Introduction

Carbon dioxide (CO2) is a cheap, non-toxic and abundant carbon-one (C1) source for chemical processes [1,2,3,4,5,6,7] and its transformations into fuel offer solutions to the problem of global warming as well as helping to meet the world’s increasing energy needs [8].

The catalytic hydrogenation of CO2 into methane (natural gas) by the Sabatier reaction is an important process as natural gas has a range of applications such as electricity generation by gas and steam turbines, heating of buildings and cooking [9, 10].

$$ {\text{CO}}_{ 2} + {\text{ 4 H}}_{ 2} \to {\text{CH}}_{ 4} + {\text{ 2 H}}_{ 2} {\text{O}}\;\Delta {\text{H}}_{{ 2 9 8 {\text{K}}}} = \, - 2 5 2. 9 {\text{ kJ}}\;{\text{mol}}^{ - 1} . $$

Despite the simplicity of the reaction, CO2 methanation mechanism appears quite difficult to establish as several different opinions have been expressed on the nature of intermediate compounds involved and the rate-determining step [7]. Generally, two mechanisms have been proposed for CO2 methanation, i.e., by the associative mechanism (non-CO pathway) or by the decomposition mechanism, where there is CO2 direct dissociation into CO prior to methane formation, with the further reduction of CO through the CO methanation pathway [11,12,13,14]. Also for CO methanation, there is no consensus for the mechanism, whether by the alkoxy (CHxO) intermediate or the CO decomposed carbide intermediate [7].

Late 3d metals, i.e., Fe, Ni, Cu, Co and Zn are metals thought to be responsible for CO2 reduction in nature [15,16,17,18,19]. These transition metals in iron sulfide clusters are thought to provide the needed electrons for the reduction process in the pre-biotic processes leading to the onset of life at the deep sea vents [18, 19], whereby CO2 was converted into diverse organic molecules under reducing conditions at ambient temperature and pressure. Although Fe, Co, Ni, Cu and Zn surfaces have been identified for CO2 activation and reduction experimentally, the reaction mechanism to producing hydrocarbons like methane is still not well understood on these surfaces [20, 21] and the earlier hydrogenation mechanism studies have focused mainly on Cu [22] and Ni surfaces [11,12,13, 23,24,25,26,27].

On clean Ni surfaces, most of these results supported the decomposition mechanism. Bartholomew and Weatherbee [11] earlier on in 1982 had studied CO2 hydrogenation on Ni and reported CO2 dissociation to CO. Peebles and Goodman [12] later experimentally studied CO2 methanation on the Ni (100) surface and reported CO and C intermediates leading to CH4 formation. Marwood et al. [13] submitted that the formate species is a spectator and CO is the key intermediate to methane formation. On the other hand, other studies supported the formate pathway. For example, Fujita et al. [24] observed that the kinetics of CO2 and CO were different during the methanation process. The amount of carbide (C) on Ni was lower for CO2 methanation than that in the CO methanation reaction, and hence inferred that CO2 and CO methanation occurred via different pathways. Schild et al. [28] reported the formate intermediate and pathway on nickel. Formate and other compounds like carbonates, formaldehyde, methylate and methanol were observed on copper and palladium in the hydrogenation of CO2 and CO, where formate was the primary compound reduced to methane on both surfaces [29].

With the spin-polarized density functional theory with a generalized gradient approximation (DFT-GGA) exchange–correlation functional, the complete hydrogenation reaction pathways of CO2 reduction to methane have been explored on Cu (211) [22] and Ni (110) [27] surfaces. It was found on Cu (211) that methane formation was preferred through the CO pathway via the carboxylate intermediate. However, the studies on Ni (110) revealed that the methane formation via hydroxycarbene intermediate requires a lower energy barrier than via carbon monoxide and formate intermediates. The mechanism of CO2 methanation has been underexplored on iron; we have investigated both the kinetics and thermodynamics of CO2 and CO methanation on Fe (111) surface.

Computational details

All geometry optimizations and total energy calculations were carried out using the spin-polarized density functional theory generalized gradient approximation (DFT-GGA) method. The plane-wave basis sets and ultra-soft pseudopotentials were employed within the Quantum ESPRESSO Package [30], which performs full self-consistent DFT calculations to solve the Kohn–Sham equations [31]. The Perdew, Burke, Ernzerhof (PBE) [32] GGA exchange–correlation functional was employed. The Fermi-surface effects were treated by the smearing technique of Fermi–Dirac, using a smearing parameter of 0.003 Ry. An energy convergence threshold defining self-consistency of the electron density was set to 10−6 eV and a beta defining mixing factor for self-consistency of 0.2 was used. The Grimme-D2 Van der Waals correction was employed in all calculations. The graphics of the atomic structures and the iso-surfaces of the differential electron density plots in this manuscript have been prepared with the XCrysDen software [33].

The surface was created from the optimized bulk using the METADISE code [34]. Surfaces were described with the slab model, where periodic boundary conditions are applied to the central super-cell, so that it is reproduced periodically throughout space [35]. A vacuum region of 12 Å perpendicular to each surface was tested to be sufficient to avoid interactions between periodic slabs. An energy cut-off of 40 Ry (544 eV) and charge density cut-off of 320 Ry (4354 eV) were employed for the expansion of the plane-wave basis set. This is sufficient to converge the total energy of the iron systems and the Brillion zone was sampled using (9 × 9 × 9) and (3 × 5 × 1) Monkhorst–Pack [36] k-points mesh for the bulk and p(3 × 2) surface, respectively. Each slab is made up of the 36 atoms whereby there are 6 layers and 6 atoms in each layer. In all calculations, the top 3 layers and adsorbate are allowed to relax and bottom 3 layers fixed to mimic the bulk material as employed in earlier computations [37, 38]. The Climbing Image Nudged Elastic Band (CI-NEB) method was used to determine all transition-state structures along the reaction coordinate. The importance of zero-point energy correction has been checked for smaller models and found to follow the same trend.

Results and discussion

Reaction energies for CO2 hydrogenation

To explore the intermediates involved in the hydrogen-assisted CO2 and CO methanation on the Fe (111) surface, several starting geometries were optimized by the stepwise hydrogen addition to CO2 and CO, which were optimized to obtain stable conformations (see Figure S1 of the supporting information file). The inter-atomic distances of the structures in Figure S1 are reported in Table S1 of the supporting information file. Upon obtaining all the optimized ground-state structures, the transition-state structures were sought for along two possible pathways, i.e., the non-CO pathway through the formate intermediate and the CO pathway through the carboxylate intermediate. Series of elementary steps were considered within each of the two reaction pathways and a systematic representation is illustrated in Figs. 1, 2 and Table 1.

Fig. 1
figure 1

A schematic representation of the possible transformations via the non-CO pathway

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Fig. 2
figure 2

A schematic representation of the possible pathways via the CO pathway

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Table 1 Elementary steps, illustrations as seen in reaction schemes (Figs. 1, 2) for the transformation of CO2 via the non-CO and CO pathways
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The relative energies (∆E) for the ground-state structures and the transition-state structures were calculated relative to the isolated slab, CO2(g) and x½ H2(g), using the formula shown below;

$$ \Delta E = E_{{\left( {\text{final}} \right)}} - E_{{\left( {\text{initial}} \right)}} , $$

where \( E_{{\left( {\text{final}} \right)}} \) is the energy of the ground-state or transition-state structure and \( E_{{\left( {\text{initial}} \right)}} \) is the energy of the gas-phase starting materials.

CO2 adsorption on Fe (111) is seen to require an energy barrier of − 4.6 kJ mol−1 [38]. In this study, hydrogenation of the Fe (111) surface is also seen to be barrier less and dissociative; hence, atomic hydrogen co-adsorption is explored in each elementary step via the Langmuir–Hinshelwood-type reaction. As shown in Fig. 3, along the non-CO path, formate formed from CO2 hydrogenation (reaction barrier = 0.1 kJ mol−1) could be hydrogenated into CHO and OH (via TS1a), formic acid (via TS1b) or dihydride-CO2 species (via TS1c). It is seen that formate goes through the highest barrier to form decomposed species (CHO+OH) (barrier = 271.1 kJ mol−1). Formate transformation into formic acid is more favorable (barrier = 120.6 kJ mol−1); however, a much lower kinetic barrier is seen for the production of the dihydride-CO2 species, i.e., H2CO2 (65.9 kJ mol−1). H2CO2 is transformed into aldehyde (CHO) upon further hydrogenation (barrier = 98.4 kJ mol−1). Although the formation of the aldehyde is thermodynamically and kinetically challenging, the further hydrogenation of the aldehyde through TS1e requires a moderate barrier of 20.6 kJ mol−1 to produce a stable methoxy species of energy − 198.4 kJ mol−1. Methanation of methoxy is very challenging requiring an energy barrier of 186.5 kJ mol−1 and thus making it a very slow process which might not be realized. However, methanol formation requires a lower barrier of 115.6 kJ mol−1. Kinetically, the methanation of CO2 via the non-CO pathway will selectively proceed via the following intermediates; formate, dihydride-CO2, aldehyde and methoxy. Methanol formation is more favored kinetically through this pathway, with the rate-limiting step for formic acid, methanol, methane formation to be 127.6 kJ mol−1, 115.6 kJ mol−1 and 186.5 kJ mol−1, respectively.

Fig. 3
figure 3

Energy profile diagram along the non-CO pathway

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Along the CO pathways, CO2 hydrogenation into carboxylate requires an energy barrier of 96 kJ mol−1 (see Fig. 4). Carboxylate hydrogenation leads to dihydroxycarbene formation with a barrier of 146.2 kJ mol−1. Dihydroxycarbene, being an unstable intermediate, once formed prefers to decompose into CO (TS2b = 28.9 kJ mol−1) than to rearrange into formic acid (TS2c = 156.2 kJ mol−1). The further decomposition of CO into carbide is seen to be both kinetically and thermodynamically challenging through TS2e, (with an energy barrier of 137.2 kJ mol−1) implying the carbide formation is unlikely to occur. CO would rather produce HCO requiring an energy barrier of 91.6 kJ mol−1. Further hydrogenation of HCO could lead to the formation of three possible intermediates, a decomposed CH + hydroxyl intermediate (with the highest barrier i.e. 191.8 kJ mol−1), an alcohol group (barrier of 114.3 kJ mol−1) or the alkoxy group (which has the least energy barrier i.e. 55.9 kJ mol−1). Therefore, the carbon center of HCO is further hydrogenated to form H2CO. H2CO could further be hydrogenated into H3CO (TS2j = 4.5 kJ mol−1) or CH2OH (TS2k = 28.8 kJ mol−1). CH2OH is preferred and decomposes into CH2 through a barrier of 65.4 kJ mol−1 (TS2l). CH2 is then protonated into CH3 and methane. Kinetically via the CO pathway, CO2 selectively converts into methane through the carboxylate, dihydroxycarbene, CO, alkoxy and alkyl intermediates. The slowest step for formic acid, CO, methanol and methane formation via the CO pathway involves the energy barriers, 156.2 kJ mol−1, 146.2 kJ mol−1, 146.2 kJ mol−1, 146.2 kJ mol−1, respectively.

Fig. 4
figure 4

Energy profile diagram along the CO pathway

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Comparing the rate-limiting step leading to the formation of the desired products, i.e. CO, formic acid, methanol and methane along both the CO and non-CO pathways, the preferred pathway leading to the formation of these products can be determined. Of the two pathways explored (CO and non-CO pathways), the one providing the least rate-limiting step indicates selectivity and is the preferred pathway. Formic acid is preferentially produced via the non-CO pathway through the following intermediates: CO2 and formate intermediates, with the rate-determining step being the hydrogenation of formate into formic acid (127.6 kJ mol−1). Methanol production from CO2 is favored via the non-CO pathway as well as through the following intermediates: CO2, formate, dihydride-CO2, CH2O and methoxy intermediates, with rate-determining step being the hydrogenation of methoxy to methanol (115.6 kJ mol−1). Methanol will be selectively produced from CO (over CO2) via the following intermediates: carboxylate, dihydroxycarbene, CO, HCO, CH2O and methoxy intermediates. The slowest step is the hydrogenation of CO into HCO (91.6 kJ mol−1).

Methane and CO formation will occur via the carbonyl pathway; methane formation will proceed through the following intermediates: carboxylate, dihydroxycarbene, CO, HCO, H2CO, H2COH, CH2 and CH3. The slowest step for both the methanation and CO formation process involves carboxylate hydrogenation into dihydroxycarbene (146.2 kJ mol−1). CO methanation is more favorable on Fe (111) over CO2 methanation, occurring via the intermediates HCO, H2CO, H2COH, CH2 and CH3. CO methanation proceeds with the slowest step involving CO hydrogenation into HCO (91.6 kJ mol−1), as seen earlier for methanol production from CO. CO hydrogenation controls both the rate of methanol and methane formation from CO; hence, these reactions are very competitive for CO reduction on Fe (111) and lowering the barrier for CO protonation is desirable to speed up both processes. Formate hydrogenation, methoxy hydrogenation and carboxylate hydrogen-assisted transformation into CO control the rate of CO2 transformation to formic acid, methanol and methane, respectively. Thus, modified Fe (111) surfaces enhancing these reaction steps have the potential to improve the CO2 conversion processes.

Our results show that CO2 methanation on Fe (111) occurs via the CO pathway through the following transformations: carboxylate protonation to dihydroxycarbene (HOCOH), decomposition to carbon monoxide (CO), protonation of CO to HCO, protonation to H2CO to alkoxy, protonation on alkoxy (CH2–OH) and water production, leading to CH2 and CH3 formation. CO2 methanation on Cu (211) using the computational hydrogen electrode is seen to proceed via the CO and carboxylate intermediates as well [22]. Also, on the Ni (110) surface, dihydroxycarbene, CO and CH2OH are reported to be intermediates leading to methane production, with water removal from the surface been the rate limiting step [27]. The mechanism of CO2 methanation on Ni (100) shows that large amount of CO is formed over methane as activation energies of 88.7 and 72.8–82.4 kJ/mol are observed for methane and CO production, respectively. However, on Fe (111), the activation energies for CO formation and methanation are same, i.e., 146.2 kJ mol−1 [12]. Again, Fe (111) does not favor the carbide pathway as reported on Ni (100). Cu is also seen to reduce CO2 via the carboxylate, CO, HCO and methoxy intermediates; while the reaction barriers were not considered [22].

Conclusion

Our spin polarized-D2-GGA-DFT calculations reveal that CO2 methanation will occur via the CO pathway and not the non-CO pathway. Fe (111) selectively favors CO methanation over CO2 methanation, since although the reaction pathways are similar, the highest energy barrier for CO2 methanation is encountered during the hydrogen-assisted CO2 transformation into CO via the carboxylate and dihydroxycarbene intermediates. Both the formation of formic acid and methanol will proceed via the non-CO pathway, while CO and methane will be formed via the CO pathway from CO2. CO2 methanation on Fe (111) will involve the initial sequential hydrogenation of CO2 into carboxylate, dihydroxycarbene, CO, HCO, H2CO, and CH2OH. CH2OH is then decomposed into CH2 and protonated into CH3 and methane. Altering the rate-determining steps on modified Fe (111) surface is promising for CO2 transformation and valorization.