTþU formation energy. Apart from the dependence on U, other factors that can influence this difference include the error in the binding energy of O2 with DFT79 and the improved description of electronic states with HSE06. It is possible that the differences between DFTþU and HSE06 may not be so important for the question at hand, so long as the two methods are consistent; e.g., if both methods predict a particular defect site or reaction pathway to be the most favorable, then one can use DFTþU. One should always be mindful that an assessment of errors in the DFTþU energies, e.g., by comparison to a more accurate approach, needs to be undertaken. Further studies of the comparison of the energetics of oxygen vacancy formation will be helpful in deepening our understanding of this point. Turning now to the electronic structure, the DFTþU band gap from the present setup is too small. Although the correct band gap can be recovered with a large value of U (ca. 810. eV80), such values of U impact negatively on other properties. Thus, one must strike a compromise in the value of U to describe material properties. To examine one aspect, Table S2 (Supporting Information) shows the position of the Ce 4f states in doped bulk rutile and in the (110) surface and the position of the reduced Ti3þ and Ce3þ states after oxygen vacancy formation in Ce-doped bulk TiO2 and in the (110) surface. Comparing DFTþU and HSE06, we see that the closest agreement between the two approaches is in the position of the defect states relative to the conduction band. In doped TiO2, with no oxygen vacancies, the Ce 4f states are very close to the conduction band. DFTþU predicts them to lie lower than the oxide conduction band, while HSE06 predicts the Ce 4f states to lie above the CB in bulk and at the CB edge in the (110) surface. In experiments, the oxide is usually a film or in nanoparticle form, rather than the bulk structures in the present paper, and the observed small red shift of the absorption edge could arise from the structure of TiO2 in the sample; we are studying doped TiO2 nanostructures to examine this point. With the DFTþU underestimation of the band gap, the offset of the dopant states to the oxide valence band is underestimated. The precise position of the dopant states in a DFTþU calculation will depend on the value of U used and to which species it is applied. When applying U to the Ti 3d states, this raises the empty Ti 3d states to higher energy. If we apply U = 5 eV to the Ce 4f states, then these move higher in energy and lie above the Ti 3d conduction band (Figure S2, Supporting Information). One can therefore choose U on the cations that can place the Ce 4f states where one wishes. This illustrates that extreme care must be taken in making quantitative statements about the position of dopant states from DFTþU calculations without making reference to higher quality calculations or experimental data. In the structures with an oxygen vacancy, we see differences in the distribution of the two electrons released upon removal of oxygen, with DFTþU spreading the two electrons over three cations and HSE06 fully localizing the electrons on two cations.

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This difference does affect the comparison between DFTþU and HSE06. However, we can focus on the position of the gap state associated with the fully localized Ti3þ cation. In bulk TiO2, Table S2 (Supporting Information) shows that the biggest difference between HSE06 and the present DFTþU setup is in the position of the Ti3þ state relative to the valence band, with a smaller error for the offset to the conduction band. The same situation is found for the Ti3þ species in the oxygen-deficient (110) surface. While this result will depend on U, the value of U we use localizes electrons on Ti3þ sites in oxygen-deficient pure TiO2. Since the Ti3þ states come from the Ti 3d derived conduction band, it is not surprising that the offset to the conduction band is better with this value of U than is the offset to the valence band. Of course, one could choose a value of U to give similar valence band offset to the HSE06 result, but this would then introduce a large error in the conduction band offset. Thus, with the band gap underestimation inherent in the DFTþU approach, it is not possible to obtain a position for the gap state that is consistent with HSE06. A similar issue exists for reduced CeO260 and doped TiO2.77 It remains to be investigated how important this intrinsic DFTþU error is for the reactivity of oxides.

5. CONCLUSIONS Ce and Zr doping of rutile TiO2 has been studied using DFTþU and the HSE06 screened exchange implementation of hybrid DFT. While both approaches give some qualitatively similar results, namely, favorable incorporation of the dopants, reduced oxygen vacancy formation energies with Ce doping, and larger oxygen vacancy formation energies for Zr doping, the HSE06 results highlight some issues with DFTþU. These include the DFTþU oxygen vacancy formation energy and the inherent band gap underestimation in DFTþU. The latter can lead to incorrect conclusions regarding the effect of the dopant on the band gap of the oxide, which given the substantial effort presently deployed in studying doped TiO2 for renewable energy applications is cause for concern. In addition, the position of defect states resulting from oxygen vacancy formation will always show errors with DFTþU. Work on other dopants and defects in TiO2 and CeO2 show that these errors with DFTþU are general, and in the future, using DFTþU to study defects and dopant in metal oxide, one must assess the error in the DFTþU calculation and its importance, which is achieved by comparison with accurate hybrid DFT calculations. ’ ASSOCIATED CONTENT

bS

Supporting Information. Figures S1S6 and Tables S1 and S2. This information includes the effect of a small core Ti PAW potential on the density of states of Ce-doped bulk rutile, the effect of the U parameter on Ti and Ce on the DOS, data for the (2 4) rutile (110) supercell, the effect of the U parameter on the oxygen vacancy formation process in bulk rutile, and data for an oxygen vacancy in the (2 4) rutile (110) surface supercell. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 13005



’ ACKNOWLEDGMENT This work was supported by Science Foundation Ireland through the Starting Investigator Grant Program (EMOIN SFI SIRG/09/I1620). We also acknowledge SFI-funded computational resources at Tyndall and the SFI/Higher Education Authority funded Irish Centre for High Performance Computing for the generous provision of computing resources. ’ REFERENCES (1) Diebold, U. Surf. Sci. Rep. 2003, 48, 53. (2) Fujishima, A.; Zhang, X.; Tryk, D. A. Surf. Sci. Rep. 2008, 63, 515. (3) Nowotny, J. Energy Environ. Sci. 2008, 2, 565. (4) Gesenhues, D. Solid State Ionics 1997, 101103, 1171. (5) Cui, Y.; Du, H.; Wen, L. S. J. Mater. Sci. Techol. 2008, 24, 675. (6) Peng, H. W.; Li, J. B.; Li, S. S.; Xia, J. B. J. Phys. Condens. Matter 2008, 20, 125207. (7) Nie, X. L.; Zhou, S. P.; Maeng, G.; Sohlberg, K. Int. J. Photoenergy 2009, 294042. (8) Di Valentin, C.; Pacchioni, G.; Onishi, H.; Kudo, A. Chem. Phys. Lett. 2009, 469, 166. (9) Yu, J. G.; Xiang, Q. J.; Zhou, M. H. Appl. Catal., B 2009, 90, 595. (10) Bian, L.; Song, M. X.; Zhou, T. L.; Zhao, X. Y.; Dai, Q. Q. J. Rare Earth 2009, 27, 461. (11) Zhu, W. G.; Qiu, X. F.; Iancu, V.; Chen, X. Q.; Pan, H.; Wang, W.; Dimitrijevic, N. M.; Rajh, T.; Meyer, H. M.; Paranthaman, M. P.; Stocks, G. M.; Weitering, H. H.; Gu, B. H.; Eres, G.; Zhang, Z. Y. Phys. Rev. Lett. 2009, 103, 2264101. (12) Zhang, J.; Pan, C. X.; Fang, P. F.; Wie, J. H.; Xiong, R. ACS Appl. Mater. Interfaces 2010, 2, 1173. (13) Gai, Y. Q.; Li, J. B.; Li, S. S.; Xia, J. B.; Wei, S. H. Phys. Rev. Lett. 2009, 102, 036402. (14) Morgan, B. J.; Scanlon, D. O.; Watson, G. W. J. Mater. Chem. 2009, 19, 5175. (15) Di Valentin, C.; Finazzi, E.; Pacchioni, G.; Selloni, A.; Livraghi, S.; Paganini, M. C.; Giamello, E. Chem. Phys. 2007, 339, 44. (16) Stashans, A.; Bermeo, S. Chem. Phys. 2009, 363, 100. (17) Yin, W. J.; Tang, H. W.; Wei, S. H.; Al-Jassim, M. M.; Turner, J.; Yan, Y. F. Phys. Rev. B 2010, 82, 045106. (18) Pacchioni, G. J. Chem. Phys. 2008, 128, 182505. (19) Lany, S. Phys. Status Solidi B 2011, 248, 1052. (20) Lany, S.; Zunger, A. Modell. Simul. Mater. Sci. Eng. 2009, 17, 084002. (21) Pacchioni, G.; Frigoli, F.; Ricci, D.; Weil, J. A. Phys. Rev. B 2001, 63, 054102. (22) Laegsgaard, J.; Stokbro, K. Phys. Rev. B 2002, 65, 075208. (23) Zhang, Y.; Yuwomo, A. H.; Wang, J.; Li, J. J. Phys. Chem. C 2009, 113, 21406. (24) Sidheswaran, S.; Tavlarides, L. L. Ind. Eng. Chem. Res. 2009, 48, 10292. (25) Zhu, J. J.; Ao, Y. H.; Fu, D. G. Appl. Surf. Sci. 2009, 256, 884. (26) Ma, T. Y.; Cao, J. L.; Shao, G. S.; Zhang, X. J.; Yuan, Z. Y. J. Phys. Chem. C 2009, 113, 16658. (27) Silva, A. M. T.; Silva, C. G.; Drazic, G.; Farina, J. L. Catal. Today 2009, 144, 13. (28) Chen, S. W.; Lee, J. M.; Lu, K. T.; Pao, C. W.; Lee, J. F.; Chan, T. S.; Chen, J. M. Appl. Phys. Lett. 2010, 97, 012104. (29) Fu, C.; Li, T.; Qi, J.; Pan, J.; Chen, S.; Cheng, C. Chem. Phys. Lett. 2010, 494, 117. (30) Liu, H. J.; Liu, G. G.; Zhou, Q. X. J. Solid State Chem. 2009, 182, 3238. (31) Wang, G. P.; Qiu, W.; Ren, C. J.; Chai, J. J.; Dong, W.; Chen, Y. Q.; Gong, M. C. Chin. J. Catal. 2009, 30, 931. (32) Luo, S. X.; Wang, F. M.; Shi, Z. S.; Xin, F. Mater. Res. Innovations 2009, 13, 64. (33) Lippens, P. E.; Chadwick, A. V.; Weibel, A.; Bouchet, R.; Knauth, P. J. Phys. Chem. C 2008, 112, 43. (34) Long, R.; English, N. J. Chem. Phys. Lett. 2010, 498, 338.

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Electronic Structure and Reactivity of Ce- and Zr-Doped TiO2

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