Theoretical Studies of the Formation and Reactivity of C2 Hydrocarbon

J. Phys. Chem. C 2007, 111, 13149-13162

13149

Theoretical Studies of the Formation and Reactivity of C2 Hydrocarbon Species on the Fe(100) Surface John M. H. Lo and Tom Ziegler* Department of Chemistry, UniVersity of Calgary, Calgary, Alberta, T2N 1N4 Canada ReceiVed: May 15, 2007; In Final Form: June 25, 2007

The adsorption and reactions of organic fragments containing C2 unit on the iron surface have been investigated employing periodic density functional theory with a plane-wave basis set and pseudopotentials, as well as a slab model representing the p(2 × 2) Fe(100) surface topology. The calculations demonstrate that the most favorable C2 species on the Fe(100) surface are those containing the acetylenic carbon at the R position (i.e., C-CH, C-CH2, and C-CH3). Both the hydrogenation reactions and C-C bond coupling that are responsible for the chain growth process have been explored; it is observed that the most likely mechanism of C-C bond propagation involves the recombination of adsorbed C and CH2/CH3 followed by the migratory insertion of hydrogen at the R C atom. The subsequent β-hydride or reductive elimination results respectively in the evolution of ethylene or ethane. The present computational study indicates that the production of ethane is preferred over ethylene, which agrees with the product selectivity observed in the industrial Fischer-Tropsch synthesis catalyzed by iron.

1. Introduction There has been a continuing interest in understanding the reaction of organic molecules with transition metal surfaces in connection with the development of heterogeneous catalysts for important industrial processes such as steam cracking of ethane,1 alkene hydrogenation,2,3 and Fischer-Tropsch synthesis.4,5 This work shall focus on the Fischer-Tropsch process where readily available syn-gas (CO + H2) is converted into valuable longchain hydrocarbon containing various functional groups.6 Although the process is widely used, it suffers from the lack of product selectivity; a wide spectrum of compounds is formed within the range of industrial reaction conditions. Furthermore, the product distribution of the Fischer-Tropsch reaction is dependent upon the catalyst employed; the products vary from CH4 when Ni is used to high-weighed olefins and waxes when Fe and Co are utilized, respectively.7 In order to resolve the complexity of the reaction mechanisms involved in the Fischer-Tropsch synthesis, a large number of kinetic8-11 and spectroscopic measurements12-20 have been performed to identify possible reactive intermediates on the surfaces and construct the reaction mechanisms that are consistent with the experimental observations. Usually, these measurements are augmented by theoretical calculations which, on one hand, help confirm the assignments of spectra and the determinations of adsorption energies of surface adsorbates, and on the other hand, provide the rationale for the proposed reaction mechanisms. While the methane activation involved in the FischerTropsch synthesis has been investigated computationally for a wide range of first-row21-23 and heavier transition metals,24-27 computational studies are more sparse for the subsequent polymerization step. They are further mostly restricted to Co,28,29 Ru,29,30 and Pt.31-34 Only a few theoretical studies were conducted on the adsorption of C2 organic molecules on the * Corresponding author. E-mail: [email protected].

Fe(100) surfaces,35,36 although this surface has been investigated in many experimental studies concerned with the FischerTropsch process. Further, none of these provided an extensive examination of the many possible hydrogen and oxygen containing C2 species and their interconnection on an iron surface. In order to fill this void, the current study will focus on the adsorption of C2Hn (n ) 0-5) fragments on the Fe(100) surface. The most stable geometries of various C2Hn species on the c(2 × 2) Fe(100) surface were determined. Utilizing these configurations, we calculate the reaction paths that lead to the formation and decomposition, as well as the associated activation barriers, of these species. This work shall in addition discuss the most likely pathway for the growth of C1 to C2 species. 2. Computational Details All the electronic structure calculations were performed using plane-wave periodic density functional theory as implemented in the Vienna ab initio simulation package (VASP).37-39 The ion-electron interactions were described by the nonlocal Vanderbilt ultrasoft pseudopotentials (usPPs),40 and the exchange and correlation energies were calculated by the generalized gradient approximation (GGA) and the PW91 functional.41 Spin polarization was assumed in all calculations in order to accurately account for the magnetic properties of Fe. The Fe(100) surface was modeled by a 5 layer p(2 × 2) supercell containing 20 Fe atoms. The determined equilibrium lattice constant of 2.8553 Å is in good agreement with the experimental value of 2.8665 Å.42 In the calculations involving surface adsorbates, a Monkhorst-Pack43 k point mesh of 7 × 7 × 1 was employed as a good energy convergence could already be achieved with this mesh. The Methfessel-Paxton technique44 with a smearing width of 0.2 eV was used. The energy cutoff of the plane wave basis sets used to expand the one-electron pseudo-orbitals was set to be 360 eV. The surface species were adsorbed on only one side of the (2 × 2) supercell, and the periodic boundary conditions were

10.1021/jp073757m CCC: $37.00 © 2007 American Chemical Society Published on Web 08/11/2007

13150 J. Phys. Chem. C, Vol. 111, No. 35, 2007

Lo and Ziegler

applied. Two slabs were separated by a vacuum layer of 10 Å so as to eliminate the dipole-dipole interactions induced because of the adsorption of molecules. Within a (2 × 2) unit cell, there are four on-top, bridge, and hollow adsorption sites. Adsorption of only one hydrocarbon fragment was allowed at a time; in other words, the surface coverage was fixed at 0.25 ML. The ionic geometry optimization was done by the quasiNewton method with the force convergence criteria of 0.01 eV/Å on each unconstrained atom, and the adsorbed species and the Fe atoms at the top two layers were allowed to relax. To locate the transition states, the nudged-elastic band method of Jo´nsson and Mills45 as implemented in VASP was utilized. Eight to 10 intermediate configurations between the initial and final states were generated by interpolation, and were optimized simultaneously along the minimum energy path. A force tolerance of 0.01 eV/Å was used in all transition state searches. The adsorption energy of a species was calculated as the difference of the energy of the surface-adsorbate system and those of the isolated surface and isolated adsorbate. That is,

Eads ) Esurf/ads - Esurf - Eads

(1)

The energies of isolated adsorbates were determined by assuming the adsorbates encapsulated in a 10 × 10 × 10 Å3 box. 3. Results and Discussions 3.1. Chemisorption of C2Hn Intermediates. C2 is a proposed intermediate in the synthesis of the single-wall carbon nanotubes from acetylene catalyzed by Fe,35 although no spectroscopic evidence of its presence as a decomposition product of chemisorbed acetylene on the Fe(100) surface was noticed up to 393 K.46 C2 is a singlet diatomic molecule in the gas phase, but the first triplet state lies only 2 kcal/mol above the singlet ground state.47 Consequently, a strong interaction of C2 with the Fe(100) is expected. The C2 fragment can be adsorbed on the Fe(100) surface in either parallel or perpendicular mode. For the adsorption on all possible sites, the parallel modes are always more preferred; in general, the C2 unit parallel to the metal surface is 18 kcal/mol more strongly bound than the corresponding perpendicular counterpart. As in the case of surface carbide, C2 favors the coordination at the hollow position. There is an additional coordination mode of C2 in which the fragment is tilted from the surface normal. This state, as shown in Figure 1a, corresponds to the most stable configuration, possessing an adsorption energy of 179.5 kcal/mol. The computed C-C bond length is 1.356 Å and is tilted by 28.6° from the surface. A similar adsorption mode has also been observed in the adsorption of CO on the Fe(100) surface.48 Ethynyl (C-CH) is a species detected by high-resolution electron energy loss spectroscopy (HREELS) during the decomposition of acetylene on the Fe(100) surface.46 An openshell radical, it interacts strongly with the partially vacant Fe surface d band, giving rise to the high adsorption energy. Only the vertical mode of adsorption of C-CH on the three available adsorption sites was considered, according to the observations of C2; nevertheless, they all do not correspond to the minimum energy configuration. The most stable geometry was found to be the tilted C-CH at the fourfold site with the computed adsorption energy of 138.9 kcal/mol. It is given in Figure 1b. In this configuration, the C-C bond is 1.385 Å and about 31.9° tilted from the surface. The nonlinear C-CH structure (∠CCH

Figure 1. Structures of C2 species on the Fe(100) surface in their most stable geometries. (a) C2; (b) ethynyl (C-CH); (c) acetylene (CHCH); and (d), (e), and (f) vinylidene (C-CH2) in the fourfold, tilted, and bent configurations, respectively. Labels: brown, Fe atoms; black, C atoms; blue, H atoms.

) 138°) and long C-C bond infer the rehybridization of ethynylic C during the adsorption. The hydrogenation of ethynyl yields either acetylene (CHCH) or vinylidene (C-CH2). Acetylene was found to be adsorbed on the Fe(100) surface at 98 K.49 A later study by Hung and Bernasek proposed the coordination of CH-CH at the fourfold position.46 The theoretical calculations employing the cluster models50 supported this binding mode and estimated the binding energy of 92.9 kcal/mol. However, more recent calculations using DFT found a minimum energy configuration in which CH-CH is coordinated to the Fe(100) surface along the [011] direction as depicted in Figure 1c.35 The present work agrees with the later conclusions. The computed C-C bond length is 1.383 Å while a smaller adsorption energy of 53.0 kcal/mol compared with that yielded by the cluster calculations is obtained. The C-H bond is bent by 60.0° with respect to the Fe surface, in excellent agreement with the value of 59.6° predicted by Ihm et al.35 While acetylene is only moderately bound to Fe via its C-C π orbitals, the structural isomer C-CH2 is strongly adsorbed at the hollow site of the Fe(100) surface through the interaction of its lone pair of electrons on the vinylidenic C and the surface Fe d orbitals. The adsorption energy of C-CH2 at the fourfold site (Figure 1d) is 97.7 kcal/mol, which is 31.0 kcal/mol and 21.1 kcal/mol more stabilized than the on-top and bridged configurations, respectively. In the fourfold configuration, the methlyene (CH2) unit lies on the [010] plane perpendicular to the Fe-Fe bridges. The computed C-C bond distance of 1.389 Å is indicative of the rehybridization of C-CH2 which results in the single-bond character of C-CH2 upon the adsorption. An additional 1.3 kcal/mol of stability is gained when C-CH2

C2 Hydrocarbon Species on the Fe(100) Surface

J. Phys. Chem. C, Vol. 111, No. 35, 2007 13151

Figure 2. Structures of C2 species on the Fe(100) surface in their most stable geometries. (a) Ethylidyne (C-CH3); (b) vinyl (CH-CH2) in planar configuration; and (c) vinyl in spinal configuration. Labels: brown, Fe atoms; black, C atoms; blue, H atoms.

is tilted toward a Fe-Fe bridge (Figure 1e), accompanied by the elongations of the C-C bond and the C-H bond that orients to the Fe surface. The studies of decomposition of acetylene on the Fe(100) surface by Hung and Bernasek46 suggested, on the basis of the measured HREELS and TPD spectra, that C-CH2 should adopt a planar structure in which the two acetylenic C atoms are σ bonded to the neighboring four Fe atoms at the fourfold site. This proposed configuration was investigated in the current study, and it is indeed the most favorable geometry, possessing the adsorption energy of 104.4 kcal/mol and the C-C bond distance of 1.427 Å (Figure 1f). As the C atoms become more sp3 hybridized during the adsorption, the two C-H bonds are not contained on the molecular plane of C-CH2; instead, a slight upward bending of C-H bonds is noticed. Ethylidyne (C-CH3) was found to prefer the capping site rather than the on-top site on the Pt(111) surface because of the better coupling overlap of the C 2p orbitals of C-CH3 and the surface orbitals.51 A similar preference is noticed in the present case as illustrated in Figure 2a; the coordination of C-CH3 at the fourfold site of the Fe(100) surface is the most favorable, possessing the adsorption energy of 130.9 kcal/mol which is 23.3 and 33.6 kcal/mol higher than those of C-CH3 adsorbed on respectively the bridged and on-top positions. The computed C-C bond distance of 1.537 Å is equivalent to the experimental value of 1.536 Å measured for ethane in the gas phase,66 indicating that the single-bond character of C-CH3 is preserved in the adsorbed species. A transient species, vinyl (CH-CH2) has been identified as a hydrogenation product on the Fe(100) surface at 100 K by HREELS during the adsorption of acetylene.46 The theoretical calculations by Nieskens et al.53 predicted the asymmetric adsorption mode on the bridged position on the Rh(100) surface as the most stable configuration of vinyl. The similar configuration, however, is not located in the current study. CH-CH2 favors the adsorption at the hollow site, with the molecular plane along the [100] direction (Figure 2b). The adsorption energy of 62.5 kcal/mol is calculated on the basis of this geometry. A substantial rehybridization of the C atoms from sp2 to sp3 is inferred by the stretched C-C bond (1.445 Å compared with 1.316 Å as determined for a gas-phase vinyl radical54). Another configuration of adsorbed vinyl at the fourfold site, as depicted in Figure 2c, has also been considered. The methylenic C possesses a pseudotetrahedral geometry and forms a weak Fe-C bond of 1.979 Å which is considerably longer than that of 1.596 Å estimated for FeC using laser-induced fluorescence (LIF)

Figure 3. Structures of C2 species on the Fe(100) surface in their most stable geometries. (a) and (b) Ethylene (CH2-CH2) on the fourfold and onefold sites, respectively; (c) and (d) ethylidene (CH-CH3) in the eclipsed and gauche configurations, respectively; and (e) ethyl (CH2-CH3) in the gauche configuration. Labels: brown, Fe atoms; black, C atoms; blue, H atoms.

spectroscopy.55 This adsorption mode is 3.9 kcal/mol less stable than the planar configuration at the fourfold site. The binding energy of ethylene (CH2-CH2) on a clean Fe(100) surface was estimated to be smaller than 14.4 kcal/mol in the studies of Hung and Bernasek using the temperatureprogrammed desorption (TDP) spectroscopy.46 They also proposed that ethylene is adsorbed at the hollow site in a skewed position. The calculated adsorption energy of this configuration in the present work is 10.2 kcal/mol, and its structure is shown in Figure 3a; however, it is not the most preferred geometry. According to the present calculations, the adsorption at the ontop position is more favored by 4.2 kcal/mol; in this configuration, the C-C bond lies along the direction 45° rotated from the [001] plane (Figure 3b). Ethylene is adsorbed to the Fe(100) surface likely through a π interaction which leads to the modest stretching of the C-C bond (0.072 Å) and small upward bending of C-H bonds (11.8°). A barrier of 0.6 kcal/mol is found for the rotation of a weakly adsorbed CH2-CH2 about the preferred onefold site, suggesting the free rotation of adsorbed ethylene at room temperatures. The barrier increases drastically to 7.3 kcal/mol and 11.2 kcal/mol for the rotation about the fourfold and twofold sites, respectively. It has been postulated that the conversion of ethylene to ethylidyne on the Rh(111) and Pt(111) surfaces involves the ethylidene (CH-CH3) intermediate.56,57 On these hexagonal surfaces, ethylidene exclusively prefers the twofold bridge site. However, a fourfold hollow site is found more favorable when it is adsorbed on the cubic Fe(100) surface; the calculated adsorption energy of CH-CH3 at the fourfold site is 83.2 kcal/ mol while for the adsorbed CH-CH3 at the twofold bridge this value drops to 76.4 kcal/mol. The calculated C-C bond length is 1.549 Å, consistent with the sp3-hybridized C-C bond distance (1.536 Å) in ethane. Two types of conformational isomers of CH-CH3 are possible because of the internal rotation of CH3 about the C-C bond. In the case of ethane, the staggered conformation is more favored because the intramolecular steric hindrance is minimized. To estimate conformational effects on the adsorption of ethylidene on the Fe(100) surface, two sets of conformers, one

13152 J. Phys. Chem. C, Vol. 111, No. 35, 2007 TABLE 1: Calculated Binding Energies (B.E.) of C2Hn (n ) 0 to 6) at Their Most Stable Configurations on the Fe(100) Surfacea species

configuration

B.E. (kcal/mol)

CC C-CH C-CH2 C-CH3 CH-CH CH-CH2 CH-CH3 CH2-CH2 CH2-CH3 CH3-CH3

fourfold (tilted) fourfold (tilted) fourfold (planar) fourfold (upright) fourfold (di-σ) fourfold (tilted) fourfold (tilted) onefold (along [110]) twofold twofold (across)

179.5 138.9 104.4 130.9 53.0 62.5 83.2 14.5 35.8 0.5

a Binding energy of ethane is calculated by assuming its most stable geometry at the bridge site as shown in Figure 17.

with the eclipsed geometry (Figure 3c) and the other with the gauche geometry (Figure 3d), were investigated. The gauche conformation is about 1.3 to 1.9 kcal/mol more favorable than the corresponding eclipsed conformation for CH-CH3 at the on-top and bridge sites. The smaller energy difference compared with that for a gas-phase ethane (3 kcal/mol) is expected as two C-H bonds are absent in CH-CH3, resulting in a weaker intramolecular steric interaction. On the other hand, the computed adsorption energy of CH-CH3 in gauche conformation at the hollow site is 2.3 kcal/mol less stable than the eclipsed conformer. The stability of the eclipsed configuration is possibly due to the stronger Fe-H interaction with the metal surface that compensates for the larger repulsion between the eclipsed C-H bonds. Molecular adsorption of ethylene on the hydrogen preadsorbed Fe(100) surface has been observed by Burke and Madix at 110 K.58 Raising the temperature to 160 K resulted in the desorption of ethylene competing with the formation of adsorbed ethyl (CH2-CH3) groups via the migratory insertion of ethylene. Their subsequent work proposed the moderately strong adsorption of CH2-CH3, with the binding energy of 38 kcal/mol, at the hollow site.59,60 The value of 35.8 kcal/mol determined in the present study is in good agreement with the experimental estimate, but the most favorable adsorption site is found to be the twofold bridge, as given by Figure 3e, instead of the hollow site whose corresponding adsorption energy is only 18.6 kcal/mol. On the basis of the fact that both ethane and the adsorbed ethylidene prefer the gauche conformation, only the adsorbed CH2-CH3 in the staggered configuration was considered in the calculations. The calculated binding energies of various C2Hn species on the Fe(100) surface are summarized in Table 1. 3.2. Hydrogenation of C2Hn Intermediates. The large diversity of hydrocarbon products in the Fischer-Tropsch synthesis is the consequence of the growth of surface species via either hydrogenation or C-C bond formation. Depending on the relative feasibility of these processes, a spectrum of aliphatic saturated and unsaturated compounds with uneven product distribution is collected. Figure 4 describes the hydrogenation steps that convert the most unsaturated C2 to ethane which is only weakly bound to the Fe(100) surface. In the next section, the formation of C2Hn+m from the dimerization of CHn and CHm will be considered. In search of the transition states and the minimum energy paths (MEPs) corresponding to these hydrogenation reactions, the C2 fragments and H atom are both assumed occupying their most stable configurations on the p(2 × 2) Fe(100) supercell unit. This approach enables the consideration of the influence of lateral interaction between the coadsorbed C2 and H species

Lo and Ziegler on their adsorption energies. For instance, in the current study, it is estimated that the presence of a pre-adsorbed H atom weakens the adsorption of C2 by 7.1 kcal/mol. The steps 1 and 2 in Figure 4 constitute one of the decomposition pathways of surface-adsorbed acetylene which leads to the formation of C2. The GGA-PBE calculations performed by Ihm et al.35 predicted the activation barrier of 35.5 kcal/mol for the CCH f CC + H reaction which is the backward reaction of step 1. A similar value is found in the present study. The computed MEP for the hydrogenation of C2 is displayed in Figure 5. The estimated backward barrier is 37.0 kcal/mol which is only slightly higher than the value deduced by Ihm et al. This hydrogenation process is found to be highly exothermic and possess a small activation barrier of 10.0 kcal/ mol. This path contains a late transition state whose C-H bond distance is 1.364 Å while that of the adsorbed C-CH is 1.087 Å. The subsequent hydrogenation on the acetylenic carbon bonded to the Fe surface gives rise to CH-CH adsorbed at the hollow position. This reaction is slightly endothermic by about 4.0 kcal/mol as illustrated by the MEP in Figure 6. The initial state comprises the coadsorbed H and C-CH at two adjacent fourfold sites. The H atom migrates over the Fe-Fe bridge and forms a C-H bond with the C-CH fragment. This process is accompanied by the rotation of C-CH about the fourfold site, resulting in CH-CH in the di-σ adsorption mode in which C atoms are bonded respectively to two diagonal Fe atoms of a primitive Fe(100) unit. At the transition state, the calculated bond distance between the acetylenic carbon and the H atoms is 1.893 Å. The estimated forward and backward activation barriers of this reaction step are 14.9 and 11.2 kcal/mol, respectively. These values are smaller than the values of 22.6 and 22.1 kcal/mol reported by Ihm et al.35 but in excellent agreement with the upper limit of barrier of 15.2 kcal/mol determined by HREELS.46 The discrepancy between the calculated values is possibly attributed to the choice of functionals; the PBE exchange-correlation functional employed in the calculations by Ihm et al. may under-estimate the adsorption energy of the transition state which consequently increases the computed activation barrier. There exist two reaction channels for the formation of vinylidene from the hydrogen attachment to ethynyl. The first pathway displayed in Figure 7a describes the in-plane attack of the hydrogen from the adjacent hollow site. This reaction pathway possesses a small barrier of 9.3 kcal/mol and the final state of C-CH2 in the tilted configuration which is 2.4 kcal/ mol less stable than the initial state. Note that the tilted configuration of C-CH2 is not the most favorable geometry; the species is 5.5 kcal/mol more stabilized when it is adsorbed in the planar configuration (Figure 1f). Consequently, this conversion further lowers the energy of the final state, leading to the resulting reaction pathway which is instead exothermic by 3.1 kcal/mol with respect to the initial state. The computed C-H bond length for the transition state is 1.631 Å which lies between the corresponding values of 2.092 and 1.150 Å for the initial and final states, respectively. The other channel is concerned with the out-of-plane attack of an adsorbed hydrogen in a neighboring site as shown in Figure 7b. This reaction path has a similar forward activation barrier as the first channel (9.6 kcal/mol cf. 9.3 kcal/mol), but is only marginally exothermic, with the final state of planar C-CH2 being favored by 0.6 kcal/mol. When the hydrogenation reaction occurs, the adsorbed hydrogen first moves toward a Fe-Fe bridge, followed by the migration over the Fe atom.



Figure 4. Schematic representation of possible transformation reactions of adsorbed C2 species on the Fe(100) surface. All hydrogenation reactions are denoted by numbered solid arrows, while C-C bond formation reactions are shown by dashed lines.

Figure 5. Minimum energy pathway for CC + H a C-CH. (Step 1 in Figure 4)

Meanwhile, the adsorbed C-CH tilts about the C-C bond in order to allow for the attack of hydrogen trans to the C-H bond. At the transition state, the calculated C-H bond distance is 1.411 Å, and the dihedral angle is 133.8°. The thermochemical data obtained in the present work indicates that the second channel is the dominant reaction pathway for the formation of C-CH2 from the hydrogenation of surface ethynyl. The second reaction path lies approximately 2.5 kcal/mol lower in energy than the first path although both possess similar reaction barriers. Moreover, the modest preference of vinylidene over ethynyl and hydrogen strongly suggests the existence of an equilibrium between these two states at the temperatures at which the Fischer-Tropsch synthesis takes place. The acetylene-vinylidene isomerization in the gas-phase has been an intense subject of both experimental and theoretical research for over two decades, and it has been found that the reactive vinylidene species transforms into acetylene by overcoming a barrier less than 990 cm-1 (∼2.8 kcal/mol)61,62 although the barrier for the reverse process was measured to be higher than 15 407 cm-1 (∼44.1 kcal/mol). The short lifetime of vinylidene is attributed to the strong overlap of this state

Figure 6. Minimum energy pathway for C-CH a CH-CH. (Step 2 in Figure 4)

with the molecular states of highly excited acetylene. This instability is, however, not observed in the cases of acetylene and vinylidene adsorbed on the iron surface; both species have been detected on the Fe(100) surface by HREELS and found to be stable. It has been proposed by Hung and Bernasek that this transformation takes place at the adsorption temperature of 100 K; nevertheless, the reaction proceeds via the stepwise dehydrogenation and hydrogenation instead of the intramolecular 1,2 H shift.46 In the present work, the transformation between the acetylene molecule adsorbed in the tilted configuration and the vinylidene species in the upright configuration at the hollow site via the 1,2 H-shift mechanism was studied. The calculated reaction path and the transition state configuration are included in Figure 8. The calculations reveal that vinylidene is about 2.4 kcal/mol more stabilized compared with acetylene. The energy difference is reduced to 0.8 kcal/mol when acetylene and vinylidene are in the di-σ and tilted geometries, respectively, but a similar reaction profile is retained. As seen in Figure 8, the process has the forward barrier of 51.5 kcal/mol and the backward barrier of 53.9 kcal/mol. These values are much higher than


Lo and Ziegler

Figure 8. Minimum energy pathway for the acetylene-vinylidene isomerization. (Step 4 in Figure 4)

Figure 7. Minimum energy pathways for the hydrogenation of C-CH leading to (a) the tilted C-CH2; and (b) the planar C-CH2. (Step 3 in Figure 4)

the corresponding values estimated for the gas-phase counterpart. The hydrogen migrates via a planar transition state in which an asymmetric CCH unit with the respective C-H bond distances of 1.658 and 1.773 Å is formed. The high activation energies of this transformation may explain the absence of such a hydrogen-shift reaction that converts the surface adsorbed acetylene to vinylidene. Vinyl (CH-CH2) is a proposed intermediate resulting from the hydrogenation of adsorbed acetylene via either the diffusion of surface hydrogen or the concerted dehydrogenation and hydrogenation of two acetylene molecules at high surface coverage.46 This hydrogenation occurs at the temperature below the desorption temperature of hydrogen (260 K), inferring the activation barrier in the range of 16 kcal/mol. According to the computed MEP shown in Figure 9, the estimated barrier height for the hydrogenation of acetylene is 14.2 kcal/mol which is in good agreement with the experiment. This reaction has the transition state resembling the reactant state; the C-H bond length between the acetylenic C and incoming H is 1.670 Å, while the corresponding bond distance in surface vinyl is 1.138 Å.

Figure 9. Minimum energy pathway for the hydrogenation of acetylene to vinyl. (Step 5 in Figure 4)

Depending on the C-H bond to be activated, the surface vinyl may decompose in two ways: the dehydrogenation on the β carbon yields the di-σ-bonded acetylene (backward reaction in Figure 9) while the hydrogen extraction from the R carbon generates vinylidene (backward reaction in Figure 10). The corresponding activation barriers are 7.6 and 4.3 kcal/mol, respectively. These small barrier heights suggest that the vinyl species formed on the Fe(100) surface is only metastable and rapidly decomposes to either acetylene or vinylidene, the latter being approximately 7.0 kcal/mol more stable. The consistent experimental evidence has also been noticed in which no transient vinyl can be detected below 200 K unless an exposure greater than 0.2 L is applied and all vinyl species decompose upon heating to 393 K regardless of the surface coverage.46 While the hydrogenation of vinylidene (C-CH2) on the R carbon is endothermic with the barrier of 12.3 kcal/mol, the attachment of hydrogen on the β carbon is favorable. Figure 11 a-c illustrates three possible reaction schemes in which the β carbon is hydrogenated. In these schemes, the hydrogen is


Figure 10. Minimum energy pathway for C-CH2 + H a CH-CH2. (Step 6 in Figure 4)

assumed to attack in the direction perpendicular to the molecular plane of vinylidene. In the first two pathways, the reactant state is the vinylidene species in the tilted configuration at the fourfold site. The coadsorbed hydrogen is situated at the adjacent (Figure 11a) and diagonal (Figure 11b) hollow sites, respectively. These pathways result in the same final state of ethylidyne (C-CH3) at the fourfold site. As shown, both pathways are exothermic but possess a large forward reaction barrier. The computed barrier for the first pathway is 19.1 kcal/mol while that for the second pathway is 21.8 kcal/mol. The higher activation energy for the latter reaction channel is the consequence of the associated transition state structure in which the hydrogen atom lies over the Fe atom and forms only a weak C-H bond (1.779 Å) with vinylidene. On the other hand, the smaller barrier height for the first pathway is resulted from the lateral interaction; the coadsorbed hydrogen at the adjacent site significantly destabilizes the vinylidene species and lowers the barrier of hydrogenation reaction. The estimated lateral effect induced by the migration of coadsorbed hydrogen from the diagonal to adjacent hollow site is 5.1 kcal/mol. The third pathway involves the vinylidene species in the most stable planar configuration and the coadsorbed hydrogen atom at the adjacent fourfold site (Figure 11c). Because of the proper orientation of C-CH2 that favors the hydrogen attack from the front side, the forward reaction barrier is reduced to 17.7 kcal/ mol compared with 19.1 and 21.8 kcal/mol for the first two pathways. The resulting transition state resembles the reactant state, with the C-H bond distance being 1.292 Å. Nevertheless, the enthalpy of reaction is small; the product state, ethylidyne, is only 2.0 kcal/mol more favorable than the reactant state. Hence, an equilibrium between these species may exist in the polymerization reactions involved in the Fischer-Tropsch synthesis. The formation of ethylidyne (C-CH3) from vinyl has been experimentally observed on the Pd(111) surface at 160 K,63 and the DFT-GGA/PW91 calculations performed by van Santen and co-workers predicted a high barrier for this one-step isomerization.64 No evidence for the presence of ethylidyne on the Fe(100) surface is, however, available, although the characteristic band at 1410 cm-1 in the HREELS spectra of the adsorbed acetylene on the Fe(100) surface might be ascribed to the methyl C-H bonds of ethylidyne.46 Contrary to the case of the Pd-

J. Phys. Chem. C, Vol. 111, No. 35, 2007 13155 (111) surface, ethylidyne is found to be 14.6 kcal/mol more favorable than vinyl on the Fe(100) surface, as shown in Figure 12. The conversion involves the forward barrier of 28.8 kcal/ mol and the backward barrier of 43.5 kcal/mol. The high reaction barrier of this isomerization is possibly due to the rehybridization of the carbon atoms and the breaking of strong interaction between the CdC π bond and the iron surface. Unlike the acetylene-vinylidene isomerization, the transition state is not planar; instead, the shifting hydrogen attacks the β carbon from one side of the vinylidene unit to achieve the pseudotetrahedral configuration of the β carbon that resembles the final product state. In addition to the dehydrogenation and isomerization processes described by steps 5, 6, and 8 in Figure 4, vinyl can undergo two low-barrier hydrogenation reactions, yielding respectively ethylene and ethylidene (CH-CH3). Figure 13 depicts the energy profile concerning the hydrogenation reaction of vinyl at the R carbon that forms surface ethylene at the most favorable on-top position. The calculated MEP indicates that ethylene is thermodynamically more favorable than vinyl and hydrogen. The reaction of hydrogen addition to the R carbon is energetically feasible, having the barrier height of only 8.7 kcal/ mol. Note that the reactant state contains the adsorbed vinyl in the alkyl configuration which indeed lies 3.9 kcal/mol above the global minimum corresponding to the tilted geometry shown in Figure 2c. An attempt to determine the MEP linking the tilted vinyl to the ethylene at the on-top position has been made, but no definitive reaction pathway could be located. Nevertheless, an activation energy of approximately 12.6 kcal/mol may still be estimated for the hydrogenation at the R position of the tilted vinyl at the hollow site. On the other hand, the hydrogenation of vinyl at the β carbon leads to the formation of ethylidene which has been proposed as an intermediate in the conversion of ethylene to ethylidyne on the Pt(111) surface.65 Despite the small activation barrier of 9.5 kcal/mol as calculated in the present study, no direct indication of this species has been found in the HREELS studies of ethylene adsorption on the Fe(100) surface.46 The calculations (Figure 14a) show that both the reactant and the product states are of similar stability, and the attachment of hydrogen at the β carbon does not induce a significant structural distortion of the transition state from vinyl and ethylidene. At the transition state, the computed C-H bond length is 1.596 Å which implies a weak interaction between the vinyl and the hydrogen species. A reason accounting for the absence of ethylidene on the Fe(100) surface during the decomposition of ethylene is that, once it is formed, it rapidly undergoes the dehydrogenation at the R carbon to generate ethylidyne. As shown in Figure 14b, this reaction proceeds by overcoming a barrier height of only 2.7 kcal/mol. In other words, ethylidene can be considered as a metastable intermediate which may have a lifetime too short for any spectroscopic detection to be made. On the other hand, the recombination of ethylidyne and hydrogen to form ethylidene is rather unlikely as the activation barrier is higher than 15 kcal/ mol. It has been suggested on the basis of experiments that the isomerization of ethylene and ethylidene initiates the interconversion of ethylene to ethylidyne on the Pt(111) surface.65 This isomerization process, however, is not feasible on the Fe(100) surface like the acetylene-vinylidene and vinyl-ethylidyne isomerizations because of the enormous forward and backward activation barriers as illustrated in Figure 15. Although smaller than those of the other two isomerization reactions due to the weaker coordination of ethylene to the Fe(100) surface, the


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Figure 11. Minimum energy pathways for the hydrogenation of vinylidene species. (a) and (b) Attack of hydrogen to C-CH2 in the tilted configuration; and (c) attack of hydrogen to C-CH2 in the planar configuration.

Figure 12. Minimum energy pathway for the vinyl-ethylidyne isomerization. (Step 8 in Figure 4)

activation barrier of 26.5 kcal/mol, for the forward reaction, and 24.0 kcal/mol, for the backward reaction, associated with the transformation of ethylene to ethylidene are still higher than the barriers for the direct hydrogenation and dehydrogenation reactions of the surface C2 species. It is worth noting that this isomerization involves an unusual transition state at which the C-H bond length is only 1.132 Å which is comparable to the C-H bond in ethane (1.091 Å).52 In addition, the transition state adopts a vinyl-like configuration; no significant C-C bond rotation is noticed in the 1,2 H shift.

Figure 13. Minimum energy pathways for the formation of ethylene from vinyl in the alkyl configuration. (Step 9 in Figure 4)

The direct hydrogenation of ethylene on the Fe(100) precovered with hydrogen has been investigated by Madix et al.,58,67 and they estimated the activation barrier of 12.2 kcal/mol for the β-hydride elimination of ethyl and the barrier of 6.0 kcal/ mol for the ethyl formation. The consistent values are found in the present study; the calculated activation energies for the forward and backward reactions of the migratory insertion of hydrogen to ethylene are 9.4 and 10.8 kcal/mol, respectively,



Figure 15. Minimum energy pathway for ethylene-ethylidene isomerization. (Step 12 in Figure 4)

Figure 14. Minimum energy pathway for the hydrogenation reaction of CH-CH2 on (a) the β-carbon, and (b) the R-carbon. (Steps 10 and 11 in Figure 4)

and the energy profile is given in Figure 16a. The transition state has an exceptionally long C-H bond distance of 1.963 Å; the hydrogen-bond-like feature in the transition state may result from the good overlap of the vacant π* orbital of ethylene and the orbital of electron-rich surface hydride. On the other hand, the detachment of hydrogen at the R position of ethyl has the reaction barrier of 18.9 kcal/mol which is 75% higher than that for the β-hydride elimination. The high barrier of this process can explain the nonexistence of ethylidene on the Fe(100) surface during the decomposition of ethylene. The reverse reaction step concerning the hydrogen addition to ethylidene at the R carbon also possesses a relatively large reaction barrier. As shown in Figure 16b, the approximate activation energy is 14.4 kcal/mol which is 5 kcal/mol higher than the hydrogenation at the β carbon of ethylene. The high activation energies for the conversion of ethylidene to ethyl can be rationalized by the extensive bond reorganization of the R carbon of ethylidene. Notice that in the transition state, ethylidene migrates to a bridge position while the hydrogen

remains essentially at the neighboring fourfold site forming a very long C-H bond (1.916 Å). Consequently, the high activation energy is mainly attributed to the energy required for the shift of ethylidene. On the clean Fe(100) surface, the ethylidene at the bridge site is 8.2 kcal/mol less stable than at the hollow site. The presence of coadsorbed hydrogen therefore further destabilizes the ethylidene at the twofold site and increases the reaction barrier. It has been observed from the TDP and kinetic studies conducted by Burke and Madix59 that no ethane is evolved when ethylene is adsorbed on the H-presaturated Fe(100) surface while the coadsorption of CO induces the facile formation of ethane whose activation energy is approximately 5.3 kcal/mol. Because of the fact that the β-hydride elimination of ethyl possesses a reaction barrier of 13.2 kcal/mol, they proposed that the activation energy associated with the ethane formation should be greater than 13 kcal/mol when no CO is present on the Fe(100) surface. In the present study, the formation of ethane from the coadsorbed ethyl and hydrogen was considered in which ethane is assumed to be adsorbed at the twofold site. The calculated MEP is depicted in Figure 17. Because of the steric hindrance of the bulky methyl group, the backside attack of hydrogen on the R carbon should be more preferred which results in the formation of ethane at the bridge site. The corresponding reaction barrier is 19.1 kcal/mol which agrees well with the experimental prediction. Similar to methane, the saturated ethane molecule does not strongly interact with the Fe(100) surface. The calculated adsorption energy of ethane at the bridge site is only 0.5 kcal/ mol, which is comparable to that of methane.23 Therefore, it is likely that ethane is only weakly physisorbed on the Fe(100) surface. However, its formation from ethyl is thermodynamically favorable, in contrast to the observation that no ethane is formed from ethylene on the H-presaturated Fe(100) surface without CO. Consequently, this reaction should be kinetically controlled; higher reaction temperatures may be required to trigger the hydrogenation reaction of ethyl in the absence of coadsorbed CO. In the Fischer-Tropsch synthesis where a continuous flow of CO/H2 mixture and high reaction temperature are applied, the high kinetic barrier can be partly overcome by the coadsorbed CO; therefore, the production of ethane is facilitated.


Lo and Ziegler

Figure 17. Minimum energy pathway for the dehydrogenation of ethane. (Step 15 in Figure 4)

Figure 16. Minimum energy pathways for the formation of ethyl from (a) ethylene and (b) ethylidene. (Steps 13 and 14 in Figure 4)

But still, the lower selectivity of ethylene and ethane than methane observed in the product distributions measured in the Fischer-Tropsch synthesis catalyzed by Fe slurry at 508 K7 is correlated to the lower barrier of methane formation23 (11.5 kcal/ mol) compared with that of ethane formation (19.1 kcal/mol). 3.3. C-C Coupling of Surface Species. While the hydrogenation and dehydrogenation reactions account for the presence of versatile configurational isomers of the same carbon chain length, the coupling of surface species is responsible for the chain growth of hydrocarbons on the Fe(100) surface in the Fischer-Tropsch synthesis. The possible coupling reactions between the stable surface C1 species which lead to the formations of various C2 fragments are listed in Figure 4. In these calculations, the reactant states are composed of the C1 species coadsorbed in their most favorable configurations on the p(2 × 2) Fe(100) surface, and the product states are the corresponding C2 species in their most stable geometries as shown in Figures 1-3. Because of the strong binding of carbide to the Fe(100) surface, the C-C bond coupling involving surface carbide is expected to be kinetically hindered. Figure 18 shows the reactant and transition states for the four coupling reactions of surface

Figure 18. Adsorption geometries of the reactants (on the left) and transition states (on the right) of the recombination reactions of C and CHn species on the Fe(100) surface. (Labels: brown, Fe; black, C; blue, H)

carbide. Large activation barriers are obtained for these reactions, but a decreasing trend consistent with the variation of binding energies of CHn is noticed. The reaction barrier for C + C a C2 is 50.2 kcal/mol while that for C + CH3 a C-CH3 is only 19.9 kcal/mol. The diminishing values of activation energies are anticipated because of the weaker binding to the surface of CH3 compared with that to the surface of C that facilitates its migratory insertion to the surface carbide. It is also observed that while the formation of the CC fragment is thermodynamically and kinetically highly unfavorable, the recombination reactions to yield C-CH, C-CH2, and C-CH3 are feasible, and these C2 species are 3.6, 5.0, and 5.4 kcal/mol more stabilized with respect to the separated counterparts. Three C-C bond coupling reactions with the methylidyne (CH) group were considered in the present study, and unlike those reactions with surface carbide, they are all thermodynamically unfavorable. The coupling of two adsorbed CH to generate


Figure 19. Adsorption geometries of the reactants (on the left) and transition states (on the right) of the recombination reactions of CH and CHn species on the Fe(100) surface. (Labels: Brown, Fe; black, C; blue, H)

acetylene has been investigated by Ihm and co-workers;35 the estimated barrier for C-C bond formation was 40.8 kcal/mol, and acetylene was 12.0 kcal/mol less stable than the separate CH fragments. In the present work, a smaller barrier of 33.2 kcal/mol is obtained while acetylene is 14.4 kcal/mol destabilized with respect to the separated methylidynes. The slight difference between the computed activation barriers may be due to the use of different functionals and the sizes of the Fe slabs that model the Fe(100) surface. The relative stability of acetylene and the separate CH fragments agree with the experimental observations that CH is found as a decomposition product of acetylene on the Fe(100) surface at 253 K.46 The formations of vinyl and ethylidene from CH are also disfavored thermodynamically despite the lower energy barriers compared with those of acetylene. The structures of the initial states for these reactions are illustrated in Figure 19. Because of the lower binding energy of CH3 than CH2,23 the migratory addition of the former species to CH possesses a much lower activation barrier than that for the latter species. The energy required for the shift of CH3 from a twofold site to CH at the adjacent hollow site is determined to be 20.0 kcal/mol; the barrier is increased to 27.2 kcal/mol when CH2 at the fourfold site migrates to react with the neighboring CH. The coupling reactions of CH2 and CH3 with methylene are energetically demanding processes. Two possible pathways leading to the formation of ethylene have been considered; the structures of the corresponding initial and transition states for these routes are illustrated in Figure 20 (the top two panels). As shown, the two methylene species can approach each other from either two diagonal hollow sites or two adjacent fourfold sites. The former pathway gives rise to ethylene at the on-top position which is the most favorable geometry of ethylene on the Fe(100) surface. This, however, requires the migration of CH2 over the surface Fe atoms which is highly endothermic. The resulting activation barrier is enormous (52.9 kcal/mol), and the whole process has the energy loss of about 6.0 kcal/ mol. The second pathway starts with two CH2 at the adjacent fourfold sites, and the final state is the ethylene adsorbed parallel to the Fe(100) surface at the hollow site with each C bonded to two Fe atoms as described in Figure 3d. The initial state is


Figure 20. Adsorption geometries of the reactants (on the left) and transition states (on the right) of the recombination reactions of CH2 and CHn species on the Fe(100) surface. (Labels: brown, Fe; black, C; blue, H)

approximately 12 kcal/mol less stable compared with the initial state of the first pathway due to the strong lateral interaction. The weakened surface-methylene bond, however, lowers the reaction barrier for the shift of CH2 over the Fe-Fe bridge site, forming the C-C bond with the neighboring CH2. The computed barrier height is reduced significantly to 34.9 kcal/ mol, and the reaction is marginally exothermic by 3.4 kcal/ mol. It is noticed that ethylene adsorbed at the fourfold site (Figure 3d) is destabilized by 4.2 kcal/mol compared with that adsorbed at the onefold position (Figure 3c). Including this extra stabilization enhances the exothermicity of reaction to 7.6 kcal/ mol. The coadsorbed CH2 and CH3 prefer the configuration in which they occupy respectively the most distant fourfold and twofold sites in order to minimize the steric repulsion. The most stable geometry is shown in Figure 20. In the process of C-C bond formation, both CH2 and CH3, which are strongly bound to the Fe(100) surface, move toward each other and form the ethyl species at the bridge position. The substantial surfaceadsorbate bond rearrangement causes the high reaction barrier that kinetically impedes the formation of ethyl. The forward barrier height is estimated to be 34.5 kcal/mol. Nevertheless, the overall reaction is exothermal, possessing an energy gain of about 5.7 kcal/mol. 3.4. Likely Reaction Pathways for the Synthesis of Ethane. The computed activation barriers of the reaction steps considered in the present study are tabulated in Table 2. On the basis of these values, the thermodynamic energy profile concerning the formation of ethane could be deduced (Figure 21). Two plots are illustrated in the figure: one is obtained ignoring the lateral interaction of surface H, while the other one is constructed including the steric interaction of neighboring H. Both profiles demonstrate the same trend of relative stability of different C2 species; it is predicted that C-CH, C-CH2, and C-CH3, all of which have the most unsaturated R carbon bonded at the fourfold site, are among the stable species on the surface. They differ only in that, without the lateral interaction due to the surface H, the synthesis of ethane is disfavored thermodynamically by 12.5 kcal/mol, whereas taking into account the influence of neighboring H leads to the favorable production (by 6.8 kcal/ mol) of ethane. The latter observation is consistent with the


Lo and Ziegler

TABLE 2: Calculated Forward (Ef) and Backward (Eb) Activation Energies (in kcal/mol) of Hydrogention Reactions and C-C Bond Coupling Reactions Involved in the Catalytic CH3-CH3 Formation on the Fe(100) Surface Including Important Structural Parameters (in Å) of the Transition States Associated with These Reaction Steps reaction step

Ef

Eb

r(C-H)

CC + H a C-CH C-CH + H a CH-CH C-CH + H a C-CH2 CH-CH a C-CH2 CH-CH + H a CH-CH2 C-CH2 + H a CH-CH2 C-CH2 + H a C-CH3 CH-CH2 a C-CH3 CH-CH2 + H a CH2-CH2 CH-CH2 + H a CH-CH3 C-CH3 + H a CH-CH3 CH2-CH2 a CH-CH3 CH2-CH2 + H a CH2-CH3 CH-CH3 + H a CH2-CH3 CH2-CH3 + H a CH3-CH3

10.0 14.9 9.6 51.5 14.2 12.3 17.7 28.8 8.7 9.5 15.8 26.6 9.4 14.4 19.1

37.0 11.2 10.2 53.9 7.6 4.3 19.7 43.5 16.1 11.1 2.7 24.0 10.8 18.9 28.9

1.364 1.893 1.411 1.773 1.670 1.795 1.292 1.294 2.461 1.596 1.703 1.132 1.963 1.916 1.615

C + C a C-C C + CH a C-CH C + CH2 a C-CH2 C + CH3 a C-CH3 CH + CH a CH-CH CH + CH2 a CH-CH2 CH + CH3 a CH-CH3 CH2 + CH2 a CH2-CH2 CH2 + CH3 a CH2-CH3

50.2 29.3 19.8 19.9 33.2 27.2 20.0 34.9 34.5

25.5 32.9 24.8 25.4 15.6 19.8 10.1 38.2 40.2

r(C-C)

1.879 2.221 1.880 2.213 1.993 1.960 2.299 2.083 2.014

experimental fact that ethane is evolved as one of the major products in the Fischer-Tropsch synthesis.7 According to the reactions shown in Table 2, two schemes could be developed that describe the synthesis of ethane from CO and H2. The first route involves the C2 formation from surface C followed by the hydrogenations on both the R and the β carbons which result in the various C2Hn including ethane. This pathway makes use of the fact that C is one of the most abundant surface species on the Fe(100) surface in the FischerTropsch reactions. Nevertheless, the formation of C2 via the diffusion of C on the Fe(100) surface is both thermodynamically and kinetically unfeasible because of the large endothermicity (∆Hrxn ) +24.6 kcal/mol) and reaction barrier (Ef ) 50.2 kcal/ mol). Therefore, there exists no considerable amount of C2 that may undergo the hydrogenation reactions leading to ethane. In other words, this mechanism should be of little importance in the Fischer-Tropsch synthesis. Another reaction route leading to the production of ethane comprises the C-C bond formation between the coadsorbed CHn species on the surface. While most of these C1 species are thermodynamically more stable compared with the C2 counterparts, their coupling reactions are kinetically inhibited because of the large barrier heights. For instance, the most kinetically feasible C + CH2 coupling reaction (Table 2) already has the activation barrier higher than those of all of the hydrogenation reactions. In addition, many of these coupling reactions are in fact energetically disfavored; the C-C bond formations involving CH at the R position are endothermic by 7.4 to 17.6 kcal/ mol. Consequently, it is believed that only the reactions C + CH2 and C + CH3 may be of importance in the chain initiation in the Fischer-Tropsch synthesis as these reactions are exothermic and kinetically achievable under the Fischer-Tropsch conditions. These findings agree well with the carbene route developed on the basis of extensive ab initio and DFT calculations on the Ru systems,26,69 in which the alkyl chains propagate through the insertion of adsorbed C and CH into the metal-carbon bonds of surface CHn.

However, the possibility of C-C bond formation utilizing the CH2 building blocks could not be ruled out. In the alkenyl mechanism proposed by Maitlis,8 the chain growth starts with the vinyl which is formed from surface CH and CH2. The vinyl, thus formed, reacts with methylene yielding an allyl species that may undergo either isomerization to produce internal vinylic species that may react further or R-hydride reductive elimination to generate terminal propene. It is found from the present work that the C-C bond coupling of CH and CH2 is unfavorable by 7.4 kcal/mol; but the resulting vinyl is reactive toward the hydrogenation yielding CH-CH3 or ethylene which can be hydrogenated to produce ethyl and ethane. The problem of the high kinetic barrier (27.2 kcal/mol) could be alleviated by the presence of structural defects of the Fe(100) surface. Steps and kinks are found often in catalysts which facilitate the surface chemical reactions by reducing the corresponding activation barriers. In the studies by Liu and Hu, they have illustrated that the steps on the Ru(0001) surface could lower the activation barrier by as much as 57% in the coupling reaction of C + CH.69 Accordingly, it is likely that the stepped Fe surface would be able to assist the formation of vinyl and thus make the alkenyl route70 more accessible during the course of chain growth. The formation of vinyl may also be promoted by the coupling of vinyl with surface CH2 species which corresponds to the chain propagation in the alkenyl mechanism. Although no reactions concerning the formation of C3 species have been considered in the present work, the previous DFT study of Ru-catalyzed C-C bond formations69 suggests that such processes should have the reaction barriers lower than those for C2 species. Hence, the transient vinyl formed from C-CH2 may be quickly transformed to more stable C3 species (such as allyl) that participate in the polymerization process. By eliminating the possibility that surface C2Hn species are formed from the direct hydrogenation of C2, the following simplified scheme that leads to the formation of ethane can be drawn: C + CH2/CH3 f C-CH2/C-CH3 + surface hydrogen f ethane. Along this pathway, the reaction that converts ethyl to ethane is the rate-determining step, having the activation barrier of 19.1 kcal/mol. However, when the synthesis of methane is also taken into account, the rate-limiting reaction would become the dissociation of adsorbed CO, which requires to overcome the barrier height of 24.7 kcal/mol.23 The current energy profile for the formation of ethane is also able to account for the lower selectivity of ethylene relative to ethane in the Fischer-Tropsch synthesis catalyzed by iron slurry catalysts.7 Assume that the C-C backbone is formed from the coupling of C with CH2. The resulting C-CH2 can undergo a low-barrier two-step hydrogenation reaction on the R carbon to generate ethylene; however, this process is energetically unfavorable. On the other hand, the hydrogenation may occur on the β carbon of CH-CH2 yielding CH-CH3; the barrier of this reaction step is only 1 kcal/mol higher than the former step. The CH-CH3, thus formed, may then undergo two consecutive exothermic hydrogen addition reactions to produce ethane, and the overall reaction pathway is exothermic. Therefore, the exothermicity of the ethane formation from C-CH2 constitutes the driving force that causes the higher selectivity of ethane over ethylene in the Fischer-Tropsch synthesis. Furthermore, the high barrier of the coupling between CH2, the proposed means of generating ethylene in the alkenyl mechanism, plays a crucial role of suppressing the synthesis of ethylene, contributing to the low proportion of ethylene in the Fischer-Tropsch product mixtures.



Figure 21. Thermodynamic profile for the formation of CH3-CH3 from adsorbed C and H. The relative energies (in kcal/mol) are given with respect to the adsorbed CC and six H.

It is worth mentioning the isomerization of surface species via H shift. In the Maitlis’ alkenyl mechanism, H migrations between carbon atoms are responsible for the interconversion of terminal and internal alkenes, and their feasibility controls the selectivity of various types of olefins in the products of the Fischer-Tropsch process. The three isomerization reactions (steps 4, 8, and 12 in Figure 4) investigated in the present work are the most kinetically unfavorable among all hydrogenation reactions, although the reaction barriers for the last two transformations are indeed comparable to those of the coupling reactions of surface CHn species. Because of the observation that the replacement of H substituent by CHn (e.g., CH2 versus CH-CH3) generally reduces the bonding interaction of the R carbon with the surface, the 1,3 H shift of propenyl should be more achievable than the corresponding 1,2 H shift of vinyl. The work on verifying this issue is currently underway. 4. Conclusion Utilizing periodic GGA-PW91/usPPs calculations, we have determined the structures and energetics of the adsorbed C2Hn (n ) 0 - 5) species on the Fe(100) surface. The minimum energy profiles concerning the hydrogenation reactions as well as the C-C bond formations that lead to the synthesis of these C2 species have been computed. On the basis of the calculated reaction barriers, the complete potential energy diagram for the relative stability of the various C2 fragments with respect to the adsorbed C and H has been constructed. It is found that most of the C2 species prefer the adsorption at the hollow site, with the exceptions of ethylene and ethyl which favor respectively the onefold and twofold sites. In general, the adsorption energies of the surface species are inversely proportional to the degree of hydrogenation at the R position; the binding energy decreases from 179.5 kcal/mol for CC to 35.8 kcal/mol for CH2-CH3. This trend is parallel to the variation of the adsorption energies of C1 species and is attributed to the better overlap of the sp hybridized C orbitals than the sp2 and sp3 hybridized C orbitals with the surface Fe d bands. It is also noticed that closed-shell species such as acetylene, ethylene, and ethane are more weakly bound to the surface than the open-shell radical species because of the weaker

π orbital electron donation to the vacant d bands of the surface Fe atoms. The present work has revealed that ethane, as methane, is physisorbed on the Fe(100) surface with the estimated binding energy of only 0.5 kcal/mol. C-CH, C-CH2, and C-CH3 are the thermodynamically stable adsorbates with respect to the adsorbed C and H atoms. These results are consistent with the observations of the adsorption experiments of acetylene and ethylene on the Fe(100) surface that signals representative of -CH, -CH2, and -CH3 have been detected. Surprisingly, adsorbed ethane is among the most favorable C2 surface species, although it can be easily evolved from the surface at high-temperature because of the delicate adsorption. Two types of reactions involving the C2 species on the Fe(100) surface have been studied: C-H bond formation and C-C bond coupling. The minimum energy profiles of the hydrogenation reactions described in Figure 4 that lead to the production of various C2Hn have been computed, and the corresponding transition state structures determined. It is noted that hydrogen insertion at both the R and β C atoms are generally facile, with the reaction barriers varying from 8.7 to 19.1 kcal/ mol. On the other hand, the intramolecular H-shift reactions are extremely difficult; for instance, the isomerizations of acetylene requires overcoming the barriers higher than 51.5 kcal/ mol. Nine possible C-C bond coupling reactions have been considered in the present study. In contrast to the abovementioned C-H bond formations, these chain propagations are all kinetically formidable. The computed barrier heights range from 19.8 to 50.2 kcal/mol which surpass those for the hydrogenation reactions. Note also that only the coupling of CHn with surface C is exothermic; therefore, the current calculations would suggest that the chain propagation possibly initiates via the C + CHn reactions rather than the CH + CHn or CH2 + CHn reactions. Acknowledgment. The authors would like to acknowledge the financial support from the Alberta Ingenuity Funds in terms of a postdoctoral fellowship (to J.M.H.L.) and the computer resources provided by the Western Canada Research Grid and the Department of Chemistry at the University of Calgary. T.Z.

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Theoretical Studies of the Formation and Reactivity of C2 Hydrocarbon

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