C, N, S, and Fe-Doped TiO 2 and SrTiO 3 Nanotubes for Visible-Light- Driven Photocatalytic Water Splitting: Prediction from First Principles

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1 pubs.acs.org/jpcc C, N, S, and Fe-Doped TiO 2 and SrTiO 3 Nanotubes for Visible-Light- Driven Photocatalytic Water Splitting: Prediction from First Principles Sergei Piskunov,*, Oleg Lisovski, Jevgenijs Begens, Dmitry Bocharov, Yuri F. Zhukovskii, Michael Wessel, and Eckhard Spohr Institute for Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV-1063, Latvia Department of Theoretical Chemistry, University of Duisburg-Essen, Universitaẗstr. 2, D Essen, Germany *S Supporting Information ABSTRACT: The ground state electronic structure and the formation energies of both TiO 2 and SrTiO 3 nanotubes (NTs) containing C O,N O,S O, and Fe Ti substitutional impurities are studied using first-principles calculations. We observe that N and S dopants in TiO 2 NTs lead to an enhancement of their visible-lightdriven photocatalytic response, thereby increasing their ability to split H 2 O molecules. The differences between the highest occupied and lowest unoccupied impurity levels inside the band gap (HOIL and LUIL, respectively) are reduced in these defective nanotubes down to 2.4 and 2.5 ev for N and S doping, respectively. The band gap of an N O +S O codoped titania nanotube is narrowed down to 2.2 ev (while preserving the proper disposition of the gap edges relatively to the reduction and oxidation potentials, so that ε HOIL < ϵ O2 /H 2 O < ϵ H + /H2 < ϵ LUIL ), thus decreasing the photon energy required for splitting of H 2 O molecule. For C- and Fe-doped TiO 2 NTs, some impurity levels lie in the interval between both redox potentials, which would lead to electron hole recombination. Our calculations also reveal in sulfur-doped SrTiO 3 NTs a suitable band distribution for the oxygen evolution reaction, although the splitting of water molecules would be hardly possible due to an unsuitable conduction band position for the hydrogen reduction reaction. INTRODUCTION Finding alternative energy sources is among the most urgent contemporary research problems because traditional fossil fuels run out at an extreme rate since their depleting rate surpasses the rate of restoration. Photocatalytic water splitting for H 2 production under the influence of solar light on semiconducting photoelectrodes in aqueous electrolyte is a potentially clean and renewable source for hydrogen fuel. The process is often considered as artificial photosynthesis and as such is an attractive and challenging research topic in the field of chemistry and renewable energy. 1 3 The efficiency of the water splitting reactions 4 depends on the relative position of the semiconductor band edges (hole and electron energies) with respect to the redox levels, which are defined as measure of the affinity of the semiconducting substance for electrons (its electronegativity) compared with hydrogen. Redox couples in electrochemical reactions are characterized by molecules or ions in a solution which can be reduced and oxidized by a pure electron transfer. 5 This requires the semiconductors to exhibit a proper band alignment relative to the water redox potentials, e.g., the conduction band minimum of the p-type photocathode should be higher than the water reduction potential H + /H 2, while the valence band maximum of the n-type photoanode, should be lower than the water oxidation potential O 2 /H 2 O. 6 Major limitations for the solar light conversion by photocatalysis relate to the band gap position in the corresponding photocatalytic materials and their stability in an aqueous environment. A number of binary and ternary metal oxide semiconductors have been intensively studied so far. 3,4,6 SrTiO 3 and, especially, TiO 2 (which distinguishes itself due to its superior chemical and optical stability and commercial availability) possess rather large band gaps (3.2 ev for TiO 2 anatase and 3.0 ev for TiO 2 rutile 7 as well as 3.25 ev for cubic SrTiO 3 perovskite 8 ). This consequently limits their photocatalytic activity to the nearultraviolet region of the sunlight spectrum, so that less than 5% of the sun s irradiation energy can be harvested by such substances. On the basis of research advances achieved during the past decades, one can outline several strategies 9 to produce a catalyst capable of using visible light energy. In this paper, we discuss results obtained for such an approach when the semiconductor with a wide band gap is doped with different metal or/and nonmetal ions. 10 Doping should result in the appearance of additional levels in the band gap, thus creating a new optical absorption edge. It reduces the energy threshold, and visible light photons become capable to overcome the gap. 11 For instance, Fe 3+ -doped TiO 2 also exhibits enhanced photocatalytic activity. Moreover, Fe 3+ 3d Received: April 17, 2015 Revised: July 10, 2015 Published: July 15, American Chemical Society 18686

2 electrons induce additional levels in the TiO 2 CB As to doped strontium titanate, its photocatalytic applications have been studied not so well up to now as those for doped titania. Unlike metal ions, nonmetallic dopants were usually considered to induce no new energetic levels. They directly narrow the band gap by shifting the top of the VB upward. 3 TiO 2 doped by nonmetal ions exhibits a red-shift of the absorption spectrum and possesses a higher photocatalytic activity than pure TiO 2, especially in the visible part of the solar irradiation spectrum. 11 Nevertheless, Chen et al. 15 used X-ray photoelectron spectroscopy to show that in the electronic structure of C-, N-, or S-doped TiO 2 there exist additional electron levels above the top of the VB. This additional density of electronic states explains the aforementioned red-shift. Braun et al. 16 discovered an additional e g resonance in the band gap of TiO 2, which was caused by introduced N dopants. This is the reason for the enhanced photocatalytic activity of N-doped TiO 2 under visible light. Yuan et al. 17 synthesized N-doped TiO 2 by heating a mixture of urea and TiO 2 at C in an air atmosphere. The analysis performed using X-ray photoelectron spectroscopy proved that N, both as a substitute and chemisorbed on the TiO 2 surface, increases its photocatalytic activity. Thus, substitutional N is thought to be a dominating factor. Lin et al. 18 demonstrated that N-doped titania synthesized by the two-microemulsion technique exhibited a high activity near neutral ph in a water/methanol solution. The activity of S-doped titania was thoroughly studied, too. S dopants may be introduced into the TiO 2 structure as anions (substituting O) or as cations (substituting Ti). In both cases an improved photocatalytic activity is observed. Nishijima et al. 22 reported that S-doped TiO 2 possesses an even higher photocatalytic activity as compared to the N-doped catalyst. Khan et al. 23 synthesized a C-doped TiO 2 compound by pyrolysis in a natural gas flame in which the rutile phase is dominated. C-doped TiO 2 exhibits a narrowed band gap and a much higher photocatalytic activity than pure TiO 2 with mixed rutile and anatase domains. It was shown that C-doped TiO 2 nanotubes (NTs) also possess higher photocatalytic activity. Levels induced in the band gap were shown to broaden the activity of C-doped TiO 2 NTs from the visible to the infrared region. 24 Unlike the case of TiO 2, only few publications describe SrTiO 3 as a photocatalyst and its possibilities for band gap engineering. 25 In spite of all aforementioned efforts, the current understanding of fundamental changes in the electronic structure depending on the morphology of doped semiconducting nanotubes is not sufficient to rationally design the atomic composition of new compounds. To guide the search, a theoretical procedure is necessary in order to prudently predict the electronic structure and the charge transition in nanotubular materials. One of the critical issues that are important for photocatalysis but not well treated in the conventional density functional theory (DFT) packages is the inaccuracy of current DFT functionals in describing the redox levels of oxides (e.g., the band gap and the valence band position relative to the H + /H 2 and H 2 O/O 2 levels). 26 Thus, great challenges exist for the computation of photocatalytic reaction kinetics as driven by excess holes/electrons accumulated on the catalyst surfaces. Using the projected augmented wave (PAW) method, Nolan found that small iron oxide clusters are stable at the TiO 2 surface and that their presence leads to a narrowing of the band gap toward the frequency range of visible light, arising from the presence of iron oxide states lying above the valence band of TiO C-, N-, and S-doped (TiO 2 ) n nanoparticles were studied using both DFT and time-dependent DFT methods by Shevlin and Woodley. 28 Asahi et al. studied the band structure of the C-, N-, F-, P-, and S-doped anatase structure of titania using the FP LAPW method. 29 They discovered that the substitution of O by N (which led to mixing of N 2p and O 2p states) produces the best conditions for photocatalysis since as a result of such modification the top of the VB was shifted upward, thus reducing the width of the band gap. A number of doped materials exhibit a large mismatch between the length scales over which the photon absorption takes place (up to micrometers), and the relatively short distances over which the electronic carriers can be extracted (often limited to few tens of nanometers), which leads to fast photoelectron hole recombination. 7 One of the approaches suggested to overcome this challenge is to synthesize nanostructured electrodes where the directions of photon propagation and charge transport are orthogonalized. This type of geometry can be accomplished, e.g., in nanowire arrays or other nanostructures with large surface-to-volume ratios Among them, hollow nanotubes produced from semiconductors have some particular advantages, such as larger specific surface area, higher mechanical stability, integrity, and unique shape with few interfacial grain boundaries, which promote both charge transport and electron hole pair separation Therefore, one of the promising approaches is the usage of doped nanotubes or other nanostructures. Titania nanotube arrays, formed as regularly distributed bundles of (6,6) TiO 2 NTs built from the reconstructed singlewalled sheet consisting of three rutile (110) monolayers, were simulated using a plane-wave (PW) approach. 39 The calculated band structure of such a bundle was found to be close to the one of pure TiO 2. By employing the LSDA+U method, Zhang and Yang calculated the electronic structures of the doped TiO 2 anatase-type nanowires including the monodoping by C, N, V, and Cr atoms as well as codoping of bulk by C/V, C/Cr, N/V, and N/Cr pairs of atoms. 40 According to their obtained results, they recommended C/Cr and C/V codoping as the most suitable one for photocatalysis. C-doped TiO 2 nanotubes with anatase structure were experimentally studied using X-ray diffraction (XRD), field-emission scanning electron microscopy (FE-SEM), and synchrotron-based X-ray photoemission spectroscopy (XPS). The possibilities of the band gap modification in C-doped TiO 2 NTs were estimated within the PAW approach. 41 However, very little has been reported in the literature so far on the computer simulations of realistic defective nanotubes, mainly because the lack of periodicity makes their theoretical study computationally very time-consuming and expensive. Another obstacle is the consequence of the fact that a consistent first-principles computational methodology has been missing until recently, which could exploit periodic rototranslation symmetry for efficient ground-state calculations as well as detailed simulations of the excited-state and charge transfer processes. According to the data published in the literature, the C, N, S, and Fe substitutional impurities are known to induce in-gap energy levels in both TiO 2 and SrTiO 3 photocatalysts. 12,15,25 Therefore, these dopants are chosen as the most promising dopants to be used for the modeling of the photocatalytic water splitting. In the present study, we address this issue by calculating the electronic and atomic structure of doped anatase-type TiO 2 (001) NTs 42 and cubic perovskite

3 type SrTiO 3 (110) nanotubes, 43 which both possess negative strain energies. THEORETICAL BACKGROUND Computational Details. We have performed first-principles calculations on the aforementioned titania and strontium titanate nanotubes doped by C, N, S, or Fe (for the titania NT type, we have considered also N + S codoping) using the formalism of localized Gaussian-type functions (GTFs), which form the basis set (BS) for each chemical element, and exploit the periodic rototranslation symmetry. For efficient groundstate calculations on defective nanotubes, we employ the formalism implemented in the ab initio code CRYSTAL, which represents periodic NT orbitals as linear combinations of localized atomic orbitals (LCAO). 44 This approach has been successfully applied by us recently for simulations of perfect, both single- and double-walled (SW vs DW) TiO 2 nanotubes of both anatase and fluorite phases, 42,45 47 [001]- and [110]- oriented titania nanowires (NWs) of rutile phase, 48,49 and perfect SW SrTiO 3 NTs 43 and [001]-oriented NWs, 50 both of cubic perovskite phase. To provide a balanced summation over the direct and reciprocal lattices of defective nanotubes, the reciprocal space integration has been performed by sampling the Brillouin zone (BZ) of extended 2 2 supercells with the Pack Monkhorst k-mesh, 51 which results in four evenly distributed k- points over the segment of the irreducible BZ. The threshold parameters in the CRYSTAL code (ITOLn) for evaluation of different types of bielectronic integrals (overlap and penetration tolerances for Coulomb integrals, ITOL1 and ITOL2, overlap tolerance for exchange integrals ITOL3, and pseudo-overlap tolerances for exchange integral series, ITOL4 and ITOL5) 44 have been set to 7, 8, 7, 7, and 14, respectively. (These parameters determine that if the overlap between the two atomic orbitals is smaller than 10 ITOLn, the corresponding integral is truncated.) Further increase of k-mesh and threshold parameters results in much more expensive calculations yielding at the same time a negligible change in the total energy ( 10 7 au). Calculations are considered as converged when the total energy obtained in the self-consistent field procedure differs by less than 10 7 au in two successive SCF cycles. For Fe- and N- doped NTs of both types as well as for the S + N codoped TiO 2 NT spin-polarized calculations have been performed. Effective charges on atoms as well as net bond populations have been calculated according to the Mulliken population analysis. 44 The analysis of charge redistribution in doped nanotubes is available in the Supporting Information. The following configurations of basis sets have been adopted: (i) for Sr and Ti atoms in TiO 2 and STO NTs, the BSs have been chosen in the form of 311sp 1d and 411sp 311d, respectively, using the efficient core potentials (ECP) implemented by Hay and Wadt; 52 (ii) full-electron BSs were adopted for all other atoms in calculations of doped titania and strontium titanate nanotubes, i.e., O: 8s 411sp 1d; C: 6s 411sp 11d; N: 6s 31p 1d, S: 8s 63111sp-11d, and Fe: 8s 6411sp 41d. 44,53 Using this computational scheme, a reasonable agreement between experimentally measured and theoretically calculated equilibrium lattice constants of both TiO 2 and STO bulk solids has been achieved by us previously. 42,53 In the current study, coordinates of all atoms as well as lattice constant (length of the translation vector related to the unit cell volume) have been optimized to reach their equilibrium positions. The formation energies of a single substitutional impurity defect A h in nanotubes have been estimated as follows: form tot tot tot tot Ah A/NT h h Ah NT (1) E = E + E E E tot where E Ah /NT is the calculated total energy of a nanotube containing substitutional impurity A h, E tot h is the total energy of the host atom, which is removed from the nanotube, E tot Ah is the tot total energy calculated for the impurity atom, and E NT stands for the total energy calculated for the perfect nanotube. Modeling of Doped TiO 2 Nanotubes. A modified B3LYP hybrid exchange-correlation functional has been adopted within the density functional theory in order to perform all calculations on the doped titania nanotubes. To obtain a quantitative agreement with the experimentally observed band gap for bulk anatase TiO 2 (δ = 3.18 ev) and the positions of band edges, the admixture of nonlocal Hartree Fock (HF) exchange in the B3LYP functional has been reduced to 14% 42 from the standard 20%. 44 The band gap calculated for a thick anatase titania (101) slab has been found to be 3.13 ev instead of 3.64 ev (Table 1). This modified exchange-correlation Table 1. Positions of the CB Bottom (E CB, ev), the VB Top (E VB, ev), and the Band Gap (δ, ev) As Calculated for the 20-Layered Anatase TiO 2 (101) and 15-Layered TiO 2 - Terminated SrTiO 3 (001) Slabs of Cubic Structure Using the Hybrid DFT Approaches As Described in the Text a B3LYP 14% TiO 2 (101) SrTiO 3 (001) B3LYP 20% exp B3PW 15% B3PW 20% exp E CB E VB δ a Data for both standard and modified exchange-correlation potentials are listed. The energy levels are calculated with respect to the vacuum level. Experimental values are taken from ref 3. functional has been further used in the current study for all calculations on TiO 2 nanotubes. To be consistent with earlier studies, we have substituted host atoms by impurities in the energetically stable TiO 2 NT folded from a 9-layered anatase slab cut parallel to the (001) surface (Figure 1). According to our preliminary calculations, 42 9-layered (001) NTs with (0, n) chirality indices possess a negative strain energy; i.e., it is energetically more favorable to form nanotubes than to retain the original 2D structure. It is worth mentioning that our prediction is in a good agreement with earlier theoretical studies performed by Ferrari et al. 54 On the basis of our strain energy calculations, we have chosen for further TiO 2 NT substitutional doping the 2 2 supercell of the 9-layered anatase (001) nanosheet, extended along its chiral and translation vectors, rolled up to (0,36) nanotube with an internal diameter of 3.47 nm and a wall thickness of 0.67 nm, which has 648 atoms per NT unit cell. In our model, substitutional C, N, and S impurities replace the host oxygen atoms in six possible positions, while three possible substitutional positions have been considered for Fe Ti (inset of Figure 1). We define the defect concentration as the ratio of the number of dopant atoms relative to the number of atoms per supercell of periodic structure which can be substituted by the dopant. Since the extended periodically repeated 2 2 supercell consists of 12 TiO 2 formula units, 18688

4 The Journal of Physical Chemistry C Figure 2. Schematic images of a unit cell monoperiodically repeated along a (18, 0) SrTiO3(110) nanotube containing the substitute atoms as point defects: (a) NT top view; (b) side view for two NT periods. Ti atoms are shown as middle-size gray balls, oxygens as small red (dark gray) balls, and strontium atoms as nonbonded green (gray) ones. The inset shows the 2 2 basic unit cell of the (18, 0) SrTiO3 nanotube extended along its chiral and translation vectors, which is repeated by 9 rototranslational symmetry operators (i.e., rotation axis is of 9th order). The numbered atoms are the Ti and O atoms substituted for impurity defect atoms (Ah, where h stands for host ). Figure 1. Schematic images of a unit cell monoperiodically repeated along a (0, 36) TiO2(001) nanotube with external diameter of 4.81 nm containing the substitute atoms as point defects: (a) NT top view; (b) side view for two NT periods. Ti atoms are shown as middle-sized gray balls and oxygens as small red (dark gray) balls. The inset shows the 2 2 basic unit cell of the (0, 36) TiO2 NT extended along its chiral and translation vectors, which is repeated by 18 rototranslational symmetry operators (i.e., the rotation axis is of 18th order). The numbered Ti and O atoms denote the sites which are substituted by impurity defect atoms (Ah, where h stands for host ). tional position has been considered for FeTi (inset of Figure 2). As in the extended periodically repeated unit cell, there are 4 SrTiO3 formula units, and the overall defect concentration in doped SrTiO3 nanotube is estimated as 25% per NT unit cell on a Ti site and 8.33% on an O site. We did not consider N + S codoping for STO NTs. Evaluation of Photocatalytic Abilities. The absorption of a photon higher in energy than the band gap of the material generates an electron hole pair.4 The electric field present at an n-type semiconductor electrolyte interface will facilitate the charge carrier separation, with the hole (h+) being driven toward the interface (H2O/O2 oxidation reaction): 1 H 2O(aq) + 2h+ O2 (g) + 2H+(aq) (2) 2 A p-type photocatalyst (or a working metallic electrode such as Pt) would act as the cathode, promoting the reduction of H+ to H2 using the photogenerated electrons (e ), which results in the H+/H2 reduction reaction: substitution of the impurity dopant for one of the host atoms leads to the overall defect concentration in the TiO2 NT unit cell of 8% on a Ti site and 4% on an O site. To simulate N + S codoping of the TiO2 nanotube with the same defect concentration, we have consequently substituted oxygens of sites O1 and O2 (Figure 1) by S- and N-dopants, respectively, and the remaining other oxygens in their regular NT sites. We note that further decrease of defect concentration would result in an enlargement of the supercell, thus leading to much too expensive calculations, which are beyond our current computer facilities. For the same reason, charge compensation defects for anionic dopants are not considered in this study at all. Modeling of Doped SrTiO3 Nanotubes. To perform calculations on defective SrTiO3 (STO) NTs, we employ the hybrid exchange-correlation scheme which accurately reproduces the basic bulk and surface properties of a number of perovskites The modified hybrid B3PW exchangecorrelation functional with 15% of nonlocal HF exchange yields a band gap of a thick cubic SrTiO3 slab of 3.13 ev instead of 3.63 ev obtained with the standard 20%44 HF exchange (Table 1), which is in good agreement with the experimental value of 3.25 ev.8 The modified B3PW exchange-correlation functional has been further used in the current study for all calculations on SrTiO3 nanotubes. Host atoms are substituted by impurities in STO nanotubes with a (18, 0) chirality index (Figure 2) rolled up from a nanosheet cut parallel to the (110) surface of cubic SrTiO3 bulk. Such a type of pristine NT possesses a negative strain energy and has been found to be energetically more stable as compared to the SrTiO3(110) nanosheet.43 Doped nanotubes can be rolled up from a SrTiO3 nanosheet containing one substitutional atom per 2 2 supercell consisting of 180 atoms. In our model, oxygen substitutional impurities can replace host oxygen atoms in three possible configurations, while only one possible Ti substitu- 2H+(aq) + 2e H 2(g) (3) + The position on the energy scale of the E(H /H2) level relative to the vacuum level has been calculated earlier using a Born Haber thermochemical cycle.5 Reactions 2 and 3 complete the overall water-splitting reaction: 1 H 2O(aq) O2 (g) + H 2(g) (4) 2 The difference of the redox Gibbs energies (ΔG ) estimated experimentally corresponds to 1.23 ev.5 The thermodynamics of the H2O splitting reactions depends on the relative position of the semiconductor band edges (hole and electron energies) with respect to the (H+/H2) and (O2/H2O) redox levels.4 The valence band of the semiconductor (or highest occupied impurity level ϵhoil in a doped nanotube) must be below the oxidation level (5.67 ev below the vacuum level) in order to make the oxygen oxidation reaction thermodynamically favorable, while the conduction band position (or lowest 18689

5 unoccupied impurity level ϵ LUIL in doped nanotube) must be above the standard hydrogen electrode (SHE) level (4.44 ev below the vacuum level) for the hydrogen reduction reaction to occur spontaneously: ϵ < ϵ < ϵ + < ϵ HOIL O 2/H2O H /H2 LUIL (5) If these conditions are not fulfilled simultaneously in a single material, an external bias voltage may be applied or a tandem device could be constructed, using two or more active materials to generate charge carriers with sufficient energy to complete the overall reaction. The aforementioned redox potentials were determined for standard conditions in acidic aqueous medium (ph = 0); both redox levels synchronously shift toward the vacuum level with increasing ph. 58 In a number of experimental and theoretical studies, the energy balance between the band gap edges and the redox levels described by eq 5 was considered as a criterion for the effectiveness of photocatalytic water splitting. 3,4,6,26,58 Figures 3 and 4 incorporate this balance in the form of vertical lines corresponding to redox levels inserted in the DOS plots calculated for both pristine and doped titania and strontium titanate nanotubes. To justify such a comparison, the band gap edges of the energetically preferable TiO 2 anatase (101) and SrTiO 3 (001) slabs are compared with the corresponding experimental values as present in Table 1. In this study, we evaluate the abilities of semiconductors (taking into account their energy levels estimated using ab initio calculations) for photocatalytic applications. On the other hand, the position of the band edges with respect to the redox potentials is a very important factor for the kinetics of photoelectrochemical reactions. 59 Moreover, the thermodynamic driving force that determines the rate of these reactions is derived from the difference in energy between the band edge and the redox level: the efficiency of the whole process is determined by optimal values of these differences. 59 RESULTS Verification of TiO 2 and SrTiO 3 Band Gap Edges. To estimate the effectiveness of semiconducting photocatalysts, the band edge positions of the CB minimum and the VB maximum are critical because they define the chemical potential of photogenerated holes/electrons and thus determine the thermodynamic tendency for the H 2 O splitting reaction 4 to occur. Hence, accurate calculations of the bottom of the CB and the top of the VB are prerequisites for understanding the kinetics of photocatalytic reactions. However, due to the selfinteraction problem in density functionals, there is a tendency for the delocalization of electrons using the local density approximation and its generalized gradient extension, which results in the underestimation of the band gap as well as wrong VB, CB, and dopant impurity levels. As mentioned in the Theoretical Background section, to minimize this effect in our study, we have proposed changes of nonlocal Fock exchange of hybrid exchange-correlation functionals in such a way that the band edge positions of TiO 2 and SrTiO 3 slabs are very similar to those experimentally observed. To prove that our predictions on doped nanostructured materials are reliable, we have calculated the band gap edges and widths of the band gaps of (i) symmetric stoichiometric anatase TiO 2 (101) slab composed of ten layers containing O O Ti Ti O O atomic planes each as well as (ii) a symmetric nonstoichiometric TiO 2 - terminated SrTiO 3 (001) slab consisting of 31 alternating TiO 2 and SrO atomic planes. (Obtained values are compared in Figure 3. Total and projected density of states (PDOS) for both perfect and doped TiO 2 NTs as calculated using DFT-B3LYP method: (a) perfect TiO 2 NT, (b) C-doped TiO 2 NT, (c) N-doped TiO 2 NT (upper panel for spin-up electrons, while lower panel for spin-down electrons), (d) S-doped TiO 2 NT, (e) N + S-codoped TiO 2 NT (upper panel for spin-up electrons, while lower panel for spin-down electrons), and (f) Fe-doped TiO 2 NT (upper panel for spin-up electrons, while lower panel for spin-down electrons). Vertical lines crossing all the DOS plots correspond to O 2 /H 2 O and H + /H 2 redox potentials as described at the end of the Theoretical Background section. Zero of the energy scale corresponds to the vacuum level. Table 1 with results of the experimental observations. 3 )We note that the band gap edge positions calculated in this study differ not more than ev from those experimentally observed, which gives us reason to believe that predictions we make on the electronic structure of doped TiO 2 and SrTiO

6 Table 2. Defect Formation Energies (E form Ah, ev) in Doped TiO 2 NTs Calculated Using Eq 1 a n C On N On S On Fe Tin bulk a Host atoms A n substituted by impurities h n are labeled according to Figure 1. The lowest formation energies are shown in bold. The last row contains the formation energy calculated for substitutional impurities at anatase bulk using 2 2 supercell. Figure 4. Total and projected density of states (PDOS) for both perfect and doped SrTiO 3 NTs as calculated using the DFT-B3PW method: (a) perfect SrTiO 3 NT, (b) C-doped SrTiO 3 NT, (c) N- doped SrTiO 3 NT, (d) S-doped SrTiO 3 NT, and (e) Fe-doped SrTiO 3 NT (upper panel for spin-up electrons, lower panel for spin-down electrons). Vertical lines crossing all the DOS plots correspond to O 2 / H 2 O and H + /H 2 redox potentials as described at the end of the Theoretical Background section. The zero of the energy scale corresponds to the vacuum level. nanotubes are at least qualitatively and possibly semiquantitatively reliable. Doped TiO 2 Nanotubes. Energy of Defect Formation. In this study, impurity atoms have substituted each possible irreducible host oxygen or titanium atom in the nanotubes with rototranslationally and periodically repeated cells as shown in Figure 1. Therefore, one of the six types of O atoms and one of the three types of Ti atoms have been consequently substituted by C O,N O,S O, and Fe Ti. According to our calculations, the carbon and sulfur dopants would prefer to be positioned at the site of the outermost oxygen, while nitrogen would prefer the second oxygen layer counting from the outer side (Table 2). The lowest formation energy among anion dopants is predicted for C O as 1.16 ev. The next lowest energy of 2.61 ev is predicted for S O -doped titania NT, while 3.56 ev is necessary to substitute an oxygen atom in the nanotube s wall by an N O dopant. Note that sulfur compared to carbon has a significantly larger ionic radius which results in a larger defect formation energy for S in both doped bulk and nanotubes except for position n = 6(Table 2 and Figure 1). The energetically most favorable position for the host Ti atom to be substituted by iron is the Ti layer closest to the inner wall of the nanotube (Table 2). The formation energy for the Fe Ti substitute is often equal to 5.37 ev. (As it is typical for oxides, the formation of cation defects is energetically less favorable.) For the calculations of the electronic structure of the doped NTs, only the nanotubes with the lowest defect formation energies (bold numbers in Table 2) have been considered. However, we note that the influence on the nanotube s electronic structure of those dopants which are close in formation energy, e.g., nitrogen dopants, are very similar. The formation energy of the N + S pair of atoms has been calculated to be 5.64 ev, which fulfills the inequality 2E form (S O )<E form (S O +N O )<2E form (N O ), thus confirming the approximate additivity of estimated dopant formation energies, when these contain different numbers of impurity atoms, irrespectively of their chemical nature. If for doped nanotubes formation of C O1 and S O1 dopants result in the lowest energy, then for the same dopants in bulk formation energies are much higher (Table 2). This can be explained by a large difference in their coordination number in nanotubes (two) and bulk (four). In the case of N O2 dopants, the formation energies in nanotube and bulk do not directly depend on coordination number (three and four, respectively) which can be caused by different nature of chemical bonding of nitrogen with Ti atoms as compared to C and S leading to noticeable structural reconstruction in nanotubes (Table 3). As to Fe Ti3 dopants in bulk and nanotubes (coordination numbers are five and four, respectively), their presence results in noticeable structural reconstruction in the latter case (as described at the end of the next subsection) which demands additional energy for dopant. Atomic Structure. The lattice distortion in anatase-type TiO 2 NTs caused by introducing different dopants is analyzed by comparison of the structures possessing the lowest formation energy (Table 2) with that of the perfect TiO 2 nanotube (Figure 1). All doped TiO 2 NT configurations exhibit changes of the bond length between the neighboring atoms (Table 3). The change of the inner NT diameter is negligible, as the largest change is only 0.4% for the C-doped TiO 2 nanotube. Both C O - and N O -substituted TiO 2 NTs exhibit only 18691

7 Table 3. Changes in the Bond Length of the Doped TiO 2 Nanotubes Relatively to the Undoped Case a bond C O1 N O2 S O1 Fe Ti3 Ti 1 C/O/S (C)/ 1.5(O) (S)/-2.8(O) 0.3 Ti 1 N/O 2 0.9/ / / / 1.5 Ti 1 O Ti 2 N/O (N)/ 3.2(O) Ti 2 O / / / Ti 2 O / 2.4 Ti 2 O / /+5.6 Ti 3 O Ti 3 O Ti 3 O Fe 3 O Fe 3 O Fe 3 O a All values are given in percentages, and changes of more than 3% are shown in bold. Host atoms A n substituted by impurities h n are labeled according to Figure 1. local lattice distortions. These distortions are mainly restricted to the Ti dopant bonds, e.g., the Ti 1 C 1 bond (+9.1% increase relative to the Ti O bond length of the undoped nanotube) and the Ti 2 N 2 bond (+10.3%). The increase of the bond length leads to a small outward movement of the dopant as compared to the oxygen site per se. Similar effects with larger magnitude can be observed in the case of S O substitutes. Here, the Ti 1 S 1 bond experiences a large increase in the bond length (+23.4%), and the sulfur dopant is moved outward (this can be grounded by a large difference of Ti O and Ti S bond lengths, which have been found to be 1.95 and 2.44 Å, respectively, in our calculations). Because of the increased ion radius of the introduced anionic dopants, the corresponding bonds are elongated, while some of the remaining Ti O bonds are slightly compressed. When the TiO 2 NT is doped with Fe on the Ti 3 position (Figure 1), a restructuring of its first coordination sphere can occur. Table 3 shows that the Fe 3 O 4 distance increases by 20.5%, while the remaining Fe 3 O n bonds are slightly shorter than those in the undoped compound. In the TiO 2 NT, the Ti 3 site is located in the base of a square pyramid consisting of five O atoms, while the Fe 3 site is located in a distorted tetrahedron as one oxygen atom is pushed out of the first coordination sphere. Electronic Structure. Figure 3 shows the projected density of states (PDOS) calculated for both perfect and doped TiO 2 nanotubes. Substitutional point defects in titania NTs reveal a tendency to form defect-induced levels inside the optical band gap. In the case of the C O1 /TiO 2 NT, the filled band is positioned 2.2 ev above the top of the VB, while in the case of the N O2 /TiO 2 NT impurity, the induced level is found to be closer to the top of the VB, just 0.9 ev above it. (In the case of carbon doped anatase bulk an occupied defect level is positioned 1.2 ev above the top of the VB, while for N- doped bulk anatase nitrogen induced levels form the top of the VB.) The defect-induced level calculated for the S O1 /TiO 2 NT actually forms the top of the VB (for the S-doped bulk, the defect level lies 0.2 ev above the top of the VB), and in the case of Fe Ti3 /TiO 2 NT, the vacancy-induced level is positioned in the middle of the band gap. (A similar electronic structure is also predicted for the Fe-doped bulk anatase, except for the fact that in the bulk phase defect-induced levels lie closer to the bottom of the conduction band.) The top of the VB in the case of the perfect TiO 2 NT is formed by O 2p orbitals, while the bottom of the CB consists of Ti 3d states. The PDOS calculated for the N + S-codoped titania nanotubes are shown for the pristine, the N-doped, and the S-doped titania nanotubes (Figure 3a,c,d,e). For the N and S- codoped titania NT, the nitrogen-dominated gap state shifts downward in energy by about 0.3 ev, bringing the occupied gap level 0.3 ev below the oxygen O 2 /H 2 O redox level. Simultaneously, due to the presence of the S codopant, the bottom of the conduction band also shifts downward yielding an energy gap of about 2.2 ev, which reduces the photon energy required for water splitting. The N and S-codoped system exhibits a gap state which is somewhat lowered relative to the top of the valence band due to defect defect interactions. For this system, also the top of the valence band and the bottom of the conduction band shift downward relative to the N-doped system. Relative to the bottom of the conduction band of the S-doped system, the conduction band shifts back upward again toward the conduction band position of the pristine or the N-doped system, which are similar in energy. The overall effect of codoping gives rise to visible-lightdriven excitation from the gap level of approximately 2.3 ev, which is slightly smaller than for the N-doped nanotube. This allows us to predict that N and S-codoped titania nanotubes can be suggested as a promising candidate for the visible-lightdriven photocatalytic application, in good agreement with recent experimental observations. 60 Doped SrTiO 3 Nanotubes. Energy of Defect Formation. Similarly to doped titania NTs, each irreducible host oxygen or titanium atoms in the 2 2 rototranslationally and periodically repeated unit cell is substituted in turn by impurity atoms (Figure 2). Therefore, one of the three types of oxygen atoms and only one type of titanium have been substituted by C O,N O, S O, and Fe Ti, respectively. According to our calculations, the carbon and nitrogen dopants would prefer to be positioned at the site of the innermost oxygen, while sulfur would prefer the position in the outermost oxygen layer. The lowest formation energy of 2.01 ev among anion dopants is predicted for sulfur (Table 4). The reason for this is the morphology of nanotube s surface allowing for relatively large relaxation of the atom of large ionic radius. The next lowest energy of 3.52 ev is predicted for the nitrogen dopant, and 4.50 ev is required to substitute oxygen in the nanotube s wall by carbon. The formation energy of the Ti substituent is equal to 5.97 ev

8 Table 4. Defect Formation Energy (E form Ah, ev) in Doped SrTiO 3 NTs As Calculated Using Eq 1 a n C On N On S On Fe Tin bulk a Host atoms A n substituted by impurities h n are labeled according to Figure 2. The lowest formation energies are shown in bold. The last row contains the formation energy calculated for substitutional impurities at cubic SrTiO 3 bulk using 2 2 supercell. Analogously to TiO 2, the formation of cation defects in perovskites is energetically less favorable. In our calculations of the NT electronic structure (see below), only the doped nanotubes with the lowest defect formation energies have been considered. The difference between formation energies for C, N, S, and Fe dopants in strontium titanate nanotubes and bulk (Table 4) can be explained analogously to that for anatase-structured titania. In the case of a sulfur dopant located in the surface nanotube area, its coordination number (one closest Ti atom) is twice as smaller as compared to bulk (two closest Ti atoms). In the case of C O3 and N O3 dopants, their coordination numbers are close in nanotubes and bulk which results in close values of formation energies. Fe Ti3 dopants in nanotubes cause noticeable structural reconstruction which leads to a larger formation energy as compared to bulk (analogous explanation has been done for the same dopant in anatase-structured titania) Atomic Structure. The lattice distortion of cubic-type SrTiO 3 NTs caused by introducing the different dopant elements is analyzed as it has been done for the TiO 2 nanotubes, and the observed changes of bond length are given in Table 5. The inner NT diameter is found to be slightly increased for all doped STO nanotubes. The largest change has been found again in the case of carbon doping (+2.5%), followed by the iron doping (+1.7%). The larger overall expansion is most likely due to the thinner and, thus, more flexible nature of the SrTiO 3 nanotube. Analogously to TiO 2 nanotubes, the substitution of oxygen in the STO NT by one of the three anion species causes only a local distortion. Again, the largest increase of bond length can be found for sulfur (+28.5% increase relative to the bond length of the undoped nanotube due to a large difference between Ti O and Ti S bond lengths), followed by carbon (+8.8%). Table 5 shows that the extension of the cation dopant bond length correlates with the ion radii of the dopants and that altered bond lengths are not restricted to Ti X bonds only but also occur in Sr X bonds. Doping SrTiO 3 with iron does not have an effect similar to the TiO 2 case. Here, the Fe ion is already located in a distorted tetrahedron, so that the rearrangement of the anions around iron is quite small (Table 5). Electronic Structure. In Figure 4, we have plotted the PDOS calculated for both perfect and defective SrTiO 3 NTs. The PDOS graphs show that the top of their VB and the bottom of their CB consist of O 2p and Ti 3d orbitals, respectively, as in bulk SrTiO 3. Because of quantum confinement the NTs band gap becomes larger (δ = 5.18 ev) with respect to the bulk phase, which made us predict that doping of such a wide-gap nanotubes may lead to the formation of a larger number of defect states in the band gap. The PDOSs calculated for SrTiO 3 NTs containing substitutional point defects indeed reveal such a tendency for the formation of defect-induced levels inside the optical band gap. In the case of the C O3 /STO NT, the filled band is positioned 2 ev above the top of the VB, while in the case of N O3 /STO NT the filled impurity-induced level is found to be 0.8 ev above the top of the VB. (For the C-doped STO bulk we predict occupied defect-induced levels 0.2 ev above the top of the VB, while in the case of N-doped STO bulk defect induced levels form the top of the VB.) The defectinduced level calculated for the S O1 /STO NT is localized 4.3 ev above the top of the VB (S-induced levels form the top of the VB for S-doped STO bulk). In the case of Fe Ti1 /STO NT the occupied dopant-induced level is positioned just 1.0 ev above the top of the VB (similarly to the Fe-doped STO bulk). Because of the large widths of the computed band gaps for N- and S-doped STO NTs we do not consider N + S codoping of this nanotube at all, since the energy gap for water splitting would lie in the far-ultraviolet region. According to our recent study, 50 much more effective STO nanostructures for visiblelight-driven photocatalytic applications have been found to be nonstoichiometric TiO 2 -terminated [001]-oriented nanowires. DISCUSSION On the basis of the standard thermodynamic conditions of an active photocatalyst for water splitting, we discuss and evaluate the influence of the incorporated cation and anion species on the photocatalytic activity of TiO 2 and SrTiO 3 nanotubes. We have calculated the band structure of the C-, N-, S-, and Femodified NTs, as discussed in the previous section, and Table 5. Changes in Bond Length of the Doped SrTiO 3 NT Relative to the Undoped Case a bond C O3 N O3 S O1 Fe Ti1 Sr 1 O/S (S)/ 1.0(O) 0.6 Sr 1 O Sr 1 C/N/O (C)/ 3.6(O) +0.2(N)/ 1.5(O) Ti 1 O/S (S)/ 0.7(O) 0.1 Ti 1 O Ti 1 C/N/O (C)/ 0.5(O) +3.5(N)/ 0.1(O) Fe 1 O/S Fe 1 O Fe 1 C/N/O a All values are given in percentages and changes of more than 3% are shown in bold. Host atoms A n substituted by impurities h n are labeled according to Figure

9 compared with that of perfect TiO 2 and SrTiO 3 nanotubes. The projected densities of states calculated for pristine and doped TiO 2 as well as SrTiO 3 nanotubes are shown in Figures 3 and 4, respectively. The schematic representation of the band edges and midgap states of pristine and doped TiO 2 and SrTiO 3 nanotubes is shown in the Figure 5. Figure 5. Schematic representation of the band edges and midgap states of pristine and doped TiO 2 and SrTiO 3 nanotubes. Blue and red horizontal dashed lines correspond to the redox potentials for H + /H 2 and O 2 /H 2 O dissociation, respectively. Zero of the energy scale corresponds to the standard hydrogen electrode (SHE). As one can see from Table 2, the most energetically favorable positions for anion dopant on titania NT are the outer host oxygen atoms, while iron prefers to substitute the inner host Ti atom. When considering SrTiO 3 nanotubes, on the basis of results of our first-principles modeling (Table 4), we predict that due to their small ionic radii, carbon and nitrogen tend to replace the inner host oxygens, while sulfur, due to its larger ionic radius, prefers to substitute the outer host oxygen. Considering the electronic structure of doped nanotubes with similar formation energies (for example, N O1 and N O2 cases of titania NT; see Table 2), we note that the midgap states induced by those dopants are also close in energy. For the perfect TiO 2 (001) nanotube, the bottom of the conduction band is 1.0 ev above the H + /H 2 potential, whereas the top of its valence band is 1.2 ev below the O 2 / H 2 O potential (Figures 5 and 3a). A carbon substitutional impurity in a TiO 2 NT induces an occupied defect level 0.2 ev above the O 2 /H 2 O potential (Figures 5 and 3b). This leads to an unsuitable valence band position for the oxygen evolution reaction. The N-doped TiO 2 NT possesses an occupied impurity level practically at the O 2 /H 2 O potential (Figures 5 and 3c), while the bottom of the conduction band with respect to the pristine nanotube remains almost unchanged. This means that its ability to reduce protons to hydrogen remains mostly unchanged while its ability to produce oxygen is improved. In the case of the S-doped TiO 2 NT, our calculations predict that the bottom of the CB is practically at the H + /H 2 potential, whereas the top of the VB remains almost unchanged as compared to the pristine nanotube (Figures 5 and 3d). This essentially lowers efficiency of reduction of protons as compared to N-doped nanotubes, while the oxygen evolution reaction is still feasible but not very efficient. The Fe-doped TiO 2 nanotube contains defect-induced levels 0.5 ev lower than the H + /H 2 potential (Figures 5 and 3f), which leads to a reduction of protons. Therefore, when considering the doped TiO 2 nanotubes, we can conclude that the most promising nanostructured photocatalyst for the visible-light-driven H 2 O splitting could be N- and S-doped titania nanotubes. When simulating N + S codoping of the titania nanotube (Figures 5 and 3e), we indeed obtain a very favorable TiO 2 NT configuration for photocatalytic application. For the perfect SrTiO 3 (110) nanotube, the bottom of the CB is 3.7 ev above the H + /H 2 potential, whereas the top of its VB is 0.7 ev below the O 2 /H 2 O potential (Figures 5 and 4a). This means that its ability to reduce hydrogen is very low while oxygen evolution is still possible. The C-doped SrTiO 3 nanotube exhibits an occupied defect level 1.1 ev above the O 2 /H 2 O potential (Figures 5 and 4b), which practically excludes the oxygen evolution reaction. The N-doped SrTiO 3 NT contains an occupied impurity level 0.2 ev above the O 2 / H 2 O potential (Figures 5 and 4c), similarly to the C-doped nanotubes. In the case of the S-doped SrTiO 3 nanotube, our calculations predict that the bottom of the conduction band remains almost unchanged as compared to the pristine nanotube, while an occupied defect-induced level is 0.2 ev below the O 2 /H 2 O potential (Figures 5 and 4d). This leads to an enhanced oxygen evolution reaction, while its ability for reduction to hydrogen remains very low. The Fe-doped SrTiO 3 NT contains occupied defect-induced levels 0.1 ev above the O 2 /H 2 O potential (Figures 5 and 4e), which does not favor oxygen evolution. Comparing parameters of the DOS obtained for the doped SrTiO 3 nanotubes and for the perfect nonstoichiometric TiO 2 -terminated STO NWs, 50 we can conclude that the latter type of strontium titanate nanostructures is much more effective for water splitting under solar light irradiation. Summing up, we can quite generally say that the electronic structure of both TiO 2 and SrTiO 3 nanotubes can be modulated remarkably by the substitutional impurities. In fact, monodoping in wide-gap materials suffers from three obstacles: 61 (i) the dopants may have only limited solubility, (ii) the dopants have sufficient solubility, but they result in lowlying defect levels, and (iii) the NT doping may result in the spontaneous formation of compensating defects. To overcome these obstacles, codoping of these nanomaterials has to be studied. In codoped systems the solubility can be improved by the Coulomb coupling of the anion cation pairs, and the compensating vacancy defects can be avoided. While most doping approaches do result in a material with a reduced band gap, dopants can also lead to formation of localized electronic states, which enhance electron/hole recombination, thus reducing the overall photocatalytic efficiency. Codoping in principle alleviates the last problem as well. 62 Therefore, on the basis of our calculations, nitrogen- and sulfur-containing codoped TiO 2 nanotubes might be the most promising candidates for further investigation of photocatalysts for visible-light-driven hydrogen production from water. CONCLUSIONS In the current study, band gap engineering of TiO 2 and SrTiO 3 nanotubes has been simulated within the formalism of localized atomic orbitals as implemented in the CRYSTAL code. Nonequivalent oxygen or titanium atoms in the nanotube wall have been consequently substituted by C O,N O,S O, and Fe Ti atoms. The energetically most favorable positions of impurity atoms and the reconstruction of the host atomic 18694