An optimal density functional theory method for GaN and ZnO

Chemical Physics Letters 512 (2011) 231–236

Contents lists available at ScienceDirect

Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

An optimal density functional theory method for GaN and ZnO Hua-Gen Yu Department of Chemistry, Brookhaven National Laboratory, Upton, NY 11973, USA

a r t i c l e

i n f o

Article history: Received 30 March 2011 In final form 11 July 2011 Available online 18 July 2011

a b s t r a c t We report an optimal DFT method (bBLYP) for studying the GaN and ZnO systems. It is developed by modifying the exchange functional in the hybrid BLYP method in order to overcome the flaw of traditional DFT that often predict a rather small band gap for those semiconductors. Results show that the bBLYP method can describe not only correct band gaps of both GaN and ZnO wurtzite crystals, but also accurate properties of relevant small molecules. The application study of crystal-cut nanoparticles and nanowires reveals a new mechanism for band gap narrowing in GaN/ZnO. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Photocatalytic water splitting is an attractive subject owing to producing clean and renewable hydrogen energy [1]. Most practical photocatalysts are metal oxides because of their stability and low cost of preparations. However, metal oxides often have a large band gap that substantially reduces the photo-efficiency of water splitting without taking the advantage of visible light of solar energy. In 2005, Domen et al. [2,3] discovered that the GaN-rich GaN/ZnO solid solution is stable and efficient photocatalyst for water splitting in the visible region in acid solutions loaded with Rh2xCrxO3. The high efficiency is determined by its smaller band gap of 2.5 eV (with 13% ZnO) [4] than the 3.4–3.5 eV band gaps [5–8] of individual ZnO and GaN. The stability is mainly attributed to the fact that GaN and ZnO are isoelectronic, and have nearly identical wurtzite structures. Recently, the GaN/ZnO solid solution has received a few investigations both experimentally [9–20] and theoretically [9,10,14,21–25]. Experimentally, Domen’s group focuses on the GaN-rich Ga1xZnxN1xOx solid solutions. In addition, Chen et al. [16] reported a novel high pressure and high temperature pathway to synthesize ZnO-rich GaN/ZnO solid solutions with a ZnO content up to about 75%. Han et al. [17] developed an attractive chemical synthesis route to prepare GaN/ZnO solid solution nanocrystals with a wide range of Zn/(Ga+Zn) ratios. It was found that the nanocrystals have a narrowest band gap of 2.21 eV with a Zn/(Ga+Zn) atomic ratio of 0.482. Until now, however, the photocatalytic water splitting efficiency of those ZnO-rich GaN/ZnO solid solutions has not been investigated. Density functional theory (DFT) calculations have played an important role in understanding the mechanism of the band gap reduction of GaN/ZnO solid solutions. Unfortunately, the mecha-

E-mail address: [email protected] 0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2011.07.034

nism is still in extensive debate. There are several theoretical mechanisms including the strong p–d repulsion between the N 2p and Zn 3d states [9,21–24], Zn impurity levels [10,14,23], the volume deformation and structural relaxations [21], and the strong short range order in a uniform GaN/ZnO solid solution [25]. Here, one key issue is the uncertainty of the popular DFT calculations using the local density approximation (LDA) and/or the generalized gradient approach (GGA) [9,10,14,21,23,25]. Those standard DFT methods often underestimate the band gap of semiconductors and insulators [24,26–29]. Although the DFT+U approach [21,23] has been utilized to partially improve the description of the d states of Zn and Ga, the calculated band gaps of GaN and ZnO are still substantially smaller than the experimental results of both materials. In order to compare with experiments, a brute force or ad hoc approach is often employed [22,25]. This could arise another ambiguity for revealing the mechanism of the band gap of GaN/ ZnO solid solutions. It is well-known that the underestimate of band gap of semiconductors arises from the approximation of exchange functional in DFT [26–30]. This main flaw of DFT can be overcome by introducing some advanced techniques such as the many-body GW and quasi-particle schemes [28], exact Kohn–Sham exchange potential approach [27], and hybrid DFT methods based on Hartree–Fock exchange potentials [24,31,32]. Most recently, Valentin [24] has demonstrated that the hybrid B3LYP functional [26,33] is one of good DFT methods for describing the GaN/ZnO system. Nevertheless, the B3LYP method was optimized for isolated molecular systems. Its parameters are not equally optimal for the study of bulk GaN and/or ZnO materials. In order to fully exploit the advantage of the hybrid DFT method, here, we will re-optimize the parameters of the B3LYP method for GaN and ZnO by including their bulk properties to obtain an improved hybrid DFT method. In the optimization procedures, the energetics of some molecules involving in the photocatalytic water splitting

232

H.-G. Yu / Chemical Physics Letters 512 (2011) 231–236

dmCEP-31G). The modifications are made in two aspects: (1) replace the two most diffuse d orbitals with one d orbital with an exponential parameter vd = 0.62145; and (2) replace the most diffuse sp orbital with one s orbital with as = 0.075. These modifications have small effect on the properties of isolated Zn-contained molecules, but are essential in studying bulk ZnO materials. Otherwise, it is almost impossible to achieve a convergent calculation with the CEP-31G basis set. In the crystal structure calculations, the wurtzite crystal of GaN or ZnO is simulated by a supercell containing 16 atoms of (GaN)8 (or (ZnO)8) formed by a set of 2  2  1 unit bulk cells. The k-point meshes are determined by a set of 8  8  10 Monkhorst–Pack grids. The convergence of k-space mesh-points, cell size and the cell number is tested. Those parameters used are able to achieve the band gap of GaN or ZnO within an error of 0.02 eV. We have determined the optimal parameters in Eq. (2) as:

to form hydrogen and oxygen molecules are also considered owing to their importance in the overall processes. As similar to B3LYP, only the Becke [26] and LYP [33] functionals are used. 2. Optimal density functional theory method for GaN and ZnO Generally, the DFT energy of a hybrid density functional theory can be written as local

non-local EDFT ¼ cElocal þ aEHF þ dEC X X þ bDEX

þ cDEnon-local ; C

ð1Þ

which is comprised of the exchange (denoted by the subscript ‘X’) and correlation (labeled by the subscript ‘C’) energies. Both energies contain the local and non-local contributions in addition to the nonlocal correction terms (labeled as DE). As a hybrid DFT method, the parameter a is non-zero (positive) so that it includes a mixture of Hartree–Fock (HF) and standard density functional exchanges. Here, we will follow the protocol of the B3LYP method [33] to choose those local and non-local functional in Eq. (1). That is, for the exchange energies, the local term is determined by the Slater functional while the non-local correction is given by the Becke functional. For the correlation part, the local correlation energy is described by the VWN III functional whereas the non-local term is determined by the non-local part of the LYP functional. The final expression is then obtained as VWN;III

Becke EDFT ¼ cESlater þ aEHF þ dEC X X þ bDEX

þ cDEnon-local;LYP : C

8 a ¼ 0:215 > > > > > > < b ¼ 0:69

c ¼ 0:785 > > > c ¼ 0:81 > > > : d ¼ 0:19

ð3Þ

The corresponding optimized hybrid DFT method is denoted as bBLYP for convenience. A comparison of the bBLYP results with experiments and/or other DFT calculations is summarized in Table 1 for small molecules and in Table 2 for the bulk GaN and ZnO wurtzite structures. It clearly shows that the theoretical results are in very good agreement with the experiments in both energy and geometry. Compared to the experiments, the bBLYP method gives a root-mean-square (rms) error of 0.16 eV (or 3.7 kcal/mol) with a maximum error of 0.24 eV (or 5.53 kcal/mol) for H2O. The B3LYP method gives an average rms error of 4.2 kcal/mol with a maximum error of 6.68 kcal/mol for the band gap of GaN instead of 5.83 kcal/mol for H2O, which are similar to the overall performance of B3LYP for isolated molecules in the ground electronic states [30]. Therefore, the performance of bBLYP is somewhat better than that of B3LYP, especially, for the bulk systems. The error in the most important band gap of GaN is reduced to 0.07 eV from 0.29–0.41 eV of B3LYP. As shown in Table 2, the bBLYP method is capable of predicting accurate band gaps of both GaN and ZnO wurtzite crystals. It gives a band gap of 3.40 eV for GaN or 3.61 eV for ZnO, which are very close to the experimental values of 3.47 eV (GaN) and 3.44 eV (ZnO), respectively. The experimental errorbars are about 0.1 eV. Compared to those GGA/GGA+U values, the bBLYP method substantially improves the band gap calculations. In addition, the calculated crystal structure parameters are also in good agreement with the experiments. In short, the bBLYP DFT method can accurately describe the properties of the diatomic molecules and bulk crystal structures

ð2Þ

The parameters {a, b, c, c, d} will be optimized according to these most important quantities: the dissociation energy of the GaN, ZnO, H2O, and OH molecules, the band gap and structure of GaN and ZnO wurtzite crystals, and the bond length of the ZnO molecule. All electronic structure calculations are carried out using the GAUSSIAN 09 program package. The electrons of the H, N, and O atoms are described by the polarization function basis set 631G(d,p). For both Ga and Zn, a pseudopotential approach is employed. The 18 core electrons in Zn (or Ga) are included in the effective core potential (ECP) of LanL2DZ for Zn or of Stuttgart ECP18MWB [34] for Ga. That is, the 3d electrons in Ga (or Zn) are explicitly treated because these electrons can play an important role in forming chemical bonds and determining the electron interactions for band gap. The 13 valence electrons of Ga are described by a [7s6p7d/2s2p2d] contracted basis set. This contracted basis set is obtained from the original [8s6p7d/1s1p1d] basis set [34] of ECP18MWB by removing two most diffuse GTOs in the s contracted orbital, adding one extra s GTO with an exponential parameter of as = 0.060936, splitting the 6p GTOs into two 3p contract bases, and splitting the 7d GTOs into 6d and 1d ones. The resulting basis set has the quality of double-zeta basis set. Furthermore, the 12 valence electron of Zn are described by a modified SBK ECP split valance basis set CEP-31G [35] (or denoted as

Table 1 Comparison of bond length (Re), bond angle (h), and dissociation energy (De) between the bBLYP/B3LYP results and experiments for some small molecules, where the values in bold face are included in the optimization. Molecule

This work Re/Å

GaN(X3R) ZnO(X1R+) H2O H2 OH O2 a b

1.9129 1.7190 0.9644 0.7428 0.9789 1.2123

Expt. h/deg.

(1.9142)b (1.7206) (0.9650) (0.7428) (0.9797) (1.2142)

104.04 (103.97)

De/eV 1.927 3.605 5.205 4.839 4.548 5.362

The best theoretical values are taken since no experimental results are available. The B3LYP results are shown in parentheses.

Re/Å (1.944) (3.619) (5.199) (4.844) (4.5487) (5.382)

2.041– 1.7047 0.9585 [39] 0.7414 0.9696 [41] 1.2075

h/deg.

104.34 [39]

De/eV 2.054a [37] 3.456 [38] 5.447 [40] 4.747 [41] 4.644 [40] 5.213 [41]

233

H.-G. Yu / Chemical Physics Letters 512 (2011) 231–236

Table 2 Comparison of calculated structures and energies of GaN and ZnO wurtzite structures with other calculations and experiments, where the values in bold face are included in the optimization. Species

This work

GGA [42]

GGA [43]

GGA+U

B3LYP

Expt.

GaN a (Å) c (Å) u– Eg(eV)

3.256 5.268 0.378 3.40

3.245 5.296 0.3762 1.45

3.219 5.244 0.377 1.69

3.114 [21] 5.066 [21] 0.377 [21] 2.795 [21] 2.44 [23]

3.205 5.184 0.379 3.18 3.75 [31] 3.88 [24]

3.190 [44] 5.190 [44] 0.377 [44] 3.47 (0 K)[7] 3.39 (300 K) [6]

This work

GGA [45]

GGA [36]

GGA+U

B3LYP

Expt.

3.295 5.219 0.385 3.61

3.283 5.289 0.378 0.75

3.292 5.310 0.3793 0.71

3.222 [21] 5.187 [21] 0.381 [21] 1.568 [21] 1.60 [23]

3.294 5.218 0.385 3.23 3.38 [24]

3.250 [46] 5.206 [46] 0.3817 [46] 3.44 (0 K) [8] 3.3 (300 K) [47]

ZnO a(Å) c(Å) u– Eg(eV) –

The closest spacing between Ga and N (or Zn and O) layers is (1/2  u)c.

of GaN and ZnO in addition to those H2O-related species. Since the diatomics and bulk materials represent two asymptotic limits, one can expect that the bBLYP method would be a reliable and accurate DFT method for studying the photocatalytic water splitting processes of the GaN/ZnO system including their nanoparticles, nanowires, solid surfaces, and bulk materials.

3. A preliminary application to nanoclusters and nanowires Here, we will report some preliminary calculations that study the size effect on the band gap of individual GaN and ZnO materials, and the mixture effect of ZnO in GaN (or GaN in ZnO) using a crystal-cut cluster model. The cluster model has been used by Brena and Ojamae [31] for GaN. One-dimensional (1D) nanowire of GaN (or ZnO) is modeled using a supercell consisting of (GaN)26 (or (ZnO)26) with a periodic boundary condition (PBC) along the polar axis of the system. A set of 1  1  10 Monkhorst–Pack grids are used in the calculations. Figure 1 shows the optimized geome-

Figure 2. Calculated band gaps of (GaN)n and (ZnO)n as a function of cluster size or nanowire (1D) and bulk (3D) wurtzite crystals.

Figure 1. Top and side views of optimized crystal-cut (GaN)n clusters and 1D GaN nanowire ((GaN)26), where the unit number of GaN is labeled by n. The blue/yellow balls refer to N/Ga atoms. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

234

H.-G. Yu / Chemical Physics Letters 512 (2011) 231–236

tries of GaN clusters and 1D nanowire. For ZnO, similar structures are obtained. Figure 2 displays the evolution of band gaps of GaN and ZnO from small clusters, to 1D nanowire, and to bulk (3D) wurtzite structures. The band gap of clusters is computed using energy difference between LUMO and HOMO. For the 1D and 3D cases, the band gap is determined by the minimum energy difference between LUCO and HOCO at each k point. It is noticed that the minimum direct band gap occurs at the C point for both GaN and ZnO. From Figure 2, one can see that the size effect on the band gaps is different for GaN and ZnO. Roughly, the band gap gradually grows with increasing the GaN cluster size, and becoming 1D and 3D materials. There is a large increase in the band gap for the transition from 1D (2.57 eV) to 3D (3.40 eV). Normally, the size effect of a semiconductor often shows an opposite trend according to the confinement effect of electrons in nanoparticles or nanowires. However, here, it is found that the surface states have played a crucial role in determining the band gap of GaN. The surface states are attributed not only by the dangling bonds of atoms at surface but also by the ionic characteristics of the system. The effect of surface states has clearly demonstrated in the optimized structures of (GaN)n clusters as shown in Figure 1, where four-member rings are formed at the surfaces of clusters, and surface atoms have largely adjusted along the polar axis. As a result, the calculated dipole moments nearly vanish for all GaN clusters except for (GaN)26. The latter has a dipole moment of 2.38 D, but it is still slightly smaller than that (2.46 D) of the diatomic GaN(X3R) molecule. On the other hand, the size effect on the band gap of ZnO clusters and 1D/3D materials shows a normal behavior although the influences of surface states are also well recognized. This finding is consistent with the GGA calculations [36]. Nevertheless, we found that the size-dependence of the band gaps is only medium for ZnO in contrast to the strong dependence of the GGA methods, e.g., see Ref. [36] and references therein. For instance, the bBLYP predicts a band gap reduction of 0.3 eV for the transition from the 1D nanowire to the 3D bulk while the GGA calculations gives a value of about 0.9 eV. This discrepancy may imply the importance of exact exchange functional that has been included in this work. On the other hand, the traditional LSD and GGA methods are rather cheaper than a hybrid DFT method. Hence, we also perform a LSD/GGA-bBLYP correlation study of HOMOs and band gaps of all species used in this work. The GGA method is defined by the rev-PBEPBE functional. Results show that the correlations are not so bad with a deviation of about 12%. Therefore, the traditional LSD and GGA DFT methods can be served as a pre-screened approach for the GaN/ZnO systems of interest. Furthermore, it is a hot and challenging topic to investigate the band gap change once GaN is mixed with ZnO. In order to explore the band gap narrowing mechanism of GaN/ZnO, we preliminarily use a cluster model that is simulated by using either (GaN)25(ZnO) or (ZnO)25(GaN) nanoparticle. The nanoparticles have the same crystal-cut structure as (GaN)26 in Figure 1. Configuration ensembles are represented by (GaN)25(ZnxOy) and (ZnO)25(GaxNy) where (x,y) are the position indices of substituted atoms. For instance, a pair of (x,y) for (GaN)25(ZnxOy) stand for that the Ga atom at the x position and the N atom at y in the original (GaN)26 nanoparticle are replaced with Zn and O, respectively. The numbering of (GaN)26 (or (ZnO)26) are shown in Figure 3a, where the blue and red balls refer to N and/or O atoms whereas the metal atoms are displayed in yellow. In addition, we only substitute chemically bound GaN (or ZnO) unit by ZnO (or GaN) since previous studies [21,24] have shown that it is a preferable substitution in GaN/ZnO solid solutions. In total, there are 17 distinguishable configurations in a C3V symmetry. Calculated results for those nanoparticles are shown in Figure 3b and c. Usually, the GaN or ZnO unit substitution can signifi-

Figure 3. Results for the (GaN)25(ZnO) and (ZnO)25(GaN) nanoparticles: (a) the numbering of parent (GaN)26 or (ZnO)26 cluster; (b) the HOMO and LUMO energy levels; and (c) the band gap shifting of (GaN)25(ZnxOy) and (ZnO)25(GaxNy) with respect to their parent clusters (0,0).

cantly push the HOMO energy levels toward high energies. The largest energy lifts occur at the position (x, y) = (5, 27), and are obtained as 0.26 eV for (GaN)25(ZnO) and 1.36 eV for (ZnO)25(GaN). In contrast, the influence of the substitution on the LUMO energy levels is small. For the (GaN)25(ZnO) nanoparticles, their LUMO energies vary within ±0.05 eV around the LUMO energy level (4.14 eV) of (GaN)26. On the other hand, for the (ZnO)25(GaN) nanoparticles, most mixed nanoparticles have a lower LUMO

H.-G. Yu / Chemical Physics Letters 512 (2011) 231–236

energy level than (ZnO)26 does although the energy shifting is small (<0.21 eV). These results indicate that the band gap narrowing in the mixed nanoparticles is mainly attributed by the upward shifting of the HOMO energy levels. The LUMO energy shifting may have some noticeable contributions, especially, for (ZnO)25(GaN). Figure 3c displays the change of band gaps as a function of relative stability of the nanoparticles, where the energy reference is taken as the mean unit dissociation energy of (GaN)26 for (GaN)25(ZnO) (6.2413 eV) or of (ZnO)26 for (ZnO)25(GaN) (6.1872 eV). It clearly shows that the band gap narrowing is not well correlated with the stability of the nanoparticles as shown in Figure 3c. The less stable nanoparticles often have a large band gap reduction. These results are consistent with previous work [21,25]. Although the band gap reductions for (ZnO)25(GaN) are much larger than those for (GaN)25(ZnO), the resulting band gaps of (ZnO)25(GaN) are still bigger than the band gap (2.08 eV) of the (GaN)26 nanoparticle in most cases because the band gap of (ZnO)26 is as large as 3.49 eV. However, the two (ZnO)25(GaN) nanoparticles with a (5, 27) or (11,37) replacement already have a comparable band gap of 2.03 eV or 2.19 eV, respectively. The detailed molecular orbital investigations show that the upward shifting of HOMO energy levels in the mixed nanoparticles is driven by the formation of a localized orbital over a Ga–N–Zn fragment in addition to the p–d repulsion. This finding is illustrated by using the (5, 27) substitution in Figure 4. For both (GaN)26 and (ZnO)26, their HOMOs are characterized by the p–d repulsive interactions, in which the p-orbital components dominate. Similar p–d interactions also persist in those occupied MOs just below HOMO but the components of the d-orbitals of metal atoms gradually increase. In particular, when one GaN unit in (GaN)26 is replaced with ZnO, the resulting (GaN)25(ZnO) nanoparticle has a distinct HOMO character. One can see a localized p-like orbital formed over a Ga–N–Zn moiety. This orbital has the nature of chemical bonding but happens only in a rather small range. The rest part remains the typical p–d repulsive interactions. As a result,

235

Figure 5. Highest occupied crystal orbitals (HOCOs) of GaN/ZnO wurtzite solid solutions in a (ZnO)(GaN)7 or (GaN)(ZnO)7 supercell.

the chemically bound p-like orbital region has a repulsive interaction with other part of molecular orbital in HOMO. In addition, such a localized p-like orbital over a Ga–N–Zn fragment is also well recognized in the HOMO of (ZnO)25(GaN). Nevertheless, in this case, the p-like orbital is encountered by the anti-p orbitals of the four nearest oxygen atoms. The p–d repulsion is rather weaker in (ZnO)25(GaN) than that in (GaN)25(ZnO). These results may imply that the mechanism for the band gap narrowing could be different for ZnO-rich and GaN-rich GaN/ZnO materials. In particular, besides the p–d repulsive interactions, the finding of the localized p-like orbital segmentation over a short range Ga–N–Zn fragment in GaN/ZnO nanoparticles is apparently different from the previously proposed mechanisms [9,10,14,21– 24] mentioned above. Since the localized p-like orbital mechanism is concluded from the nanoparticle studies, it could result from the confinement effects and/or surface states of nanoparticles. In order to clarify this issue, we carried out a preliminary study of the wurtzite GaN/ZnO solid solutions using the (ZnO)(GaN)7 and (GaN)(ZnO)7 supercells with a concentration value of x = 0.125. There are two possible substitutions, e.g., the ZnO unit locating along either the c-axis or the a-axis in (ZnO)(GaN)7. Nevertheless, both substitutions give very similar results. All calculations confirm the persistence of localized p-like orbitals in the HOCOs of GaN/ZnO solid solutions. Figure 5 shows the HOCO orbitals for the a-axis substitution in both cases. The localized p-like orbitals are mainly formed over adjacent Zn–N and N–Ga bonds. They demonstrate the nature of chemical bonding. Also displayed are the p–d repulsive interactions. In addition, for these two solid solutions, we predict a direct band gap of 2.64 eV (2.40 eV for the c-axis substitution with a relative energy of 2.04 kcal/mol to the a-axis one) for (ZnO)(GaN)7, and of 2.27 eV (2.18 eV for the c-axis substitution with a relative energy of 0.64 kcal/mol) for (GaN)(ZnO)7. The former is in excellent agreement with the experimental result [4] of 2.5 eV with x = 0.13.

4. Summary

Figure 4. Highest occupied molecular orbitals (HOMOs) of four crystal-cut nanoparticles, where the substitution position for either (GaN)25(ZnO) or (ZnO)25(GaN) is at (5, 27) in Figure 3a.

In summary, an optimal density functional theory (bBLYP) method has specifically developed for studying the GaN and ZnO systems. It can accurately describe the band gaps of both GaN and ZnO bulk materials as well as the properties of some relevant small molecules. The method has successfully been applied for studying the evolution of the band gaps from molecules to bulk materials, and the mixture effect on the band gaps of GaN/ZnO

236

H.-G. Yu / Chemical Physics Letters 512 (2011) 231–236

nanoparticles. The results obtained are very promising, and already show the importance of the appropriate treatments of exchange functional. A new localized p-like orbital mechanism for band gap narrowing in GaN/ZnO solid solutions has been discovered. Therefore, it can be expected that the optimal bBLYP is an accurate and unambiguous method for exploring the mechanism of band gap narrowing, and for understanding the photocatalytic water splitting processes of GaN/ZnO solid solution, a key solar fuel material. Acknowledgments The author thanks Dr. W.-Q. Han for discussions. This work was performed at the Brookhaven National Laboratory under Contract No. DE-AC02-98CH10886, and used resources of the National Energy Research Scientific Computing Center (NERSC) under Contract No. DE-AC02-05CH11231, with the U.S. Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences. References [1] A.J. Nozik, J.R. Miller, Chem. Rev. 110 (2010) 6443. [2] K. Maeda, K. Teramura, D.L. Lu, T. Takata, N. Saito, Y. Inoue, K. Domen, Nature 440 (2006) 295. [3] K. Maeda, T. Takata, M. Hara, N. Saito, Y. Inoue, H. Kobayashi, K. Domen, J. Am. Chem. Soc. 127 (2005) 8286. [4] M. Yashima, K. Maeda, K. Teramura, T. Takata, K. Domen, Chem. Phys. Lett. 416 (2005) 225. [5] B. Monemar, Phys. Rev. B 10 (1974) 676. [6] R.D. Vispute et al., Appl. Phys. Lett. 73 (1998) 348. [7] M.E. Levinshtein, S.L. Rumyantsev, M.S. Shur, in Properties of Advanced Semiconductor Materials GaN, AlN, InN, BN, SiC, SiGe, John Wiley & Sons, Inc., New York, 2001. [8] D.C. Reynolds, D.C. Look, B. Jogai, C.W. Litton, G. Cantwell, W.C. Harsch, Phys. Rev. B 60 (1999) 2340. [9] K. Maeda et al., J. Phys. Chem. B 109 (2005) 20504. [10] T. Hirai, K. Maeda, M. Yoshida, J. Kubota, S. Ikeda, M. Matsumura, K. Domen, J. Phys. Chem. C 111 (2007) 18853. [11] T. Hisatomi, K. Maeda, D. Lu, K. Domen, ChemPhysChem 2 (2009) 336.

[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39]

[40] [41] [42] [43] [44] [45] [46] [47]

M. Yashima, H. Yamada, K. Maeda, K. Domen, Chem. Commun. 46 (2010) 2379. K. Maeda, K. Domen, Chem. Mat. 22 (2010) 612. M. Yoshida et al., J. Phys. Chem. C 114 (2010) 15510. H.Y. Chen et al., J. Phys. Chem. C 113 (2009) 3650. H.Y. Chen et al., J. Phys. Chem. C 114 (2010) 1809. W.-Q. Han, Z.X. Liu, H.-G. Yu, Appl. Phys. Lett. 96 (2010) 183112. W.-Q. Han, Y. Zhang, C.Y. Nam, C.T. Black, E.E. Mendez, Appl. Phys. Lett. 97 (2010) 083108. J.H. Kou, Li. ZS, Y. Guo, J. Gao, M. Yang, Z.G. Zou, J. Mol. Catal. A: Chem. 325 (2010) 48. C.H. Lee et al., Appl. Phys. Lett. 94 (2009) 213101. L.L. Jensen, J.T. Muckerman, M.D. Newton, J. Phys. Chem. C 112 (2008) 3439. W. Wei, Y. Dai, K. TYang, M. Guo, B. Huang, J. Phys. Chem. C 112 (2008) 15915. M.N. Huda, Y. Yan, S.-H. Wei, M.M. Al-Jassim, Phys. Rev. B 78 (2008) 195204. C. Di Valentin, J. Phys. Chem. C 114 (2010) 7054. S.Z. Wang, L.W. Wang, Phys. Rev. Lett. 104 (2010) 065501. A.D. Becke, J. Chem. Phys. 98 (1993) 5648. M. Stadele, J.A. Majewski, P. Vogl, A. Gorling, Phys. Rev. Lett. 79 (1997) 2089. P. Rinke, A. Qteish, J. Neugebauer, C. Freysoldt, M. Scheffler, New J. Phys. 7 (2005) 126. S.-H. Wei, A. Zunger, Phys. Rev. B 37 (1988) 8958. Y. Zhao, D.G. Truhlar, J. Phys. Chem. A 110 (2006) 13126. B. Brena, L. Ojamae, J. Phys. Chem. C 112 (2008) 13516. P.G. Moses, M. Maio, Q. Yan, J. Chem. Phys. 134 (2011) 084703. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. T. Leininger, A. Berning, A. Nicklass, H. Stoll, H.-J. Werner, H.-J. Flad, Chem. Phys. 217 (1997) 19. W.J. Stevens, M. Krauss, H. Basch, P.G. Jasien, Can. J. Chem. 70 (1992) 612. X. Shen, P.B. Allen, J.T. Muckerman, J.W. Davenport, J.-C. Zheng, Nano Lett. 7 (2007) 2267. D. Tzeli, A.A. Tsekouras, J. Chem. Phys. 128 (2008) 144103. L.N. Zack, R.L. Pulliam, L.M. Ziurys, J. Mol. Spectroc. 256 (2009) 186. G. Herzberg, Molecular Spectra and Molecular Structure II. Infrared and Raman Spectra of Polyatomic Molecules, Krieger Publishing Company, Malabra, FL, 1991. B. Ruscic et al., J. Phys. Chem. A 106 (2002) 2727. K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, Van Nostrand Reinhold Cop, NY, 1979. C. Stampfl, Phys. Rev. B 59 (1999) 5521. X. Shen, P.B. Allen, M.S. Hybertsen, J.T. Muckerman, J. Phys. Chem. C 113 (2009) 3365. H. Schulz, K.H. Thiemann, Solid State Commun. 23 (1977) 815. P. Erhart, K. Albe, A. Klein, Phys. Rev. B 73 (2006) 205203. E.H. Kisi, M.M. Elcombe, Acta Crystallog. C 45 (1989) 1867. U. Ozgur et al., J. Appl. Phys. 98 (2005) 041301.