Hydrocarbon chain growth and hydrogenation on V(100): a density functional theory study

Abstract

The activation of CO, hydrogenation of CH_x (x = 0–4) and C₂H_y (y = 0–5) species and carbon chain propagation on V(100) were studied by means of periodic density functional theory (DFT) calculations. The results indicate that the activation of CO is very facile on V(100) via direct dissociation rather than H-assisted pathways. The hydrogenation of CH_x/C₂H_y (except for CC) and the C–C coupling elementary steps are thermodynamically and kinetically unfavorable. The energy barriers to the former reactions are lower than those to the latter ones. The high coverage of reactants and the entropic effect may be the dominant factors responsible for the hydrogenation and carbon chain propagation. The simple microkinetic model built on the basis of the above results shows that CH₂ is the dominant CH_x species on the surface in the temperature range of 300–800 K. Starting from a high coverage of CH₂, the building block of the C-chain, CH₂CH₂ forms via a coupling reaction and then desorbs from the surface. CH₂CH, appearing as the precursor, mainly forms from the coupling of CH₂ + CH followed by CH₂ insertion leading to CH₂CHCH₃. Although CH is more likely responsible for the chain propagation than CH₂ in view of energy barriers, its contribution suffers from its low coverage at the considered conditions. These results are in good agreement with the experimental results.

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Introduction

As a typical catalytic process to produce hydrocarbons via hydrogenation of CO, Fischer–Tropsch (F–T) synthesis has been widely investigated since being discovered in 1923,¹ and its importance is recognized once again with the increase of worldwide energy demand and environmental constraints in recent years. To find and design catalysts with better activity and selectivity, knowledge of the reaction mechanism is desirable.

Extensive experimental studies have been carried out on a variety of transition metal surfaces, and the carbene mechanism of Fischer and Tropsch,^2,3 which proposes that the alkyl chain growth proceeds via CH₂ insertion following the dissociation of CO, is widely accepted.^4–11 Generally, the activation of CO is more facile on the early transition metals than on the late ones, while the case of the carbon coupling is opposite.¹² However, the mechanism remains to be investigated and many issues are under debate, such as the activation of CO via the direct dissociation or H-assisted pathways, the chemical identity and the stability of the participating species, and the chain growth pathways.^9,11,13–15 Though knowledge on the relative stabilities of various intermediates involved in the early steps of F–T process and the relevant potential energy surface is crucial to fully understand the F–T mechanism, it is difficult to obtain experimentally.

The development of advanced computational models and the growing computational power in recent years makes it feasible to study the mechanism of heterogeneous catalytic reactions by using the first-principles methods¹⁶ and many theoretical works related to F–T process were carried out on a wide range of commonly used catalysts such as Fe,^17–24 Co,^{12,19,24–28} Ni^13,29 and Ru,^{12,20,24,30–32} as well as other potential metallic catalysts, e.g. Rh,^{20,24,32–35} Pt,^36,37 Pd.^33,38 These studies show that the reaction mechanism displays strong dependence on the nature of metal surfaces. For CO activation, the H-assisted mechanism is proved more favorable than the direct dissociation on Fe and Co.^22,27 For the path C → CH → CH₂ → CH₃ → CH₄, the largest activation energy corresponds to hydrogenation reaction of CH₂ on Fe(100),¹⁷ while the last step was considered as rate-determining at defects on studied Rh, Co, Ru, Fe and Re surfaces and an increase in the binding strength of C + 4H to the surface may suppress the production of methane.²⁴ The RC + C (R = alkyl or H) and CH + CH pathways occurring on Ru and Rh surfaces was suggested to be responsible for F–T chain propagation, while on the Fe surface, the pathway of C + CH₂/CH₃ may dominate, and on the Re surface C + CH does the job. When Co catalysts were employed, CH₂ + CH₂ and CH₃ + C appear more important, and the coupling reactions of RC + C and RC + CH also contribute to the chain growth on Co after CH_x coupling in addition to the pathways of RCH + CH₂ and RCH₂ + C.^16,20,24,32

A recent work by Shen and Zaera³⁹ studied the hydrocarbon chain growth on V(100) starting from CH₂I₂ and provided experimental evidence to identify CH₂CH as a plausible chain-propagation intermediate which may work as a precursor to produce CH₂CHCH₃ by coupling with CH₂. However, the information obtained from experimental work is limited and many fundamental issues concerning the mechanism and the selectivity remain to be solved. As far as we known, there is no theoretical study of the F–T process on V(100) until now. Herein, DFT and microkinetic modeling methodologies were employed to investigate the reaction mechanism of the F–T process on V(100), which covers the activation of CO, the adsorption stability of intermediate species and the possible pathways for chain growth from CH_x to C₂H_y and C₃H_z.

Computational details

In this work all calculations were carried out with the Vienna ab initio simulation package (VASP).^40,41 The projector augmented wave (PAW)^42,43 method was used to describe ion-electron interactions and plane-wave basis set with an energy cutoff of 400 eV was used to expand the one-electron wave function. The Perdew–Burke–Ernzerhof (PBE)⁴⁴ functional within the generalized gradient approximation (GGA) was used to describe the electron correlation. Spin polarization was considered in all calculations. Geometries were relaxed using the conjugate gradient algorithm until the forces on all unconstrained atoms were smaller than 0.04 eV Å⁻¹. As described in our earlier work,⁴⁵ a (2 × 2 × 1) supercell cell with a five-layered periodic slab separated by a vacuum region of 15 Å was used to model the V(100) surface. The three lower layers were fixed and the two upper ones were allowed to relax. The calculations were performed with (6 × 6 × 1) Monkhorst–Pack k-point.

The climbing-image nudged elastic band (CI-NEB) method^46,47 was used to search the transition states (TSs). The nature of each optimized structures, both minima and TSs, was identified by vibrational analysis, from which zero-point energy (ZPE) corrections were obtained and included in the barrier and reaction energy calculations. The adsorption energy (E_ads) for each possible adsorbate was calculated according to the following equation:

E_ads = E_gas-surf − (E_surf + E_gas)

where E_gas-surf, E_surf and E_gas are the total energies of the surface with adsorbed species, the clean surface and the gas-phase species, respectively. The energy barrier for the bimolecular reaction was calculated relative to the energy of the infinite separation state. To evaluate the effect of van der Waals interaction on the adsorption and the kinetics of species on the metal surface, several key points were checked by an empirical dispersion correction using DFT-D3(BJ) method.^48,49

Results and discussion

Various configurations of CO, CH_x and C₂H_y, the most important species in the F–T synthesis, at three adsorption sites on V(100) (top, bridge and hollow as shown in Fig. 1) were considered, and only the most stable ones are discussed here. For each elementary step we have investigated several possible reaction paths, and here only those with the minimum energy are reported.

Fig. 1 Top (left) and side (right) views of the V(100) surface. The three possible adsorption sites of adsorbates at 0.25 mL, i.e. hollow, bridge and top sites, are labeled H, B and T, respectively. The light blue and navy blue spheres represent the even and odd layers of V atoms, respectively.

The activation of CO and H₂

The direct dissociation of CO is found facile on the V(100) surface. As described in our earlier work,⁴⁵ the adsorption of CO prefers to the hollow site and tiled from the surface, which assists its direct dissociation. The adsorption energy is −3.28 eV including ZPE and the value is calculated to be −3.60 eV with VDW-D3 correction in this work. The calculated energy barrier is as low as 0.33 eV (0.36 eV without ZPE and 0.37 with dispersion correction). In the transition state of the dissociation reaction, the C–O bond stretches to 1.83 Å from 1.14 Å, beyond which the O atom moves to the neighbour hollow site while the C atom stays at its binding site. This step is highly exothermic by 2.20 eV (see Fig. 2).

Fig. 2 Energy profile including ZPE correction (black) and also the vibrational entropy correction at 500 K (red) for the hydrogenation of CH_x (x = 0–3). The data of the hydrogenation of CH₂ and CH₃ (in gray) are from ref. 45. The gray and white spheres represent C and H atoms, respectively.

It's known that the activation of CO on most metals is via its hydrogenation to CHO and/or COH,^22,27 however, on V(100), both hydrogenation steps are calculated to be endothermic by 0.60 and 1.41 eV, respectively, and the energy barrier for the former step is 0.90 eV, thus much less favorable than the direct dissociation. The dissociation of H₂ is barrierless and strongly exothermic on V(100). Following the initial dissociation of CO and H₂, other C-chain growth and hydrogenation steps may occur and will be discussed in detail in the next sections.

The adsorption and hydrogenation of CH_x

Both C atom and CH radical prefer to adsorb at the hollow site, with C interacting with four V atoms of the first layer (V_I) and one V atom of the second layer (V_II), and for CH radical the C–H bond (1.11 Å) is found to be perpendicular to the surface (see Fig. 2). The bond lengths of C–V_I and C–V_II are 2.05 and 2.10 Å, respectively in the case of C atom, and 2.16 and 2.10 Å in the case of CH radical. The longer distance between CH radical and V_I is consistent with the smaller adsorption energy of CH than that of C on the surface (−7.84 versus −8.95 eV), suggesting a weaker interaction between the CH radical and the surface than that for the adsorbed C atom. The adsorption of CH_x (x = 2–4) species has been studied in previous work,⁴⁵ and an adsorption energy of −8.20 eV for CH₂, which is close to that of C and CH, and of −2.17 eV for CH₃ was reported, indicating the highest mobility for CH₃ while the least for C atom. The adsorption energy of CH and CH₂ including dispersion correction is calculated to be −8.11 and −8.60 eV, respectively. Meanwhile, the adsorption of CH₃ at the bridge site was found to be more stable than at the hollow site. CH₄ is only weakly physisorbed on the surface. These results are similar to those on other surfaces.^17,18,34

The potential energy profile for the hydrogenation of C atom to produce methane in a stepwise manner is plotted in Fig. 2 (the black one) and the PES curve including vibrational entropy term using the harmonic approximation (see the ESI†) at 500 K is also given (the red line). Both of the hydrogenation of C and CH are endothermic by 0.42 and 0.73 eV, respectively. During the reaction, C (or CH) remains at the hollow site, and the H atom moves to it by overcoming a barrier of 0.83 (0.92) eV. The value without ZPE is 0.91 (0.91) eV and becomes 0.92 (0.93) including dispersion effects. The C–H bond length in the transition states (TS1 and TS2) are similar, 1.58 and 1.57 Å, respectively. According to our earlier study,⁴⁵ the subsequent hydrogenation of CH₂ and CH₃ was found to be also endothermic (1.37 and 0.54 eV, respectively) with energy barriers of 1.25 and 1.03 eV, respectively, and the diffusion of H atoms is facile on V(100), which benefits the hydrogenation of CH_x. These results indicate that all elementary reaction processes starting from C to produce CH₄ are endothermic, leading to an overall endothermicity of 3.06 eV. The largest energy barrier corresponds to the third step, CH₂ hydrogenation, similar to that on Fe(100) with an energy barrier of 0.86 eV.¹⁷

In order to take into account the influence of temperature on chemical behavior of some adsorbed species, AIMD simulations on the adsorbed CH₂ was carried out at three temperatures of 300, 500 and 800 K respectively for more than 20 ps each. Fig. S1† shows how the C–H bond of CH_x evolves during AIMD simulation at 300 and 800 K with nearest image convention imposed.

As seen in Fig. S1a,† on the clean V(100) surface, we didn't observe the dissociation of CH₂ during the simulation at 300 K, which is the case at 500 K. At 800 K, as seen in Fig. S1b,† the dehydrogenation of CH₂ was observed. The leaving H atom first moved to the adjacent hollow site, then moved to the diagonal hollow site, but the yielded CH did not dissociate. These results indicate that the dissociation of CH is more difficult than that of CH₂, which is consistent with the higher energy barrier.

In order to investigate the influence of surface H atoms, a simulation of CH₂ at 800 K was carried out with an H atom adsorbed at the diagonal hollow site (see Fig. S1c†). The presence of the H atom was found to have little effect on the dissociation of CH₂, but do limit the motion of the released H atom and lead to its immobilization at the adjacent hollow site.

These results indicate that the dissociation of CH₂ and CH may be difficult on the V(100) surface under considered condition, thus may appear with long lifetime and lager coverage, which is verified by the microkinetic model, as discussed in the latter section. CH₃ is much less stable for two reasons: on one hand, it is easy to dissociate, and on the other hand, its hydrogenation gives CH₄, which may desorb from the surface easily.

The adsorption, formation and hydrogenation of C₂H_y on V(100)

Starting from CH_x species, the C–C coupling reaction initiates the chain propagation, and there is no doubt that C₂H_y are important intermediates. To better understand the chain growth mechanism, in this section, we first discussed the adsorption of C₂H_y species, followed by the investigation of all possible C–C coupling reactions that produce C₂H_y species and their hydrogenation on V(100).

Adsorption of C₂H_y. The most stable structures, selected geometric parameters together with the adsorption energies are shown in Fig. 3 and Table 1. Most C₂H_y species have similar configurations except for CH₂CH₂ and CH₂CH₃ (see Fig. 3). In these configurations, the C atom baring less H atoms (denoted as C1) sits above a hollow site and interacts with four V_I and one V_II atoms, similar to CH_x (x = 0–2), and another C atom (C2) locates at the adjacent bridge site and binds with two V_I atoms. Such trends are similar to that on Pt(110).³⁶

Fig. 3 The most stable structures of C₂H_y on V(100). The C–V bond lengths (in Å) are given in black and the C–C bond lengths (in Å) in red.

Table 1 The adsorption energies (E_ads, in eV) and geometric parameters (distance in Å and angle in degree) of the most stable C₂H_y on V(100)

Species	Configurations	dC1–VI^a	dC1–VII	dC2–VI	Angle^b	dC1–C2	Eads
a C1 refers to the C atom with less H atoms.b The angle of the C–C bond tiled from the surface.c Data from ref. 45.
CC	C1-hollow, C2-bridge	2.09	2.13	1.97	35.94	1.40	−8.62
CHC	C1-hollow, C2-bridge	2.08	2.13	2.05	37.23	1.43	−6.87
CH3C	C1-hollow, C2-bridge	2.15	2.13	2.47	41.69	1.51	−6.77
CH2C	C1-hollow, C2-bridge	2.07	2.16	2.19	55.19	1.46	−5.67
CH3CH	C1-hollow, C2-bridge	2.19	2.19	2.50	50.69	1.53	−4.83
CH2CH	C1-hollow, C2-bridge	2.19	2.21	2.15	35.02	1.48	−4.28
CHCH	C1-hollow, C2-bridge	2.18	2.18	2.02	29.64	1.47	−3.49
CH3CH2	C1-bridge, C2-hollow	2.25	—	3.27	39.76	1.53	−1.85
CH2CH2^c	C1-hollow, C2-bridge	2.32	2.52	2.23	20.82	1.51	−0.57

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In general, shorter C–V bond means stronger binding. The C1–V_I bond in CH_xC (x = 0–3) is the shortest with values of 2.07, 2.08 and 2.09 Å for CH₂C, CHC and C₂, and 2.15 Å for CH₃C respectively. The bond length becomes longer when going to CH_xCH (x = 1–3), which is around 2.19 Å. The C1–V_II bond length is the shortest in CC, CHC and CH₃C (2.13 Å) and is around 2.16–2.19 Å in other C₂H_y species. The distance of C2–V_I in CH_xC (x = 0–3) increases with the number of H atoms (1.97 < 2.05 < 2.19 < 2.47 Å), and this is also the case for CH_xCH (x = 1–2) (2.02 < 2.15 < 2.50 Å).

For all species, the C–C bond is tilted from the surface with the bridge C farther from the V(100) surface, and the distance between the two C atoms increases with the number of H atoms on C2 atom (C–CH_x (x = 0–3): 1.40 < 1.43 < 1.46 < 1.51 Å; CH–CH_x (x = 1–3): 1.47 < 1.48 < 1.53 Å). Same trend is observed for the angle of the C–C bond tiled from the surface (C–CH_x (x = 0–3): 35.94 < 37.23 < 41.69 < 55.19°; CH–CH_x (x = 1–3): 29.64 < 35.02 < 50.69°) and the C–H bond length of CH fragment in CHCH, CHCH₂ and CHCH₃ (1.16 < 1.18 < 1.20 Å). The configuration of CH₂CH₂ has been described in our earlier work.⁴⁵ CH₂CH₃ adsorbs on V(100) with CH₂ located at the bridge site, which is different from other C₂H_y species, with a C–C bond length of 1.53 Å, C–V of 2.25 Å and an angle of 39.76°.

A correlation between the adsorption stability of most C₂H_y on V(100) and the C1–V distance and the number of H atom on the C atom bound with the surface may be deduced from the data in Table 1: the shorter the C1–V distance or the less saturated the C atom, the stronger the binding. Among all C₂H_y species, the adsorption of C₂ is the most exothermic by −8.62 eV. In the case of CHC and CH₃C, the energies decrease to −6.87 and −6.77 eV, respectively. The exothermicity is even less for CH₂C which is around −5.67 eV, and for the CH_xCH species, which are −4.83, −4.28 and −3.49 eV for CHCH, CH₂CH and CH₃CH, respectively, suggesting the stability of CH_xCH on V(100) decreases with the number of H atom on the C2 atom. The adsorption energy of CH₃CH₂ is −1.85 eV, and CH₂CH₂ is found only weakly bound to the surface with an adsorption energy of −0.57 eV, thus it is likely to desorb from the surface.⁴⁵ The adsorption energy including dispersion correction is calculated to be −4.87 and −1.92 eV for CH₂CH and CH₂CH₂, respectively.

In brief, CH_xCH_y (y ≥ x) have preferred adsorption modes with less saturate C atom bound on the surface rather than other configurations, and the adsorption sites are similar to the corresponding CH_x species. For the isomers, the configuration with less saturate C1 is more stable in view of adsorption energy on the surface, e.g. the binding of CH₂C, CH₃C and CH₃CH are stronger than CHCH, CH₂CH and CH₂CH₂, respectively, similar to that on Fe(100).¹⁸

C–C coupling. C–C coupling reaction may occur between two adsorbed CH_x close to each other and the transition states were shown in Fig. 4. As mentioned above, CH_x radicals with more H atoms bind relatively weaker to the surface, and it is easier for these species to diffuse on the surface towards those CH_x with less H atom in the coupling processes. For example, to approach to the transition state for the coupling of CH₂ and CH, TS8, the adsorbed CH₂ migrates toward the CH group and the activated CH remains at its initial hollow site. TS8 is similar to that on Co and Ru surfaces in the presence of a multi-centered bond.¹²

Fig. 4 The TS structures (in Å) of the C–C coupling on V(100).

The nascent C–C bond lengths in the TSs are also shown in Fig. 4 and all of them are around 2.00 Å. In the transition states for the coupling reactions of C atom with CH_x (x = 0–3), TS3–TS6, the forming C–C bond lengths are 1.80 < 1.92 < 1.97 < 2.07 Å, respectively. For the coupling of CH with CH_x (x = 1–3), these values in TSs7–9 are 1.92 < 1.95 < 2.04 Å, respectively. When going to more saturated CH_x species, i.e. the coupling reactions of CH₂ with CH₃ and CH₂, the values become even longer to 2.08 and 2.09 Å in TS10 and TS11, respectively. It is clear that the length of the forming C–C bond is related to the unsaturation of the CH_x fragment, similar to that in C₂H_y species.

In view of energy barriers (see Fig. 5), the coupling paths studied here may be classified into three groups. The first group includes the CH₃ + C and CH₃ + CH coupling reactions, which are inherent with the lowest barriers of 1.05 and 1.28 eV, respectively, which may be resulted from the participation of the relatively highly diffusive CH₃ in the reactions. The coupling reactions with moderate difficulty constitute the second group, including the paths of C + CH, C + CH₂, CH + CH and CH + CH₂ with similar energy barriers of 2.02, 1.97, 2.00 and 2.03 eV, respectively, which is because the diffusion ability of CH and CH₂ is similar and much weaker than CH₃ involved in the first group. The values without ZPE for the CH + CH and CH + CH₂ are 1.85 and 1.95 eV, which become 1.84 and 1.99 including dispersion correction. The reactions with the highest energy barriers belong to the third group, i.e. the coupling reactions of C + C, CH₂ + CH₂ and CH₂ + CH₃, the barriers of which are 2.70, 2.71 and 2.49 eV, respectively. In this group, either it is hard for both reactants to migrate (C + C) or significant repulsive interaction is present between the two reactants, which makes it difficult for the coupling reactions to happen. These results reflect the composite effect of the diffusion ability of the migrating CH_x and the repulsive interaction between the radical pair. Overall, for the radical pair that with the less repulsive interaction and/or higher diffusion ability, the barrier to overcome is lower, and the lowest value is obtained to the C + CH₃ coupling reaction, which is same as that on Fe and Co surface.¹⁹

Fig. 5 Energy profile for the C–C coupling steps (in eV). The coupling of CH₂ (in gray) is from ref. 45.

In addition, we note that for coupling reactions C + CH_x, the reaction energy barriers correlate with the lengths of the partially formed C–C bond in the TSs, i.e. the longer the C–C bond length, the lower the energy barrier. This, together with the correlation between the C–C bond length, the diffusion ability and the unsaturation of the CH_x fragment mentioned above, shows that it is possible that these reactions are determined essentially by unsaturation of the CH_x.

All of the coupling reactions studied here are endothermic and the strongest endothermicity was found in the reaction between the C + C radical pair with a value of 2.40 eV. It decreases to 1.76, 1.54, 1.24 and 1.03 eV, respectively for the reactions of CH + CH, CH + C, CH + CH₂ and CH₂ + CH₃, and the lowest value (0.27 eV) is for C + CH₃. It is clear from Fig. 5 that, for the coupling reaction of C with CH_x, the step with lower energy barrier appears with smaller endothermicity, which is same as the case for CH (or CH₂) with CH_x, except for the CH + CH step.

The diffusion ability of CH₃ makes the coupling steps CH₃ + C (or CH) more favorable both in view of kinetics and thermodynamics. According to our calculations, the effective energy barriers, which is defined as the energy difference between the highest transition state (TS) and the C + yH species, increase in the order CH + CH < C + CH < C + C < C + CH₂ < CH + CH₂ < C + CH₃ < CH + CH₃ < CH₂ + CH₂ < CH₂ + CH₃ with the values 2.42 < 2.44 < 2.70 < 3.12 < 3.18 < 3.57 < 3.80 < 3.86 < 5.01 eV. On the surface of V(100), C is the most stable species and its hydrogenation and coupling reactions are endothermic, thus by referring to the energy of the thermodynamically most stable species, it is clear that, all C–C coupling steps are more difficult to happen than the formation of CH₂ (1.34 eV) in energy barriers.

Hydrogenation of C₂H_y. In order to evaluate the propensity of the transformation of C₂H_y species discussed above, all potential hydrogenation pathways of C₂H_y were investigated here. The energy barriers and reaction energies of these reactions, together with those of all C–C coupling steps mentioned above are collected in Fig. 6, and the configurations of transition states are shown in Fig. 7 with the newly formed C–H bond length given. Since the direct 1,2-H shift have been proven difficult in previous studies,^37,38 they were not studied in this work. In this section, the stepwise hydrogenation steps starting from the C₂ species, followed by the possible pathways in F–T process, were discussed.

Fig. 6 Paths of C–C coupling reactions to produce C₂H_y species and the subsequent hydrogenations. ZPE correction is included in the energy barrier (in eV) of each path.

Fig. 7 The TS structures of the hydrogenation of C₂H_y on V(100) with the newly formed C–H bond length in Å.

The data in Fig. 6 indicate that most hydrogenation processes of C₂H_y are endothermic except for the step C₂ + H → C₂H which is exothermic by 0.45 eV with an energy barrier of 0.72 eV. The hydrogenation of C₂H may produce CH₂C or CHCH, which are endothermic by 0.32 and 0.64 eV, respectively, and the corresponding energy barriers are 0.75 and 0.81 eV. The highly unsaturated CH₂C may be reduced further to CH₂CH or to CH₃C by overcoming an energy barrier of 0.78 or 0.89 eV and both are endothermic by 0.66 and 0.51 eV respectively. In principle, CH₂CH may be also produced via the hydrogenation of CHCH with a higher barrier of 1.16 eV. The further hydrogenation of CH₃C and CH₂CH gives CH₃CH, both of which are calculated to be endothermic by 0.80 and 0.65 eV, and the barriers are 0.82 and 0.99 eV, respectively. A second path for the hydrogenation of CH₂CH is to reduce the less saturated C1 atom and give ethylene molecule (CH₂CH₂) with a much higher energy barrier of 1.44 eV and strong endothermicity by 1.34 eV. The subsequent hydrogenation of both CH₃CH and CH₂CH₂ gives CH₃CH₂, with an energy barrier of 1.92 eV to the former compared to a lower value of 0.62 eV to the latter (Fig. 6).

Starting from the C + H to form CH₂CH₂, the effective energy barrier to the path via the coupling of CH₂ is smaller than the other paths since the hydrogenations of CH₂CH and CHCH are endothermic and face high energy barriers, according to our calculations. This is in consistent with the experimental observations,³⁹ in which CH₂ appears as the reactant, and explains the formation of CH₂CH₂ via direct coupling reaction of two CH₂.

Regarding to the pathway for the formation of CH₂CH, according to our calculations, in addition to the direct coupling of CH₂ and CH, there may exist two other possibilities. The first one is the dehydrogenation of CH₂CH₂ which is inherent with a very low energy barrier (0.10 eV) and large exothermicity (1.34 eV), and the other one is a three-step process starting from CHCH, i.e. along the path CHCH → CHC → CH₂C → CH₂CH. In principle, the direct CHCH may also produce CH₂CH, however, its much higher effective energy barrier, which amounts up to 1.16 eV makes it uncompetitive against the stepwise pathway to which the E_eff is calculated to be 0.22 eV. Note that both pathways involve the dehydrogenation steps, low coverage of the surface is required to guarantee the availability of extra surface site, otherwise the dissociation steps may be blocked.

Microkinetic model

On the basis of our DFT calculations, a 16-step microkinetic model was developed to further investigate the coverage and the role of CH_x and C₂H_y species under the typical experimental condition (P_CO = 4 atm, P_H2 = 8 atm and T = 300–800 K) on V(100). In this work, we focus on discussing the C-chain growth on clean V(100) and the effect of oxygen was not studied. Thus the simple microkinetic model corresponding to a very low O* coverage (θ_O = 0) is given and the effect of the coverage of surface species on the adsorption energy of CO and H₂ was neglected. The elementary steps and the corresponding energy barriers and reaction energies were shown in Table 2. Typical pre-exponential factors of 10¹³ s⁻¹ were used.⁵⁰ The details about the microkinetic modelling are given in the ESI and the results are collected in Tables S1 and S2.†

Table 2 Calculated activation barriers and the reaction energy including ZPE for elemental steps^a

	Surface reactions	Ef (eV)	ΔH (eV)
a An asterisk represents a free site on the surface.
1	CO(g) + * ↔ CO*		−3.28
2	H2(g) + 2* ↔ 2H*		−1.36
3	CO* + * → C* + O*	0.33	−2.20
4	C* + H* → CH* + *	0.83	0.42
5	CH* + H* → CH2* + *	0.92	0.73
6	CH2* + H* ↔ CH3* + *	1.37	0
7	CH3* + H* → CH4(g) + 2*	1.03	0.54
8	C* + C* ↔ C2* + *	2.70	2.40
9	C* + CH* ↔ CCH* + *	2.02	1.54
10	C* + CH2* ↔ CH2C* + *	1.97	1.13
11	C* + CH3* ↔ CH3C* + *	1.05	0.27
12	CH* + CH* ↔ CHCH* + *	2.00	1.76
13	CH* + CH2* ↔ CH2CH* + *	2.03	1.24
14	CH* + CH3* ↔ CH3CH* + *	1.28	0.67
15	CH2* + CH2* ↔ CH2CH2* + *	2.71	1.98
16	CH2* + CH3* ↔ CH3CH2* + *	1.46	1.03

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Our results show that, under the studied condition, CH₂ is the dominant CH_x surface species in the whole temperature range (300–800 K) (see Table S1†). However, when the dissociation of CH₂ becomes possible (step 5r) and is included in the model at high temperature of 800 K, CH coverage becomes the highest, followed by that of CH₂. This suggests that both CH₂ and CH are important CH_x species responsible for the C-chain growth in the considered temperature range 300–800 K, consistent with the above discussion.

The forward reaction rate of CH₂ + CH, CH₂ + C and CH₃ + C coupling top the other channels from 300 to 800 K and the CH₂CH, CH₂C and CH₃C coverage are the highest among all C₂H_y species except CH₂CH₂ and CH₂CH₃ (see Table S2†). It is noted that the desorption of CH₂CH₂ and CH₃CH₂ by hydrogenation were not considered in the model which may decrease the coverage of these two species. If the step 5r is included in the model at 800 K, the forward reaction rate of CH₂ + CH tops the other channels and both CH₂CH and CHCH become dominant as a consequence of the higher coverage of CH than that of CH₂. Thus at experimental temperature, CH₂CH is the important C₂H_y species and may be responsible for the C-chain growth.

In summary, CH₂ is the most possible reactant for the C–C coupling reaction because of its high coverage, and CH is also recognized as a highly possible species responsible for the C–C coupling in view of energy barrier while its significance may be limited by its lower coverage at experimental temperature. Starting from the high coverage of CH₂, the reaction of CH₂ + CH₃ is most favourable, but the formed CH₂CH₃ will be desorbed from the surface after hydrogenation. The reaction CH₂ + CH₂ to CH₂CH₂ desorbing from the surface may be also favourable although need overcome a high energy barrier of 2.71 eV. The other reactions with lower effective energy barriers such as CH + CH and CH + CH₃ seem possible, but the much lower coverage of CH and CH₃ make them much less competitive than CH + CH₂. Thus, CH₂CH may be the most possible C₂H_y species from the C–C coupling on V(100) responsible for the C-chain growth in considered condition, as proven in Shen's experiment.³⁹

The formation of C₃H_z on V(100)

The further chain growth reactions are more complicated concerning the possibility for multiple CH_x and C₂H_y species to co-exist on the surface. Here we limited our calculations on two reactions based on the thermostabilities of the CH_x and C₂H_y building blocks: (1) CH₂CH reacts with the CH₂ to from CH₂CHCH₂ by overcoming a barrier of 2.60 eV (ZPE correction not included), (2) CH₂CH reacts with CH to form CH₂CHCH by overcoming a barrier of 2.04 eV, followed by a further hydrogenation step to give CH₂CHCH₂ after passing a barrier of 0.69 eV. The reaction energies of the three steps are 1.22, 1.09 and 0.69 eV, respectively. The terminal CH₂ group of the newly formed CH₂CHCH₂ can abstract an H atom from the neighboring binding site and produce CH₂CHCH₃, which may then desorb from the surface. The barrier and the reaction energy for this step is 1.31 and 0.86 eV, respectively. These results show that CH displays higher reactivity than CH₂ in the C–C coupling reactions towards the formation of CH₂CHCH₂, as implied by the lower energy barrier to the second path than to the first one (2.60 versus 2.04 eV).

However, as discussed above, the reactions that require the participation of CH suffer from the low coverage of CH compared to that of CH₂ at experimental temperature, which nevertheless benefits the coupling between CH₂CH and CH₂. This suggests that CH₂ may be responsible for the C-chain growth to form the dominant C₃H_z product via the path CH₂CH → CH₂CHCH₂ → CH₂CHCH₃, which agrees with the speculation in Shen's experiment.³⁹

Conclusions

In this work, the activation of CO, hydrogenation of CH_x and C₂H_y, as well as the C–C coupling process were studied by periodic DFT. The results indicate that CO and CH_x (x = 0–2) prefer to locate at the hollow site on V(100). Most C₂H_y species prefer to adsorb at the hollow site through the less saturated C atom and another C atom at the bridge site, with an exception that CH₃CH₂ binds at the bridge site through its CH₂ moiety. The adsorption strength of the CH_x and C₂H_y species is related to the extent of their unsaturation. The binding strength of CH_x is relatively strong on the surface, which does not facilitate their diffusion on the surface.

The activation of CO is facile via the direct dissociation rather than H-assisted pathways on V(100). The hydrogenation of CH_x, C₂H_y (except CCH) and the C–C coupling reactions are all kinetically and thermodynamically unfavorable and their occurrence depends on the high coverage of reactants and entropy effect. For the C–C coupling steps, the larger the difference in the saturation of the two C atoms, the more favorable the reactions are both in terms of thermodynamics and kinetics.

In F–T synthesis, starting from the reactants of C + H on the surface, CH₂ may be the dominant CH_x species at experimental temperature. Starting from high coverage of CH₂, CH₄ may form from its hydrogenation and desorbs from the surface as the CH_x product at high H coverage. C₂H₄ forms from its direct coupling and desorbs from the surface and the key chain-propagation intermediate, CH₂CH, comes from the its coupling with CH. Both the coupling steps and the continue coupling of CH₂CH with CH or CH₂ leading to the product CH₂CHCH₃ are unfavorable kinetically and thermodynamically. Note that, van der Waals interaction may increase the adsorption energies of hydrogen-containing species which may be enhanced as chain grows,^16,22 but the effect on the energy barrier of reaction on the metal surface is negligible. The high coverage of CH_x and H and the entropic effect may appear as the dominant factor responsible for the C-chain growth as well as the hydrogenation, and the contribution of CH may be limited by the its low coverage compared to that of CH₂ although the reactions involved CH with lower energy barriers. The results are in good agreement with the experimental results.³⁹ The whole process can be described as follows:

CO(g) + * → CO* (1)

H₂(g) + 2* → 2H* (2)

CO* + * → C* + O* (3)

C* + H* → CH* + * (4)

CH* + H* → CH₂* + * (5)

CH₂* + H* → CH₃* + * (6)

CH₃* + H* → CH₄(g) + 2* (7)

CH₂* + CH₂* → C₂H₄* + * (8)

C₂H₄* → C₂H₄(g) + * (9)

CH₂* + CH* → CH₂CH* + * (10)

CH₂CH* + CH₂* → CH₂CHCH₂* + * (11)

CH₂CHCH₂* + H* → CH₂CHCH₃ * + * (12)

CH₂CHCH₃* → CH₂CHCH₃(g) + * (13)

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China to Z. Chai (no. 91026000), to J. Liu (nos 20973077 and 21373098), to D. Wang (no. 91226105), by the Chinese Academy of Sciences in the framework of a Frontier of Novelty program to D. Wang (no. Y2291810S3), and by the Program for New Century Excellent Talents in University (NCET) to J. Liu, which are gratefully acknowledged. Calculations were done on the computational grids in the computer center of the Institute of High Energy Physics (IHEP) maintained by Drs Jingyan Shi and Bowen Kan, in the Supercomputing Center of Chinese Academy of Sciences (SCCAS) and in the National Supercomputing Center in Tianjin (NSCC-TJ).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c4ra15368e

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