J. Phys. Chem. B 2006, 110, 18363-18367
18363
Dissociative Adsorption of Carbon Monoxide on Mo(110): First-Principles Theory Zhi Ji† and Jun-Qian Li*,†,‡ Department of Chemistry, Fuzhou UniVersity, Gongye Rd 523, Fuzhou 350002, China, and State Key Laboratory of Structural Chemistry, Fuzhou 350002, China ReceiVed: May 24, 2006; In Final Form: August 1, 2006
The adsorption and dissociation of carbon monoxide on Mo (110) surface is studied with density functional theory. The results at different sites (atop, short bridge, long bridge, and hollow) are presented. The hollow site is found to be the most stable adsorption site for CO. The CO molecule is found to adsorb in end-on configurations (R states) at high coverage and inclined configurations (β states) at low coverage. The dissociation activation energy from β states is found to be ∼1 eV lower than from R state. The adsorption of dissociation products, C and O, on Mo(110) has also been studied. The most stable adsorption site for C and O is long bridge and hollow site, respectively. The adsorption of C and O at low coverage is, in general, stronger than at high coverage, which is partly responsible for the high reactivity of CO dissociation at low coverage, since the binding energy of CO is not very sensitive to the coverage.
1. Introduction The adsorption of CO on metal surfaces has become the prototype system for molecular chemisorption, and a rather simple bonding model has in general been accepted. Activation of CO by transition metals is an important step in many industrial processes such as car exhaust catalysis and FischerTropsch synthesis. CO adsorption on molybdenum and modified molybdenum surfaces has been studied experimentally because of their potential use in methanol reforming and fuel cell technology.1-5 Various experimental techniques have been used to characterize CO adsorption and dissociation on low-index surfaces of Mo.6-9 Yates and Co-workers studied CO adsorption on Mo (110) using electron energy-loss spectroscopy (EELS).6 They report vibrational frequencies of 1345 cm-1 for low CO coverage on Mo (110) and 2000cm-1 for high coverage. They also found a CO species with very low frequency, 1130 cm-1. Goodman has studied the adsorption of CO on clean and O-, C- and H-precovered Mo (110) surfaces using infrared reflection absorption spectroscopy (IRAS).7 They also report a CO frequency around 2000 cm-1 for high coverage. Lundgren et al. studied the thermally activated dissociation of CO molecules at low and high initial CO coverages by high-resolution corelevel spectroscopy (HRCLS).9 They found the onset of dissociation is found to differ considerably between low (125-160 K) and high (208 K) initial CO coverages. They argue that steric effects caused by self-poisoning of the surface by the dissociation products play a major role in causing this difference. As far as we know there is not any theoretical study of CO on Mo(110) surface in the literature, though there are many studies about adsorption and dissociation of CO on transition metals.10-16 The aim of this paper is to use ab initio DFT calculations to provide insight into the coverage sensitivity of CO dissociation on Mo(110) surface. We performed DFT investigations on CO dissociation pathways on Mo(110). Two distinct * Corresponding author: Fax: (+86) 5918 7892522. E-mail: zhij2008@ gmail.com. † Fuzhou University. ‡ State Key Laboratory of Structural Chemistry.
reaction pathways have been identified. The reaction barriers for the CO dissociation were determined. We also computed binding energies and vibrational frequencies of CO on Mo(110), and compare our results with experimental data where available. The paper is organized as follows: In Section 2, we present the theoretical method employed. We first study the bare Mo(110) surface in Section 3.1. Results for CO adsorption at 0.11, 0.25, 0.5, and 1 ML are presented in Section 3.2. The adsorption and coadsorption of C and O are shown in Sections 3.3 and 3.4, respectively. We then show the results for CO dissociation in Section 3.5. Finally, we conclude and summarize in Section 4. 2. Computational Details All calculations were performed using spin polarized DFT within the generalized gradient approximation (GGA) as implemented in the Vienna ab initio simulation package.17-19 In our calculations, electron-ion interactions were described by ultrasoft pseudo-potentials and the PW9120 exchange correlation functional was used. The Monkhorst-Pack scheme was used to generate k-points. Calculations on (110) surface used an 8 × 8 × 2 mesh in k-space. Ionic relaxations were performed using the conjugate gradient method until the forces on all unconstrained atoms were less than 0.03 eV/Å. An energy cutoff of 400 eV was used for the plane wave basis set in all calculations. The PW91 calculated lattice constant for bulk molybdenum is 3.89 Å, which agrees well with the experimental values of 3.92 Å. The calculated gas-phase CO bond length is 1.14 Å, which also agrees well with the experimental value of 1.13 Å. CO was only placed on the unconstrained side of each surface with the C atom closest to the surface, and each supercell contained a single CO molecule. This produces a dipole due to the charge rearrangement on the surface caused by adsorption. We apply an a posteriori dipole correction in the direction of surface normal; the correction to the energy is ∼0.07 eV per CO. The energy of adsorption per CO molecule was defined as Eads ) ECO + Eslab - ECO/slab, where the three terms on the right-hand side of this expression are the spin polarized energies of a gas-phase CO, the bare surface, and the surface with the
10.1021/jp063200r CCC: $33.50 © 2006 American Chemical Society Published on Web 08/30/2006
18364 J. Phys. Chem. B, Vol. 110, No. 37, 2006
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TABLE 1: Layer Relaxation, ∆ (%), Given in the Percentage Change of the Unrelaxed Interlayer Distance for Mo(110) Surface.a study this work
GPTb LDAc experiment.d b
layers
∆12
∆23
∆34
4 5 6 7
-1.36 -1.81 -1.65 -1.68 -5.8 -4.3 -1.6
+2.3 +2.9 +2.65 +2.25 +1.8 -0.2
-1.35 +2.19 +2.11 +2.11
11
-0.4
a Available data from other studies are also listed for comparison. Ref 25. c Ref 24. d Ref 23.
adsorbed molecule, respectively. With this definition, a positive Eads corresponds to stable binding of CO on the surface. Vibrational frequencies were calculated by diagonalizing the Hessian matrix of selected atoms. The Hessian matrix was calculated within VASP by a finite difference method. The atoms in the top four Mo layers and CO were independently displaced by 0.02 Å along each Cartesian coordinate direction. We compared C-O stretching frequencies calculated by allowing all Mo atoms in the first four layers to move with those computed by fixing all Mo atom positions. The C-O frequencies were the same to within a few wavenumbers, indicating that coupling of the C-O vibration to the underlying Mo lattice is negligible. The nudged elastic band (NEB) method of Jo´nsson and coworkers21,22 was used to compute dissociation pathways. Initial and final states were chosen, and the number of images was increased to achieve a smooth curve. At least eight images were used for each calculation. The NEB method is a chain-of-states method. Two points in the hyperspace containing all degrees of freedom are needed (initial and final state), and a linear interpolation can be made to produce the images along the elastic band. The program will simultaneously run each image and will communicate at the end of each ionic cycle in order to compute the force acting on each image. The term “nudge” indicates that the projection of the parallel component of true force acting on the images and the perpendicular component of spring force are canceled. A smooth switching function is introduced that gradually turns on the perpendicular component of the spring force where the path becomes kinked at large difference in the energies between images. 3. Results and Discussions 3.1. Surface Relaxation. To characterize the surface relaxation of the clean Mo(110) surface, we monitored the interlayer relaxation with respect to the bulk interlayer spacing. Table 1 presents the calculated relaxation of the Mo(110) slab. In each calculation, we used a supercell containing a 14 Å vacuum space and kept the bottom layer fixed. Available theoretical and experimental results are quoted for comparison. ∆ij is the fraction change of the interlayer distance between the ith and jth layer. We find ∆12 ) -1.65% in the six layer slab, in good agreement with experimental findings of -1.6%.23 The agreement between our work and the experiments is excellent and that gives us confidence in our CO/Mo(110) results. The data in Table 1 indicate that a large supercell with at least six layers is necessary to accurately model the surface relaxation of Mo(110); including more layers does not improve the accuracy dramatically. A model containing only five layers did not predict relaxation very well. Therefore, in the subsequent calculations, we chose to use a supercell containing six Mo layers with a vacuum spacing of 14 Å. All results presented below are from energy minimizations
Figure 1. Top view of a Mo(110) surface showing (1 × 1), (2 × 1), (2 × 2), and (3 × 3) surface unit cells with the high-symmetry sites labeled (a) top, (b) short bridge, (c) long bridge, and (d) hollow.
in which all degrees of freedom of the adsorbed CO and the metal layers were allowed to relax, except the bottom layer. 3.2. CO Adsorption. We considered the adsorption of CO in the four higher high-symmetry sites, indicated in Figure 1, namely the top, short bridge, long bridge, and hollow sites. For each site, surface coverage of 1, 1/2, 1/4, and 1/9 ML were examined by using (1 × 1), (2 × 1), (2 × 2), and (3 × 3) ad-layers, respectively. The adsorption energies, vibrational frequencies, and structural properties for CO on Mo(110) at different coverage are summarized in Table 2. Normal-mode analysis shows that the short bridge and hollow sites are true minima, while the long bridge sites are transition states and top sites are higher order saddle points for CO adsorption on Mo(110) We first examined CO adsorbed on Mo(110) at coverage of 1 ML in a (1 × 1) ad-layer. Our calculations show that the hollow site is the most stable binding site for CO on Mo(110) at 1 ML. We find that the C-O oriented almost parallel to the normal surface. The calculated CO stretching frequency for the hollow site (2004 cm-1) agrees well with the experimental value of ∼2000 cm-1,6 which is another indication that CO adsorbs at the Mo hollow site. We examined a CO ad-layer at coverage of 0.5 ML by using a (2 × 1) ad-layer. The same four high-symmetry adsorption sites as listed above were examined. Our calculations show that the hollow site is the most stable binding site for CO on Mo(110) at 1 ML. We find that the C-O oriented almost parallel to the surface normal as seen in (1 × 1) ad-layer. In contrast, Goodman et al.7 found that CO located at top and bridge sites at similar coverage. It must be pointed out that, in our optimization results, the hollow site at this coverage is not a classic 3-fold hollow site. It is more like a “distorted” top site; CO molecules are displaced off-center from the top site by 0.73 Å toward the hollow site. The calculated C-O vibrational frequencies for the two sites are 1968.5 and 1828.4 cm-1, respectively, as shown in Table 2. These frequencies are qualitatively in agreement the experimental peaks at 2004 and 1888 cm-1.7 We also explored CO adsorbed on Mo(110) at coverage of 0.25 ML in a (2 × 2) allayer. The calculations show that the hollow sites are favored adsorption sites, as it for the 1 and 0.5
Dissociative Adsorption of Carbon Monoxide on Mo(110)
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18365
TABLE 2: Adsorption Energies, Vibrational Frequencies, and Structural Properties for CO on Mo(110) at Different Coverages coverage 1 ML
1
/2 ML
1
/4 ML
1
/9ML
state
Eads (eV)
a*a(°)
dC-O (Å)
dMo-C (Å)
ωMo-C (cm-1)
ωC-O (cm-1)
hollowb
R
1.76
8.7
1.17
490.4
atopd short bridgeb long bridgec hollowb
R R R R
1.59 1.62 1.39 2.02
0.0 0.0 0.0 16.7
1.16 1.17 1.18 1.17
2004.6 2000e 2065.3 1938.9 1880.6 1946.5
long bridgec atopd
R R
1.95 2.02
0.0 0.0
1.19 1.16
2.71 × 2 2.04 2.05 2.18 2.19 2.91 × 2 2.03 2.22 2.03
short bridgeb
R
1.73
0.0
1.18
2.20
337.2
hollowb
R
2.08
0.0
1.17
338.5
hollowb
β
2.13
60.9
1.27
Atopd short bridgeb long bridgec hollowb
R R R R
2.04 1.86 2.04 2.06
0 0 0.0 20.2
1.17 1.19 1.20 1.18
hollowb
β
2.16
63.0
1.35
2.35 × 2 2.15 2.33 2.25 1.98 2.03 2.19 2.16 2.81 × 2 2.03 1.73 2.29 2.16 2.04 2.17 2.21
site
447.2 400.9 394.4 435.7 349.5 428.4
1760.2 1968.5 2004f 1828.4 1888f 1672.4
505.6
1395.9 1345e
423.30 343.0 339.7 436.4
1910.3 1761.3 1667.5 1844.9
906.9
1145.9 1130e
Atopd R 2.07 0 1.18 433.8 1922.7 short bridgeb R 1.93 0 1.20 383.2 1876.4 long bridgec R 2.01 0 1.19 364.9 1793.8 CO PW91 1.14 2154.6 experimentalg 1.13 2143.0 a *a is title angle of CO respect to the surface normal. b Minimum. c Transition state. d Higher order saddle point. e Ref 6. f Ref 7. g Ref 26.
ML ad-layers described above. Furthermore on these sites we found two different configurations: end-on configuration and inclined configuration, with inclined configuration more favorable. In accordance with convention, we define the R state as end-on adsorption with the C-O oriented parallel to the surface normal and β state as being inclined with respect to the surface normal and almost parallel to the surface. The side views of these configurations are shown in Figure 2. EELS study shows that the CO stretching frequency is 1345 cm-1 at 0.25 ML (Table 2). Our prediction of CO stretching-frequency (1395.8 cm-1) for the hollow site β configuration agrees quite well with
Figure 2. Side view of R (above) and β (below) states for CO adsorption on Mo (110) surface. The O atoms were shown in white and the C atoms were shown in light gray.
experimental results except for the systematically shifted of the DFT methods. At last we explored CO adsorbed on Mo (110) at coverage of 0.11 ML in a (3 × 3) allayer. At the most stable hollow sites we also found two different configurations: R state and β state with the β state more favorable. Chen et al., have reported that a CO species exists which has an unusually low frequency of 1130 cm-1 and to be a molecule with its axis aligned with the surface plane.6 The calculated stretching frequency of CO with β state at this coverage is 1145.9 cm-1 which is very agreement with the experimental value. So our calculations confirm the existence of the CO speciesand the parallelism of the molecules with the surface reported by Chen.6 At the most stable hollow sites with different coverage, the experimental and calculated stretching frequency of CO are ∼2000 cm-1 and 1672.4-2004.6 cm-1, respectively, for R state, and 1130-1345 cm-1 and 1145.9-1395.9 cm-1 for β state. The experimental and calculated gas-phase C-O frequencies are 2143 and 2154.6 cm-1, respectively. Hence, the red shifts measured experimentally and theoretically are 143 cm-1 and 150-482.2 cm-1 for R state, and 1013-798 cm-1 and 1008.758.7 cm-1 for β state. The large red shifts are due to the weakening of the C-O triple bond, which indicates that the CO at β state is more likely to dissociate. As mentioned in our introduction, experimental studies of CO dissociation on Mo(110) surfaces at high- and low-coverage has shown that the rate of this reaction is much faster at the low coverage. Although our results for CO adsorption cannot provide a complete explanation for this observation, they do point out one possibility: the differences in reactivity between high and low coverage may stem from differences that at high coverage CO adsorbed with R state and at low coverage CO adsorbed with β state, which is more likely to dissociation. We
18366 J. Phys. Chem. B, Vol. 110, No. 37, 2006
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TABLE 3: Binding Energies (eV) of C and O on Mo(110) A. C on Mo(110) 1 ML hollow short bridge atop long bridge
1
/2 ML
6.11 5.59 4.28 6.37
1
/4 ML
6.65 6.31 4.76 7.18
1
/9 ML
7.29 6.76 5.09 7.34
7.33 6.83 5.22 7.65
B. O on Mo(110) 1 ML hollow short bridge atop long bridge
6.10 5.83 5.44 6.03
1
/2 ML 6.85 6.29 5.76 6.47
1
/4 ML 7.18 6.62 6.15 7.08
1
/9 ML 7.22 6.74 6.34 7.14
will extend our calculations to examine the reaction pathways that lead to CO dissociation and will report on these pathways in section 3.5. 3.3. C and O Adsorption. To study CO dissociation with the NEB method, we need to know the preferred adsorption sites for C and O atoms on Mo(110). We have studied the energtics of adsorbed C and O atoms on the Mo(110) surface as part of our study of CO dissociation. The top, short bridge, long bridge, and hollow sites were examined. The calculated results are summarized in Table 3, which lists the binding energies of the most favorable binding site of the atoms at 1 ML, 1/ ML, 1/ ML, and 1/ ML coverage. 2 4 9 Both atomic C and atomic O strongly adsorb to the Mo(110) surface. The 2-fold long bridge site is the most favorable binding site for a carbon atom, while the hollow site is the most favorable binding site for oxygen atom. Unlike CO, we found that the adsorption energies for C and O at high coverage are general lower than that at low coverage. This indicates that the C-C and O-O interactions are more significant at high coverage than at low coverage. The coadsorption of C and O on their most favorite sites will be studied in Section 3.4 and the optimized configuration will be used as the final state for CO dissociation calculations. At the most stable long bridge site, the Mo-C distances are 1.93 Å, 1.96 Å, 2.02 Å, and 2.00 Å for the 1, 1/2, 1/4, and 1/9 ML, respectively. Atomic O is adsorbed on hollow site, have the following Mo-O distances: 1.84 Å, 1.96 Å, 2.05 Å, and 2.08 Å for the 1, 1/2, 1/4, and 1/9 ML, respectively. 3.4. C/O/Mo(110), CO/C/O/Mo(110). For the coadsorption of C and O on the Mo surface, C long bridge + O hollow configurations for C and O coadsorption were studied. On the 1 × 1 and 2 × 1 structures, C and O spontaneously recombine to form CO during energy minimization. On the 2 × 2 structures, if C and O are placed initially in adjacent long bridge and hollow sites, they spontaneously recombine to form CO during energy minimization. If we take them apart (seen in Figure 3), they remain at these sites after energy minimization. At this time a C atom in one long bridge site is 2.96 Å in the in-plane direction from O in a hollow site. The adsorption energies, with respect to C and O in gas phase and bare Mo surface is 13.94 eV. The independent adsorption of atomic C and atomic O leads to 14.51 eV. The interaction between two adsorbates in a coadsorbed system can be defined as Eint ) Eads (C) + Eads(O) - Eads (C + O), where Eads (C) and Eads (O) are adsorption energies for two atomic species as isolated adsorbates and Eads(C + O) is the adsorption energy for the coadsorbed system. At this time we find Eint to be 0.54 eV. In the 3 × 3 structure, we take C and O apart for the same reason in 2 × 2 structure (seen in Figure 4). The adsorption energy is 14.43 eV. The independent adsorption of atomic C
Figure 3. Dissociation of CO on the Mo(110) surface from β state at 0.25 ML. The insets show the initial (left), transition (middle), and final (right) states. The O atoms were shown in white and the C atoms were shown in light gray.
Figure 4. Dissociation of CO on the Mo (110) surface from R state at 0.25 ML. The insets show the initial (left), transition (middle), and final (right) states. The O atoms were shown in white and the C atoms were shown in light gray.
and atomic O leads to 14.56 eV. That is to say Eint is reduced to 0.13 eV. The low value of Eint shows a very little lateral repulsion between adsorbed C and adsorbed O on the Mo(110) surface at low coverage. The geometries of adsorbed atomic C and atomic O follow. In the 2 × 2 structures, the Mo-C bond lengths are 2.00 Å, and Mo-O bond lengths are 2.09 Å. In the 3 × 3 structure, the Mo-C bond lengths are 2.01 Å, whereas the Mo-O lengths are 2.10 Å. In general, the geometries of atomic C and atomic O coadsorption do not differ significantly from the independent adsorption. The effect of coadsorbed CO on the binding energy of C and O was also examined by comparing binding strengths of C and O in CO/C/O/Mo(110) with that in the C and O coadsorption system. We estimated the adsorption energy of C, O, on CO precovered Mo(110) surface in the following equation
∆EC,O,CO//Mo ) ECO/C/O/Mo - ECO/Mo - EC - EO where ECO/C/O/Mo, ECO/Mo, EC, and EO are the total energy of CO/C/O/Mo (110), CO/Mo, C, and O atom, respectively. The adsorption energies are listed in Table 4. It can be seen that the adsorption energy of C and O on CO precovered Mo(110) surface is almost identical with that in the C and O coadsorption
Dissociative Adsorption of Carbon Monoxide on Mo(110) TABLE 4: Comparisons Between Chemisorption Energies (eV) of C and O in C/O/CO/Mo(110) and C/O/Mo(110) 1
/2 ML
CO precovered Mo(110) Pure M (110)
13.89 13.94
1
/9 ML
14.40 14.43
system, which means that the presence of preadsorbed CO have little effect on C and O adsorption in CO/C/O/Mo(110) system. 3.5. CO Dissociation. To probe this reaction more directly, we have examined the dissociation of CO on Mo(110) at high and low coverage. As describe above, C and O spontaneously recombine to form CO during energy minimization at 1 and 0.5 ML. We, therefore, focus on CO dissociation from R and β state at 25 and 11.1% coverage. As mentioned above, our calculations show that the β states have higher binding energies and larger red shifts than R state, which indicates weakening of the C-O bond. Therefore, we first examine CO dissociation from β state at hollow site at 0.25 ML. We determined the activation energy for CO dissociation on Mo(110) by using NEB method to construct a minimum energy path (MEP) connecting a CO molecule adsorbed in a hollow site and a final state with carbon and oxygen atoms sitting in long bridge and hollow sites, respectively. Our NEB calculation used eight images along the reaction path in addition to the end points. The resulting reaction path from the β state is shown in Figure 3. The left, middle, and right insets show the initial, transition, and final states, respectively. Fitting a cubic spling to the images along the path yields an estimated dissociation barrier of 1.71 eV. At the transition state, the C atom located at the long bridge site, and the O atom is very close to the short bridge site, as shown in Figure 2. The C-O bond is very elongated (∼1.80 Å). This type of transition state is very common for the CO dissociation on transition metals surface.27,28 We then examine CO dissociation from state at hollow site at 0.25 ML. Figure 4 displays the predicated MEP starting from R state. The CO reorients itself and goes through a transition state where CO lies almost flat on the hollow site with C-O bond elongated (∼1.96 Å). The C atom located at the long bridge site, and the O atom is very close to the short bridge site. That is to say, two transition states from different initial states are similar. For CO dissociation from R state, we obtain a dissociation barrier of 2.58 eV which is 0.87 eV higher than that from β state, indicating that R state is less active for dissociation, and provides direct support for the experimental observation that CO dissociation occurs much more rapidly at low coverage than at high coverage. In the 3 × 3 structure, the reaction barriers from R and β states are 2.43 and 1.68 eV, respectively, which confirm the result given above. All the transition states are similar to the ones in the 2 × 2 structure with bond elongated (1.93 Å for R state and 1.78 Å for β state). That is to say, all the transition states observed in our calculations are “late” in the sense that the structure of the transition state is quite similar to the finial state. 4. Summary and Conclusions Employing first principles GGA technique, we have studied CO adsorption on Mo(110) at high and low coverage. We find that CO is preferentially adsorbed on hollow site. At high coverage CO adsorbed in a R state, with the C-O bond almost aligned to the surface normal, and in β state at low coverage, inclined to the surface normal. The β states have larger C-O stretching frequency red shift, which show that they are more
J. Phys. Chem. B, Vol. 110, No. 37, 2006 18367 likely to dissociation. In all cases the results are in good agreement with experimental data and previous calculations where available. The results for the adsorption of atomic C and O on Mo surfaces showed that adsorption at low coverage is, in general, stronger than at high coverage. Since the binding energy of CO is not very sensitive to the coverage, the enhanced binding of atomic C and O at low coverage has direct consequences for the higher reactivity for CO dissociation at low coverage. This conclusion gives indirect support for the experimental observation that CO dissociation proceeds more rapidly at low coverage than at high coverage. To probe this reaction more directly, we have examined the dissociation of CO on Mo(110) at high and low coverage. We determined the activation barriers for CO dissociation on Mo(110) at low and high coverage. The barriers to CO dissociation are ∼1 eV lower from β state than that from R state. This result gives direct support for the experimental observations that compare CO dissociation rates at low and high coverage. References and Notes (1) Grgur, B. N.; Markovic, N. M.; Ross, P. N., Jr. J. Phys Chem. B 1998, 102, 2494. (2) Samjeske, G.; Wang, H.; Loffler, T.; Baltruschat, H. Electrochim. Acta 2002, 47, 3681. (3) Grgur, B. N.; Markovic, N. M.; Ross, P. N., Jr. Electrochim. Acta 1998, 43, 3231. (4) Mukerjee, S.; Lee, S. J.; Ticianelli, E. A.; McBreen, J.; Grgur, B. N.; Markovic, N. M.; Ross, P. N.;. Giallombardo, J. R.; Castro, E. S. D. Electrochem. Solid-State Lett. 1999, 2, 12. (5) Grgur, B. N.; Zhang, G.; Markovic, N.; Ross, P. N., Jr. J. Phys. Chem. B 1997, 101, 3910. (6) Chen, J. G.; Colaianni, M. L.; Weinberg, W. H.; Yates, J. T., Jr. Chem. Phys. Lett. 1991, 177, 113. (7) He, J. W.; Kuhn, W. K.; Goodman, D. W. Surf. Sci. 1992, 262, 351. (8) Ibach, H.; Mills, D. L. Electron Energy Loss Spectroscopy and Surface Vibrations; Academic Press: New York, 1982. (9) Jaworowski, A. J.; Smedh, M.; Borg, M.; Sandell, A.; Beutler, A.; Sorensen, S. L.; Lundgren, E.; Andersen, J. N. Surf. Sci. 2001, 492, 185. (10) Ciobica, I. M.; van Santen, R. A. J. Phys. Chem. B 2003, 107, 3808. (11) Shah, V.; Li, T.; Baumert, K. L.; Cheng, H.; Sholl, D. S. Surf. Sci. 2003, 537, 217. (12) Li, T.; Bhatia, B.; Sholl, D. S. J. Chem. Phys. 2004, 121, 10241. (13) Jiang, D. E.; Carter, E. A. Surf. Sci. 2004, 570, 167. (14) Bleakley, K.; Hu, P. J. Am. Chem. Soc. 1999, 121, 7644. (15) Liu, P.; Hu, P. J. Chem. Phys. 2001, 114, 8244. (16) Corriol, C.; Darling, G. R.; Holloway, S.; Brenig, W.; Andrianov, I.; Klamroth, T.; Saalfrank, P. J. Chem. Phys. 2002, 117, 4489. (17) Kresse, G.; Furthmuller, J. J. Comput. Mater. Sci. 1996, 6, 15. (18) Kresse, G.; Hafner, J. Phys. ReV. B 1993, 48, 13115. (19) Kresse, G.; Furthmuller, J. Phys. ReV. B 1996, 54, 11169. (20) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Pederson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (21) Mills, G.; Jonsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305. (22) Jonsson, H.; Mills, G.; Jacobsen, K. W. Nudged Elastic Band Method for Finding Minimum Energy Paths of Transitions. In Classical and Quantum Dynamics in Condensed Phase Simulations; Berne, B. J., Ciccotti, G., Coker, D. F., Eds.; World Scientific: River Edge, NJ, 1998; 21, 22 (23) Morales de la Garza, L.; Clarke, L. J. J. Phys. C 1981, 14, 5391. (24) Che, J. G.; Chan, C. T.; Jian, W. E.; Leung, T. C. Phys. ReV. B 1998, 15, 1875. (25) Moriarty, J. A.; Phillips, R. Phys. ReV. Lett. 1991, 66, 3036. (26) Huber, K. P.; Herzberg, G. In: Constants of Diatomic Molecules, Molecular Spectra and Molecular Structure; Van Nostrand Reinhold: New York, 1979; vol. IV. (27) Norskov J. K. J. Catal. 2002, 209, 275. (28) Greeley, J.; Norskov, J. K.; Mavrikakis, M. Annu. ReV. Phys. Chem. 2002, 53, 319.
