Quantum-Chemical DFT Study of Direct and H- and C-Assisted CO Dissociation on the χ-Fe5C2 Hägg Carbide.

The first step in the Fischer-Tropsch reaction is the production of C1 monomers by the dissociation of the C-O bond. Although Fe is the active metal, it is well known that under typical reaction conditions, it changes into various carbide phases. The Hägg carbide (χ-Fe5C2) phase is usually considered as the catalytically active phase. We carried out a comprehensive DFT study of CO dissociation on various surface terminations of the Hägg carbide, selected on their specific site topology and the presence of stepped sites. Based on the reaction energetics, we identified several feasible CO dissociation pathways over the Hägg carbide. In this study, we have compared the direct CO dissociation with H- and C-assisted CO dissociation mechanisms. We demonstrated that the reaction rate for CO dissociation critically depends on the presence and topology of interstitial C atoms close to the active site. Typically, the CO dissociation proceeds via a direct C-O bond scission mechanism on the stepped sites on the Fe carbide surface. We have shown a preference for the direct CO dissociation on the surfaces with a stepped character. The H-assisted CO dissociation, via a CHO intermediate, was preferred when the surface did not have a clear stepped character. We have also shown that activation barriers for dissociation are highly dependent on the surface termination. With a consistent data set and including migration corrections, we then compared the CO dissociation rates based on a simplified kinetic model. With this model, we showed that besides the activation energy, the adsorption energy of the CO, the C and the O species are important for the reaction rate as well. We found that the most active surface termination is a (111̅) surface cut in such a way that the surface exposes B5 sites that are not occupied by the C atoms. On these B5 sites, the direct CO dissociation presents the highest rate.

Introduction

Fischer–Tropsch (FT) synthesis has proven to be an economically attractive route for the conversion of natural gas and coal into synthetic fuels and chemicals in certain settings.[1] The products obtained from CO hydrogenation depend critically on the transition metal used. Ru and Co mainly produce long-chain hydrocarbons, whereas Fe-based catalysts find application in the production of long-chain hydrocarbons, gasoline, or light olefins, depending on the process conditions. The active phase in commercial FT catalysts is typically based on Co or Fe. The Fe catalysts are less expensive and more active in the water–gas shift reaction than Co. The latter is important when the synthesis gas with a low H2/CO ratio needs to be processed.[2] The Fe-based FT catalysts are usually prepared by precipitation. Promoters such as Cu and K are used to improve the Fe reduction degree and increase the FT activity and selectivity, respectively.

Similar to Co, the nature of the active sites in Fe-based FT catalysts and the mechanism by which CO is converted into hydrocarbons remain the topics of considerable debate. It is well known that under FT conditions, the Fe-oxide precursor is rapidly converted into Fe carbide. Hägg carbide (χ-Fe5C2) has been identified as the most likely catalytically active phase.[3] Accordingly, besides studies on metallic Fe surfaces in the FT mechanism,[4−7] most computational investigations have focused on Fe carbide model surfaces.[4,8−17] For the Hägg carbide, several surface terminations display comparable thermodynamic stability at the FT conditions.[18] It is, therefore, important to involve these stable surfaces in mechanistic studies of the FT reaction. The CO dissociation, which initiates the FT reaction, is one of the crucial elementary reaction steps and key to understanding the structure–performance in FT catalysis. Until now, most studies have considered direct CO dissociation on Fe carbides.[4,8−15] The H-assisted CO dissociation involving CHO as an intermediate has been considered as an alternative way of activating CO on metallic[19] and Hägg carbide surfaces.[8−12,14,15,20] Another relevant aspect is that Fe carbides can expose C atoms at their surface, which can also be involved in the FT reaction. The C–O bond scission via a CC–O intermediate has been only scarcely investigated[16,21] and, when considered, it has not been compared to H-assisted CO dissociation. Compared to these earlier studies, we have performed a migration correction to our data. In such a correction, we take into account the migration of the adsorbates before and after the elementary reaction step to and from the most stable adsorption state, respectively. These aspects are essential to properly compare different C–O bond scission pathways.

In the present work, we use the quantum-chemical density functional theory (DFT) to determine the preferred CO dissociation pathways on the Hägg carbide surfaces. We first computed the surface free energies of various surface terminations of the Hägg carbide and established how CO is adsorbed on these surfaces. Then, we determined the activation energies for different CO dissociation pathways on the most stable surface terminations. These data are compared to the literature data. With a consistent data set and including migration corrections, we then compared the CO dissociation rates based on a simplified kinetic model.

Method

All spin-polarized density functional theory (DFT) calculations were conducted using the projector-augmented wave method and the Perdew–Burke–Ernzerhof functional implemented in the Vienna ab initio simulation package code.[22,23] Solutions of the Kohn–Sham equations were calculated using a plane-wave basis set with a cutoff energy of 400 eV. The sampling of the Brillouin zone was done using 5 × 5 × 1 k-points. A higher cutoff energy or a finer Brillouin zone sampling did not lead to significant energy differences. Electron smearing was employed using a first-order Methfessel–Paxton technique,[24] with a smearing width of 0.2 eV. The tetrahedron method with Blöchl corrections with a smearing width of 0.2 eV was used for the calculation of the bulk structure. All the atoms were allowed to relax for the calculation of the bulk structure, as well as the calculation of the empty surfaces. The thickness of the empty unit cells was taken between 6.4 and 10.3 Å, depending on the miller index plane. We used a slab containing 40 Fe atoms and 16 C atoms for the (010)0.25 surface, 60 Fe atoms and 24 C atoms for the (111̅)0.0 and (111̅)0.5 surfaces, and 80 Fe and 32 C atoms for the (100)0.0 and (100)0.287 surfaces. The adsorption of adatoms was done on the top side of the slab, and the lower half of the slab was frozen. A dipole correction was performed for all the adsorbed states. A vacuum layer of 15 Å was added perpendicular to the surface to avoid spurious interactions between neighboring system images.

The adsorption energies of the gas phase molecules were determined by subtracting both energies of the empty surface and the free adsorbate from the adsorbed state. The energy of the adsorbate in the gas phase was performed by placing a molecule at the center of a 10 × 10 × 10 Å3 unit cell, using the Γ-point for k-point sampling. For the electron smearing, a Gaussian smearing width of 0.002 eV was used. The adsorption energies, after zero-point energy corrections, are in good agreement with the tabulated thermodynamic data.[25]

For all calculations, the convergence criterion was set to 10–4 eV for the ionic steps and to 10–5 eV for the electronic convergence. All the geometry optimizations were conducted using the conjugate-gradient algorithm. The transition states were acquired using the nudged elastic band method.[26] A frequency analysis was performed to confirm that all transition geometries corresponded to a first-order saddle point on the potential energy surface with an imaginary frequency in the direction of the reaction coordinate. The Hessian matrix was constructed using a finite-difference approach with a step size of 0.02 Å for the displacement of individual atoms along each Cartesian coordinate. The corresponding normal-mode vibrations were also used to calculate the zero-point energy correction. We corrected the barriers for the migration of fragments after dissociation by considering the energy difference of the geometry directly after dissociation and their most stable adsorption positions at infinite distance.

The surface energies were calculated usingwhere E refers to the total energy of the slab, containing n times the conventional monoclinic bulk cell (Fe20C8), Eb to the bulk energy, A to the area of the surface, and Esurface to the surface energy of the surface. This procedure is valid for stoichiometric and symmetric surfaces (i.e., surfaces with equivalent top and bottom surfaces). In our study, we have also used stoichiometric and asymmetric surfaces. An average surface energy was calculated for the asymmetric surfaces using the above-mentioned procedure.

The rate constant (k) of an elementary reaction step can be determined using the Eyring equation, which is defined as followswhere ΔEact stands for the activation energy, kB for the Boltzmann constant, T for temperature, and v for the pre-exponential factor. This pre-exponential factor can be calculated for the forward and backward reaction and is defined as followswhere vfarward and vbackward refer to the pre-exponential factors for the forward and the backward reaction, respectively, qvib stands for the vibrational partition function of the initial state and the transition state, and h for Planck’s constant.

To compare the CO dissociation rates on the different surfaces, we employed a simplified kinetic model, similar to the one used by Liu et al.[27] For these calculations, we used a temperature of 500 K and a CO pressure of 3 × 10–5 Pa. The relatively low pressure was chosen to simulate conditions of low CO coverage, consistent with the low coverage used in the transition-state calculations. For more complex reaction pathways involving prehydrogenation to CHO and COH, we used the overall reaction barrier for the C–O bond scission and a H2 pressure of 6 × 10–5 Pa. For C-assisted CO dissociation pathways, we took into account two separate steps, namely the adsorption of CO and the formation of CCO before the cleavage of the C–O bond in CCO. The rate is described by the following rate equationwhere K1 and K2 are the equilibrium rate constants for CO adsorption and C–CO coupling, respectively, k3 is the rate constant for the rate-limiting step (the CO dissociation), and PCO is the partial pressure of CO. The derivation of this equation can be found in the Supporting Information (SI).

Results and Discussion

The DFT calculations were performed to investigate the energetics of CO dissociation on various Hägg carbide surfaces. First, we will present the bulk structure and surface energies of the candidate surface terminations of Hägg carbide. Then, we will discuss CO and H adsorption. Finally, we will discuss direct and assisted C–O bond scission pathways for the five most stable surfaces and employ simplified kinetic models to compare the CO dissociation rate on these surfaces.

Bulk and Surface Hägg Carbide Models

Hägg carbide has a monoclinic unit cell with a space group C2/c and cell dimensions a = 11.588 Å, b = 4.579 Å, c = 5.059 Å, and β = 97.75°.[28] Optimized cell parameters determined by our DFT calculations are a = 11.504 Å, b = 4.524 Å, c = 5.012 Å, and β = 97.75° (α = γ = 90°). Figure shows the orthographic representations of the top (green), front (blue), and side (red) views of the bulk structure of Hägg carbide. As described by Steynberg et al.,[18] there are nine unique low Miller index planes for the Hägg carbide. For each of these planes, more than one unique surface termination is possible, as cleaving the unit cell in the direction perpendicular to the Miller plane at fractional distances results in different surface terminations. This is due to the presence of interstitial C atoms present in the Hägg carbide. In this study, we adopted the notation introduced by Steynberg et al. to indicate the cut that generates the different surfaces. A guiding example can be found in Figure . Steynberg et al. only considered the 14 symmetric surfaces. Sorescu stressed the importance of including nonsymmetric surfaces, as some have lower surface free energies than the symmetric ones.[16] In this work, we considered two such asymmetric surfaces, namely (100)0.0 and (100)0.287, because they are among the most stable surface termination and also because they contain surface topologies akin of B5 sites, i.e., adjacent 4- and 3-fold sites. The (100)0.287 surface does not contain C atoms in the surface and the subsurface layer. The calculated surface energies of the various surfaces investigated herein are collected in Table . The differences in surface free energies are consistent with literature reports.[16,18]

Figure 1

Orthographic representations of the a–b plane (green), b–c plane (blue), and a–c plane (red) of the monoclinic (C2/c) unit cell for the bulk structure of Hägg carbide. The orange and black atoms represent the Fe and C atoms, respectively.

Figure 2

Graphical depiction of the notation of the surface terminations. The surface orientation is denoted using Miller indices. For the surfaces spanned at the origin of the two vectors composing the Miller index planes, we use the subscript 0.0. A nonzero subscript refers to a translation of the plane in the direction of the surface normal indicated by the particular Miller index. This subscript is fractional, i.e., a subscript of 1.0 would indicate that the cutting plane is translated exactly by one unit cell.

Table 1

Surface Energies of the Various Hägg Carbide Terminationa

surface termination	surface energy (J/m2)	surface termination	surface energy (J/m2)
(100)0.0	2.19	(011)0.0	2.54
(010)0.25	2.24	(101̅)0.0	2.65
(111̅)0.0	2.24	(011)0.25	2.66
(100)0.287	2.42	(010)0.429	2.69
(111̅)0.5	2.45	(111)0.5	2.70
(111)0.0	2.46	(010)0.0	2.76
(110)0.0	2.47	(101)0.0	2.90
(110)0.5	2.48	(100)0.25	3.01
(001)0.0	2.54

The surface energies are calculated with respect to the monoclinic bulk unit cell Fe20C8 (C2/c).

On the basis of these surface free energies, we constructed a Wulff particle taking into account only the lowest surface free energy of a specific Miller index plane. For instance, for the (010) plane, the (010)0.25 was included (i.e., the (010)0.0 surface was excluded, as the (010)0.25 is more stable by 0.52 J/m2). The resulting Wulff particle is shown in Figure . Nearly two-thirds of the surface of the Wulff particle is made up by (010)0.25, (111̅)0.0, and (100)0.0 surfaces, as the Wulff particle consists of 10% of the (010) surfaces, 25% of the (100) surfaces, and 30% of the (111̅) surfaces. On the basis of this analysis, we selected the five surfaces with the lowest surface energies, i.e., the (010)0.25, (111̅)0.0, (100)0.0, (111̅)0.5, and (100)0.287 surface terminations as models to study CO dissociation. For the Wulff construction, we only took the most stable Miller index plane into account. However, the possibility remains that, depending on the reaction conditions, the (100)0.287 surface is present instead of the (100)0.0. So, even though the (111̅)0.0 and the (100)0.0 surfaces are more stable as compared to the (111̅)0.5 and (100)0.287 surface terminations, the latter terminations were also taken into consideration. Here, we will show that the most active surface termination is a (111̅) surface cut in such way that the surface exposes B5 sites not occupied by C atoms.

Figure 3

Visualization of the Wulff particle, taking only the lowest surface free energy of a specific Miller index plane. The a, b, and c axes are represented by red, green, and blue arrows, respectively. Nearly three-quarters of the surface of the Wulff particle is made up of (010)0.25, (111̅)0.0, and (100)0.0 surfaces.

CO Adsorption and CO Bond Dissociation

To identify the preferred adsorption site for CO, we explored the adsorption on top, bridge, 3-fold, 4-fold, 5-fold, and 6-fold sites. Moreover, we considered the adsorption on pseudo B5 sites, i.e., sites with a topology that resembles a B5 site. Figure presents the most stable adsorption modes for CO and H on the selected surfaces. A complete overview of the configurations is given in the SI. Then, direct, H- and C-assisted C–O bond dissociation reactions were taken into account. For the H-assisted CO dissociation mechanism, we considered the pathways via COH and CHO intermediates. The activation barriers and corresponding pre-exponential factors for the calculated elementary reaction steps are listed in Table . The most favorable reaction pathways for CO dissociation will be discussed for the five most stable surfaces. To have a quantitative approach to compare different pathways, we define an overall barrier for CO dissociation (ΔEtotal) as the difference between the highest lying transition states along the potential energy surface that yields dissociated CO and the most stable adsorption state of CO. We also define ΔΔE as the difference in ΔEtotal with the most favorable pathway characterized by the lowest ΔEtotal for a particular surface. Reaction pathways with a relatively small ΔΔE can still contribute to the CO bond dissociation under practical conditions. This will be taken into account by a simplified kinetic model. The values for ΔEtotal and ΔΔE for the different surfaces are given in Table . A graphical representation of ΔEtotal and ΔΔE values is given in the SI. The structures of the C–O scission steps are shown in Table .

Figure 4

Surface topology of the five most stable surface terminations of the Hägg carbide. The most stable adsorption configurations and the corresponding adsorption energies of CO and H are also shown. CO tends to adsorb on a 4-fold site, unless this is hampered by the interstitial C atoms. The notation 2B3 indicates that CO is adsorbed in two adjacent 3-fold sites. H prefers to be adsorbed on a 3-fold site.

Table 2

Forward Activation Energy (Ef) and Backward Activation Energy (Eb) in kJ/mol and Forward (νf) and Backward (νb) Pre-Exponential Factors for Direct and H-Assisted CO Dissociation on the Five Most Stable Fe5C2 Surfacesa

surface	dissociation site	elementary reaction step	Ef (kJ/mol)	νf	Eb (kJ/mol])	νb
(010)0.25	2B3	CO → C + O	166	1.2 × 1012	178	1.1 × 1013
(010)0.25	2B3	CO + H → CHO	119	4.0 × 1012	68	4.6 × 1013
(010)0.25	2B3	CO + H → COH	216	5.7 × 1012	134	7.5 × 1012
(010)0.25	2B3	CHO → CH + O	53	7.6 × 1012	143	1.2 × 1013
(010)0.25	2B3	COH → C + OH	133	1.8 × 1012	130	3.1 × 1012
(010)*0.25	B5	CO → C + O	137	2.2 × 1012	215	5.3 × 1012
(010)*0.25	B5	CO + H → CHO	120	4.0 × 1012	50	1.2 × 1013
(010)*0.25	B5	CO + H → COH	122	1.3 × 1013	71	6.1 × 1012
(010)*0.25	B5	CHO → CH + O	48	1.1 × 1012	186	1.7 × 1013
(010)*0.25	B5	COH → C + OH	2	6.1 × 1012	35	7.2 × 1012
(111̅)0.0	xx	CO → C + O	156	8.6 × 1011	144	9.1 × 1012
(111̅)0.0	B3	CO + H → CHO	173	1.1 × 1012	4	3.9 × 1012
(111̅)0.0		CO + H → COH	226	6.2 × 1012	60	1.6 × 1013
(111̅)0.0	2B3	CHO → CH + O	10	3.1 × 1012	152	9.4 × 1012
(111̅)0.0		COH → C + OH	67	4.4 × 1012	173	6.6 × 1012
(111̅)0.0	B5	C* + CO → C*CO	80	2.6 × 1012	16	6.0 × 1013
(111̅)0.0	B5	C*CO → C*C + O	98	2.6 × 1012	120	1.1 × 1013
(111̅)0.0	B5	C*CO + H → C*CHO	97	4.5 × 1013	71	3.9 × 1013
(111̅)0.0	B5	C*CO + H → C*COH	135	5.5 × 1012	85	8.5 × 1012
(111̅)0.0	B5	C*CHO → C*CH + O	31	1.7 × 1013	167	1.4 × 1013
(111̅)0.0	B5	C*COH → C*C + OH	63	8.7 × 1012	87	1.5 × 1012
(100)0.0	B5	CO → C + O	128	7.9 × 1011	108	5.6 × 1012
(100)0.0	B5	CO + H → CHO	97	1.7 × 1012	11	1.5 × 1013
(100)0.0	B5	CO + H → COH	136	3.2 × 1012	27	7.0 × 1012
(100)0.0	B5	CHO → CH + O	98	5.7 × 1013	183	1.6 × 1013
(100)0.0	B5	COH → C + OH	58	6.0 × 1012	129	2.3 × 1012
(111̅)0.5	B5	CO → C + O	118	1.2 × 1012	139	1.2 × 1013
(111̅)0.5	B3	CO + H → CHO	152	2.2 × 1012	89	1.6 × 1013
(111̅)0.5	B5	CO + H → COH	224	1.9 × 1013	82	1.9 × 1013
(111̅)0.5	2B3	CHO → CH + O	65	1.2 × 1013	94	1.4 × 1013
(111̅)0.5	B5	COH → C + OH	47	2.2 × 1012	141	7.4 × 1012
(100)0.287	B5	CO → C + O	128	5.1 × 1012	220	1.1 × 1013
(100)0.287	B3	CO + H → CHO	139	3.0 × 1013	37	3.7 × 1013
(100)0.287	B3	CO + H → COH	192	3.0 × 1013	53	2.9 × 1013
(100)0.287	B5	CHO → CH + O	46	9.2 × 1012	182	1.1 × 1013
(100)0.287	B5	COH → C + OH	31	1.3 × 1013	179	9.1 × 1012

C* indicates that a C atom from the surface is involved. The (010)0.25 surface with a C vacancy is noted as (010)*0.25.

Table 3

ΔEtotal and ΔΔE Values for CO Dissociation Over the Five Most Stable Surfaces via the Direct CO Dissociation and the H-Assisted Pathways for CO Dissociationa

surface	CO dissociation pathway	ΔEtotal* (kJ/mol)	ΔΔE (kJ/mol)	rate limiting step
(010)0.25	direct	166	55	CO → C + O
	H-assisted via CHO	119	0	CO + H → CHO
	H-assisted via COH	216	98	CO + H → COH
(010)*0.25	direct	141	15	CO → C + O
	H-assisted via CHO	124	0	CO + H → CHO
	H-assisted via COH	126	2	CO + H → COH
(111̅)0.0	C-assisted via CCO	162	6	CCO → CC+O
	direct	156	0	CO → C + O
	H-assisted via CHO	179	23	CHO → CH + O
	H-assisted via COH	233	77	CO + H → COH
	H/C-assisted via CCHO	161	5	CCO+H → CCHO
	H/C-assisted via CCOH	199	43	CCO+H → CCOH
(100)0.0	direct	128	0	CO → C + O
	H-assisted via CHO	184	56	CHO → CH + O
	H-assisted via COH	167	39	COH → C + OH
(111̅)0.5	direct	118	0	CO → C + O
	H-assisted via CHO	152	34	CO + H → CHO
	H-assisted via COH	224	106	CO + H → COH
(100)0.287	direct	128	0	CO → C + O
	H-assisted via CHO	148	20	CHO → CH + O
	H-assisted via COH	192	64	CO + H → COH

ΔEtotal is defined as the difference between the energy of the adsorbed species and the energy of the energetically highest lying transition state of the energetically lowest pathway. The ΔΔE is defined as the difference in the value for ΔEtotal for the energetically most favorable pathway and the ΔEtotal for a different pathway. The (010)0.25 surface with a C vacancy is noted as (010)*0.25.

Table 4

Modes for the Rate-Limiting C–O Scission Stepsa

Depicted are the configurations of the CO or CHO molecule as the initial state with the corresponding transition state and the configurations of C, CH, and O in the transition and final state.

(010)0.25 Surface

The (010)0.25 surface contains two C atoms in 4-fold positions, whereas two C atoms are located in the interstitial locations below the surface. The surface exposes top, 3-fold, and 4-fold Fe sites for adsorption. Binding of CO to the 4-fold site of the B5 ensemble is not possible because of the presence of the interstitial C atom below the adsorption site. No stable adsorption configuration of CO on top or 3-fold sites was identified and, in these cases, CO reverted to a 4-fold adsorption mode involving binding to two adjacent 3-fold sites. This site is termed as a 2B3 site. The CO adsorption on this site is slightly more stable than the bridged adsorption on the edge of a 3-fold site. We also found that CO can adsorb on top of a surface C atom with an energy of 77 kJ/mol. Other adsorption modes involving simultaneous coordination to C and Fe atoms were found to be unstable. The dissociative adsorption energy of H2 is 101 kJ/mol and the H atoms prefer to bind to 3-fold Fe sites.

The C–O bond dissociation may start from different adsorption modes. Direct dissociation from the 2B3 site involves a barrier of 166 kJ/mol, close to the value reported by Sorescu for the same dissociation pathway.[16] In the transition state, the C atom remains in the 2B3 site, whereas the O atom moves to a bridge position on one of the 3-fold sites of the 2B3 site. Finally, the repulsion is relieved by the migration of the O atom to an adjacent 3-fold site. The H-assisted pathways were considered as well. The hydrogenation of CO adsorbed in the 2B3 site to COH has a barrier of 209 kJ/mol. The barrier for CHO formation, on the other hand, is only 119 kJ/mol. In the initial state, the H atom is located at a 3-fold site adjacent to the CO, which is located in the 2B3 site. Upon CHO formation, the C and O atoms in the final state are bound in a 3-fold and bridged manner to the surface, respectively. The transition state for CHO formation resembles the final state, with the exception of a slight rotation. The barrier for dissociating the CHO intermediate from this configuration is only 53 kJ/mol. From these data, it is clear that the H-assisted pathway via CHO is the preferred mode of CO dissociation on this surface. Huo et al.[10] compared the direct and H-assisted mechanisms for CO dissociation on this surface and also concluded that the H-assisted CO dissociation via CHO is the more favorable reaction pathway. On the other hand, Petersen and Janse van Rensburg reported similar barriers for direct and H-assisted CO dissociation on this surface.[14] The main difference is their choice to remove the C atoms from the surface, rendering the surface more reactive for direct CO bond dissociation. Therefore, we also explored the CO dissociation in a vacancy site. This vacancy was created by removing a 4-fold C atom from the surface and the resulting surface is denoted by (010)*0.25. The most stable CO adsorption site is the 4-fold site, i.e., the vacancy obtained by C removal. Direct CO dissociation is more facile on the defective surface and shows an activation energy of 141 kJ/mol, in good agreement with the value found by Petersen and Janse van Rensburg.[14] Dissociation via the COH intermediate is also more facile, as the activation energy is lowered from 216 to 126 kJ/mol. The pathway via CHO remains nearly unaffected, as the CHO intermediate is slightly less stable in the vacancy as compared to the 2B3 site. Overall, the dissociation of CO in a vacancy site is most likely via a H-assisted pathway, although direct CO dissociation is still possible. The difference between the overall barrier for direct CO and H-assisted C–O bond scission is only 15 kJ/mol (ΔΔE = 15 kJ/mol).

(111̅)0.0 Surface

The (111̅)0.0 surface contains four C atoms in the 5-fold coordination and two C atoms in interstitial locations below the 4-fold sites. At the surface, there are top, 3-fold, 4-fold, and B5 sites available for CO adsorption. One of the two 3-fold sites is part of a B5 site, the other is a B3 site. Despite the presence of a B5 site, CO adsorption is not possible because of the interstitial C atom below the 4-fold site. When CO was adsorbed on either the 3-fold or the 4-fold sites of the B5 site, the CO migrated to the nearby top sites. The top adsorption energy is 88 kJ/mol. However, CO adsorption on the 3-fold site resulted in an adsorption energy of 184 kJ/mol. The adsorption energy of H2 is 105 kJ/mol with the H atom preferring to bind to a 3-fold site.

We also explored CO adsorption on C atoms of the Fe carbide, giving rise to Fe–C and C–C bonds. Adsorption of CO to the 3-fold and 4-fold sites resulted in coordination to one C atom and 2 or 3 Fe atoms (sites denoted as 2Fe1C and 3Fe1C), respectively. The CO adsorption energies on these sites are lower than on the other sites (112 kJ/mol and 103 kJ/mol for the 3Fe1C and 2Fe1C sites, respectively).

Direct C–O bond dissociation can occur from different adsorption states. Starting from a Fe-only adsorption site, the forward activation barrier is 156 kJ/mol. This barrier is relatively high because the C–O bond scission proceeds over a terrace-like site. Direct CO dissociation starts from the most stable adsorption site, i.e., the 3-fold site. The final state holds the C atom in the same 3-fold position with the O atom located bridged in an adjacent 3-fold site. The transition state has a late character. The C–O bond scission starting from a CCO intermediate has a forward activation barrier of 98 kJ/mol, which is 58 kJ/mol lower compared to direct CO dissociation. Sorescu reported values of 175 kJ/mol for direct CO dissociation and 66 kJ/mol for C–O dissociation in CCO.[16] It is important to use migration-corrected energies for these two pathways. Then, we find values of 156 kJ/mol for the direct CO dissociation pathway and 162 kJ/mol for the CCO pathway. These data compare very well to the migration-corrected Sorescu data of 156 kJ/mol and 154 kJ/mol, respectively. The important conclusion is that, although the CO-bond dissociation in CCO is facile, the overall barrier is nearly the same as that for direct CO-bond dissociation. Zhao and co-workers[21] investigated the direct CO dissociation and C-assisted CO dissociation pathways. For direct CO dissociation, a much higher barrier was reported than found by us. For C-assisted CO dissociation, a barrier of 70 kJ/mol was computed. The CCO pathway was not considered by these authors.

In addition to the C-assisted pathway, we also investigated the H-assisted pathways. CO hydrogenation to either CHO or COH involve relatively high activation barriers because both CO and H are strongly bound compared to the intermediate hydrogenated species. However, the barrier for CCO hydrogenation to CCOH is considerably lower compared to the hydrogenation of CO to COH, which is due to the higher stability of the CCO species. This reduces the barrier for hydrogenation by approximately 91 kJ/mol, and the overall barrier from 233 to 199 kJ/mol. The associated ΔΔE for this pathway is 43 kJ/mol, suggesting that this pathway will not significantly contribute to the overall CO dissociation rate. The overall barrier for CCH–O bond scission is similar to the barrier for the CC–O bond scission. Accordingly, both CC–O and CCH–O bond scission are likely candidates for direct C-assisted pathway. Furthermore, direct C–O bond scission remains a likely pathway.

(100)0.0 Surface

The (100)0.0 surface is completely made up from B5 sites, without any exposed C atoms. The interstitial C atoms in the first subsurface layer are located below the 4-fold sites. As a consequence, CO adsorption on this surface is not possible on the 4-fold sites. CO adsorption can occur on top, 3-fold, and 5-fold sites. The 5-fold adsorption is similar to adsorption on a B5 site, with the exception of the location of the C atom. In a regular B5 site, the C atom is bound to the 4-fold site of the B5 site. Due to the interstitial C atom below the 4-fold site, the C from CO is not bound to the 4-fold site, but to the 3-fold site adjacent to it. The O atom of CO is located in a regular bridged fashion at the edge of the 4-fold site of the B5 site. Adsorption on a 3-fold site is comparable (181 kJ/mol) to adsorption on a top site (180 kJ/mol). The adsorption of CO in a 5-fold site is slightly less favorable (166 kJ/mol). Bridged adsorption of CO led to the migration to a 3-fold adsorption. The energy of dissociative adsorption of H2 is 120 kJ/mol, the H atoms are located in 3-fold sites.

Both direct and H-assisted pathways were considered for CO dissociation. Direct C–O bond scission starts from CO adsorbed in a 5-fold site and has an activation energy of 128 kJ/mol. In the transition and final states, the C atom remains in the 3-fold site. The O atom proceeds via a bridged position in the transition state to a 3-fold position in the final state. Sorescu reported a CO adsorption energy of 186 kJ/mol on the (100)0.0 surface, which is close to our value (181 kJ/mol).[16] For direct CO dissociation, a barrier of 113 kJ/mol was reported. Migration correction would increase this barrier to 129 kJ/mol, which is close to the value found by us. Sorescu[16] did not take the H-assisted CO dissociation pathways into account. Sorescu[16] did not take the H-assisted CO dissociation pathway into account.

The formation of the CHO intermediate has an activation barrier of 97 kJ/mol. However, due to the instability of the CHO intermediate, the ΔΔE for this pathway is 56 kJ/mol, implying that direct CO dissociation is preferred. However, CO hydrogenation toward a COH intermediate is only approximately 8 kJ/mol higher in energy as compared to direct CO dissociation; the COH intermediate is also less stable, resulting in an overall barrier of 167 kJ/mol (ΔΔE = 39 kJ/mol). Thus, a direct CO dissociation on a B5 site is the most likely pathway. Different conclusions were reached by Gracia et al.,[9] who compared direct and H-assisted CO dissociation via a COH intermediate for this surface, but did not consider the CHO pathway. It must be noted that the computations of Gracia et al. were done for the (100)0.05 surface. This is a cut in the same direction of the unit cell but at a slightly different height, resulting in a carbon-terminated surface. The carbon at the surface hampers direct CO dissociation, which explains the different results obtained for the (100)0.0 surface obtained by us. Another reason is their use of a relatively small unit cell, implying that lateral interactions will play a more prominent role than in our study. Furthermore, Gracia et al. determined the mechanism solely on the basis of the stability of the intermediates. They did not discuss the activation barriers, which will predominantly determine the preferred CO dissociation pathway. Although they did not report activation barriers, based on the stabilities of the intermediates, they contended that the COH pathway is preferred over direct CO dissociation, which contrasts our findings.

(111̅)0.5 Surface

The (111̅)0.5 surface contains four C atoms in 5-fold coordination and two C atoms in interstitial locations below the 4-fold Fe sites. The difference with the (111̅)0.0 surface is the location of the interstitial C atoms, which are now located below the 3-fold sites. However, CO adsorption on a 4-fold site of a B5 site is not stable and CO reverts to a 3-fold position due to the proximity of a surface C atom. CO preferably adsorbs in a 4-fold fashion on a 2B3 site with an adsorption energy of 191 kJ/mol. The adsorption energy of H2 is 151 kJ/mol and the preferred adsorption site is the 3-fold one.

Direct CO dissociation proceeds by adsorbing CO in the B5 site in the initial state. In the transition state, the C atom remains in a 4-fold position, whereas the O atom is located in a bridged mode. In the final state, the O atom proceeds to a 3-fold site, whereas the C atom remains in place. Sorescu compared the direct CO and C-assisted CO dissociation pathways for the (111̅)0.5 surface but did not consider the CCO formation step.[16] As the difference between the values of CO and CCO dissociation was small and migration corrections were not taken into account, the C-assisted CO dissociation is not likely on this surface. Sorescu’s value for CO adsorption (202 kJ/mol) is close to our value (190 kJ/mol) for CO adsorption on a bridge site. The reported values for C–O and CC–O bond scission are 77 and 80 kJ/mol, respectively. By applying a migration correction to these data, the activation barriers increase to 131 and 205 kJ/mol, respectively. Sorescu’s migration-corrected value for direct CO dissociation is thus close to our computed value of 118 kJ/mol. Sorescu[16] did not take the H-assisted CO dissociation pathway into account. Our calculations show that hydrogenation to either CHO or COH has ΔΔE values of 34 and 106 kJ/mol, respectively. Therefore, the C–O bond scission will most likely occur in a direct fashion over a B5 site on this surface.

(100)0.287 Surface

The (100)0.287 surface is similar to the (100)0.0 surface, apart from the absence of C atoms in the surface and the first subsurface layer. This results in substantially higher CO adsorption energies. CO can adsorb in top, 3-fold, or 4-fold modes. The most stable site for CO adsorption is the B5 site, where the C atom is bound in a 4-fold manner and the O atom is bound bridged. The CO adsorption energy is 221 kJ/mol. The dissociative adsorption energy of H2 is 167 kJ/mol, with the H atoms ending up in a 3-fold site.

CO dissociation can proceed in a direct manner from the most stable adsorption site. In the transition state, the C atom moves to a 3-fold site, whereas the O atom remains in a bridged position. In the final state, the O atom moves to a 3-fold site, whereas the C atom remains in the 3-fold position. The activation energy for direct CO dissociation is 128 kJ/mol. The hydrogenation of CO to form either CHO or COH species has higher overall barriers (ΔΔE = 20 and 64 kJ/mol, respectively) due to the strong adsorption of both CO and H. Therefore, CO dissociation is most likely to proceed on a B5 site in a direct manner. Cheng et al.[4] computed the direct CO dissociation on this surface, but started their transition state search from gaseous CO.

Kinetic Model

To explore the differences in CO dissociation rates on the investigated surfaces, we used simplified kinetic models. Figure shows the reaction rates for CO dissociation involving direct and H-assisted (via CHO or COH) pathways. The site-based rates are shown relative to the rate of direct CO dissociation on the Co(0001) terrace. Positive values indicate a higher rate compared to the Co(0001) surface, whereas negative values depict a lower rate. Data for the Hägg carbide surfaces are compared to the stepped Co(112̅1) surface. The CO dissociation kinetic data for Co(112̅1) and Co(0001) are taken from literature.[27] For the (010)0.25 surface, we also included the data for the surface containing a C vacancy. For the (111̅)0.0 surface, the pathway involving CCO was included.

Figure 5

Reaction rates for direct CO dissociation (red) and for CO dissociation involving H-assistance via CHO (blue) and COH (green). These rates are shown relative to the rate of direct CO dissociation on Co(0001). Positive values imply a higher reaction rate compared to the direct CO dissociation on the Co(0001) surface, whereas negative values imply a lower reaction rate. The rate for the Co(112̅1) surface is given for comparison (data for Co surfaces taken from Liu et al.[27]). CO dissociation involving the (010)0.25 surface with a C vacancy is denoted by (010)*0.25, whereas the data for the C-assisted pathway (CCO) on the (111̅)0.5 are given.

For the (111̅)0.0, (100)0.0, (111̅)0.5, and (100)0.287 surfaces, direct CO dissociation is much faster than H-assisted pathways. The C-assisted pathways involving CC–O and CCH–O bond cleavage reactions on the (111̅)0.0 display comparable rates, whereas H-assisted CO dissociation on the (111̅)0.0 surface proceeds at a lower rate compared to direct CO dissociation. The most active surface is the (111̅)0.5 surface, followed by the (100)0.0 surface. On both these surfaces, direct CO dissociation is preferred over the H-assisted CO dissociation. The (010)0.25 surface displays a preference for the CHO pathway, as the site for direct CO dissociation is blocked by C atoms. Removing a surface C atom from this surfaces changes the preferred mechanism to direct CO dissociation. The (111̅)0.0 and (100)0.287 surfaces exhibit a lower rate for the COH pathway, when compared to the direct CO dissociation on Co(0001). The rest of the surfaces are more active compared to direct CO dissociation on Co(0001). The (100)0.287 is the least reactive one. As follows from the literature,[15,29] higher Miller index surfaces with a terrace-like surface topology such as the (510)0.0 surface prefer a direct CO dissociation pathway instead of the H-assisted CO dissociation. Figure also includes the data for the (510)0.0 surface based on the literature data[15] (see the SI for details of the calculations). These results show that direct CO dissociation is preferred on the (510)0.0 surface. The computed rate of H-assisted CO dissociation via COH is considerably lower than that of H-assisted CO dissociation via a CHO intermediate. It is interesting to compare the preferred mechanism for the terrace-like (510)0.0 and (010)0.25 surfaces. Whereas direct CO dissociation is preferred on the former, the CHO pathway is the dominant one on the latter. This further underpins the conclusion that the C–O bond dissociation mechanism is highly dependent on the presence of surface or interstitial C atoms just below the surface.

General Discussion

We have compared the surface free energies of different terminations of the Hägg carbide and selected on this basis the five most stable surfaces for a detailed study of CO dissociation relevant to the Fischer–Tropsch reaction. A general trend observed is that CO binds stronger to the surfaces that lack interstitial C atoms present in the first subsurface layer. CO prefers to be adsorbed on a 4-fold site, unless this adsorption mode is hampered by interstitial C atoms. The adsorption of H atoms was also considered as relevant to CHO and COH dissociation pathways. In all the cases, H is adsorbed on 3-fold sites. Adsorption energies increase with increasing surface free energies. Some of the explored surfaces contain stepped sites, which give rise to relatively low barriers for direct CO dissociation. The computed barriers for the different CO dissociation pathways on the Hägg carbide are higher than the barriers for the preferred (direct) CO dissociation pathways on stepped Co and Ru surfaces.

Overall, increasing occupancy of interstitial sites below the surface with C atoms results in a higher barrier for direct CO dissociation. This phenomenon was recently discussed by Chen et al.,[20] who also showed a strong correlation between the charge in the Fe atom and the CO activation barrier. These authors showed that the presence of surface and interstitial C atoms near the surface Fe atoms decrease the charge on the Fe atoms, as the C atoms withdraw electrons from the surface Fe atoms. This results in a weaker activation of CO. This interstitial C occupancy is highest for the (010)0.25 surface. In this case, the alternative pathway involving CHO shows a much lower overall activation barrier. This is at odds with the results obtained by Petersen and Janse van Rensburg,[14] who found similar values for direct CO dissociation and H-assisted CO dissociation on the (010)0.25 surface. The main difference here is that they considered a surface from which the C atoms were removed. We verified that creating such vacancies indeed results in higher direct and COH dissociation rates, whereas the CHO pathway becomes less favorable. The reason is that on the surface with a vacancy, the C atoms of CO and COH are bound in a 4-fold manner. On the other hand, the CHO intermediate is not stable when the C atom is bound in this site, requiring the migration from a bridged configuration of both the C and the O atom on this site. Overall, the introduction of a vacancy results in a change in the preferred CO dissociation mechanism.

Summarizing, one can state that CO dissociation proceeds via the direct pathway, when a B5 type site is present on the surface. Otherwise, usually due to the presence of (interstitial) C atoms, the H-assisted mechanisms contribute to the overall rate of CO dissociation. On the (111̅)0.0, a C-assisted mechanism is possible, as it presents comparable rates for direct and H-assisted CO dissociation. Taken into account the results of the Wulff construction and noting that usually Fe carbide particles are relatively large,[17] making it reasonable that particles will adopt this shape, we observe that lowered free energy of a particular surface results in a lower reaction rate for CO dissociation. The (111̅) and (010) surfaces enclose about 30 and 10% of the Wulff particle. The rate on the former surface is substantially lower than on the latter. However, it is clear that, for a particular low Miller-index surface, the rate for CO dissociation can vary substantially depending on the way the surface is cut. For instance, the (111̅)0.5 surface presents a much higher CO dissociation rate than the (111̅)0.0 surface. Moreover, these data show that, due to the complexity of the Fe carbide surface terminations, there is more competition between different modes of CO dissociation than for metallic Co surfaces.

Conclusions

We explored the CO adsorption and dissociation on five stable surface terminations of the Hägg carbide, selected on the basis of the presence of stepped B5 type sites and low surface free energies. The strength of CO adsorption depends on the presence of interstitial C atoms in the first subsurface layer. CO adsorbs on a 4-fold site unless hampered by interstitial C atoms. The H atoms adsorb on 3-fold sites on all investigated surfaces. The H adsorption energy directly correlates with the surface free energy. In general, there is competition between direct and H-assisted pathways for CO dissociation on the considered surfaces. Direct CO dissociation becomes easier with increasing adsorption strength of CO (due to less subsurface interstitial C atoms). CO dissociation proceeds via the direct pathway, when a B5 type site is present on the surface. Otherwise, usually due to the presence of (interstitial) C atoms, the H-assisted mechanisms contribute to the overall rate of CO dissociation. For instance, CHO dissociation is preferred over direct CO dissociation for the (010)0.25 surface with a large occupancy of subsurface C atoms. Direct CO dissociation on the (111̅)0.5 surface presents the highest CO dissociation rate of all considered surfaces. These rates are typically lower than those observed for the stepped Co surface. We have also shown that on a surface like the (111̅)0.0 surface, C-assisted pathways can contribute to CO dissociation. Although these calculations have all been performed at a relatively low CO coverage, we expect that the contribution of C-assisted pathways may become more important under typical FT conditions.