Chemisorption and Reactivity of CHx (x = 0−4) on ... - ACS Publications

The present work reports results from density functional theory studies of the methanation on the FeCo(110) surface for the surface coverage below 0.2...
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13642

J. Phys. Chem. C 2008, 112, 13642–13649

Chemisorption and Reactivity of CHx (x ) 0-4) on Fe-Co Alloy Surfaces John M. H. Lo and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, Alberta, T2N 1N4 Canada ReceiVed: April 30, 2008; ReVised Manuscript ReceiVed: June 27, 2008

The present work reports results from density functional theory studies of the methanation on the FeCo(110) surface for the surface coverage below 0.25 ML. Except for CH3 which favors the adsorption at the longbridge Fe sites, all CHx (x ) 0-2) species are chemisorbed preferentially at the long-bridge Co and 3-fold Fe sites. On the other hand, CH4 is only physisorbed on FeCo(110) with the tripod configuration and does not exhibit an apparent site preference. The effects of surface coverage on the adsorption energies are not significant when the surface concentration of CHx increases from 0.125 to 0.250 ML; but geometrically, the less compact p(2 × 2)R45 is more favorable than the p(1 × 2) configuration. Among all possible C1 species, CH is identified to be the most dominant on the surface, and the resulting kinetic potential energy surface, which includes the lateral interactions between coadsorbed species, shows that the formation of CH4 is exothermic. These observations are in good agreement with the experimental observations that FeCo catalysts, which are immune to carbon deposition in the Fischer-Tropsch (FT) synthesis, possess similar FT catalytic properties to the conventional Co catalysts. 1. Introduction There has been an increasing interest in employing bimetallic alloys as catalysts in industrial hydrocarbon transformations because of their distinct properties and enhanced activity compared to either of their single components. It has been observed that dissolving early transition metals such as Ta, Mo, or W into Pd tunes the resulting alloys to bind atomic hydrogen atoms as weakly as noble metals (e.g., Cu, Au) while more effectively decomposing H2 molecules.1 On the other hand, depositing Pd on ZnO, which induces the formation of a 1:1 Pd-Zn alloy, makes the catalyst more selective and thermally stable in the methanol steam reforming (MSR) process2 than the common MSR catalyst Cu/ZnO in spite of being inferior to Pd in terms of activity. In addition to enhancing the catalytic properties, alloying may even result in the entire change of surface chemistry of a catalyst. For instance, the endothermic NO decomposition on a Cu(111) plane yields N2 molecules and O adatoms. In the presence of Sn (in the form of a Sn-terminated CuSn alloy), however, the process becomes highly exothermic and the nitrogen-containing product turns to gaseous N2O instead of N2.3 The catalytic activity and product selectivity of Fe-Co alloy catalysts in the Fischer-Tropsch synthesis (FT) have been extensively studied. A series of investigations carried out by Butt et al. has revealed the suppression of carbide formation and the enhanced water-gas shift activity of Fe-Co supported on SiO2.4,5 They also found that switching the oxide support to zeolite induces a higher selectivity toward high molecular-weight products and aromatics.6,7 The selectivity to C5+ hydrocarbons was confirmed by the tube-wall reactor (TWR) experiments of Dalai, Bakhshi, and Esmail;8 in this work, they also noticed almost a complete conversion of CO (98.5%) at 275 °C using the 2:1 H2/CO feed gas. On the other hand, the FT studies of Fe-Co metal/oxide composite materials demonstrated that light olefins (C2-C4) are more preferred while the CO2 formation is strongly hindered because of the promoted reversed water-gas * Corresponding author. E-mail: [email protected].

shift reaction.9-11 Fierro et al. attributed the differences in observed selectivity to the relative compositions of Fe and Co in the catalysts.12 They showed that Co-rich Fe-Co alloys favor methanation while the Fe-rich counterparts exhibit a selectivity toward C5+ hydrocarbons. Meanwhile, they also demonstrated that lowering the Co:Fe ratio from 10:5 to 10:1 lifts up the alcohol selectivity remarkably from 20% to 29% of the product mixture. As for attempts to understand Fe-Co bimetallic catalysts have been largely experimental, little has been done theoretically to understand why Fe-Co bimetallic catalysts enhance the product selectivity compared to Fe and Co in the FT synthesis. The main objective of this work is thus to yield theoretical insights into the factors controlling the product selectivity of Fe-Co FT catalysts, which may provide the foundation for future rational design of efficient bimetallic FT catalysts. This work is a continuation of the investigations previously reported by us concerning the chemisorption and reactivity of H2 and CO on Fe-Co surfaces.13,14 In the present study, we focus primarily on the CO hydrogenation reactions. 2. Computational Details The results reported in this work were obtained from the calculations based on the first-principle density functional theory as implemented in the program suite VASP15-17 in conjunction with the plane-wave basis sets with a kinetic energy cutoff of 400 eV which were used to expand the one-electron Kohn-Sham pseudo-orbitals. The Perdew-Burke-Ernzerhof (PBE) functional18,19 in the generalized gradient approximation (GGA) was used to capture the exchange-correlation effects, while the ionelectron interaction was treated using the projector augmented wave (PAW) method.20,21 Spin-polarization was assumed in all calculations in order to describe the ferromagnetic nature of Fe-Co alloys. The Fe-Co catalyst was modeled by the 1:1 Fe-Co binary system adopting the CsCl-type ferrite configuration (B2 phase); this structure can be generated by interpenetrating two simple cubic superlattices of Fe and Co. Recent density functional

10.1021/jp8038219 CCC: $40.75  2008 American Chemical Society Published on Web 08/12/2008

CHx on Fe-Co Alloy Surfaces

J. Phys. Chem. C, Vol. 112, No. 35, 2008 13643

theory (DFT) calculations22 have confirmed that this phase corresponds to the ground-state structure of Fe-Co alloys at temperatures below 1200 K with the following structural parameters: lattice constant ) 2.8571 Å,23 magnetic moment ) 2.27 µ0,24 and bulk modulus ) 2.47 mbar.25 The MonkhorstPack k-point sampling26 of 6 × 6 × 1 for the surface Brillouin zone employed in the present work yielded the corresponding parameters of 2.8418 Å, 2.23 µ0, and 2.05 mbar, respectively, which are all in fairly good agreement with experiments. The slightly large discrepancy between the observed and calculated bulk moduli may result from the shorter predicted lattice vectors compared to the experimental quantities. The (110) plane of the Fe-Co alloy was chosen in this work because, from the computations of surface energy for various available low-indexed planes of the bcc Fe-Co alloy, the (110) plane possesses a lower surface energy (2.363 J/m2) than those of the (100) and (111) planes (2.586 and 2.706 J/m2, respectively). A 4-layer periodic slab was used where the top two layers were fully relaxed in geometry optimizations. It has been shown that four layers are sufficient to reproduce the interlayer relaxation of Fe-Co detected by LEED.27 The optimized atomic positions were determined by the quasi-Newton method28 with a force tolerance of 0.01 eV/Å while all electronic optimizations were performed using the RMM-DIIS algorithm.28 A MethfesselPaxton smearing function29 of 0.1 eV was applied to facilitate the energy convergence. Chemisorption and reactions of CHx on only one side of a 2 × 2 supercell were considered, and two replica were separated by a 10 Å vacuum layer so as to reduce the artificial dipole-dipole interaction, caused by the adsorption of CHx, between slabs. The adsorption enthalpy of CHx on FeCo(110) was calculated using the following equation

Ead )

NECHx + Eslab - Eslab+NCHx N

Figure 1. High-symmetry adsorption sites on FeCo(110). Open and shaded circles represent Co and Fe respectively. Labels: (OT-Co) ontop Co site; (OT-Fe) on-top Fe site; (SB) short-bridge Fe-Co site; (TF-Co) 3-fold Co site; (TF-Fe) 3-fold Fe site; (LB-Co) long-bridge Co-Co site; (LB-Fe) long-bridge Fe-Fe site.

(1)

in which N is the number of CHx on one unit of a c(2 × 2) supercell, and ECHx is the fragment energy of CHx enclosed in a cubic box of the 10 × 10 × 10 Å3 dimension. A positive value represents an exothermic adsorption. All optimized geometries of CHx were further characterized by the normalmode analysis using a finite difference method with an atomic displacement of 0.02 Å. The zero-point energy (ZPE) correction for each adsorbed species was then computed, and was added to the associated adsorption enthalpy to yield the ZPE-corrected binding energy. The recombinations of CHx and H coadsorbed on the FeCo(110) surface were investigated by the climbing-image nudged elastic band method (ciNEB) of Jo´nsson and co-workers30-32 implemented in VASP. Eight images, generated by the linear interpolation between the reactant and product states, were considered in all transition state searches while a force tolerance of 0.03 eV/Å was imposed throughout. 3. Results and Discussion 3.1. Electronic Structure of CHx Species on FeCo(110). Four high-symmetry adsorption sites are present on an open face-centered Fe(110) surface, namely top (1-fold), bridge (2fold), 3-fold, and long-bridge (4-fold) sites.33 Notwithstanding the similar structural morphology, FeCo(110) plane possesses several new adsorption sites which are absent on Fe(110). These new sites result from replacing 50% of the surface Fe by Co which breaks the surface homogeneity; for instance, two types of top sites can be identified on FeCo(110): top sites on Fe atoms and top sites on Co atoms. In general, seven types of high-

Figure 2. Possible surface topologies for CHx adsorption on FeCo(110) at 0.250 ML surface coverage.

symmetry sites were considered in this work; the illustration and corresponding nomenclature are given in Figure 1. The present study investigated the chemisorption of CHx for the 0.125 and 0.250 ML surface coverage corresponding to one and two adsorbates per (2 × 2) supercell, respectively. In the case of 0.125 ML, the adsorbates were arranged in a stable p(2 × 2) configuration. For 0.250 ML, two surface packing schemes were allowed; the adsorbates could adopt either the p(1 × 2) arrangement, where all adsorbed species form rows along the lattice vector b a, or a less compact p(2 × 2)R45 configuration in which adsorbate molecules occupy alternate sites along each lattice axis. The surface topologies of these configurations are depicted in Figure 2. 3.1.1. C Adatoms on FeCo(110). The deposition of atomic C, resulting from the dissociation of adsorbed CO, on fcc Fe(110) has been studied by Jiang and Carter using the GGAPBE/PAW method.34 They identified the most favorable adsorption sites of C to be the LB sites with the associated binding energy of 179.2 kcal/mol at 0.25 ML surface coverage. This value is slightly larger than the value of 174.3 kcal/mol reported later by Gokhale and Mavrikakis.33 The present work yielded similar results; the most energetically preferred adsorption sites

13644 J. Phys. Chem. C, Vol. 112, No. 35, 2008

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TABLE 1: Calculated ZPE-Corrected Binding Energies (kcal/mol) of CHx (x ) 0-3) on FeCo(110) at 0.125 ML Coverage site

C

CH

CH2

CH3

OT-Co OT-Fe SB TF-Co TF-Fe LB-Fe LB-Co

121.6 121.7 148.8 163.6 167.4 162.0 167.4

118.4 119.4 143.1 153.3 155.2 151.5 155.2

76.0 75.5 90.4 97.8 96.8 94.3 96.8

40.3 40.3 46.0 43.9 49.3 51.2 49.1

TABLE 2: Calculated ZPE-Corrected Binding Energies (kcal/mol) of CHx (x ) 0-3) on FeCo(110) at 0.250 ML Coverage p(2 × 2)R45

p(1 × 2)

site

C

CH

CH2

CH3

C

CH

CH2

CH3

OT-Co OT-Fe SB TF-Co TF-Fe LB-Fe LB-Co

118.3 119.1 146.1 160.6 163.0 159.4 163.0

115.5 116.0 140.3 150.9 151.9 149.3 151.9

73.6 73.4 88.9 95.3 93.9 91.9 93.9

38.2 36.2 44.3 41.3 46.8 49.2 46.6

114.3 115.2 137.1 156.8 155.8 155.6 155.9

109.2 110.6 132.7 148.7 149.0 148.4 148.9

68.0 68.5 79.4 94.4 91.5 91.2 91.4

18.1 17.3 24.2 22.1 21.6 25.8 20.6

for C are LB-Co sites for both 0.125 and 0.250 ML. The computed adsorption energy at 0.125 ML is 167.4 kcal/mol which decreases to 163.0 kcal/mol when the surface coverage increases to 0.250 ML. The normal-mode analysis confirmed that this configuration corresponds to a true minimum on the potential energy surface up to 0.250 ML coverage. It is interesting to note that the optimized TF-Fe configuration resembles very much the most stable LB-Co configuration; they are both distanced by 0.05 Å along the lattice vector b b (see Figure 2) while the TF-Fe mode is less stable than the LB-Co mode by merely 0.02 kcal/mol (see Table 1). The TF-Fe mode also corresponds to a true minimum according to the vibrational frequency analysis. This observation is consistent with the conclusion from Jiang and Carter that the TF adsorption mode of CO on Fe(110) relaxes to the LB mode.34 Apart from the LB-Co and TF-Fe configurations, the normalmode analysis also identified the TF-Co mode of adsorbed C as a genuine minimum on the potential energy surface. This state, however, is higher in energy than both the LB-Co and TF-Fe configurations; the energy difference is about 4 kcal/ mol at 0.125 ML. The situation becomes more complicated at 0.250 ML, and the relative stability of these states shows a dependence upon the surface topology (see Table 2). For the more stable p(2 × 2)R45 surface topology, the energy separation between the TF-Co and LB-Co configurations is reduced to about 2 kcal/mol while the same trend of stability is retained. When the adsorbed CO rearrange to a more compact p(1 × 2) pattern, the steric interaction becomes prevalent, causing the TF-Co configuration to be more stable with respect to the LB-Co configuration in which the competition of bonding electrons between coadsorbed C atoms is more pronounced. 3.1.2. CH Species on FeCo(110). The site preference of CH adsorption on FeCo(110) is similar to that for C adatoms where the LB-Co sites are the most thermodynamically favorable at 0.125 ML. Nevertheless, the calculated binding energy of CH is significantly lower than that for the corresponding C species as also observed by Gokhale and Mavrikakis.33 Hydrogenation of C to CH at the LB-Co site reduces the adsorption enthalpy from 167.4 to 155.2 kcal/mol. This value is close to the binding energy of 157.7 kcal/mol determined for CH on Fe(110).33 The

weaker adsorption on FeCo(110) relative to Fe(110) is ascribed possibly to the spin disordering of Fe and Co upon alloying where the resulting surface Co d-band is lowered, giving rise to a diminished surface-adsorbate interaction.35 At the same surface coverage, there exist two other stationary configurations according to the vibrational frequency calculations: TF-Fe and TF-Co modes. The former is both energetically and structurally similar to the LB-Co configuration, being less stable by only 0.04 kcal/mol. The latter one, on the other hand, is more destabilized with respect to the TF-Fe configuration. Meanwhile, the computed C-H bond (1.101 Å) is slightly shorter than that when CH is adsorbed at the LB-Co and TF-Fe sites (1.103 Å). Increasing the surface coverage to 0.250 ML does not change significantly the relative stability of the various adsorption modes of CH on FeCo(110), the only difference being that the TF-Fe configuration becomes marginally more favorable than the LBCo configuration for both p(1 × 2) and p(2 × 2)R45 topologies. The calculated energy difference between the TFFe and LB-Co modes is 0.02 kcal/mol, and both states are found to be true minima. As shown in Tables 1 and 2, the steric destabilization arising from the increased surface coverage lowers the binding energy of CH by approximately 3 kcal/mol; the value is reduced by an additional 3 kcal/mol when the surface reorganizes from the p(2 × 2)R45 to the p(1 × 2) structure. The computed harmonic stretching νCH frequency for CH at the LB-Co site is 2890 cm-1 which is substantially lower than the C-H stretching modes of acetylene (3253 and 3278 cm-1),36 but is similar to that for the CH radical (2859 cm-1),37 suggesting that C in adsorbed CH is likely sp2- or sp3-hybridized. The C-H stretching frequency is further increased to 2910 cm-1 at 0.250 ML; this variation is possibly caused by the steric repulsion between coadsorbed CH that weakens their adsorption to the surface and, in turn, decreases the degree of saturation of C in CH. 3.1.3. CH2 Species on FeCo(110). As in the case of Fe(110),33 CH2 prefers the 3-fold adsorption sites rather than the long-bridge sites on FeCo(110). The present work showed that CH2 adsorbed at the TF-Co site is the most favorable at 0.125 ML, possessing an adsorption energy of 97.8 kcal/mol which is smaller than that of CH2 on Fe(110) (98.7 kcal/mol). Unlike the LB-configurations where the CH2 fragment is bonded symmetrically to the two bridging metal atoms, CH2 in the TFconfigurations (both TF-Fe and TF-Co) is tilted toward the surface. The calculated tilted angle between the surface normal and the rotation axis of CH2 is 15.2°. This deformation results in the two nonequivalent C-H bonds (1.146 and 1.105 Å, respectively), with the longer C-H bond being closer to the surface. The vibrational frequency calculations revealed that TF-Co is the only stable configuration of CH2 at 0.125 ML while the less energetically favorable TF-Fe, LB-Co, and LB-Fe configurations correspond to the first-order saddle points on the potential energy surface. The asymmetric CsH stretching frequencies of 2927 cm-1 is close to that for the CodCH2 (2980 cm-1)38 and FedCH2 (3011 cm-1)39 counterparts, but the symmetric CsH frequency is much lower (2561 cm-1 compared to 2918 and 2941 cm-1 for Co and Fe respectively) due to a stretched CsH bond. The computed scissoring mode of CH2 at the TFCo sites is 1321 cm-1 which is similar to the HCH bending frequency of CodCH2 (1327 cm-1). The TF-Co mode remains the only stable adsorption configuration for CH2 when the surface coverage increases to 0.250

CHx on Fe-Co Alloy Surfaces ML. The structural changes of CH2 with respect to those at 0.125 ML are not remarkable; both C-H bonds are contracted slightly (1.140 and 1.100 Å compared to 1.146 and 1.105 Å, respectively). These variations, in conjunction with the reduced calculated binding energy of 95.3 kcal/mol, suggest that the chemisorption of CH2 on FeCo(110) is weakened because of the enhanced steric interactions at high surface occupation. Meanwhile, the vibrational frequency calculations yielded 2933, 2627, and 1316 cm-1 for the asymmetric and symmetric C-H stretching modes as well as the HCH scission, respectively. As seen, the increased frequencies are in line with the shorter, and thus stronger CH bonds at 0.250 ML. Among the two possible packing schemes, the p(2 × 2)R45 configuration exhibits a higher stability than the p(1 × 2) configuration, though the difference is negligibly small (∼1 kcal/mol). 3.1.4. CH3 Species on FeCo(110). The present work predicted that the methyl CH3 fragment prefers adsorption at the LB-Fe sites; this observation differs from the results reported by Gokhale and Mavrikakis33 according to which CH3 is adsorbed exclusively on the 3-fold sites of face-centered Fe(110) plane. In addition to the different site preferences for chemisorption, the presently calculated binding energy of CH3 (51.2 kcal/mol) at the 0.125 ML surface coverage is also larger than the value for CH3 on Fe(110) (47.5 kcal/mol).33 The reason for this change is not certain, but is possibly related to the spin transfer process between neighboring Fe and Co atoms that shifts up the spin-down bands of Fe atoms,35 thus enhancing the Fe-C bonds with CH3. Only one local minimum was located for CH3 in the normalmode analysis; it corresponds to the energetically most favorable LB-Fe configuration. In this configuration, the three C-H bond distances are almost identical (1.105, 1.122, and 1.122 Å, respectively) while CH3 is 1.681 Å above the FeCo(110) surface. Interestingly, the CH3 fragment is displaced from the LB-Fe site by 0.523 Å and is only 0.479 Å away from the ideal TFCo site. This displacement results in the three similar surface C bonds: 2.210 and 2.236 Å for the Fe-C and Co-C bonds, respectively. The calculated C-H stretching frequencies (3014, 2824, and 2724 cm-1) correspond fairly well to those observed for the methane decomposition product on Fe catalyst (3015 cm-1),40 but the Fe-C stretching frequencies (326 and 215 cm-1) are substantially red-shifted compared to that for a gaseous H-Fe-CH3 complex (524 cm-1) whose Fe-C bond is considerably stronger.41 Due to its bulkiness, the chemisorption of CH3 on FeCo(110) at 0.250 ML surface coverage is highly susceptible to steric interactions. Despite the same site preference (i.e., LB-Fe mode remains as the most favorable configuration), a large difference in the calculated adsorption energies for CH3 was observed when the CH3 monolayer reconstructs from the p(2 × 2)R45 configuration to the p(1 × 2) configuration; as shown in Table 2, the more compact p(1 × 2) configuration of CH3 is destabilized by 23.4 kcal/mol with respect to the p(2 × 2)R45 configuration due to a stronger repulsion between coadsorbed CH3. In the p(1 × 2) packing mode, the shortest H-H distance between two adjacent CH3 species is only 1.293 Å, squeezing one of the geminal HCH angles to 91.4° (compared to the corresponding angle of 102.7° for CH3 in the p(2 × 2)R45 configuration). It was also noticed that the OT-Fe and OT-Co adsorption modes of CH3 become unstable with respect to its free space configuration (Table 2) when the surface topology turns into the p(1 × 2) pattern, which is attributed to the strong repulsion between coadsorbed CH3 species.

J. Phys. Chem. C, Vol. 112, No. 35, 2008 13645 TABLE 3: Calculated ZPE-Corrected Binding Energies (kcal/mol) of CH4 on FeCo(110) 0.250 MLa

0.125 ML site

1-fold

2-fold

3-fold

1-fold

2-fold

3-fold

OT-Co OT-Fe SB TF-Co TF-Fe LB-Fe LB-Co

4.3 4.6 5.0 3.7 3.4 3.6 3.3

4.3 4.9 3.9 3.7 5.0 5.0 5.0

4.9 5.1 5.0 4.3 4.9 5.0 4.9

2.8 2.7 2.9 2.9 2.9 2.9 2.9

2.8 2.6 2.9 2.9 2.9 2.8 2.9

2.8 2.9 2.9 2.9 2.7 2.8 2.7

a

For the p(2 × 2)R45 configuration only.

3.1.5. CH4 Species on FeCo(110). The adsorption of nonpolar methane molecules on transition metal surfaces is generally classified as a process of physisorption where the attractive interaction arises from the van der Waals force. It has been shown in many cases that the magnitude of such an attraction falls within the realm of milli-electronvolts,33,42-44 and there exist versatile adsorption configurations for the CH4 mono- and multilayers.43 The present work only considered the monolayer of CH4 on FeCo(110) up to the 0.250 ML surface coverage; however, three possible orientations were taken into account: 1-fold, 2-fold, and 3-fold (or tripod) configurations on various adsorption sites on FeCo(110). Table 3 lists the computed binding energies of CH4 on FeCo(110) with various configurations at 0.125 ML coverage. All these values are substantially smaller than the adsorption energies for C, CH, CH2, and CH3 (Tables 1 and 2). It is anticipated as the van der Waals interaction is the only force that ties nonpolar CH4 molecules to the FeCo(110) surface. Among the three possible coordination modes, the tripod configuration is the most favorable for CH4, giving rise to the binding energies ranging from 4.3 kcal/mol at the TF-Co sites to 5.1 kcal/mol at the OT-Fe sites. A similar site preference has also been noticed for the CH4 physisorption on Fe(110)33 in spite of much smaller predicted adsorption energies (∼0.7 kcal/mol). Both the p(1 × 2) and p(2 × 2)R45 packing schemes for CH4 at 0.250 ML coverage have been explored, and distinct results were obtained. In the former configuration, the calculated adsorption energies of CH4 are all highly negative; the average value is about -20 kcal/mol. The observed instability is related to the close proximity of coadsorbed CH4 on FeCo(110); for instance, the nearest H · · · H separation of 1.228 Å between two neighboring CH4 molecules at the OT-Fe sites is even shorter than the sum of the van der Waals radii of two hydrogen atoms. On the other hand, the p(2 × 2)R45 configuration is more favorable for CH4 at 0.250 ML coverage. As shown in Table 3, all binding energies are positive. The most stable coordination mode corresponds to CH4 adsorbed at the OT-Fe sites in a tripod manner. Meanwhile, many quasi-degenerate states exist which are higher in energy by less than 0.1 kcal/mol. It is important to emphasize that the present study of CH4 physisorption on FeCo(110) is by no means decisive and fully reliable as the current implementation of DFT in VASP is not capable of accurately describing the physics of van der Waals interactions. 3.2. Stepwise Formation of CH4 on FeCo(110). On the basis of the stable structures of adsorbed C, H, and CHx on FeCo(110) described in the previous sections, the reaction paths concerning the synthesis of CH4 from C and H adatoms were determined for 0.125 and 0.250 ML coverage, respectively. The

13646 J. Phys. Chem. C, Vol. 112, No. 35, 2008

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TABLE 4: Activation Barriers (kcal/mol) for CHx (x ) 0-3) Hydrogenation Reactions on FeCo(110)a 0.125 ML

0.250 ML

reaction

Ef

Eb

∆E

Ef

Eb

∆E

C + H a CH CH + H a CH2 CH2 + H a CH3 CH3 + H a CH4

7.6 21.9 14.7 28.9

21.8 10.1 14.3 27.1

-14.2 +11.8 +0.4 + 1.8

7.9 20.8 9.3 26.2

22.7 14.5 16.8 22.1

-14.8 +6.3 -7.5 +4.1

a

All energies are ZPE-corrected.

results are summarized in Table 4 while the schematic kinetic profiles are given in Figure 3. The sequential hydrogenation reactions start with the recombination of C and H adatoms which are at their most favorable configurations: the LB-Co and TF-Co modes,13 respectively. This process has a rather low barrier; the computed activation energy at 0.125 ML is 7.6 kcal/mol which increases to 7.9 kcal/ mol when the surface coverage reaches 0.250 ML. The low reaction barrier is likely due to the high hopping frequency of H adatoms on FeCo(110),13 which favors the migration of H toward C and, thus, the formation of CH. Meanwhile, the hydrogen addition to surface C is exothermic, giving up the energy of 14.2-14.8 kcal/mol for the surface coverage below 0.250 ML. The transition state associated with the CH formation corresponds to a stretched CH fragment lying almost parallel to the FeCo(110) surface. Increasing the surface coverage essentially does not influence the transition state structure. The calculated C-H distances are 1.634 and 1.675 Å at 0.125 and 0.250 ML, respectively. This is not unexpected due to the negligible mutual repulsion between small C and H adatoms on FeCo(110) even at 0.250 ML. Unlike the hydrogenation reaction of surface C, the hydrogen addition to CH possesses a rather large activation barrier and the reaction is endothermic regardless of the surface coverage. The hindrance of the reaction stems mainly from the fact that a strongly bound CH fragment is required to shift from its most favorable LB-Co site to a neighboring LB-Fe site where the newly formed CH2 prefers to reside energetically (Figure 3). The resulting transition state structure at 0.125 ML consists of CH located over a SB site, with the Fe-C and Co-C bonds of approximately equal length (1.833 and 1.829 Å, respectively), while a very weak covalent bond is formed between C and the incoming H atom (1.671 Å). Interestingly, the computed transition state structure at 0.250 ML is similar to that at lower coverage; the only remarkable difference is that the C · · · H bond is compressed by about 0.1 Å. It is found that the calculated forward activation energy is fairly unaffected by the surface concentration of CH and H; the reaction barrier (Ef in Table 4) changes marginally from 21.9 kcal/mol for 0.125 ML to 20.8 kcal/mol at 0.250 ML. Nevertheless, the backward barrier (Eb) is substantially altered when the surface coverage varies; at 0.125 ML, the barrier is only 10.1 kcal/mol, but it is increased to 14.5 kcal/mol when the coverage is doubled. It is partly related to the great release of steric interaction between coadsorbed species at 0.250 ML when CH2 is formed. Such a reduction of steric repulsion is much less pronounced when the surface coverage is only 0.125 ML in which adsorbates are far separated. The formation of surface methyl is accomplished by the recombination of CH2 and H adatom at the adjacent TF-Co and TF-Fe sites, respectively. The calculated reaction barrier is much lower than that for the CH + H reaction step, although it is

still less kinetically favorable compared to the C + H reaction. The low barrier of this reaction can be attributed to the rather labile surface bonding of CH2 at the TF-Co sites of FeCo(110). The transition state associated with this process corresponds to a twisted CH2 fragment with its molecular plane toward the attacking hydrogen which is slightly displaced from its favorable configuration at a neighboring TF-Fe site (Figure 3). The energy required for CH2 to achieve this configuration is estimated to be about 4 kcal/mol. However, the transition state is destabilized by the short distance between Fe and H (1.573 Å), thus raising the reaction barrier to be higher than that for the C + H reaction step. The influence of surface coverage on the reaction profile is substantial in this process. As illustrated in Figure 3, the feasibility of CH2 + H a CH3 is critically controlled by the surface occupation of FeCo(110). Whereas it is approximately thermally neutral (∆E ≈ +0.4 kcal/mol) at 0.125 ML, this process turns out to be exothermic by 7.5 kcal/mol at 0.250 ML, and the associated activation energy is reduced from 14.7 to 9.3 kcal/mol. The increased stability of the product state at 0.250 ML, and thus a larger reaction energy, likely results from the compromise between the reactive transition state containing an unstable Fe-H interaction and the elimination of the competition of the surface bonding electrons between H and CH2, both of which are bonded to the same Fe atom at the reactant state. The hydrogen addition of CH3 is the rate-limiting step in the sequential hydrogenation reactions of CO yielding methane on FeCo(110) regardless of the surface coverage. In both 0.125 and 0.250 ML, the process is sparingly endothermic (