Silicon Carbide Nanotubes Functionalized by Transition Metal Atoms

(DSSP) were considered for their core electrons. Mulliken population analysis was used to obtain both the charge and the net spin population on each a...
0 downloads 0 Views 635KB Size
Download PDF
2558

J. Phys. Chem. C 2008, 112, 2558-2564

Silicon Carbide Nanotubes Functionalized by Transition Metal Atoms: A Density-Functional Study Jing-xiang Zhao†,‡ and Yi-hong Ding*,† State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin UniVersity, Changchun 130023, People’s Republic of China, and Department of Chemistry, Harbin Normal UniVersity, Harbin 150080, People’s Republic of China ReceiVed: May 15, 2007; In Final Form: October 25, 2007

Single-walled carbon nanotubes (SWCNTs) functionalized by metals have great potential for applications in hydrogen storage, chemical sensors, and nanodevices. Because the exterior of single-walled silicon carbide (SiC) nanotubes has a higher reactivity than that of SWCNTs, it is highly desirable to investigate the functionalization of single-walled SiC nanotubes by transition metal atoms. In this article, we report the first study of the adsorption of a series of transition metal atoms on single-walled SiC nanotubes using density functional theory (DFT) calculations. We found that many transition metal atoms can be chemically adsorbed on the outer surface of single-walled SiC nanotubes, with binding energies ranging from 1.17 eV (for Cu) to 3.18 eV (for Pt). The physical properties of the single-walled SiC nanotubes are changed significantly by metal functionalization. Moreover, the modifications in the electronic structures of most of the metalfunctionalized single-walled SiC nanotubes are little influenced by the location of the adsorption site. An exception is Ti, for which the electronic properties can vary with the adsorption site. Interestingly, the (8,0) single-walled SiC nanotube exhibits metallic characteristics when Ti adsorbs on H sites and characteristics of a smaller-band-gap semiconductor when Ti adsorbs on C sites. Our results suggest that transition metal-SiC nanotube materials could be used in interesting applications in the fabrication of gas-sensor devices, catalysts, or one-dimensional nanoconductors or nanomagnets, among others.

1. Introduction Single-walled carbon nanotubes (SWCNTs) have been shown to exhibit interesting optical, electronic, superconducting, and magnetic properties. Because of their unique structures, SWCNTs also provide a unique opportunity for fabricating novel onedimensional systems, created by functionalizing the SWCNT surface with transition metals.1-3 It has been experimentally shown that metal particles can be adsorbed onto SWCNTs.4 The metal-adsorbed SWCNT materials have potential applications in areas such as catalysis,5 hydrogen storage,6 and sensing7 and the fabrication of magnetic nanodevices.8 The adsorption of transition metal atoms on SWCNTs and their interactions with foreign species have been extensively studied theoretically.6,9-11 Advances in both experimental and theoretical investigations have inspired the development of novel nanodevices through transition metal atom adsorption on nanotubes. Silicon carbide (SiC) nanotubes, which were first synthesized in 2001, are analogous to carbon nanotubes in many respects and exhibit one-dimensional tubular forms.12,13 The structure and stability of single-walled SiC nanotubes have been investigated in detail by ab initio theory.14-17 It was found that SiC nanotubes with a Si-to-C ratio of 1:1 are stable. The energetically favored configuration has been predicted to consist of alternating Si and C atoms without any adjacent Si or C atoms.14 Furthermore, theoretical studies have shown that single-walled SiC nanotubes are semiconductors independent of the helicity, * To whom correspondence should be addressed. E-mail: yhdd@ mail.jlu.edu.cn. † Jilin University. ‡ Harbin Normal University.

Figure 1. Detailed description of different binding sites of a single transition metal atom adsorbed on a zigzag (8,0) single-walled SiC nanotube. Grey and black balls denote carbon and silicon atoms, respectively. H, hexagonal; C, carbon; Si, silicon; A, axial; Z, zigzag sites.

unlike the case for carbon nanotubes.16,18 It was also found that SiC nanotubes have a highly reactive exterior surface, which facilitates sidewall decoration. For example, the electronic structures of single-walled SiC nanotubes can be manipulated by selective hydrogenation,19 and SiH3 and CH3 radicals can also be chemically adsorbed onto SiC nanotubes to form acceptor or donor levels depending on the adsorption sites.20 Froudakis et al.21 also found that pure SiC nanotubes are more suitable materials for hydrogen storage than pure carbon nanotubes. In light of the facts that the high reactivity of the exterior surface facilitates sidewall decoration of SiC nanotubes as compared with that of carbon nanotubes and that metal functionalization of SWCNTs is effective, we feel that it is

10.1021/jp073722m CCC: $40.75 © 2008 American Chemical Society Published on Web 01/25/2008

SiC Nanotubes Functionalized by Metal Atoms

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2559

Figure 2. Band structure and density of states (DOS) near the Fermi level of a pure (8,0) single-walled SiC nanotube.

TABLE 1: Calculated Binding Energies (Eb) of Single Transition Metal (TM) Atoms Adsorbed on an (8,0) Single-Walled SiC Nanotube at Two Stable Binding Sites, C-TM (dC-TM) and C-TM (dSi-TM) Bond Distances, Net Magnetic Moments (µ), and Amounts of Charge Transferred (C) from the Metal Atom to the SiC Nanotube TM

site

dC-TM (Å)

dSi-TM (Å)

Eb (eV)

µ (µB)

C (e)

Sc

Ha C H C H C H C H C H C H C H C H C H C A C A

2.53b 2.06 2.47 1.91 2.61 2.15 2.58 2.05 2.45 1.91 2.35 1.90 2.44 1.92 2.32 1.86 2.57 2.03 3.10 2.08 2.10 2.01 2.05

2.67c 2.60 2.70 2.64 2.55 2.57 2.51 2.38 2.60 3.11 2.46 2.45

2.30 2.25 2.55 2.66 2.07 1.70 0.99 1.07 1.13 1.30 2.02 1.97 2.61 2.64 2.29 2.62 1.17 1.19 0.02 1.99 2.06 3.16 3.18

0.66 0.77 1.86 0.00 3.06 4.63 4.21 4.08 4.48 3.00 2.13 2.33 1.07 1.02 0.00 0.00 0.00 0.26 0.00 0.00 0.00 0.00 0.00

0.51 0.50 0.36 0.37 0.28 0.24 0.21 0.36 0.13 0.19 0.22 0.16 0.06 0.08 0.14 0.13 0.03 0.09 0.07 -0.24 -0.26 -0.40 -0.41

Ti V Cr Mn Figure 3. Variation of the calculated binding energies, Eb, of singlewalled SiC nanotubes (at the most stable configuration of the metal atoms) with respect to the number of d electrons, Nd, of the first-row transition metal atoms. Ec denotes the binding energies of metalfunctionalizated SWCNTs from ref 10.

highly desirable to study the interactions between single-walled SiC nanotubes and transition metal atoms. Knowledge of such properties should be useful for finding potential applications of SiC nanotubes as nanowires and functional nanodevices (such as nanomaterials for hydrogen storage and catalysis). Unfortunately, to the best of our knowledge, there have been no reports on the metal decoration of single-walled SiC nanotubes. In this article, we report the first systematic investigation of the adsorption of 12 different transition metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Pd, and Pt) onto an (8,0) zigzag singlewalled SiC nanotube and 4 different transition metals (Ti, Mn, Ni, and Pt) on a (6,6) armchair single-walled SiC nanotube using density functional theory (DFT) methods. The following questions were explored: (i) What is the stable geometry and nature of the bonding for a single transition metal atom adsorbed on a single-walled SiC nanotube? (ii) How are the physical properties of single-walled SiC nanotubes modified by functionalization with transition metal atoms? (iii) For single-metalatom adsorption on single-walled SiC nanotubes, what are the differences from the behavior reported previously for metaldecorated carbon nanotubes? Our results are useful not only to understand the interactions between transition metal atoms and SiC nanotubes, but also to further studies related to SiC nanotube functionalization and the construction of nanodevices. 2. Models and Methods In this work, we used DFT methods, implemented in the Dmol3 package,22 to study the interactions between a single

Fe Co Ni Cu Zn Pd Pt

a Final effective configuration. b Average carbon-adatom bond distance. c Average silicon-adatom bond distance.

TABLE 2: Calculated Binding Energies (Eb) of Single Metal Atoms Adsorbed on an Armchair (6,6) Single-Walled SiC Nanotube at the Most Favorable Binding Site, C-TM (dC-TM) and C-TM (dSi-TM) Bond Distances, Net Magnetic Moments (µ), and Amounts of Charge Transferred (C) from the Metal Atom to the SiC Nanotube TM

site

dC-TM (Å)

dSi-TM (Å)

Eb (eV)

µ (µB)

C (e)

Ti Mn Ni Pt

H H C C

2.49a 2.39 1.87 2.20

2.56b 2.43 -

2.41 0.98 2.55 2.65

1.824 3.28 0.00 0.00

0.29 0.07 0.11 -0.29

a Average carbon-adatom bond distance. b Average silicon-adatom bond distance.

transition metal atom and a single-walled SiC nanotube. This method has been widely used in the theoretical calculation of nanotube systems, including functionalizations with transition metal atoms.6,10,11,23 All-electron calculations were employed with the double numerical basis sets plus polarization functional

2560 J. Phys. Chem. C, Vol. 112, No. 7, 2008

Zhao and Ding

Figure 4. Band structures and densities of states (DOS) near the Fermi level of (a) Sc adsorbed on an H site of an (8,0) single-walled SiC nanotube, (b) Ti adsorbed on a C site of an (8,0) single-walled SiC nanotube, (b) V adsorbed on an H site of an (8,0) single-walled SiC nanotube, (d) Cr adsorbed on a C site of an (8,0) single-walled SiC nanotube, (e) Mn adsorbed on a C site of an (8,0) single-walled SiC nanotube, (f) Fe adsorbed on an H site of an (8,0) single-walled SiC nanotube, (g) Co adsorbed on a C site of an (8,0) single-walled SiC nanotube, (h) Ni adsorbed on a C site of an (8,0) single-walled SiC nanotube, (i) and Cu adsorbed on a C site of an (8,0) single-walled SiC nanotube. The Fermi level is set as zero.

SiC Nanotubes Functionalized by Metal Atoms

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2561

(DNP) and the generalized-gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) correction.24 For the 5d transition metal atoms Pd and Pt, scalar relativistic effects (DSSP) were considered for their core electrons. Mulliken population analysis was used to obtain both the charge and the net spin population on each atom. Spin-unrestricted DFT calculations were carried out for a single metal atom adsorbed on a single-walled SiC nanotube in a periodically repeating tetragonal supercell with lattice constants of a ) b ) 30 Å and c taken to be twice the one-dimensional lattice parameter of a pure single-walled SiC nanotube. The Brillouin zone of the supercell was sampled by 1 × 1 × 3 k points within the Monkhorst-Pack scheme.25 The binding energies of a single transition metal (TM) atom, Eb, adsorbed on the exterior surface of a SiC nanotube were calculated according to the expression where ET(SiC) denotes

Eb ) ET(SiC) + ET(TM) - ET(SiC + TM)

(1)

the total energy of the optimized pure single-walled SiC nanotube, ET(TM) is the energy of a single transition metal atom, and ET(SiC + TM) is the energy of the SiC with the adsorbed TM atom. Eb > 0 corresponds to a stable optimized configuration and indicates bonding. 3. Results and Discussion 3.1. Pure Single-Walled SiC Nanotubes. We first optimized the structures of pure zigzag (8,0) and armchair (6,6) singlewalled SiC nanotubes. The calculated Si-C bond length of an (8,0) single-walled SiC nanotube (Figure 1) was found to be about 1.79 Å and the average diameter about 7.92 Å, in accordance with previously reported values.15,18 These results suggest that the method used in the present calculations is suitable for describing the behavior of SiC nanotubes. We obtained a rippled surface similar to that of single-walled boron nitride (BN) nanotubes:14-20 the more electronegative atoms (C atoms) move outward, and the more electropositive atoms (Si atoms) move inward. The structure of the optimized (6,6) singlewalled SiC nanotube shows properties similar to those of the (8,0) single-walled SiC nanotube. We obtained a similar rippled surface, with a Si-C bond length of 1.78 Å and a calculated average diameter of about 10.2 Å. The calculated band structure and density of states (DOS) of the (8,0) single-walled SiC nanotube are shown in Figure 2. Obviously, we obtain a direct semiconductor, where the minimum of the conduction band edge (CBM) and the maximum of the valence band edge (VBM) are at the Γ point. The calculated GGA band gap was about 1.30 eV, compared to 1.21 eV reported in an earlier study.18 Gali used a local spin density approximation (LSDA) in the calculations, which might result in a difference because LDA band gaps are usually smaller than GGA band gaps. We also note that there is a continuous charge transfer of more than one-half of an electron from Si to C, which suggests that different electronic properties can be achieved through decorations of the SiC nanotubes by the same element on different sites. 3.2. Functionalizations of SiC Nanotubes by Single Transition Metals. We next studied the stable configurations of single transition metal atoms on single-walled SiC nanotubes. Twelve transition metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Pd, and Pt) were considered for adsorption on the (8,0) single-walled SiC nanotube, and four different transition metals (Ti, Mn, Ni, and Pt) were considered for adsorption on the (6,6) single-walled SiC nanotube. For the adsorption of a single

transition metal atom, we considered five different initial adsorption sites as depicted in Figure 1. The five sites are (1) the on-top site of the carbon atom (C), (2) the on-top site of the silicon atom (Si), (3) the hexagonal site (H), (4) the zigzag Si-C bond (Z), and the axial Si-C bond (A). Using Ti as an example, two stable configurations at the H and C sites were obtained, and the C site was more favorable in energy (Eb ) 2.66 eV). This result is different from that of an earlier study,26 which found that the Ti atom prefers to locate at the H site with a binding energy of 2.44 eV. Meng and coworkers26 used a nonperiodic structure and considered the dangling bonds at the ends of the tubes to be saturated with hydrogen atoms, which might explain the difference. A Ti atom initially placed at an A or Z site spontaneously migrated to a C or H site upon geometry optimization. However, we could not obtain a stable configuration when initially placing a Ti atom on a Si site. At a C site, the C-Ti bond length was 1.91 Å. At an H site, the three C-Ti bonds lengths were 2.23, 2.56, and 2.62 Å, and the three Si-Ti bonds lengths were 2.39, 2.66, and 2.74 Å. These results show that the interactions between the Ti atom and the C sites are stronger than those between the Ti atom and the Si sites. For other adsorbed transition metal atoms on the (8,0) singlewalled SiC nanotube, we found that the most stable adsorption sites were different. For example, Sc and V exhibited strong binding at the H site. Cr, Mn, Fe, Co, Ni, and Cu seemed to prefer the C site. The C-adatom distance, dC-TM (where TM denotes the adsorbed transition metal atom), ranged from 1.86 to 2.61 Å, and the Si-TM distances ranged from 2.38 to 2.70 Å. In Table 1, one can see that most of the transition metal atoms adsorbed on the (8,0) single-walled SiC nanotube have relatively high binding energies. We also note that the transition metal atoms with a small number of d electrons, such as Sc and Ti, form strong bonds with binding energies of 2.66 and 2.30 eV, respectively. In contrast, Cr, Mn, and Cu have relatively lower binding energies ranging from 1.1 to 1.3 eV, and the binding energy of Zn is almost zero (Eb ) 0.02 eV). For the transition metal atoms adsorbed on the (6,6) single-walled SiC nanotube, reported in Table 2, the binding energies are lower than those in Table 1, perhaps because of the effects of curvature.27 We also plotted the variation of the binding energies, Ed, of the most stable structures with respect to the number of d electrons, Nd, as shown in Figure 3. We note that the shape of the variation of the binding energies with Nd is similar to that in the case of transition metal atoms adsorbed on SWCNTs.10 The values of the binding energies of transition metal atoms adsorbed on an (8,0) single-walled SiC nanotube are larger than those of transition metal atoms adsorbed on an (8,0) SWCNT,10 which is easily understood because SiC nanotubes have a more reactive exterior surface than SWCNTs. This curve shows two maxima: the first maximum occurs at Nd ) 2 for the 3d24s2, and the second is at Nd ) 8 (Ni). The binding energy of Ti is highest among the 10 transition metals considered, whereas that of Cu (Nd ) 10) is small, and the value decreases to 0 for Zn, which has a filled valence shell. In Figure 4, we present the band structures and local densities of states for the most stable configurations of single transition metal atoms adsorbed on an (8,0) single-walled SiC nanotube. The electronic properties of the single-walled SiC nanotube undergo some significant changes. The originally degenerate states of the pure (8,0) single-walled SiC nanotube are split in both the valence and conduction bands because of the chemical adsorption of the transition metal atoms. We also note that some

2562 J. Phys. Chem. C, Vol. 112, No. 7, 2008

Zhao and Ding

Figure 5. Band structures and densities of states (DOS) near the Fermi level of (a) a Ti atom adsorbed on a C site of an (8,0) single-walled SiC nanotube and (b) a Ti atom adsorbed on an H site of an (8,0) single-walled SiC nanotube. The Fermi level is set as zero.

impurity states are induced within the band gap of the pure (8,0) single-walled SiC nanotube. In most cases, the band gap is reduced in different ranges. For example, for Sc adsorption on an H site, the band gap of the pure SiC nanotube is significantly reduced to 0.23 eV. An increase in density of states around the Fermi level results in a higher electrical conductivity, and the (8,0) single-walled SiC nanotube becomes metallized because of the crossing of the Fermi level near the Γ point. The results for the projected density of states (PDOS) show that the electronic states mainly come from the contribution of the d and s electrons of transition metal atom. Interestingly, we found that the band structures and densities of states near Fermi level of the (8,0) single-walled SiC nanotube depend only weakly on the location of the adsorption site for most of the transition metals. However, an exception is the Ti atom. Figure 5a and b shows the different changes in electronic properties resulting from the adsorption of a Ti atom on different sites. For H-site adsorption, the band gap of the (8,0) singlewalled SiC nanotube is significantly reduced to 0.37 eV, and the nanotube becomes metallized, because this band crosses the Fermi level and also overlaps with the other conduction bands. However, when the Ti atom is adsorbed at a C site, a smaller band gap (1.23 eV) is obtained, the nanotube retains its semiconducting character. These results suggest that SiC nanotubes with different electronic properties can be obtained through functionalizations of the nanotubes by the same type of atom at different sites. To deeply understand the changes in the physical properties of single-walled SiC nanotubes resulting from the adsorption of transition metal atoms, it is necessary to comment the charge transfer values obtained using Mulliken population analysis. We note that some charge is transferred from the transition metal

to the (8,0) single-walled SiC nanotube, ranging from 0.51 e (for Sc) to 0.08 e (for Co), which further explains the changes in conductivity of the single-walled SiC nanotubes. Moreover, most of the transition metal atoms adsorbed on the (8,0) singlewalled SiC nanotube have a net magnetic moment from 5.00 µB (for Mn) to 0 (for Ni), and the net spin is located mainly on the transition metal. These systems of transition metal atoms adsorbed on single-walled SiC nanotubes can exhibit ferromagnetic properties and have potential applications as nanomagnets. Unlike the case of adsorption of transition metal atoms on a single-walled BN nanotube,23 the changes in the magnetic moments of these metal-decorated single-walled SiC nanotubes depend on the adsorption site, as shown in Table 1. For example, Ti adsorbed on a C site of an (8,0) single-walled SiC nanotube exhibits zero magnetic moment, whereas Ti adsorbed on an H site exhibits a significant magnetic moment (1.86 µB). Increasingly, this variation of the magnetic moment seems related to the band structure of the Ti-functionalized (8,0) single-walled SiC nanotube. Finally, we also studied the adsorption of two group VIIIA transition metal atoms (Pd and Pt) on an (8,0) single-walled SiC nanotube. Both transition metal atoms exhibited the strongest binding at the A site. The C-TM and Si-TM (TM ) Pd and Pt) distances range between 2.05 and 2.46 Å. The calculated binding energies are 2.06 and 3.18 eV, respectively. Figure 6a and b shows that, upon adsorption of a single Pd and Pt atom, the electronic properties are modified dramatically. The TM-adsorbed SiC nanotube systems remain semiconducting, and the band gaps increase to 1.45 and 1.40 eV, respectively. The charge-transfer study shows that about 0.26 and 0.11 e is transferred from the SiC nanotube to the Pd and Pt atoms, respectively, leaving more holes for the SiC nanotubes; as a

SiC Nanotubes Functionalized by Metal Atoms

J. Phys. Chem. C, Vol. 112, No. 7, 2008 2563

Figure 6. Band structures and densities of states (DOS) near Fermi level of (a) a Pd atom adsorbed on an A site of an (8,0) single-walled SiC nanotube and (b) a Pt atom adsorbed on an A site of an (8,0) single-walled SiC nanotube. The Fermi level is set as zero.

result, the p-type conductance increases. We note that Pd and Pt adsorption on single-walled SiC nanotubes differs from that on single-walled BN nanotubes.23 Upon Pd or Pt adsorption, about 0.22 or 0.12 e, respectively, is transferred from the metal to the BN nanotube, and the band gap is reduced from 3.65 to 2.10 eV. The above-discussed results are useful for further investigations related to the functionalization and decoration of SiC nanotubes because of the high reactivity of their exterior surface and, thus, their potential for wider technological applications. 4. Conclusion In this article, we have, for the first time, presented a detailed analysis of the adsorption of a series of transition metal atoms adsorbed on a single-walled SiC nanotube using density functional theory methods. Our results show that interesting physical properties of single-walled SiC nanotubes can be achieved by the adsorption of a single transition metal atom. Therefore, such studies have the potential not only of explaining the character of the bonding between the transition metal atom and the single-walled SiC nanotubes, but also of showing how the physical properties of single-walled SiC nanotubes are influenced by the adsorption of the metal atoms. The results of this work might be helpful for fabricating nanodevices, such as nanomagnets, metallic connects, and spintronic devices, as well as for further studies of nanotube-based sensors, catalysts, and storage materials. Acknowledgment. This work was supported by the National Natural Science Foundation of China (Nos. 20103003, 20573046),

Excellent Young Teacher Foundation of Ministry of Education of China, Excellent Young People Foundation of Jilin Province, and Program for New Century Excellent Talents in University (NCET). References and Notes (1) Satio, S. Science 1997, 278, 77. (2) Bauguman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (3) Tasis, D.; Tagmatarchis, N.; Bianco, A.; Prato, M. Chem. ReV. 2006, 106, 1105. (4) Gregory, G. W.; Craig, E. B.; Richard G. C. Small 2006, 2, 182. (5) Ricardo, A.; Guirado-Lopez, M. S.; Rincon, M. E. J. Phys. Chem. C 2007, 111, 57. (6) Dag, S.; Ozturk, Y.; Ciraci, S.; Yildirim, T. Phys. ReV. B 2005, 72, 155404. (7) Kong, J.; Chapline, M. G.; Dai, H. J. AdV. Mater. 2001, 13, 1384. Lu, Y. J.; Li, J.; Han, J.; Ng, H. T.; Binder, C.; Partridge, C.; Meyyappan, M. Chem. Phys. Lett. 2004, 391, 344. Star, A.; Joshi, V.; Skarupo, S.; Thomas, D.; Jean-Christophe, P. G. J. Phys. Chem. B 2006, 110, 21014. (8) McKinley, S. S. G. J. Fluids Eng. 2007, 129, 429. (9) Zhao, Y. F.; Kim, Y. H.; Dillon, A. C.; Heben, M. J.; Zhang, S. B. Phys. ReV. Lett. 2005, 94, 155504. Yildirim, T.; Ciraci, S. Phys. ReV. Lett. 2005, 94, 175501. (10) Durgun, E.; Dag, S.; Bagci, V.; Gulseren, T.; Yildirim Ciraci, S. Phys. ReV. B 2003, 67, 201401. Durgun, E.; Dag, S.; Ciraci, S.; Gulseren, O. J. Phys. Chem. B 2004, 108, 575. (11) Miao, L.; Venkat, R. B.; Ossowski, M. M.; Joseph, B. J. Phys. Chem. B 2006, 110, 22415. (12) Sun, X. H.; Li, C. P.; Wong, W. K.; Wong, N. B.; Lee, C. S.; Lee, S. T.; Teo, B. K. J. Am. Chem. Soc. 2002, 124, 14464. (13) Pham, H. C.; Keller, N.; Ehret, G.; Ledouxi, M. J. J. Catal. 2001, 200, 400. (14) Miyamoto, Y.; Yu. B. D. Appl. Phys. Lett. 2002, 80, 586. (15) Menon, M.; Richter, E.; Mavrandonakis, A.; Froudakis, G.; Andriotis, A. N. Phys. ReV. B 2004, 69, 115332.

2564 J. Phys. Chem. C, Vol. 112, No. 7, 2008 (16) Zhao, M.; Xia, Y.; Li, F.; Zhang, R. Q.; Lee, S. T. Phys. ReV. B 2005, 71, 085312. (17) Mavrandonakis, A.; Froudakis, G.; Andriotis, A. N. Nano Lett. 2003, 3, 1481. (18) Gali, A. Phys. ReV. B 2006, 73, 245415. (19) Zhao, M.; Xia, Y.; Zhang, R. Q.; Lee, S. T. J. Chem. Phys. 2005, 122, 21470. (20) Li, F.; Xia, Y. Y.; Zhao, M. W.; Liu, X. D.; Huang, B. D.; Yang, Z. H.; Ji, Y.-J.; Song, C. J. Appl. Phys. 2005, 97, 104311. (21) Mpourmpakis, G.; Froudakis, G. E.; Lithoxoos, G. P.; Samios, J. Nano Lett. 2006, 6, 1581.

Zhao and Ding (22) Delley, B. J. Chem. Phys. 1990, 92, 508. Delley, B. J. Chem. Phys. 2000, 113, 7756. (23) Wu, X. J.; Zeng, X. C. J. Chem. Phys. 2006, 125, 044711. Wu, X. J.; Yang, J. L.; Zeng, X. C. J. Chem. Phys. 2006, 125, 044704. (24) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. B 1996, 77, 3865. (25) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (26) Meng, T.; Wang, C. Y.; Wang, S. Y. Chem. Phys. Lett. 2007, 437, 224. (27) Gulseren, O.; Yildirim, T.; Ciraci, S. Phys. ReV. Lett. 2001, 87, 116802.