Molecular Modeling of Ethylidyne Adsorption and Diffusion on Pt(111)

Feb 1, 1996 - Z. Nomikou, M. A. Van Hove,* and G. A. Somorjai. Materials Sciences Division, Lawrence Berkeley Laboratory, and Department of Chemistry,...
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Molecular Modeling of Ethylidyne Adsorption and Diffusion on Pt(111) Z. Nomikou, M. A. Van Hove,* and G. A. Somorjai Materials Sciences Division, Lawrence Berkeley Laboratory, and Department of Chemistry, University of California, Berkeley, California 94720 Received May 19, 1995. In Final Form: November 16, 1995X The adsorption geometry and diffusion behavior of ethylidyne (CCH3) on Pt(111) is studied in order to help elucidate the role of this hydrocarbon species during ethylene hydrogenation and dehydrogenation over Pt catalysts. A variant of the extended Hu¨ckel method is used, which allows bond-specific parametrization in molecules. It is adapted to geometrically infinite periodic systems, and empirical parameter values suitable for hydrocarbons on Pt surfaces are developed. The 3-fold fcc and hcp hollows are found to be the most stable adsorption sites, with an energy barrier of about 0.11 eV between them. This barrier suggests relatively easy diffusion of ethylidyne along the Pt(111) surface (subject only to steric intermolecular constraints), allowing unimpeded ethylene approach by opening up sites where subsequent hydrogenation reactions could take place with preadsorbed hydrogen.

1. Introduction Fundamental understanding of small hydrocarbon reactions on metal surfaces, such as hydrogenation and dehydrogenation of ethylene on platinum crystal surfaces, is of dominant importance in heterogeneous catalysis. This explains the plethora of published studies, both experimental and theoretical, probing the nature of the catalysts in hydrogenation reactions of unsaturated compounds, starting as early as the end of last century.1 Yet, until today, the reaction pathways and the important transition states of most such seemingly simple reactions remain unknown. We have recently performed computational simulations, using the extended Hu¨ckel theory2,3 within the tightbinding approximation,4 to study the dehydrogenation of ethylene on the Pt(111) and Pt(100) single-crystal surfaces.5 By contrast, in this paper, we are interested in the hydrogenation of ethylene on Pt(111). Specifically, we will probe the role of ethylidyne (CCH3) present on the hexagonal-lattice platinum surface during the hydrogenation. Recently, Anderson et al. carried out an atom superposition and electron delocalization-molecular orbital (ASED-MO) study6 that contributed significantly to the elucidation of the mechanism of ethylene hydrogenation on Pt(111). Also, theoretical studies based on the extended Hu¨ckel theory have been performed to trace in detail the bonding of ethylidyne on square-lattice metal surfaces like fcc(100)7 and hexagonal-lattice metal surfaces like fcc(111).8 It is known that catalytic dehydrogenation and hydrogenation of ethylene on Pt(111) take place in the presence of a tightly bound, dense ethylidyne overlayer.9 Horiuti and Polanyi suggested early on that the basic mechanism should be sequential addition of surface bound hydrogen X Abstract published in Advance ACS Abstracts, February 1, 1996.

(1) Sabatier, P.; Senderens, J. B. Compt. Rend. 1899, 128, 1173. (2) Hoffmann, R.; Lipscomb, W. N. J. Chem. Phys. 1962, 37, 2872. (3) Hoffmann, R. J. Chem. Phys. 1963, 39, 1397. (4) Whangbo, M.-H.; Hoffmann, R. J. Am. Chem. Soc. 1978, 100, 6093. (5) Ditlevsen, P. D.; Van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1993, 292, 267. (6) Anderson, A. B.; Choe, S. J. J. Phys. Chem. 1989, 93, 6145. (7) Schiøtt, B.; Hoffmann, R.; Awad, M. K.; Anderson, A. B. Langmuir 1990, 6, 806. (8) Silvestre, J.; Hoffmann, R. Langmuir 1985, 1, 621. (9) For instance, see: Zaera, F.; Somorjai, G. A. J. Am. Chem. Soc. 1984, 106, 2288.

atoms.10 Thomson and Webb more recently proposed that hydrogenation occurs via the adsorbed hydrocarbon layer, relegating the metal to a secondary role.11 Despite the subsequent controversial arguments that appeared in the literature in the 1980s, today we are certain that this p(2×2) ethylidyne overlayer does not participate in any way in the reaction. It is now established that ethylidyne is neither a reactive intermediate nor is it a reactive site blocking poison to the catalytic hydrogenation.12 The recent theoretical work of Anderson et al.6 also disproved the earlier proposition9 that ethylidyne participates in the hydrogenation process via its conversion to ethylidene (>CHCH3) and subsequent transfer of the R-hydrogen to ethylene molecules weakly adsorbed as a second overlayer outside the ethylidyne layer. Most recently, sum frequency generation (SFG) studies of the ethylene hydrogenation process strongly suggested the presence of π-bonded ethylene on the Pt(111) surface, during highpressure, catalysis even in the presence of a saturation coverage of ethylidyne.13 Low-energy electron diffraction (LEED) studies14,15 have investigated the ethylidyne adsorption sites on Pt(111) at 0.25 monolayer and shown that ethylidyne occupies fcc 3-fold hollow sites (defined below) and orders in a p(2×2) structure (i.e. occupying every other equivalent site in both surface dimensions). This coverage is sufficiently high that the methyl groups of the ethylidyne moieties (if they don’t move sideways or bend over) block ethylene molecules from approaching the metal surface and from hydrogenating by directly subtracting hydrogen atoms preadsorbed on the surface. However, large-amplitude ethylidyne vibrations and displacements are still possible, as recent scanning tunneling microscopy (STM) investigations conclude.16,17 Studies have shown that the residence time of 14Clabeled ethylidyne is substantially larger than the turn(10) Horiuti, J.; Polanyi, M. Trans. Faraday Soc. 1934, 30, 1164. (11) Thomson, S. J.; Webb, G. J. Chem. Soc., Chem. Commun. 1976, 526. (12) Beebe, T. P., Jr.; Yates, J. T., Jr. J. Am. Chem. Soc. 1986, 108, 663. (13) Cremer, P.; Somorjai, G. A. to be published. (14) Kesmodel, L. L.; Stair, P. C.; Baetzold, R. C.; Somorjai, G. A. Phys. Rev. Lett. 1976, 36, 1316. (15) Starke, U.; Barbieri, A.; Materer, N.; Van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1993, 286, 1. (16) Land, T. A.; Michely, T.; Behm, R. J.; Hemminger, J. C.; Comsa, G. Appl. Phys. 1991, A 53, 414. (17) Land, T. A.; Michely, T.; Behm, R. J.; Hemminger, J. C.; Comsa, G. J. Chem. Phys. 1992, 97, 6774.

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over rate of ethylene hydrogenation on Pt(111).18 So the question remains, what exactly is the role of ethylidyne during ethylene hydrogenation? In this study we address the question of structure and mobility of ethylidyne on Pt(111), from a theoretical standpoint. We once again confirm the hollow adsorption site found experimentally. In addition, we argue that ethylidyne diffuses on the surface, thus allowing enough space for ethylene to approach the metal surface and hydrogenate. This last point is also supported by Anderson et al.6 Moreover, recent STM investigations of ethylidyne on Pt(111) could resolve no clear structure at the usual catalytic temperature of 300 K, suggesting significant mobility.16,17 Only cooling of the sample as low as 230 K allowed STM observation of an ordered hexagonal ethylidyne layer. Land et al. assigned this effect to the fast vibrational motion of the ethylidyne species at 300 K. We argue that this disorder could also be due to fast translational motion of ethylidyne on the surface, at 300 K. We will address these issues with an analysis of the Pt(111)-p(2×2)-ethylidyne potential energy surface obtained from a variant of the extended Hu¨ckel theory within a tight-binding formalism. We will invoke bond specific parameters that are included within the Hamiltonian matrix elements (Hij), needed to calculate all the interaction energies (∆E) between every two atomic orbitals (i and j), as we recall from the simple perturbation theory expression

∆E )

|Hij|2 E0i - E0j

(1)

These parameters were introduced by Calzaferri et al.19-22 and later developed for organometallic compounds by Savary et al.23 To this end we have developed parameters which are suitable for the surface adsorbate system Pt(111)-p(2×2)-CCH3 and which are sensitive to bond type, namely different for Pt-C, C-C, and C-H bonding interactions, in analogy to the work of Savary et al.23 This procedure can be generalized to any surfaceadsorbate system. 2. Theoretical Method and Parameter Optimization In this study we use a modified version of the extended Hu¨ckel programs within a tight-binding formalism4,24 to investigate the adsorption and diffusion of ethylidyne on the Pt(111) surface. This variant, proposed by Calzaferri et al.,19-22 employs a distance-dependent extended Hu¨ckel constant K and calculates approximate two-body electrostatic interaction terms.25 The constant K is given by the distance-dependent Wolfsberg-Helmholtz formula: (18) Davis, S. M.; Zaera, F.; Gordon, B. E.; Somorjai, G. A. J. Catal. 1985, 92, 240. (19) Calzaferri, G.; Forss, L.; Kamber, I. J. Phys. Chem. 1989, 93, 5366. (20) Calzaferri, G.; Hoffmann, R. J. Chem. Soc., Dalton Trans. 1991, 917. (21) Bra¨ndle, M.; Calzaferri, G. Helv. Chim. Acta 1993, 76, 924. (22) Bra¨ndle, M.; Calzaferri, G. Helv. Chim. Acta 1993, 76, 2350. (23) Savary, F.; Weber, J.; Calzaferri, G. J. Phys. Chem. 1993, 97, 3722. (24) Hoffmann, R. Solids and SurfacessA Chemist’s View of Bonding in Extended Structures; VCH: New York, 1988. (25) Anderson, A. B.; Hoffmann, R. J. Chem. Phys. 1974, 60, 4271.

K ) 1 + ke-δ(R-d0) with k ) κ + ∆2 - ∆4κ and Hii - Hjj ∆) (2) Hii + Hjj where κ and δ are small positive empirical parameters and do is the sum of atomic orbital radii rA + rB, as detailed by Calzaferri et al.19-22 This allows a more reliable investigation of the intermediate surface species present during the hydrogenation process (here we focus only on ethylidyne), both from a geometric and an electronic point of view. We also performed charge iteration, as described in the Appendix. The goal is to calculate the energetics of ethylidyne adsorption and diffusion, and to trace the bonding and electronic factors that influence the preference among the various adsorption sites on the metal surface. We first performed geometric optimizations with respect to energy for adsorbed ethylidyne using the standard values κ ) 0.75 and δ ) 0.30 in (2), suggested by Savary et al.,23 i.e., with the same parameter values for all bonds. We allowed all but two of the 3 × 5 ) 15 degrees of freedom to relax. The two constrained coordinates were the lateral surface coordinates (i.e. site) of the first carbon atom of ethylidyne, the one nearest the metal surface, which we stepped through a sequence of preassigned locations describing likely diffusion pathways across the surface. Otherwise, all ethylidyne interatomic bond lengths, bond angles, and dihedral angles and the overall ethylidyne rotational and tilt angles were allowed to relax. The latter two permitted C-C tilting and methyl group rotations. We used a conjugate direction set minimization algorithm (Powell’s method) to perform the geometric optimizations within the modified extended Hu¨ckel molecular orbital (EHMO) program in its tight-binding formulation. For simplicity, as in ref 5, all calculations were performed while all platinum atoms were kept frozen in their unrelaxed bulk positions, with a Pt-Pt nearest neighbor distance of 2.775 Å. LEED studies15 have shown this to be a reasonable assumption, as the adsorption of ethylidyne causes no platinum atom buckling or displacement greater than 0.11 Å. The adsorbate system was represented by a two-dimensional p(2×2) unit cell containing 12 platinum atoms, arranged in a three-layer metal slab, and one ethylidyne species, altogether forming the Pt(111)-p(2×2)-CCH3 extended adsorbate structure. Reciprocal space was represented by a set of 18 k points, generated according to the geometrical method of Ramirez and Bo¨hm.26 This set of k points is suitable even for the lowest symmetry configurations, so the same was chosen for all positions along the diffusion pathway to minimize the computing error in energy difference that could otherwise arise. These initial optimizations yielded structures with unrealistic Pt-C distances of 1.442-1.633 Å; typical Pt-C bond lengths should be about 2.00 Å. Carbon-carbon distances were abnormally long, within the 1.74-1.88 Å range (representing a very weak C-C bonding interaction); for comparison, the C-C bond length of ethane is 1.53 Å and of ethylene 1.34 Å. However, all the C-H bond lengths were near 1.16 Å, the C-C-H angles 105110°, and the dihedral H-C-H angles about 120°, so the methyl group remained realistic. Evidently, the extended Hu¨ckel method so parametrized failed, presumably due to the typical extended Hu¨ckel weakness of inadequate electronic repulsion between a transition metal atom and a non-metal element. Next we explored other values of κ and δ, but could not find a single pair of values that successfully represented (26) Ramirez, R.; Bo¨hm, M. C. Int. J. Quantum Chem. 1986, 30, 391.

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Table 1. Optimized K and δ Values for the Pt(111)-p(2×2)-CCH3 System κ δ

Pt-C

C-C

C-H

0.302 0.000

0.629 0.923

0.573 0.947

the Pt(111)-p(2×2)-CCH3 adsorbate system. Hence, we focused on bond-type-specific κ and δ values, as suggested by Savary et al.23 These authors structurally optimized various classes of organometallic clusters and succeeded to best reproduce their experimental geometries only after adequate individual bond-type-specific κ and δ parametrization of the interactions of interest. We thus optimized the κ and δ parameters separately for the Pt-C, C-C, and C-H bonds. During the optimization routine we kept the standard values for κ and δ suggested by Savary et al.23 (κ ) 0.75, δ ) 0.30) for Pt-H and Pt-Pt interactions as well as for the Hamiltonian matrix elements Hnn that correspond to the same atom center. The aim was to reproduce the experimental LEED geometry of ethylidyne on the Pt(111) surface, as reported by Starke et al.15 The quantity we sought to minimize is the relative root mean square (RRMS) of the error of the calculated Pt-C, C-C, and C-H bond distances of ethylidyne in its most stable site (3-fold fcc hollow), relative to the experimentally observed distances15 (Pt-C ) 2.01 Å and C-C ) 1.49 Å, and we assumed C-H ) 1.10 Å):

RRMS )

[(

)

[(Pt-C)calc - (Pt-C)exp]2

(

2 (Pt-C)exp

+

)

[(C-C)calc - (C-C)exp]2 2 (C-C)exp

(

+

)]

[(C-H)calc - (C-H)exp]2 2 (C-H)exp

1/2

(3)

The value of RRMS for the relaxed ethylidyne structure at the fcc site with the standard κ and δ parameters for all bonds was 0.414. The corresponding value with the optimized κ and δ parameters was reduced to 0.020. The optimized κ and δ parameters are listed in Table 1. Notice the similarity in the κ and δ values for C-C and C-H bonds in ethylidyne. This confirms that the two types of bonds are chemically and electronically similar in this species.27 For comparison, Savary et al.23 report the values κ ) 0.60 and δ ) 0.90 for C-H bonds in the organometallic compounds they studied. The striking agreement reveals the similarity in nature of C-C and C-H bonds in molecular organometallic compounds with those in our extended surface-adsorbate system. We shall make the important assumption that these optimized values can be used for other adsorption sites of the same ethylidyne species on Pt(111). As we shall see, this is justified up to a point, namely as long as the coordination number does not change much, especially between the metal and C atoms. We expect the same to hold for Pt-C bonds in structurally and electronically related molecular clusters and solid-state structures.28 We emphasize that such κ and δ parametrization can be also implemented for other adsorbed CxHy carbonaceous species on different metal surfaces. 3. Explored Adsorption Geometries Now that we have an adequate parametrization of the bond description, we address our goal to characterize, for (27) Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1982, 12, 711. (28) Nomikou, Z.; Schubert, B.; Hoffmann, R.; Steigerwald, M. L. Inorg. Chem. 1992, 31, 2201.

Figure 1. Pt(111) surface with a (1×1) unit cell outlined, indicating the traced path of an ethylidyne molecule. Each dot represents a constrained lateral position of the first carbon atom of one ethylidyne molecule: at each such position, the ethylidyne geometry was fully optimized, keeping the Pt substrate bulklike. A complete p(2×2) overlayer of ethylidyne molecules moves in step with this molecule. The 3-fold fcc and hcp hollows differ by the absence or presence of a second-layer Pt atom below them, respectively.

ethylidyne on the Pt(111) surface, optimum adsorption geometries and diffusion pathways with associated barriers. We shall rigidly shift our ethylidyne layer across the surface and optimize the molecular adsorption structure at each lateral location. The p(2×2) arrangement leaves sufficient space between adjacent molecules to remove any significant intermolecular interactions, so that our molecular adsorption geometries would also hold at any smaller coverages, i.e. for larger intermolecular distances. Diffusion, however, poses a different problem: diffusion of a single molecule among a nondiffusing set of neighboring molecules can no longer be modeled in a p(2×2) arrangement, since all molecules are equivalent to each other by translational periodicity. One would need a substantially larger unit cell than p(2×2) with a correspondingly larger number of independent ethylidyne species to model such behavior. Anderson et al.6 used three independent molecules on a Pt cluster to model this situation; however, the computational cost of optimizing all free parameters in this approach is prohibitive. We shall thus focus on the collectively rigid diffusion in the absence of intermolecular interactions, as derived from p(2×2) models. To map out the energy surface for ethylidyne at all locations on Pt(111), we selected a dozen sites along a straight line segment joining two top sites and passing through both types of hollow sites (fcc and hcp) as well as the bridge site, as depicted in Figure 1. By symmetrical equivalence (due to the 3-fold and mirror symmetries of the metal substrate) these sites cover the entire surface with a dense enough grid to permit the prediction of diffusion pathways. We ran geometric optimizations of ethylidyne at the 12 positions indicated along the diffusion path shown in Figure 1. The conditions and constraints involved in these minimizations were the same as in the previous section. Selected results of these ethylidyne optimizations are listed in Table 2. An excellent, in-depth discussion of the bonding and electronic factors involved in the chemisorption of ethylidyne at the higher symmetry top, bridge, and hollow sites on Pt(111) can be found in ref 8. As the experimentally observed adsorption site of ethylidyne on Pt(111) is the fcc hollow, we take its calculated extended Hu¨ckel energy with an optimized

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Table 2. Selected Pt(111)-p(2×2)-Ethylidyne Optimization Results ∆E (eV) sitea

total

0 (top) 1 2 3 4 (fcc) 5 6 (bridge) 7 8 (hcp) 9 10 11 12 (top)

0.109 0.124 0.133 0.088 0.000 0.088 0.109 0.099 0.025 0.097 0.135 0.126 0.109

Pt-C (Å) ext Hu¨ckel shortest longest 0.622 0.652 0.675 0.615 0.000 0.210 0.283 0.257 0.069 0.651 0.684 0.655 0.622

1.832 1.842 1.861 1.883 1.996 1.927 1.927 1.927 1.996 1.887 1.864 1.843 1.832

3.325 2.964 2.704 2.420 1.996 2.455 2.750 3.017 1.996 2.423 2.706 2.964 3.325

C-C (Å)

tilt angle, θ (deg)

1.845 1.842 1.837 1.793 1.470 1.513 1.534 1.528 1.488 1.817 1.844 1.842 1.845

0 14 14 10 -1 -3 13 9 1 -11 -15 -15 0

a Sites refer to numbered positions in Figure 1. The “total” energy includes two-body repulsions, which are not included in the “ext. Hu¨ckel” results. The “shortest” and “longest” Pt-C distances refer to the three Pt atoms nearest the metal-bonded C of ethylidyne. The tilt angle describes the bending of the C-C bond away from the surface normal.

geometry as the energy zero value. The calculated potential energy at the hcp site is less stable by only 0.025 eV, which happens to be near kT at room temperature. Although this preference for the fcc hollow is consistent with experiment, such small numerical differences within our model are not significant and imply no real distinction between the two sites. The calculated preferred relative orientation of the methyl group in both cases is the staggered conformation with respect to the underlying three platinum atoms of the surface (i.e. the C-H bonds projected onto the surface point toward nearest bridge sites). The 2-fold bridge position, a saddle point in the three-dimensional potential energy surface of the Pt(111)p(2×2)-CCH3 chemisorbed system, lies 0.109 eV higher than the fcc hollow site (actually, the saddle point need not lie exactly on the geometrical bridge site, because of the slight asymmetry between fcc and hcp hollow sites on either side). The instability derives from the lesser cooperative bonding of two Pt atoms with the ethylidyne frontier orbitals e and a1 (for details see ref 8), at a distance of 1.927 Å from the first carbon atom of ethylidyne. The bonding at the fcc hollow site, on the other hand, is stronger. Three platinum atoms at a distance of 1.996 Å from CCH3 cause a 0.719 overlap population (OP) between ethylidyne and the surface. (The corresponding OP for the bridge site is 0.631). The weakening and therefore elongation of the C-C bond at the bridge site (1.534 Å) is also an important factor; the C-C OP at the bridge site is 0.698 vs 0.819 at the fcc site (where C-C ) 1.470 Å). Our results for the sites away from both 3-fold sites, toward the top sites (points 0-3 and 9-12 in Figure 1), are practically symmetrical about the bridge site and they show a tendency toward dissociation of ethylidyne, which however does not take place in reality. The C-C distances range between 1.793 and 1.845 Å, indicating extensive weakening of C-C bonding. The Pt-C bonds, on the other hand, while shorter than at the other sites, stay within a reasonable distance range of 1.832-1.883 Å. The C-C overlap populations at these sites range between 0.322 and 0.370 and so remain significant. For comparison, the overlap population of C-C of an isolated ethylidyne species with C-C distance of 1.490 Å is 0.772, whereas with C-C ) 1.845 Å the OP is reduced to 0.388. The C-C overlap population goes down to 0.003 when the C-C bond is two times longer than 1.845 Å.

4. Optimized Adsorption Geometries and Surface Diffusion The geometric optimizations of ethylidyne along the path of Figure 1 resulted in the one-dimensional potential energy profile shown in Figure 2 (also listed in column 2 of Table 2). As mentioned before, the energetically most favorable site for ethylidyne to bind on Pt(111) is the fcc 3-fold hollow site, with the hcp site being almost as favorable; the fcc site is preferred over the hcp by only 0.025 eV. The activation energy for the translational motion inbetween these two sites is only 0.109 eV, equal to the instability of the 2-fold bridge site relative to the fcc optimized position. The top site, which has about the same energy as the bridge site, is surrounded by a rim about 0.135 eV above the fcc hollow site (i.e. about 0.024 eV above the top site which forms the bottom of a crater). For reasons to be discussed below, we expect this top site energy to be an underestimate, i.e. too favorable. But on the basis of these values and considering low coverages, i.e. no intermolecular interactions, ethylidyne will at nonzero temperatures primarily occupy fcc and fewer hcp sites, and a very occasional top site. Diffusion between hollow sites over the on-top sites is thus less likely than over the bridge sites near room temperature (kT ∼0.025 eV). As a result, given thermal energy, ethylidyne most likely diffuses along the Pt(111) surface in a zigzag fashion, passing alternate 3-fold fcc and hcp positions, but residing longest near fcc hollow sites. On the basis of these results, if ethylidyne moieties did approach top sites, they would very nearly dissociate into adsorbed carbon atoms and free methyl groups. However, this is not observed experimentally. The energy values near this top site, which entails 1-fold Pt-C coordination, are likely to be rather higher in reality. The source of these low values is the calculation of much smaller twobody repulsion energy terms for all positions near the top sites. These are lower by about 0.5 eV relative to the repulsion energy values for the sites between the two 3-fold sites. This is because the two-body repulsive energy is calculated in an additive way, irrespective of the number of bonds on the atom center. To clarify, the repulsion that is calculated for one Pt-C bond in our system does not depend on the coordination of the site, i.e. the existence or not of other Pt-C bonds on the same Pt atom. So, for the same Pt-C bond distance, three different top Pt-C bonds contain the same repulsion energy as three Pt-C bonds within the same 3-fold hollow. This illustrates the relative exaggeration of the calculated repulsion at the fcc and hcp sites. If we omit the two-body repulsions, the energy barrier for diffusion toward the top sites would be 0.675 eV, the energy of point 2 in Figure 1 relative to the extended Hu¨ckel energy of the fcc site (without including the two-body repulsion energy). The relative extended Hu¨ckel energy values for all sampled points in Figure 1 are listed in the third column of Table 2. The energy differences exhibit the same trends but are relatively small compared to those calculated earlier by Minot et al.:29 the earlier and present values (taking those in the third column of Table 2, since the earlier Minot values included no repulsions) are, respectively, 0.00 vs 0.00 eV on fcc sites (equal by definition), -0.02 vs 0.069 eV on hcp sites, 0.68 vs 0.283 eV on bridge sites, and 2.39 vs 0.622 eV on top sites. The differences between the earlier and present values are due to our extensive optimizations of extended Hu¨ckel and structural parameters and our charge iterations for the Pt Hii, parameters. To obtain the two-dimensional energy profile of eth(29) Minot, C.; Van Hove, M. A.; Somorjai, G. A. Surf. Sci. 1983, 127, 441.

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Figure 2. Potential energy profile of ethylidyne moving along the path shown in Figure 1 on Pt(111). The energy is set to zero at the fcc hollow site.

5. Conclusions

Figure 3. Three-dimensional potential energy surface of the Pt(111)-p(2×2)-CCH3 adsorbate system. The x- and y-axes corresponds to the [-101] and [1-21] crystallographic directions on Pt(111), respectively.

ylidyne on Pt(111) across the entire surface, shown in Figure 3, we interpolated the relative energy results (including the two-body repulsions) shown in Figure 2, together with the corresponding energy value for one other position halfway between a top site and a bridge site nearest to it, using the point group symmetry of the adsorbate system. One can clearly see the saddle points on the bridge sites and the higher, almost 6-fold symmetrical barriers around the top sites. Diffusion at low coverages would primarily occur over these bridge sites between adjacent hollow sites (whether fcc or hcp). At higher coverage, such diffusion could occur to the extent that intermolecular interactions allow it. This requires either vacancies or bending away of the ethylidyne molecules (as discussed by Anderson et al.6). Concerted diffusion of several molecules, while in principle possible, in practice seems unlikely because of higher energy and space requirements: several molecules need extra energy simultaneously to surmount the energy barriers, while there is a need for a patch of bare metal surface for this group to move onto.

We have modeled the adsorption of ethylidyne on Pt(111) with extended Hu¨ckel calculations that incorporate empirical modified bond-specific interaction parameters, which should be appropriate for a variety of other hydrocarbon species on Pt(111). This results in favored adsorption on the fcc 3-fold hollow sites, as also found experimentally.15 The hcp hollow site is calculated to be only slightly less favorable. By modeling diffusion through simultaneous and parallel motion of a complete 0.25 monolayer of adsorbed ethylidyne, we calculate an energy barrier of 0.109 eV for the diffusion of ethylidyne from the 3-fold fcc hollow site over a bridge site to the nearest hcp hollow site on Pt(111). Diffusion toward the top sites would require overcoming an energy barrier of at least 0.133 eV to reach the top sites with an adsorption energy of 0.109 eV (these latter two energy values are likely to actually be rather larger by an amount on the order of 0.5 eV). Thus, we conclude that ethylidyne at low coverages diffuses along the platinum surface in a zigzag fashion from one hollow site to its nearest neighbors across bridge sites. At higher coverages, diffusion would require vacancies or tilting out of the way of the nearby molecules. This same mechanism would open up space between ethylidyne molecules and thus allow ethylene to approach the metal from the gas phase and subsequently hydrogenate in the presence of preadsorbed hydrogen, confirming Anderson’s conclusions on this point.6 Furthermore, this suggestion is strongly supported by the recent results of Cremer et al.13 showing π-bonded ethylene being coadsorbed with ethylidyne on the Pt(111) surface during ethylene hydrogenation. An important result of this work is the determination of suitable pairs of κ and δ values within the extended Hu¨ckel extended structure calculations. These bondspecific κ and δ parameters corresponding to the Pt-C, C-C, and C-H interactions resulted in the preservation of the chemical nature of ethylidyne during the diffusion on the metal surface (as long as the coordination number does not change radically). The parameters κ and δ also have a more general value, far beyond the ethylidyne case,

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and should allow the realistic simulation of a wide variety of surface reaction intermediates that contain Pt-C, C-C, and C-H bonds. Similar interaction models for other main elements (e.g. O, S, N) and transition metals can be obtained in the same fashion. This modeling can thus be extended to many more types of surface reactions and catalysts. Required is prior knowledge of representative adsorption structures to fit the parameters. A limitation of this approach is that, apparently, such bond-specific empirical parametrization may not in general be transferable between geometries with highly differing coordination numbers (as from 3-fold hollow to 1-fold top site here). On the other hand, the relative energies obtained by this method are meaningful for qualitative studies of relative stabilities of and diffusion between not-too-dissimilar adsorption sites, since they are obtained by fitting to a known geometry rather than an experimental energy. Acknowledgment. We are grateful for insightful discussions with Mr. M. Quinlan, Dr. A. Barbieri, Mr. N. Materer, Dr. A. Kyrlidis, and Mr. P. Cremer. Acknowledgment is also made to Dr. A. Schach von Wittenau for assistance at the early stage of this work. The main support for this work was provided by the Advanced Industrial Concepts Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. Z.N. especially thanks Dr. Y.-T. Wong for the initial modifications to and support of the original extended Hu¨ckel extended structure codes, originating from Dr. Roald Hoffmann’s group at Cornell University.

Nomikou et al. Table 3. Extended Hu 1 ckel Parameters Used in All Calculations atom

orbital

Hii(eV)

ζ1

ζ2

C1a

C1a

H C

1s 2s 2p 6s 6p 5d

-13.60 -21.40 -11.40 -9.10 -5.49 -12.62

1.30 1.62 1.62 2.55 2.55 6.01

2.70

0.63

0.55

Pt

a

Coefficients used in the double-ζ expansion of the d Slater orbitals.

Appendix One of the very familiar flaws of the non-self-consistent extended Hu¨ckel method is the exaggeration of electron transfer. Therefore, we performed a charge iteration on the valence-state ionization energies (Hii) of the 6s, 6p, and 5d orbitals of Pt. We assumed a quadratic dependence on charge of the metal Hii.30 As in all calculations in this paper, the metal surface was represented by a three-layer slab consisting of 12 Pt atoms, and ethylidyne was placed on top of the center of an fcc hollow site, at a distance of 1.210 Å from the surface when the charge iteration was performed (with a C-C bond length of 1.490 Å). The metal charge distribution reached self-consistency when the Hii obtained the values listed in Table 3. The amount of charge shifted from ethylidyne to the platinum surface for the configuration just described was calculated to be 0.278 of an electron charge. LA9503921 (30) McGlynn, S. P.; Vanquickenborne, L. G.; Kinoshita, M.; Caroll, D. G. Introduction to Applied Quantum Chemistry; Holt, Rinehart and Winston, Inc.: New York, 1972; Appendix D, pp 138-139.