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Major Difference in Visible-Light Photocatalytic Features between Perfect and Self-Defective Ta3N5 Materials: A Screened Coulomb Hybrid DFT Investigation Moussab Harb,* Luigi Cavallo, and Jean-Marie Basset KAUST Catalysis Center (KCC), King Abdullah University of Science and Technology (KAUST), 4700 KAUST, Thuwal 23955-6900, Kingdom of Saudi Arabia (KSA) S Supporting Information *

ABSTRACT: Relevant properties to visible-light overall water splitting reactions of perfect and self-defective bulk Ta3N5 semiconductor photocatalysts are investigated using accurate first-principles quantum calculations on the basis of density functional theory (DFT, including the perturbation theory DFPT) within the screened coulomb hybrid (HSE06) exchangecorrelation formalism. Among the various explored self-defective structures, a strong stabilization is obtained for the configuration displaying a direct interaction between the created N- and Ta-vacancies. In the lowest-energy structure, each of the three created Tavacancies and the five created N-vacancies is found to be in aggregated disposition, leading to the formation of cages into the lattice. Although the calculated structural, electronic, and optical properties of the two materials are found to be very similar and in good agreement with available experimental works, their photocatalytic features for visible-light overall water splitting reactions show completely different behaviors. On the basis of calculated band edge positions relative to water redox potentials, the perfect Ta3N5 (calculated band gap of 2.2 eV) is predicted by HSE06 to be a good candidate only for H+ reduction while the self-defective Ta3N5 (calculated band gap of 2.0 eV) reveals suitable band positions for both water oxidation and H+ reduction similar to the experimental data reported on Ta3N5 powders. Its ability to reduce H+ is predicted to be lower than the perfect one. However, the strongly localized electronic characters of the valence band (VB) and conduction band (CB) edge states of the self-defective material only on the N 2p and Ta 5d orbitals surrounding the aggregated N- and Ta-vacancies are expected to strongly limit the probability of photogenerated carrier mobility through its crystal structure.

1. INTRODUCTION Solar hydrogen production through the challenging photocatalytic water splitting using powder semiconductors still remains a promising technology because of the relatively low cost required.1−4 Tantalum nitride (Ta3N5) has received considerable attention over the past years for its small band gap estimated at 2.1 eV.5−9 Although this key parameter is required to absorb a wide range of the visible range which counts for 43% of the solar spectrum, two additional challenging parameters must also be justified in the semiconductor photocatalyst for achieving efficient water splitting: (1) suitable valence band (VB) and conduction band (CB) edge positions with respect to water redox potentials to give the power to the photogenerated holes and electrons to oxidize water and to reduce H+; (2) strongly delocalized electronic characters of the band edge states to minimize the electron/ hole recombination in the bulk and to help for their required mobility to the reactive sites at the surface. Ta3N5 powders were mainly prepared from high-temperature ammonolysis of crystalline or amorphous Ta2O5 under various temperatures and heating times.5−9 Using neutron powder diffraction technique, the obtained samples were analyzed, and an orthorhombic crystal structure was identified. It has been reported that this material can generate H2 or O2 under visible© 2014 American Chemical Society

light irradiation in the presence of appropriate sacrificial reagents. In contrast, it was observed that the photocatalytic properties in the visible region of the prepared samples varied with the preparation method. However, the origin of this variation still remains unclear and needs to be clarified. A few theoretical studies10−12 were reported only on the density of states of Ta3N5 calculated by standard density functional theory (DFT)-GGA and -LDA methods, and respective band gaps of 1.1 and 1.5 eV were predicted. It is important to stress here that the two standard methods adopted here are well-known to strongly underestimate the band gaps of semiconductors.13,14 The weakness of these methods can be much more improved using recent hybrid functionals like HSE06.14−18 In addition, neither the optical absorption response nor the band edge positions of Ta3N5 relative to water redox potentials were calculated from the DFT-HSE06 method, which would enable a more relevant interpretation of the experimental results and which would help improve the photocatalytic performance of this material. Received: June 18, 2014 Revised: August 13, 2014 Published: August 21, 2014 20784

dx.doi.org/10.1021/jp506066p | J. Phys. Chem. C 2014, 118, 20784−20790

The Journal of Physical Chemistry C

Article

In the present work, we address the challenging aspects invoked above by performing advanced first-principles quantum calculations based on DFT (including the perturbation theory DFPT) with the screened coulomb hybrid (HSE06) exchangecorrelation functional to ensure much more accurate band gap and optical transition predictions of these materials than the standard DFT calculations. We investigate the electronic structure, UV−visible optical absorption properties, and most importantly the VB and CB edge positions relative to water redox potentials of perfect and self-defective bulk Ta3N5 materials that might be obtained in the experiments. We further analyze the hybridization (localized or delocalized) character of their band edge states in terms of electron densities.

2. COMPUTATIONAL METHODS For the simulation of self-defective Ta3N5 structures, we considered the 3 × 1 × 1 orthorhombic Ta3N5 supercell model containing 12 functional Ta3N5 units (or 96 atoms). We explored a large number of geometrical configurations by removing three neutral N atoms and five neutral Ta atoms from various possible sites in the supercell. We paid particular attention to key structures showing separated or aggregated Nand Ta-vacancies (see Figure 1) that had not been invoked in previous works. We optimized the various generated structures using DFT, as implemented in VASP5.219−22 with the PBE functional23 and the PAW approach.24 We sampled the Brillouin zone with 3 × 3 × 3 Monkhorst−Pack k-point grid.25 We fully relaxed the ion coordinates and the lattice parameters to reach residual force component values below 0.01 eV/Å. We fixed at 10−5 eV the convergence criterion for the self-consistent field (SCF) cycles. For density-of-state calculations of perfect and self-defective Ta3N5 materials, we employed the screened coulomb hybrid (HSE06) exchange-correlation functional,26 as implemented in VASP 5.2.19−22 We used the optimized geometries obtained at PBE level. We adopted the tetrahedron method with Bloch corrections for the Brillouin zone integration. As reported in our recent theoretical papers on reference systems,14−18 we used the HSE06 functional here to reach once again a high accuracy in the prediction of the experimental band gap of these materials. For UV−vis optical absorption calculations of perfect and self-defective Ta3N5 materials, we applied the density functional perturbation theory (DFPT) implemented in VASP5.219−22 by employing the HSE06 functional.26 Then, we calculated the optical absorption coefficient α(ω) using the equation α(ω) = (4π/λ)k(ω), where λ and ω are the wavelength and the frequency of the incident light and k(ω) is the extinction coefficient, which is defined by k(ω) = {[(ε21 + ε22)1/2 − ε1]/ 2}1/2.27−29 ε1(ω) and ε2(ω) are the real and imaginary parts of the frequency-dependent complex dielectric function. Once again, we used the HSE06 functional to accurately describe the optical transition energies in these materials as a result of the accurate band gap determination provided by this approach.14−18 For band edge position calculation of the semiconductor, the electronic band structure needs energetically to be aligned on a common scale. This can be achieved by modeling a semiconductor−vacuum interface for providing a vacuum reference to the electrostatic potential.30,31 The procedure requires two separate slab calculations: the first one is to reproduce the band gap of the bulk material and the second

Figure 1. (a) Lowest-energy and (b, c) metastable structures obtained with PBE for pure Ta3N5: (a) perfect material, (b) self-defective material with aggregated N- and Ta-vacancies, and (c) self-defective material with separated N- and Ta-vacancies. Color legend: Ta in light blue, N in dark blue, and Ta- (N-) vacancies in light (dark) blue empty circles.

one is to obtain the alignment of the electrostatic potential within the material with respect to the vacuum level. Then, the VB and CB edge positions of the semiconductor relative to the vacuum level can be obtained by subtracting the energy of the vacuum level from the energies of VB and CB edges obtained using the slab calculations. 20785



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For the simulation of Ta 3N 5 −vacuum interface, we considered the (001) direction by building the (2a ⃑ × 1b ⃑ ) slab (vacuum built along the c ⃑ direction) containing nine atomic layers. We fully relaxed the slab by fixing the bulk optimized cell parameters. We carefully optimized the vacuum thickness separating each neighboring slab to avoid any electronic interaction between the two sides of the slab. Moreover, we carefully optimized the crystal thickness of the slab to ensure an accurate band gap reproduction of the bulk material. A slab thickness of 15 Å and a vacuum thickness of 15 Å allowed a good reproduction of the bulk properties of this material. For the determination of the vacuum energy, we calculated the averaged electrostatic potential over plans parallel to the surface of the semiconductor by employing the HSE06 formalism following a methodology described in VASP5.2.19−22 We also added the dipole corrections to the local potential to correct any possible error introduced by the periodic boundary conditions.32

discussion because such slightly metastable systems can be experimentally obtained from the high-temperature preparation conditions adopted for this material. In contrast, the other defective structure displaying well-separated Ta- and Nvacancies (Figure 1c) was found 0.63 eV/Ta less stable than the perfect one (Table 1). In this case, the various ions upon relaxation were strongly moved from their initial positions, leading to different lattice parameters (in particular the angles) from those obtained in the two previous cases (Table 1). Therefore, this structural configuration should be excluded from the following discussion. 3.2. Electronic Structure and Absorption Properties of Perfect and Self-Defective Ta3N5. As shown in Figure 2a, the calculated density of states with HSE06 for perfect Ta3N5 gives a band gap of 2.2 eV. The analysis reveals a VB dominated by filled N 2p states and a CB governed by fully empty Ta 5d states. As expected, our predicted band gap of 2.2 eV with HSE06 matches very well the available experimental data.5−9 The lowest-energy band gap in this compound involves transitions between N 2p6 orbitals and Ta 5d0 orbitals. As a result of this predicted electronic structure, the calculated UV− vis optical absorption spectrum with the DFPT-HSE06 method shows a broad absorption edge extending up to 564 nm, as displayed in Figure 3a. If we discuss now the self-defective Ta3N5 material with its lowest-energy structure reported in Figure 1b, the calculated density of states with HSE06 reveals a band gap of 2.0 eV as shown in Figure 2b. Also in this case, the predicted band gap of 2.0 eV is found to be in excellent agreement with the available experimental data.5−9 Similarly to perfect Ta3N5, the VB of this material is governed by occupied N 2p states and the CB is mainly composed of unoccupied Ta 5d states. However, the VB and CB edges of this self-defective material are completely different from those of the perfect one, and consequently, different photocatalytic behavior is expected. Also, the UV−vis optical absorption response was found to be identical to that of the perfect one (Figure 3b). Consequently, our calculations show remarkable similarities of lattice parameters, band gaps, and also optical absorption properties between the perfect and self-defective Ta3N5 materials. This highlights this particular self-defective Ta3N5 material with aggregated N- and Ta-vacancies as being a competitive structure with the perfect one. Although the structural and optoelectronic properties of these two materials are very similar, their photocatalytic features for water-splitting reactions might be completely different on the basis also of their band edge positions relative to water redox potentials. 3.3. Band Edge Positions of Perfect and Self-Defective Ta3N5. The photocatalytic ability of a semiconductor to undergo photoinduced electron/hole transfer to adsorbed species on its surface is governed by the VB and CB edge positions relative to water redox potentials. Thermodynamically, the VB edge position must be lower in energy than the O2/H2O level to give the driving force to the photogenerated hole to oxidize water. Similarly, the CB edge position must be higher in energy than the H+/H2 level to give the driving force to the photogenerated electron to reduce H+. On the basis of this, we evaluate here the photocatalytic abilities of perfect and self-defective Ta3N5 materials for overall water splitting reactions. As shown in Figure 4a, the calculated electronic density of states with HSE06 for the (001) perfect Ta3N5 slab model shows a good reproduction of bulk properties of the material

3. RESULTS AND DISCUSSION 3.1. Relaxed Perfect and Self-Defective Ta3N5 Structures. We discuss here the relative stability of the various explored materials. Figure 1 shows the most relevant relaxed structures, and Table 1 reports their relative energy along with the corresponding lattice parameters. Table 1. Relative Energies per Ta Atom (eV/Ta) and Lattice Parameters Obtained with PBE for the Various Relaxed Structures Reported in Figure 1 lattice parameters

structure self-defective Ta3N5 (1c) self-defective Ta3N5 (1b) perfect Ta3N5 (1a) expta a

relative energy (eV/Ta)

a (Å)

b (Å)

c (Å)

α (°)

β (°)

γ (°)

0.63

3.94

10.26

10.32

91.4

89.6

90.2

0.28

3.87

10.24

10.36

90

90

90

0.00

3.89

10.25

10.27

90

90

90

3.89

10.22

10.28

90

90

90

Reference 7.

As shown in Table 1, our calculated lattice parameters for the perfect Ta3N5 (Figure 1a) are found to be in excellent agreement with the available experimental data.7 Considering now the self-defective Ta3N5 material modeled by removing three neutral Ta atoms and five neutral N atoms from the 96atom orthorhombic Ta3N5 supercell, a strong stabilization is obtained for the configuration displaying a direct interaction between the three created Ta-vacancies and the five created Nvacancies (see Figure 1b). In the lowest-energy structure, the three created Ta-vacancies and the five created N-vacancies are found to be in aggregated disposition, leading to the formation of a cage into the lattice. Interestingly, this structure after relaxation keeps very similar lattice parameters (lengths and angles) to the orthorhombic perfect Ta3N5 (Table 1), revealing also very good agreement with the available experimental data. Although this self-defective structure is found to be 0.28 eV/Ta less stable than the perfect one, it cannot be excluded from the 20786



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Figure 2. Density of states (DOS) obtained with HSE06 for the optimized lowest-energy structures reported in Figure 1: (a) perfect Ta3N5 and (b) self-defective Ta3N5 with aggregated N- and Ta-vacancies. Color legend: total DOS in black, projected DOS on Ta 5d orbitals in blue, and N 2p orbitals in red. The black dashed horizontal line indicates the top part of the VB. The energy scale here allows a direct comparison between the two cases.

positions from the DOS plots (Figure 2) on the basis of its relative positions with respect to the perfect one. Considering first the perfect Ta3N5, the calculated VB edge position with HSE06 is found to be 0.3 eV higher in energy than O2/H2O level as shown in Figure 5a. The CB edge position is found to be 1.3 eV higher in energy than H+/H2 level (Figure 5a). Because of its unsuitable VB edge position with respect to O2/H2O potential, the perfect Ta3N5 material is predicted by HSE06 to be a good candidate only for hydrogen evolution reaction. Note that available general data on the ionization potentials and electron affinities of molecular systems indicate a mean absolute error close to 0.2 eV. In any case, however, even if we assume such error bars in the orbital energy positions, the VB edge position will not be below the O2/H2O level, and consequently, the holes created upon photon absorption in the perfect Ta3N5 will have a very limited power to oxidize water. In contrast, the CB edge position is undoubtedly located above the H+/H2 level, and so, the excited electrons will hence have a strong capability to reduce H+. To the best of our knowledge, this result has never been invoked in previous theoretical studies. Discussing now the self-defective Ta3N5, the VB edge position is found to be shifted downward by 0.7 eV over perfect Ta3N5. It hence becomes 0.4 eV lower in energy than O2/H2O level (Figure 5b), and consequently, its power to oxidize water is expected to be greatly improved over perfect Ta3N5. The CB edge position is also shifted downward by 0.9 eV over perfect Ta3N5 (e.g., 0.4 eV higher in energy than H+/ H2 level), and so, its ability to reduce H+ still remains preserved. It is indeed expected to be lower than the perfect one (Figure 5b). Our predicted band edge positions match well the experimental data reported on Ta3N5 powders.6,9

Figure 3. UV−vis optical absorption spectra obtained with HSE06 for the two materials reported in Figure 2: (a) perfect Ta3N5 and (b) selfdefective Ta3N5 with aggregated N- and Ta-vacancies.

(same band gap of 2.2 eV) with energies of VB and CB edges of −0.84 and +1.36 eV, respectively. Moreover, the corresponding profile of the averaged electrostatic potential over plans parallel to the surface obtained at HSE06 level reveals an energy of the vacuum level of 4.56 eV, as shown in Figure 4b. As described in Computational Methods, we then obtained the band edges of the perfect Ta3N5 material with respect to the vacuum level (or normal hydrogen electrode (NHE) potential) by subtracting the energy of the vacuum level (4.56 eV) from the energies of VB (−0.84 eV) and CB (+1.36 eV) edges within the slab. For the self-defective Ta3N5 material, we deduced the band edge 20787



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Figure 4. (a) Electronic density of states obtained with HSE06 for the (001) perfect Ta3N5 slab model. The band gap of the bulk material is well reproduced. Color legend: total DOS in black and projected DOS on subsurface Ta in blue and on subsurface N in red. (b) Total local potential profile averaged over plans parallel to the surface obtained with HSE06 for perfect Ta3N5.

overall water splitting reactions are retained on the VB and CB edge states, respectively, as discussed in section 3.3. Hence, it is extremely important to analyze the hybridization character (localized or delocalized nature) of these specific electronic states in order to understand the photocatalytic behavior of these materials. Figure 6a and b shows the distribution of electron densities corresponding to the VB edge states of the perfect and selfdefective Ta3N5 materials, respectively. Analysis of perfect Ta3N5 reveals strongly delocalized VB edge states because of the large contribution of p-orbitals distributed on all the N species in the cell as displayed in Figure 6a. This strongly delocalized nature of the VB edge is expected to give good hole mobility to the reactive site at the surface of this material. In contrast, the analysis of self-defective Ta3N5 shows contributions from p-orbitals localized only on the N species surrounding the cage created by the aggregated N- and Tavacancies (Figure 6b). This behavior is consistent with the DOS result revealing a disconnected VB edge from the deeper states (Figure 2b). Consequently, this strongly localized character of p-orbitals only on a few N species in the cell is expected to strongly limit the probability of hole mobility through the crystal structure of this self-defective Ta3N5 material with respect to the perfect one. The distributions of electron densities associated with the CB edge states of perfect and self-defective Ta3N5 are shown in Figure 6c and d, respectively. For the perfect Ta3N5, the electron density analysis shows important contributions from dorbitals distributed on all Ta species in the cell as presented in Figure 6c. This strongly delocalized nature of the CB edge is expected to give good electron mobility to the reactive site at the surface of this material. In contrast, the analysis of the self-

Figure 5. Valence and conduction band edge positions obtained with HSE06 for the two explored materials: (a) perfect Ta3N5 and (b) selfdefective Ta3N5 with aggregated N- and Ta-vacancies. The values are given with respect to the vacuum level (in eV) as well as with respect to the NHE potential (in V).

As a consequence, our HSE06 calculations clearly show that a formation of aggregated N- and Ta-vacancies into the lattice of Ta3N5 greatly enhances its power for water oxidation and O2 evolution but lowers its ability for H+ reduction and H2 evolution. To the best of our knowledge, these significant effects of aggregated N- and Ta-vacancies on the photocatalytic ability of Ta3N5 for overall water splitting have never been reported in previous theoretical studies. 3.4. Analysis of Band Edge States on the Basis of Electron Densities. The photogenerated carriers after excitation must migrate from bulk to reactive sites at the surface of the semiconductor, where the relevant redox chemistry takes place. The holes and electrons utilized for 20788



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Figure 6. Electron density contour plots obtained with HSE06 for the VB edge states (on the bottom) and the CB edge states (on the top) of (a, c) perfect Ta3N5, and (b, d) self-defective Ta3N5. Isovalue is 0.003 au.

defective Ta3N5 reveals contributions from d-orbitals localized only on a few Ta species surrounding the cage created by the aggregated N- and Ta-vacancies (Figure 6d). This trend is also consistent with the DOS result showing a disconnected CB edge from the other states located within higher energy range (Figure 2b). As a consequence of this strong localization of dorbitals only on a few Ta species in the cell, a strong limitation in the probability of electron mobility through the crystal structure of this self-defective Ta3N5 is also expected as compared with the perfect material.

their photocatalytic features for visible-light overall water splitting reactions showed completely different behaviors. On the basis of calculated VB and CB edge positions relative to water redox potentials, the perfect Ta3N5 (calculated band gap of 2.2 eV) was predicted by HSE06 to be a good candidate only for H+ reduction because its calculated VB edge position was found to be 0.3 eV higher in energy than O2/H2O. The CB edge position of this material was calculated to be 1.3 eV higher in energy than H+/H2 level. In contrast, the self-defective Ta3N5 (calculated band gap of 2.0 eV) revealed suitable band positions for both water oxidation and H+ reduction similar to the experimental data reported on Ta3N5 powders.6,9 The VB edge position of this material was predicted to be 0.4 eV lower in energy than O2/H2O level, and so, its capacity to oxidize water is expected to be greatly improved over the perfect material. The CB edge position of this material was predicted to be 0.4 eV higher in energy than H+/H2 level, and consequently, its ability to reduce H+ is expected to be lower than the perfect one. From our electronic analysis, the VB and CB edge states of the self-defective structure were found to be strongly localized only on the N 2p and Ta 5d orbitals surrounding the aggregated N- and Ta-vacancies into the lattice. This strongly localized electronic character of the band edges is expected to lead to very limited probability of hole and electron mobility through the crystal structure of the self-defective material as compared with the perfect one. In conclusion, we have shown a major difference in visiblelight photocatalytic features for overall water splitting reactions between perfect and self-defective bulk Ta3N5 materials. The

4. CONCLUSION In summary, we have investigated relevant properties to visiblelight-driven overall water splitting reactions of perfect and selfdefective bulk Ta3N5 semiconductor photocatalysts using accurate first-principles quantum calculations on the basis of DFT (including the perturbation theory DFPT) within the screened coulomb hybrid (HSE06) exchange-correlation formalism. Among the various explored self-defective structures, a strong stabilization was obtained for the configuration displaying a direct interaction between the created N- and Tavacancies. In the lowest-energy structure, each of the three created Ta-vacancies and the five created N-vacancies was found to be in aggregated disposition, leading to the formation of cages into the lattice. Although the calculated lattice parameters, band gaps, and UV−vis optical absorption coefficient spectra of the perfect and self-defective materials were found to be very similar and in good agreement with available experimental data obtained on Ta3N5 powders,5−9 20789



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(14) Harb, M.; Sautet, P.; Raybaud, P. Origin of the Enhanced Visible-Light Absorption in N-Doped Bulk Anatase TiO2 from FirstPrinciples Calculations. J. Phys. Chem. C 2011, 115, 19394−19404. (15) Harb, M.; Sautet, P.; Raybaud, P. Anionic or Cationic S-Doping in Bulk Anatase TiO2: Insights on Optical Absorption from First Principles Calculations. J. Phys. Chem. C 2013, 117, 8892−8902. (16) Harb, M. Screened Coulomb Hybrid DFT Study on Electronic Structure and Optical Properties of Anionic and Cationic Te-Doped Anatase TiO2. J. Phys. Chem. C 2013, 117, 12942−12948. (17) Harb, M.; Masih, D.; Ould-Chikh, S.; Sautet, P.; Basset, J.-M.; Takanabe, K. Determination of the Electronic Structure and UV-Vis Absorption Properties of (Na2‑xCux)Ta4O11 from First-Principle Calculations. J. Phys. Chem. C 2013, 117, 17477−17484. (18) Harb, M. New Insights into the Origin of Visible-Light Photocatalytic Activity in Se-Modified Anatase TiO2 from Screened Coulomb Hybrid DFT Calculations. J. Phys. Chem. C 2013, 117, 25229−25235. (19) Kresse, G.; Hafner, J. Ab-Initio Molecular Dynamics Simulation of the Liquid-Metal-Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B 1994, 49, 14251−14269. (20) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (21) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for AbInitio Total Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (22) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B 1999, 59, 1758− 1775. (23) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approxmation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (24) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979. (25) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (26) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2004, 118, 8207−8215. (27) Gajdoš, M.; Hummer, K.; Kresse, G.; Furthmüller, J.; Bechstedt, F. Linear Optical Properties in the Projector-Augmented Wave Methodology. Phys. Rev. B 2006, 73, 045112/1−045112/9. (28) Launay, M.; Boucher, F.; Moreau, P. Evidence of a Rutile-Phase Characteristic Peak in Low-Energy Loss Spectra. Phys. Rev. B 2004, 69, 035101/1−035101/9. (29) Saha, S.; Sinha, T. P.; Mookerjee, A. Electronic Structure, Chemical Bonding and Optical Properties of Paraelectric BaTiO3. Phys. Rev. B 2000, 62, 8828−8834. (30) Van de Walle, C. G.; Martin, R. M. Theoretical Study of Ban Offsets at Semiconductor Interfaces. Phys. Rev. B 1987, 35, 8154− 8165. (31) Franciosi, A.; Van de Walle, C. G. Heterojunction Band Offset Engineering. Surf. Sci. Rep. 1996, 25, 1−140. (32) Markov, G.; Payne, M. C. Periodic Boundary Conditions in Ab Initio Calculations. Phys. Rev. B 1995, 51, 4014−4022.

use of the advanced quantum method described in this study can certainly be extended to the identification of good candidate photocatalysts for visible-light-driven overall water splitting reactions among novel semiconducting materials.

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ASSOCIATED CONTENT

S Supporting Information *

Fractional coordinates of all relaxed structures presented in Figure 1. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +966.2.808.07.88. Fax: +966.2.802.12.72. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully thank the High Performance Computing department (HPC) at King Abdullah University of Science and Technology (KAUST) for the CPU hours attributed to this work.

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REFERENCES

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