J. Phys. Chem. B 2001, 105, 8149-8154
8149
First-Principles Pseudo-Potential Study of the Pd(110)-c(2×2)-Ethylene Adsorption System Fabio Pichierri,* Toshiaki Iitaka, and Toshikazu Ebisuzaki Computational Science DiVision, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako-shi, Saitama-ken 351-0198, Japan
Maki Kawai Surface Chemistry Laboratory, RIKEN (The Institute of Physical and Chemical Research), 2-1 Hirosawa, Wako-shi, Saitama-ken 351-0198, Japan
David M. Bird Department of Physics, UniVersity of Bath, Bath BA2 7AY, U.K. ReceiVed: January 9, 2001; In Final Form: June 8, 2001
The interaction of molecular ethylene with the Pd(110) surface has been investigated by means of periodic first-principles density functional theory slab calculations. At 0.5 ML coverage, DFT-GGA-PW91 calculations favor the formation of a short bridge (di-σ type) adsorption mode over an atop (π-bonded) ethylene state by 196 meV. On the other hand, HREELS, NEXAFS, and STM measurements unambiguously reveal the presence of π-bonded ethylene on Pd(110). The possible causes of this wrong site preference in DFT-GGA calculations are discussed.
1. Introduction In recent years different nonlocal exchange-correlation (XC) functionals1-3 have been developed within the generalized gradient approximation (GGA)4 of density functional theory (DFT).5 These nonlocal XC functionals have considerably improved the adsorption energies of molecule/transition metal surface systems6 in comparison to those calculated with the local density approximation (LDA).7 However, despite these improvements, some puzzling results concerning the wrong prediction of adsorption sites by DFT-GGA calculations are emerging from the current literature. Feibelman et al.8 have recently analyzed state-of-the-art DFT results for the CO/Pt(111) system. A large body of experimental data suggests the occurrence of atop CO binding on Pt(111). In sharp contrast, however, a variety of well-converged DFT calculations, employing either atomic pseudo-potentials or allelectron basis sets, favor adsorption sites with high coordination, i.e., 2-fold and 3-fold over 1-fold sites. The theoretical fcc vs atop site-preference energy of CO/Pt(111) corresponds to ca. 0.25 eV.8 In this paper we present a further example of the wrong site preference in DFT-GGA calculations for the Pd(110)-c(2×2)ethylene adsorption system. In contrast to recent HREELS,9 NEXAFS,10 and STM11 measurements, which unambiguously indicated that ethylene is π-bonded onto an atop Pd atom of the (110) surface of palladium at temperatures below 280 K, our well-converged DFT-GGA calculations favor the formation of a short bridge (di-σ type) adsorption mode. 2. Computational Details All the calculations were performed with a parallel version of the ab initio molecular dynamics program CASTEP12-14 on * Corresponding author. Present address: RIKEN-GSC, 1-7-22 Suehirocho, Tsurumi-ku, Yokohama 230-0045, Japan. E-mail:
[email protected].
Figure 1. Schematic illustration of the adsorption sites investigated: atop (A), short bridge (B), long bridge (C), and hollow (D). For each site, two orientations of the C-C axis of ethylene were considered, namely, one along [11h0] and the other along [001].
the Fujitsu VPP/700E supercomputer of RIKEN. We employed the gradient-corrected XC functional of Perdew and Wang (PW91),1 as implemented in CASTEP by White and Bird.15 The core-valence interactions in the Pd, C, and H elements were treated with Vanderbilt-type ultrasoft pseudo-potentials,16 with a plane-wave cutoff of 340 eV. The Pd(110)-c(2×2) surface cell depicted in Figure 1 was employed. With one ethylene molecule per surface unit cell, the resulting coverage regime corresponds to 0.5 ML. Four adsorption sites were considered; namely an atop site (A), a short bridge site (B), a long bridge site (C), and a hollow site (D). Two orientations of the ethylene molecule were considered for each of the adsorption sites (A-D), namely, one with the C-C axis oriented along the [11h0] row and the other with the molecular axis oriented along the [001] direction (Figure 1). Hence, a total of eight adsorption modes were investigated. The resulting supercell consists of seven layers of bulk Pd and a vacuum region with a thickness of ca. 11 Å, which corresponds to seven Pd layers. The supercell has dimensions of a ) b ) 4.780 Å, c ) 19.319 Å, and γ ) 70.53°. The initial distance between Pd layers corresponds to that of a converged DFT calculation on the bulk metal which gave an equilibrium
10.1021/jp010113k CCC: $20.00 © 2001 American Chemical Society Published on Web 08/03/2001
8150 J. Phys. Chem. B, Vol. 105, No. 34, 2001
Pichierri et al.
Figure 2. Convergence behavior of the binding energy for the atop [11h0] state as a function of the (n × n × 1) k-point grid, with n ) 1-7.
TABLE 1: Adsorption Energy (-∆Eb) and Selected Structural Parameters of Ethylene Adsorbed on Pd(110)
parametera
atop [11h0]
atop [001]
short bridge [11h0]
long bridge [001]
Zeise’s saltb
-∆Eb (meV) 771 660 967 575 1236 [533] C-C (Å) 1.387 1.373 1.425 1.431 1.375(4) C-H (Å) 1.086 1.078 1.088 1.087 1.096(7),1.087(7) 1.079(8),1.086(8) Pd-C (Å) 2.139 2.141 2.081 2.081 2.128(3),2.135(3) h (Å) 2.02 2.03 1.98 1.78 2.022(3) HCC (deg) 120.4 120.2 117.2 113.8 120.6(4),121.7(4) 121.2(5),120.8(5) HCH (deg) 115.4 116.8 114.1 113.9 115.2(5),114.6(6) CCH2 (deg) 174.4 175.2 170.5 168.0 174.8,175.5 PdCC (deg) 72.2 71.3 107.7 120.9 71.4(2),70.9(2) a For the Zeise’s salt, the parameters Pd-C and PdCC are to be substituted by Pt-C and PtCC, respectively. b Reports the binding energy and structural parameters of the Zeise’s salt. The structural parameters of the Zeise’s salt refer to the neutron diffraction structure of Love et al. (ref 19a); the experimental standard deviations are given in parentheses. The theoretical values of the binding energies of ethylene coordinated to the PtCl3- and PdCl3- (in square brackets) fragments are taken from ref 19b.
lattice constant of 3.903 Å. This compares well with the experimental value of 3.8903 Å determined at 298 K.17 To take into account the effect of the substrate, the bottom three Pd layers were frozen at their bulk configuration during all the geometry optimizations. The tolerance for the root-mean-square force on the atoms was set at 0.1 eV/Å and no symmetry constraints were imposed on the system except for time reversal symmetry. The Brillouin zone was sampled with a 7 × 7 × 1 mesh, corresponding to a set of 25 equally spaced k-points, which was generated with the Monkhorst-Pack (MP) method.18 This MP k-point set yielded a converged value of the binding energy (-∆Eb) for the π-bonded ethylene state, as shown in Figure 2. ∆Eb is given by
∆Eb ) EPd/et - (EPd + Eet) where EPd and Eet are the total energies of the relaxed bare Pd slab and of the free ethylene molecule, respectively, while EPd/et represents the total energy of the fully relaxed Pd(110)-c(2×2)ethylene adsorption system. The binding energies for the other adsorption configurations were computed in the same manner. 3. Results Stability of the adsorption states. The converged values of the calculated binding energies (-∆Eb) for the stable adsorption states are reported in Table 1, together with the corresponding optimized structural parameters. Among the eight adsorption
Figure 3. Plan views of the stable adsorption states on Pd(110): (a) atop [11h0], (b) atop [001], (c) short bridge [11h0], and (d) long bridge [001]. Each view refers to a Pd(110)-c(2×2)-ethylene slab. Light balls refer to the Pd atoms of the topmost layer while dark balls to those of the second layer.
configurations investigated (Figure 1), only four are found to be stable on the (110) surface of palladium. Figure 3a-d shows the four stable adsorption modes viewed from the direction normal to the surface. Two atop states, both with the ethylene molecule π-bonded to the underlying Pd atom, are stable. The first, depicted in Figure 3a, has the C-C axis oriented along the [11h0] direction while the second, shown in Figure 3b, has the molecular axis oriented along [001]. The calculated adsorption energies are 771 and 660 meV respectively. This result indicates that the preferred orientation of atop ethylene on Pd(110) is the one along the [11h0] row, in agreement with the recent experimental HREELS measurements performed by Okuyama et al.9,10 Relaxation of the short bridge site with ethylene oriented along [11h0] and [001] yielded only one stable configuration. The former short bridge mode (Figure 3c) is stable, with a calculated binding energy of 967 meV, whereas the latter mode is unstable, and the ethylene molecule moves toward the neighboring atop site. The strong binding calculated for this di-σ adsorption state, however, is in contrast with experimental measurements suggesting a preferential formation of π-bonded (atop) ethylene at a temperature below 260 K.9 An analogous, although opposite, trend is observed when ethylene sits on the long bridge site (C). In this case, the adsorption state with ethylene oriented along [001] is stable (Figure 3d) with a binding energy at 575 meV, whereas that with the ethylene molecule oriented along [11h0] is unstable, and the molecule again moves toward the atop site. A movement of the molecule was also observed at the hollow site (D). Configurations in which ethylene is oriented along the [11h0] and [001] directions are both unstable and the molecule shifts toward the stable short bridge and long bridge sites, respectively. Adsorbate Structure. Table 1 also gives the optimized structural parameters of the four stable adsorption configurations of ethylene on Pd(110)-c(2×2). These are compared with those of a single-crystal neutron diffraction structure of the Zeise’s salt,19a whose anion is depicted in Chart 1. This coordination compound is considered to be a model of π-bonded ethylene and it was used as a reference in the assignment of the vibrational frequencies of adsorbed ethylene.9,10 The following discussion will refer to the optimized structures of the adsorbates that are shown in Figure 4. The bond lengths and bond angles of the adsorbed ethylene states reported in Table 1 show that deviations from the
Pd(110)-c(2×2)-Ethylene Adsorption System
J. Phys. Chem. B, Vol. 105, No. 34, 2001 8151
Figure 4. Ball-and-stick representations of the optimized structures of the four stable adsorption configurations of ethylene on Pd(110): (a) atop [11h0], (b) atop [001], (c) short bridge [11h0], and (d) long bridge [001]. Some Pd atoms of the first (light balls) and second (dark balls) layers are also shown in the figure.
CHART 1
geometry of the free molecule arise as a consequence of interaction with the metal surface. Two structural features are important here, namely, the lengthening of the C-C bond with respect to that of gaseous ethylene (C-C is 1.317 Å for ethylene and 1.510 Å for ethane, calculated with the GGA-PW91 method) and the loss of molecular planarity. The latter structural property is quantified by the angle formed by the C-C bond and the plane containing the atoms of the CH2 moiety (see CCH2 parameter in Table 1), together with the value of the HCC angle. The C-C bond lengths of the two atop states are slightly different, with values of 1.387 Å for ethylene oriented along the [11h0] direction (Figure 4a), and 1.373 Å for the [001] orientation (Figure 4b). The latter distance is very close to the experimental C-C bond length of ethylene in the Zeise’s salt (Chart 1), which corresponds to 1.375(4) Å.19a The corresponding vertical heights, represented by the h parameter, are both close to 2.0 Å. Hence, the difference in adsorption energy of about 111 meV can be mainly ascribed to the different orientations of the ethylene molecule. To test the validity of this assumption, we have performed a series DFT-GGA-PW91 calculations with the ethylene molecule oriented both along
[11h0] and [001] inside the c(2×2) supercell, but without the Pd slab. The results indicate that the intermolecular repulsion along [001] is ca. 130 meV stronger than that along [11h0]. The loss of planarity in the adsorbed ethylene molecule originates from the acquisition of p atomic orbital character by the valence sp2 orbitals of carbon upon interaction with the electronic bands of the metal surface that are close to the Fermi level.20 However, according to Ge and King,21 the π character in the chemisorbed ethylene is retained even in the strongly bridge-bonded ethylene state on Pt(111) thereby suggesting that the carbon valence orbitals do not achieve the sp3 hybridization present in ethane. The most significant deformation of ethylene geometry occurs when the molecule occupies the short bridge site (Figure 4c), where the CCH2 angle is at 170.5°, and for the long bridge configuration (Figure 4d) where this parameter decreases to 168°. Also, the values of the HCC angles show a significant degree of rehybridization, being 117.2° for the short bridge and at 113.8° for the long bridge configurations, respectively. These adsorption states are also characterized by a consistent lengthening of their C-C bond lengths, being 1.425 Å for the short bridge and 1.431 Å for the long bridge configurations. Slab Relaxation Effect. In Table 2 we report the optimized interlayer distances (d12 and d23) of the four adsorption states that are stable on Pd(110) and their deviations (∆d12 and ∆d23) from the theoretical bulk interlayer distance (dPd ) 1.38 Å). Also included in Table 2 are a parameter (s) concerning the displacement of the central atop Pd atom (Figure 1) as well as the distances between nearest neighbor Pd atoms of the topmost layer along both [11h0] and [001]. A pictorial representation of some of these parameters is given in the slab cross section of Figure 5. The seven structural parameters given in Table 2 are compared with those of the clean Pd(110) slab. Warren and Thiel22 have performed low-energy electron diffraction measurements of the clean Pd(110) surface and found a contraction of 4.4 ( 1.5% in the first interlayer distance (d12) and an expansion of 1.5 ( 1.5% in the second interlayer distance (d23). We observe a similar trend for our clean Pd(110) slab; d12 is 1.27 Å and d23 1.42 Å, in excellent agreement with the experimental estimates of 1.31 ( 0.02 Å and 1.39 ( 0.02 Å, respectively. Upon adsorption of ethylene, d12 tends to slightly expand with respect to the clean slab, whereas d23 remains nearly constant. The largest expansion of d12 occurs when ethylene is adsorbed at the long bridge site, when d12 is 1.35 Å. The first interlayer distance for the adsorption of ethylene at the short bridge site corresponds to 1.32 Å, whereas a weak expansion effect occurs
TABLE 2: Interlayer Distances (d12 and d23) and Corresponding Slab Relaxation Parameters (∆d12 and ∆d23) of the Clean and Ethylene-Covered Pd(110) Surfaces, and Also Reported Are the out-of-Plane Displacement of the Atop Pd Atom, the Distances between nearest Neighbor Pd Atoms of the Topmost Layer along [11h0] and [001], and the Slab Deformation Energy (-∆Ed) systema clean slab atop [11h0] atop [001] short bridge [11h0] long bridge [001]
Pd-Pd (Å) [11h0]
Pd-Pd (Å) [001]
0.00
2.760
3.903
0
+0.03
+0.05
2.760
3.903
16
d12 (Å)b
∆d12 (Å)
d23 (Å)b
∆d23 (Å)
1.27 (1.31 ( 0.02) 1.29
-0.11
1.42 (1.39 ( 0.02) 1.41
+0.04
-0.09
s (Å)
-∆Ed (meV)c
1.28
-0.10
1.41
+0.01
+0.09
2.761
3.904
25
1.32
-0.06
1.40
+0.02
0.00
2.827
3.900
25
1.35
-0.03
1.40
+0.02
+0.01
2.777
3.581
109
a See Figures 3 and 5. The calculated bulk interlayer distance corresponds to 1.38 Å. b The experimental values of d and d (in parentheses) 12 23 for the clean slab are taken from ref 22. c ∆Ed ) (EPd - EPd*).
8152 J. Phys. Chem. B, Vol. 105, No. 34, 2001
Figure 5. Cross-section of the Pd(110)-c(2×2) slab. The Pd atoms of the first, third, fifth and seventh layer are represented by dark balls.
at both atop sites where d12 is 1.29 and 1.28 Å. For the latter atop configurations, however, we do observe a strong out of plane displacement of the topmost Pd atom interacting with ethylene. This effect is larger for the atop configuration with ethylene oriented along [001], where s ) +0.09 Å, while s decreases when the molecule is oriented along [11h0], being equal to +0.05 Å. In Table 2 we also report the calculated Pd-Pd distances between the nearest neighbor Pd atoms of the topmost layer along two perpendicular directions (Figure 1). The largest deformation from the structure of the clean slab occurs when ethylene is adsorbed at the long bridge site. Here, the interatomic distance between Pd atoms along [001] shortens from 3.903 to 3.581 Å, while the Pd-Pd distance along [11h0] increases from 2.760 to 2.777 Å. At the short bridge site, the distance between neighboring Pd atoms along the [11h0] direction lengthens from 2.760 to 2.827 Å, whereas no effect is seen along [001]. There is little change in the two Pd-Pd for both atop states.
Pichierri et al. The last column of Table 2 gives the amount of energy (-∆Ed) involved in the deformation of the metal slab upon adsorption of ethylene. This quantity was calculated by subtracting the total energy of the clean Pd(110)-c(2×2) slab (EPd) from those of the corresponding deformed slabs without ethylene (EPd*). The results indicate that the long bridge configuration possesses the highest slab deformation energy, with ∆Ed at 109 meV, whereas the two atop states and the short bridge configuration are characterized by lower ∆Ed values ranging from 16 to 25 meV. Diffusional Potentials. The lateral motion of ethylene that we observed for four of the eight adsorption states, as well as the experimental evidence for a small tilting of the atop ethylene state along the [11h0] direction, prompted us to calculate the diffusional potentials for ethylene on Pd(110). We follow an approach similar to that presented by Ge and King23 in their first-principles DFT study on the CO/Pt(110) system. Figure 6 shows the 1-D lateral potential energy surfaces of the two most stable adsorption configurations, namely, the atop (Figure 4a) and short bridge (Figure 4c) modes, both of them with the C-C bond aligned along [11h0]. The points on each of the four graphs were obtained by carrying out single-point energy GGA-PW91 calculations. The curves of Figure 6a,b correspond to the lateral tilt of ethylene along the [11h0] and [001] directions, respectively. In both cases the molecule was tilted in steps of 2.0° starting from the optimized configuration (tilt angle at 0°) with the C-C axis lying parallel to the surface. The graph in Figure 6c corresponds to the in-plane rotation of ethylene about the axis connecting the middle point of the C-C bond and either the Pd atom of the topmost layer (for the atop site) or that of the second metal layer (for the short bridge site). In this case also the initial atop and short bridge configurations were rotated away from the [11h0] direction in steps of 2°. The fourth graph (Figure 6d) shows the potential energy curves corresponding to the translation of both atop and short bridge
Figure 6. Potential energy curves for the lateral diffusion of atop (() and short bridge (9) ethylene [11h0] states on Pd(110): (a) tilt along [11h0], (b) tilt along [001], (c) rotation about the Pd-ethylene axis, and (d) translation of the center of mass along [11h0].
Pd(110)-c(2×2)-Ethylene Adsorption System ethylene along the [11h0] close-packed row by steps of 0.1 Å, up to a final shift of the C2H4 center of mass of 0.5 Å. The graphs of Figure 6 indicate that both the lateral displacement and in-plane rotation of atop ethylene are characterized by a shallower potential energy well than for the short bridge configuration. The most striking difference is observed in the curves of Figure 6a, where a 4° lateral tilt of ethylene along [11h0] costs an additional 80 meV amount of energy if the molecule occupies the short bridge site rather than the atop site. As a result, the lateral tilt of short bridge ethylene along the close-packed Pd row is a hindered motion. An interesting experimental result concerns the small tilting of the π-bonded ethylene molecule along the [11h0] direction, which lowers the local site symmetry to Cs.9,10 To probe the stability of tilted states, the atop ethylene molecule (Figure 4a) was tilted a few degrees along the [11h0] direction and the resulting configuration was fully relaxed. The adsorption energy calculated for the tilted state corresponds to 771 meV, the same as that obtained for the flat state, and the resulting tilt angle corresponds to only 2°. Overall, the atop ethylene molecule is floppy in the range (2°, as indicated by the shallow potential energy well of Figure 6a. 4. Discussion The converged values of the adsorption energies obtained in the present first-principles total energy DFT-GGA-PW91 calculations suggest that the short bridge site, with ethylene oriented along the [11h0] row, is favored over the atop site by about 196 meV. This result, however, is in sharp contrast with a series of recent experiments which suggested the formation of stable π-bonded atop ethylene on Pd(110).9-11 To investigate whether this discrepancy is due to the choice of the PW91 functional, we have tested the RPBE functional of Hammer, Hansen, and Nørskov,3 which has been incorporated in the latest version of the CASTEP code.13 RPBE is a modified version of the Perdew-Burke-Ernzerhoff (PBE) functional2 in which the exchange enhancement factor has a different mathematical form. Both PBE and RPBE fulfill the same physical criteria and are constructed in similar ways. The most important differences with respect to the PW91 functional concern a better description of the linear response of the uniform electron gas, a smoother XC potential, and a correct behavior under uniform scaling.2,3 The RPBE functional leads to the same prediction as that of PW91, with the adsorption energies for the atop and short bridge sites corresponding to 566 and 741 meV, respectively. The difference between these values is 175 meV, which is close to the GGA-PW91 value of 196 meV. Interestingly, the error of ca. 0.2 eV in the short bridge/atop site preference is of a similar size to that reported by Feibelman et al.8 for the CO/Pt(111) system. The effect of vibrational entropy has been invoked by King and co-workers23,24 as a possible cause for the erroneous site preference of DFT calculations. In the case of CO on Pt(111), the calculated vibrational entropy amounts to only 25 meV in favor of the atop site at 300 K, which is about 1/10 of the error (ca. 0.25 eV) given by Feibelman et al.8 The contribution of vibrational entropy to the free energy is likely to be a determinant only in those cases where the calculated binding energies of two sites differ only by a small amount (ca. 10-30 meV). Within the limit of the harmonic approximation, we estimate from the data of Figure 6a a vibrational entropy difference of ca. 34 meV between the atop and short bridge ethylene configurations at 300 K. It is therefore difficult to
J. Phys. Chem. B, Vol. 105, No. 34, 2001 8153
Figure 7. Approximate potential energy curve for atop-to-bridge transformation of ethylene along the close-packed Pd row. The first point (from the left) corresponds to the atop state, while the last corresponds to the short bridge configuration. The data were fitted with a fifth-order polynomial.
conclude that this effect is important in favoring the atop site against the short bridge site in the case of ethylene adsorption on Pd(110). Another possible reason for an incorrect site preference might be related to the effect of temperature, which plays a key role in the dynamics of molecules adsorbed on metal surfaces.25 For instance, the adsorption of ethylene on Pt(111) is a process activated by temperature.26 Below 50 K, ethylene is π-bonded at an atop Pt site and it transforms to a short bridge di-σ state at above 60 K. The barrier of activation for the atop-to-bridge site transformation has been recently estimated by Watson et al.27 using the elastic band method28 to be ca. 124 meV. This value is about one-third of the calculated energy difference of 430 meV between the energies of the two stable adsorption sites. For the present Pd(110)-c(2 × 2)-ethylene adsorption system, an approximate estimate of the activation barrier for atop-toshort bridge transformation can be obtained by fitting the potential energy curves for the lateral displacement of ethylene along the [11h0] direction. These curves derive from single-point calculations performed on the geometries resulting from the sliding of atop ethylene along the close-packed row. As shown in Figure 7, fitting the data with a fifth order polynomial suggests that the activation barrier should be at least 80 meV. This value is about half of the calculated energy difference (196 meV) between the two stable adsorption configurations (Table 1). It follows that, in order for the site-to-site transformation to occur, the activation temperature should be above the temperature of annealing (260 K).9 However, it is worth noting that, at temperature regimes above 280 K, ethylene starts to decompose with formation of ethylidyne. 9-11 5. Conclusions In the present theoretical study we have found that the atop ethylene site is less favorable than the short bridge site by ca. 0.2 eV for both the GGA-PW91 and GGA-RPBE exchangecorrelation functionals. However, recent HREELS, NEXAFS, and STM experiments9-11 performed by us suggest that the atop site is in fact more stable. Another representative system where striking contradictions with experiments have been found is the adsorption of CO onto the Pt(111) surface. Among all the possible causes of failure examined by Feibelman et al.,8 none could explain the wrong trend in the DFT calculations. These contradictions between theoretical predictions and experiments indicate that current state-of-the-art DFT-GGA calculations cannot be relied upon for the successful prediction of adsorption sites.
8154 J. Phys. Chem. B, Vol. 105, No. 34, 2001 Acknowledgment. The research presented here was undertaken within a joint collaboration between the Advanced Computing Center of RIKEN (The Institute of Physical and Chemical Research, Wako-shi, Japan) and the United Kingdom Car-Parrinello (UKCP) consortium. Dr. J. R. Trail (University of Bath) is gratefully acknowledged for porting the parallel version of the CASTEP 4.2 code on the Fujitsu VPP/700E supercomputer of RIKEN and for his technical assistance. Prof. N. M. Harrison (CLRC, Daresbury) with Drs. Y. Morikawa (AIST, Tsukuba), H. Kato (RIKEN, Wako-shi), T. Yamamoto (RIKEN, Wako-shi), and P. J. D. Lindan (CLRC, Daresbury) are gratefully acknowledged for stimulating scientific discussions. We are indebted to Prof. J. K. Nørskov (Technical University of Denmark, Lyngby) for providing to us a copy of his manuscript prior to publication (see ref 8). F.P. is thankful to RIKEN for hospitality and financial support. References and Notes (1) Perdew, J. P. In Electronic Structure of Solids ‘91; Ziesche, P.; Eschrig, H., Eds.; Akademie Verlag: Berlin, 1991. Perdew, J. P.; Wang, Y. Unpublished. (2) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865. (3) Hammer, B.; Hansen, L. B.; Norskov, J. K. Phys. ReV. B 1999, 59, 7413. (4) 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. (5) Hohenberg, P.; Kohn, W. Phys. ReV. 1964, 136, B864. (6) Brivio, G. P.; Trioni, M. I. ReV. Mod. Phys. 1999, 71, 231. (7) Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133.
Pichierri et al. (8) Feibelman, P. J.; Hammer, B.; Nørskov, J. K.; Wagner, F.; Scheffler, M.; Stumpf, R.; Watwe, R.; Dumesic, J. J. Phys. Chem. B. 2001, 105, 4018. (9) Okuyama, H.; Kato, H.; Kawai, K.; Yoshinobu, J. J. Chem. Phys. 2000, 113, 2866. (10) Okuyama, H.; Ichihara, S.; Ogasawara, H.; Kato, H.; Komeda, T.; Kawai, M.; Yoshinobu, J. J. Chem. Phys. 2000, 112, 5948. (11) Ichihara, S.; Yoshinobu, J.; Ogasawara, H.; Nantoh, M.; Kawai, M.; Domen, K. J. El. Spectrosc. Relat. Phenom. 1998, 88-91, 1003. (12) Payne, M. C.; Teter, M. P.; Allan, D. C.; Arias, T. A.; Joannopoulos, J. D. ReV. Mod. Phys. 1992, 64, 1045. (13) CASTEP 4.2 academic version, licensed under the UKCP-MSI Agreement, 1999. (14) Lindan, P.; The Guide 2.0 to CASTEP (covering version 4.2), October 2000. (15) White, J. A.; Bird, D. M. Phys. ReV. B 1994, 50, 4954. (16) Vanderbilt, D. Phys. ReV. B 1990, 41, 7892. (17) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 80th Ed.; 1999-2000; CRC Press: Boca Raton, FL, 1999. (18) Monkhorst, H. J.; Pack, J. D. Phys. ReV. B 1976, 13, 5188. (19) (a) Love, R. A.; Koetzle, T. F.; Williams, G. J. B.; Andrews, L. C.; Bau, R. Inorg. Chem. 1975, 14, 2653. (b) Hay, P. J. J. Am. Chem. Soc. 1981, 103, 1390. (20) Bocquet, M.-L.; Sautet, P. Surf. Sci. 1998, 415, 148. (21) Ge, Q.; King, D. A. J. Chem. Phys. 1999, 110, 4699. (22) Warren, O. L.; Thiel, P. A. Phys. ReV. B 1992, 47, 10848. (23) Ge, Q.; King, D. A. J. Chem. Phys. 1999, 111, 9461. (24) Gu, J.; Sim, W. S.; King, D. A. J. Chem. Phys. 1997, 107, 5613. (25) Barth, J. V. Surf. Sci. Rep. 2000, 40, 75. (26) Cremer, P. S.; Somorjai, G. A. J. Chem. Soc., Faraday Trans. 1995, 91, 3671. (27) Watson, G. W.; Wells, R. P. K.; Willock, D. J.; Hutchings, G. J. J. Phys. Chem. B 104 2000 6439. (28) Mills, G.; Jonsson, H.; Schenter, G. K. Surf. Sci. 1995, 324, 305.
