J. Phys. Chem. 1994, 98, 10906-10912
10906
Influence of the Surface Atom Metallic Coordination in the Adsorption of Ethylene on a Platinum Surface: A Theoretical Study J.-F. Paul and P. Sautet* Institut de Recherche sur la Catalyse, 2 Av A. Einstein, 69626 Villeurbanne Cedex, France, and Laboratoire de Chimie thtorique, Ecole Normale Supirieure, 69364 Lyon Cedex 07, France Received: June 15, 1994@
A theoretical analysis of the chemisorption of ethylene on a platinum surface is presented as a function of the metallic coordination of the platinum surface atom. Adsorption sites with coordinations ranging from 9 to 3 are considered and modeled by clusters of size between 7 1 and 114 atoms, with a special emphasis on step and kink sites. From extended-Huckel calculations, the ethylene molecule is shown to adsorb in a di-a mode for sites with high metallic coordinations while the n chemisorption becomes more stable for coordinations 7 and below. The binding energy of the molecule is increased when the surface atom coordination is reduced. These changes are explained by a strong reduction of the four-electron repulsion between occupied molecular orbitals of ethylene and filled states of the cluster for sites with low metal coordination. This sensitivity of the molecule adsorption on the structure of the surface could have important implications on the ethylene reaction pathway.
1. Introduction The molecular chemisorption is a fundamental step in heterogeneous catalysis, and the case of ethylene has been the subject of many e ~ p e r i m e n t a l l -and ~ ~ t h e ~ r e t i c a l ~studies. ~-~~ For the catalytic reactivity it has been underlined, since a long time ago, that defective sites such as steps or edge^'^-^^ on the metal catalyst could play a major role in the reaction turnover, due to a postulated increased activity, even if they are only a small amount of the total available sites. It is indeed often supposed that the entire surface is not active18but only a small portion of specific sites. From a surface science view point, stepped or open surfaces have been studied?’ they are more reactive and yield stronger binding with adsorbates. However, going to more defective sites, such as kinks or adatoms is difficult. On the theoretical side,26-33much of the work has been done on perfect surfaces, such as the (1 11) of a fcc metal and only a very few studies have been devoted to the influence of steps3’ or other defects. In particular, no systematic study of molecular adsorption as a function of the type of metallic site for a given metal has been published to our knowledge. In this paper we present such a study in the case of ethylene chemisorption on platinum. The choice of ethylene and platinum is of course related to the very large importance of the hydrogenation reaction of unsaturated molecules on metal catalysts in the field of heterogeneous catalysis. The calculation method and the geometrical description of the considered sites will be presented in section 2. The binding of the molecule on the site will be discussed in section 3 with an emphasis on the electronic origin of the chemisorption differences as a function of the metallic coordination of the surface site. 1324,25
2. Theoretical Method and Structure of the Sites In order to provide a systematic approach, sites with surface atom coordination ranging between 9 and 3 have been generated. The starting point is a Ptll4-like cluster describing a (111) surface, built from four layers containing 44, 33, 23, and 14
* Author to whom correspondence should be addressed at the Institut de Recherche sur la catalyse. @Abstract published in Advance ACS Abstracts, September 15, 1994. 0022-3654/94/2098- 10906$04.50/0
atoms from the surface to the last layer. The surface atoms in the center of the surface layer have nine neighbors. Fractions of this surface layer have been successively removed in order to generate surface atoms with three to eight neighbors. The clusters describing the surface sites of metallic coordinations 9-4 are shown in Figure 1. Their sizes are 114, 134, 96, 134, 84, and 72 Pt atoms, respectively. The case of a surface metal atom with coordination 3 has also been studied, modeled by one metal adatom on a (1 11) surface (cluster of 71 atoms). The (single) cluster for the coordinations 8 and 6 deserves a special comment, since it does not follow the building rule previously mentioned. It corresponds to a kink on a (111) surface and contains a site of metal coordination 6 at the kink atom and an atom of coordination 8 on the inner row. The kink site has been chosen because it is a very probable defect on a (1 11) Pt surface and it has been modeled by a somewhat larger cluster in order to correctly describe the environment of both sites (6 and 8). Similarly, the coordination 7 case is a step while the coordination 3 is an isolated adatom on a (1 11) terrace. It is clear that the chosen description is not unique: there could be different arrangements for a given surface atom coordination. The first neighbor atoms could be located differently around the site, and the same stands for the second neighbors and so on. Here the choice has been oriented toward the most compact (and hence stable) situations. However it should be noted that the precise metal environment for a given site coordination has only a marginal influence on the chemisorption results. This was tested in several cases. For example a different site of coordination 8 has been considered, built from a Ptlld-like cluster with a sector of 120’ of the first layer removed. This site gives a very small difference compared to the inner atom of the kink considered in Figure 1. Another example is that the step atom (coordination 7) gives very similar results to the surface atom of a (1 10) surface,32which has the same metal coordination. As a consequence it is believed that the situations described here are representative of a large number of individual arrangements. The calculations are of the extended-Huckel type.29,30,32,33,37 These semiempirical calculations allow one to deal with large clusters, and they are usually reliable to study trends in binding 0 1994 American Chemical Society
Adsorption of Ethylene on a Platinum Surface
J. Phys. Chem., Vof. 98,No. 42,1994 10907 -di
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Figure 2. Binding energy for the di-o (solid line) and the n (dashed line) chemisorption modes of ethylene as a function of the metallic coordination of the site (see Figure I for the description of the clusters representing the sites).
CHART 1
Figure 1. V&aus clusters describing the considered surface sites with decreasing metallic coordinations9-4 (in lines, fmm top left to bottom right). The preferred adsorption mode of ethylene on these clusters is shown. The site corresponding to the coordination 3 (adatom) is not shown.
energy. The parameters for platinum are taken from the literature?O and the ones for carbon and hydrogen are adapted from standard values by a global shift up of all atomic orbital energies of 1.5 eV, in order to simulate self-consistency and to yield an overall charge transfer close to zero for the case of the (1 11) surface. These parameters are kept fixed for all calculations, so that the variation in the molecular binding is only related to the change in the site topology. The edge effect introduced by the finite size of the cluster has been corrected by a projection of wave function on the core part. which contains all metal atoms with a correct first neighbor envir~nment.’~ The seven clusters describing the sites do not have the same number of atoms. However the number of atoms is large enough so that. with the correction of edge effects, a variation of the number of atoms in the cluster would only yield a very small change in the molecular binding. For example, in the case of the perfect ( I 11) surface, going from the chosen 114 atoms cluster to the smaller 49 atoms, one only changes the binding energy by less than 1 kcal/mol.)z On these various sites, two modes of coordination have been envisaged for ethylene (see Chart 1). The di-a mode involves two metal atoms, and therefore a neighbor atom of the given site atom has to be used. The n coordination only involves one metal atom. It is known, from spectroscopy, that the ethylene molecule is hybridized toward sp3 upon chemisorption, and it is essential to take this distortion into account. Due to the limited capabilities of the extended-HUckel method to optimize geometries. all C-Pt bond lengths were kept fixed to 2.1 8, and a distortion of the ethylene molecule was imposed by a simultaneous linear variation of all geomeuic coordinates, controlled by a single parameter h, between the gas-phase geometry (h = 0.C - C = 1.34 C-C-H = H-C-H = 120”) and a fully hybridized ethane-like situation (h = 1, C-C = 1.54 C-C-H = H-C-H = 109.5”).The calculated optimum hybridization h for the isolated molecule is zero, as it should be, while the chemisorption on the Pt(lI1) surface yields
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an optimum of h = 0.85. This corresponds to a C - C bond length of 1.51 in good agreement with experimental values
A.
(1.48-1.52 A).”-36
In the case of t h e n chemisorption mode, the azimuthal angle @ of the ethylene molecule has been optimized for each case, and for both the di-a and the n cases, the tilt angle 0 of the molecule with respect to the [111] direction has also been calculated (see Chart I).
3. Ethylene Binding as a Function of Site Coordination The di-a and the n adsorption modes have been compared on the selected sites, and the result for the adsorption energy is shown in Figure 2. The best adsorption geomehy is also illustrated in Figure 1 for each considered adsorption site. The optimum ethylene hybridization is not significantly modified when the site is changed The di-amode corresponds to a value of h = 0.85, and the n mode, to a value of h = 0.4. The difference between these two optimal hybridizations has already been explained for the (1 11) ~urface.’~For this high cooniination site (9)the di-a adsorption is calculated to be more stable than the n one, in agreement with experimental data. The adsorption energy of the di-a mode is rather constant until a site coordination of 5 and then significantly increases in absolute value for the last calculated site coordination of 4. On the contrary the n situation shows a marked increase in binding energy when the coordination is decreased between 9 and 7, only a small change between 7 and 5. and again an increase for coordinations lower than 5. The general trend is therefore an increase of the binding energy on sites with lower metal coordination, in agreement with the experimental trend.” The
Paul and Sautet
10908 J. Phys. Chem., Vol. 98, No. 42, 1994 consequence of the different behavior for the di-o and the n mode is that the n case becomes the most stable one for coordinations lower than or equal to 7. It has been shown experimentally that ethylene adopts such a n adsorption on a (110) surface of Pt,s-10 where the surface atoms have a coordination of 7, and also on the (210) surface," with a surface atom coordination of 6 . For the coordination 9 the tilt angle 8 of the ethylene molecule is zero, for both the di-o and the n adsorption modes. However, starting at the site coordination 8 for the n mode and at the coordination 6 for the di-a mode, a tilt angle of 25-30" toward the lower terrace is found. In the case of the di-o mode on the coordination 8 site, the variation of the energy is very small for tilt angles between 0 and 30". For the n coordination mode the preferred azimuthal angle is such that the molecule is perpendicular to the upper terrace edge, mediating the angle formed by this edge at the site atom. This tilt and these azimuthal angles have a significant influence on the adsorption energy of the molecule. In the n adsorption of ethylene perpendicular to the step (coordination 7, see Figure l), a 27" tilt toward the lower terrace yields an energy stabilization of -0.25 eV, about half the difference between coordinations 9 and 7. For that tilt value, an orientation of the molecule parallel to the step would destabilize the system by 0.1 eV. Therefore the tilt process, possible only for defective sites, plays a nonnegligible role in the binding energy increase with decreasing coordination. In order to analyze the origin of this change in chemisorption mode for sites with low metallic coordination, the first step is to study the frontier orbital two-electron interactions. The occupied n orbital of ethylene gives a donation interaction with the surface vacant levels (mainly s) while the unoccupied n* orbital takes part in the back-bonding interaction, involving filled metal states (mainly d). The total electron transfer, that is to say the sum of the absolute values of these electron transfers, is given in Figure 3. The di-o case corresponds to a strong two-electron interaction, while this interaction is weaker for the n adsorption. The total transfers both slowly decrease if the site coordination is reduced, indicative of a smaller interaction. This decrease is even stronger in the case of the n adsorption mode. The individual electron transfers from the n orbital and toward the ,z* orbital all follow the same trend. A consequence of these electron flows is to weaken the C-C bond, since a bonding orbital is depopulated while an antibonding one is populated. Therefore a decrease of the electron transfers is associated with an increase of the C-C overlap population for low-coordination sites, as seen in Figure 3c. This analysis of the frontier orbital two-electron interactions is therefore completely unsatisfactory since it concludes in a smaller moleculesurface interaction for sites with reduced metallic coordination, while the binding energy is increased. As seen before for ethylene and formaldehyde on Pt( 1 1 1),32,37 the four-electron interactions play a major role in the molecule binding to the surface. These four-electron interactions occur between occupied orbitals on the molecule and on the surface. As a consequence the antibonding combination is filled or almost filled, which results in a repulsive interaction. The only way to avoid such a filling of the antibonding orbital is to have this orbital pushed above the surface Fermi level as a result of the interaction. Even if such a process is important for chemisorption, it can only happen in a case of strong interaction and for a molecular orbital lying not too far below the Fermi level. We will see that this is not the case for the four-electron interactions described here. The four-electron interactions are
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03 5 6 7 8 9 10 site coordination Figure 3. As a function of the site coordination, for the di-a (solid line) and n (dashed line) modes of ethylene: (a) total electron transfer between molecule and surface (sum of absolute values, this is not the net charge); (b) separate electron transfer from n molecular orbital (thick line) and toward n* molecular orbital (thin line) (absolute values); (c)
2
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carbon-carbon overlap population. not associated with any electron transfer. In this study they were quantified by the squared overlap between ethylene and cluster molecular orbitals, summed over every possible couple of occupied orbitals (noted SZ in the following). In the present analysis all the occupied orbitals of ethylene are included, in contrast with the previous study on Pt(l1 where only the n orbital was considered. The electronic repulsion described here results from the spatial overlap of molecule and surface electronic densities and can therefore be associated with Pauli repulsion or steric repulsion. The 9 value, characteristic of the four-electron repulsion, is plotted in Figure 4 as a function of surface site coordination. It shows a strong decrease when the site coordination is reduced, especially for the z coordination, where the repulsion is decreased by a factor more than 2 between coordination 9 and coordination 3. This explains the increase of binding energy: the diminution of the repulsive interactions dominates the lowering of the attractive ones described above in the binding energy. The decrease of the four-electron repulsion is large between coordination 9 and coordination 7, intermediate between coordinations 7 and 5, and rather small below coordination 5 .
Adsorption of Ethylene on a Platinum Surface
J. Phys. Chem., Vol. 98, No. 42, 1994 10909 -0.2
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Figure 4. As a function of the site coordination, for the di-a (solid line) and n (dashed line) modes of ethylene: (a) total four-electron repulsion (SZ value, thick line) and four-electron repulsion obtained
when the secondary interactions between the molecule and the metal atoms not bonded to it are removed (see text, 9 value, thin line); (b) difference four-electron repulsion (Pvalue) resulting from the interactions between the molecule and the metal atoms not bonded to it.
In order to understand this decrease of the four-electron repulsion, the following decomposition was performed. For all the sites a distinction was made between the metal atoms directly bonded to the molecule (Le. the site atoms, 1 for the n coordination and 2 for the di-a one) and the other atoms of the cluster which only have nonbonding or indirect interactions with the molecule. In each case a calculation was performed with all the overlap and Hamiltonian matrix elements set to zero between the molecule and those nonbonded atoms, therefore neglecting these secondary molecule-surface interactions but keeping all the metallic neighborhood connectivity of the surface site. As seen in Figure 4, the four-electron repulsion is then significantly reduced, especially for the coordinations between 7 and 9 and for the n chemisorption mode. It should be noted that the distances between the carbon or hydrogen atoms and the metal neighbors of the site are smaller for the n coordination than for the di-a one, since only one metal atom is involved in the site. A large part of the repulsion is therefore represented by the secondary overlap between occupied MOs on the molecule and occupied states on metal atoms neighboring the surface site. This effect is of course stronger when the metallic site coordination is large and is rather specific of the molecule(metal surface) interaction compared for example to the molecule-(organometallic complex) one. Even if some ligandligand repulsion can occur in the latter, these repulsions are usually strong only in the case of bulky ligands. These secondary interactions are rather weak; therefore, the antibonding combinations are not pushed high enough to cross the Fermi level and they are occupied, leading to a true fourelectron interaction, similar to the two-orbitals-four-electrons He-He textbook case. They mainly involve electrons of the C-H bonds in ethylene. The decrease of the repulsion with lower metal coordination fo the site is hence straightforward. The adsorption energies,
if these secondary interactions are removed, are given in Figure 5 as a function of site coordination together with the normal ones. The change is important, especially for the n coordination, until coordination 6. For the site of the (111) surface for example, the two adsorption modes have then a very similar binding energy, while the di-a one is strongly favored if all interactions are included. If the secondary interactions are removed, the evolution of the binding energy is small (even a slight decrease for the di-a mode) when the coordination is lowered from 9 to 5. It is a clear indication that the main effect on the binding energy is the change in the repulsion with secondneighbor metal atoms in that range of coordinations. It can be interesting to analyze the influence of the eventual tilt of the molecule on the four-electron repulsion. Let us describe for example the case of the n adsorption mode on the step site (coordination 7). The tilt of the molecule induces a reduction of the four-electron repulsion by 0.025, which is half of the repulsion difference between coordinations 9 and 7. Therefore half of the repulsion variation between 9 and 7 is induced by the removal of two metal neighbors of the site when making the step, while the second half comes from the tilt which allows a release of the repulsion arising from the upper terrace. It should be noted that, if the overlap and Hamiltonian matrix elements with the metal atoms other than the site are set to zero, the four-electron repulsion is then almost identical between the tilted and nontilted situation, which confirms the previous analysis. Below a coordination of six, the repulsion from metal atoms neighboring the site only slowly changes, as can be seen from Figure 4b, even if the total repulsion still significantly drops. Other components of the repulsion are then modified: They come either from direct interaction between the molecule and the site atoms or from indirect interactions between the molecule and the metallic neighbors of the site, which result from throughbond interactions mediated by the site atom. In other words, surface atoms different from the site still have an effective interaction with the molecule even if the direct coupling elements are set to zero because they are all linked to the site atoms. This is why the repulsion obtained in the calculation where the couplings are set to zero (Figure 4)is non-zero and decreases, when the coordination is reduced, toward a theoretical limit obtained when the cluster is limited to the one or two site atoms. This limit repulsion value is 0.05 for the n mode and 0.07 for the di-a one, the difference being related to the number of atoms forming the site. Therefore the increased binding energy of ethylene on a defective low-coordination site is explained by a reduction of the four-electron destabilizing interactions and not by stronger
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Paul and Sautet
10910 J. Phys. Chem., Vol. 98, No. 42, I994 0-
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is indicated by a dotted line, and the Fermi level, by a dashed line.
two-electron interactions, which are on the contrary slightly reduced. These two-electron interactions are illustrated in the projected densities of states displayed in Figures 6 and 7. Figure 6 shows the density of states projected on the site atom of the studied clusters without ethylene as a function of its coordination. The change in the aspect of the d band is small between coordinations 9 and 7. It is known from moment theory that the d bandwidth of the projected density of states evolves like the square root of the coordination number. This is why the variation is small for large coordinations and the reduction of d bandwidth between coordinations 9 and 4 is only 2/3. This d bandwidth decrease is accompanied by a lowering of the density of states contribution just below the Fermi level.
This is indicative of a less efficient donor character of the cluster when the coordination of the site decreases. This is clearly seen in Figure 7b, where the density of states projected on the n* orbital of ethylene is shown in the case of the n adsorption mode. This n* orbital, originally located at E = -7.8 eV for the considered ethylene geometry, is split over a large energy range due to its interaction with the cluster. Bonding contributions are located below the Fermi level, and they give rise to the back-bonding electron transfer, since they correspond to a fractional electronic occupation of the n* orbital. This splitting and the associated back-bonding electron transfer are clearly reduced when the coordination is decreased. In the case of low coordination (4), the picture is very similar to the organometallic
Adsorption of Ethylene on a Platinum Surface Projection on the
J. Phys. Chem., Vol. 98, No. 42, 1994 10911 orbital
Projection on the 7c* orbital 0
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Figure 7. Density of states projected on the n (a, left) and n* (b, right) orbitals of ethylene for the n chemisorption mode on the sites of coordination 9 (top), 7 (middle), and 4 (bottom). The integrated density of states is indicated by a dotted line, and the Fermi level, by a dashed line.
case with two almost discrete energy levels in the projected spectrum: the first one mainly centered on the a* orbital is the antibonding contribution with the metal dyzorbital, while the bonding level only has a small contribution on the ethylene a* orbitaI. We are therefore progressively moving from a picture of delocalized metal states involved in the bonding with the molecule for high coordinations to a situation of quasi-localized metal states for the low coordinations, going from the perfect surface to the nearly single-atom behavior. The situation is similar for the projected density of states on the ethylene R orbital (Figure 7a), which gets more and more localized, with
reduced contributions above the Fermi level resulting in a slow decrease of the electron donation transfer. 4. Conclusion
The metal coordination of the surface atom is found from the calculations to have a significant influence on the binding of an ethylene molecule on a platinum surface. The general trend is an increase of binding energy when the site coordination is reduced; that is to say that ethylene is more strongly bound on defective sites than on perfect (111) terraces. This binding
10912 J. Phys. Chem., Vol. 98, No. 42, 1994
energy increase is much more effective for the rc chemisorption mode, and this yields an inversion in the preferred adsorption geometry. For sites with high metal coordination, the di-a mode is more stable, but the n chemisorption gets more favorable for coordinations 7 and below. As a consequence the ethylene is di-a on the terrace but it is n on steps or on kink sites. It can be postulated that the di-a and the n adsorption modes are associated to different hydrogenation reaction rates, the n mode giving a higher activity. Indeed on all surfaces where the ethylene is known to adsorb in a x mode (Pt(110),39340Pd( 111),41342 the hydrogenation activity is higher than on those where the molecule is di-a (such as Pt( 11l)40.42). This hypothesis is now being tested by calculations. For F’t catalysts, it would imply an increased activity for step and kink sites, compared to (1 11) terraces. The step site would then be similar to the (1 10) surface site for its activity. This change in binding strength and mode is explained by a marked reduction of the four-electron repulsion between occupied MOs of the molecule and filled states on the cluster when the site coordination is reduced. A large part of that repulsion is induced by the secondary overlap between the molecule and surface metal atoms neighboring the site. This part is obviously reduced with lower surface atom coordinations. More open sites also allow a tilt of the molecule toward the lower terrace yielding a further decrease of that electronic repulsion. The attractive frontier-orbital two-electron interactions are slightly reduced if the site coordination is decreased, which would imply on the contrary a smaller binding. Their effect however is completely dominated by the reduction of the fourelectron repulsions. The d bandwidth of the density of states projected on the site atom is slowly reduced between coordinations 9 and 4, and the interaction with the molecule is progressively changing from a delocalized picture for high metal coordinations to a localized discrete scheme for low coordinations. This influence of the surface atom coordination on the molecular binding certainly goes beyond the specific example of ethylene studied here (similar results have been found for aldehydes and ketones). The developed concept of a reduced electronic repulsion at defective sites is general and could be applied to several cases. This could explain the general experimental trend of a stronger binding on sites of low coordinations.
References and Notes (1) Koestner, R. J.; Van Hove, M. A.; Somojai, G.A. J. Phys. Chem. 1983, 87, 203.
Paul and Sautet (2) Zaera, F. J. Phys. Chem. 1990, 94, 5090. (3) Salmeron, M.; Somojai, G.A. J. Phys. Chem. 1982, 86, 341. (4) Avery, N. R.; Sheppard, N. Proc. R. SOC. London 1986, A405, 1. (5) Avery, N. R.; Sheppard, N. Proc. R. SOC.London 1986, A405,27. (6) Sheppard, N. Annu. Rev. Phys. Chem. 1988, 39, 589. (7) Hatzikos, G.H.; Masel, R. I. Surf. Sci. 1987, 185, 479. (8) Yagasaki, E.; Masel, R. I. Surf. Sci. 1989, 222, 430. (9) Yagasaki, E.; Backman, A. L.; Masel, R. I. J. Phys. Chem. 1990, 94, 1066. (10) Yagasaki, E.; Masel, R. I. Surf. Sci. 1990, 226, 51. (11) Backman, A. L.; Masel, R. I. J. Phys. Chem. 1990, 94, 5300. (12) Rekoske, J. E.; Cortrigh, R. D.; Goddard, S. A,; Sharma, S. B.; Dumesic, J. A. J . Phys. Chem. 1992, 96, 1880. (13) Somojai, G.A,; Van Hove, M. A.; Bent, B. E. J . Phys. Chem. 1988, 92, 973. (14) Cortrigh, R. D.; Goddard, S. A.; Rekoske, J. E.; Dumesic, J. A. J . Catal. 1991, 127, 342. (15) Creighton, J. R.; White, J. M. Surf. Sci. 1983, 129, 327. (16) Bandy, B. J.; Chesters, M. A,; James, D. I.; McDougall, G. S.; Pemble, M. E.; Sheppard, N. Philos. Trans. R. London 1986, A381, 141. (17) Bertolini, J. C.; Massardier, J. In The Chemical Physics OfSolid Surfaces and Heterogeneous Catalysis;King, D. A., Woodruff, D. P. Eds.; Elsevier: Amstersam, The Netherlands, 1984; Vol. 3, p 107. (18) Somojai, G.A. In Elementary Reaction Step in Heterogeneous Catalysis; Joyner, R. W., Van Santen, R. A. Eds.; Kluwer Academic: Dordrecht, The Netherlands 1993; p 3. (19) Albert, M. R.; Sneddon, L. G . Surf. Sci. 1982, 120, 19. (20) Cassuto, A.; Mane, M.; Jupille, J. Surf.Sci. 1991, 249, 8. (21) Cassuto, A.; Mane, M.; Jupille, J.; Tourillon, G.;Parent, P. J. Phys. Chem. 1992, 96, 5987. (22) Cassuto, A.; Mane, M.; Tourillon, G.;Parent, P.; Jupille, J. Surf. Sci. 1993, 287, 460. (23) Steininger, H.; Ibach, H.; Lehwald, S. Surf. Sci. 1982, 117, 685. (24) Kaukonen, H.-P.; Nieminen, R. M. Surf. Sci. 1991, 247, 43. (25) Netzer, F. P.; Wille, R. A. Surf. Sci. 1978, 74, 547. (26) Felter, T. E.; Weinberg, W. H. Surf. Sci. 1981, 103, 265. (27) Baetzold, R. C. Langmuir 1987, 3, 189. (28) Anderson, A. B.; Choe, S. J. J. Phys. Chem. 1989, 93, 6143. (29) Maurice, V.; Minot, C. Langmuir 1989, 5, 734. (30) Silvestre, S.; Hoffmann, R. Langmuir 1985, I, 621. (31) Kang, D. B.; Anderson, A. B. Surf. Sci. 1985, 155, 639. (32) Paul, J. F.; Sautet, P. Catal. Lett. 1991, 9, 245. (33) Wong, Y.-T.; Hoffmann, R. J. Chem. SOC.,Faraday Trans. 1990, 86, 4083. (34) Stohr, J.; Sette, F.; Johnson, A. L. Phys. Rev. Lett. 1984, 53, 1684. (35) Demuth, J. E. Surf.Sci. 1979, 84, 315. (36) Demuth, J. E. IBM J. Res. Dev. 1978, 22, 265. (37) Delbecq, F.; Sautet, P. Surf. Sci. 1993, 295, 353. (38) Massardier, J.; Bertolini, J. C.; Ruiz, P.; Delichbre, P. J . Catal. 1988, 112, 21. (39) Pradier, C. M.; Margot, E.; Berthier, Y.; Oudart, J. J. Appl. Catal. 1988, 43, 177. (40) Massardier, J.; Bertolini, J. C. J. Catal. 1984, 90, 358. (41) Massardier, J.; Bertolini, J. C.; Renouprez, A. Proc. Znt. Con$ Catal. 1988, 3, 1222. (42) Ouchaib, T.; Massardier, J.; Renouprez, A. J. Catal. 1989, 119, 517.
