Exploring reaction mechanisms for CO₂ reduction on carbides

Abstract

The electrocatalytic conversion of carbon dioxide (CO₂) into valuable fuels offers immense promise in pursuing sustainable energy solutions. Transition metal carbides (TMCs) with their robustness and intriguing electronic properties have traditionally emerged as captivating contenders in the quest for efficient catalysts for the CO₂ reduction reaction (CO₂RR). The presence of carbon atoms in TMC structures unlocks a unique reaction mechanism for the CO₂RR, namely the Mars–van Krevelen (MVK) mechanism, facilitating CO₂ capture and more efficient conversion to high-value-added chemicals. This work is the first report on the use of TMCs for the CO₂RR where comprehensive reaction pathways for different product formations are investigated. This theoretical study delves into the electronic intricacies of TMCs, unraveling their potential to drive the transformative journey toward a greener tomorrow. Here, we analyzed 11 TMCs to explore the reactivity trends toward CO, formic acid, methane, methanediol, and methanol formation. VC is the best candidate explored to produce formic acid at 0 V onset potential. In addition, WC is the best candidate explored to produce methanol at an onset potential of −0.36 V. These results demonstrate that our studied TMCs as electrocatalysts are more promising than previously studied materials (metals and oxides) for application in the CO₂RR, and thus require more attention and investigation.

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1. Introduction

Since the start of the 20^th century, the world climate has been changing more noticeably. The balance in nature is lost due to dramatically increasing CO₂ emissions due to burning of carbonaceous fuels which results in global warming. An urgent effort is needed to overcome this problem to reduce the ratio of CO₂ and turn it into fuel and other useful chemical products. On the other hand, the large-scale use of unsustainable fossil fuels for energy has led to an energy crisis in the world and increased the amount of CO₂ in the atmosphere. Due to this, the world climate is changing day by day, and scientific effort is needed to overcome the emission of CO₂ in the air by converting the already present CO₂ into green energy fuels.^1–3 Previous experimental and theoretical research concluded that conversion of CO₂ into valuable products can be achievable, but not yet efficient for commercialization. In the whole process of the CO₂ reduction reaction (CO₂RR), the catalyst plays a key role in capturing CO₂ and converting it into valuable chemical products and fuels. CO₂ is considered a chemically stable molecule, which presents challenges when attempting to reduce it electrochemically due to the high reduction overpotential, poor product selectivity, and low current efficiency. To tackle this challenge, researchers and scientists have been investigating innovative catalyst materials that can effectively overcome these obstacles and enhance this electrochemical process.^4–8

In the previous decades, many experimental studies have been done for the electrochemical CO₂RR on different metal catalysts i.e. pure metals of Cu, Ag, Au, and Pt have been studied as catalysts for the CO₂RR.^9–12 It is well known that Cu is considered a widely used catalyst for the reduction of CO₂ to CH₄ but its overpotential is high (∼0.9 V) and moreover it produces 15 different carbon-containing products which require a large amount of energy to separate them. In addition to pure Cu, polycrystalline Cu was also examined for application in the CO₂RR, but this has the same problem as pure Cu.^1,6,13–16

In addition to pure metal electrocatalysts, metal oxide catalysts i.e. TiO₂ studied by the DFT method were considered impressive and more efficient for CO₂ conversion to CH₃OH and CH₄ products.¹⁷ In another study, RhO₂ was predicted to be a novel candidate for the formation of formic acid at −0.20 V onset potential.¹⁸ However, the stability and electron conductivity of oxides as cathode materials are insufficient, which limits their application in the CO₂RR.^19,20 There are numerous studies conducted to explore novel catalyst materials for the CO₂RR such as graphene-based materials, metals, metal oxides, zeolites, sulfides, and metal–organic frameworks, but yet activity and efficiency are not optimal for the commercialization purposes and the utilization of catalysts for large-scale implementation is still a challenge and more study is required to overcome this problem.^21–30 Traditional catalysts may have limitations in terms of selectivity, efficiency, or cost. By searching for other materials, researchers aim to identify catalysts that can enhance the performance of CO₂RR processes, making it more economically viable and environmentally friendly. The surface chemistry of transition metal carbides (TMCs) is comparable to that of precious Pt-group metals, which was already described by Levy and Boudart.^31,32 Some of the TMCs were investigated and showed promise for reactions such as CO oxidation,³³ hydrogenation,³⁴ methane dry reforming,35 desulfurization,³⁶ conversation of methane to gas and water gas shift reaction.^37,38 TMCs demonstrate significant efficacy in facilitating various transformations and are regarded as attractive candidates for catalytic applications.³⁹ Consequently, they are considered a potential alternative to precious metal catalysts owing to their high chemical and thermal stability⁴⁰ high mechanical stability,⁴¹ and low cost.⁴² Hence these materials have received great attention for application in catalysis, but there is no comprehensive investigation of TMCs for the CO₂RR. Utilizing advanced quantum mechanical simulations and computational models, we explored the binding energies and different reaction pathways of 11 TMCs (CrC, HfC, MoC, YC, ScC, NbC, ZrC, TaC, TiC, WC, and VC), with a focus on their suitability for catalyzing CO₂ reduction. Here we are doing screening studies on 11 different TMCs to find out which one is more favourable and promising for the CO₂RR thermodynamically for more in-depth investigation in the future. These data provide valuable information about the activity of these TMCs. The difference in the PDS values associated with different products can be an indication of selectivity to some extent, however, kinetic barrier calculations are needed to determine product selectivity which is not the scope of the present work.

2. Computational method

The interaction of CO₂ with TMC surfaces and the formation of different intermediates were studied by DFT calculations with Generalized Gradient Approximation (GGA) using the RPBE exchange–correlation functional.⁴³ The Vienna ab initio simulation package (VASP) was used for the modeling, with a cutoff energy of 450 eV and a 4 × 4 × 1 Monkhorst–Pack K-point.⁴⁴ The Projector augmented wave (PAW) method was implemented due to the full wavefunction by utilizing computationally efficient pseudopotentials, significantly reducing the computation time.⁴⁵ The TMC surface was considered in the rocksalt (RS) crystallographic structure with the texture orientation of (100). The electrodes modeled consisted of 5 layers with each layer made of 4 atoms of carbon and 4 atoms of metal, 40 atoms in total in the unit cell of each TMC structure. The boundary condition was periodic with a 20 Å vacuum along the z direction to avoid self-interaction of neighboring layers. The bottom two layers were fixed, and the top 3 layers were allowed to fully relax together with any adsorbates on the surface as shown in Fig. 1.

Fig. 1 Schematic representation of a TMC, the dark brown color shows carbon atoms and the red color shows metal atoms. The dotted line shows that the bottom two layers are fixed.

The binding energy of an adsorbate was calculated according to eqn (1):⁴⁶

ΔE_ads = E_{(adsorbate/TMC slab)} − E_{(TMC slab)} − E_(adsorbate) (1)

Here E_{(adsorbate/TMC slab)} is the total energy of the system with an adsorbate on the TMC slab, E_{(TMC slab)} is the total energy of the pristine TMC slab, and E_(adsorbate) is the total energy of the adsorbate. The negative ΔE_ads corresponds to the exothermic adsorption of species. The computational hydrogen electrode (CHE) model as proposed by Nørskov et al.⁴⁷ was used to calculate the free energy diagram for the CO₂RR along different paths at certain applied potentials. According to this method, at room temperature, the kinetic barrier is negligible for the proton-coupled electron step and the potential limiting step is the most positive energy difference between the two adjacent steps. The reaction free energy of an adsorbate for the CO₂RR at any arbitrary potential U vs. RHE and any arbitrary pH was calculated using the equations:

ΔG_(URHE) = ΔG_(URHE=0) + neU_RHE (2)

eU_RHE = eU_RHE + 2.3k_bTpH (3)

where U_RHE is the applied potential referred to the standard hydrogen electrode (SHE), n is the number of electrons, e is the charge of electrons, k_b is the Boltzmann constant and T is the temperature. By putting eqn (2) into eqn (3) we will get:

ΔG_(URHE) = ΔG_(URHE=0) + n(eU_RHE = eU_RHE + 2.3k_bTpH) (4)

Generally, overpotential is independent of the pH of the electrolyte so in this study we will consider pH = 0. Hence for each elementary step, ΔG (U = 0) is calculated by

ΔG_(U=0) = ΔE_DFT + ΔE_ZPE − TΔS + ΔE_{0 K→T} (5)

where ΔG is the Gibbs free energy, ΔE_DFT is the electronic energy calculated by DFT, ΔE_ZPE is the zero-point energy correction and TΔS is entropy differences between the gas phase and adsorbed species calculated by vibrational frequencies for the adsorbed species. ΔE_{0 K→T} is the change in internal energy because of temperature and its value is where C_p(T′) represents specific heat at constant pressure and the integral of this equation contributes negligibly at room temperature. The value of the gas phase is taken from the thermodynamic tables from textbooks.⁴⁸

A crucial step towards a rational design of new catalysts that are selective in reducing CO₂ to specific hydrocarbons and alcohols is to determine the detailed reaction mechanism for the process. To accomplish this, a detailed description of the electrochemical solid–liquid interface is also required. It has been observed that a detailed description of the electrochemical solid–liquid interface model is successful in capturing the experimental trends of product distribution for the CO₂RR on pure metals.^49,50 Although the more approximated thermochemical model (TCM) and the implicit computational hydrogen electrode (CHE) cannot completely capture these trends, they do capture the onset potentials for the CO₂RR and other electrochemical reactions quite well.^50–54 The molecular level structure of water on noble transition metals is qualitatively well known and therefore realistic model systems can be used. Unfortunately, for transition metal carbide (TMC) surfaces and especially for the (100) facets of rocksalt structures, the molecular scale structure of water is still controversial, and hence, realistic model systems have not been fully developed yet. Therefore, most of the analyses in this work are based on the calculated thermodynamics of adsorbed intermediates on the TMC surfaces, and the TCM and CHE models are used to capture the onset potentials for the CO₂RR. For pure metals, activation energies can be calculated for each of the proton–electron transfer steps (toward different intermediates and products) by setting up a charged double-layer model including a solid electrode and an aqueous electrolyte solution as has been done for the metal–liquid interface for the CO₂RR^49,55 There, the charge difference in the double layer sets up the applied electric potential explicitly and therefore the proton–electron transfer barriers can be calculated as a function of explicitly varied potential. This approach is helpful in reproducing the experimentally observed product distribution as a function of both the metal type and the applied potential. However, for these TMCs and as elaborated above, there is a lack of understanding on the water layer structure in modeling plus the fact that there are not many experimental reports on these TMCs to compare the computational results and trends with. Furthermore, previous reports on Cu pure metal, in the (111) facets of hexagonal structures, suggest stabilization energies of 0.1–0.25 eV for CO* and CHO* when water layers are included in the model. This correction has not been included in our analysis, as we are conducting a screening study focused on identifying trends across 11 different surfaces based on thermodynamic data. Readers interested in this work are strongly advised to pay attention to the fact that the conclusion made in this paper is mainly based on thermodynamics where the authors tried to provide some hints and understanding on the possibility of using TMCs, opening the path for further investigation of their utilization for the CO₂RR.

3. Results and discussion

The thermochemical model⁵⁰ was employed to predict favorable reaction pathways and onset potentials for the CO₂RR on the (100) facets of the RS structure of TMCs. A number of studies have been carried out using this model successfully i.e., hydrogen evolution reaction (HER),^56,57 and nitrogen reduction reaction (NRR)^58–61 and here we have employed the same method. From the earlier transition metals, 11 carbides including CrC, HfC, MoC, YC, ScC, NbC, ZrC, TaC, TiC, WC, and VC were selected for this investigation, as the later transition metals form carbides in structures other than the RS.^62,63 The electronic structure of these TMCs has been reported in our previous publication.⁶⁴ In the initial phase, the adsorption-free energy of all species was systematically investigated on the metal, bridge, and carbon sites of each TMC. This investigation revealed that the carbon sites are particularly more active for adsorption compared to the metal sites. We have undertaken a comprehensive exploration involving the absorption of various species to analyze their poisoning effects on TMCs, as illustrated in Fig. 2.

Fig. 2 Comparison of adsorption energies of different species onto the clean surface of TMCs, and CH and MH represent the adsorption of protons on carbon and metal sites of TMCs. For some of the carbides (ScC, YC, ZrC, TiC), the MH adsorption is not shown as it is not feasible for protons to adsorb on the metal site.

The findings reveal positive binding energies of H, O, and OH species for most TMCs rendering a lower likelihood of poisoning, with the exceptions being ScC and YC where O binds exergonically. Consequently, these materials (ScC and YC) have been selected only for investigation within the framework of methane formation via the Mars–van Krevelen (MvK) mechanism. Adsorption of other key species such as COOH and OCHO was found to be exergonic for most of these surfaces. A unique property of TMC is to unlock a special reaction mechanism, namely the MvK. In this mechanism, the carbon atom already incorporated in the catalyst structure reacts with protons and converts to CH₄, releasing from the surface spontaneously and leaving a carbon vacancy on the surface which should be refilled with atmospheric CO₂ to sustain the catalytic cycle of methane formation. This MvK does not work on most of the other catalyst materials and thus TMCs offer an advantage. The other most common and possible mechanism on all the other catalyst surfaces is the conventional surface mechanism where CO binds the clean surface in the form of COOH or OCHO. We investigate both of these mechanisms here.

3.1. CO₂RR pathways via the MvK mechanism

In actual experiments, it is important to note that TMCs might exhibit some defects in the form of carbon vacancies, primarily due to the inherent difficulty in always achieving complete stoichiometry. Another possible reason for the formation of vacancies would be coming from the electrochemical conditions where the catalytic cycle starts with surface protonation until a surface carbon atom is reduced to methane (CH₄) and released. The carbon vacancy is then formed which should be filled with atmospheric CO₂ where the C atom of CO₂ fills the vacancy of TMCs, and two oxygen atoms are further reduced to two water molecules as mentioned in eqn (6) and (7) followed by the Kröger–Vink notation:⁶⁵

* + 4(H⁺ + e⁻) → CH_4(g) + ^CVac (6)

^CVac + CO₂ + 4(H⁺ + e⁻) → 2H₂O + * (7)

To consider the effect of proton coverage on the surface, we investigated surface protonation by adding protons one after the other and explored all the possible adsorption sites, which are the metal site, the bridge site, and the carbon site. It was found that all the protons tend to bind the carbon site only to make CH₄ (as shown in Fig. 3). Thus, no proton coverage builds on the surface and thus it is an indication of unfavourable HER on these surfaces.

Fig. 3 Free energy diagram for methane formation via the MvK mechanism on the surface of NbC.

Our findings conclude NbC as the optimal candidate for CH₄ formation via the MvK with a predicted onset potential of −0.39 V and its free energy diagram is shown in Fig. 3.

The other promising candidates for CH₄ formation via the MvK mechanism are WC, MoC, VC, and TiC with onset potentials of −0.41, −0.44, −0.44, and −0.46 V, respectively, as shown in the free energy diagram of Fig. S1.† Further reduction of oxygen atoms of CO₂ is an exergonic process for HfC, WC, ZrC, TaC, TiC, and VC, except for MoC, CrC, ScC and YC where more potential is needed for water release. The onset potential required for methane formation on the surface of ScC and YC is −1.24 and −1.68 V, respectively. Due to these high onset potential values and energy steps, we have excluded ScC and YC for further investigations.

A volcano plot has been generated by using the linear relations of various reaction steps. The Gibbs free energy change of the OH (ΔG_OH) has been found as a reliable descriptor in previous research,^18,66 for investigating the CO₂RR on transition metal oxide surfaces and also found reliable in our work. The theoretical volcano plot for the formation of methane via the MvK mechanism was constructed from the scaling relations and is shown in Fig. 4. NbC is located on top of the volcano as the most promising catalyst among the TMCs studied. The left leg of the volcano is related to the reaction between OH and water, while the right leg depicts the formation of CH₂ after the formation of the CH intermediate.

Fig. 4 Theoretical volcano for the formation of methane via the MvK mechanism.

3.1.1. Stability against decomposition via vacancy migration. For most of these surfaces, it is relatively facile to form methane and then fill the vacancy with atmospheric CO₂ and complete the catalytic cycle. In the MvK, there is a possibility of migration of the surface vacancy into the bulk which means migration of the C atoms from the bulk to the surface. If this process is facile (thermodynamically and kinetically) it can contribute to further reduction of C atoms of the material and conversion of the carbide to its pure metal, rendering decomposition and material instability. Therefore, it is crucial to investigate this phenomenon carefully. Using the Climbing Image Nudged Elastic Band (CI-NEB) method we have investigated the diffusion barrier of migration of carbon atoms from the sublayer to the surface. For our promising candidate, VC, the carbon migration barrier is 2.38 eV as shown in Fig. 5 which means that this process should be very slow under ambient conditions and this catalyst should be stable. Similarly, for our other investigated candidates, CrC, HfC, MoC, NbC, TaC, TiC, WC, and ZrC the diffusion barrier for carbon migration is calculated to be 1.77, 3.87, 1.87, 2.69, 3.55, 2.96, 1.91, and 3.30 eV, respectively, and the conclusion is that these TMCs should be very stable against decomposition to parental metals.

Fig. 5 Schematic diagram for migration of carbon atoms from the sublayer to surface vacancies. (a) Represents the visualization of the motion of carbon atoms from the sublayer to the surface, orange color indicates the carbon atoms, silver color indicates the metal atoms and white color indicates the proton. (b) Represents the minimum energy path for the migration of carbon atoms from the sublayer to the surface.

3.2. CO₂RR pathways via the conventional method

In the first step of the CO₂RR two possible intermediates, OCHO and COOH, can be formed by the first electron–proton transfer step, and further protonation on OCHO and COOH continues until the product(s) is(are) formed as shown in Fig. 6. Our analysis concludes that the carbon sites of TMCs exhibit the highest level of activity and the carbon of COOH and OCHO attaches with the carbon of TMCs as shown in the schematic of the adsorption of COOH and OCHO in Fig. S3.† Additionally, in the majority of situations, the adsorption of COOH is more energetically favorable compared to OCHO, as illustrated in Fig. 2. However, OCHO adsorption is favorable on HfC and VC only. Regarding HfC, the progression through OCHO after a few protonation steps exhibits endergonic characteristics. This is why we have chosen to analyze the COOH pathway, which displays the lowest energy values on the free energy diagram as shown in Fig. S1.†

Fig. 6 Proposed mechanism of the CO₂ reduction reaction via OCHO and COOH.

CO₂ adsorption is the bottleneck in the CO₂RR and the majority of the materials explored and reported so far cannot bind it favorably, and thus researchers working with DFT usually investigate the protonation form of CO₂ (COOH or OCHO) as well^67–69 and as such we followed the same approach. However, we looked into the direct adsorption of CO₂ on the clean surface of these TMCs, and we found out that only HfC, ScC, YC, and ZrC bind CO₂ exergonically. Conducting protonation of CO₂ on these 4 surfaces, the PDS was found to be high for ScC and YC and thus we have not considered ScC and YC for further investigation. For HfC and ZrC, however, COOH was found to be more exergonic than direct adsorption of CO_2.

3.2.1. Selectivity between CO₂RR versus HER. The first step of protonation provides information on selectivity towards the CO₂RR or HER. Our calculated free energies for all the TMCs suggest that the HER is of no concern as COOH always binds the surface stronger than H. For example, the calculated Gibbs free energies of H adsorption for TaC and WC are 0.37 and 0.38 eV, respectively. Although these free energies are considered small and thus HER-susceptible, the COOH binding free energies for TaC and WC are only 0.21 and 0.22 eV, respectively. This indicates that the active site should be occupied by the COOH rather than H and thus more selectivity towards the CO₂RR is expected. Similarly, (COOH or OCHO) adsorption vs. hydrogen adsorption for CrC, HfC, MoC, NbC, ZrC, TiC, and VC shows more tendency towards the CO₂RR rather than the HER (refer to Fig. 2 and 7). Fig. 7 shows that our predicted catalyst systems possess weaker adsorption energy for atomic H adsorption, suggesting poor HER activity/selectivity. Therefore, the impediment against the HER indicates that the TMC system can act as an efficient catalyst for the CO₂RR.

Fig. 7 Free energy diagram for H adsorption on the metal site as an indication of the HER.

3.2.2. CO₂RR pathways towards the formation of formic acid (HCOOH) and CO. In the second protonation step, formic acid and CO are the main products of the CO₂RR before the formation of methane, methanol, and methanediol. The reactions follow the protonation steps as:

*COOH or *OCHO + H⁺ + e⁻ → *HCOOH (8)

*COOH or *OCHO + H⁺ + e⁻ → *CO + H₂O (9)

Our investigation reveals that only VC does not bind the *HCOOH intermediate on its surface and this catalyst has the potential to produce aqueous formic acid with 0 V onset potential as shown in the free energy diagram (Fig. 8), and thus this candidate is the best TMC to produce formic acid. The VC needs a relatively large onset potential of around −1.08 V to form methanol and methanol. Therefore, the selectivity is easily tunable for VC by tuning the onset potential applied and only producing formic acid.

Fig. 8 Free energy for VC and the green line indicates the formation of formic acid at 0 V. CO and HCOOH are formed via different paths and not together via the same path. The HCOOH formation is followed by the green path which comes from OCHO which is an exergonic step, while the CO formation is followed by the black path which comes from COOH and is endergonic.

In addition to VC, other carbides like TaC, WC, NbC, and HfC are explored as good candidates to produce formic acid with small onset potentials of −0.25, −0.31, −0.40, and −0.46 V, respectively as shown in Fig. 9.

Fig. 9 Onset potential for the formation of methanol, methane, formic acid, CO, and methanediol. The representation of the steric effects indicates that the mentioned products in specific colors are formed with 0 V onset potential.

In addition, we have developed a volcano diagram for the production of formic acid using scaling relations. Fig. 10 illustrates the model, where each line represents a reaction involved in the production of formic acid. We have utilized OH as a descriptor, which is analogous to the volcano plot used for methane creation via the MvK mechanism. The results indicate VC as a promising candidate on the top of the volcano. The CrC, HfC, ZrC, TaC, and VC are expected to convert CO₂ to CO spontaneously. These materials are promising for CO formation at 0 V. MoC, NbC, TiC, and WC are also good candidates for the formation of CO with an appropriate onset potential of −0.12, −0.29, −0.06, and −0.20 V, respectively.

Fig. 10 Theoretical volcano for the formation of HCOOH.

3.2.3. CO₂RR pathways toward the formation of methanol. The CO₂RR towards methanol formation involves 6 proton–electron transfer steps as shown in Table 1. In this work, we have investigated two routes to produce methanol, one route is *COOH to *HCOOH and another route is *COOH to *CO + H₂O.

Table 1 Possible pathways for methanol formation

Pathways	(e + H^+) steps
	1	2	3	4	5	6
A	*COOH	*HCOOH	*H2COOH	*CH2O + H2O	*CH2OH	CH3OH (aq)
B	*OCHO	*HCOOH	*H2COOH	*CH2OH + OH	CH3OH (aq) + *OH	H2O(l)
C	*COOH	*HCOOH	*H2COOH	*CH2OH + OH	*CH2OH + H2O(l)	CH3OH (aq)
D	*COOH	*HCOOH	*H2COOH	*CH3O + OH	*CH3O + H2O(l)	CH3OH (aq)
E	*COOH	*CO + H2O(l)	*COH or *CHO	*CHOH or *CH2O	*CH2OH or *CH3O	CH3OH (aq)

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The route followed through COOH to CO + H₂O is more promising as compared to the other one because in this route we have required less onset potential as shown in the free energy diagrams of Fig. S2.† For seven TMCs (CrC, HfC, MoC, NbC, ZrC, Tic, WC) the COOH adsorption is favorable, while for TaC and VC the OCHO adsorption is more favorable for methanol formation. The mechanisms for methanol formation differ among various TMCs. To simplify the representation of these reactions, we focus on the most energetically favorable stages in the minimal free energy pathways, disregarding other reaction steps. The surfaces of HfC, WC, MoC, ZrC, TiC, and CrC followed path E, NbC followed path C, TaC followed path B, and VC followed path A as mentioned in Table 1 for the formation of methanol. Our analysis reveals that WC is the best candidate for methanol formation with the potential determining step of 0.36 eV via the black pathway. The free energy diagram for the WC is shown in Fig. 11 for both methane and methanol formation and the adsorption configuration of each intermediate is shown in Fig. S4.† In addition to WC, the studied TiC, NbC, and CrC are also good candidates for methanol formation with corresponding onset potentials of −0.40 V, (−0.44 V, −0.67 V) and −0.53 V, respectively. The scaling relations for methanol formation were investigated by considering several possible descriptors, but the correlation was not good mainly due to the fact that each TMC follows a different reaction path for the formation of methanol and also the PDS for each TMC is not associated with a similar step. Thus, TMC showed to deviate from the scaling relations.

Fig. 11 Free energy diagram for the methanol formation on WC.

The potential determining step values for formic acid, CO, methanediol methanol, and methane formation on each TMC are shown in Table 2.

Table 2 Onset potential (V) for the CO₂RR towards the various products and intermediates (╳ represents these products are not formed on these catalysts)

Catalyst	Formic acid	CO	Methanol	Methanediol	Methane	HER on the metal site (MH)
CrC	−1.67	0.00	−0.53	╳	Unstable	−0.66
HfC	−0.46	0.00	−0.69	╳	−0.52	−1.60
MoC	−0.58	−0.12	−0.87	−0.58	−0.87	−0.75
NbC	−0.40	−0.29	−0.44	╳	Unstable	−0.67
ZrC	−0.79	0.00	−0.83	╳	−0.83	—
TaC	−0.25	╳	−0.69	╳	−0.69	−0.37
TiC	−0.90	−0.06	−0.4	╳	−0.9	—
WC	−0.31	−0.20	−0.36	╳	−0.69	−0.38
VC	0.00	0.00	−1.08	−1.08	╳	−0.90

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3.2.4. CO₂RR pathways towards the formation of methanediol and methane. Among the TMCs explored here, only MoC and VC are found to catalyze methanediol formation with the onset potentials of −0.58 V and −1.08 V, respectively. The path followed for methanediol consists of 4 steps as COOH/OCHO → HCOOH → H₂COOH → CH₂(OH)_2(aq). On all the other TMCs, further protonation of H₂COOH breaks it into other intermediates and thus methanediol formation cannot be achieved.

Through the conventional mechanism, TiC and NbC are found suitable candidates for the formation of methane with the onset potentials of −0.40 and −0.44 V, respectively, and interestingly these candidates have the same onset potential for the formation of methanol, meaning that both of these products are expected to be produced at these applied potentials. In addition, HfC, MoC, ZrC, TaC, and WC are also suitable for the formation of methane with the required onset potential values of −0.69, −1.06, −0.83, −0.72, and −0.69 V, respectively, but these materials are more selective towards formic acid formation as compared to methane with onset potentials of −0.46, −0.58, −0.79, −0.25, and −0.41 V, respectively. Only the pathways with minimum free energy are used and shown for methane formation in the free energy diagram for each candidate in Fig. S2.†

3.3. Comparison of CO₂RR onset potentials for TMCs studied in this work with some other metal-based catalysts previously reported

We have compared these results with previously studied metal-based catalysts as shown in Fig. 12. In this research work except CrC other TMCs show small onset potentials as compared to previously studied TMOs, pristine metals, and dopants. HfC, MoC, NbC, and TiC offer selectivity towards formic acid, methanol, and methane and are better than previously studied oxides of the same parental metal (HfO₂, NbO₂, TiO₂, RuO₂ and (TiO₂)₃/Ag and pristine Ti). The conclusion drawn from Fig. 12 shows that our findings from the TMCs for the CO₂RR are more novel than previously studied metals.

Fig. 12 Comparison of CO₂RR onset potentials for different product formations on TMCs studied in this work with similar metal-based catalysts previously reported for formic acid, methanol, and methane.^18,70–78

4. Conclusion

Our comprehensive theoretical analysis reveals that specific TMCs exhibit remarkable catalytic activity for CO₂ reduction, surpassing the performance of conventional catalysts. The electronic structure of these TMCs plays a pivotal role in facilitating the conversion of CO₂ into valuable chemical products, offering a glimpse into the potential applications of these materials in renewable energy technologies. Our novel findings concluded that the presence of carbon atoms in the TMCs is fruitful for the CO₂RR. Exploring the performance of a range of TMCs, we found out that the VC is the best candidate for the formation of formic acid with 0 V required onset potential, the WC is the best candidate to produce methanol with −0.36 V onset potential, and the MoC is the best candidate to produce methanediol with −0.58 V onset potential. Through an extensive literature survey, we conducted a thorough comparison of our results with those of transition metal oxides and pristine metals studied in the past. This analysis revealed that the TMCs demonstrated a smaller onset potential, rendering them ideal for CO₂RR applications. This theoretical exploration of transition metal carbides for CO₂ reduction reactions opens new frontiers in the quest for green energy solutions. As we stand at the cusp of a sustainable energy revolution, the theoretical novelties presented here pave the way for experimental endeavors to unlock the full potential of transition metal carbides in catalyzing a greener future.

Data availability

The calculations have been performed using the Vienna ab initio simulation package VASP (6.3.2 version).⁷⁹ The data that support the article have been uploaded in the ESI† in the form of free energy diagrams.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The calculations were carried out utilizing the Icelandic high-performance computer cluster, Elja. The Technology & Development Fund has provided financial support under grant no. 2215496-0611.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta05592f

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