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Influence of Nickel Catalyst Geometry on the Dissociation Barriers of H2 and CH4: Ni13 versus Ni(111) Bin Liu,† Mark T. Lusk,‡ and James F. Ely*,† Chemical Engineering Department, Colorado School of Mines, Golden, Colorado 80401-1887, and Physics Department, Colorado School of Mines, Golden, Colorado 80401-1887 ReceiVed: January 12, 2009; ReVised Manuscript ReceiVed: May 29, 2009
The role of catalyst size and geometry in hydrocarbon decomposition is elucidated using density functional theory (DFT). For the sake of clarity, the work focuses on the dissociative adsorption of H2 and CH4 on an icosahedral Ni13 cluster and a Ni(111) surface. Both H2 and CH4 adsorb molecularly at t1 sites of the cluster. Subsequent dissociation leaves H atoms most strongly bound to c3 sites, while CH3 favors t1 and b2 sites. A hybrid linear synchronous transit/quadratic synchronous transit (LST/QST) transition state search algorithm allows transition state structures to be located and dissociation barriers to be obtained. The lowest H2 and CH4 dissociation barriers are estimated to be 3.5 and 9.9 kcal/mol, respectively. The corresponding values for Ni(111) are 0.6 and 21.4 kcal/mol. Molecular orbital (MO) theory is employed to explain how local distortion in the electronic structure of the nickel atoms lowers these barriers. 1. Introduction The efficient decomposition and manipulation of hydrogen and hydrocarbon molecules is central to a wide variety of chemical processes. From conventional synthesis gas production processes,1-4 such as steam reforming and partial oxidation, to more recent interest in direct oxidation of hydrocarbons in solidoxide fuel cell (SOFC) operations,5-8 tremendous efforts have focused on the search for more effective catalysts to break down hydrocarbons. The use of nanosized clusters offers particular promise in this area. For instance, the presence of a nanosized iron oxide aerosol results in a 4-5 order increase in the rate of acetic acid oxidation in both laboratory and pilot scale experiments.9 In an application closer to that considered here, Nevskaya et al.10 discovered that the use of laser-dispersed Ni nanostructures supported on Si/SiO2 increased the rate of chlorinated hydrocarbon isomerization and olefin hydrogenation reactions by 2-4 orders of magnitude as compared with catalysis using a nickel film. Although the use of ultrafine particles as catalysts seems very promising, controversy involving the effectiveness of nanoparticles still remains. For example, Weber et al.11 used the methanation reaction of carbon monoxide to investigate the catalytic effectiveness of air-borne nickel particles and pointed out that graphite formation on the particles could lead to a serious loss of specific surface and consequently deactivate the catalysts. Hence, small size does not necessarily translate into improved performance. The function of a nanoparticulate system in each chemical process must be carefully explored. A theme developed in this work by calculating electronic density, combined with molecular orbital theory analysis, can shed light on the interplay between catalyst geometry and electronic structure as a means of predicting catalytic performance. Although a large body of theoretical and experimental data listed in Table 1 for the dissociation of H2 and CH4 over various planar surfaces of nickel exists in the literature, only a handful * To whom correspondence should be addressed. E-mail:
[email protected]. † Chemical Engineering Department. ‡ Physics Department.
of studies have been undertaken for nickel clusters. In early ab initio studies, such cluster calculations simply served as computational expedients for analyzing planar surfaces.12,13 One of the earliest investigations to actually focus on catalytic methane dissociation on nickel particles was reported by Burghgraef et al.14 In that work, the barrier to insertion of a single nickel atom into the C-H bond of a CH4 molecule was estimated to be 9.7 kcal/mol. By calculating the destabilization energy of the requisite C-H bond stretching, it was shown that the nickel atom lowers the energy by 10.5 kcal/mol. In a follow up study, Burghgraef et al.13 identified a correlation between cluster size/configuration and the barrier to CH4 dissociation: clusters for which surface nickel atoms have the same number of nearest neighbors as a Ni(111) surface were found to have the lowest barrier. Burghgraef’s calculations were somewhat idealized, however, because the positions of the Ni atoms were fixed. Charlot et al.15 subsequently investigated the catalytic dissociation of H2 on icosahedral Ni13 clusters using the extended Hu¨ckel theory to find that H2 dissociates at the center sites. Alvarez et al.16 also used this geometry to study the dissociation dynamics of H2 and its isotopic equivalent, D2, with a parametrized, empirical potential energy surface. This study intends to systematically investigate the dissociation of H2 and CH4 on icosahedral Ni13 clusters using DFT method. For each case, the results are followed by an analysis of the degree to which geometry-induced distortions of the electronic structure affect the adsorption/dissociation of H2 and CH4. This is accomplished by making comparisons with the corresponding behavior on Ni(111) surfaces. The catalytic effects identified, above and beyond those associated with increased surface area, can be exploited in the design of the more efficient hydrocarbon oxidation processes. 2. Materials and Methods All calculations presented in this article were performed with DMol3.17,18 A generalized gradient approximation (GGA) was adopted using a Perdew-Wang (PW91) functional to account for exchange and correlation effects.19 Double numerical plus
10.1021/jp9003196 CCC: $40.75 2009 American Chemical Society Published on Web 07/14/2009
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TABLE 1: Summary of Previous Experimental and Computational Measurements of Dissociation Barriers of H2 and CH4 over Nickel (111) and Ni13 Cluster Surfaces H2 surface Wortman et al. 195727 Sherman et al. 193528 Lee, DePristo et al. 198629
Ni wire tip Ni(100) Ni(110) Ni(111)
Beebe et al. 198730
CH4 barrier (kcal/mol)
method
surface
cryostatic, field emission no barrier Hu¨ckel’s method 24.0 empirical potential ∼19.59a energy surface no barrierb ∼5.76c
Ceyer et al. 198722 Chorkendorff et al. 1990 Nielson et al. 199531 Chorkendorff et. al. 200132 Siegbahn et al. 198333 Whitten, Yang 19916 Zhang et al. 200534 Henkelman et. al 200618 Charlot et al.9 Alvarez et al. 199710
barrier (kcal/mol)
method
Ni(111) DFTf icosahedral Ni13 extended Hu¨ckel icosahedral Ni13 empirical potential energy surface
∼0.5 dissociation at triangular surface 4.6-13.8
Ni(100) sticking coefficient vs coverage Ni(110) Ni(111) Ni(111) supersonic molecular beam, HREELS Ni(100) XPS Ni(100) thermal activation Ni(111) XPS, sticking coefficient vs coverage ab initio, CIg Ni(111) ab initio, CIg and embedding theory Ni(100) DFTe Ni(111) DFTf
6.4 13.3 12.6 12.0 12.44 14.1 17.7 ( 2.4 18.0 16.7 16.82 18.9
a H2 dissociates from the atop site to either bridge site or center site. b H2 dissociates above the short bridge site. c H2 dissociates above the center, but parallels the unit cell. d ADF. e VASP. f VASP. g CI for configuration interaction.
TABLE 2: Geometries of the Icosahedral Ni13
polarization (DNP)17 basis sets were employed, and all calculations were spin-unrestricted to account for the magnetic properties of nickel. The convergence criterion for the energy, maximum force, and maximum displacement changes were set at 2.0 × 10-5 hartree (Ha), 4.0 × 10-3 Ha/Å, and 5.0 × 10-3 Å, respectively. Self-consistent field convergence was declared when at least two of the above criteria were satisfied. A thermal smearing value of 5.0 × 10-3 Ha was used throughout the study. Suitable charge and spin density mixing parameters also turn out to be useful to aid the convergence of the self-consistent calculations. For the periodic planar surface calculations, a five-layer (3 × 3) slab was chosen to represent the Ni(111) surface for H2 and CH4 molecular dissociation. A 2 × 2 × 1 Monkhorst-Pack k-point mesh20 was used to sample the Brillouin zone of the unit cell. The bottom two layers of the nickel slab were fixed, while all other atoms were allowed to relax. Cluster calculations were set up and conducted within one isolated box with the same analysis setting as the slab calculations unless otherwise stated. A complete linear synchronous transit (LST) and quadratic synchronous (QST) search algorithm was employed to identify the transition state of a reaction.21 The strategy used by the LST/ QST transition state (TS) search is to start with given reaction-product configurations, e.g., H2/CH4(g) + surface and H2/CH4(s) + surface. Intermediate configurations based on those two end points are then generated via a linear interpolation algorithm. From this set of configurations, the one with the highest energy is subsequently optimized on the potential energy surface using conjugate gradient (CG) minimization. The two end points and this third configuration from the CG calculation are the initial configurations sent to the QST algorithm. Each time a new peak along the QST curve is located, a round of the
method Charlot et al.
RNi-Ni (Å) 9
Reuse et al.17 this work
θNi-Ni-Ni (°)e
a
2.50 2.63b 2.18c 2.30d 2.34c 2.46d
108.0
a Distance measured from center atom to an external atom. Distance measured from one external atom to an adjacent external atom. c Distance is the average of that measured from the center to external atoms. d Distance is the average of that measured between pairs of adjacent external atoms. e Two types of angles are of primary interest. Only the obtuse angle is shown here. The other angle type is 60°. b
conjugate gradient minimization is carried out. This iterative process is continued until convergence is reached. The reaction barrier is then calculated. At the end of every analysis, the Hessian matrix for the transition state was analyzed and verified to have one imaginary frequency. 3. Results and Discussion 3.1. Icosahedral Ni13 Clusters. The icosahedral Ni13 cluster consists of a core nickel atom surrounded by 12 equidistant neighbors. Ni13 has a magic number of atoms and exhibits a high binding energy and structural stability as compared with those of other members in the Ni cluster family.22-25 The icosahedral geometry provides adsorption sites similar to the planar (111) surface so that a more direct comparison can be made on the effect of curvature on the dissociation barrier. The 1-fold atop, 2-fold bridge, and 3-fold adsorption sites on Ni13 are denoted by t1, b2, and c3, respectively, and the same notation will be applied to the Ni(111) cluster as well.
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Figure 1. Partial density of states (PDOS) and schematic representations of the H atom adsorptions on various sites of the Ni13 cluster: (a) t1; (b) b2; (c) c3 (all units are in atomic units).
Unlike the analogous sites for Ni(111), each corresponding site on Ni13 cluster surfaces are subject to the influence of edge effects. The dihedral angles for the icosahedral Ni13 cluster are 138°, while the angle formed between one face and its opposite edge is 110°. The geometry of an optimized Ni13 structure compares well with those obtained elsewhere as shown in Table 2. No symmetry restriction was imposed on the cluster during optimization, and the values listed in the table are averaged because there is a small but noticeable deviation in Ni-Ni bond lengths. The electronic and magnetic properties of icosahedral Ni13 have been examined by Reuse et al.,26 who also observed such deviations from perfect Ih symmetry in their study and identified it as a form of Jahn-Teller distortion. Unlike Ni(111), which is characterized by uniform and almost neutral surface charge distribution, the overlap Mulliken population on each of the icosahedral Ni13 surface atoms is -0.015 and 0.163 at the core. The partial density of states (PDOS) data calculated for Ni13 shows an apparent dispersion of the valence electrons (3d and 4s electrons), resembling that of a (111) surface of a crystal for the Ni atoms on the surface. Hence, we believe that the surface of Ni13 already carries some of the crystal surface characteristics. 3.2. H2 Dissociation on Ni13. Analogous to Ni(111), the Ni13 cluster offers atop (1-fold), bridge (2-fold), and center (3-fold) sites for H binding. Figure 1a-c illustrates the adsorption of H atom at these t1, b2, and c3 sites. The relevant binding energies, calculated using EH - binding ) EH - cluster - (Ecluster + EH), are listed in Table 3 for direct comparison with those associated with Ni(111). The c3 site is much more favored, b2 is second in preference, and the t1 site follows last, obeying the same order of preference for Ni(111). Figure 1 also plots the corresponding PDOS for H binding at these sites. The bonding between H and the cluster is indicated by the overlap of the sp-orbital of Ni with the s-orbital of H, which is primarily in the range of -0.3 to -0.2 Ha below the Fermi level. The resonance between the Ni sp-band with H s-orbital is stronger than that associated with the Ni d-band; therefore, we conclude that the d-band plays only a modulating role in the bonding process. It should also be noted that the H(s)-Ni(sp) resonance is lower for c3 than t1
TABLE 3: Binding Energies of H on Ni13 and Ni(111) Surface site
Ebinding (kcal/mol) on Ni13
Ebinding (kcal/mol) at Ni(111)
t1 b2 c3
-64 -71 -72
-59 -65 -68a/-67b
a This value corresponds to the fcc site (no Ni atom beneath the 3-fold site). b This value corresponds to the hcp site (there is a Ni atom beneath the 3-fold site).
site bonding, with the resonance range shifting from -0.2 to -0.1 Ha down to -0.3 to -0.2 Ha below the Fermi level. This is consistent with the increased binding energy of the c3 sites. An H2 molecule was subsequently introduced, and the resulting relaxation leads to H2 adsorption on a t1 site. The H2 molecule is nearly horizontal, and the Ni-H distance is at 1.54 Å, while the H-H distance is 0.86 Å. This suggests that there could be a dissociation precursor for the dissociation of H2 at the Ni13 cluster. An adsorption energy of 6.6 kcal/mol indicates that the molecule is bonded to the cluster. To investigate how the surface responds to an approaching H2, we compared changes of the PDOS of H2 and the Ni atom at the adsorption site in Ni13 (Figure 2a) as well on the (111) surface (Figure 2b) before and after the adsorption. The positive part of the curve represents the emerging new states, while negative part indicates states not present in the adsorbed state. The presence of H2 induces the appearance of an sp-band and a d-band at a lower energy level within -0.3 to -0.4 Ha on both Ni13 and (111) surfaces to resonate with the s-band of H2. A slightly antibonding interaction above the Fermi level is also noticeable. The 6.4 kcal/mol adsorption energy can be accounted for from the H(s)Ni(sp) and H(s)-Ni(d) resonance. Compared to Ni13, the interaction between H2 and the Ni(111) surface is much weaker; this explains why there is no apparent adsorption of H2 at the Ni(111) surface. The dissociation of an H2 molecule from this local t1 potential well was then considered. Its transition state (TS) structure and TS energy barrier were determined using the same approach established for the analogous calculations for H2 and CH4
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Figure 2. Changes of partial density of states (PDOS) before and after H2 adsorption on Ni13 and Ni(111) surfaces, respectively: (a) Ni13; (b) Ni(111) (all units are in atomic units).
Figure 3. Schematic representation of the H2 dissociation reaction pathways at t1 and b2 sites of Ni13 and Ni(111), respectively (all units are in kcal/mol).
dissociations on Ni(111). For our LST/QST TS search calculation, the H2 dissociation over Ni(111) b2 site was chosen. The H2 molecule orientated perpendicular to the surface was chosen as the reactant state, and the dissociated atomic H fell to adjacent c3 sites. The LST/QST reaction barrier was calculated to be 0.6 kcal/mol, in good agreement with previous studies.27 The dissociative adsorption of H2 on Ni(111) is 18.9 kcal/mol, exothermic, in good agreement with the DFT calculation by Watwe et al.28 The dissociated H positions were chosen to be the c3 and b2 sites as shown in Figure 3 along with that for the H2 dissociation at the (111) surface. The energy of this configuration is 13.3 kcal/mol lower than the reactant state (molecular adsorption), and a 3.5 kcal/mol reaction barrier was estimated via the LST/ QST TS search. The reaction of the dissociation path for H2 on Ni(111) from a b2 site onto adjacent c3 sites was also examined for Ni13. These are no longer local energy minima. Similar to the (111) surface, the potential energy surface for H2 above the b2 site is quite flat. There is, however, a barrier of approximately 2.0 kcal/mol to incoming H2 molecules. Geometry optimization
TABLE 4: Binding Energies of Methyl on Ni13 and Ni(111) site
Ebinding (kcal/mol) on Ni13
Ebinding (kcal/mol) on Ni(111)
t1 b2 c3
-60 -59 -58
-45 -43 -48a/-47b
a
3-Fold fcc site. b 3-Fold hcp site.
of an H2 molecule placed within 2.0 Å of the b2 site leads directly to H2 dissociation. Two complete H2 dissociation pathways starting at t1 and b2 sites are presented in Figure 3. The potential energy surface along the t1 path shows a steeper slope and deeper well which tends to draw approaching H2 molecules into the chemisorbed state at the t1 site. Even though a TS search using an unoptimized reactant state indicates that there is no barrier to subsequent dissociation, the dissociation of H2 at the t1 site Ni13 is still considered as a more favorable pathway as a result. The imaginary frequency corresponding to the TS is -423 cm-1. Even though the binding energies show promising signs of H2 dissociation on Ni13 cluster energetically, our DFT estimates
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Figure 4. Partial density of states (PDOS) and schematic representations of the CH3 atom adsorptions on various sites of the Ni13 cluster: (a) t1; (b) b2; (c) c3 (all units are in atomic units).
Figure 5. Changes of partial density of states (PDOS) before and after CH4 adsorption on Ni13 and Ni(111) surfaces, respectively: (a) Ni13; (b) Ni(111) (all units are in atomic units).
of reaction barriers indicate that Ni13 does not obey this rule since Ni(111) offers a lower reaction barrier to H2 dissociation. This suggests that in addition to the catalyst’s surface area and its coordination number, H2 dissociation could be influenced by the catalyst surface geometries. In order to validate this hypothesis, we found other analogous t1 sites to investigate the dissociation of H2, i.e., Ni1 and the t1 on Ni4 tetrahedral cluster. The single Ni atom can be considered as an extreme case of the Ni cluster; while Ni4 was chosen because it is the next simplest in three-dimensional geometry and possesses some geometrical features similar to those of the icosahedral Ni13. However, such Ni4 clusters have sharper angles. The dihedral angle for the Ni4 cluster is 70.5°, while the angle between one face and an edge is 54.8°. H2 and a Ni atom form the NiH2 complex with a bent geometry without requiring any external energy. The H-H bond was stretched to 1.97 Å, while the Ni-H bond lengths are 1.4 Å. In contrast to the H2 response to Ni1, H2 showed a similar behavior on Ni4 as it did on Ni13 except that the chemisorption site is not directly above the t1 site; rather, it is between the t1
and c3 sites. This is due to the asymmetry of the bonding orbitals between Ni4 and H2. The adsorption energies for these two systems are 34.5 and 19.2 kcal/mol, respectively. The dissociation barrier for H2 at the t1 site of Ni4 cluster was subsequently calculated, and a value of 3.8 kcal/mol was obtained. The adsorption energies obtained from these surfaces reveal a trend that the ability of the Ni surface holding molecular H2 decreases with the increase of the coordination numbers of the surface Ni atoms as well as the decrease of surface curvatures. The calculations performed on the dissociation of H2 at Ni(111) confirmed that the H-H bond can be easily broken at very low barriers because of the partially unfilled d bands of surface Ni atoms.29 H2 has an affinity for the tips of the surface and prefers to bind to the site in its molecular form. This results in lowering the energy of the reactant state, thus making dissociation more unfavorable. 3.3. CH4 Dissociation on Ni13. The interaction of H2 with Ni13 leads naturally to the more industrially relevant issue of the C-H bond breaking for hydrocarbons on such nickel surfaces. CH4 was chosen as a prototype for this study. The
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Figure 6. (a) Transition state of CH4 dissociation on atomic Ni; (b) transition state of CH4 at the t1 site of Ni4 cluster; (c) transition state of CH4 on Ni13 icosahedral cluster; (d) transition state of CH4 on Ni(111) surface (all units are in Å).
primary dissociation of CH4 in the presence of Ni13 leading to the coadsorption of methyl (CH3) and H was studied in order to explain how surface geometry affects the adsorbate-surface interaction and subsequently influences dissociation. The CH3 binding energies on the Ni13 cluster listed in Table 4 are close in magnitude but instead follow a t1 > b2 > c3 order which is opposite to that at Ni(111) surface.30-32 Not very obvious, but as indicated by the PDOS plot in Figure 4a, this is because the CH sp hybridization adapts better with the available orbitals in terms of the better overlapping of the CH sp orbitals with the sp orbitals and d orbitals (at -0.2 Ha level) of the surface Ni atoms of the Ni13 cluster. This shows that in a cluster environment, the binding of a methyl fragment displays a more evident tendency to fulfill the sp3 hybridization of the C atom. CH4, like H2, is also attracted and able to adsorb onto the t1 site of Ni13. The pyramidal character of the cluster at this location admits a dovetailing of methane because the H-C-H (109°) angle fits with one H atom pointing the bridge of the cluster, while the other one pointing the 3-fold region. It should be noted that such a molecularly adsorbed state of CH4 on Ni13 does not have a counterpart on planar Ni surfaces, such as, Ni(111). Previous experiments33,34 have shown that incident CH4 molecules must have sufficient incident translational kinetic energy to overcome surface repulsion and distort the molecular structure of CH4 enough to facilitate dissociation into CH3 and H. A corresponding theoretical investigation corroborated the experimental observations by calculating repulsion energies ranging from 27.7 to 120 kcal/mol from various CH4 orientations.12 Analogous to Figure 2, Figure 5a is showing the changes of CH sp hybridization bands, Ni sp bands, and d bands after CH4 adsorbs at the Ni13 t1 site. The sp hybridization bands belonging to CH4 disappeared and reappeared at lower energy levels corresponding to the bonding between CH4 and Ni13 at -0.6 to -0.5 Ha as well as -0.3 to -0.2 Ha. Meanwhile, the unfilled CH4 antibonding orbital has shifted down around the Fermi level indicating the charge transfer from the nickel cluster. Similar behavior has been observed for the sp hybridization orbital in the CH4 molecule near Ni(111) surface, but the magnitude of resonance between CH4 and the surface is much weaker. The much smaller scale of interaction between Ni(111) and CH4 with repulsive nature is attributed to the Pauli exclusion principle,35,36 which subsequently causes high CH4 dissociation barriers. Figure 6d shows the CH4 TS structure on Ni(111) obtained via the same TS analysis technique as for H2 dissociation. The
Figure 7. Schematic representation of CH4 dissociation reaction pathways at t1 and b2 sites of Ni13, Ni atom, Ni4 cluster, and Ni(111) surfaces (all units are in kcal/mol). Transition states are omitted for clarity because they are shown in Figure 6.
TS geometry obtained from our TS analysis was compared with that from different approaches of Whitten12 and Henkelman.27 Since all of these studies show that CH4 dissociates over a Ni atom, the distances between C and that Ni atom, and that of the dissociating H-C bond were examined. Our Ni-C distance is 2.05 Å, which compares well with Henkelman’s 2.08 Å. Whitten and Yang obtained a value of 2.41 Å, which we believe was mainly caused by the fixation of the surface. The C-H bond length of 1.52 Å also compares well with Henkelman’s 1.62 Å and Whitten and Yang’s 1.53 Å. Frequency analysis identified the imaginary frequency corresponding to the transition state to the -1194 cm-1, while the lowest real frequency found from CH4 dissociation on the Ni(111) surface is 372 cm-1, corresponding to the rotation of the remaining CH3 group. On the basis of the adsorption geometry of CH4 at the t1 site of the icosahedral cluster, there are two plausible paths through
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TABLE 5: Summary of H2 and CH4 Dissociation Barriers Calculated in This Study on Both Ni(111) and Ni13 Clusters H2 surface Ni atom Ni4 Ni(111) icosahedral Ni13 a
method DFT DFT DFT DFT
a
CH4 results (kcal/mol)
surface
method
results (kcal/mol)
0.0 3.8 0.6 3.45b
Ni atom Ni4 Ni(111) icosahedral Ni13
DFT DFT DFT DFT
1.7 10.1 21.43 9.9
DMol3 in Materials Studio unless stated otherwise. b H2 dissociates at the t1 site.
which the C-H bond can be broken. The CH3 could relax to the b2 site with the H atom adsorbed on a c3 site. Alternatively, the positions of CH3 and H groups could be switched. Both of these were explored, resulting in the same transition state structure as shown in Figure 6c. The length of the C-H bond to be broken increases by about 0.42 Å. The H atom moves toward the b2 site, while the CH3 group is positioned above the t1 site. The corresponding reaction barrier is 9.9 kcal/mol. The barrier of methane decomposition on Ni13 is 11.5 kcal/mol lower than that associated with Ni(111). Similarly, an imaginary frequency of -1096 cm-1 was found for the transition state, while the lowest real frequency found from CH4 dissociation on the Ni(111) surface is 256 cm-1, corresponding to the wagging motion of CH4 in transition state. Unlike the t1 site, the b2 site of the Ni13 cluster does not provide a stable configuration for CH4 adsorption. An ad hoc initial placement of CH4 over the cluster b2 site was therefore chosen as the reactant state. We assumed that dissociation is to adjacent c3 sites. However, the CH3 and H repulse each other, and this results in CH3 being pushed to a c3 site that is further away. A TS search found a much higher barrier of 16.7 kcal/ mol as compared to that of the t1 pathway. Hence, CH4 dissociation on Ni13 would proceed in straightforward fashion as there is no significant competition with a dissociation starting from t1 sites. An illustration of these two dissociation pathways is shown in Figure 7. The dissociation barriers for methane dissociations are also summarized in Table 5. The investigation of CH4 dissociation at Ni13 clusters indicates that CH4 molecules adsorb via binding with t1 sites, which are not available on close-packed Ni(111). This admits the conclusion that the primary contribution to the barrier for CH4 dissociation stems from the repulsion of the Ni surface. The cluster geometry offers a Ni atom that is raised above its neighbors, though, and this arrangement breaks the symmetry of surface molecular orbitals and charge distribution so that the surface geometry is able to effectively lower the surface repulsion. In the separate studies conducted by Henkelman et al. on CH4 dissociation at Ni(111) and Ir(111) surfaces,27,37 the surface transition metal (Ni and Ir) where CH4 dissociates has been observed to raise above the surface. In order to better understand the role of cluster geometry on CH4 dissociation, the molecule was also allowed to dissociate onto a single Ni atom and a tetrahedral Ni4 cluster. Each corresponding transition state has been illustrated in Figure 6a and b. In the case of atomic nickel, the reaction barrier was lowered dramatically from 21.4 to 1.7 kcal/mol because the repulsion between CH4 and the surface can be considered to be completely eliminated. Like the situation with H2, the reactant state was also stabilized by a favorable chemisorption condition. However, the dissociation barrier has been compensated much more by lowering the interaction between the adsorbates and surfaces. The tetrahedral Ni4 cluster shows that it provides an energetically similar potential surface for CH4 with a similar chemi-
sorption state (an adsorption energy of 9.1 kcal/mol) and a dissociation energy barrier of similar magnitude (10.1 kcal/mol). This indicates that once CH4 is able to approach to the surface close enough to break the C-H bond, the dissociation barrier may not be that sensitive to the surface curvature. It seems, however, that surfaces that are able to provide favorable coadsorption configurations for the dissociation product can play a more influential role. This hypothesis needs to be confirmed by testing additional surface geometries. 4. Summary and Conclusions While nanoparticles are commonly used to improve catalytic activity via increased surface area, the relationship between particle geometry and catalytic performance is not well understood. This issue has been explored within the context of Ni13 dissociation of H2 and CH4 using density functional theory. To establish a most probable end state for dissociation, the site-dependent binding energies of H and CH3 were determined. It was found that t1, b2, and c3 sites on Ni13 have comparable binding energies for H atoms, but show a slight preference for c3 sites with values of 63.88, 70.53, and 72.16 kcal/mol, respectively. CH3 binds more strongly to the t1 and b2 sites of Ni13 than it does to the c3 site, with binding energies of 59.59, 59.33, and 58.04 kcal/mol, respectively. These results enabled transition state analyses for Ni13 and comparisons of reaction barriers between this cluster and those associated with a Ni(111) surface. Despite the reasonable supposition that transition metals exhibit greater reactivity in an environment with low coordination number,38 H2 dissociation barrier calculations on clusters showed that the geometry of the dissociation surface plays an important role. For molecules, such as H2, which show strong affinity to surface regardless of its configuration, a stabilized reactant state would hinder the dissociation process. Therefore, the barriers go down in the order of Ni4, Ni13, and Ni(111). The factor that affects CH4 dissociation is based on a different theory. Because the repulsive nature of the CH4-(111) surface is dominant in the process of dissociation, eliminating or diminishing the repulsion would favor forward proceeding of the dissociation reaction. The reason that icosahedral geometry enables a lower dissociation barrier for methane molecules as compared with that for Ni(111) with values of 9.9 and 21.4 kcal/mol is attributable to curvature-induced lowering of the molecule-surface repulsion. For dissociation on a single Ni atom, this barrier drops even further to 1.7 kcal/mol. In all of the cases investigated in this work, there is a barrier to methane decomposition that must be overcome by supplying the energy to pump charge to a C-H antibonding orbital. Acknowledgment. We express our gratitude and respect to Drs. Henkelman, Arnaldsson, and Jo´nsson for their helpful interactions and insights. This work was partially supported by the US Department of Energy, Office of Science, Grant DEER9542165.
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