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Sep 22, 2016 - Bo Zhang,*,† and Xiao Cheng Zeng*,‡,§. †. Laboratory of Amorphous Materials, School of Materials Science and Engineering, Hefei University ...
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Rutile TiO2(011)‑2 × 1 Reconstructed Surfaces with Optical Absorption over the Visible Light Spectrum Rulong Zhou,*,† Dongdong Li,† Bingyan Qu,† Xiaorui Sun,† Bo Zhang,*,† and Xiao Cheng Zeng*,‡,§ †

Laboratory of Amorphous Materials, School of Materials Science and Engineering, Hefei University of Technology, Hefei, Anhui 230009, China ‡ Department of Chemistry and Nebraska Center for Materials and Nanoscience, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States § Hefei National Laboratory for Physical Sciences at Microscale and Collaborative Innovation Center of Chemistry for Energy Materials, University of Science and Technology of China, Hefei, Anhui 230026, China S Supporting Information *

ABSTRACT: The stable structures of the reconstructed rutile TiO2(011) surface are explored based on an evolutionary method. In addition to the well-known “brookite(001)-like” 2 × 1 reconstruction model, three 2 × 1 reconstruction structures are revealed for the first time, all being more stable in the high Ti-rich condition. Importantly, the predicted Ti4O4-2 × 1 surface model not only is in excellent agreement with the reconstructed metastable surface detected by Tao et al. [Nat. Chem. 3, 296 (2011)] from their STM experiment but also gives a consistent formation mechanism and electronic structures with the measured surface. The computed imaginary part of the dielectric function suggests that the newly predicted reconstructed surfaces are capable of optical absorption over the entire visible light spectrum, thereby offering high potential for photocatalytic applications. KEYWORDS: surface reconstruction, Rutile TiO2, first-principles calculation, electronic structure, photocatalysis

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INTRODUCTION Titanium dioxide has attracted extensive research interests because many of its special functionalities can be exploited in broad areas of applications such as photocatalysis,1−7 hydrogen production from water8 or organic chemicals,9 air and water purification,10 self-cleaning surfaces,11 oxygen gas sensors,12 dye-sensitized solar cells,13 rechargeable batteries/supercapacitors,14 and biomedical devices.15 In photocatalytic applications, for example, the ground-state electrons of TiO2 are excited via absorbing photon energy followed by subsequent electron transfer and/or energy transfer to adsorbed molecules.1 Hence, the optical absorption efficiency is critical to the use of TiO2 in photocatalysis. However, most TiO2 polymorphs with a relatively wide bandgap (3.0 eV) can absorb light only in the ultraviolet region with the energy being only ∼5% of the sunlight spectrum. Over the past few decades, many efforts have been made for reducing the bandgap of TiO2 to harvest a wider spectrum of sunlight. One common strategy is to dope TiO2 with impurities.16−18 It is known that the dopants can not only introduce donor or accept states in the band gap to reduce the band gap of TiO2 but also serve as the charge carrier trapping or recombination sites. Although the strategy of doping TiO2 has led to success in achieving the visible light activity, the photocatalytic efficiency of TiO2 is still downgraded. In recent years, the self-structural modification of surfaces has received increasing attention because the dangling © 2016 American Chemical Society

bonds on the surfaces can introduce different states within the band gap while having little influence on the charge carriers in the bulk part. Ariga et al. reported photo-oxidation, within the visible light spectrum, on a pure rutile TiO2(001) surface in 2009.19 Two years later, a metastable rutile TiO2(011)-2 × 1 reconstructed surface was reported by Tao et al., which has an optical band gap of ∼2.1 eV.20 More recently, Dette et al. reported a new anatase TiO2(101) surface with a reduced band gap of ∼2 eV and high chemical reactivity.21 These experimental achievements imply that some metastable reconstructed surfaces of TiO2 may possess photocatalytic properties even better than those of the bulk. To date, although extensive studies have been devoted on the clean surfaces of rutile and anatase TiO2, only a few stably reconstructed surfaces have been observed in experiments. For anatase, the most studied reconstructed surface is the (001) surface which exhibits the 1 × 4 reconstruction.22 For rutile, reconstruction of the (110) surface has been extensively studied both experimentally and theoretically.23 The reconstructions of 1 × 1,24,25 single-linked 1 × 2,23,26 cross-linked 1 × 2,27,28 and pseudohexagonal rosette structures29 have been observed, and several structural models, e.g. the Ti2O3-1 × 2,26 Ti2O-1 × Received: August 25, 2016 Accepted: September 22, 2016 Published: September 22, 2016 27403

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

Research Article

ACS Applied Materials & Interfaces 2,24,25 and Ti3O6-1 × 2 models,28 have been proposed theoretically. However, a consistent conclusion has yet to be achieved. Until recently, Wang et al. confirmed that the previously proposed Ti2O3-1 × 2 and Ti2O-1 × 2 models as well as two newly predicted Ti3O2-1 × 2 and Ti3O3-2 × 1 reconstructions are stable based on an extensive search using the evolutionary method.30 More recently, the studies of reconstruction of the rutile (011) surface become more active due to suggested higher photocatalytic activity. The most favorable reconstruction of the rutile (011) surface is the 2 × 1 reconstruction, whose STM image shows zigzag bright spots.31−34 Several models, e.g. the titanyl,31 microfaceting missing-row structural,33 and “brookite(001)-like” models,34,35 are proposed for the rutile (011) 2 × 1 reconstruction. The brookite(001)-like models proposed by Torrelles et al.35 and Gong et al.34 are proven to be the most energetically stable, consistent with the experimental results. Besides the most stable brookite(001)-like rutile (011) 2 × 1 reconstruction surface, the metastable reconstruction reported by Tao et al. is of particular interest because its band gap matches the visible light and thus possibly gives high reactivity.20 The obtained STM image shows a (distorted) hexagonal arrangement of bright spots, not predicted by any structural models proposed previously. Very recently, Wang et al. suggested that the titanyl model is possibly the structure obtained by Tao et al. based on the simulated STM image and calculated band gap.36 However, their results may be not sufficiently accurate due to the use of asymmetric models with only four TiO2 layers, while the calculated relative surface energies and electronic structures seemed strongly dependent on the model symmetry, the thickness of the slabs, the existence of the fixed atoms, and the dangling bonds on the bottom atoms.33 The inconsistency in the orders of surface energies between those computed by Wang et al. using the asymmetric models and those computed by Gong et al. using the symmetric models indicates that using of asymmetric models for the TiO2 surfaces is not the best choice.34 So, the structure of the metastable reconstructed surface obtained by Tao et al. is still unresolved. Clearly, knowledge of the atomic structure of this new metastable reconstructed surface is of importance both for fundamental understanding of its photocatalytic reactivity and for future applications. In this work, we performed an extensive search for the stable and metastable reconstructions of the rutile (011) surface using the evolutionary method. From our search, besides the brookite(001)-like model, three new 2 × 1 reconstruction structures are revealed, which are more stable in the high Tirich condition. The predicted Ti4O4-2 × 1 model is in good agreement with the metastable surface revealed by Tao et al. in their experiment,20 particularly in the arrangement of surface atoms, simulated STM image, and computed electronic structure, indicating it is most likely the metastable surface found in the experiment. The computed imaginary part of the dielectric function shows that the Ti4O4-2 × 1 model can absorb sunlight over nearly all the wavelengths, thereby offering high potential for photocatalytic applications.

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surfaces.30,40 For the surface structure search, each candidate surface structure is divided into the vacuum, surface region, and substrate, and only the surface region is optimized. Here, we separately performed two distinct searches so that we could confirm the most stable and metastable rutile TiO2(011) reconstruction surfaces observed experimentally while predicting some new stable or metastable surface structures. The first one is a fixed-cell search, and the second one is a variable-cell search; for both, the compositions are allowed to vary. For the fixed-cell search, only the 2 × 1 reconstruction is considered as only the 2 × 1 reconstruction is reported from experiments. Each supercell contains a vacuum layer of 10−12 Å, a surface region with maximally four Ti atoms and eight O atoms, and a substrate layer of three TiO2 layers. The atoms in the surface region and those in the top region of 2.5 Å of the substrate are fully relaxed. One hundred populations are generated randomly in the initial generation, and then 30 populations are generated according to the evolution operations in the following generations. At most, 30 generations and more than 1000 structures are explored in the entire fixed-cell search. For the variable-cell search, the 1 × 1, 1 × 2, and 2 × 1 supercells are considered, and at most two Ti and four O atoms are added in the surface region per surface unit cell. Different from the fixed-cell search, 200 populations and 40 populations are generated for the initial generation and the following generations, respectively, and 40 generations are explored. Two different substrate structures are employed in our search to ensure nonmissing of any low-energy reconstructed surfaces. One is the cleaved slab with the top surface terminated with O atoms, while the bottom surface is terminated with Ti atoms. Another one is the unreconstructed rutile (011) surface with the same top and bottom surfaces. Each structure is relaxed using the first-principles method at medium accuracy level, and the low-energy structures are collected for ensuing high-level optimization and detailed analysis. To obtain accurate relative formation energies, a symmetric slab containing 11 TiO2 layers for the lowest-energy structure of each stoichiometry is made for structural relaxation without any constraints, followed by electronic structural calculations. The spin-polarized density functional theory (DFT) computations for structural relaxation and electronic structural calculation are performed using the VASP package.43,44 The Perdew−Burke− Enzerhof (PBE)45 exchange-correlation functional within the generalized gradient approximation is adopted. An all-electron plane-wave basis set with an energy cutoff of 450 eV is used. The projector augment wave (PAW) pseudopotentials are chosen to describe the interactions of elements, where the valence configurations of O and Ti are 2s22p4 and 3p63d24s2, respectively. A dense K-point sampling with the grid spacing less than 2π × 0.04 Å−1 in the Brillouin zone is selected for the structural relaxation. The ionic positions are fully relaxed until the residual force acting on each ion is less than 0.01 eV/ Å. In the electronic computation, a more dense K-point sampling with the grid spacing less than 2π × 0.02 Å−1 is selected together with the GGA + U (U = 4.1 eV)30 method.

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RESULTS AND DISCUSSION

The relative stabilities of different surface structures can be evaluated according to the formation energies given by the following formula: Eformation =

1 [Etot − nOμO − n TiμTi ] N

(1)

where Etot is the total energy of the surface under consideration, nO and nTi are the number of O and Ti atoms in the supercell, respectively, μO and μTi are the chemical potentials of O and Ti, respectively, and N is the number of surface unit cells in the supercell. Chemical potentials (μO and μTi) have the 1 constraints: μO ≤ 2 μO , μTi ≤ μTibulk , and μTi + 2 μO = ETio2, in

COMPUTATIONAL METHODS

The search for the stable and metastable structures of the rutile (011) surface is performed using the evolutionary algorithm implemented in the USPEX package.37−40 The algorithm has been shown by many previous researchers to be very effective in predicting the most stable structures of bulk crystals,39,41,42 nanostructures,37 and solid

2

which ETio2 is the internal energy of the bulk rutile TiO2 unit cell. Eq 1 can be converted to 27404

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

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ACS Applied Materials & Interfaces 1 [Etot − n TiE TiO2 − μO(nO − 2n Ti)] (2) N According to the constraints of the chemical potentials, the 1 1 permitted range of μO is 2 (E TiO2 − μTibulk ) ≤ μO ≤ 2 μO . 2 The computed formation energies of different stoichiometric surfaces with respect to the chemical potential of O are shown in Figure 1. Clearly, within most of the permitted range of μO

atoms in the supercell). Therefore, it is difficult to determine which structure is more likely to be formed experimentally just based on the calculated formation energies. As shown in Figure 1, the O-rich surface structures are all less stable than the unreconstructed and brookite(001)-like 2 × 1 reconstructed rutile (011) surfaces, even at high O-rich conditions. The microfaceting missing-row structural model is energetically the least stable among all the structural models considered. ΔEformation between the microfaceting missing-row model and the unreconstructed surface at μOmax is 1.4 eV, and that between the microfaceting missing-row model and the brookite(001)-like model is 2.2 eV. Therefore, it may be challenging to synthesize the microfaceting surface experimentally. We found an O-rich reconstructed structure (denoted as Ti4O9-2 × 1) more stable than the microfaceting model. The formation energy of Ti4O9-2 × 1 at μOmax is 0.38 and 1.15 eV higher than that of the unreconstructed and brookite(001)-like surface, respectively. Compared to the microfaceting missingrow structural model, the Ti4O9-2 × 1 model is more likely to be formed under high O-rich conditions. Structures of the reconstructed surfaces predicted are shown in Figure 2. For comparison, the structures of the O-terminated

Eformation =

Figure 1. Computed formation energies of stoichiometric surfaces vs chemical potentials of O.

(μO > −8.94 eV), the previously proposed brookite(001)-like 2 × 1 reconstruction model possesses the lowest formation energies, suggesting it has the highest stability and likelihood to be formed. The unreconstructed surface is less stable and 0.76 eV higher in formation energy compared to the brookite(001)like model. The titanyl model proposed by Beck et al.31 is less stable than the unreconstructed surface and the brookite(001)like model, with their formation energies being 0.30 and 1.06 eV higher, respectively. The energetic order of these three stoichiometric TiO2 surfaces from our calculation is the same as that calculated by Gong et al.34 but different from that obtained by Wang et al., which indicates that the slab model adopted in the calculation can have significant influence on the results for TiO2 surfaces. Besides the brookite(001)-like model, four additional stable structures close to the low limit of μO, denoted as Ti4O4-2 × 1, Ti2O2-2 × 1, Ti4O7-2 × 1, and MF(111)-TiO, respectively, also exist. The MF(111)-TiO structure was obtained by Wang et al. from their extensive search (also found in our search),36 which is the most energetically stable for μO < ∼−9.0 eV based on our calculation. Ti2O2-2 × 1 has the same surface stoichiometry as MF(111)-TiO model but with a different structure. Its formation energy is slightly higher (0.16 eV higher) than that of the MF(111)-TiO model. The Ti4O7-2 × 1 model is also more stable than the brookite(001)like model for μO < ∼−9.0 eV but a little less stable than MF(111)-TiO. It is the lowest-energy metastable structure within the μO range of −9.32 to −9.00 eV. The Ti4O4-2 × 1 structural model is energetically more stable than the brookite(001)-like model when μO is < −9.28 eV and becomes the lowest-energy metastable surface for μO< −9.44 eV. Within the μO range of −9.32 to −9.44 eV, Ti2O2-2 × 1 is energetically more stable than the Ti4O4-2 × 1 and Ti4O7-2 × 1 models. Although the Ti4O4-2 × 1, Ti2O2-2 × 1, and Ti4O3-2 × 1 models are energetically less stable than the MF(111)-TiO model, the energy differences among them are quite small (ΔEformation < 0.3 eV for μO > 9.30 eV; with more than 100

Figure 2. Optimized structures of the predicted reconstructed surfaces. Here, the top and bottom panels are the side- and top-view of the structure, respectively. The Ti and O atoms in the surfaces and in the sublayers are shown in balls and frame mode, respectively. Atoms in sky blue and red colors represent Ti and O atoms, respectively. The added Ti and O atoms on the substrate in our structure search are highlighted in dark blue and green color, respectively. As a comparison, structures of the O-terminated cleaved surface used in our search, the unreconstructed surface, and the brookite(001)-like model are also shown.

cleaved surface, the unreconstructed surface, and the brookite(001)-like model are also shown. As shown in Figure 2, two O atoms are in one-fold coordination in each unit cell of the O-terminated cleaved rutile (011) surface. These O1c atoms form atomic rows along the [010] direction (denoted as O1crow). Removing the O1c atoms results in the unconstructed rutile (011) surface. The brookite(001)-like model exhibits a ridge- and valley-like surface structure. It can be considered as being formed by adding four Ti atoms and four O atoms on the O-terminated cleaved surface or adding four Ti atoms and eight O atoms on the unreconstructed surface. Because the maximum 27405

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

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ACS Applied Materials & Interfaces

after seven generations in the fixed-cell search. The structures of the added Ti2O2 rows are similar to those in the Ti4O4-2 × 1 model, where one O atom is located higher than the other O atom for each Ti2O2 unit and they are in twofold and threefold coordination, respectively. There is only one Ti2O2 unit above the valley of the unreconstructed surface in each 2 × 1 supercell for the Ti2O2-2 × 1 model. The structure of the Ti2O2-2 × 1 model is similar to that of the MF(111)-TiO model reported by Wang et al.36 (also found in our fixed-cell search after 13 generations), except that the two O atoms of the added Ti2O2 unit are at the same height as in the MF(111)-TiO model (see Figure S1). We also find a Ti2O2-1 × 1 structure in our variablecell search with the substrate of O-terminated cleaved surface after 17 generations. The same Ti2O2 unit as that in the Ti2O22 × 1 model is added on the unreconstructed surface above each valley (see Figure S1). The Ti2O2-1 × 1 model is metastable compared to the Ti4O4-2 × 1 model with a formation energy 0.8 eV higher. The finding of the Ti4O4-2 × 1, Ti2O2-2 × 1, and Ti2O2-1 × 1 models in different searches indicates that this type of reconstruction is favored for the rutile (011) surface. For the Ti4O7-2 × 1 model (found after five generations in our variable-cell search using the O-terminated cleaved surface as substrate), four Ti atoms and three O atoms are added onto the O-terminated cleaved surface, respectively. It can be viewed as a defective brookite(001)-like model with one O vacancy in each unit cell of the 2 × 1 reconstructed surface. One of the highest O atoms in the unit cell of the brookite(001)-like model is removed. As a result, in each surface unit cell, one Ti atom with fivefold coordination is changed into fourfold coordination, and one O atom with threefold coordination in the O1c-row is changed into twofold coordination. More fourfold coordinated Ti atoms and twofold coordinated O atoms render the Ti4O7-2 × 1 model with reactivity higher than that of the brookite(001)-like model. It is well-known that the twofold coordinated O atoms in the rutile (011) surface can be easily removed, so the Ti4O7-2 × 1 may be synthesized experimentally from the most stable brookite(001)-like surface. The metastable Ti4O9-2 × 1 model can be viewed as adding one O atom onto the surface of the brookite(001)-like model above a valley site, so it may be formed under high O-rich conditions from the brookite(001)-like surface. The added O atom draws Ti atoms in the valley to some extent, making one Ti atom having fourfold coordination and the other valley Ti atom having sixfold coordination in each unit cell. Both the fourfold coordinated Ti atoms and the added twofold coordinated O atoms can increase reactivity of the Ti4O9-2 × 1 model more than the brookite(001)-like model. To compare with the experiments, the STM images of the predicted structures as well as those of the brookite(001)-like model are simulated using the Tersoff method,46 as shown in Figure 3. Here, the lowest-energy empty states within 1.0 eV are taken into account, and the tip height is kept at about 2 Å. Obviously, the simulated STM of the brookite(001)-like model exhibits a zigzag pattern, which is in agreement with experimental observations.31−34 The bright spots in the simulated STM of the predicted Ti4O7-2 × 1 are arranged in straight rows, which is also consistent with the STM experiment after electron irradiation.32 As addressed above, the Ti4O7-2 × 1 structure is just a defective brookite(001)-like model with one O vacancy in each unit cell, and it is energetically quite stable. Dulub et al.32 and Wang et al.36 have suggested that the perfect and defective titanyl models are the surfaces before and after

number of the added Ti atoms and O atoms in a 2 × 1 supercell are four and eight, respectively, in our structure search, the brookite(001)-like model is unlikely to emerge in the search with the substrate of the unreconstructed surface but more likely when using the O-terminated cleaved surface as substrate (in four generations during our variable-cell search). The Ti4O4-2 × 1 reconstructed surface is found in our fixedcell search with O-terminated cleaved surface as the substrate after five generations. Four Ti atoms are added in the 2 × 1 cell of the O-terminated cleaved surface. These Ti atoms are located below the center of neighboring O1c atoms in the Oterminated cleaved surface, not above or beside the O1c atoms as in the brookite(001)-like model. Because of the added Ti atoms, the adjacent O atoms are pushed upward a little. As seen in Figure 2, the added Ti atoms in the same O1c-row of the Oterminated cleaved surface are not at the same height as in the Ti4O4-2 × 1 reconstructed surface but are at the same height in the brookite(001)-like model. As a result, one O1c atom is pushed upward more than the other O1c atom in the same row. The coordination of the higher O1c atom becomes twofold due to insertion of the Ti atoms, while that of the lower O1c atom even becomes threefold. This is a reason why the added Ti atoms in the same O1c-row are arranged nonequivalently. All of the added Ti atoms are in the fivefold coordination. The arrangement of the Ti atoms and O atoms in O1c-row is similar, while the higher and lower Ti atoms and the twofold and threefold coordinated O atoms in the two rows are different. This particular arrangement of the surface atoms results in a nearly hexagonal-symmetrized pattern, as marked in Figure 2. This pattern of surface atoms can result in a hexagonally symmetrized arrangement of charge densities and STM pattern (see Figure 3). Note that the STM image of the metastable

Figure 3. Simulated STM image of the predicted stable reconstructed surfaces and the brookite(001)-like model. The empty states within 1.0 eV and the tip distance of about 2 Å are considered (scale bars: 2 Å).

rutile (011) 2 × 1 surface synthesized by Tao et al. also shows the hexagonal pattern of bright spots.20 Thus, the Ti4O4-2 × 1 model may be just the surface observed in the experiment. The structure of the Ti4O4-2 × 1 model can also be viewed as adding two Ti2O2 units on the unreconstructed surface above each valley in each 2 × 1 supercell. The Ti2O2-2 × 1 reconstructed surface can be obtained only from the search using the unreconstructed surface as the substrate because only two more O atoms exist in this model while there are four more O atoms in the O-terminated substrate compared to the unreconstructed surface. We see it 27406

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

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ACS Applied Materials & Interfaces electron irradiation observed in the experiment, respectively. Here, we show that the perfect and defective brookite(001)-like reconstructed surfaces also fit the experiment well, so they are more likely to be the surfaces observed in the experiment due to their energetic stability higher than that of the titanyl models. The STM of Ti4O4-2 × 1 shows an obvious hexagonal pattern, which is consistent with that of the metastable surface observed by Tao et al.,20 implying that Ti4O4-2 × 1 may be the structure observed in the experiment. As addressed in ref 20, the mechanism of the new metastable reconstructed surface formation is through reoxidation of the interstitial Ti atoms diffused from the sublayers during the annealing process. As shown in Figure S2, the Ti4O4-2 × 1 structure may be formed when two interstitial Ti atoms diffuse into the larger room beside the zigzag Ti2O2 row and two other interstitial atoms diffuse to the valley site of the brookite(001)-like 2 × 1 reconstructed surface for each unit cell, respectively, and are then oxidated by the adsorbed O atoms on the surface. Notice that the interspaces between atoms in the (111) and (1̅11) lattice planes (marked with green shadows in Figure 2) are much larger than those in other planes and are large enough for a Ti atom passing so that the interstitial Ti atoms may easily diffuse from the sublayers to the surface by passing through (111) and (1̅11) planes. As shown in Figure S2, the large room beside the zigzag Ti2O2 rows can be easily occupied by the interstitial Ti atoms, forming the Ti2O2-2 × 1 structure or the MF(111)-TiO structure. When more interstitial Ti atoms diffuse to the surface, the Ti4O4-2 × 1 structure will form. Wang et al.36 suggested that the titanyl model is the surface observed by Tao et al. based on its hexagonal-patterned STM image. However, the titanyl model cannot match the formation mechanism of Tao’s metastable surface. Our predicted Ti4O4-2 × 1 structure can match Tao’s metastable surface not only in the STM images but also in the formation mechanism. The bright spots in the simulated STM image of the predicted Ti2O2-2 × 1 structure are also arranged in straight lines. As discussed above, the Ti2O2-2 × 1 structure may be the intermediate phase during the process of the reoxidation of interstitial Ti atoms. When the interstitial Ti atoms are scarce, the Ti2O2-2 × 1 structure may be formed through annealing at a low-pressure O2 atmosphere. The computed projected density of states (PDOS) of the predicted reconstructed surface models as well as that of the brookite(001)-like model are shown in Figure 4. For the brookite(001)-like model, the computed band gap is about 2.5 eV at PBE level with U = 4.1 eV. The experimentally measured band gap of this surface is 3.0 eV. Therefore, the PBE computation underestimates the band gap by about 0.5 eV. Apparently, for all the surface models, the states of valence bands and those of the low conduction bands are mainly contributed by O atoms and Ti atoms, respectively. For the Ti4O4-2 × 1 model, there are two wide bands located in the band gap originated from the 3d orbital states of the surface Ti atoms. Similar gap bands are also found for the Ti2O2-2 × 1 model. However, they are a little narrower and closer to the conduction band than those in the Ti4O4-2 × 1 model. There are also two narrow gap bands with low density of states for the Ti4O7-2 × 1 model. We note that gap states were also found for the anatase (101) surfaces with terraces, which were confirmed to be associated with the 3d states of the exposed fourfold coordinated Ti atoms (Ti4c) but not the fivefold coordinated Ti atoms (Ti5c).21 In the Ti4O7-2 × 1 structure of rutile TiO2, Ti4c atoms exist, so the appearance of the gap states is easily

Figure 4. Projected density of state of the (a) brookite(001)-like model and the predicted reconstructed surfaces of (b) Ti4O4-2 × 1, (c) Ti2O2-2 × 1, and (d) Ti4O7-2 × 1.

understood. However, in the Ti4O4-2 × 1 structure, the presence of high density of gap states is quite surprising because no Ti4c atoms exist in the surface. To find the origin of the gap states of the Ti4O4-2 × 1 structure, we examined all of the five Ti−O bonds of each surface Ti atoms and found that there is one Ti−O bond which is more than 10% longer than the other four Ti−O bonds, indicating that it is much weaker than the other bonds. Hence, the surface Ti atoms in the Ti4O4-2 × 1 structure should be in the state between Ti4c and Ti5c, which may be a reason for the appearance of gap states. Furthermore, note that the interlayer distance between the surface and subsurface layers is very small (only 1.4 Å), and the interaction between the atoms in surface and subsurface layers should be very strong, which may be the real reason for the presence of high density of gap states for the Ti4O4-2 × 1 structure. As shown in Figure S3a, the PDOS shows that not only the Ti atoms in the surface layer but also those in the subsurface layer can contribute significantly to the gap states. Therefore, the origin of the gap states in the rutile (011) reconstructed surface is different from that in the anatase (101) surface. For the Ti4O4-2 × 1 model, the gap between the VBM and the bottom of the surface band is about 1.2 eV, while that between the top of the surface band and the CBM is only about 0.3 eV. It is easy for the electrons transiting from the surface bands into the conduction bands. All electrons in the surface bands can be excited by applying visible light. Some electrons in the surface bands are excited, leaving empty states; the electrons in the valence band can absorb energy of visible light and transit into the surface bands. The Ti4O4-2 × 1 model should have high visible light absorption capability. Moreover, the empty surface states can also serve as electron traps to 27407

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

Research Article

ACS Applied Materials & Interfaces reduce electron−hole combination and to increase photocatalytic capability. Compared to the metastable surface reported by Tao et al. experimentally, the band gap of the Ti4O0-2 × 1 model is a bit smaller (1.7 eV with the correction of 0.5 eV). However, because the band gap obtained in the experiment was from photoemission spectra, the real bad gap may be smaller. Hence, the computed band structure of the Ti4O4-2 × 1 model is also in good agreement with the measured photoemission spectra. Based on the experimental scanning tunneling spectroscopy (STS) spectra, Tao et al. suggested that the gap states should be close to the valence band. However, our calculation shows that the gap states of the Ti4O4-2 × 1 model are closer to the conduction band. Dette et al. computed the DOS of the anatase (101) surface with terraces using DFT + U and PBE0 methods. They showed that the gap states are closer to the valence bands even though they do not match the STS spectra exactly.21 The disagreement of the position of gap states between our calculation and Tao’s experiment may be due to the inaccuracy of the calculation method and the STS experiment. For the STS, because of the strong electric field between the measuring probe and the sample, the lowest-energy empty states and the highest-energy filled states are bent upward and downward, respectively (enlarging the band gap). Therefore, the filled gap states may be pushed closer to the VBM of the surface. On the method aspect, the value of Hubbard U may have significant influence to the position of gap states. The main difference between our and Dette’s calculations is that in our calculation the surface structures are optimized without U while in Dette’s calculation the structures are optimized with GGA + U. We also computed PDOS of the Ti4O 4-2 × 1 structure after optimization using PBE + U (4.1 eV) method. As shown in Figure S3b, apparently the gap states move downward and connect with the valence band, more consistent with Tao’s suggestion. A larger Hubbard parameter may also shift the positions of gap states downward more. As shown in Figure S3c, when U = 6.0 eV is adopted, the gap states of the Ti4O4-2 × 1 structure optimized without U are also shifted downward significantly and connect with the valence band; however, their bands are wider than that of U = 4.1 eV. Because which value of U and whether structural optimization with U are more reliable for the DFT + U method are still open questions, hybridization functional methods may give more reliable results. However, the computational demands are beyond our computation capability. Nevertheless, the computed electronic structures of the Ti4O4-2 × 1 structure are in reasonable agreement with the experimental results. The computed imaginary part of the dielectric function of Ti4O4-2 × 1, Ti2O2-2 × 1, and Ti4O7-2 × 1 models are shown in Figure 5. The optical absorption intensity is in proportion to the imaginary part of the dielectric function. Clearly, two absorption peaks arise for the Ti4O7-2 × 1 model, both located at about 0.3 and 4.3 eV. The peak at 0.3 eV is originated from the electron transition from the surface bands to the conduction band, and the peak at 4.3 eV is due to the electron transition between the valence band and the conduction band. The absorption edge of the higher-energy peak is close to 3.0 eV, indicating that this structure can absorb only ultraviolet light. For the Ti4O4-2 × 1 model, besides the peaks at about 0.3 and 4.3 eV similar to the Ti4O7-2 × 1 model, high absorption peaks also show up in the range of 1.0−3.0 eV, which cover the whole wavelength range of sunlight (considering an energy shift of 0.5 eV). Therefore, the Ti4O4-2 × 1 model may have

Figure 5. Computed imaginary part of dielectric function of Ti4O4-2 × 1, Ti2O2-2 × 1, and Ti4O7-2 × 1 models.

excellent photocatalytic properties for applications. For the Ti2O2-2 × 1 model, a wide peak covering the energy range of 0.5−2.0 eV appears. With the consideration of the underestimation of the band gap of our calculation, the Ti2O2-2 × 1 surface may absorb light within the range of 1.0−2.5 eV, which also almost covers the whole wavelength range of sunlight.

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CONCLUSION In conclusion, we predict three additional and stable rutile (011) 2 × 1 reconstructed surfaces besides the well-known brookite(001)-like model on the basis of an extensive structural search using the evolutionary method. For the predicted Ti4O42 × 1 model, the arrangement of surface atoms, simulated STM image, and computed electronic structure all suggest that the Ti4O4-2 × 1 model is most likely the metastable surface found by Tao et al. experimentally.20 The computed imaginary part of the dielectric function shows that the Ti4O4-2 × 1 model can absorb sunlight over nearly all of the wavelengths. If confirmed, this study would resolve the long puzzle of the atomic structure of the rutile (011) 2 × 1 reconstructed surface. This surface may entail excellent visible light absorption, a key photocatalytic property for the TiO2 through surface modification.

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ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge via the Internet at pubs.acs.org. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acsami.6b10718. Optimized structure of the MF(111)-TiO structure proposed by Wang et al. and the metastable Ti2O2-1 × 1 structure predicted in this study, an illustration of how the Ti4O4-2 × 1 structure can be formed from the brookite(111)-like reconstructed surface through oxidation of interstitial Ti atoms, PDOS of the Ti atoms in surface and subsurface layers of the Ti4O4-2 × 1 structure, and DOS of the Ti4O4-2 × 1 structure calculated with different DFT + U methods (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. *E-mail: [email protected]. 27408

DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410

Research Article

ACS Applied Materials & Interfaces Notes

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grants 51302059, 51171055, 51322103, 11404085, and 11104056). The numerical calculations in this paper have been done in the supercomputing system in the Supercomputing Center of University of Science and Technology of China. X.C.Z. is supported a Qianren-B fund (1000 Talents Plan B for summer research) from USTC.

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DOI: 10.1021/acsami.6b10718 ACS Appl. Mater. Interfaces 2016, 8, 27403−27410