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CH2I2 adsorption and dissociation on Ag(1 1 1) surface using density functional theory study
Chemical Physics Letters 461 (2008) 47–52
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CH2I2 adsorption and dissociation on Ag(1 1 1) surface using density functional theory study Bo-Tao Teng a,*, Wei-Xin Huang b, Feng-Min Wu c, Xiao-Dong Wen a, Shi-Yu Jiang a a
Zhejiang Key Laboratory for Reactive Chemistry on Solid Surfaces, Institute of Physical Chemistry, Zhejiang Normal University, Jinhua 321004, China Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China c Institute of Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China b
a r t i c l e
i n f o
Article history: Received 3 March 2008 In final form 26 June 2008 Available online 2 July 2008
a b s t r a c t Density functional theory (DFT) calculation has been performed to study the adsorption and dissociation of CH2I2 on Ag(1 1 1) surface at different coverages. CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) is the main stable adsorbed species at low coverage, while CH2I2(a) with one iodine atom bonded to Ag(1 1 1) will dominate on the surface at high coverage. The dissociation barriers of CH2I2 to generate CH2(a) species on Ag(1 1 1) also increase with the increase of coverage. Analysis of density of states shows that relatively strong interactions between CH2I2(a) and Ag(1 1 1) surface exist. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Methods and models
The adsorption and reaction of alkyl fragments on transitional metals is of great importance in the mechanistic understanding of some important heterogeneous catalytic reactions, such as Fischer–Tropsch synthesis [1]. A routine method to generate alkyl fragments is the employment of alkyl iodides. CH2I2 have been always used to generate CH2 in the fundamental investigations of its reactivity on transitional metal surfaces [2–5]. Recently, Huang and White have employed reflection–adsorption infrared spectroscopy (RAIRS) to study the adsorption and reaction of CH2I2 on Ag(1 1 1) surface, which identified the reaction intermediates of carbon–carbon chain propagation reactions via CH2(a) insertion [6–8]. Meanwhile, it was also observed that co-adsorbates on the metal surface have more or less influences on the reaction of alkyl fragments [9]. It is obvious that co-adsorbed halides are inevitable when alkyl halides are used to generate alkyl fragments, which might complicate the case. Alternatively, the application of quantum chemistry in heterogeneous catalysis has recently great success in providing detailed information of reaction mechanisms in consistent with experimental results. In addition, theoretical study can offer some valuable information, which is usually difficult to be obtained experimentally [10]. Comparing with the systematic experimental investigations of adsorption and reaction of CH2I2 on Ag(1 1 1), few theoretical studies have been reported. In this Letter, we report a detailed DFT study of CH2I2 adsorption and dissociation on Ag(1 1 1) and clarify the adsorption structures and dissociation reactivity of CH2I2(a) at different coverages.
The calculations were based on the density functional theory, using Vienna ab initio simulation package (VASP) code [11–13]. The generalized gradient approximation (GGA) of Perdew– Burke–Ernzerhof (PBE) was adopted for all the calculations [14]. The Kohn–Sham one-electron wave functions were expanded in a plane wave basis with an energy cutoff of 350 eV, using projector augmented wave (PAW) potentials [15,16]. A Methfessei–Paxton smearing of 0.1 eV was utilized. Brillouin zone integration was approximated by a sum over special k points chosen using the Monkhorst–Pack scheme. The Kohn–Sham equations were solved self-consistently, and the convergence criteria for the structure optimization and energy calculation was set to be a SCF tolerance of 1.0 104 eV and a maximum Hellmann–Feynman force tolerance of 0.03 eV/Å , which yields total energy convergence down to a level of 1 meV. The calculated bulk lattice constant (4.17 Å) with k point of 9 9 9 agrees well with the experimental data (4.09 Å) and the values reported in the literature [17,18]. We have calculated the adsorption energies and structures of CH2I2 at the hexagonal-close-packed (hcp) site on Ag(1 1 1) using a slab with four, five and six layers with two topmost layers relaxed and found that the differences of the bond length and adsorption energy for the optimized structures among these models were less than 0.001 Å and 0.01 eV, respectively. Therefore, a slab with four layers in which the two topmost layers were allowed to relax was chosen to investigate the adsorption of CH2I2 on Ag(1 1 1). The CH2I2 coverage was defined in monolayer (ML) and three kinds of coverages, 1/4, 1/6 and 1/12 ML, were studied in this work, giving the p(2 2), p(2 3), and p(3 4) unit cell, respectively.
* Corresponding author. Fax: +86 579 82282595. E-mail address: [email protected] (B.-T. Teng). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.06.082
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52 Table 1 The calculated adsorption energies (Eads) and optimized structural parameters of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/12 ML coverage Eads CH2I2
1.094 1.094
dI(1)–Ag
dI(2)–Ag
hICI 115.6
0.12
2.135 2.196
1.094 1.094
3.112
115.5
br
0.19
2.131 2.233
1.094 1.095
3.167 3.171
115.4
fcc
0.20
2.128 2.242
1.095 1.095
3.194 3.199 3.213
114.7
hcp
0.21
2.131 2.237
1.095 1.095
3.229 3.255 3.238
115.0
br-fcc
0.24
2.172 2.199
1.095 1.095
3.323 3.324
2.999 3.554 3.559
113.9
br-hcp
0.24
2.173 2.207
1.096 1.096
3.152 3.442
3.082 3.377 3.328
113.6
tp-fcc
0.24
2.151 2.235
1.096 1.096
3.128
3.067 3.160 3.210
113.8
tp-hcp
0.25
2.155 2.226
1.095 1.095
3.088
3.116 3.168 3.290
113.9
The adsorption energy per CH2I2(a) molecule was defined as:
Here, the E(CH2I2/slab) was the total energy of the surface with CH2I2(a); E(slab) is energy of the bare surface; and E(CH2I2) is that of free CH2I2 molecule. Therefore, a negative Eads value means an exothermic adsorption process whereas a positive one means an endothermic adsorption process. The more negative the energy, the stronger the adsorption [19]. The activation energies for the C–I bond dissociation of CH2I2(a) was evaluated using the nudged elastic band (NEB) method of Jónsson and Mills [20], in which the reaction path was discretized with the discrete configurations (or images) between minima connected by elastic springs to prevent the images from sliding to the minima during the course of optimization [21,22].
dC–H
2. 146 2. 145
tp
Fig. 1. Top view of Ag(1 1 1) surface and adsorption sites for CH2I2.
Eads ¼ EðCH2 I2 =slabÞ ½EðslabÞ þ EðCH2 I2 Þ;
dC–I
to two different sites, defined as CH2I2 (tp-br, tp-fcc, tp-hcp, brbr, br-fcc, br-hcp), etc. 3.1. Low coverage (h = 1/12 ML)
3. Results and discussion Fig. 1 shows four kinds of likely adsorption sites on Ag(1 1 1): top (tp), bridge (br), face-centered cubic (fcc) and hcp sites. The possible bonding atoms in CH2I2 are hydrogen and iodine, but based on the calculation results, the structures of CH2I2(a) with H bonded to Ag(1 1 1) are not stable and spontaneously convert to the corresponding structures with I bonded to the surface. Therefore, only two kinds of adsorption species of CH2I2(a) adsorbed on Ag(1 1 1) were fully calculated in the present study: CH2I2(a) with a single iodine atom bonded to one site, defined as CH2I2 (tp, br, fcc and hcp) and CH2I2(a) with two iodine atoms bonded
The calculated adsorption energies and structural parameters of CH2I2(a) at a coverage of 1/12 ML are summarized in Table 1, and the corresponding structures are shown in Fig. 2. When CH2I2 bonds to a top-site silver atom to form one Ag–I bond, defined as CH2I2(tp)-L (top site at low coverage), the corresponding C–I bond is elongated to 2.196 Å from 2.145 Å in the free CH2I2. In CH2I2(br)L in which one iodine forms two Ag–I bonds with adjacent silver atoms, the C–I bond with the iodine atom bonded to surface is elongated to 2.233 Å, while the other C–I bond is shortened to 2.131 Å. Similar changes in the C–I bond length were also observed in CH2I2(fcc)-L and CH2I2(hcp)-L. The adsorption energies for
Fig. 2. The optimized structures of CH2I2(a) on Ag(1 1 1) at 1/12 ML coverage.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
Fig. 3. The optimized structures of CH2I2(a) on Ag (1 1 1) at 1/6 ML coverage.
structures with one iodine atom adsorbed on bridge site and the other on bridge or top sites, but the iodine atom falls into the fcc or hcp sites during the course of optimization and eventually form the br-fcc, br-hcp, tp-fcc or tp-hcp structures. An important finding here is that the adsorption energies of CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) are always larger than those with one iodine bonded to Ag(1 1 1). Therefore, at a coverage of 1/12 ML, we believe that CH2I2(a) mainly bonds to Ag(1 1 1) with both iodine atoms.
CH2I2(tp)-L, CH2I2(br)-L, CH2I2(fcc)-L, and CH2I2(hcp)-L are 0.12, 0.19, 0.20, and 0.21 eV, respectively, demonstrating that the adsorption of CH2I2 on Ag(1 1 1) is exothermic and thermodynamically favorable. The adsorption energies and structures of CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) were also systematically investigated. In CH2I2(br-fcc)-L (one iodine atom adsorbed on bridge sites and the other one at fcc sites at low coverage), the C–I bonds are elongated to 2.172 and 2.199 Å, respectively. The corresponding adsorption energy is 0.24 eV, which is larger than those of CH2I2 adsorbed on the single bridge (0.19 eV) or fcc (0.20 eV) sites. This might be attributed to the relatively stronger interaction when two iodine atoms bonded to surface silver atoms than that only one iodine atom. This conclusion will be further supported in the following density of states analysis. Similar results also were obtained for other structures, such as CH2I2(br-hcp)-L, CH2I2(tpfcc)-L, and CH2I2(tp-hcp)-L. We also considered the initial CH2I2(a)
The various initial structures studied at a coverage of 1/12 ML were optimized when the CH2I2(a) coverage increases to 1/6 ML. The optimized structures are displayed in Fig. 3 and the calculated adsorption energies and structural parameters are listed in Table 2. The results show that the optimized structures at a coverage of
Table 2 The calculated adsorption energies (Eads) and optimized structures of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/6 ML coverage
Table 3 The calculated adsorption energies (Eads) and optimized structures of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/4 ML coverage
Eads CH2I2
dC–I
dC–H
2. 146 2. 145
1.094 1.094
dI(1)–Ag
dI(2)–Ag
3.2. Moderate coverage (h = 1/6 ML)
Eads
hICI 115.6
CH2I2
dC–I
dC–H
2. 146 2. 145
1.094 1.094
dI(1)–Ag
dI(2)–Ag
hICI 115.6
tp
0.15
2.136 2.197
1.094 1.096
3.097
115.4
tp
0.20
2.145 2.192
1.097 1.097
3.212
115.1
br
0.23
2.136 2.224
1.096 1.095
3.153 3.210
114.9
br
0.27
2.137 2.230
1.097 1.098
3.147 3.241
115.2
fcc
0.24
2.135 2.233
1.096 1.096
3.204 3.311 3.242
115.2
fcc
0.28
2.140 2.235
1.096 1.096
3.206 3.263 3.266
115.4
hcp
0.23
2.130 2.238
1.094 1.095
3.163 3.196 3.212
114.7
hcp
0.29
2.140 2.234
1.097 1.098
3.238 3.246 3.312
115.1
br-fcc
0.23
2.162 2.219
1.097 1.097
3.283 3.414
3.006 3.444 3.505
113.8
br-fcc
0.15
2.141 2.229
1.096 1.098
3.784 4.205
2.909 3.502 3.567
115.2
br-hcp
0.23
2.173 2.207
1.096 1.096
3.152 3.442
3.082 3.328 3.377
113.6
br-hcp
0.12
2.160 2.221
1.097 1.097
3.206 3.658
3.048 3.276 3.336
114.1
tp-fcc
0.23
2.149 2.237
1.095 1.095
3.144
3.205 3.081 3.180
113.7
tp-fcc
0.14
2.148 2.230
1.096 1.097
3.211
3.019 3.265 3.490
114.4
tp-hcp
0.24
2.155 2.224
1.095 1.096
3.144
3.196 3.229 3.159
113. 9
tp-hcp
0.14
2.149 2.230
1.095 1.096
3.241
3.000 3.333 3.435
114.5
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
1/6 ML are similar to those of 1/12 ML. The C–I bond with I bonded to Ag(1 1 1) is elongated more or less in CH2I2(tp)-M (top site at moderate coverage), CH2I2(br)-M CH2I2(fcc)-M, and CH2I2(hcp)-M. The adsorption energies for CH2I2(tp)-M, CH2I2(br)-M CH2I2(fcc)M, and CH2I2(hcp)-M are calculated to be 0.15, 0.23, 0.24, and 0.23 eV, respectively, which are larger than the corresponding structures at a coverage of 1/12 ML. In CH2I2(a) with two iodine atoms bonded to Ag(1 1 1), both C–I bond are elongated. The adsorption energies for CH2I2(tp-fcc)-M, CH2I2(tp-hcp)-M CH2I2(br-fcc)-M and CH2I2(br-hcp)-M are 0.23, 0.24, 0.23, and 0.23 eV, respectively. It is interesting that the adsorption energies of CH2I2(a) with one or two iodine atoms bonded to Ag(11 1) are almost equivalent to that with two iodine atoms bonded to the surface. It could be thus deduced that both adsorbed species of CH2I2(a) might coexist on Ag(11 1) at moderate coverage. 3.3. High coverage (h = 1/4 ML) We further optimized similar initial structures at a coverage of 1/4 ML. The corresponding adsorption energies and structural parameters are listed in Table 3. The most interesting observation is that the adsorption energies of CH2I2(tp)-H, CH2I2(br)-H, CH2I2(fcc)-H, and CH2I2(hcp)-H are 0.20, 0.27, 0.28 and
0.29 eV, respectively whereas those for CH2I2(tp-fcc)-H, CH2I2(tp-hcp)-H, CH2I2(br-fcc)-H and CH2I2(br-hcp)-H are 0.14, 0.14, 0.15, and 0.12 eV, respectively. The relatively lower adsorption energies of CH2I2(a) with two iodine atoms interacted with surface are mainly due to the higher repulsion at 1/4 ML. In this case, the repulsive force of CH2I2(a) will be minimum when CH2I2(a) stands (tp, br, fcc and hcp) instead of lies (br-fcc, br-hcp, tp-fcc, tp-hcp) on Ag(1 1 1) surface. Therefore, CH2I2(a) with one iodine atom bonded to Ag(1 1 1) dominates at high coverage. In summary, the DFT calculations clearly demonstrate that the adsorption structures of CH2I2 on Ag(1 1 1) depend on its coverage. The adsorption energy of CH2I2(a) with one iodine atom bonded to the surface increases with the increasing coverage whereas that of CH2I2(a) with two iodine atoms bonded to surface decreases. Therefore, CH2I2(a) with two iodine atoms bonded to the surface might be the main species on Ag(1 1 1) at low coverages, and with the increasing of coverage, CH2I2(a) with one iodine atom bonded to the surface becomes dominant. 3.4. C-I bond dissociation Although the adsorption of CH2I2(a) on Ag(1 1 1) is dependent on coverages according to the study above, the differences of
Energy (eV)
1.0
a
0.5 0.0 -0.5
Energy (eV)
1.0 -1.0
b
0.5 0.0 -0.5
Energy (eV)
-1.0 1.0
c
0.5 0.0 -0.5
Energy (eV)
-1.0
d
1.5 1.0 0.5
Energy (eV)
0.0
e
0.5 0.0 -0.5 -1.0 0
2
4
6
8
10
Image number Fig. 4. Potential energy surfaces for iodine atom dissociation reaction of CH2I2 at different coverages. (a) CH2I2(hcp)-H, (b) CH2I2(br-fcc)-M, (c) CH2I2(br-fcc)-L for the first iodine atom dissociation reaction; (d) CH2I2(br-fcc)-M, (e) CH2I2(br-fcc)-L for the second iodine atom dissociation reaction.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
to CH2I(a) and I(a) species. These results indicate that CH2I2(a) on Ag(1 1 1) at low coverage is much more prone to dissociate and generate CH2(a) species than those at high coverage, which agree well with experimental results that CH2I2(a) dissociates on Ag(1 1 1) at low coverages but associatively adsorbs at high coverages [9].
adsorption energies are relatively little, which is generally less than 0.1 eV. This might be attributed to the relatively low interactions between CH2I2 and Ag(1 1 1) surface. Therefore, it is necessary to further investigate iodine atom dissociation reactions to explore how CH2I2 coverage affects on reactivity. In order to generate CH2(a), the C–I bond in CH2I2(a) must be broken, thus CH2I2(a) on Ag(1 1 1) at different coverages might exhibit different probabilities of dissociation. We performed CH2I2(a) dissociation reactions by the NEB method. CH2I2(hcp)-H, CH2I2(br-fcc)-M and CH2I2(brfcc)-L with the largest adsorption energy at the corresponding coverage were selected for the comparison of CH2I2(a) dissociation reaction at different coverages, and the corresponding potential energy surfaces for iodine atom dissociation reaction of CH2I2(a) are shown in Fig. 4. It can be learned from Fig. 4 that the first iodine atom dissociation reactions of CH2I2(a) at 1/6 and 1/12 ML coverages are thermodynamic favorable whereas that of CH2I2(hcp)-H is unfavorable. The corresponding barrier for the dissociation of CH2I2(hcp)-H is ca. 0.76 eV, higher than those of CH2I2(br-fcc)-M (0.48 eV) and CH2I2(br-fcc)-L (0.52 eV). Furthermore, the barrier for second iodine atom dissociation of CH2I2(br-fcc)-M is ca. 1.80 eV, which is much higher than that of CH2I2(br-fcc)-L (0.42 eV). The corresponding stable species on Ag(1 1 1) for CH2I2(a) with two iodine atoms dissociated are CH2(a) and I2(a) at 1/6 ML coverage, and CH2(a) and two I(a) at 1/12 ML coverage, seen in Fig. 4d and e, respectively. Whereas CH2(a) species cannot coexist with 2I(a) or I2(a) at 1/4 coverage during geometric optimization, which leads
3.5. Electronic structures and density of states We further investigated the electron structures of CH2I2(a) on Ag(1 1 1) by calculating the local density of states (LDOS). The calculated LDOS of some stable structures of CH2I2(a) at different coverages and typical surface silver atoms bonded to CH2I2(tp-hcp)-L were presented in Fig. 5. The highest occupied molecular orbital (HOMO) of CH2I2 is defined as nI, which is situated on the nonbonding orbital of iodine atoms, and the lowest unoccupied molecular orbital (LUMO) of CH2I2 is the antibonding orbital of CH2I2 situated on the carbon and two iodine atoms. Comparing free CH2I2, the nI bands of CH2I2(a) shift downward, which indicates the relatively strong interaction of CH2I2(a) with the Ag(1 1 1) surface. The peak maximum of nI bands of CH2I2(hcp) at 1/4, 1/6 and 1/12 ML locates at 2.6, 2.3 and 2.4 eV, respectively. The peak maximum of CH2I2(a)(tp-hcp)-L is 2.9 eV, indicating the stronger interactions of CH2I2(a) with two iodine atoms bonded to the surface than CH2I2(a) with one iodine atom bonded to the surface, which is consistent with its higher adsorption energy than that of CH2I2(hcp)-L. Similarly, the d band peak of
15 10
a
nI
b
nI
c
nI
d
nI
nI
σ*C-I
5
Local Density of States (electrons/eV)
15 10 5 15 10 5 15 10 5 20
e
15
d
10 5 0 -10
-8
-6
-4
-2
0
2
4
Energy (eV) Fig. 5. The local density of states (LDOS) of CH2I2(a) and Ag atoms. Solid line: (a) CH2I2(hcp)-H, (b) CH2I2(hcp)-M, (c) CH2I2(hcp)-L, (d) CH2I2(tp-hcp)-L for CH2I2(a), (e) CH2I2(tp-hcp)-L for Ag atoms bonded to CH2I2(a). Dashed line: (a)–(d) free CH2I2; (e) clean surface Ag atoms.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
LDOS for surface Ag atoms interacted with CH2I2(tp-hcp)-L also shift downward compared with clean surface Ag atoms, indicating that the energies of Ag slab lower and relatively strong interactions exist between surface Ag atoms and CH2I2(a).
08-905). W.X.H. gratefully acknowledged the financial support from National Natural Science Foundation of China (Grant 20503027), the ‘Hundred Talent Program’ of Chinese Academy of Sciences, the MOE program for PCSIRT (IRT0756), and the MPGCAS partner group.
4. Conclusions References The adsorption of CH2I2 on Ag(1 1 1) was systematically investigated by DFT calculation in this work. The adsorption and dissociation reaction of CH2I2(a) were found to depend on the coverage. At low coverage, adsorption of CH2I2 on Ag(1 1 1) forms CH2I2(a) with two iodine atoms bonded to the surface, which subsequently undergoes the C–I rupture to generate CH2(a) on the surface. With the increasing coverage, intact CH2I2(a) with one iodine atom bonded to the surface becomes more stable and thus dominates on the surface. Furthermore, the first iodine atom dissociation barrier at 1/4 ML coverage is higher than those at 1/6 and 1/12 ML coverages; while the successive iodine atom dissociation barrier at 1/6 ML coverage is much higher than that at 1/12 ML coverage. The analysis of density of states of CH2I2(a) demonstrates relatively strong interaction of CH2I2(a) with Ag(1 1 1) surface. Acknowledgements This work was supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. Y407163), the Natural Science Foundation of Education Bureau of Zhejiang Province, China (Grant No. 20071159) and the Opening-Foundation of State Key Lab of Coal Conversion, Chinese Academy of Science, China (Grant No.
[1] R.B. Anderson, The Fischer–Tropsch Synthesis, Academic Press, New York, 1984. [2] A. Kis, K.C. Smith, J. Kiss, F. Solymosi, Surf. Sci. 460 (2000) 190. [3] G. Klivényi, F. Solymosi, Surf. Sci. 342 (1995) 168. [4] R.P. Deng, E. Herceg, M. Trenary, Surf. Sci. 573 (2004) 310. [5] J.N. Kondo, T. Higashi, H. Yamamoto, M. Hara, K. Domen, T. Onishi, Surf. Sci. 349 (1996) 294. [6] W.X. Huang, J.M. White, J. Am. Chem. Soc. 125 (2003) 10798. [7] W.X. Huang, J.M. White, J. Am. Chem. Soc. 126 (2004) 14527. [8] W.X. Huang, J.M. White, J. Phys. Chem. B 108 (2004) 7911. [9] W.X. Huang, J. Mol. Catal. A 245 (2006) 147. [10] Y. Wang, W.N. Wang, K.N. Fan, J.F. Deng, Surf. Sci. 487 (2001) 77. [11] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [12] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [13] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [14] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [15] P.E. Bloechl, Phys. Rev. B 50 (1994) 17953. [16] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [17] Y. Wang, W.W. Wang, K.N. Fan, J.F. Deng, Surf. Sci. 490 (2001) 125. [18] A. Montoya, A. Schlunke, B.S. Haynes, J. Phys. Chem. B 110 (2006) 17145. [19] S.G. Wang, D.B. Cao, Y.W. Li, J.G. Wang, H.J. Jiao, J. Phys. Chem. B 109 (2005) 18956. [20] H. Jónsson, G. Mills, K.W. Jacobsen, in: B.J. Berne, G. Ciccotti, D.F. Coker (Eds.), Classical Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore, 1998, p. 385. [21] G. Henkelman, B.P. Uberuaga, H. Jónsson, J. Chem. Phys. 113 (2000) 9901. [22] G. Henkelman, H. Jónsson, J. Chem. Phys. 113 (2000) 9978.
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CH2I2 adsorption and dissociation on Ag(1 1 1) surface using density functional theory study Bo-Tao Teng a,*, Wei-Xin Huang b, Feng-Min Wu c, Xiao-Dong Wen a, Shi-Yu Jiang a a
Zhejiang Key Laboratory for Reactive Chemistry on Solid Surfaces, Institute of Physical Chemistry, Zhejiang Normal University, Jinhua 321004, China Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China c Institute of Condensed Matter Physics, Zhejiang Normal University, Jinhua 321004, China b
a r t i c l e
i n f o
Article history: Received 3 March 2008 In final form 26 June 2008 Available online 2 July 2008
a b s t r a c t Density functional theory (DFT) calculation has been performed to study the adsorption and dissociation of CH2I2 on Ag(1 1 1) surface at different coverages. CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) is the main stable adsorbed species at low coverage, while CH2I2(a) with one iodine atom bonded to Ag(1 1 1) will dominate on the surface at high coverage. The dissociation barriers of CH2I2 to generate CH2(a) species on Ag(1 1 1) also increase with the increase of coverage. Analysis of density of states shows that relatively strong interactions between CH2I2(a) and Ag(1 1 1) surface exist. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Methods and models
The adsorption and reaction of alkyl fragments on transitional metals is of great importance in the mechanistic understanding of some important heterogeneous catalytic reactions, such as Fischer–Tropsch synthesis [1]. A routine method to generate alkyl fragments is the employment of alkyl iodides. CH2I2 have been always used to generate CH2 in the fundamental investigations of its reactivity on transitional metal surfaces [2–5]. Recently, Huang and White have employed reflection–adsorption infrared spectroscopy (RAIRS) to study the adsorption and reaction of CH2I2 on Ag(1 1 1) surface, which identified the reaction intermediates of carbon–carbon chain propagation reactions via CH2(a) insertion [6–8]. Meanwhile, it was also observed that co-adsorbates on the metal surface have more or less influences on the reaction of alkyl fragments [9]. It is obvious that co-adsorbed halides are inevitable when alkyl halides are used to generate alkyl fragments, which might complicate the case. Alternatively, the application of quantum chemistry in heterogeneous catalysis has recently great success in providing detailed information of reaction mechanisms in consistent with experimental results. In addition, theoretical study can offer some valuable information, which is usually difficult to be obtained experimentally [10]. Comparing with the systematic experimental investigations of adsorption and reaction of CH2I2 on Ag(1 1 1), few theoretical studies have been reported. In this Letter, we report a detailed DFT study of CH2I2 adsorption and dissociation on Ag(1 1 1) and clarify the adsorption structures and dissociation reactivity of CH2I2(a) at different coverages.
The calculations were based on the density functional theory, using Vienna ab initio simulation package (VASP) code [11–13]. The generalized gradient approximation (GGA) of Perdew– Burke–Ernzerhof (PBE) was adopted for all the calculations [14]. The Kohn–Sham one-electron wave functions were expanded in a plane wave basis with an energy cutoff of 350 eV, using projector augmented wave (PAW) potentials [15,16]. A Methfessei–Paxton smearing of 0.1 eV was utilized. Brillouin zone integration was approximated by a sum over special k points chosen using the Monkhorst–Pack scheme. The Kohn–Sham equations were solved self-consistently, and the convergence criteria for the structure optimization and energy calculation was set to be a SCF tolerance of 1.0 104 eV and a maximum Hellmann–Feynman force tolerance of 0.03 eV/Å , which yields total energy convergence down to a level of 1 meV. The calculated bulk lattice constant (4.17 Å) with k point of 9 9 9 agrees well with the experimental data (4.09 Å) and the values reported in the literature [17,18]. We have calculated the adsorption energies and structures of CH2I2 at the hexagonal-close-packed (hcp) site on Ag(1 1 1) using a slab with four, five and six layers with two topmost layers relaxed and found that the differences of the bond length and adsorption energy for the optimized structures among these models were less than 0.001 Å and 0.01 eV, respectively. Therefore, a slab with four layers in which the two topmost layers were allowed to relax was chosen to investigate the adsorption of CH2I2 on Ag(1 1 1). The CH2I2 coverage was defined in monolayer (ML) and three kinds of coverages, 1/4, 1/6 and 1/12 ML, were studied in this work, giving the p(2 2), p(2 3), and p(3 4) unit cell, respectively.
* Corresponding author. Fax: +86 579 82282595. E-mail address: [email protected] (B.-T. Teng). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.06.082
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52 Table 1 The calculated adsorption energies (Eads) and optimized structural parameters of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/12 ML coverage Eads CH2I2
1.094 1.094
dI(1)–Ag
dI(2)–Ag
hICI 115.6
0.12
2.135 2.196
1.094 1.094
3.112
115.5
br
0.19
2.131 2.233
1.094 1.095
3.167 3.171
115.4
fcc
0.20
2.128 2.242
1.095 1.095
3.194 3.199 3.213
114.7
hcp
0.21
2.131 2.237
1.095 1.095
3.229 3.255 3.238
115.0
br-fcc
0.24
2.172 2.199
1.095 1.095
3.323 3.324
2.999 3.554 3.559
113.9
br-hcp
0.24
2.173 2.207
1.096 1.096
3.152 3.442
3.082 3.377 3.328
113.6
tp-fcc
0.24
2.151 2.235
1.096 1.096
3.128
3.067 3.160 3.210
113.8
tp-hcp
0.25
2.155 2.226
1.095 1.095
3.088
3.116 3.168 3.290
113.9
The adsorption energy per CH2I2(a) molecule was defined as:
Here, the E(CH2I2/slab) was the total energy of the surface with CH2I2(a); E(slab) is energy of the bare surface; and E(CH2I2) is that of free CH2I2 molecule. Therefore, a negative Eads value means an exothermic adsorption process whereas a positive one means an endothermic adsorption process. The more negative the energy, the stronger the adsorption [19]. The activation energies for the C–I bond dissociation of CH2I2(a) was evaluated using the nudged elastic band (NEB) method of Jónsson and Mills [20], in which the reaction path was discretized with the discrete configurations (or images) between minima connected by elastic springs to prevent the images from sliding to the minima during the course of optimization [21,22].
dC–H
2. 146 2. 145
tp
Fig. 1. Top view of Ag(1 1 1) surface and adsorption sites for CH2I2.
Eads ¼ EðCH2 I2 =slabÞ ½EðslabÞ þ EðCH2 I2 Þ;
dC–I
to two different sites, defined as CH2I2 (tp-br, tp-fcc, tp-hcp, brbr, br-fcc, br-hcp), etc. 3.1. Low coverage (h = 1/12 ML)
3. Results and discussion Fig. 1 shows four kinds of likely adsorption sites on Ag(1 1 1): top (tp), bridge (br), face-centered cubic (fcc) and hcp sites. The possible bonding atoms in CH2I2 are hydrogen and iodine, but based on the calculation results, the structures of CH2I2(a) with H bonded to Ag(1 1 1) are not stable and spontaneously convert to the corresponding structures with I bonded to the surface. Therefore, only two kinds of adsorption species of CH2I2(a) adsorbed on Ag(1 1 1) were fully calculated in the present study: CH2I2(a) with a single iodine atom bonded to one site, defined as CH2I2 (tp, br, fcc and hcp) and CH2I2(a) with two iodine atoms bonded
The calculated adsorption energies and structural parameters of CH2I2(a) at a coverage of 1/12 ML are summarized in Table 1, and the corresponding structures are shown in Fig. 2. When CH2I2 bonds to a top-site silver atom to form one Ag–I bond, defined as CH2I2(tp)-L (top site at low coverage), the corresponding C–I bond is elongated to 2.196 Å from 2.145 Å in the free CH2I2. In CH2I2(br)L in which one iodine forms two Ag–I bonds with adjacent silver atoms, the C–I bond with the iodine atom bonded to surface is elongated to 2.233 Å, while the other C–I bond is shortened to 2.131 Å. Similar changes in the C–I bond length were also observed in CH2I2(fcc)-L and CH2I2(hcp)-L. The adsorption energies for
Fig. 2. The optimized structures of CH2I2(a) on Ag(1 1 1) at 1/12 ML coverage.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
Fig. 3. The optimized structures of CH2I2(a) on Ag (1 1 1) at 1/6 ML coverage.
structures with one iodine atom adsorbed on bridge site and the other on bridge or top sites, but the iodine atom falls into the fcc or hcp sites during the course of optimization and eventually form the br-fcc, br-hcp, tp-fcc or tp-hcp structures. An important finding here is that the adsorption energies of CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) are always larger than those with one iodine bonded to Ag(1 1 1). Therefore, at a coverage of 1/12 ML, we believe that CH2I2(a) mainly bonds to Ag(1 1 1) with both iodine atoms.
CH2I2(tp)-L, CH2I2(br)-L, CH2I2(fcc)-L, and CH2I2(hcp)-L are 0.12, 0.19, 0.20, and 0.21 eV, respectively, demonstrating that the adsorption of CH2I2 on Ag(1 1 1) is exothermic and thermodynamically favorable. The adsorption energies and structures of CH2I2(a) with two iodine atoms bonded to Ag(1 1 1) were also systematically investigated. In CH2I2(br-fcc)-L (one iodine atom adsorbed on bridge sites and the other one at fcc sites at low coverage), the C–I bonds are elongated to 2.172 and 2.199 Å, respectively. The corresponding adsorption energy is 0.24 eV, which is larger than those of CH2I2 adsorbed on the single bridge (0.19 eV) or fcc (0.20 eV) sites. This might be attributed to the relatively stronger interaction when two iodine atoms bonded to surface silver atoms than that only one iodine atom. This conclusion will be further supported in the following density of states analysis. Similar results also were obtained for other structures, such as CH2I2(br-hcp)-L, CH2I2(tpfcc)-L, and CH2I2(tp-hcp)-L. We also considered the initial CH2I2(a)
The various initial structures studied at a coverage of 1/12 ML were optimized when the CH2I2(a) coverage increases to 1/6 ML. The optimized structures are displayed in Fig. 3 and the calculated adsorption energies and structural parameters are listed in Table 2. The results show that the optimized structures at a coverage of
Table 2 The calculated adsorption energies (Eads) and optimized structures of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/6 ML coverage
Table 3 The calculated adsorption energies (Eads) and optimized structures of CH2I2 at different adsorption sites on Ag(1 1 1) surface at 1/4 ML coverage
Eads CH2I2
dC–I
dC–H
2. 146 2. 145
1.094 1.094
dI(1)–Ag
dI(2)–Ag
3.2. Moderate coverage (h = 1/6 ML)
Eads
hICI 115.6
CH2I2
dC–I
dC–H
2. 146 2. 145
1.094 1.094
dI(1)–Ag
dI(2)–Ag
hICI 115.6
tp
0.15
2.136 2.197
1.094 1.096
3.097
115.4
tp
0.20
2.145 2.192
1.097 1.097
3.212
115.1
br
0.23
2.136 2.224
1.096 1.095
3.153 3.210
114.9
br
0.27
2.137 2.230
1.097 1.098
3.147 3.241
115.2
fcc
0.24
2.135 2.233
1.096 1.096
3.204 3.311 3.242
115.2
fcc
0.28
2.140 2.235
1.096 1.096
3.206 3.263 3.266
115.4
hcp
0.23
2.130 2.238
1.094 1.095
3.163 3.196 3.212
114.7
hcp
0.29
2.140 2.234
1.097 1.098
3.238 3.246 3.312
115.1
br-fcc
0.23
2.162 2.219
1.097 1.097
3.283 3.414
3.006 3.444 3.505
113.8
br-fcc
0.15
2.141 2.229
1.096 1.098
3.784 4.205
2.909 3.502 3.567
115.2
br-hcp
0.23
2.173 2.207
1.096 1.096
3.152 3.442
3.082 3.328 3.377
113.6
br-hcp
0.12
2.160 2.221
1.097 1.097
3.206 3.658
3.048 3.276 3.336
114.1
tp-fcc
0.23
2.149 2.237
1.095 1.095
3.144
3.205 3.081 3.180
113.7
tp-fcc
0.14
2.148 2.230
1.096 1.097
3.211
3.019 3.265 3.490
114.4
tp-hcp
0.24
2.155 2.224
1.095 1.096
3.144
3.196 3.229 3.159
113. 9
tp-hcp
0.14
2.149 2.230
1.095 1.096
3.241
3.000 3.333 3.435
114.5
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
1/6 ML are similar to those of 1/12 ML. The C–I bond with I bonded to Ag(1 1 1) is elongated more or less in CH2I2(tp)-M (top site at moderate coverage), CH2I2(br)-M CH2I2(fcc)-M, and CH2I2(hcp)-M. The adsorption energies for CH2I2(tp)-M, CH2I2(br)-M CH2I2(fcc)M, and CH2I2(hcp)-M are calculated to be 0.15, 0.23, 0.24, and 0.23 eV, respectively, which are larger than the corresponding structures at a coverage of 1/12 ML. In CH2I2(a) with two iodine atoms bonded to Ag(1 1 1), both C–I bond are elongated. The adsorption energies for CH2I2(tp-fcc)-M, CH2I2(tp-hcp)-M CH2I2(br-fcc)-M and CH2I2(br-hcp)-M are 0.23, 0.24, 0.23, and 0.23 eV, respectively. It is interesting that the adsorption energies of CH2I2(a) with one or two iodine atoms bonded to Ag(11 1) are almost equivalent to that with two iodine atoms bonded to the surface. It could be thus deduced that both adsorbed species of CH2I2(a) might coexist on Ag(11 1) at moderate coverage. 3.3. High coverage (h = 1/4 ML) We further optimized similar initial structures at a coverage of 1/4 ML. The corresponding adsorption energies and structural parameters are listed in Table 3. The most interesting observation is that the adsorption energies of CH2I2(tp)-H, CH2I2(br)-H, CH2I2(fcc)-H, and CH2I2(hcp)-H are 0.20, 0.27, 0.28 and
0.29 eV, respectively whereas those for CH2I2(tp-fcc)-H, CH2I2(tp-hcp)-H, CH2I2(br-fcc)-H and CH2I2(br-hcp)-H are 0.14, 0.14, 0.15, and 0.12 eV, respectively. The relatively lower adsorption energies of CH2I2(a) with two iodine atoms interacted with surface are mainly due to the higher repulsion at 1/4 ML. In this case, the repulsive force of CH2I2(a) will be minimum when CH2I2(a) stands (tp, br, fcc and hcp) instead of lies (br-fcc, br-hcp, tp-fcc, tp-hcp) on Ag(1 1 1) surface. Therefore, CH2I2(a) with one iodine atom bonded to Ag(1 1 1) dominates at high coverage. In summary, the DFT calculations clearly demonstrate that the adsorption structures of CH2I2 on Ag(1 1 1) depend on its coverage. The adsorption energy of CH2I2(a) with one iodine atom bonded to the surface increases with the increasing coverage whereas that of CH2I2(a) with two iodine atoms bonded to surface decreases. Therefore, CH2I2(a) with two iodine atoms bonded to the surface might be the main species on Ag(1 1 1) at low coverages, and with the increasing of coverage, CH2I2(a) with one iodine atom bonded to the surface becomes dominant. 3.4. C-I bond dissociation Although the adsorption of CH2I2(a) on Ag(1 1 1) is dependent on coverages according to the study above, the differences of
Energy (eV)
1.0
a
0.5 0.0 -0.5
Energy (eV)
1.0 -1.0
b
0.5 0.0 -0.5
Energy (eV)
-1.0 1.0
c
0.5 0.0 -0.5
Energy (eV)
-1.0
d
1.5 1.0 0.5
Energy (eV)
0.0
e
0.5 0.0 -0.5 -1.0 0
2
4
6
8
10
Image number Fig. 4. Potential energy surfaces for iodine atom dissociation reaction of CH2I2 at different coverages. (a) CH2I2(hcp)-H, (b) CH2I2(br-fcc)-M, (c) CH2I2(br-fcc)-L for the first iodine atom dissociation reaction; (d) CH2I2(br-fcc)-M, (e) CH2I2(br-fcc)-L for the second iodine atom dissociation reaction.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
to CH2I(a) and I(a) species. These results indicate that CH2I2(a) on Ag(1 1 1) at low coverage is much more prone to dissociate and generate CH2(a) species than those at high coverage, which agree well with experimental results that CH2I2(a) dissociates on Ag(1 1 1) at low coverages but associatively adsorbs at high coverages [9].
adsorption energies are relatively little, which is generally less than 0.1 eV. This might be attributed to the relatively low interactions between CH2I2 and Ag(1 1 1) surface. Therefore, it is necessary to further investigate iodine atom dissociation reactions to explore how CH2I2 coverage affects on reactivity. In order to generate CH2(a), the C–I bond in CH2I2(a) must be broken, thus CH2I2(a) on Ag(1 1 1) at different coverages might exhibit different probabilities of dissociation. We performed CH2I2(a) dissociation reactions by the NEB method. CH2I2(hcp)-H, CH2I2(br-fcc)-M and CH2I2(brfcc)-L with the largest adsorption energy at the corresponding coverage were selected for the comparison of CH2I2(a) dissociation reaction at different coverages, and the corresponding potential energy surfaces for iodine atom dissociation reaction of CH2I2(a) are shown in Fig. 4. It can be learned from Fig. 4 that the first iodine atom dissociation reactions of CH2I2(a) at 1/6 and 1/12 ML coverages are thermodynamic favorable whereas that of CH2I2(hcp)-H is unfavorable. The corresponding barrier for the dissociation of CH2I2(hcp)-H is ca. 0.76 eV, higher than those of CH2I2(br-fcc)-M (0.48 eV) and CH2I2(br-fcc)-L (0.52 eV). Furthermore, the barrier for second iodine atom dissociation of CH2I2(br-fcc)-M is ca. 1.80 eV, which is much higher than that of CH2I2(br-fcc)-L (0.42 eV). The corresponding stable species on Ag(1 1 1) for CH2I2(a) with two iodine atoms dissociated are CH2(a) and I2(a) at 1/6 ML coverage, and CH2(a) and two I(a) at 1/12 ML coverage, seen in Fig. 4d and e, respectively. Whereas CH2(a) species cannot coexist with 2I(a) or I2(a) at 1/4 coverage during geometric optimization, which leads
3.5. Electronic structures and density of states We further investigated the electron structures of CH2I2(a) on Ag(1 1 1) by calculating the local density of states (LDOS). The calculated LDOS of some stable structures of CH2I2(a) at different coverages and typical surface silver atoms bonded to CH2I2(tp-hcp)-L were presented in Fig. 5. The highest occupied molecular orbital (HOMO) of CH2I2 is defined as nI, which is situated on the nonbonding orbital of iodine atoms, and the lowest unoccupied molecular orbital (LUMO) of CH2I2 is the antibonding orbital of CH2I2 situated on the carbon and two iodine atoms. Comparing free CH2I2, the nI bands of CH2I2(a) shift downward, which indicates the relatively strong interaction of CH2I2(a) with the Ag(1 1 1) surface. The peak maximum of nI bands of CH2I2(hcp) at 1/4, 1/6 and 1/12 ML locates at 2.6, 2.3 and 2.4 eV, respectively. The peak maximum of CH2I2(a)(tp-hcp)-L is 2.9 eV, indicating the stronger interactions of CH2I2(a) with two iodine atoms bonded to the surface than CH2I2(a) with one iodine atom bonded to the surface, which is consistent with its higher adsorption energy than that of CH2I2(hcp)-L. Similarly, the d band peak of
15 10
a
nI
b
nI
c
nI
d
nI
nI
σ*C-I
5
Local Density of States (electrons/eV)
15 10 5 15 10 5 15 10 5 20
e
15
d
10 5 0 -10
-8
-6
-4
-2
0
2
4
Energy (eV) Fig. 5. The local density of states (LDOS) of CH2I2(a) and Ag atoms. Solid line: (a) CH2I2(hcp)-H, (b) CH2I2(hcp)-M, (c) CH2I2(hcp)-L, (d) CH2I2(tp-hcp)-L for CH2I2(a), (e) CH2I2(tp-hcp)-L for Ag atoms bonded to CH2I2(a). Dashed line: (a)–(d) free CH2I2; (e) clean surface Ag atoms.
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B.-T. Teng et al. / Chemical Physics Letters 461 (2008) 47–52
LDOS for surface Ag atoms interacted with CH2I2(tp-hcp)-L also shift downward compared with clean surface Ag atoms, indicating that the energies of Ag slab lower and relatively strong interactions exist between surface Ag atoms and CH2I2(a).
08-905). W.X.H. gratefully acknowledged the financial support from National Natural Science Foundation of China (Grant 20503027), the ‘Hundred Talent Program’ of Chinese Academy of Sciences, the MOE program for PCSIRT (IRT0756), and the MPGCAS partner group.
4. Conclusions References The adsorption of CH2I2 on Ag(1 1 1) was systematically investigated by DFT calculation in this work. The adsorption and dissociation reaction of CH2I2(a) were found to depend on the coverage. At low coverage, adsorption of CH2I2 on Ag(1 1 1) forms CH2I2(a) with two iodine atoms bonded to the surface, which subsequently undergoes the C–I rupture to generate CH2(a) on the surface. With the increasing coverage, intact CH2I2(a) with one iodine atom bonded to the surface becomes more stable and thus dominates on the surface. Furthermore, the first iodine atom dissociation barrier at 1/4 ML coverage is higher than those at 1/6 and 1/12 ML coverages; while the successive iodine atom dissociation barrier at 1/6 ML coverage is much higher than that at 1/12 ML coverage. The analysis of density of states of CH2I2(a) demonstrates relatively strong interaction of CH2I2(a) with Ag(1 1 1) surface. Acknowledgements This work was supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. Y407163), the Natural Science Foundation of Education Bureau of Zhejiang Province, China (Grant No. 20071159) and the Opening-Foundation of State Key Lab of Coal Conversion, Chinese Academy of Science, China (Grant No.
[1] R.B. Anderson, The Fischer–Tropsch Synthesis, Academic Press, New York, 1984. [2] A. Kis, K.C. Smith, J. Kiss, F. Solymosi, Surf. Sci. 460 (2000) 190. [3] G. Klivényi, F. Solymosi, Surf. Sci. 342 (1995) 168. [4] R.P. Deng, E. Herceg, M. Trenary, Surf. Sci. 573 (2004) 310. [5] J.N. Kondo, T. Higashi, H. Yamamoto, M. Hara, K. Domen, T. Onishi, Surf. Sci. 349 (1996) 294. [6] W.X. Huang, J.M. White, J. Am. Chem. Soc. 125 (2003) 10798. [7] W.X. Huang, J.M. White, J. Am. Chem. Soc. 126 (2004) 14527. [8] W.X. Huang, J.M. White, J. Phys. Chem. B 108 (2004) 7911. [9] W.X. Huang, J. Mol. Catal. A 245 (2006) 147. [10] Y. Wang, W.N. Wang, K.N. Fan, J.F. Deng, Surf. Sci. 487 (2001) 77. [11] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558. [12] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [13] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [14] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [15] P.E. Bloechl, Phys. Rev. B 50 (1994) 17953. [16] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758. [17] Y. Wang, W.W. Wang, K.N. Fan, J.F. Deng, Surf. Sci. 490 (2001) 125. [18] A. Montoya, A. Schlunke, B.S. Haynes, J. Phys. Chem. B 110 (2006) 17145. [19] S.G. Wang, D.B. Cao, Y.W. Li, J.G. Wang, H.J. Jiao, J. Phys. Chem. B 109 (2005) 18956. [20] H. Jónsson, G. Mills, K.W. Jacobsen, in: B.J. Berne, G. Ciccotti, D.F. Coker (Eds.), Classical Quantum Dynamics in Condensed Phase Simulations, World Scientific, Singapore, 1998, p. 385. [21] G. Henkelman, B.P. Uberuaga, H. Jónsson, J. Chem. Phys. 113 (2000) 9901. [22] G. Henkelman, H. Jónsson, J. Chem. Phys. 113 (2000) 9978.