J. Phys. Chem. C 2010, 114, 6511–6517
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Theoretical Confirmation of the Enhanced Facility to Increase Oxygen Vacancy Concentration in TiO2 by Iron Doping Alberto Rolda´n,†,‡ Merce´ Boronat,§ Avelino Corma,*,§ and Francesc Illas† Departament de Quı´mica Fı´sica & Institut de Quı´mica Teo`rica i Computacional (IQTCUB), UniVersitat de Barcelona, C/ Martı´ i Franque`s 1, 08028 Barcelona, Spain, Departament de Quı´mica Fı´sica i Inorga`nica, UniVersitat RoVira i Virgili, C/ Marcel · lı´ Domingo s/n, 43007 Tarragona, Spain, and Instituto de Tecnologı´a Quı´mica, UPV-CSIC, AV. los Naranjos, s/n, Valencia, Spain ReceiVed: December 15, 2009; ReVised Manuscript ReceiVed: February 24, 2010
The effect of Fe-doping on the oxygen vacancy energy formation and on the electronic structure of stoichiometric bulk and (001) surface of TiO2 anatase has been studied by means of periodic density functional calculations within the GGA+U approach. The vacancy energy formation is always lower for the surface than for the bulk. The presence of Fe causes only a minor perturbation of the atomic structure of anatase but strongly reduces the oxygen vacancy energy formation, especially at the surface. The present results provide additional and independent support to the claim that the enhanced catalytic activity of Au nanoparticles supported on Fe-doped TiO2 toward CO oxidation has its origin in the ease to create oxygen vacancies in the support. 1. Introduction Titanium dioxide is widely used in several fields related to energy conversion, heterogeneous catalysis, and photocatalysis.1-4 The discovery of the high catalytic activity of gold nanoparticles supported on transition metal oxides5-11 and, specially, the remarkable activity and selectivity for CO and alcohol oxidation12,13 increased the interest in TiO2 as a support for heterogeneous oxidation catalysts. Since then, numerous experimental14-18 and theoretical19-25 studies have been published about the mechanism of CO oxidation by supported gold. Although the way in which oxygen is activated is not completely clear, the positive role of oxygen vacancy defects on reduced oxide surfaces has been stressed.26-29 In this sense, the high catalytic activity of gold supported on nanostructured ceria has been related to the ability of Ce to change oxidation state from Ce4+ to Ce3+ thus facilitating the formation of surface oxygen vacancies.30-33 It has also been demonstrated that doping of CeO2 with other elements such as Zr, Ti, Hf, Ni, or Pd results in an increased concentration of oxygen vacancies, presumably because doping with these elements reduces the oxygen vacancy formation energy, and a concomitant enhancement of the corresponding surface reactivity.34-38 In a similar way, it has been reported that doping of TiO2 with Fe increases the oxidation activity of Au/TiO2 catalyst and this has been related to a higher density of oxygen vacancies which contribute to activate O2.39,40 Again, this catalytic enhancement has been attributed to the increased presence of oxygen vacancies whose formation would be facilitated by the presence of Fe. In the case of CO oxidation by Au clusters supported on Fedoped TiO2, the experiments provide clear indication that the main effect due to the presence of Fe is likely to facilitate O vacancy formation28 although one must realize that this is rather indirect evidence. Unfortunately, the direct measurement of the oxygen vacancy formation energy at the surface of the support †
Universitat de Barcelona. Universitat Rovira i Virgili. § UPV-CSIC. ‡
and the effect of Fe on this quantity is very hard if not impossible. Theoretical models offer, no doubt, a good alternative since the calculations based on density functional theory have proven to be very robust, predictive, and useful although they are not exempt of problems. Obtaining a direct estimate of the effect of the presence of Fe on the energy formation of oxygen vacancies is precisely the aim of the present work. The structural and electronic properties of the most common phases of TiO2, rutile and anatase, have been extensively investigated from a theoretical point of view.41-46 These studies have concluded that standard DFT methods in the GGA approximation fail to describe the nature of oxygen vacancy defects present in reduced TiO2. This is due to the well-known shortcomings of standard LDA and GGA to describe the electronic structure of simple and transition metal oxides.47 In fact, these methods usually lead to too small values of the calculated band gap, which impedes the study of changes in the electronic structure induced by the presence of these point defects and predict these materials to be metallic even when many of them are commonly antiferromagnetic insulators. Therefore, a correct description of these systems requires methods that go beyond the standard LDA and GGA implementations of density functional theory such as the use of hybrid functionals or the inclusion an on-site correlation Hubbard term resulting in the so-called LDA+U or GGA+U methods.48 In the present work, the formation energy of an isolated oxygen vacancy in the bulk of anatase and on different surface and subsurface positions of its (001) crystal face have been calculated using standard GGA and also GGA+U density functional theory based methods. The choice for the anatase polymorph of TiO2 comes form the fact that this is the most abundant phase of the TiO2 catalyst. Likewise, the choice of the (001) surface is justified because this is the most reactive and hence the one which, in principle, is active in the catalyst and has been the object of special methods of preparation to increase its surface in TiO2 nanoparticles.49 The influence of the methodology on the computed oxygen vacancy formation energies, geometrical distortions, degree of localization of the
10.1021/jp911851h 2010 American Chemical Society Published on Web 03/12/2010
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electrons in the point defect, and electronic structure of the reduced material have been analyzed in detail, and has allowed us to go one step further and to study the effect of Fe on the electronic structure and energetics of oxygen vacancy formation. We present compelling evidence that the presence of Fe does indeed largely facilitates the formation of oxygen vacancies at the bulk and at the (001) surface of anatase. 2. Computational Details and Materials Models Calculations have been performed within the usual Kohn-Sham (KS) implementation of density functional theory using the VASP code.50,51 The generalized gradient approximation (GGA) has been employed with the PW91 functional.52 The inner electrons have been described by the projector augmented wave (PAW) method53 and the KS valence states expanded in a planewaves basis set with a cut off at 515 eV for the kinetic energy. Because removal of one oxygen atom leaves two electrons localized in adjacent Ti atoms which are reduced from Ti4+ to Ti3+ and because the introduction of a Fe cation in the lattice will necessarily include unpaired electrons it is strictly necessary to take spin polarization effects into account. States with different number of unpaired electrons (NR - Nβ ) 0, 2, and 4) have been considered in the study of the reduced and doped systems. Charge distributions and spin densities were estimated by making use of the theory of atoms in molecules (AIM) of Bader.54 Calculations have also been carried out using the GGA+U method48,55,56 that improves the description of localized states in this type of systems where standard LDA and GGA functionals fail.47 A problem with the GGA+U method is the rather empiric character of the choice of the U parameter, a feature which also appears when using hybrid functionals since the amount of Fock exchange is system dependent.47,57-61 Therefore, we followed the approach used by Loschen et al.62 to determine the U value for ceria and employed a wide range of U values from 4 to 10 eV for the Ti 3d orbitals. An optimum value of U ) 4 eV has been chosen on the basis of comparison of the computed lattice parameters, bulk modulus and band gap with the available experimental data. Indeed, this is close to the value used recently to study complex catalytic systems containing metals supported on a mixed CeOx/TiO2 support.63 Anatase TiO2 was modeled by means of a 3 × 3 × 1 supercell containing 36 Ti atoms and 72 O atoms. The optimized lattice parameters are a ) b ) 3.80 Å and c ) 9.60 Å for a pure GGA optimization and a ) b ) 3.876 Å and c ) 9.639 Å for the GGA+U (U ) 4) calculation, in close agreement with the experimental values (a ) b ) 3.791 Å and c ) 9.515 Å).64 A model for Fe-doped anatase (Fe-TiO2) was created by substituting one Ti atom in the 108 atom anatase supercell by one Fe atom, resulting in a model with 2.8% Fe. The lattice parameters obtained for pure TiO2 were also employed for Fe-TiO2. Oxygen vacancy defects were created by just removing one oxygen atom from the TiO2 and Fe-TiO2 models, without further optimization of the lattice parameters. The reciprocal space of these cells was described by a Monkhorst-Pack mesh65 with 3 × 3 × 3 k-points. In these supercell bulk calculations, the atomic positions of all Fe, Ti, and O atoms were fully relaxed until calculated forces on relaxed atoms are lower than 0.03 eV/Å. The (001) surface of anatase was modeled by means of a 3 × 3 supercell slab model containing 4 TiO2 trilayers, that is, 12 atomic layers (36 Ti atoms and 72 O atoms), and a vacuum width of 10 Å between vertically repeated slabs. A model for an Fe-doped surface was created by substituting one five-
Figure 1. Bulk of stoichiometric (left) and reduced (right) TiO2 with the labeling of the distances summarized in Table 1. Ti atoms are blue, O atoms are red, and the black circle shows the position of the oxygen vacancy defect.
coordinated Ti atom at the surface by a Fe atom. The atomic positions of the four uppermost layers were fully relaxed, and a Monkhorst-Pack mesh with 3 × 3 × 1 k-points was employed in these calculations. Oxygen vacancy defects were created by removing one oxygen atom from either TiO2 or Fe-TiO2 models and optimizing the positions of the two Ti layers and three O layers closer to the vacancy. Test calculations carried out for the stoichiometric TiO2(001) surface and for the same system with a surface oxygen vacancy show that full relaxation of three Ti and six O layers lowers the energy of the former by 0.02 eV only and that of the latter by 0.25 eV. Consequently, the O vacancy formation energy at the surface of TiO2(001) is only affected by 0.23 eV. In the discussion below we will show that the conclusions of the present work are based on much larger energy differences. Therefore, the models used in the present work are adequate enough although one must admit that more accurate values of surface oxygen vacancy formation energy may require the use of slab models with an increased number of atomic layers and also to include full relaxation of a larger number of layers. 3. Results and Discussion 3.1. Bulk Stoichiometric and Reduced TiO2. The geometries of stoichiometric and reduced bulk TiO2 were optimized at GGA and GGA+U levels including spin polarization and considering two possible states, a low spin state with all electrons paired (NR - Nβ ) 0) and a high spin state with two unpaired electrons (NR - Nβ ) 2). Unless otherwise specified a value of U ) 4 eV has been employed in the GGA+U calculations. As could be expected for stoichiometric TiO2, the low spin closed-shell solution is the most stable at both GGA and GGA+U levels. The optimized geometries are equivalent at both theoretical levels, with Ti-Ti distances in the xy plane (r(Ti-Ti)a in Figure 1 and Table 1) larger than those between layers (labeled as r(Ti-Ti)b), and no relevant differences are found either in the charge distribution. The effect of the U term is only reflected in the electronic structure. In fact, the band gap predicted by pure GGA is 1.9 eV, similar to other published DFT values66,67 but clearly underestimated when compared to the experimental value of 3.2 eV.68,69 Inclusion of a U term helps to correct this deficiency but only in a modest way. Hence, the GGA+U calculated band gap is 2.7 eV, in agreement with previous estimations at similar levels42,46 but still far from the experimental value. A calculated value of 3.1 eV, much closer to experiment, is obtained for U ) 10 eV. However, such a high value for the U term has no physical meaning and, therefore, has not been further used. Accordingly, GGA+U calculations have been performed with a value of U ) 4 eV similar to that used by other authors to describe the electronic structure of TiO2, either anatase42 or rutile.43,44
Increasing Oxygen Vacancy Concentration
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TABLE 1: Optimized Values of Selected Ti-Ti and Ti-O Distances in Stoichiometric and Reduced TiO2, Net Atomic Charges and Spin Densities on Ti Atoms, and Oxygen Vacancy Formation Energies (Ef) Calculated at the GGA and GGA+U (U ) 4 eV) Levels of Theory TiO2-VO
TiO2 NR - N β r(Ti-Ti)a (Å) r(Ti-Ti)b (Å) r(Ti-Ti)V (Å) r(Ti-O)a (Å) r(Ti-O)b (Å) qTi (e) µTi Ef (eV)
GGA
GGA+U
GGA
GGA
GGA+U
GGA+U
0 3.820 3.067
0 3.876 3.092
1.952 1.997 2.19 0
1.979 2.010 2.30 0
0 3.820 3.067 4.098 1.949 2.011 2.18 0.20 4.95
2 3.779 3.065 4.281 1.936 2.020 2.16 0.04 4.45
0 3.84-3.88 3.083 3.943 1.96 - 1.99 1.98 - 2.01 2.30 0.00 5.23
2 3.77-3.88 3.049 4.092 1.94 - 1.98 2.00 - 2.06 1.98 0.84 5.26
The description of reduced TiO2 is more complex and varies with the computational method employed as has been elegantly shown by Finazzi et al.42 Therefore, we will only report the most salient features which are related to the main goal of the present work. At the pure GGA level the low spin solution, with the excess electrons associated to the defect fully delocalized over all Ti atoms in the oxide, is the most stable but clearly against experimental evidence.70,71 At the GGA+U level, however, both solutions (localized and delocalized) are similar in energy, with a difference between them of less than 0.04 eV. The low spin solution is of closed shell type and the electron density arising from the trapped electrons is delocalized, with calculated atomic net charges around 2.3 e on all Ti atoms and with a negligible spin density on any of them. The high spin GGA+U solution corresponds, however, to two electrons fully localized at the two Ti atoms near the vacancy. Obviously, a nearly degenerate open-shell low spin solution exists with the two unpaired electrons antiferromagnetically coupled which has not been considered since it differs from the high spin one only in the number of unpaired electrons (see for instance ref 72). The atomic charge on the two Ti atoms near the oxygen vacancy is 1.98 e, and the calculated spin density is 0.84, indicating that they have been reduced from Ti4+ to Ti3+. The nature of the solution is also reflected in the local geometry distortion around the defect. When the solution is delocalized, the optimized value of the distance between the two Ti atoms involved in the defect, r(Ti-Ti)V in Figure 1 and Table 1, is only 0.1 Å larger than the other r(Ti-Ti)a distances. This is not the case when the two electrons are localized on the Ti atoms close to the vacancy, since the GGA+U high spin solution predicts that the distance between these two atoms increases up to 4.092 Å, that is, 0.322 Å larger than the other r(Ti-Ti)a distances. The oxygen vacancy energy formation (Ef) has been calculated as
Ef ) E(Ti36O71) + 1/2E(O2) - E(Ti36O72)
It has already been mentioned that the presence of Ti3+ species in reduced TiO2 causes the appearance of electronic states in the gap at ∼1 eV below the bottom of the conduction band,41 a feature that is not well reproduced by pure GGA methods. Figure 2 shows the density of states (DOS) obtained at the GGA+U level for bulk anatase which is enough to highlight the main feature of the electronic structure. In stoichiometric TiO2, the valence band is dominated by the O 2p states whereas the conduction band consists mainly of Ti 3d states resulting in a GGA+U calculated band gap of 2.67 eV. The analysis of the DOS by appropriate projection (not shown), evidence considerable hybridization beween O 2p and Ti 3d states which indicates a large degree of covalence in agreement with previous analysis of chemical bond in rutile showing that net charges on the Ti atom in TiO2 are far from the formal +4 oxidation state.73 In the reduced system, states 0.5 eV below the conduction band, but below the Fermi level, appear in the DOS plot which are associated to the electrons localized on the 3d orbitals of the two Ti atoms close to the vacancy that are formally Ti3+. This picture is in qualitative
(1)
where E(Ti36O72) is the total energy of the low spin solution for bulk TiO2, using the 3 × 3 × 1 supercell described above, E(O2) is the total energy of a oxygen molecule in the “triplet” state calculated with the same computational setup used for the oxide, and E(Ti36O71) is the energy of the same supercell with one oxygen removed thus resulting in a TiO1.972 stoichiometry for the reduced system. All energies are obtained at the corresponding computational level, as described in Table 1. The calculated Ef values range between 4.5 and 5.3 eV, in agreement with previous estimations,41,42,45,46 and provide the necessary reference for further comparison (see below).
Figure 2. Total density of states calculated at GGA+U level for bulk TiO2 and Fe-TiO2. Vertical dashed line shows the position of the Fermi level.
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TABLE 2: Optimized Values of Selected Ti-Ti and Ti-O Distances in Stoichiometric and Reduced TiO2 Surfaces, and Oxygen Vacancy Formation Energies (Ef) Obtained at the GGA+U Level for Vacancies at the Surface (VO1) and up to the Fourth Atomic Layer (VO2-VO4) surface r(Ti-Ti)a (Å) r(Ti-Ti)b (Å) r(Ti-Ti)V (Å) r(Ti-O)a (Å) r(Ti-O)b (Å) Ef (eV)
3.876 3.049 1.965, 1.995 1.937
VO1
VO2
VO3
VO4
3.29 - 3.91 3.055 5.048 1.85-2.00 2.034 2.73
3.74-3.90 3.177 4.166 1.93-2.04 1.95-2.03 4.80
3.68-3.89 3.101 4.262 1.82-1.99 1.89-2.02 4.87
3.72-3.88 3.084 4.179 1.84-2.00 1.97-2.04 5.85
agreement with the experimental information and with previous studies using GGA+U and hybrid functionals42,46 and allows us to conclude that the GGA+U method (with U ) 4 eV) correctly reproduces the structural and electronic features of bulk TiO2. The rest of the study has therefore been performed only at this computational level. 3.2. Stoichiometric and Reduced Anatase (001) Surface. As previously found for bulk TiO2, the stoichiometric TiO2 (001) anatase surface is clearly described by a low spin, closed shell, solution. Structural optimization of the surface slab model leads to a small contraction of the structure in the z axis, that is, perpendicular to the surface, reflected in a shortening of the r(Ti-Ti)b and r(Ti-O)b distances in relation to the bulk (see Tables 1 and 2). Oxygen vacancy defects were created on the TiO2(001) anatase surface at the different positions depicted in Figure 3. For each position the oxygen atom was removed from the stoichiometric surface model, and then, two titania and three oxygen layers around the selected position were fully relaxed. For the reduced surfaces, the high spin solutions with two unpaired electrons are more stable than the low spin ones, although the energy difference between them decreases from 0.96 eV in VO1 to nearly zero in VO3 and VO4. The formation energy of an oxygen vacancy at VO1 position on the surface is the lowest. The two electrons associated to the defect are clearly localized on the two Ti atoms in direct contact with the vacancy, that are reduced from Ti4+ to Ti3+ as indicated by the calculated atomic charges (1.97) and spin densities (0.94). The local geometry distortion around the defect at the surface is considerably larger than in the bulk. The distance between the two reduced Ti3+ atoms increases to 5.048 Å, and as a consequence, some of the other Ti-Ti distances in the surface decrease from 3.876 Å (the optimized value in the stoichiometric surface) to 3.292 Å. The formation of a oxygen vacancy in any of the other three positions considered in the present work requires at least 2 eV more. The calculated Ef values for VO2, with the oxygen atom belonging to the first TiO2 layer, and for VO3, with the oxygen atom being under the surface, are similar, 4.8 and 4.9 eV, respectively. The formation of an oxygen vacancy on VO4 position requires an energy of 5.85 eV, a value that should converge to that obtained for the bulk, 5.26 eV. The discrepancy between these two values is
Figure 3. Oxygen vacancy defects created at the (001) surface of anatase viewed along a (left) and b (right) crystallographic axis.
TABLE 3: Optimized Values of Selected Fe-Ti and Fe-O Distances, Net Atomic Charges, and Spin Densities on Fe and Ti Atoms Obtained for Stoichiometric and Reduced Fe-TiO2 at the GGA+U Level r(Fe-Ti)a (Å) r(Fe-Ti)b (Å) r(Fe-Ti)V (Å) r(Fe-O)a (Å) r(Fe-O)b (Å) qFe (e) qTi (e) µFe µTi µO-Fe
bulk
bulk-VO
3.875 3.073
3.75-3.85 3.033 4.132 1.98-1.99 2.04-2.08 1.38 2.35 (2.30) 3.56 0 0.10
1.996 1.848 1.63 2.35 3.17 0 0.10
surface 3.885 3.041 1.87-1.92 2.077 1.66 2.35 3.06 0 0.27, 0.18
surface-VO 3.16-3.91 3.015 4.979 1.88-2.07 2.035 1.35 2.35 (2.26) 3.52 0 0
caused by the different degree of geometry relaxation in bulk and surface calculations. In the last case, a number of layers is kept fixed during the geometry optimizations in order to simulate the bulk, thus allowing a poorer geometrical relaxation around the defect that results in a larger value of Ef. Nevertheless, the clear conclusion from these calculations is that formation of oxygen vacancy defects is easier at surfaces than in the bulk. This is in agreement with the results obtained by Carrasco et al.74 for the formation of O vacancies in MgO although MgO and TiO2 are chemically very different. We close this subsection by mentioning a recent paper by Cheng and Selloni75 where these authors reported that in anatase oxygen vacancies are more stable at subsurface than at surface sites. However, we must point out that these authors employed different surface models and, more importantly, a pure GGA exchange-correlation potential without including spin polarization into account. Therefore, it is not possible to compare their results to those described in the present work which, in principle, are more accurate. 3.3. Fe-TiO2. Doping TiO2 with iron results in a more complex electronic structure since one does also need to determine the oxidation state of Fe and the total number of unpaired electrons in the system. From simple chemical arguments one would expect Fe3+ and since the unit cell is neutral and contains an even number of electrons it is possible to have a high spin state with four unpaired electrons (NR - Nβ ) 4), a low spin state with just two unpaired electrons (NR - Nβ ) 2) and even a singlet state of closed-shell type. Calculations were carried out for all these possible cases and it was found that, for bulk Fe-doped anatase, the high-spin solution is the ground state in agreement with Mo¨sbauer spectra data.27 At the GGA+U level (U ) 4 eV), the low spin solution with two unpaired electrons is only 0.13 eV higher in energy, while the singlet solution is by far the most unstable. The energy difference between the high spin and low spin solutions increases to 0.29 eV when an oxygen vacancy defect is created in bulk Fe-TiO2, and to 0.45 eV for the stoichiometric and reduced Fe-TiO2(001) surfaces. Therefore, only the results obtained for the high spin solution are discussed in this section.
Increasing Oxygen Vacancy Concentration
Figure 4. Bulk of reduced Fe-TiO2 with the labeling of the distances summarized in Table 3. Ti atoms are blue, O atoms are red, Fe atom is yellow, and the black circle shows the position of the oxygen vacancy defect.
Figure 5. Optimized structure of stoichiometric (left) and reduced (right) (001) Fe-TiO2 surfaces with the labeling of the distances summarized in Table 3. The calculated spin density on selected O atoms of the stoichiometric surface is also shown.
The geometry of bulk Fe-doped anatase summarized in Table 3 is quite similar to that of pure TiO2 (see Table 1) as expected from the low concentration of dopant. Thus, the optimized Fe-Ti distances are almost equivalent to the Ti-Ti values, and only the Fe-O distances in the c direction (r(Fe-O)b) are 0.16 Å shorter than the corresponding Ti-O values. This is not surprising if we take into account that the ionic radius of Fe3+ and Ti4+ are 0.64 and 0.68 Å respectively, so that substitution of one Ti4+ by a Fe3+ in the oxide structure should not imply important structural deformations. The same is observed for the stoichiometric surfaces, although in this case the Fe-O distance along c is slightly longer than the corresponding Ti-O value. Creation of an oxygen vacancy defect in bulk Fe-TiO2 results in an elongation of the (Fe-Ti)V distance from 3.875 to 4.132 Å, a structural change similar to that produced in bulk TiO2. However, the geometry distortion around the defect in the case of the Fe-TiO2 surface is much more important. The (Fe-Ti)V increases from 3.885 to 4.979 Å, and as a result, the (Fe-Ti)a distance marked in Figure 5 shortens to 3.160 Å, while one of the O atoms bonded to Fe moves upward slightly protruding from the surface. One additional important aspect of the anatase doping with Fe is the energy cost to substitute one Ti cation by Fe. For the bulk Fe-doped anatase, we estimated this substitution cost from eq 2 below
Esubs ) {E(FeTi35O72) + E(Ti)} - {E(Ti36O72) + E(Fe)} (2) where E(FeTi35O72) is the energy of the doped 3 × 3 × 1 supercell, E(Ti) the energy of one isolated Ti atom, E(Ti36O72) the energy of the anatase 3 × 3 × 1 supercell, and E(Fe) the energy of one isolated Fe atom. In all cases, spin polarization is taken into account and the structure fully relaxed. A similar
J. Phys. Chem. C, Vol. 114, No. 14, 2010 6515 procedure is used to compute Esubs for the surface slab models. At the GGA+U level, Esubs is 5.21 and 4.91 eV for the bulk and surface, respectively. This indicates that while doping is possible, as experimentally demonstrated,39 it is by no means an easy task. Here, one may claim that a U term is needed for the Fe 3d states as it is needed for the Ti 3d ones. Using U ) 3 for Fe 3d76 slightly increases the Esubs value from 5.21 to 5.64 eV indicating that the qualitative description of the Fe-doped anatase system provided by the GGA+U calculations with U in the Ti 3d states only remains unaltered when adding a U term to Fe too. Let us now focus on the electronic structure of these systems with some more detail. The calculated atomic charges and spin densities on Fe and Ti suggest that, in the process of creating an oxygen vacancy defect, Fe3+ is reduced to Fe2+ while Ti4+ maintains its oxidation state. The net atomic charge on Fe decreases by ∼0.3 e when either the bulk or the surface are reduced by removing one oxygen atom from the supercell, while the net atomic charge on the Ti atom in contact with the vacancy decreases by 0.05-0.09 e only. The calculated spin densities summarized in Table 3 indicate that, on stoichiometric Fe-TiO2, three of the four unpaired electrons of the system are fully localized on the Fe atom, while the other one is shared among the oxygen atoms directly bonded to Fe. Particularly large are the spin densities on the O atoms of the Fe doped surface shown in Figure 5. On the reduced models the spin density on the Fe atom increases to 3.5, indicating that Fe3+ is reduced. However, the calculated spin density on Ti atoms is negligible in all cases, showing that it always exists (formally) as Ti4+ and its oxidation state is not modified during the process. The description of the electronic structure arising from net charges and spin density analysis above is consistent with the picture arising from the qualitative density of states (DOS). Figure 2 reports the DOS obtained for stoichiometric Fe-TiO2 and shows a valence band corresponding to the O 2p states in both spin manifolds mixed with the Fe 3d states in the majority spin manifold while the conduction band consist of Ti 3d states. An intermediate state for the minority manifold only associated to the empty Fe 3d orbitals appears at 1.36 eV above the valence band. This is consistent with an Fe3+ oxidation state and hence a d5 configuration. Consequently, the minority spin 3d states are empty and the majority spin counterpart is mixed with the valence band and occupied. This picture is in complete agreement with the recently reported density functional theory calculations of Thimsen et al.67 using the PBE functional. Note, however, that one should expect a more defined and narrow feature corresponding to the occupied 3d states in the majority spin manifold. The lack of such a feature is due to the failure of pure GGA described above since no U term is used for the Fe 3d states. Introduction of a U term for the 3d states results in a localized state and also leads to some small changes in the relatives energies (see above). In the forthcoming discussion we will show that the energy differences supporting the main conclusions of the present work about oxygen vacancy energy formation are large enough and will not be affected by the description of the Fe 3d levels. This will also avoid introducing a second empirical U term. A better description is achievable by means of hybrid functionals but unfortunately this is computational too demanding for the large unit cells used in this work. The band gap calculated for Fe-TiO2 is 2.44 eV, which is narrower than that obtained for pure TiO2. Such a reduction of direct transition energies with increasing iron-dopant concentration has also been observed by UV-vis diffuse reflectance
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TABLE 4: Oxygen Vacancy Formation Energies (Ef) in eV Calculated at GGA+U Level TiO2 Fe-TiO2
bulk
surface
5.26 2.76
2.73 0.82
spectra in TiO2 nanopowders.27 In reduced Fe-TiO2 (Figure 2, bottom) states in the gap disappear as expected from the fact that now Fe gets one extra electron becoming essentially d6 and now there are occupied Fe 3d states in both majority and minority spin manifolds which again are delocalized in the valence band. As occurs with pure TiO2, creation of an oxygen vacancy in the bulk results in a slight increase of the band gap that has a calculated value of 2.67 eV. Finally, let us discuss the effect of Fe on the energy formation of the oxygen vacancy which is the conundrum of the present work. As mentioned in the introduction, it has been proposed that the increase in the oxidation activity of Au/TiO2 catalyst when the support is doped with iron is related to a higher density of oxygen vacancy defects in the Fe-doped TiO2 material.39 The oxygen vacancy formation energies Ef calculated in this work for TiO2 and Fe-TiO2 and summarized in Table 4 confirm that doping with Fe reduces the energy necessary to create an oxygen vacancy in TiO2 by more than 2 eV. And this is true both for the bulk and for the surface. The effect is so large that is unlikely that it will be affected by a better treatment of the Fe 3d level. The Ef obtained for the Fe-TiO2 surface, 0.82 eV, is lower than the values reported for the widely used CeO2, between 1.99 and 2.87 eV,34,36 and only slightly higher than the values reported for Ti-, Zr-, or Hf-doped CeO2.34 This is therefore the reason for the high activity for CO oxidation obtained with Fe-doped Au/TiO2 catalyst. 4. Conclusions The effect of Fe-doping on the oxygen vacancy energy formation and on the electronic structure of stoichiometric bulk and (001) surface of TiO2 anatase has been studied by means of periodic density functional calculations within the GGA+U approach including spin polarization. For the undoped bulk anatase, present calculations are essentially in agreement with previous work,42 although here we also show that the oxygen vacancy formation is easier at the surface than in the bulk. In both cases, the ground state results in the reduction of two Ti4+ cations to Ti3+ with two open shells coupled in a high spin state. The presence of Fe causes only a minor perturbation of the atomic structure of anatase. However, the perturbation in the electronic structure is much larger due to the presence of 3d states which results in a high spin state, in agreement with experiment. Here, it is worth to mention that the accurate description of the electronic structure of reduced anatase, and also of Fe-doped anatase, depends rather strongly on the exchange-correlation functional used and hence some of the fine details may be still under discussion. However, the present results provide compelling evidence that the presence of Fe strongly reduces the oxygen vacancy energy formation, especially at the surface. This conclusion is likely to be much less dependent on the theoretical method used to describe the electronic structure of these materials and provides additional and independent support to the interpretation of Carrettin et al.28 for the enhanced catalytic activity of Au nanoparticles supported on Fe-doped TiO2 toward CO oxidation. Acknowledgment. A.R. is grateful to the Universitat Rovira i Virgili for supporting his predoctoral research through a Ph.D.
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