J. Phys. Chem. B 2000, 104, 6439-6446
6439
Density Functional Theory Calculations on the Interaction of Ethene with the {111} Surface of Platinum Graeme W. Watson,*,† Richard P. K. Wells,‡ David J. Willock,‡ and Graham J. Hutchings‡ Department of Chemistry, Trinity College, Dublin 2, Ireland, and Department of Chemistry, UniVersity of Wales, Cardiff, P.O. Box 912, Cardiff, CF10 3TB, U.K. ReceiVed: February 10, 2000; In Final Form: April 4, 2000
We have performed density functional theory calculations on the adsorption of ethene onto the {111} surface of platinum. We find that the adsorption energy is sensitive to the k-point sampling used, with low k-point sampling giving rise to overestimated adsorption energies, close to the values predicted from small cluster calculations. Six adsorption modes (bridge, fcc hollow, hcp hollow, atop bridge, atop hollow, and cross bridge) were investigated on a rigid Pt {111} surface. The most stable site was the bridge site (di-σ type adsorption) with an adsorption energy of 108.7 kJ mol-1 and C-C bond length of to 1.483 Å, which is significantly longer than the calculated gas-phase ethene bond length of 1.334 Å. The recently proposed fcc hollow site adsorption was found to be significantly less stable (63.6 kJ mol-1) although slightly more favorable than the atop (π adsorbed) modes. The effect of surface relaxation on the adsorption energy and structure was investigated by allowing the entire Pt {111} slab to relax, giving rise to large changes in the positions of the coordinating Pt atoms. The bridge site shows displacements of 0.235 Å out of the surface for the two Pt atoms directly coordinated to the ethene C atoms with an increase in the adsorption energy of 18.6 kJ mol-1 compared to the rigid surface case from 108.7 to 127.3 kJ mol-1. The effect of Pt relaxation was greatest on the atop sites with the single Pt atoms coordinated to the ethene moving 0.356 Å out of the surface for both adsorption modes. This was accompanied by an increase of the adsorption energy of 26 kJ mol-1 with the atop bridge (85.8 kJ mol-1) slightly more stable than the atop hollow (84.8 kJ mol-1). The hollow sites were affected by surface relaxation so much so that the energetic order of the atop and hollow sites is reversed when surface relaxation is included, indicating that the latter are unlikely to be observed. We conclude that the large effect of both the k-point sampling and surface relaxation on the adsorption energy is based on a compromise between the extended electronic states and localized bonding. The effect of periodic calculations with converged k-point sampling is to accurately treat the repulsion between the extended electronic states and the molecule. The effect of surface relaxation is to allow the atoms involved in localized bonding to move out of the surface, reducing the repulsion due to the extended electronic states and so increasing the adsorption energy. As such, the use of cluster calculations, especially for molecules with weak interactions with the surface, would be expected to result in significant overestimation of the adsorption energies.
Introduction The adsorption of hydrocarbons onto the surfaces of transition metals is a subject of great interest to workers in both surface science and catalysis due to its importance in many catalytic processes, e.g., hydrogenation/dehydrogenation and isomerization. The electronic interaction of alkenes with the surface will play a role in the bonding of reactants to the surfaces of the catalyst. Because of this, the adsorption of ethene has been used as a model system and has been studied extensively on a variety of transition metals using a broad range of methods. In this study we focus on the most stable surface of platinum, the close-packed {111}, for which the adsorption of ethene is well characterized experimentally.1 Below 50 K ethene is physisorbed on the {111} surface with the C-C bond parallel to the surface.2 The molecule interacts weakly with the surface through the electron density of its π bond, and so this adsorption * Corresponding author: Tel +353 (0)1 608 1357; e-mail
[email protected]. † Trinity College. ‡ University of Wales.
mode is usually referred to as π bonded ethene. Above about 60 K the ethene molecule becomes chemisorbed, which is considered to occur via the breaking of the π bond resulting in a single C-C bond and the carbon atoms attaining an sp3-like hybridized geometry. This is often considered to occur due to the formation of two Pt-C σ bonds, and this adsorption mode is therefore usually referred to as di-σ bonded ethene. In practice this is an oversimplification and the adsorption modes can vary from π to di-σ. Experimentally the adsorption modes are characterized by the vibrational frequencies of the adsorbed molecule, from which the Pt-C bonding character is inferred.3 As the π bond is weakened by interaction with the metal surface, the carbon atoms attain a geometry closer to sp3 which is accompanied by a characteristic lowering of the frequency of the CH2 symmetric stretching mode.4 Above about 240 K the di-σ bound molecule dehydrogenates at the surface forming an ethylidyne species which can also be identified using vibrational spectroscopy.1 Because of the reactivity of ethene on the Pt {111} surface it is very difficult to obtain the activation energy for desorption
10.1021/jp000541a CCC: $19.00 © 2000 American Chemical Society Published on Web 06/16/2000
6440 J. Phys. Chem. B, Vol. 104, No. 27, 2000 using temperature programmed desorption methods (TPD). TPD studies5 indicate an activation energy for desorption of between 37.6 and 71.4 kJ mol-1, which is low when compared to the collision-induced desorption study of Szulczewski and Levis,6 which indicates a well depth of 202.6 kJ mol-1. The conclusion from these studies is that thermally induced desorption is a multistage process involving breaking of the Pt-C bonds separately to leave a π bonded species which then desorbs. The energetics from the collision-induced desorption study will thus provide a better comparison to calculated adsorption energies, although, because these measurements represent the activation energy for desorption in a single step, they will provide only an upper limit of the adsorption energy. More recently microcalorimetric studies have been carried out to measure directly the adsorption energy of ethene on Pt{111},7 Pt{110},8 and Pt powders.9,10 Initial adsorption on the Pt {111} is attributed to ethylidyne formation with an energy of 174 kJ mol-1. However, because the experiment was carried out at 300 K no other species were observed. On the Pt {110} surface a di-σ type adsorption was assigned an adsorption energy of 136 kJ mol-1 and π adsorption 120 kJ mol-1. On Pt powders at 300 K ethylidyne was formed, but at 173 K an adsorption energy of 120 kJ mol-1 was obtained corresponding to a mixture of di-σ and π adsorbed ethene. Investigations of the structure of the di-σ adsorbed molecule have been made using electron energy loss spectroscopy (EELS),11 ultraviolet photoelectron spectroscopy (UPS),12 and near edge X-ray absorption fine structure spectroscopy (NEXAFS).13,14 These all indicate a simple adsorption mode in which the ethene carbon atoms coordinate to separate single Pt atoms in a bridge-type configuration. The C-C bond was shown to be parallel to the surface with a bond length of approximately 1.50 Å, which is significantly closer to that of gas-phase ethane (1.541 Å) than ethene (1.337 Å). However, a recent diffuse low energy electron diffraction (LEED) study indicated15 that the adsorption of a disordered di-σ layer at 200 K resulted in the molecule being tilted by approximately 12° with respect to the surface. The molecule was found to preferentially adsorb on the fcc hollow site with a C-C bond length of 1.56 ( 0.5 Å. However, the uncertainty in the atom positions in this study was large, and it is not clear if this adsorption mode is realistic. Computer simulation has also been applied to ethene adsorption on platinum. Extended Huckel theory16,17 and the atom superposition and electron delocalization molecular orbital methods18 have been used to show that a di-σ type adsorption to two metal sites is favored over π adsorption on a single metal site. All of the studies predicted significant distortion of the molecular structure. These methods, however, are not reliable for absolute adsorption energies, and predicted values range from 56 to 197 kJ mol-1. Density functional theory studies have also recently been applied to ethene on Pt {111}. Watwe et al.19 performed a cluster study using the B3LYP exchange and correlation functional in which a 10-atom cluster was used to represent the surface. They calculated a number of adsorption modes for ethene with energies of 149 and 103 kJ mol-1 for di-σ and π modes. This is substantially greater than the periodic calculations of Ge and King20 who employed a plane wave basis set with norm conserving pseudopotentials and the Perdew-Wang exchange and correlation energy. They obtained adsorption energies of 121.8 and 53.4 kJ mol-1 for the same species. This may be a consequence of the cluster approach of Watwe et al. in which the ethene interacted directly with Pt atoms from the cluster edge. These atoms are likely to be more reactive than those of
Watson et al.
Figure 1. Schematic illustration of the six adsorption modes investigated: (a) cross bridge, (b) atop-bridge, (c) bridge, (d) atop-hollow, (e) fcc hollow, and (f) hcp hollow.
an extended {111} crystal surface and so are not a good a representation of the surface. This is also indicated by more recent calculations by Watwe10 in which a 19-atom cluster was used, giving adsorption energies of 116 and 71 kJ mol-1 for the di-σ and π adsorbed species. We have employed periodic density functional theory (DFT) to study the structure and energetics of the adsorption of ethene on the {111} surface of platinum. This method has shown considerable success in recent years in the study of molecular adsorption onto metal surfaces including the adsorption of H2,21,22 CO,23,24 NO,25,26 O2,27 and CH428 and C2H4.20 Computational Method Our calculations have been performed using the DFT method, as implemented in the code VASP (Vienna Ab initio Simulation Program).29,30 Six adsorption modes of ethene have been considered and are shown in Figure 1. The modes are labeled cross bridge, atop-bridge, bridge, atop-hollow, fcc hollow, and hcp hollow. The {111} surface of platinum was represented using the slab methodology in which a slab of material is generated by introducing a vacuum gap perpendicular to the surface in a 3-dimensional periodic cell (Figure 2a). In this study we have employed a p(2 × 2) surface unit cell 3 platinum layers thick with a vacuum gap of 9.2 Å. When ethene is adsorbed onto the surface this gives rise to a nearest intermolecular H-H distance of around 3 Å and is the same surface converge as used in the study by Ge and King.20 For example, the atopbridge mode has intermolecular H-H distances of 3.06 and 3.16 Å and is shown Figure 2b. The adsorption energy (Eads) is calculated by comparing the energy of the adsorbed molecule (Eadsorbate/surface) with that of
Interaction of Ethene with the {111} Surface of Platinum
J. Phys. Chem. B, Vol. 104, No. 27, 2000 6441
Figure 2. Periodic cell showing the slab method for simulating surfaces. (a) Illustration of the vacuum gap and the periodic array of slabs resulting in two surfaces. (b) Plan view of the periodic array of ethene images generated by the p(2 × 2) cell.
the free surface (Esurface) and gas-phase molecule (Eadsorbate) using
Eads ) -(Eadsorbate/surface - (Esurface + Eadsorbate))
(1)
The adsorption energy is therefore the heat evolved on adsorption and will be positive for exothermic adsorption. Within our DFT calculations the exchange and correlation energies are described using the generalized gradient approximation (GGA) with the parameterization of Perdew et al.31 The calculations are carried out with periodic boundary conditions allowing the expansion of the crystal wave functions in terms of a plane wave basis set. The use of a plane wave basis set has a number of advantages. The forces on the atoms can be calculated simply using the Hellmann-Feynman theorem and are used to perform a conjugate gradient or quasi-Newton relaxation. In addition the plane wave basis set does not suffer from basis set superposition error (BSSE). This error is introduced into localized basis set calculations when a molecule can lower its energy by representing its electron density using basis set functions assigned to another molecule (or the surface). In that case the comparison of a gas phase molecule with a surface adsorbed molecule will introduce errors due to changes in basis set as a function of the atom positions. When using plane waves, the basis available to the molecule is the same in the gas phase and in the adsorbed state, as it is dependent only on the cell volume and the plane wave kinetic energy cutoff and thus no BSSE errors occur.
The number of plane waves required to represent the oscillations of the valence orbitals near the atomic cores is prohibitive. To reduce the computational cost we have used ultrasoft pseudopotentials,32,33 allowing us to employ a plane wave cutoff of 300 eV. The phase combinations of the orbitals within adjacent unit cells (the extended electronic states) were represented by the introduction of phase factors into the wave functions at a series of k-points in reciprocal space. The k-points were obtained using the Monkhurst-Pack34 scheme with convergence of the total energy with respect to k-point sampling accelerated using second-order Methfessel-Paxton smearing35 with a width of 0.1 eV. Effect of k-Point Sampling. Summation over k-points allows the band structure of the extended surface to represent, using a relatively small real space unit cell, a factor which is absent in the alternative cluster approach. Previous calculations of ethene adsorption on copper {111}36 show that this can have a large effect on the energy and molecular conformation of the adsorbed molecule. We have therefore carried out test calculations on one adsorption mode, the bridge site, to establish the k-point density required. Figure 3 shows the adsorption energy as a function of the n × n × 1 k-point grid; sampling perpendicular to the surface is unnecessary as the electronic states are not coupled through the vacuum gap. These calculations indicate that although ethene adsorption on Pt {111} is not as sensitive to k-point sampling density as adsorption on Cu {111}, a significant effect is still observed on the predicted adsorption
6442 J. Phys. Chem. B, Vol. 104, No. 27, 2000
Figure 3. Bridge adsorption energy as a function of k-point grid.
energy. The effect on the conformation of the molecule is much less pronounced than that previously observed for Cu {111}. In this study we have used a k-point sampling of 9 × 9 × 1 which converges the adsorption energy to within approximately 3 kJ mol-1. If we compare these results with the previous DFT calculations from the literature we find that the 10 atom cluster calculation18 with an adsorption energy of 149 kJ mol-1 is in closer agreement with our poorly converged 1 × 1 × 1 k-point calculation which also gives 149 kJ mol-1. The larger 19-atom cluster10 gives rise to an adsorption energy of 116 kJ mol-1, which is much closer to our calculations at high k-point sampling (108.7 kJ mol-1 for a 9 × 9 × 1 grid) and the previous periodic calculations of Ge and King20 (107.3 kJ mol-1). The effect of cluster size on the predicted adsorption energy has been noted before. For example, van Daelan et al.37 examined the effect of cluster size on the adsorption of NO on Cu {111}. They found an adsorption energy of 38 kJ mol-1 for a 5-atom cluster, reducing to 5.9 kJ mol-1 for a 10 atom cluster and increasing again to 18.0 kJ mol-1 for a 43 atom cluster. Thes calculations on k-point dependence presented here illustrate an important contribution to the error which arises from an incorrect treatment of the metal band structure. This results in cluster calculations being in good agreement with periodic calculation with a single k-point. Additional errors will be introduced into cluster calculation because of binding to metal atoms with lower coordination than would be expected for the surface which will also increase the binding energy due to the more reactive nature of edge atoms. This will be offset by relaxing the cluster which will reduce the reactivity of the edge atoms but will result in metal-metal distances that are not typical of the metals surface. This means that if calculations are to be compared directly with the results of surface science experiments or catalytic data obtained using large metal particles (in the context of the clusters simulated), great care must be taken when using the cluster approach. The cluster size may have significant effects on the adsorption energy, although if the results are compared to data obtained from very small, nanoscale, metal particles then the cluster approach may be the most appropriate method. Adsorption of Ethene to the {111} Surface of Platinum Table 1 shows the adsorption energy and geometric data for the six adsorption modes investigated. The C-C bond length is used as a measure of the activation of the molecule as this indicates the degree of double bond character. This is expected to vary from the calculated gas-phase ethene double bond of 1.334 Å to the calculated value of a single bond in gas-phase ethane 1.527 Å. Both of these extremes are in excellent agreement with experimental values of 1.337 and 1.541 Å.38
Watson et al. Associated with the change from double to single bond character is a change in the planar nature of the molecule that we monitor using the angle between the C-C bond and each of the CH2 planes (the C-CH2 angles). This indicates the degree of distortion away from the planar structure and should range from 180.0° for gas-phase ethene to 128.1° for gas-phase ethane. This distortion is accompanied by a change in the C-C-H bond angle, which is associated with the change from sp2 to sp3 hybrid geometries of the carbon atoms. The C-C-H bond angles take values of 122.2° for ethene reducing to 111.5° for ethane. The final structural parameter is the Pt-C distance and is used as a measure of the strength of the interaction between the molecule and the surface atoms. The cross bridge site is clearly much less stable than the other modes with an adsorption energy of only 9 kJ mol-1. The large Pt-C distances and close-to gas-phase angles and C-C bond length indicate that the interaction between the surface and the cross bridge molecule is very weak. The two π adsorbed modes (atop-bridge and atop-hollow) have adsorption energies (59.9 and 58.8 kJ mol-1) and structures very similar to the atop-bridge shown in Figure 4a. For atop-bridge and atop-hollow there is significant extension of the C-C bond length increasing from 1.334 to 1.399 and 1.398 Å, respectively. This is accompanied by a distortion away from the planar nature of the ethene molecule toward sp3 hydridized carbon. Although these results indicate significant activation and distortion of the molecule, the structural parameters are still closer to ethene than ethane indicating that the molecule contains an activated double bond rather than a di-σ type interaction. An interesting feature of the π adsorbed modes is that the adsorption energies and structures are almost identical. This indicates that the interaction is almost exclusively with the single metal center and suggests that the adsorption of ethene on atop sites on other Pt surfaces will be similar. The slight modification due to the Pt atoms other than the one directly interacting with the carbon atoms can be seen by the slight inequivalence of the carbons of the atop-hollow. The platinum-carbon distances of 2.278 Å (hcp) and 2.274 Å (fcc) indicate the small difference in the interactions with the hcp and fcc hollow sites at either end of the molecule. Adsorption at either of the two hollow sites gives similar adsorption energies and structures, and the fcc hollow site adsorption mode is shown Figure 4b. These modes are slightly more stable than the atop sites with adsorption energies of 61.5 and 63.5 kJ mol-1 for the hcp and fcc sites, respectively. Unlike any of the other adsorption modes, the molecules are tilted with respect to the surface by 2.6° for the hcp site and 3.3° for the fcc site. The C-C bond elongation was larger than in the case of the atop sites with bond lengths of 1.453 and 1.454 Å for fcc and hcp hollow sites, respectively. This was accompanied by a much more pronounced distortion of the molecular plane than the atop case, indicating a more di-σ like adsorption mode. This distortion was also significantly asymmetric with the end of the molecule coordinated to a single metal center having a shorter Pt-C distance (2.217 and 2.122 Å for fcc and hcp, respectively) and a greater distortion of the molecule toward sp3-type hybridization (C-CH2 angles of 140.8° and 140.7° for fcc and hcp). The end of the molecule coordinated to two surface Pt atoms has longer Pt-C distances (2.496 and 2.482 Å for hcp and fcc) and a smaller distortion of the C-CH2 angle (146.2° and 145.6° for hcp and fcc) but still significantly greater than that observed for the atop sites. Adsorption at the bridge site (Figure 4c) results in a significantly more stable structure than the other modes with an adsorption energy of 108.7 kJ mol-1. This strong interaction
Interaction of Ethene with the {111} Surface of Platinum
J. Phys. Chem. B, Vol. 104, No. 27, 2000 6443
TABLE 1: Adsorption Energies and Structural Parameters for the Adsorption of Ethene to a Bulk Terminated {111} Surface of Pta property adsorption energ C-Cb C-Hb C-CH2 angleb C-C-H angleb Pt-Cb
gas-phase ethene
gas-phase ethane
cross bridge
atop (hollow)
atop (bridge)
hcp (hollow)
fcc (hollow)
bridge
1.334 1.099 180.0 122.2
1.527 1.098 128.1 111.5
9.0 1.334 1.089 179.5/179.4 121.6/121.6 3.735/3.763
58.8 1.398 1.089 160.5/160.2 119.9/119.9 2.278/2.274
59.9 1.399 1.089 160.5 120.2 2.275
61.5 1.453 1.094/1.098 140.7/146.2 115.1/ 117.9 2.217/2.496
63.6 1.454 1.094/1.099 140.8/145.6 115.1/117.9 2.122/2.482
108.7 1.483 1.095 138.2 121.6 2.144
b
a In cases where the two carbon atoms are inequivalent two numbers are quoted. For cross-bridge and atop-hollow adsorption modes, the first number refers to the carbon atom closest to the hcp hollow site and the second to the carbon atom closest to the fcc hollow site. For the hcp (hollow) and fcc (hollow) adsorption modes, the first number refers to the carbon atom coordinated to a single Pt atom and the second to the carbon atom bridging two Pt atoms. b Adsorption energies are given in kJ mol-1, distances are give in Å, and angles in degrees.
Figure 4. Structure of the (a) atop-bridge, (b) fcc hollow, and (c) bridge site adsorption modes of ethene on a rigid {111} surface of Pt.
between the surface and the molecule is also shown by this adsorption mode having the shortest Pt-C distances of 2.144 Å. There was also a large expansion of the C-C bond to 1.483 Å which is significantly closer to the bond length in ethane than ethene. This indicates the di-σ nature of the bonding and a significant reduction in the double bond character. This di-σ type interaction is accompanied by a distortion of the molecule toward the ethane configuration with a C-CH2 angle of 138.2° and C-Pt interactions taking up the additional coordination sites for each C atom. The C-C-H angle is actually closer to ethene that ethane, probably due to the asymmetry of the bonding around the carbon atom (2 × C-H, 1 × C-C and 1 × C-Pt), indicating that this simple bond angle is a poor measure of the type of adsorption mode. Effect of Surface Relaxation The results presented so far have all been obtained using a fixed Pt surface. In this study we have extended the simulations by repeating the calculations allowing the full relaxation of the molecule and all of the atoms in the Pt {111} slab. The reference state for the adsorption energy is now a fully relaxed Pt slab that has an interlayer spacing of 2.32 Å compared to the calculated bulk spacing of 2.30 Å. This expansion of 0.9% is in good agreement with LEED experiments,39 which indicated an expansion from 2.26 to 2.28 Å (0.9%) for the surface layer of a Pt {111} single crystal. For each of the adsorption modes an ethene molecule was placed on the relaxed surface in a geometry similar to that obtained for the fixed surface case. Geometry optimization of all the atomic positions was then performed, and the resulting adsorption energies and structures are given in Table 2. The effect of surface relaxation on the cross bridge site is minimal. The interaction with the surface without surface relaxation was very weak, and no significant changes to the energy or geometry were observed.
The π adsorbed modes, however, have been significantly stabilized. The atop-bridge is still slightly favored with an adsorption energy of 85.8 kJ mol-1, an increase of 25.9 kJ mol-1 (43%) compared to the fixed surface. The molecular structure has changed only slightly with a small increase in the C-C bond length and thus a small increase in the activation of the molecule. The most significant change is in the surface Pt layer. The Pt atom directly coordinated to the molecule relaxes 0.36 Å out of the surface toward the molecule as shown by Figure 5a. This causes a rumpling effect with the rest of the surface layer contracting and results in a smaller interlayer spacing than that observed for the reference surface state and the bulk crystal. The movement of the surface Pt atoms shows that some repulsion occurs between the molecule and the surface, which is relieved by the directly coordinated Pt atom moving out the surface. In addition this movement reduces the effective density of the surface layer and appears to allow a reduction in the strain of the surface by relaxing toward the bulk. A similar picture (see Table 2) is found for the atop-hollow with an increase in the adsorption energy of 26.0 kJ mol-1 (44%). The effect of surface relaxation on the hollow sites is less significant than on the atop sites. The adsorption energies are increased by 15.6% and 17.5% to 71.1 and 74.7 kJ mol-1 for the hcp and fcc sites, respectively. This results in the atop sites having a larger binding energy than the hollow sites, indicating that the hollow site adsorption geometries are unlikely to be observed. There is also less effect on the structure of the surface (see Figure 5b). The Pt atoms move significantly but their displacement is much smaller than in the case for atop adsorption. The asymmetry of the molecule is still present with the degree of molecular distortion similar to that obtained without surface relaxation. The end of the molecule coordinated to two Pt atoms, which was the end with least distortion when using a fixed surface, has reduced its C-CH2 angle. This results in an increase in the distortion of this end of the molecule, away from the planar ethene conformation and reducing the asymmetry. This is due to the movement of the two coordinated surface Pt atoms away from each other, allowing the carbon atom to move closer to the surface. The single coordinated Pt-C distance reduces by a greater amount resulting in an increase of the tilt angle of the C-C bond with respect to the surfaces from 2.6° to 4.1° for the hcp hollow site and from 3.3° to 5.2° for the fcc hollow site. The bridge site was still the most stable and has been stabilized by 18.6 kJ mol-1 (17%) giving rise to an adsorption energy of 127.3 kJ mol-1. Once again this has led to a small increase in the C-C bond length and a small increase in the molecular distortion compared to the fixed Pt surface results. The movement out of the surface by the Pt atoms is less than for the atop modes, due to direct interaction of each carbon
6444 J. Phys. Chem. B, Vol. 104, No. 27, 2000
Watson et al.
TABLE 2: Adsorption Energies and Structural Parameters for the Adsorption of Ethene to a Fully Relaxed {111} Surface of Pta property adsorption energy C-Cb C-Hb C-CH2 angleb C-C-H angleb Pt-Cb ∆Ζ Ptb Pt interlayer spacing
gas-phase ethene
gas-phase ethane
cross bridge
atop (hollow)
atop (bridge)
hcp (hollow)
fcc (hollow)
bridge
1.334 1.099 180.0 122.2
1.527 1.098 128.1 111.5
9.2 1.334 1.089 179.5/ 179.5 121.6/121.6 3.771/3.739
84.8 1.409 1.089 160.0/160.0 120.0/120.0 2.184/2.189 0.356 2.249
85.8 1.410 1.089 160.2 120.2 2.187 0.356 2.249
71.1 1.460 1.094/1.100 139.8/143.9 114.9/117.4 2.112/2.448 0.181/0.143(x2) 2.230
74.7 1.459 1.094/1.102 140.1/143.3 115.0/117.5 2.103/2.425 0.190/0.162(x2) 2.218
127.3 1.485 1.096 138.1 112.1 2.117 0.235(x2) 2.238
a In cases where the two carbon atoms are inequivalent the two values are ordered in the same manner as described for Table 1. b Adsorption energies are given in kJ mol-1, distances are give in Å, and angles in degrees.
1 and 2 coordinated structures of the hollow sites reduce the relaxation that can occur. Barrier to Bridge Adsorption
Figure 5. Structure of the (a) atop-bridge, (b) fcc hollow, and (c) bridge site adsorption modes of ethene on the {111} surface of Pt with full surface relaxation using ball-and-stick and space filling representations. Structural parameters are given in Å and energies in kJ mol-1, with the values in brackets those obtained with a fixed surface for comparison.
with a separate surface Pt atom, although it is still significant (0.24 Å) as show by Figure 5c. The displacement is greater than in the case of the hollow sites, indicating that the mixed
Experimental observations show that π adsorbed ethene forms below 50 K on the {111} surface of Pt and that this transforms to a di-σ mode on heating above 50 K. These observations indicate that, although the di-σ mode is more stable, direct adsorption is not possible, at least below 50 K. Direct adsorption into the π adsorbed mode must be occurring at low temperature with a barrier to transformation to the di-σ mode preventing the di-σ from forming. To understand in more detail we have conducted barrier calculations for the direct adsorption of ethene into the π (atop-bridge) and di-σ (bridge) adsorption modes using the elastic band method.40 In this method fixed start and end points are obtained from relaxed calculations (e.g., gasphase molecules and the adsorbed molecule). A series of structures are then obtained from the start structure to the final structure (usually from a linear interpolation), and these are used in a parallel computer simulation with the end points fixed. The calculations are performed within the constraint that each point remains equidistant from its neighbors, and thus the chain of structures behaves like an elastic band that is stretched and bent until the lowest energy pathway is found. Figure 6a and b shows the energy as a function of the height from the surface for the atop-bridge and bridge adsorption modes. It is clear from these calculations that there is no energy barrier to adsorption for either mode, and thus it may be expected that ethene can adsorb as either atop-bridge (π) or bridge (di-σ) at low temperature. However, if we examine the effect of rotating the molecule, while keeping it parallel to the surface, it is clear that the energy profile for the two modes will be very different. Rotating the bridge mode will cause the interaction energy to fall off rapidly as shown by the very weak adsorption of the molecule in the cross bridge site (90° rotation). In contrast, the atop-bridge, when rotated by 60°, becomes the atop-hollow with a very similar adsorption energy and structure. Indeed the lack of effect of the second layer structure means that the atop (π) adsorption is likely to be very favorable for any approaching orientation of ethene (with the molecule parallel to the surface). In contrast, only the single bridge (di-σ) orientation will adsorb readily onto the surface. It seems clear that the probability of adsorption into the atop mode will dominate the initial adsorption structure. At low temperature π (atop) adsorbed ethene is observed and therefore it must be trapped by an energy barrier to transformation into the di-σ (bridge) mode. We have thus performed an elastic band calculation for the transformation of atop-bridge adsorbed ethene to bridge adsorbed ethene to investigate this. Figure 7 shows the adsorption energy as a function of the
Interaction of Ethene with the {111} Surface of Platinum
Figure 6. Energy as a function of height of the molecule from the {111} surface of Pt, obtained from elastic band calculations: (a) atopbridge (π) and (b) bridge (di-σ) adsorption modes.
Figure 7. Energy as a function of reaction coordinate for the transformation of atop-bridge ethene to bridge ethene on the {111} surface of Pt obtained from elastic band calculations.
reaction coordinate, indicating that there is a small energy barrier of around 12 kJ mol-1 to this transformation. Discussion The calculated adsorption energies are in good agreement with the observed temperature dependence of the binding mode of ethene to the {111} surface of Pt. At low temperature π
J. Phys. Chem. B, Vol. 104, No. 27, 2000 6445 adsorption is found, which on heating transforms to a di-σ mode indicating that the di-σ mode is more stable but that its formation is an activated process. This is in agreement with our calculated energies that show di-σ to be the most stable adsorption mode but with the second most stable being π adsorption at an atop site. Barrier calculations have been performed indicating that the direct adsorption into the di-σ mode does not occur, not because of an energy barrier, but probably because of steric factors that limit the range of molecular orientations in the gas phase which can directly adsorb in a di-σ geometry. Elastic band calculations also indicate a small barrier of 12 kJ mol-1 for the transformation of atop-bridge to bridge, indicating the origin of the stability of the observe π mode at low temperature. The adsorption energies of 127.3 kJ mol-1 for di-σ and 85.8 kJ mol-1 for π adsorption are well below the upper limit of 203 kJ mol-1, obtained from collision-induced desorption.6 They are also in good agreement with the microcalorimetric study of 136 kJ mol-1 for di-σ and 120 kJ mol-1 for a mixed di-σ and π adsorption on the more reactive {110} surface,8 and 120 kJ mol-1 for a mixed π/di-σ adsorption on Pt powders.9,10 The structural results are in disagreement with recent LEED experiments15 which indicate that ethene adsorbs in the fcc hollow site although they are consistent with the older EELS, UPS, and NEXAFS data.11-14 The LEED results were analyzed on the basis that surface relaxation was minimal and this may have affected the results of the fit. The calculations presented here indicate significant movement of the surface Pt atoms, and it would be interesting to investigate the effect of using the new calculated structures presented here as initial models to fit the LEED data. Finally, we compare the results with recent DFT studies of Watwe et al.18 and Ge and King.19 The energetics and structures are in excellent agreement with the periodic calculations of Ge and King, who also found no evidence to support the LEED data. Comparison with Watwe is not as good, and we suggest that this stems from their use of the cluster approach which our tests on k-point convergence indicate can have a significant effect on the adsorption energy. We also note that the cluster size employed (10 Pt atoms) resulted in the ethene molecule directly interacting with atoms at the cluster edge which did not have sufficient Pt neighbors to represent the {111} surface. Indeed a recent study10 by the same group indicates that the adsorption energy is significantly affected by increasing the cluster size to 19 Pt atoms, giving an adsorption energy of 109 kJ mol-1 for a fixed Pt cluster, in much better agreement with the periodic calculations presented here. From our calculations we can construct a model of the interaction of ethene with Pt {111}. The adsorption is controlled by a balance between the localized attraction due to Pt-C bond formation and repulsion between the extended electronic states of the surface and the C-C double bond electron density. If the band structure is ignored, by carrying out calculations with low k-point sampling (or cluster calculations), the latter is reduced and the adsorption energy is overestimated. When surface relaxation is included the surface responds to the adsorbates presence by restructuring to maximize the local bonding interaction and minimize the repulsion of the extended electronic states. In the case of Pt-ethene, the change in the adsorption energy is approximately 50 kJ mol-1 for the bridge site (comparing the results for the highest and lowest k-points sampling grids) and is thus a significant fraction of the converged adsorption energy (108.7 kJ mol-1). In cases for which the attractive bond formation is more dominant, we expect the error incurred by ignoring this effect to be less severe, and
6446 J. Phys. Chem. B, Vol. 104, No. 27, 2000
Watson et al.
this may explain why better agreement between periodic41 and cluster42 calculations has been observed in the literature for systems such as Pt-CO. In cases where the attractive bond formation is weaker, such as ethene adsorption on Cu {111}, we would expect the significance of k-point sampling to be even greater, an effect which we have recently observed using the same techniques as employed in this study.36
Simulations Inc. The calculations presented in this paper were carried out in part using “Glyndwr”, a Silicon Graphics multiprocessor Origin 2000 machine at the Department of Chemistry, University of Wales, Cardiff. This facility was purchased with support from the EPSRC, Synetix, and OCF. We also thank the Materials Chemistry consortium for access to the CSAR service at Manchester.
Conclusions
References and Notes
These calculations indicate that the di-σ adsorption site is the most stable mode of adsorption for ethene on the {111} surface of Pt in agreement with EELS, UPS, and NEXAFS data11-14 and recent calculations by Ge and King.20 They do, however, contradict recent diffuse LEED experiments15 which indicated that adsorption occurs on the fcc hollow site. We find this adsorption mode to be significantly less stable than the di-σ mode. π Adsorption in both orientations has been shown to be favorable with respect to gas-phase ethene and adsorption at the hollow sites although less stable than di-σ. The lowtemperature observation of π-adsorbed ethene suggests that the transformation form π to di-σ and the direct adsorption to a di-σ mode may be activated processes. Barrier calculations indicate that the direct adsorption of π and di-σ adsorbed ethene are not activated processes and that direct adsorption into the di-σ mode is likely to be hindered by the narrow adsorption channel created by the very specific orientation of the molecule required for strong interaction. The transformation from π to di-σ was found to be an activated process, with an activation energy of approximately 12 kJ mol-1, indicating the origin of the stability of the π adsorbed mode below 50 K. The cross bridge mode has been shown to be only weakly adsorbed, and so is unlikely to be observed experimentally. An important finding of this paper is the large effect of surface relaxation. The energetics of molecular adsorption were found to be strongly dependent on its inclusion with the adsorption energies for the π adsorption modes increased by 43% and 44%, and the di-σ increased by 15%. The stabilization of the hollow site modes was much less, leading to an adsorption energy which was lower than the atop sites, making this mode very unlikely to occur. It is clear from this study that if accurate energetics for surface adsorptions and reactions are to be obtained, then full surface relaxation must be included in the calculations. We have proposed a model of molecular adsorption which is a balance between attraction, resulting from localized bond formation, and repulsion, due to interaction between the extended electronic states and the molecule’s electron density. If the extended electronic states are underestimated, as in cluster or low k-point calculations, the repulsion is underestimated resulting in stronger bonding to the surface and overestimation of the adsorption energy. This effect will depend on the strength of the localized bonding. For molecules with weak interaction with the surface, significant changes in adsorption energy and structure will be observed with a poor treatment of the extended electronic states (e.g., ethene of Cu {111}36). For molecules with stronger interactions, such as in this case, smaller but still significant changes in energy will be observed, but with little effect on molecular structure.
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Acknowledgment. This research is funded through an EPSRC IMI project, a collaboration between chemists, materials scientists, and chemical engineers from academia and industry, involving Cardiff, Birmingham, Cambridge, and Glasgow Universities with financial support from Synetix, Johnson Matthey, BP-Amoco, Cambridge Reactor Design, and Molecular
