Coverage effect on reactivity can be more complicated than what you believe: H2 dissociation on H-precovered Pd(111) Y. M. Sun, W. Dong, and X. H. Yan Citation: The Journal of Chemical Physics 140, 244703 (2014); doi: 10.1063/1.4883238 View online: http://dx.doi.org/10.1063/1.4883238 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/24?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The dynamic effects on dissociation probability of H2–Pt(111) system by embedded atom method J. Appl. Phys. 109, 063509 (2011); 10.1063/1.3554690 Rotational effects in the dissociative adsorption of H 2 on the Pt(211) stepped surface J. Chem. Phys. 123, 164702 (2005); 10.1063/1.2087467 Rotational effects in dissociation of H 2 on Pd(111): Quantum and classical study J. Chem. Phys. 119, 12553 (2003); 10.1063/1.1626535 Role of dynamic trapping in H 2 dissociation and reflection on Pd surfaces J. Chem. Phys. 118, 11226 (2003); 10.1063/1.1575208 Analysis of H 2 dissociation dynamics on the Pd(111) surface J. Chem. Phys. 114, 10954 (2001); 10.1063/1.1375153
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THE JOURNAL OF CHEMICAL PHYSICS 140, 244703 (2014)
Coverage effect on reactivity can be more complicated than what you believe: H2 dissociation on H-precovered Pd(111) Y. M. Sun,1,2 W. Dong,2,a) and X. H. Yan1 1
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China 2 Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France
(Received 25 March 2014; accepted 2 June 2014; published online 25 June 2014) A systematic investigation based on density-functional-theory calculations is presented for elucidating the effect of adatoms on the energetics of H2 dissociation on H-precovered Pd(111) surfaces. Surprisingly, we found that the H-adatoms do not only have a poisoning effect but can also promote H2 dissociation when they are adsorbed on sites which are sufficiently far from the dissociating H2 molecule. The presence of these antagonistic effects produces many crossovers of the minimum energy profiles for H2 dissociation when coverage is varied and thus leads to a quite perplexing picture for the adatom effects. We devised a sorting procedure which allows for rationalizing nicely the influence of H-adatoms on the energetics of H2 dissociation on H-precovered Pd(111) surfaces. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4883238] I. INTRODUCTION
Under real conditions, surface reactions in heterogeneous catalysis take place always at finite surface coverages. Langmuir proposed, a long time ago, a simple theory to account for approximately the site-blocking effect at a finite surface coverage, which shows the relative sticking coefficient, S(θ )/S0 [S(θ ): sticking coefficient at coverage, θ ; S0 = S(θ = 0)], decays monotonously as (1 − θ ) if one vacancy is required for the considered reaction and as (1 − θ )2 when two vacancies are needed.1 The scanning-tunneling-spectroscopy (STM) experiment of Mitsui et al. for H2 dissociation on Pd(111) has challenged the validity of Langmuir theory and indicated that the aggregates of three or more vacancies seem to be necessary for dissociating H2 on Pd(111) highly covered by H adatoms.2–4 It is emphasized that this experiment was carried out at very low temperatures, i.e., below 65 K. This finding has actuated the recent theoretical interest in surface coverage effect.5–10 Using density functional theory (DFT), Lopez et al. determined the minimum-energy curves for H2 dissociation along a fcc-fcc path over a dimer or a trimer vacancy on a Pd(111) surface highly covered by H adatoms.5 The minimum-energy curve for the dissociation on H-precovered Pd(111) is shifted upward compared to that on a clean surface. Over a divacancy, an up-shift of about 200 meV is found but even in this case the dissociation is still non-activated. Gross and Dianat initiated ab initio molecular dynamics (AIMD) simulations for H2 dissociation on H-precovered Pd surfaces with a limited number of adatom configurations.6 They found that a dimer vacancy is still sufficient to dissociate H2 molecules if they have sufficient kinetic energies (e.g., corresponding to the thermal energy at a temperature higher than that considered in the experiment a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/140(24)/244703/8/$30.00
of Mitsui et al.2 ) and concluded that no need to refine Langmuirian picture for surface coverage effect. Later, Lozano, Gross, and Busnengo reported that even a single isolated vacancy is enough to spontaneously dissociate low-energy H2 molecules on H-covered Pd(100).7 This blurs once again the simple Langmuirian picture for surface coverage effect but in a way somehow opposite to the STM results of Mitsui et al. The simulations in Refs. 6 and 7 focused on sticking curves and considered a very limited number of H adatom configurations on the substrate. Such simulation results cannot be compared directly to any experimental results since statistical average over H adatom configurations is lacking. Moreover, no experimental result has been reported for H2 dissociation on Pd surface at finite coverages with resolved incident translational energy. Xiao and Dong have carried out simulations for H2 dissociation on H-precovered Pd(111) with the thermal averages over H adatom configurations and the velocity of incident H2 molecules.8 The relative sticking coefficient obtained from such simulations has a coverage-dependence quite close to that predicted by Langmuir theory. More recently, Gross have published results from AIMD simulations for H2 on H-precovered Pd(100) with more H-adatom configurations being considered.9, 10 These results show that for a given coverage the relative sticking coefficient can vary significantly, e.g., variation more than 100% in some cases (see, e.g., Fig. 3 in Ref. 10). In view of the monotonous decay of reactivity predicted by Langmuir theory, it is particularly striking to see the reactivity-crossovers found in Ref. 10, i.e., one adatom configuration at a higher coverage can be more reactive than a configuration at a lower coverage. One can, of course, anticipate that averaging over adatom configurations should be resorted to for reconciling the overall decay with coverage and the reactivity-crossovers found for specific configurations. Nevertheless, the origin of such crossovers (dynamics or energetics) remains elusive until now. Identifying the origin of the reactivity-crossover and elucidating how the
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abnormal contributions from such crossovers are smeared out after the statistical average will certainly deepen our understanding of the surface coverage effect on reactivity. The objective of the present work is to address this issue theoretically by considering the H2 dissociation on H-precovered Pd(111). For this, we carried out a very systematic study of the dissociation energetics at various coverages with the help of density functional theory (DFT). The obtained results looked very irrational at first sight and a very careful sorting allowed us to identify the most poisoning H adatom sites. We were also very surprised to find that at some sites, H adatoms do not hinder at all the H2 dissociation but even promote it slightly compared to the clean surface. The paper is arranged as follows. In Sec. II, the model and method are described. We present and discuss in details our results in Sec. III and some conclusions are given in Sec. IV. II. MODEL AND METHOD
Most previous theoretical investigations6–10 on the coverage effect for H2 dissociation on Pd surfaces focused on the reaction dynamics. To the best of our knowledge, no systematic investigation of the coverage effect on dissociation energetics has been reported and we present here such a study based on electronic-structure calculations by using DFT. Our DFT calculations are performed by using the Vienna ab initio simulation package (VASP).11 The electronic exchange and correlation are described within the framework of the generalized gradient approximation of Perdew and Wang (PW91).12 Plane waves are used for expanding the wave functions with a cutoff energy, Ecut , equal to 200 eV and no spin-polarization is considered. Some test calculations with Ecut = 400 eV have been performed also, which show that the calculations with Ecut = 200 eV provide perfectly reliable results. We use ultrasoft pseudopotentials for valence electrons and a 4 × 4 × 1 kpoints grid for the k-space sampling. The supercell approach is adopted which includes a slab of five Pd layers with a (3 × 3) Pd(111) surface cell and a vacuum space corresponding to five Pd layers and the Pd slab is kept rigid. It is well known that hydrogen atoms can be also absorbed into the bulk of palladium. Nevertheless, the scope of the present work is limited to study how the surface H-adatoms affect the reactivity of Pd(111) surface at finite coverages since we believe that clear insights into the effect of subsurface species on the reactivity can be gained only after the elucidation of the role of surface adatoms. The previous works of Dong et al.13, 14 show that the fccfcc pathway (i.e., molecule parallel to the surface with the two dissociated H atoms occupying two neighbor fcc sites) is energetically favorable and allows for H2 dissociation on Pd(111) without activation. In the present work, we will use essentially the energetics of the fcc-fcc path as the probe of reactivity. More precisely, the effect of the adatoms on the minimumenergy profile (MEP) of the fcc-fcc path is examined systematically at various coverages for different adatom configurations. For each configuration, the heights of H adatoms are optimized. We recall that the MEP is determined from a 2D cut of the potential energy surface (PES) with the two considered variables being the bond length, d, and the distance
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from the center of mass of the molecule to the surface, Z. In the present work, the 2D cuts are obtained from a grid defined by d = 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 1.00, 1.20, 1.5, 1.8, 2.00, 2.30 Å with Z varying from 0.80 to 4.00 Å by an increment equal to 0.20 Å. During the calculation of the 2D cuts, the structure of the H-precovered surface is kept fixed. III. RESULTS AND DISCUSSION A. Effect of H-adatoms on H2 dissociation energetics along fcc-fcc path
1. Preliminaries
As pointed out in the Introduction, our primary concern in this work is the correlation between the surface coverage and the H2 dissociation energetics. As a possible and apparently straightforward approach for seeking such a correlation, it is tempting to plot different MEPs at various coverages, θ , together and see their variations as function of the coverage. Unfortunately, this simple approach does not work because no rational trend can be identified from such a plot due to the very erratic ordering of the MEPs as function of coverage. To illustrate this difficulty, let us consider first the dissociation along fcc-fcc path. In Fig. 1(a), a sketch of the top view of a (3 × 3) surface cell on Pd(111) is presented for fcc-fcc dissociation path. The dissociating H2 molecule is represented by the bold line and the numbered fcc sites are those on which
(a)
(b)
(c) FIG. 1. Sketch of the top view of a (3 × 3) surface cell on Pd(111) with a H2 molecule dissociating along (a) fcc-fcc path, (b) bridge-top-bridge path, and (c) fcc-top-hcp path. Bold line: dissociating H2 molecule and numbered small red spheres: fcc sites for adsorbed H atoms.
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FIG. 2. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at (a) θ = 1/9 (blue curves) with the H-adatom configurations, FF1/9 (1) (a1), FF1/9 (3) (a2), FF1/9 (4) (a3), and FF1/9 (5) (a4); (b) θ = 5/9 (red curves) with H-adatom configurations FF5/9 (11223) (b1), FF5/9 (11224) (b2), FF5/9 (11225) (b3), FF5/9 (11235) (b4), and FF5/9 (11245) (b5).
H atom can be adsorbed. When the periodic boundary condition is taken into account, some H adatom sites are equivalent with respect to the dissociating H2 molecule and they are denoted by the same number, e.g., site 1 and site 2. In order to denote different adatom configurations, we use a notation like FFθ (ijk. . . ) with FF representing fcc-fcc path, θ the coverage and i, j, k . . . indicating the numbered sites occupied by H-adatoms. For example, FF2/9 (24) denotes the case of H2 dissociating along fcc-fcc path at θ = 2/9 with H-adatoms occupying sites 2 and 4 (see Fig. 1(a)). At each coverage, the MEP is determined for all the non equivalent adatom configurations. Now, the presentation given in Fig. 2 for different MEPs at two coverages, i.e., θ = 1/9 and θ = 5/9, will illustrate clearly that the task for rationalizing the coverage effect is far from being a trivial one. In this figure, we plotted a selection of the MEPs at θ = 1/9, i.e., FF1/9 (1), FF1/9 (3), FF1/9 (4), FF1/9 (5) as well as some ones at θ = 5/9, i.e., FF5/9 (11223), FF5/9 (11224), FF5/9 (11225), FF5/9 (11235), and FF5/9 (11245). The messy appearance of Fig. 2 with many ordering crossovers with respect to the coverage does not seem to provide directly any useful hint for identifying any rational trend. Therefore, our first task is to try to elaborate a way to sort, with respect to the coverage and adatom configurations, the MEPs out of such an imbroglio.
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FIG. 3. Minimum energy profiles along fcc-fcc path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
projected (on s and d orbitals) densities of states (DOS) localized on different atoms and present them in Fig. 4. Two situations are considered, one for H2 molecule far from the substrate with d = 0.75 Å (bond length) and Z = 7.00 Å (distance from the molecule center to the surface) and one for H2 close to it with d = 1.08 Å and Z = 1.34 Å (i.e., at the maximum of the MEP just before the drop-off, see Fig. 3). From Fig. 4, we see that the dissociating H2 molecule interacts most strongly with the Pd atom labeled T1 and this is evidenced by the split peak at the bottom of the d-band localized on Pd(T1) (see the black curve in Fig. 4(b)). There is a weaker interaction with the two Pd atoms labeled with T2 (see Fig. 4(c)) and no interaction with rest of Pd atoms in the surface cell since the local DOSs on them remain intact (see Fig. 4(d)). It is worth to note also that the Pd(T1) atom is geometrically nearest to the H2 molecule (measured by the distance between the center of the Pd atom and the center of mass of H2 ), the two Pd(T2) atoms are the next nearest and the other Pd atoms are farther. One can expect intuitively that the influence of an adatom should be most important if it affects significantly the Pd atom which has the strongest interaction with the dissociating H2 molecule. This reasoning leads readily to the identification of the configuration, FF1/9 (5), as the
2. Poisoning sites
It can be intuitively anticipated that the influence of an adatom on the dissociation diminishes when its distance to the dissociating molecule becomes larger. This trend appears clearly when we consider the MEPs along the fcc-fcc path at θ = 1/9 (see Fig. 3). From Fig. 3, we see immediately that at two sites the H-adatom hinders significantly the dissociation of H2 molecule along the fcc-fcc path, i.e., site 4 and site 5. So, at these sites, the H-adatom has a clear poisoning effect with the effect of site 5 larger than that of site 4. From Fig. 3, we see also that the H-adatom adsorbed at sites 1, 2 and 3 affects hardly the H2 dissociation along the fcc-fcc path. In order to understand the results given in Fig. 3, we need first to see in more details how a H2 molecule interacts with different Pd atoms of the substrate. For this, we determined the
FIG. 4. Projected local DOS, for H2 dissociation along fcc-fcc path on a clean Pd(111), calculated on different atoms: (a) s orbital on one H atom of H2 , (b) d orbital on Pd(T1) atom, (c) d orbital on Pd(T2) atom, and (d) d orbital on another Pd atom (not T1 neither T2). The Fermi level is taken as the zero in this plot. The black and red lines represent, respectively, the situation of the H2 molecule close to the surface with d = 1.08 Å (bond length) and Z = 1.34 Å (distance from the molecule center to the surface) or far from it (d = 0.75 Å, Z = 7.00 Å).
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FIG. 5. Projected local DOS of a clean Pd(111) and a H-precovered Pd(111) at θ = 1/9 calculated at different atoms: (a) s orbital on the H adatom, (b) d orbital on a Pd atom directly bonded to the H adatom [there are 3, see the inset in (a)], and (c) d orbital on a Pd atom not directly bonded to the H adatom (there are 6). The Fermi level is taken as the zero in this plot. The red and black lines represent, respectively, the clean and H-precovered Pd(111).
most poisoning one at θ = 1/9 along fcc-fcc path since the H-adatom is bonded directly to Pd(T1). The modification of the electronic structure of the substrate by the H-adatom allows one to see why the adsorption at site 5 has the most poisoning effect. In Fig. 5, the local DOSs for a clean and a H-precovered Pd(111) at θ = 1/9 are presented. The H-adatom affects only the electronic structure of the Pd atoms directly bonded to it. A split peak at the bottom of the d-band appears and there is depletion near Fermi level (see Fig. 5(b)). The dissociation of H2 on a Pd surface results from the interaction of the antibonding orbital of H2 with the Pd d-band just below the Fermi level. So, the DOS depletion of the d-band near Fermi level reduces the interaction between the H2 antibonding orbital and the top of d-band and this is the electronic origin of the poisoning effect of an H-adatom. The above analysis is based on the orbital interaction paradigm advocated mainly by Hoffmann.15 Some approximate reactivity measures have been proposed for surface reactions, e.g., that developed by Hammer and Norskov.16 These more quantitative reactivity measures account well for the trend of reactivity change resulting from large modification of electronic structure but lose their appeal in the cases that the electronic structure is not changed very sharply (see Sec. III A 3). Therefore, we adopt only a more general and qualitative reasoning of orbital interaction for our interpretation. From the above reasoning with orbital interaction, one can readily rationalize the ordering of MEPs for θ = 1/9 shown in Fig. 3. At site 5, the H-adatom depletes the top of the DOS localized on Pd(T1) and thus up-shifts most the MEP since it is Pd(T1) which interacts most strongly with the dissociating H2 molecule. When the H-adatom is adsorbed at site 4, its distance to the center of the dissociating H2 molecule is the same as at site 5. But, the H-adatom at site 4 affects only the electronic structure of two Pd(T2) atoms which interact less strongly with the dissociating H2 molecule and this is why at site 4 the adatom has a poisoning effect less strong than at site 5. When the H-adatom is adsorbed at sites 1, 2, or 3, it affects either one Pd atom which directly interacts with H2 (i.e., one Pd(T2) at site 1) or none of Pd(T1) and Pd(T2). At these sites, the H-adatom does not hinder the dissociation
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FIG. 6. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at θ = 2/9 for H-adatom configurations, FF2/9 (14) (blue), FF2/9 (15) (red), and FF2/9 (45) (black).
of H2 molecule and later we will show that H-adatoms at these sites even promote slightly the dissociation. The above analysis allows for rationalizing the ordering of MEP at higher coverages as well. So, we can readily anticipate that when a configuration of adatoms with both sites 4 and 5 occupied will produce the strongest poisoning effect. For example, one can expect that at θ = 2/9, the configurations FF2/9 (45), FF2/9 (15), FF2/9 (14) lead to decreasing poisoning effect and this is indeed the case (see Fig. 6).
3. Promoting sites
After the discussion of the poisoning effect of H-adatoms at adsorption sites, 4 and 5, we will now show a quite unexpected effect of H-adatoms, i.e., their ability to promote H2 dissociation at sites 1, 2, and 3. Although we saw, from Fig. 3, that the H-adatom adsorbed at site 1, 2, or 3 hardly affects the MEP, some small downward shifts of the MEPs for FF1/9 (1), FF1/9 (2), and FF1/9 (3) are perceptible, compared to the MEP for the clean surface. We found that the downward shift is amplified when we add successively more H-adatoms at the sites labeled with 1, 2, and 3 (see Fig. 7). Fig. 7 shows that the MEP is shifted systematically downward when we increase the coverage by adsorbing H atoms at the sites 1, 2, and 3. Thus, the promoting effect of H-adatoms at these sites is revealed unambiguously. Moreover, such effect accumulates when the number of H-adatoms increases.
FIG. 7. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at θ = 1/9, 2/9, 3/9, 4/9, and 5/9 for the H-adatom configurations indicated in the inset of the figure.
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A question arises naturally from this observation. Why H-adatoms at sites 1, 2, and 3 can promote H2 dissociation? For this, we propose the following tentative interpretation. Upon chemisorptions, chemical bonds are formed between the H-adatoms and the surface. In a quite general way, this weakens somehow the bonding between substrate atoms, i.e., bonds between Pd atoms in the case considered here. The adsorption of some H-adatoms at sites labeled 1, 2, and 3 will weaken the Pd-Pd bonds between Pd(T1) and Pd(T2) atoms. The higher availability of the valence electrons around Pd(T1) and Pd(T2) atoms, resulting from the weakening of Pd-Pd bonds, favors their interaction with the incoming H2 molecule and thus promotes its dissociation. Since the promoting effect is relatively small, it is very difficult to find quantitatively the small modifications of electronic structure resulting from the weakening of Pd-Pd interaction.
4. Getting out from imbroglio by a smart sorting
Now, we will show how to get out from the imbroglio we were facing initially. In fact, the apparently messy variation of the dissociation energetics with respect to the coverage, as shown, e.g., in Fig. 2, results from two antagonistic effects, one poisoning and the other promoting, when the coverage is increased. Now, it becomes clear that to get out from the imbroglio, one has to abandon the consideration based purely on the adatom coverage but their poisoning as well as promoting roles have to be taken into account properly. Hence, we propose to sort the MEPs according to the strength and the number of occupied poisoning sites. Based on this idea, we can readily identify four classes for different precovered substrates, which are denoted as C0 , C1 , C2 , and C3 . In class C0 , none of site 4 or site 5 is occupied, class C1 encompasses the situations with site 4 occupied by one H-adatom and site 5 empty while class C2 takes into account the cases with site 5 occupied but site 4 empty and finally in class C3 , both sites 4 and 5 are occupied by H-adatoms. We see immediately that the poisoning strength increases in the following order, C0 < C1 < C2 < C3 . In each class, we obtain different cases for the adsorption patterns of H-adatoms by occupying successively sites 1, 2, and 3. So, in a given class, the MEP shifts downward systematically with the coverage of H-adatoms since they produce a promoting effect at sites 1, 2, and 3. We have seen such a variation in Fig. 7 for class C0 . The systematic downshift of the MEP with the increase of coverage for classes C1 , C2 , and C3 is shown in Fig. 8. By distinguishing, respectively, the two antagonistic effects (one poisoning and one promoting) of H-adatoms at different adsorption sites, the classifying procedure we propose here allows for sorting nicely the dissociation energetics at various coverages from an apparent imbroglio.
B. Effect of H-adatoms on H2 dissociation energetics along other paths
In Sec. III A, our discussion has been focused on the fccfcc dissociation path. In order to confirm the general validity of the findings presented in that subsection, we will consider
FIG. 8. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) for different classes of H-adatom configurations (see insets for Hadatom configurations): (a) C1 , (b) C2 , and (c) C3 .
now the effect of H-adatoms on H2 dissociation energetics along some other dissociation paths.
1. Bridge-top-bridge path
In Fig. 1(b), a sketch of bridge-top-bridge (b-t-b) path is shown with the different adsorption sites on which an H atom can be adsorbed. In this case, we will denote the different configurations by BTBθ (ijk. . . ) (θ : coverage; i, j, k . . . indicating the labeled sites occupied by H-adatoms). As for fcc-fcc path, we first consider the effect of H-adatoms at θ = 1/9 and present the MEPs for this case in Fig. 9. We see immediately that an H-adatom at site 5 or site 6 has a large poisoning effect for H2 dissociation along b-t-b path while an H-adatom adsorbed on the other sites has either a small poisoning or promoting effect. Moreover, the poisoning effect of an H-adatom at site 5 or site 6 is much stronger than the poisoning effect we have seen in the case of fcc-fcc path. Now, it is quite tempting to compare the poisoning effects of an H-adatom at site 5 to the H2 dissociation along fcc-fcc and b-t-b paths. The situation of b-t-b path with an H-adatom at site 5 can be obtained from that of fcc-fcc path by an upward
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FIG. 9. Minimum energy profiles along bridge-top-bridge path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
displacement of the H2 molecule by √ 3 a 6
√ 3 a 6
(a: lattice constant
FIG. 11. Minimum energy profiles along fcc-top-hcp path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
The fcc-top-hcp dissociation path is sketched in Fig. 1(c) along with the labeled non-equivalent adsorption sites for an H-adatom. We denote, this time, the different configurations by FTHθ (ijk. . . ) (θ : coverage; i, j, k . . . indicating the labeled sites occupied by H-adatoms). The MEPs at θ = 1/9 are presented in Fig. 11 for different configurations. In this case, the
H-adatom at site 5 has the strongest poisoning effect while its effect at the other adsorption sites is quite small (either slightly poisoning or slightly promoting). It is again interesting to note that the situation described by FTH1/9 (5) can be obtained from that of FF1/9 (5) by rotating, counter clockwise, the dissociating H2 molecule by an angle of 30◦ , in a plane parallel to the substrate, around one of its H atom. It is again quite straightforward to understand the consequences of this configuration change. Such a rotation brings the H2 molecule away from site 3 (denoted as site 4 for fcc-fcc path, see Fig. 1(a)). In this case, the H-adatom occupying site 3 is bonded only to one Pd(T2) atom which interacts directly with the dissociating H2 instead of two such Pd(T2) atoms as in the case of fcc-fcc path (see Figs. 1(a) and 1(c)). This is why the H-adatom in the configuration described by FTH1/9 (3) has no poisoning effect while it has a poisoning effect in the configuration FF1/9 (4). Another consequence of the rotation of H2 molecule is that it turns a slightly promoting site into a slightly poisoning one, i.e., FTH1/9 (4) (compare to FF1/9 (2) in the case of fcc-fcc path in Fig. 1(a)) since the H-adatom at site 4 are bonded now to two substrate atoms which interact directly with the dissociating H2 molecule. When two H-adatoms are bonded to Pd(T1), e.g., in configuration FTH2/9 (55), we see once again that the strength of poisoning effect is about doubled compared to the case of one H-adatom bonded to Pd(T1), i.e., FTH1/9 (5) (see Fig. 12).
FIG. 10. Minimum energy profiles along bridge-top-bridge path on a Hprecovered Pd(111) for H-adatom configurations, BTB1/9 (5), BTB1/9 (6), BTB2/9 (56), and BTB2/9 (66) (see the inset for color correspondence of the different H-adatom configurations).
FIG. 12. Minimum energy profiles along fcc-top-hcp path on a H-precovered Pd(111) for H-adatom configurations, FTH1/9 (5) (blue) and FTH2/9 (55) (red).
= 0.806 Å, see Figs. 1(a) and 1(b)) and its distance and to the H-adatom at site 5 is thus decreased. This displacement toward the poisoning H-adatom leads to a quite significant increase of the dissociation barrier, i.e., 436 meV. At θ = 1/9, the H-adatom at site 6 has the strongest poisoning effect since it is very close to one of the H atoms of the dissociating hydrogen molecule. With the insight we have gained from the discussions presented in Sec. III A, one can readily anticipate that the poisoning effect in the situations described by BTB2/9 (56), BTB2/9 (66), BTB3/9 (566) lead to even stronger poisoning effect since in these situations more H-adatoms are bonded to Pd(T1) atom which is the substrate atom interacting directly with the dissociating H2 molecule. The results shown in Fig. 10 show this is indeed true and we see that the poisoning strength is roughly doubled when two H-adatoms are bonded to Pd(T1) [compare, e.g., BTB1/9 (6) and BTB2/9 (66)]. 2. fcc-top-hcp path
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TABLE I. Probability for different classes of H-adatom configurations and configurational entropy as function of coverage. θ 0 1/9 2/9 3/9 4/9 5/9 6/9 7/9
C0
C1
C2
C3
S/kB
1 15/21 10/21 6/21 3/21 1/21 0 0
0 3/21 5/21 6/21 6/21 5/21 3/21 0
0 3/21 5/21 6/21 6/21 5/21 3/21 0
0 0 1/21 3/21 6/21 10/21 15/21 1
0 0.7963 1.1817 1.3518 1.3518 1.1817 0.7963 0
column of Table I are obtained from Gibbs formula, pi ln pi , S/kB = − i
where kB is Boltzmann constant and pi the probability of ith configuration class. The results shown in Table I shows clearly that the monotonous decrease of reactivity with coverage observed from experiments17, 18 and simulations6–8 does not correlate with the variation of entropy while the dissociation energetics plays a dominant role for poisoning strength.
IV. CONCLUSIONS
3. Energetics versus statistics
The results presented and discussed above reveal that H-adatoms can produce antagonistic effects on the energetics of H2 dissociation depending on the location of the adatom adsorption site with respect to the dissociating H2 molecule. The prediction of Langmuir theory1 and the previous experimental17, 18 and simulation6–8 results all show a monotonous decrease of the reactivity of H-covered Pd surfaces when the coverage is increased. No wonder that the finding of promoting effect of H-adatoms have provoked much perplexity to us. Now, it remains to elucidate why the promoting effect of H-adatoms does not manifest itself in some way, e.g., through the variation of relative sticking coefficient with the coverage. We will provide below a possible explanation. For this, we consider again, in details, the H2 dissociation along fcc-fcc path. From the discussions given in Secs. III A 2–III A 4, the different configurations of Hadatoms are ranked into 4 classes, i.e., C0 , C1 , C2 , and C3 , with increasing poisoning strength. One can readily expect that the probabilities with which these different classes of adsorption configurations occur at different coverages will provide useful insight into the reactivity variation of the Hprecovered Pd(111) surfaces with the coverage. For a rigorous determination of the probabilities for different H-adatom configurations, one has to take into account the lateral interaction between the H-adatoms. For our qualitative discussion here, we neglect such interaction and assume that the adatoms can occupy different fcc sites independently as in Langmuir theory. With such a simplification, one can calculate the probabilities for the four classes of H-adatom configurations, i.e., C0 , C1 , C2 , and C3 , as function of coverage in the case of a (3 × 3) surface cell and we present these results in Table I. First, we see immediately that the probability for class, C0 (no poisoning site occupied), decreases quickly with the coverage while that for class, C3 (both poisoning sites occupied), increases rapidly with the coverage. When θ ≥ 2/9, the probability to have at least one poisoning site being occupied is always larger than the probability for class C0 (no poisoning site occupied). These results explain very well why the small promoting effect of H-adatoms does not manifest itself when the statistical average over adsorption configurations is taken. It is also instructive to see how the configurational entropy varies with the coverage. The results given in the last
With the help of DFT calculations, we carried out a systematic investigation of the effect of H-adatoms on the dissociation energetics of H2 on H-covered Pd(111) surfaces. At a given coverage, an H-adatom can affect the dissociation energetics in very different ways depending on its distance to the dissociating H2 molecule. A quite surprising finding is that an H-adatom can not only poison the H2 dissociation but also promote it slightly when the adatom is not bonded to a Pd atom which interacts directly with the dissociating H2 molecule. The presence of these two antagonistic effects produces many crossovers of the minimum-energy profiles when the H-adatom coverage is varied. These crossovers give a quite perplexing image about the effect of H-adatoms. We proposed a sorting procedure based on the poisoning strength of H-adatom adsorption site and the number of occupied poisoning sites. With such a procedure, we classified the adsorption configurations into four classes which allow for rationalizing nicely the variation of minimum-energy profiles. The interplay between energetics and statistics is also discussed. The variation, with respect to the coverage, of the probabilities for the different classes of H-adatom configurations allowed us to understand why the poisoning effect of H-adatoms dominates while their promoting effect does not manifest itself when the statistical average over adsorption configurations is taken.
ACKNOWLEDGMENTS
Y.M.S. is grateful for an Eiffel scholarship of the French government (2010–2011) and a scholarship awarded by China Scholarship Council (2011–2013) which funded her Ph.D. work at ENS-Lyon. We thank H. F. Busnengo for reading the paper and making some very useful comments. 1 I.
Langmuir, J. Am. Chem. Soc. 38, 1145 (1916). Mitsui, M. K. Rose, E. Fomin, D. F. Ogletree, and M. Salmeron, Nature (London) 422, 705 (2003). 3 T. Mitsui, M. K. Rose, E. Fomin, D. F. Ogletree, and M. Salmeron, Surf. Sci. 540, 5 (2003). 4 M. Salmeron, Top. Catal. 36, 55 (2005). 5 N. Lopez, Z. Lodziana, F. Illas, and M. Salmeron, Phys. Rev. Lett. 93, 146103 (2004). 6 A. Groß and A. Dianat, Phys. Rev. Lett. 98, 206107 (2007). 7 A. Lozano, A. Groß, and H. F. Busnengo, Phys. Rev. B 81, 121402(R) (2010). 8 Y. Xiao and W. Dong, Phys. Rev. B 83, 125418 (2011). 2 T.
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Groß, ChemPhysChem 11, 1374 (2010). Groß, J. Chem. Phys. 135, 174707 (2011). 11 J. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). 12 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Phys. Rev. B 46, 6671 (1992). 13 W. Dong and J. Hafner, Phys. Rev. B 56, 15396 (1997). 10 A.
J. Chem. Phys. 140, 244703 (2014) 14 W.
Dong, V. Ledentu, P. Sautet, A. Eichler, and J. Hafner, Surf. Sci. 411, 123 (1998). 15 R. Hoffmann, Rev. Mod. Phys. 60, 601 (1988). 16 B. Hammer and J. K. Norskov, Surf. Sci. 343, 211 (1995). 17 T. Engel and H. Kuipiers, Surf. Sci. 90, 162 (1979). 18 M. P. Kiskinova and G. M. Bliznakov, Surf. Sci. 123, 61 (1982).
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THE JOURNAL OF CHEMICAL PHYSICS 140, 244703 (2014)
Coverage effect on reactivity can be more complicated than what you believe: H2 dissociation on H-precovered Pd(111) Y. M. Sun,1,2 W. Dong,2,a) and X. H. Yan1 1
College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People’s Republic of China 2 Laboratoire de Chimie, UMR 5182 CNRS, Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France
(Received 25 March 2014; accepted 2 June 2014; published online 25 June 2014) A systematic investigation based on density-functional-theory calculations is presented for elucidating the effect of adatoms on the energetics of H2 dissociation on H-precovered Pd(111) surfaces. Surprisingly, we found that the H-adatoms do not only have a poisoning effect but can also promote H2 dissociation when they are adsorbed on sites which are sufficiently far from the dissociating H2 molecule. The presence of these antagonistic effects produces many crossovers of the minimum energy profiles for H2 dissociation when coverage is varied and thus leads to a quite perplexing picture for the adatom effects. We devised a sorting procedure which allows for rationalizing nicely the influence of H-adatoms on the energetics of H2 dissociation on H-precovered Pd(111) surfaces. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4883238] I. INTRODUCTION
Under real conditions, surface reactions in heterogeneous catalysis take place always at finite surface coverages. Langmuir proposed, a long time ago, a simple theory to account for approximately the site-blocking effect at a finite surface coverage, which shows the relative sticking coefficient, S(θ )/S0 [S(θ ): sticking coefficient at coverage, θ ; S0 = S(θ = 0)], decays monotonously as (1 − θ ) if one vacancy is required for the considered reaction and as (1 − θ )2 when two vacancies are needed.1 The scanning-tunneling-spectroscopy (STM) experiment of Mitsui et al. for H2 dissociation on Pd(111) has challenged the validity of Langmuir theory and indicated that the aggregates of three or more vacancies seem to be necessary for dissociating H2 on Pd(111) highly covered by H adatoms.2–4 It is emphasized that this experiment was carried out at very low temperatures, i.e., below 65 K. This finding has actuated the recent theoretical interest in surface coverage effect.5–10 Using density functional theory (DFT), Lopez et al. determined the minimum-energy curves for H2 dissociation along a fcc-fcc path over a dimer or a trimer vacancy on a Pd(111) surface highly covered by H adatoms.5 The minimum-energy curve for the dissociation on H-precovered Pd(111) is shifted upward compared to that on a clean surface. Over a divacancy, an up-shift of about 200 meV is found but even in this case the dissociation is still non-activated. Gross and Dianat initiated ab initio molecular dynamics (AIMD) simulations for H2 dissociation on H-precovered Pd surfaces with a limited number of adatom configurations.6 They found that a dimer vacancy is still sufficient to dissociate H2 molecules if they have sufficient kinetic energies (e.g., corresponding to the thermal energy at a temperature higher than that considered in the experiment a) Author to whom correspondence should be addressed. Electronic mail:
[email protected] 0021-9606/2014/140(24)/244703/8/$30.00
of Mitsui et al.2 ) and concluded that no need to refine Langmuirian picture for surface coverage effect. Later, Lozano, Gross, and Busnengo reported that even a single isolated vacancy is enough to spontaneously dissociate low-energy H2 molecules on H-covered Pd(100).7 This blurs once again the simple Langmuirian picture for surface coverage effect but in a way somehow opposite to the STM results of Mitsui et al. The simulations in Refs. 6 and 7 focused on sticking curves and considered a very limited number of H adatom configurations on the substrate. Such simulation results cannot be compared directly to any experimental results since statistical average over H adatom configurations is lacking. Moreover, no experimental result has been reported for H2 dissociation on Pd surface at finite coverages with resolved incident translational energy. Xiao and Dong have carried out simulations for H2 dissociation on H-precovered Pd(111) with the thermal averages over H adatom configurations and the velocity of incident H2 molecules.8 The relative sticking coefficient obtained from such simulations has a coverage-dependence quite close to that predicted by Langmuir theory. More recently, Gross have published results from AIMD simulations for H2 on H-precovered Pd(100) with more H-adatom configurations being considered.9, 10 These results show that for a given coverage the relative sticking coefficient can vary significantly, e.g., variation more than 100% in some cases (see, e.g., Fig. 3 in Ref. 10). In view of the monotonous decay of reactivity predicted by Langmuir theory, it is particularly striking to see the reactivity-crossovers found in Ref. 10, i.e., one adatom configuration at a higher coverage can be more reactive than a configuration at a lower coverage. One can, of course, anticipate that averaging over adatom configurations should be resorted to for reconciling the overall decay with coverage and the reactivity-crossovers found for specific configurations. Nevertheless, the origin of such crossovers (dynamics or energetics) remains elusive until now. Identifying the origin of the reactivity-crossover and elucidating how the
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abnormal contributions from such crossovers are smeared out after the statistical average will certainly deepen our understanding of the surface coverage effect on reactivity. The objective of the present work is to address this issue theoretically by considering the H2 dissociation on H-precovered Pd(111). For this, we carried out a very systematic study of the dissociation energetics at various coverages with the help of density functional theory (DFT). The obtained results looked very irrational at first sight and a very careful sorting allowed us to identify the most poisoning H adatom sites. We were also very surprised to find that at some sites, H adatoms do not hinder at all the H2 dissociation but even promote it slightly compared to the clean surface. The paper is arranged as follows. In Sec. II, the model and method are described. We present and discuss in details our results in Sec. III and some conclusions are given in Sec. IV. II. MODEL AND METHOD
Most previous theoretical investigations6–10 on the coverage effect for H2 dissociation on Pd surfaces focused on the reaction dynamics. To the best of our knowledge, no systematic investigation of the coverage effect on dissociation energetics has been reported and we present here such a study based on electronic-structure calculations by using DFT. Our DFT calculations are performed by using the Vienna ab initio simulation package (VASP).11 The electronic exchange and correlation are described within the framework of the generalized gradient approximation of Perdew and Wang (PW91).12 Plane waves are used for expanding the wave functions with a cutoff energy, Ecut , equal to 200 eV and no spin-polarization is considered. Some test calculations with Ecut = 400 eV have been performed also, which show that the calculations with Ecut = 200 eV provide perfectly reliable results. We use ultrasoft pseudopotentials for valence electrons and a 4 × 4 × 1 kpoints grid for the k-space sampling. The supercell approach is adopted which includes a slab of five Pd layers with a (3 × 3) Pd(111) surface cell and a vacuum space corresponding to five Pd layers and the Pd slab is kept rigid. It is well known that hydrogen atoms can be also absorbed into the bulk of palladium. Nevertheless, the scope of the present work is limited to study how the surface H-adatoms affect the reactivity of Pd(111) surface at finite coverages since we believe that clear insights into the effect of subsurface species on the reactivity can be gained only after the elucidation of the role of surface adatoms. The previous works of Dong et al.13, 14 show that the fccfcc pathway (i.e., molecule parallel to the surface with the two dissociated H atoms occupying two neighbor fcc sites) is energetically favorable and allows for H2 dissociation on Pd(111) without activation. In the present work, we will use essentially the energetics of the fcc-fcc path as the probe of reactivity. More precisely, the effect of the adatoms on the minimumenergy profile (MEP) of the fcc-fcc path is examined systematically at various coverages for different adatom configurations. For each configuration, the heights of H adatoms are optimized. We recall that the MEP is determined from a 2D cut of the potential energy surface (PES) with the two considered variables being the bond length, d, and the distance
J. Chem. Phys. 140, 244703 (2014)
from the center of mass of the molecule to the surface, Z. In the present work, the 2D cuts are obtained from a grid defined by d = 0.65, 0.70, 0.75, 0.80, 0.85, 0.90, 1.00, 1.20, 1.5, 1.8, 2.00, 2.30 Å with Z varying from 0.80 to 4.00 Å by an increment equal to 0.20 Å. During the calculation of the 2D cuts, the structure of the H-precovered surface is kept fixed. III. RESULTS AND DISCUSSION A. Effect of H-adatoms on H2 dissociation energetics along fcc-fcc path
1. Preliminaries
As pointed out in the Introduction, our primary concern in this work is the correlation between the surface coverage and the H2 dissociation energetics. As a possible and apparently straightforward approach for seeking such a correlation, it is tempting to plot different MEPs at various coverages, θ , together and see their variations as function of the coverage. Unfortunately, this simple approach does not work because no rational trend can be identified from such a plot due to the very erratic ordering of the MEPs as function of coverage. To illustrate this difficulty, let us consider first the dissociation along fcc-fcc path. In Fig. 1(a), a sketch of the top view of a (3 × 3) surface cell on Pd(111) is presented for fcc-fcc dissociation path. The dissociating H2 molecule is represented by the bold line and the numbered fcc sites are those on which
(a)
(b)
(c) FIG. 1. Sketch of the top view of a (3 × 3) surface cell on Pd(111) with a H2 molecule dissociating along (a) fcc-fcc path, (b) bridge-top-bridge path, and (c) fcc-top-hcp path. Bold line: dissociating H2 molecule and numbered small red spheres: fcc sites for adsorbed H atoms.
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FIG. 2. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at (a) θ = 1/9 (blue curves) with the H-adatom configurations, FF1/9 (1) (a1), FF1/9 (3) (a2), FF1/9 (4) (a3), and FF1/9 (5) (a4); (b) θ = 5/9 (red curves) with H-adatom configurations FF5/9 (11223) (b1), FF5/9 (11224) (b2), FF5/9 (11225) (b3), FF5/9 (11235) (b4), and FF5/9 (11245) (b5).
H atom can be adsorbed. When the periodic boundary condition is taken into account, some H adatom sites are equivalent with respect to the dissociating H2 molecule and they are denoted by the same number, e.g., site 1 and site 2. In order to denote different adatom configurations, we use a notation like FFθ (ijk. . . ) with FF representing fcc-fcc path, θ the coverage and i, j, k . . . indicating the numbered sites occupied by H-adatoms. For example, FF2/9 (24) denotes the case of H2 dissociating along fcc-fcc path at θ = 2/9 with H-adatoms occupying sites 2 and 4 (see Fig. 1(a)). At each coverage, the MEP is determined for all the non equivalent adatom configurations. Now, the presentation given in Fig. 2 for different MEPs at two coverages, i.e., θ = 1/9 and θ = 5/9, will illustrate clearly that the task for rationalizing the coverage effect is far from being a trivial one. In this figure, we plotted a selection of the MEPs at θ = 1/9, i.e., FF1/9 (1), FF1/9 (3), FF1/9 (4), FF1/9 (5) as well as some ones at θ = 5/9, i.e., FF5/9 (11223), FF5/9 (11224), FF5/9 (11225), FF5/9 (11235), and FF5/9 (11245). The messy appearance of Fig. 2 with many ordering crossovers with respect to the coverage does not seem to provide directly any useful hint for identifying any rational trend. Therefore, our first task is to try to elaborate a way to sort, with respect to the coverage and adatom configurations, the MEPs out of such an imbroglio.
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FIG. 3. Minimum energy profiles along fcc-fcc path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
projected (on s and d orbitals) densities of states (DOS) localized on different atoms and present them in Fig. 4. Two situations are considered, one for H2 molecule far from the substrate with d = 0.75 Å (bond length) and Z = 7.00 Å (distance from the molecule center to the surface) and one for H2 close to it with d = 1.08 Å and Z = 1.34 Å (i.e., at the maximum of the MEP just before the drop-off, see Fig. 3). From Fig. 4, we see that the dissociating H2 molecule interacts most strongly with the Pd atom labeled T1 and this is evidenced by the split peak at the bottom of the d-band localized on Pd(T1) (see the black curve in Fig. 4(b)). There is a weaker interaction with the two Pd atoms labeled with T2 (see Fig. 4(c)) and no interaction with rest of Pd atoms in the surface cell since the local DOSs on them remain intact (see Fig. 4(d)). It is worth to note also that the Pd(T1) atom is geometrically nearest to the H2 molecule (measured by the distance between the center of the Pd atom and the center of mass of H2 ), the two Pd(T2) atoms are the next nearest and the other Pd atoms are farther. One can expect intuitively that the influence of an adatom should be most important if it affects significantly the Pd atom which has the strongest interaction with the dissociating H2 molecule. This reasoning leads readily to the identification of the configuration, FF1/9 (5), as the
2. Poisoning sites
It can be intuitively anticipated that the influence of an adatom on the dissociation diminishes when its distance to the dissociating molecule becomes larger. This trend appears clearly when we consider the MEPs along the fcc-fcc path at θ = 1/9 (see Fig. 3). From Fig. 3, we see immediately that at two sites the H-adatom hinders significantly the dissociation of H2 molecule along the fcc-fcc path, i.e., site 4 and site 5. So, at these sites, the H-adatom has a clear poisoning effect with the effect of site 5 larger than that of site 4. From Fig. 3, we see also that the H-adatom adsorbed at sites 1, 2 and 3 affects hardly the H2 dissociation along the fcc-fcc path. In order to understand the results given in Fig. 3, we need first to see in more details how a H2 molecule interacts with different Pd atoms of the substrate. For this, we determined the
FIG. 4. Projected local DOS, for H2 dissociation along fcc-fcc path on a clean Pd(111), calculated on different atoms: (a) s orbital on one H atom of H2 , (b) d orbital on Pd(T1) atom, (c) d orbital on Pd(T2) atom, and (d) d orbital on another Pd atom (not T1 neither T2). The Fermi level is taken as the zero in this plot. The black and red lines represent, respectively, the situation of the H2 molecule close to the surface with d = 1.08 Å (bond length) and Z = 1.34 Å (distance from the molecule center to the surface) or far from it (d = 0.75 Å, Z = 7.00 Å).
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FIG. 5. Projected local DOS of a clean Pd(111) and a H-precovered Pd(111) at θ = 1/9 calculated at different atoms: (a) s orbital on the H adatom, (b) d orbital on a Pd atom directly bonded to the H adatom [there are 3, see the inset in (a)], and (c) d orbital on a Pd atom not directly bonded to the H adatom (there are 6). The Fermi level is taken as the zero in this plot. The red and black lines represent, respectively, the clean and H-precovered Pd(111).
most poisoning one at θ = 1/9 along fcc-fcc path since the H-adatom is bonded directly to Pd(T1). The modification of the electronic structure of the substrate by the H-adatom allows one to see why the adsorption at site 5 has the most poisoning effect. In Fig. 5, the local DOSs for a clean and a H-precovered Pd(111) at θ = 1/9 are presented. The H-adatom affects only the electronic structure of the Pd atoms directly bonded to it. A split peak at the bottom of the d-band appears and there is depletion near Fermi level (see Fig. 5(b)). The dissociation of H2 on a Pd surface results from the interaction of the antibonding orbital of H2 with the Pd d-band just below the Fermi level. So, the DOS depletion of the d-band near Fermi level reduces the interaction between the H2 antibonding orbital and the top of d-band and this is the electronic origin of the poisoning effect of an H-adatom. The above analysis is based on the orbital interaction paradigm advocated mainly by Hoffmann.15 Some approximate reactivity measures have been proposed for surface reactions, e.g., that developed by Hammer and Norskov.16 These more quantitative reactivity measures account well for the trend of reactivity change resulting from large modification of electronic structure but lose their appeal in the cases that the electronic structure is not changed very sharply (see Sec. III A 3). Therefore, we adopt only a more general and qualitative reasoning of orbital interaction for our interpretation. From the above reasoning with orbital interaction, one can readily rationalize the ordering of MEPs for θ = 1/9 shown in Fig. 3. At site 5, the H-adatom depletes the top of the DOS localized on Pd(T1) and thus up-shifts most the MEP since it is Pd(T1) which interacts most strongly with the dissociating H2 molecule. When the H-adatom is adsorbed at site 4, its distance to the center of the dissociating H2 molecule is the same as at site 5. But, the H-adatom at site 4 affects only the electronic structure of two Pd(T2) atoms which interact less strongly with the dissociating H2 molecule and this is why at site 4 the adatom has a poisoning effect less strong than at site 5. When the H-adatom is adsorbed at sites 1, 2, or 3, it affects either one Pd atom which directly interacts with H2 (i.e., one Pd(T2) at site 1) or none of Pd(T1) and Pd(T2). At these sites, the H-adatom does not hinder the dissociation
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FIG. 6. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at θ = 2/9 for H-adatom configurations, FF2/9 (14) (blue), FF2/9 (15) (red), and FF2/9 (45) (black).
of H2 molecule and later we will show that H-adatoms at these sites even promote slightly the dissociation. The above analysis allows for rationalizing the ordering of MEP at higher coverages as well. So, we can readily anticipate that when a configuration of adatoms with both sites 4 and 5 occupied will produce the strongest poisoning effect. For example, one can expect that at θ = 2/9, the configurations FF2/9 (45), FF2/9 (15), FF2/9 (14) lead to decreasing poisoning effect and this is indeed the case (see Fig. 6).
3. Promoting sites
After the discussion of the poisoning effect of H-adatoms at adsorption sites, 4 and 5, we will now show a quite unexpected effect of H-adatoms, i.e., their ability to promote H2 dissociation at sites 1, 2, and 3. Although we saw, from Fig. 3, that the H-adatom adsorbed at site 1, 2, or 3 hardly affects the MEP, some small downward shifts of the MEPs for FF1/9 (1), FF1/9 (2), and FF1/9 (3) are perceptible, compared to the MEP for the clean surface. We found that the downward shift is amplified when we add successively more H-adatoms at the sites labeled with 1, 2, and 3 (see Fig. 7). Fig. 7 shows that the MEP is shifted systematically downward when we increase the coverage by adsorbing H atoms at the sites 1, 2, and 3. Thus, the promoting effect of H-adatoms at these sites is revealed unambiguously. Moreover, such effect accumulates when the number of H-adatoms increases.
FIG. 7. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) at θ = 1/9, 2/9, 3/9, 4/9, and 5/9 for the H-adatom configurations indicated in the inset of the figure.
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A question arises naturally from this observation. Why H-adatoms at sites 1, 2, and 3 can promote H2 dissociation? For this, we propose the following tentative interpretation. Upon chemisorptions, chemical bonds are formed between the H-adatoms and the surface. In a quite general way, this weakens somehow the bonding between substrate atoms, i.e., bonds between Pd atoms in the case considered here. The adsorption of some H-adatoms at sites labeled 1, 2, and 3 will weaken the Pd-Pd bonds between Pd(T1) and Pd(T2) atoms. The higher availability of the valence electrons around Pd(T1) and Pd(T2) atoms, resulting from the weakening of Pd-Pd bonds, favors their interaction with the incoming H2 molecule and thus promotes its dissociation. Since the promoting effect is relatively small, it is very difficult to find quantitatively the small modifications of electronic structure resulting from the weakening of Pd-Pd interaction.
4. Getting out from imbroglio by a smart sorting
Now, we will show how to get out from the imbroglio we were facing initially. In fact, the apparently messy variation of the dissociation energetics with respect to the coverage, as shown, e.g., in Fig. 2, results from two antagonistic effects, one poisoning and the other promoting, when the coverage is increased. Now, it becomes clear that to get out from the imbroglio, one has to abandon the consideration based purely on the adatom coverage but their poisoning as well as promoting roles have to be taken into account properly. Hence, we propose to sort the MEPs according to the strength and the number of occupied poisoning sites. Based on this idea, we can readily identify four classes for different precovered substrates, which are denoted as C0 , C1 , C2 , and C3 . In class C0 , none of site 4 or site 5 is occupied, class C1 encompasses the situations with site 4 occupied by one H-adatom and site 5 empty while class C2 takes into account the cases with site 5 occupied but site 4 empty and finally in class C3 , both sites 4 and 5 are occupied by H-adatoms. We see immediately that the poisoning strength increases in the following order, C0 < C1 < C2 < C3 . In each class, we obtain different cases for the adsorption patterns of H-adatoms by occupying successively sites 1, 2, and 3. So, in a given class, the MEP shifts downward systematically with the coverage of H-adatoms since they produce a promoting effect at sites 1, 2, and 3. We have seen such a variation in Fig. 7 for class C0 . The systematic downshift of the MEP with the increase of coverage for classes C1 , C2 , and C3 is shown in Fig. 8. By distinguishing, respectively, the two antagonistic effects (one poisoning and one promoting) of H-adatoms at different adsorption sites, the classifying procedure we propose here allows for sorting nicely the dissociation energetics at various coverages from an apparent imbroglio.
B. Effect of H-adatoms on H2 dissociation energetics along other paths
In Sec. III A, our discussion has been focused on the fccfcc dissociation path. In order to confirm the general validity of the findings presented in that subsection, we will consider
FIG. 8. Minimum energy profiles along fcc-fcc path on a H-precovered Pd(111) for different classes of H-adatom configurations (see insets for Hadatom configurations): (a) C1 , (b) C2 , and (c) C3 .
now the effect of H-adatoms on H2 dissociation energetics along some other dissociation paths.
1. Bridge-top-bridge path
In Fig. 1(b), a sketch of bridge-top-bridge (b-t-b) path is shown with the different adsorption sites on which an H atom can be adsorbed. In this case, we will denote the different configurations by BTBθ (ijk. . . ) (θ : coverage; i, j, k . . . indicating the labeled sites occupied by H-adatoms). As for fcc-fcc path, we first consider the effect of H-adatoms at θ = 1/9 and present the MEPs for this case in Fig. 9. We see immediately that an H-adatom at site 5 or site 6 has a large poisoning effect for H2 dissociation along b-t-b path while an H-adatom adsorbed on the other sites has either a small poisoning or promoting effect. Moreover, the poisoning effect of an H-adatom at site 5 or site 6 is much stronger than the poisoning effect we have seen in the case of fcc-fcc path. Now, it is quite tempting to compare the poisoning effects of an H-adatom at site 5 to the H2 dissociation along fcc-fcc and b-t-b paths. The situation of b-t-b path with an H-adatom at site 5 can be obtained from that of fcc-fcc path by an upward
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J. Chem. Phys. 140, 244703 (2014)
FIG. 9. Minimum energy profiles along bridge-top-bridge path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
displacement of the H2 molecule by √ 3 a 6
√ 3 a 6
(a: lattice constant
FIG. 11. Minimum energy profiles along fcc-top-hcp path of H2 dissociation on a clean Pd(111) (black curve) or a Pd(111) covered by one H adatom (i.e., θ = 1/9) at different sites (see the inset for color correspondence of the different H-adatom configurations).
The fcc-top-hcp dissociation path is sketched in Fig. 1(c) along with the labeled non-equivalent adsorption sites for an H-adatom. We denote, this time, the different configurations by FTHθ (ijk. . . ) (θ : coverage; i, j, k . . . indicating the labeled sites occupied by H-adatoms). The MEPs at θ = 1/9 are presented in Fig. 11 for different configurations. In this case, the
H-adatom at site 5 has the strongest poisoning effect while its effect at the other adsorption sites is quite small (either slightly poisoning or slightly promoting). It is again interesting to note that the situation described by FTH1/9 (5) can be obtained from that of FF1/9 (5) by rotating, counter clockwise, the dissociating H2 molecule by an angle of 30◦ , in a plane parallel to the substrate, around one of its H atom. It is again quite straightforward to understand the consequences of this configuration change. Such a rotation brings the H2 molecule away from site 3 (denoted as site 4 for fcc-fcc path, see Fig. 1(a)). In this case, the H-adatom occupying site 3 is bonded only to one Pd(T2) atom which interacts directly with the dissociating H2 instead of two such Pd(T2) atoms as in the case of fcc-fcc path (see Figs. 1(a) and 1(c)). This is why the H-adatom in the configuration described by FTH1/9 (3) has no poisoning effect while it has a poisoning effect in the configuration FF1/9 (4). Another consequence of the rotation of H2 molecule is that it turns a slightly promoting site into a slightly poisoning one, i.e., FTH1/9 (4) (compare to FF1/9 (2) in the case of fcc-fcc path in Fig. 1(a)) since the H-adatom at site 4 are bonded now to two substrate atoms which interact directly with the dissociating H2 molecule. When two H-adatoms are bonded to Pd(T1), e.g., in configuration FTH2/9 (55), we see once again that the strength of poisoning effect is about doubled compared to the case of one H-adatom bonded to Pd(T1), i.e., FTH1/9 (5) (see Fig. 12).
FIG. 10. Minimum energy profiles along bridge-top-bridge path on a Hprecovered Pd(111) for H-adatom configurations, BTB1/9 (5), BTB1/9 (6), BTB2/9 (56), and BTB2/9 (66) (see the inset for color correspondence of the different H-adatom configurations).
FIG. 12. Minimum energy profiles along fcc-top-hcp path on a H-precovered Pd(111) for H-adatom configurations, FTH1/9 (5) (blue) and FTH2/9 (55) (red).
= 0.806 Å, see Figs. 1(a) and 1(b)) and its distance and to the H-adatom at site 5 is thus decreased. This displacement toward the poisoning H-adatom leads to a quite significant increase of the dissociation barrier, i.e., 436 meV. At θ = 1/9, the H-adatom at site 6 has the strongest poisoning effect since it is very close to one of the H atoms of the dissociating hydrogen molecule. With the insight we have gained from the discussions presented in Sec. III A, one can readily anticipate that the poisoning effect in the situations described by BTB2/9 (56), BTB2/9 (66), BTB3/9 (566) lead to even stronger poisoning effect since in these situations more H-adatoms are bonded to Pd(T1) atom which is the substrate atom interacting directly with the dissociating H2 molecule. The results shown in Fig. 10 show this is indeed true and we see that the poisoning strength is roughly doubled when two H-adatoms are bonded to Pd(T1) [compare, e.g., BTB1/9 (6) and BTB2/9 (66)]. 2. fcc-top-hcp path
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J. Chem. Phys. 140, 244703 (2014)
TABLE I. Probability for different classes of H-adatom configurations and configurational entropy as function of coverage. θ 0 1/9 2/9 3/9 4/9 5/9 6/9 7/9
C0
C1
C2
C3
S/kB
1 15/21 10/21 6/21 3/21 1/21 0 0
0 3/21 5/21 6/21 6/21 5/21 3/21 0
0 3/21 5/21 6/21 6/21 5/21 3/21 0
0 0 1/21 3/21 6/21 10/21 15/21 1
0 0.7963 1.1817 1.3518 1.3518 1.1817 0.7963 0
column of Table I are obtained from Gibbs formula, pi ln pi , S/kB = − i
where kB is Boltzmann constant and pi the probability of ith configuration class. The results shown in Table I shows clearly that the monotonous decrease of reactivity with coverage observed from experiments17, 18 and simulations6–8 does not correlate with the variation of entropy while the dissociation energetics plays a dominant role for poisoning strength.
IV. CONCLUSIONS
3. Energetics versus statistics
The results presented and discussed above reveal that H-adatoms can produce antagonistic effects on the energetics of H2 dissociation depending on the location of the adatom adsorption site with respect to the dissociating H2 molecule. The prediction of Langmuir theory1 and the previous experimental17, 18 and simulation6–8 results all show a monotonous decrease of the reactivity of H-covered Pd surfaces when the coverage is increased. No wonder that the finding of promoting effect of H-adatoms have provoked much perplexity to us. Now, it remains to elucidate why the promoting effect of H-adatoms does not manifest itself in some way, e.g., through the variation of relative sticking coefficient with the coverage. We will provide below a possible explanation. For this, we consider again, in details, the H2 dissociation along fcc-fcc path. From the discussions given in Secs. III A 2–III A 4, the different configurations of Hadatoms are ranked into 4 classes, i.e., C0 , C1 , C2 , and C3 , with increasing poisoning strength. One can readily expect that the probabilities with which these different classes of adsorption configurations occur at different coverages will provide useful insight into the reactivity variation of the Hprecovered Pd(111) surfaces with the coverage. For a rigorous determination of the probabilities for different H-adatom configurations, one has to take into account the lateral interaction between the H-adatoms. For our qualitative discussion here, we neglect such interaction and assume that the adatoms can occupy different fcc sites independently as in Langmuir theory. With such a simplification, one can calculate the probabilities for the four classes of H-adatom configurations, i.e., C0 , C1 , C2 , and C3 , as function of coverage in the case of a (3 × 3) surface cell and we present these results in Table I. First, we see immediately that the probability for class, C0 (no poisoning site occupied), decreases quickly with the coverage while that for class, C3 (both poisoning sites occupied), increases rapidly with the coverage. When θ ≥ 2/9, the probability to have at least one poisoning site being occupied is always larger than the probability for class C0 (no poisoning site occupied). These results explain very well why the small promoting effect of H-adatoms does not manifest itself when the statistical average over adsorption configurations is taken. It is also instructive to see how the configurational entropy varies with the coverage. The results given in the last
With the help of DFT calculations, we carried out a systematic investigation of the effect of H-adatoms on the dissociation energetics of H2 on H-covered Pd(111) surfaces. At a given coverage, an H-adatom can affect the dissociation energetics in very different ways depending on its distance to the dissociating H2 molecule. A quite surprising finding is that an H-adatom can not only poison the H2 dissociation but also promote it slightly when the adatom is not bonded to a Pd atom which interacts directly with the dissociating H2 molecule. The presence of these two antagonistic effects produces many crossovers of the minimum-energy profiles when the H-adatom coverage is varied. These crossovers give a quite perplexing image about the effect of H-adatoms. We proposed a sorting procedure based on the poisoning strength of H-adatom adsorption site and the number of occupied poisoning sites. With such a procedure, we classified the adsorption configurations into four classes which allow for rationalizing nicely the variation of minimum-energy profiles. The interplay between energetics and statistics is also discussed. The variation, with respect to the coverage, of the probabilities for the different classes of H-adatom configurations allowed us to understand why the poisoning effect of H-adatoms dominates while their promoting effect does not manifest itself when the statistical average over adsorption configurations is taken.
ACKNOWLEDGMENTS
Y.M.S. is grateful for an Eiffel scholarship of the French government (2010–2011) and a scholarship awarded by China Scholarship Council (2011–2013) which funded her Ph.D. work at ENS-Lyon. We thank H. F. Busnengo for reading the paper and making some very useful comments. 1 I.
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