Density Functional Studies of Methanol Decomposition on

Dec 7, 2009 - Tran Dieu Hang , Huyen Thi Nguyen , and Minh Tho Nguyen. The Journal of Physical Chemistry C 2016 120 (19), 10442-10451. Abstract | Full...
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J. Phys. Chem. C 2009, 113, 21789–21796

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Density Functional Studies of Methanol Decomposition on Subnanometer Pd Clusters F. Mehmood,† J. Greeley,‡ and L. A. Curtiss*,†,‡ Materials Science DiVision, Center for Nanoscale Materials, Argonne National Laboratory, Argonne, Illinois 60439 ReceiVed: August 11, 2009; ReVised Manuscript ReceiVed: October 19, 2009

A density functional theory study of the decomposition of methanol on subnanometer palladium clusters (primarily Pd4) is presented. Methanol dehydrogenation through C-H bond breaking to form hydroxymethyl (CH2OH) as the initial step, followed by steps involving formation of hydroxymethylene (CHOH), formyl (CHO), and carbon monoxide (CO), is found to be the most favorable reaction pathway. A competing dehydrogenation pathway with O-H bond breaking as the first step, followed by formation of methoxy (CH3O) and formaldehyde (CH2O), is slightly less favorable. In contrast, pathways involving C-O bond cleavage are much less energetically favorable, and no feasible pathways involving C-O bond formation to yield dimethyl ether (CH3OCH3) are found. Comparisons of the results are made with methanol decomposition products adsorbed on more extended Pd surfaces; all reaction intermediates are found to bind slightly more strongly to the clusters than to the surfaces. 1. Introduction Palladium-based catalysts have been found to be very effective for the decomposition of methanol, a reaction of great interest because methanol can be both an attractive energy source and a reliable source of hydrogen.1–3 Methanol decomposition involves, first, adsorption from the gas phase onto the surface, followed by either desorption or decomposition via various elementary bond scission steps. Previous experimental and computational studies of this reaction on large nanoparticles and on single crystal surfaces have analyzed cleavage of C-O, C-H, or O-H bonds in methanol to initiate the catalytic cycle.4–17 The activation of these bonds, in turn, gives intermediates such as methyl, hydroxyl, hydroxymethyl, and methoxy, respectively. One general conclusion of these studies has been that C-O activation is less favorable than either C-H or O-H activation. Supported subnanometer metal clusters are an emerging class of catalytic particles that, while not greatly studied in the past because of difficulties in stabilizing the clusters under realistic reaction conditions, have recently been shown to exhibit novel catalytic properties.18–21 Studies have found, for example, that size-selected small and subnanometer gold clusters show a high catalytic activity that was not seen in larger nanoparticles or on extended single crystal surfaces.22–25 To understand the elementary processes of widely utilized industrial reactions such as dehydrogenation, oxidation, and reduction, quantum mechanical calculations on gas-phase clusters of Pd and other metals have been reported in the past.26–31 Additionally, subnanometer Pt clusters have been found to exhibit remarkably high activity and selectivity for the oxidative dehydrogenation of propane to propylene compared to any known catalysts.24 These recent results suggest that a comprehensive study of the properties of subnanometer Pd clusters for the decomposition of methanol might uncover new catalytic phenomena, beyond what has already been found on Pd single crystals and larger * To whom correspondence should be addressed. † Materials Science Division. ‡ Center for Nanoscale Materials.

nanoparticles. It is quite clear, for example, that subnanometer sized clusters will have various low-coordinated sites that may affect methanol dissociation reaction pathways. In this paper, we report a density functional study of the reaction pathways for methanol dissociation on subnanometer Pd4 clusters, and selected results are also determined on Pd8; to our knowledge, this is the first study to probe the properties of subnanometer clusters for this reaction. These clusters are representative of ones being investigated in experimental studies.32 We first determine adsorption energies, geometries, reaction pathways, and activation energy barriers for the O-H, C-H, and C-O bond activation pathways. Next, we present a detailed analysis of the corresponding transition states and energy barriers. Finally, we compare results on the small Pd clusters with previously reported reaction energies on larger nanoparticles and on single crystal surfaces. 2. Theoretical Methods The calculations performed in this study are based on density functional theory (DFT).33,34 The Kohn-Sham equations were solved with a plane-wave basis set using the Vienna ab initio simulation package (VASP).35–37 The electron-ion interactions for C, H, O, and Pd were described using ultrasoft pseudopotentials with a plane-wave energy cutoff of 400 eV. In all calculations reported in this article, the generalized gradient correction of Perdew and Wang38 (GGA-PW91) was used. A 15 × 15 × 15 Å3 cubic supercell was used for the Pd4 clusters, and it was found to be large enough to ensure that the periodically repeated cluster images do not interact with one another. For Pd8 clusters, a 17 × 17 × 17 Å3 cubic supercell was used. To improve convergence, a modest Gaussian smearing (σ ) 0.01 eV) was used for all calculations. The geometry of the clusters was determined by static relaxation using a conjugate gradient minimization and the exact Hellmann-Feynman forces. The climbing-image nudged elastic band (CI-NEB) method39 was used to determine the minimum-energy paths for the elementary reaction steps and the corresponding activation energy barriers; between 5 and 7 intermediate images are used in each CINEB pathway. Vibrational frequencies (Vi) for the

10.1021/jp907772c  2009 American Chemical Society Published on Web 12/07/2009

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Figure 1. Subnanometer Pd cluster geometries. (a,b) Pd4 top and side views, respectively. (c,d) Pd8 top and side views, respectively.

initial, transition, and final states of the reaction were calculated by numerical differentiation of the forces using a second-order finite difference approach with a step size of 0.005 Å. The massweighted Hessian matrix was then diagonalized to yield the frequencies and normal modes for each system. All calculated transition state structures were confirmed to have only one negative (imaginary) frequency. Interaction energies of coadsorbed products were not included in the reported reaction energy differences of the potential energy surfaces (PESs) in this study; instead, these plots were obtained by considering product complexes adsorbed on separate clusters. In all cases, the elementary reaction energies on the PES’s were determined by taking the best adsorption sites of the reactants and products of the corresponding elementary steps. The reported transition state energies on the PES’s, however, were taken from the NEB pathway that gave the lowest such energy; this pathway might not, in all cases, correspond to the most thermodynamically stable states of the isolated reactants and products. The elementary barriers for both the pathways corresponding to the most stable isolated reactants/products and the pathways that give the lowest transition state energy are reported in this contribution. To determine the Gibbs free energies of elementary reactions, we approximated the enthalpy (∆H) at 0 K as the ∆Ee from the DFT calculations. At this temperature, the entropy contribution is also zero, and the Gibbs free energy is thus simply approximated as ∆Ee. At temperatures greater than 0 K, however, the entropy term will have rotational, vibrational, and translational contributions. We have calculated these contributions for gas-phase (nonadsorbed) species from classical approximations at 448 K and 1 bar and use them to obtain ∆G at nonzero temperatures. Zero-point energy corrections were also calculated for initial, transition, and final states of the reaction. Although these corrections were not included the reaction energy pathway plots, we do report zero-point energy corrections to activation barriers.

3. Results and Discussion In this section, we first present the structures of the bare palladium clusters. We then discuss the adsorption energies and structures of the adsorbates that are produced during the decomposition of methanol, and we compare these results to previously reported theoretical and experimental observations on single crystal surfaces and nanoparticles. Next, we describe the transition states associated with the various elementary steps in the methanol decomposition reaction network, and we discuss the overall potential energy surface for this network. We conclude with a discussion of Brønsted-Evans-Polanyi relationships between transition state energies and thermodynamic reaction energies. 3.1. Cluster Structures. We find a slightly distorted tetrahedron to be the optimized structure of the Pd4 cluster, as shown in Figure 1. We have also analyzed two configurations of bicapped octahedron structures for the Pd8 cluster (Figures 1), and we find the configuration shown in Figure 1 to be the most stable by 0.05 eV; this structure is therefore employed in all subsequent analyses. These results are consistent with a detailed optimization reported by Futschek et al.40 showing a bicapped octahedron to be the most stable configuration for Pd8. 3.2. Adsorbate Structure and Energies. The binding energies for methanol and methanol fragments adsorbed on Pd4 are summarized in Table 1, and adsorption sites are shown in Figure 2. Methanol. A single methanol molecule adsorbed on the Pd4 cluster binds to a top site through an oxygen atom, as shown in Figure 2a. Methanol is bound to the Pd4 cluster with an interaction energy of -0.48 eV and a Pd-O bond of 2.30 Å. Although no experimental or computational results for methanol adsorption on subnanometer clusters exist to compare to our results, we can confirm their general reliability by comparing to results on single and polycrystalline Pd samples. For example, ultraviolet photoemission spectroscopy experiments of methanol

DFT of Methanol Decomposition on Subnanometer Pd Clusters TABLE 1: Adsorption Energies (Eads) in eV of Methanol and Reaction Intermediates on Preferred Adsorption Sites, As Shown in Figure 2a intermediate

Eads

CH3OH CH2OH CH3O CH2O CHO CO CH3OCH3 CHOH COH CH3 CH2 CH OH C O H

-0.48 -2.07 -2.15 -0.94 -3.00 -2.54 -0.42 -3.56 -5.16 -2.01 -4.08 -6.05 -2.68 -7.01 -4.22 -2.92

Pd-X µB dPd-X adsorption site O C O C-O C C O C C C C C C

2 1 3 2 1 0 2 0 1 1 0 1 3 0 2 1

2.30 1.98 1.97 2.15 2.01 1.99 2.28 1.95 1.90 2.00 1.95 1.93 1.97 1.90 2.01 1.66

atop atop atop atop bridge 3-fold hollow atop bridge hol atop bridge 3-fold hollow atop 3-fold hollow bridge bridge

literature -0.37b -1.86c -1.78c -0.63d,-0.45e -2.23e -1.99c -3.12f -4.26f -1.71g -3.66g -5.90g -2.21h -6.40g -3.75f -2.81e

a “X” is the atom bonded to the Pd-cluster, and dPd-X is the bond length with that atom in Å. µB is the magnetic moment of the cluster with the specified intermediate. Adsorption energies are given with respect to the corresponding gas-phase species and clean Pd4 clusters at infinite separation from one another. b Reference 17. c References 43 and 67. d Reference 12. e Reference 44. f Reference 45. g Reference 46. h Reference 47.

adsorption on polycrystalline Pd at 120 K show that methanol adsorbs molecularly on Pd through the O atom, consistent with our calculations.41 Calculations on Pd(111) also show that methanol binds through O with binding energies ranging from -0.3 to -0.5 eV,5,12,14,15 in the same range as our calculations. Finally, the calculated Pd-O bond length of 2.30 Å (Table 1) is close to what has been reported in the literature (2.25-2.46 Å).5,12,14,15 O-H bond Scission Adsorbates (Methoxy, Formaldehyde, Formyl). One of the three possible ways to decompose methanol on transition metals is by removing one hydrogen atom by O-H bond activation to yield a methoxy radical (CH3O). Experimentally, methoxy has been detected as a stable intermediate on single crystal Pd surfaces.42 On Pd4 and Pd8 clusters, we find that CH3O binds most strongly to a top site through an oxygen atom with an adsorption energy of -2.15 eV. Earlier calculations43 on Pd(111) show binding energy of -1.78 eV on fcc-hollow sites, very close to what was calculated on the (111) facet of large nanocrystalline Pd catalysts (-1.66 eV). Clearly, the adsorption energy on Pd4 is stronger than that reported on Pd(111).43 The Pd-O bond length of the methoxy adsorbate (see Table 1) is much shorter than the corresponding Pd-O bond in the methanol adsorbate. A formaldehyde (CH2O) intermediate can either be obtained by breaking a C-H bond in methoxy or by breaking an O-H bond in hydroxymethyl. Our calculations indicate that CH2O binds by 0.94 eV to Pd4 when both C and O are bonded to the Pd atom (with C-Pd and O-Pd bonds of 2.15 Å). Most earlier calculations show that formaldehyde also prefers adsorption in this manner7,13,15 on single crystal transition metal surfaces. The calculated binding energies of CH2O on Pd(111)5,12,44 have been reported to range from -0.45 to -0.63 eV, which is smaller than the cluster value. A formyl intermediate (CHO) can result from dehydrogenation of either formaldehyde or hydroxymethylene. The optimized structure of formyl on Pd4 is shown in Figure 2e. We find top and bridge sites to have binding energies of -2.61 and -3.00 eV, respectively. The adsorbed formyl has Pd-O bond lengths of 1.87 Å at a top site and 2.01 Å at a bridge site. Calculations

J. Phys. Chem. C, Vol. 113, No. 52, 2009 21791 on Pd(111)44 revealed that the bridge site is slightly more favorable (by 0.14 eV) for formyl adsorption than a top site and is 0.77 eV less favorable than that on Pd4. C-H bond Scission Intermediates (Hydroxymethyl, Hydroxymethylene, Hydroxymethylidyne). Methanol decomposition through C-H bond activation on Pd(111)43 and Pt(111)8 has been proposed as a competitive reaction pathway to decomposition through O-H scission. This leads to the formation of a hydroxymethyl (CH2OH) intermediate. The hydroxymethyl intermediate prefers to adsorb on a top site through a carbon atom, as shown in Figure 2b. The adsorption energy was calculated to be -2.07 eV on the Pd4 cluster. This is larger than what was reported on Pd(111)43 (-1.86 eV) and on a large Pd79 cluster14 (-1.62 eV). Removing a hydrogen from hydroxymethyl results in a hydroxymethylene (CHOH) intermediate. Hydroxymethylene preferentially adsorbs on a bridge site through a carbon atom with a relatively large binding energy (referenced to gas-phase CHOH) of -3.56 eV. The C-Pd bond length was calculated to be 1.95 Å at the bridge site. Additional C-H bond cleavage leads to a hydroxymethylidyne (COH) intermediate. We find COH to preferentially adsorb on a hollow site through carbon; the binding energy is -5.16 eV. Similarly strong binding energies were reported for this intermediate on other transition metals,8 but our binding energy is significantly higher compared to Pd(111), where it binds with an energy of -4.26 eV.45 The C-Pd bond length in hydroxymethylidyne is calculated to be 1.90 Å. Finally, as is the case with most other intermediates, we find the C-O bond of these intermediates to be elongated by 0.03-0.07 Å from the gas phase when they are adsorbed on the Pd4 cluster. C-O bond Scission Intermediates (Methyl, Methylene, and Methine). An important question in the decomposition of methanol on subnanometer clusters is to what extent these clusters might influence C-O bond cleavage in methanol, which is known to be the least competitive reaction step in the decomposition of methanol on other Pd surfaces.12 Activating the C-O bond in methanol itself results in methyl and hydroxyl groups adsorbed on the Pd4 cluster. We find CH3 to bind to a top site (Figure 2f) with a strength of -2.01 eV. This site preference is the same as is reported in earlier calculations on Pd(111)5,12 and on Pd79 clusters,14 where the authors found the top site to be the most energetically favorable, with a binding energy of -1.76 on Pd(111) and -1.71 eV on the (111) facet of a Pd79 cluster. Methylene (CH2) may be produced by subsequent C-H bond activation in methyl, by C-O bond activation in formaldehyde, or by C-O bond activation in hydroxymethyl. Methylene favors a bridge site on Pd4, as was reported for Pd(111) and for a Pd79 cluster.14 The binding energy at this site is relatively strong (-4.08 eV), in general agreement with results reported earlier on other surfaces,7,12,14,15,17 and adsorption at 3-fold hollow sites is only 0.14 eV weaker. These results are in agreement with previous calculations14,17 on Pd(111) which also show a small preference for the bridge site over hollow site adsorption. Finally, C-O bond activation in formyl or hydroxymethylene and C-H bond activation in methylene will result in methine (CH) formation. We find that CH binds very strongly at a 3-fold hollow site with binding energy of -6.05 eV. This energy represents modestly stronger binding (by 0.13 eV) than what was found for single crystal surfaces.46 Other Adsorbates (Hydroxyl, Carbon Monoxide, Atomic Species). Hydroxyl radicals prefer adsorption at a top site on a Pd4 cluster with a binding energy of -2.68 eV, slightly larger

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Figure 2. Most energetically favorable adsorption configurations on Pd4 clusters for methanol and selected methanol decomposition intermediates. (a) Methanol, CH3OH; (b) hydroxymethyl, CH2OH; (c) hydroxymethylene, CHOH; (d) methoxy, CH3O; (e) formyl, CHO; (f) methyl, CH3; (g) formaldehyde, CH2O; and (h) hydroxymethylidyne, COH. Pd atoms are represented by white circles, whereas carbon and oxygen are solid black and gray circles, respectively; small gray circles represent hydrogen atoms.

than the binding energy of -2.44 eV found for the bridge site. These trends are in general agreement with calculations on other surfaces.47 The O-H bond length does not change significantly (less than 0.02 Å) from its gas-phase bond length of 0.97 Å upon adsorption. The adsorption of carbon monoxide has been widely investigated on single crystal Pd and other transition metal surfaces, together with Pd nanoparticles, using both experiment and theory.10,12,48–55 On Pd4, we find that CO has a clear preference for adsorption in 3-fold-hollow sites with an adsorption energy of -2.54 eV. We note that there is a well-known difficulty with density functional theory calculations that consistently predict a preference for CO adsorption at 3-fold-hollow sites over experimentally observed top or bridge sites, particularly on transition metal surfaces. An analysis of this phenomenon was given by Fiebleman et al.;56 it is believed to be an artifact of the generalized gradient approximation (GGA) used in DFT calculations. However, in spite of this problem, CO binding energies calculated by DFT are generally reasonably accurate.45,57 We note that previous calculations have found that, on the edge of large nanoparticles, the bridge site is the most favorable, but on the facets of these nanoparticles, a 3-fold-hollow site is the preferred adsorption site.14 The adsorption of carbon, hydrogen, and oxygen atoms was also investigated. The preferred adsorption sites and energies are -7.01 eV for carbon at a 3-fold-hollow site, -4.22 eV for atomic oxygen at bridge site, and -2.92 eV for atomic hydrogen at a bridge site. For both H and O, the difference in energy between bridge and 3-fold-hollow sites is small (0.05 eV). In general, we find that the Pd4 clusters retain their slightly distorted tetrahedral shape upon molecular and atomic adsorption of most species. For most cases, the Pd-Pd

distance changes upon adsorption are less than 0.05 Å. For the case of CO and C, however, where binding is quite strong on Pd4, we find that both of these species move significantly toward the 3-fold site, thus increasing the Pd-Pd distance by 0.46 and 0.70 Å, respectively. These observations are generally consistent with calculations27,29–31 that do not report any major structural changes for adsorption of NO, O, CO, and H. However, we note that in some cases small gas phase clusters can undergo larger structural transformations, as shown for Cu and Co clusters.26,58 The major factors that contribute to structural transformations of gas-phase clusters are the strength of adsorbate binding or the binding energy per atom of the metal clusters themselves. A strong adsorbate binding energy will make it easier for adsorbing species to deform the clusters (the case for Co), and smaller per atom cluster binding energies can, in some cases, have a similar effect (the case for Cu).58 3.3. Adsorbates on a Pd8 Cluster. To probe cluster size effects on the methanol decomposition chemistry, we have studied the various C-O bond scission steps on a larger cluster, Pd8. Using knowledge developed from our analysis of Pd4, we have calculated adsorption geometries and energies on Pd8 for the most preferred sites of Pd4. In most cases, we find binding energies within (0.06 eV of what was calculated for Pd4. For CO and CHO, however, the difference in binding energies for Pd4 and Pd8 is larger by 0.18 and 0.27 eV, respectively, with both of these adsorbate species binding more strongly to the smaller cluster. We note that on Pd8 we have calculated adsorption/coadsorption energies of only those reactants that will be directly involved in C-O bond breaking steps; these results are further discussed below in our analysis of the kinetics of C-O bond scission.

DFT of Methanol Decomposition on Subnanometer Pd Clusters

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TABLE 2: Activation Energy Barriers (Ea in eV) for the Reaction Pathways Involving C-H and O-H Bond Cleavage in Methanol and Its Decomposition Intermediates on Pd4 Clustersa C-H bond activation

O-H bond activation

Ea Er,coads(Er,separated) Ea Er,coads(Er,separated) ZPE ZPE Er,coads TSx-y EZPE Er,coads TSx-y reactant EZPE a a CH3OH 0.86 0.71 CH2OH 0.61 0.46 CHOH 1.34 1.18 CH3O 0.88 0.71 CH2O 0.50 0.35 CHO 0.59 0.48 COH

+0.17(-0.26) +0.04 +0.34(-0.26) +0.20 -0.02(+0.31) -0.16 +0.23(-0.46) +0.07 +0.40(-0.96) +0.26 +0.23(-1.25) +0.16

CH3

+0.51(-0.01) +0.43 -0.04(-0.11) -0.18 +0.82(-0.09) +0.74

CH2 CH OH

0.71 0.60 0.96 0.80 1.23 1.10

1.63 0.85 0.67 1.64 1.16 0.98 1.64 0.31 0.12 1.63

+0.17(0.00) -0.02 -0.24(-0.21) -0.37 -0.66(-0.83) -0.82

1.62 1.49 1.45

1.67 1.57 0.55 0.49

-1.34(-2.39) -1.30

1.31

1.78 1.36 1.78 1.45 1.26

+0.92(+0.63) +0.81

1.70

a Er,separated and Er,coads are the reaction energies for the cases when all reactants and products are located at their most favorable adsorption sites on separate clusters and when the reactants and products are coadsorbed at their initial and final states for the NEB pathways, respectively. The zero point corrected barriers (EZPE a ) and ZPE corresponding reaction energies (Er,coads ) are given in italics. Positive and negative signs of reaction energies imply endothermic or exothermic reactions, respectively. TSx-y is the length (Å) of breaking O-H or C-H bonds at the respective transition states.

3.4. Thermodynamics and Kinetics of the Methanol Decomposition Reaction Network. Having established the basic energetic and geometric features of adsorbates on Pd4 clusters, we turn to a description of the energetics of the complex reaction networks associated with methanol decomposition on these clusters. We begin with a description of the most energetically favorable processes (methanol dehydrogenation through either C-H or O-H bond scission), and we follow this with a description of the more energetically unfavorable processes associated with C-O bond scission through the various decomposition intermediates. We conclude with a discussion of a competing pathway to methanol decomposition that has been extensively discussed in the literature, that of dimethyl ether formation. Dehydrogenation of Methanol (C-H or O-H Bond Activation). Methanol can initially dehydrogenate either via C-H bond activation to produce hydroxymethyl and hydrogen intermediates or through O-H bond activation to produce methoxide intermediates and hydrogen. The energetics of these and related elementary reaction steps are summarized in Table 2, and a free energy surface consisting of dehydrogenation pathways in methanol and its intermediates is plotted in Figure 3. In Figure 3, it is seen that the thermodynamic free energy change associated with C-H activation in adsorbed methanol is slightly negative while O-H bond activation is almost thermoneutral (we note, in passing, that the free energies of both intermediates, CH2OH and CH3O, are higher than the corresponding free energy of gaseous methanol and clean Pd4

Figure 3. Free energy surface for methanol dehydrogenation steps through O-H and C-H bond activation. The free energy reference is taken as gas-phase methanol and Pd4 clusters at infinite separation from one another. Entropy corrections for methanol, hydrogen, and carbon monoxide adsorption/desorption have been included at 448 K and 1 bar. Labels on the horizontal axis correspond to the black solid line. Labels on the plots refer to dashed lines.

clusters because of the sizable entropy loss associated with methanol adsorption from the gas phase at the high temperatures considered in this study). The C-H bond activation pathway begins with methanol adsorption on a top site of a Pd4 cluster. First, the carbon atom in methanol moves toward the nearest Pd atom, and oxygen moves away from the cluster. At the transition state (TS), both carbon and hydrogen are reasonably close to the Pd atom with bond lengths of 2.13 and 1.58 Å, respectively, while the C-H bond has been stretched from its equilibrium length of 1.1 to 1.63 Å. The C-Pd-H angle is 50°. In the final state (FS) of the C-H cleavage step, both CH2OH and H are located at a top site on a Pd atom. The activation energy barrier with respect to the adsorbed methanol was found to be 0.86 eV. A comparison of the geometrical structure of the TS and its activation barrier shows it to be quite similar to what has been reported earlier on single crystal Pd surfaces.12,45 After the initial C-H bond scission event in methanol, further dehydrogenation can occur via C-H or O-H cleavage in hydroxymethyl (CH2OH). The most thermodynamically favorable of these processes is C-H bond scission in CH2OH to yield hydroxymethylene (CHOH); this elementary step is -0.26 eV exothermic, and the barrier is 0.61 eV. O-H cleavage to yield formaldehyde (CH2O), however, has a much higher barrier (1.16 eV). Subsequent elementary steps, involving H2 desorption, CHO formation, and ultimately CO formation, all have modest kinetic or thermodynamic barriers and are expected to proceed relatively rapidly. CO desorption, on the other hand, has a relatively high thermodynamic barrier, implying that the CO coverage on the Pd4 clusters will be relatively high under reaction conditions. As with the C-H activation pathway in methanol, the O-H pathway begins with methanol adsorption on a top site of Pd4. The O-H bond elongates from its equilibrium bond length of 0.98 Å to the transition state bond length of 1.62 Å. At the TS, the methoxy intermediate and atomic hydrogen are bound to Pd with lengths of 2.12 Å (O-Pd) and 1.76 Å (H-Pd), respectively. Finally, at the end of the reaction coordinate, hydrogen attains a bridge site while methoxy remains on top of the Pd atom. The activation barrier (0.85 eV) is not substantially different from the barrier for C-H bond activation.

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TABLE 3: Activation Energy Barriers (Ea, in eV) for the Reaction Pathways Studied on Pd4 for C-O Bond Breaking Steps in Methanol and Other Reaction Intermediatesa Pd4 reaction CH3OH CH2OH CHOH CH3O CH2O CHO COH CO

Ea EZPE a

Er,coads(Er,separated) ZPE Er,coads

1.31 1.15 0.79 0.70 1.05 1.04 1.89 1.84 2.29 2.23 2.18 2.13 0.69 0.67 4.17 4.09

+0.40(+0.08) +0.28 +0.07(+0.32) -0.05 -0.02(+0.54) -0.08 +1.13(+0.71) +0.98 +1.66(+1.16) +1.63 +2.06(+2.01) +2.00 +0.56(+0.14) +0.53 +3.26(+3.17) +3.22

Pd8 TSC-O 1.94 1.96 1.87 2.06 2.36 2.55 2.18 2.05

∆Ea EZPE a

∆Er,coads ZPE ∆Er,coads

-0.05 -0.01 +0.09 +0.09 -

+0.06 +0.07 +0.63 +0.61 -

+0.15 +0.12 +0.35 +0.36 +0.06 +0.03 -

-0.05 -0.11 -0.51 -0.47 +0.37 +0.35 -

-0.06 -0.01

+1.16 +1.15

TSC-O 1.93 1.97 2.10 2.20 2.08 2.25

a Er,separated and Er,coads are the reaction energies for the cases when all reactants and products are located at their most favorable adsorption sites on separate clusters and when the reactants and products are coadsorbed at their initial and final states for the NEB pathways, respectively. Positive and negative signs for reaction energies represent endothermic and exothermic reactions, respectively. The zero point ZPE corrected barriers (EZPE a ) and corresponding reaction energies (Er,coads) are given in italics. TSC-O is the length (Å) of breaking C-O bonds at the transition states. ∆’s are the difference between Pd4 and Pd8 activation and reaction energies. The selection of the initial and final states for the Pd8 calculations was made based on the best Pd4 reaction pathways.

In comparison, calculations12 on Pd(111) find the O-H scission barrier to be 0.22 eV larger. After overcoming the modest barrier (0.85 eV) needed to create methoxy, subsequent dehydrogenation proceeds through CH2O, and ultimately CHO and CO; these steps have relatively low barriers. However, the overall free energies of the intermediates associated with this dehydrogenation pathway are slightly higher than the free energies of corresponding intermediates associated with the CH2OH pathway. These results suggest that a dehydrogenation pathway with CH3O as the initial intermediate may be competitive with, although not quite as favorable as, corresponding pathways beginning with C-H scission in methanol. These pathways are summarized schematically in the following equations

CH3OH f CH2OH, H f CHOH, H2 f CHO, H f CO, 2H2 (1) and

CH3OH f CH3O,H f CH2O, H2 f CHO, H f CO, 2H2 (2) In passing, we note that in results to be reported elsewhere32 we have investigated the kinetics of the first step in methanol decomposition for a Pd cluster on an alumina support in the absence of acidic or interfacial sites. We find a very small effect of the oxide support. In addition, a previous study provides evidence that an alumina support does not have much effect on the energetics of a similar reaction, the dehydrogenation of propane on subnanometer Pt clusters.24 Methanol Decomposition through C-O Bond Activation. Although dehydrogenation mechanisms appear to be energetically favorable in the methanol decomposition process, it is nonetheless important to consider competing pathways and elementary steps on subnanometer Pd clusters. In Table 3, we summarize the activation energy barriers, reaction energies, and C-O bond lengths at transition states for C-O bond cleavage in methanol itself and in its dehydrogenation products. For

methanol on Pd4, C-O bond activation is slightly endothermic by +0.08 eV. The main component of the reaction coordinate for this elementary step is elongation of the C-O bond over a single Pd atom. At the transition state, this bond is extended by 0.49 Å from its equilibrium bond length. After the TS, these radicals move slightly further apart, but both remain on a top site in their final, coadsorbed, state. The barrier for this step, 1.31 eV, is considerably larger than the barriers for competing steps in the most favorable dehydrogenation pathways (Table 2), but it is interesting to note that it is still ∼30% smaller than comparable barriers on single crystal Pd surfaces and on large nanoparticles.12,14,45 The C-O bond breaking steps in other dehydrogenation intermediates, including CH2OH, CHOH, and COH, are moderately endothermic by 0.32, 0.54, and 0.14 eV, respectively; still larger endothermicities are determined for C-O activation in CH3O (0.71 eV), CH2O (1.16 eV), CHO (2.01 eV), and CO (3.17 eV). Each of these elementary steps has activation barriers that are higher than the corresponding barriers for the most energetically favorable C-H or O-H bondbreaking processes in the respective intermediates, strongly implying that C-O cleavage is unlikely to be a major reaction pathway on Pd4 clusters. This general result has also been found on single crystal Pd surfaces and on large Pd nanoparticles, although slow C-O bond breaking has been shown experimentally on some Pd catalysts at very high methanol coverages, perhaps due to hydrogen bonding between coadsorbed methanol molecules.9–11,59–61 Reactions on a Pd8 Cluster. To estimate the effect of cluster size on bond-breaking energetics, we have investigated C-O bond activation in methanol and other intermediates using the same eight atom Pd cluster that was used to model adsorption energetics on larger clusters (Section 3.2). In Table 3, we provide reaction energy differences between Pd4 and Pd8 (∆Er); reactions are generally more endothermic on Pd8, although the differences are only significant for a few reactions. These differences can be explained by understanding that, for Pd8, we have performed calculations on only those adsorption/coadsorption sites that are

DFT of Methanol Decomposition on Subnanometer Pd Clusters

Figure 4. Free energy surface for dimethyl ether formation with reference to two methanol molecules in the gas phase on Pd4. Entropy corrections for methanol and water adsorption/desorption have been included at 448 K and 1 bar. Color scheme for different atoms is the same as described in Figure 2.

similar to those on Pd4. For most of the reactions, this approach gives activation energy barriers and reaction energies that are quite similar to those on Pd4. In a few cases, such as the reaction energy of C-O bond activation in CH2OH, CH2O, and CO, however, the differences are larger. In these situations, there is a spontaneous relaxation of the reactants and products into qualitatively different configurations from those found on Pd4, implying that the Pd8 clusters give more geometrical flexibility to the adsorbed species in these cases. In addition to looking at C-O bond activation in methanol decomposition intermediates, we have analyzed the other initial elementary steps in methanol decomposition (O-H, C-H, and C-O bond activation) on Pd8 clusters; we find very small differences in activation energy barriers compared to Pd4 for these three cases. On the larger Pd8 clusters, the barrier for C-H or O-H bond activation is not substantially changed compared to Pd4 (only 0.02 eV larger on Pd8); the transition state is also quite similar although the final state is slightly different with hydrogen on bridge instead of 3-fold sites. We note that experimental work of Fayet et al.62 shows modest variations in reactivity based on rate constant measurements for various adsorbates, such as D2, reacting with Pd clusters of sizes ranging from 2 to 25 atoms. For most cases, reactivity increases with increasing cluster size until a certain threshold in size is achieved and thereafter starts dropping. However, a direct comparison of our calculations to this experimental work cannot be made because different adsorbates were considered in those studies. 3.5. Formation of Dimethyl Ether. A variety of experimental studies have established that methanol, catalyzed by supported metal nanoparticles, dehydrates to dimethyl ether (DME).50,63,64 Most of these studies suggested that this reaction occurs on acid sites of the support materials,65 but relatively little mechanistic support for this proposal has been provided, and the role of the metal catalyst in the reaction, if any, has not been carefully analyzed. In this work, we study multiple reaction pathways for DME formation. In Figure 4, we show a potential energy surface for a mechanism involving adsorption of methanol, formation of methoxy, formation of methyl and, eventually, dimethyl ether and water, on Pd4. Both the thermodynamics and kinetics of this mechanism appear to be unfavorable to DME formation; indeed, the rate-limiting barrier is nearly 1.39 eV. The dissociation of the second methanol and formation of water is considered to be a simultaneous process in our

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Figure 5. Brønsted-Evans-Polanyi plot, the calculated transition state energy (ETS) versus final state energy (EFS), for all reaction pathways on the Pd4 and Pd8 clusters. Both transition and final state energies for each elementary step are calculated with reference to reactants for that particular step, where the direction of each step is defined such that the products are lower in energy than the reactants.

calculations, as shown in Figure 4. We have also explored a pathway involving dissociation of a second methanol in one step and water formation in a separate step (that is, a two step process); here, again, the energetics appear to be very unfavorable for DME formation, with DME formation being the rate limiting step with a barrier of 1.36 eV. Finally, we explored a pathway motivated by the result, shown in Table 3, that C-O bond activation in CH2OH has a relatively small barrier. This result led us to explore a DME formation pathway through CH3OCH2; this is a known radical and has been shown to be a viable pathway in past.66 We find, however, the energy barrier for the rate limiting step of CH3OCH2 formation to be quite high (1.89 eV). Therefore, we do not find any viable pathway for DME formation on these subnanometer Pd clusters. This result, in turn, provides further support for the hypothesis that acidic supports are required to catalyze DME formation. 3.6. Activation Energies versus Reaction Energies (BEP Relation). Additional information on the energetics of methanol dissociation over subnanometer Pd clusters can be obtained by plotting Brønsted-Evans-Polanyi (BEP)-type curves. These BEP relations enable us to determine quantitative relationships between the activation barriers for elementary reaction steps and the corresponding elementary reaction energy changes. BEP relations are often implicitly assumed to hold for surface reactions, but to the best of our knowledge this kind of relationship has not been considered for subnanometer clusters. Figure 5 shows a BEP plot for all elementary reactions studied for Pd4 and Pd8 clusters. According to this BEP relationship, the thermodynamically most endothermic step should have the highest activation barrier and vice versa. The C-O dissociation is the most endothermic step in Figure 5, C-O, O-H, and C-H scission have intermediate energetics, and C-H dissociation is the most exothermic. The equation relating transition and final state energies is provided in Figure 5 and has a slope of 0.85; this value, close to unity, suggests that the transition states in the studied reaction networks are generally final state-like in character, where the final state is defined in the exothermic direction for each elementary step. Conclusions A density functional theory study of the decomposition of methanol on subnanometer (Pd4 and Pd8) clusters is presented.

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