Unveiling selectivity trends for CO₂ reduction reaction over Ti₃C₂T_x MXene: the key role of less-stable intermediate states and coadsorbates

Abstract

The electrochemical conversion of carbon dioxide via the CO₂ reduction reaction (CO₂RR) is an attractive strategy for the production of value-added chemicals. However, the CO₂RR suffers from a selectivity problem due to the large number of carbon-based products that can be obtained and the competing hydrogen evolution reaction (HER). It has been experimentally shown that the ratio and chemical nature of terminal groups, T_x, present on the Ti₃C₂T_x (T_x = O, OH or F) surface under electrochemical conditions affect selectivity and activity trends of the MXene electrocatalyst. In the present manuscript, we use electronic structure theory calculations to comprehend the selectivity trends in the CO₂RR over Ti₃C₂T_x with different terminal groups, including *OH and *F adsorbates. We show that the traditional modeling approach used in calculations to derive activity and selectivity trends, which only includes the most stable intermediate state in the analysis, is not consistent with experimental observations. Rather, it is necessary to include energetically less favorable intermediate states and coadsorbates in the analysis of mechanistic pathways. Remarkably, the inclusion of less-stable intermediates, although stable on the electrode surface, and coadsorbates opens up new reaction channels that are energetically more favorable, and only by considering these extensions are we able to map our results to the experimental data. We believe that the reported finding is not only limited to the CO₂RR or MXene systems, but likely also plays an important role in other catalytic transformations under applied bias.

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New concepts

The present manuscript focuses on resolving selectivity trends for the CO₂RR over Ti₃C₂T_x MXene with different terminal groups, T_x, including *OH and *F adsorbates, using electronic structure theory calculations. The traditional approach in the community to understand selectivity in the CO₂RR involves constructing thermodynamic free-energy diagrams for the different reaction channels, where only the most stable intermediate states are considered in the mechanistic analysis. In the case of the CO₂RR over Ti₃C₂T_x MXene, this framework does not reproduce the experimentally observed selectivity trends. We demonstrate that less-stable intermediates and coadsorbates, which also lead to less-stable configurations, must be included in the analysis to determine selectivity trends that are consistent with experimental data. The inclusion of these new configurations, even if they are energetically less favorable, opens new reaction channels that are energetically more favorable and thus can change the activity and selectivity trends compared to the traditional approach. The presented concept of factoring less-stable intermediate states and coadsorbates into the mechanistic analysis based on adsorption free energies is not limited to the CO₂RR or MXene systems, and we believe that the proposed framework will guide the design of improved materials for energy conversion and storage processes using computational methods.

1 Introduction

The sustained combustion of fossil fuels required to fulfill the energy requests of our societies has led to a drastic increase in the anthropogenic CO₂ levels, causing devastating effects on the environment and life of many ecosystems. Although a transition to green energies would be desirable, it is still not feasible to cover all energy demands exclusively with green energies.¹ CO₂ valorization emerges as an appealing strategy to counteract the current situation and represents a carbon neutral route for the generation of value-added energy carriers, while simultaneously reducing the anthropogenic CO₂ levels.² Currently, different strategies are used for CO₂ conversion, which include thermo-,^3–10 photo-^11–14 and electrocatalysis,^15–23 among others. Interestingly, CO₂ conversion via the electrocatalytic CO₂ reduction reaction (CO₂RR) is a very interesting process as it is carried out under mild operating conditions, usually at room temperature and moderate pressures. In addition, renewable energy resources can provide the required electricity for electrolysis, making the electrochemical pathway also environmentally attractive.

The electrochemical CO₂RR is mainly limited by its selectivity challenge. On the one hand, the formation of H_2(g) from the hydrogen evolution reaction (HER) (i.e., eqn (1)) is observed for cathodic polarization, which is a competing side reaction under CO₂RR conditions.²⁴ On the other hand, there is the possibility of forming multiple C₁ products (i.e., eqn (2)–(5)) or multicarbon products (i.e., C₂₊).²⁵

2H⁺ + 2e⁻ → H_2(g), U₀ = 0 V vs. RHE (reversible hydrogen electrode) (1)

CO_2(g) + 2H⁺ + 2e⁻ → CO_(g) + H₂O_(l) U₀ = −0.10 V vs. RHE (2)

CO_2(g) + 2H⁺ + 2e⁻ → HCOOH_(aq) U₀ = −0.12 V vs. RHE at pH = 0 (3)

CO_2(g) + 6H⁺ + 6e⁻ → CH₃OH_(aq) + H₂O_(l) U₀ = 0.03 V vs. RHE (4)

CO_2(g) + 8H⁺ + 8e⁻ → CH_4(g) + 2H₂O_(l) U₀ = 0.17 V vs. RHE (5)

While the formation of C₂₊ products in the CO₂RR is of greater importance than the formation of C₁ products, the former products are normally obtained only from Cu-based catalysts, while CO, HCOOH and H₂ are typically observed for other transition metals.²⁵ Interestingly, the emergence of a new class of two-dimensional transition-metal carbides and nitrides, so-called MXenes, with excellent properties for energy conversion and storage, opens new avenues for the development of next-generation catalysts with improved catalytic activity and/or selectivity.²⁶ In this regard, it has been recently shown that the Cu-doped Ti₃C₂T_x (T_x = O, OH or F) MXene or even its basal planes can produce different C₁ products and even C₂₊ species for the CO reduction reaction (CORR) and CO₂RR.^27,28 These findings suggest that terminal groups can modulate the CO₂RR selectivity and pave the way for the development of MXenes-based catalysts for selective CO₂RR.

An atomistic understanding of the mechanism that governs the reaction is essential for the rational design of active and selective catalysts. Interestingly, such understanding can be achieved from electronic structure calculations, usually in the density functional theory (DFT) framework, by materials screening. Such approach offers the opportunity to investigate and identify potential candidate materials that can later be experimentally validated,^29,30 which may help overcoming the CO₂RR selectivity problem. The traditional approach used in DFT to study electrocatalytic transformations focus on the thermodynamic picture. This is justified by the consideration of Brønsted–Evans–Polanyi relation,^31–33 which connects the kinetics and thermodynamics. More precisely, the traditional approach comprises to calculate different configurations of the reaction intermediates in the CO₂RR or other electrocatalytic processes to identify the thermodynamically most stable structures.^34–38 Thereafter, free-energy diagrams are constructed for these stable reaction intermediates, which allow predicting activity and selectivity trends of materials using descriptor-based analyses.^39,40

In this contribution, we aim to introduce a new framework for constructing and analyzing free-energy diagrams to enable a thorough discussion of activity and selectivity trends. In our approach, we factor not only the thermodynamically most stable reaction intermediates but also the less-stable reaction intermediates into the analysis of the elementary reaction steps. We illustrate our methodology using the CO₂RR over the Ti₃C₂T_x MXene with different *OH/*F adsorbates as terminal groups and discuss the role of less-stable intermediates states and coadsorbates, which also give rise to less-stable configurations, on the activity and selectivity. We demonstrate that less-stable intermediate states give rise to energetically favored reaction channels compared to the common assumption of considering the thermodynamically most stable structures only. Interestingly, our predicted activity and selectivity trends are only in good agreement with experimental data if less-stable intermediate states and coadsorbates are considered in the analysis, whereas the traditional approach, focusing on the thermodynamically most stable reaction intermediates only, fails to reproduce the experimentally reported trends.

2 Computational methods

In this study, we apply periodic DFT calculations as implemented in the Vienna Ab initio Simulation Package (VASP) code^41–43 to model the CO₂RR and HER on different (3 × 3) Ti₃C₂T_x (T_x = *OH and/or *F) surface models. All calculations have been done using the Perdew–Burke–Ernzerhof (PBE) exchange correlation functional⁴⁴ alongside Grimme's D3 term to account for dispersion effects.⁴⁵ We use the computational hydrogen electrode (CHE) approach⁴⁶ to describe the energetics of proton–electron transfer steps occurring during CO₂RR and HER. Transition states (TS) have been located using the Catlearn Bayesian transition state search module (ML-NEB).⁴⁷ All computational details are provided in Section S1 of the ESI.†

3 Surface models and reaction network

Recently Krishnan et al.,²⁸ studied the CO₂RR using linear sweep voltammetry (LSV) and chronoamperometry (CA) techniques on the basal plane of the Ti₃C₂T_x (T_x = *O, *OH, or *F) MXene, which contain a considerable amount of *F adsorbates. Interestingly, they observed suppression of the HER and high selectivity towards CO and CH₃OH, while also finding considerable amounts of C₂₊ species (i.e., ethanol and acetone). Bao et al.²⁷ studied the CORR on Cu-based Ti₃C₂T_x systems by combining experimental and theoretical approaches. In their LSV experiments, they observed the formation of considerable amounts of ethanol and ethylene for the Cu-based Ti₃C₂T_x system. However, they found high HER selectivity when the CORR was studied on the basal plane of Ti₃C₂T_x, with a large fraction of *O and *OH terminal groups. Note that Pourbaix diagrams for the Ti₃C₂ MXene under cathodic conditions predict that the surface is largely covered by *OH/*O adsorbates, and *F-covered surfaces are found to be stable at low pH.^48,49

Nevertheless, a larger *F coverage can also be found at different working conditions due to the synthetic conditions used during the MXene preparation.²⁸ The above findings suggest that the *F content can play a significant role in CO₂RR selectivity. Notably, in line with the above results, the important role of surface terminations for Ti₃C₂ MXene on the catalytic HER activity was reported.⁴⁹ To analyze this effect, we study the CO₂RR on different Ti₃C₂T_x MXene surface models with different ratios of *OH/*F adsorbates (see Fig. 1).

Fig. 1 Representation of the seven Ti₃C₂T_x (T_x = OH or F) surface models considered for the study of the CO₂RR and HER as a function of the *OH and *F terminal groups. Three different surface sites (i.e., fcc_in, bridge and fcc_out) are considered as possible initial configurations for the adsorbates. Light grey, dark grey, red, white, and green balls denote Ti, C, O, H, and F atoms, respectively.

To study the CO₂RR and HER on the different surface models, we have considered two different reaction networks. The first reaction network considers the reaction intermediates in their thermodynamically most stable configuration (Fig. 2a) and comprises a total of 18 adsorbates, 7 gas-phase molecules, and 30 elementary steps. For the second reaction network, we have also included other less-stable intermediate states that better connect two intermediate states and provide a more realistic mechanistic description (Fig. 2b). This gives rise to a total of 23 intermediate states, 7 gas-phase molecules, and 41 elementary steps considered in the analysis. Let us emphasize that a proper representation of the ‘natural pathway’ of product formation (without assuming any free internal rotation) can only be achieved if less-stable intermediate states are factored into the mechanistic description. All elementary steps of the CO₂RR and HER can be found in Section S2 of the ESI† (i.e., eqn (S5)–(S34)).

Fig. 2 Schematic representation of the elementary steps considered for the CO₂RR and HER on the example of the Ti₃C₂–*7OH surface: (a) only the most stable configuration of a reaction intermediate is considered, (b) besides the most stable configuration of an adsorbate, also less-stable intermediate states are taken into account. Note that we have considered similar adsorbate configurations for the other surface models studied. For the CO₂RR, four different C₁ products have been factored into the analysis, namely: CO, HCOOH, CH₃OH, and CH₄. Black arrows represent connections between two adsorbed intermediates, while brown arrows represent product formation. Light grey, dark grey, red and white spheres denote Ti, C, O and H atoms, respectively. All elementary steps are listed in eqn (S5)–(S34) of the ESI† (Section 2).

To derive activity and selectivity trends for the CO₂RR and HER over Ti₃C₂T_x, we have used the following procedure. First, we calculated the adsorption energy of the different intermediate species for the different surface sites shown in the inset of Fig. 1 and determined the energetically preferred surface site corresponding to the fcc_in site. Note that for adsorbates that can adopt multiple configurations, we performed different geometrical optimizations and used the geometry of the most stable state (Fig. 2a), but also some geometries of the less-stable states (Fig. 2b). Second, we have also located the transition state (TS) for rotations between the less and most stable states and calculated the corresponding rotational barriers. Third, frequency calculations were performed to confirm that all configurations correspond to real minima or TS. In addition, frequency calculations are required to account for the zero-point energy and entropic contributions, which are needed to derive the Gibbs free energy of the different adsorbates. We refer the reader to Section S1.1 (ESI†) for a detailed description of how Gibbs free energies are derived. Fourth, we use the CHE approach⁴⁶ to describe the energetics of proton–electron transfer steps occurring during the CO₂RR and HER and construct free-energy diagrams for the different intermediate states. Fifth, the free-energy diagrams are analyzed using a descriptor-based approach^50–52 to derive activity and selectivity trends. Finally, the predicted trends are compared to the experimental data of Krishnan et al.²⁸

4 Results

Let us start by analyzing how the different adsorbates interact with the different Ti₃C₂T_x surfaces (cf. Fig. 1), as shown in Fig. 3. The interaction is calculated from the formation Gibbs free energy, which is derived using H_2(g), CO_2(g), H₂O_(g), and the bare Ti₃C₂T_x surfaces as references. For a detailed description of how formation Gibbs free energies are calculated, the reader is referred to Section S3 in the ESI.† Note that the more/less negative the formation Gibbs free energy, the stronger/weaker the interaction between the adsorbate and the surface.

Fig. 3 Formation Gibbs free energy for the different reaction intermediates in the CO₂RR and HER on the different surfaces (cf. Fig. 1). A description of the calculation of the formation Gibbs free energies can be found in Section S3 of the ESI.†

From Fig. 3, it appears that *H interacts similarly with all the surfaces, which implies that the HER is not largely dependent on the coverage of *F adsorbates. On the other hand, the larger the *F content, the weaker the *CO₂ interaction with the surface. As *CO₂ can limit the reaction at low cathodic potentials (vide infra), a more exergonic CO₂ adsorption is likely to limit the CO₂RR activity. Therefore, surfaces with large *F content are likely to increase the CO₂RR activity. Regarding CO and HCOOH (i.e., two possible products), the higher the *F coverage, the weaker the CO interaction with the surface, while the interaction of HCOOH remains almost the same. This suggests a positive effect of *F composition on the CO selectivity compared to HCOOH. Until now, we have shown that some trends can be derived for reactants (CO₂) and some products (CO and HCOOH) as a function of *F/*OH coverages. However, no clear trends are observed for the intermediate states (Fig. 2). Therefore, free-energy diagrams for the CO₂RR and HER for the different surface models are constructed to gain insights into activity and selectivity.

5 Discussion

Let us start this section by defining some important aspects: (i) for the discussion of our results, we have selected the Ti₃C₂–4*OH–3*F surface model unless otherwise stated. The choice for this surface is because it has a similar *F/*OH composition. (ii) The potential used in our computational setup to construct the free-energy diagrams is U = −0.4 vs. RHE, which is chosen to mimic the potential of −1.1 V vs. Ag/AgCl at pH ≈ 7–8 used in the experiments.²⁸ (iii) Gas-phase error corrections have been incorporated to correctly describe the overall thermodynamics on the free-energy diagrams.^53,54 Further details on gas-phase error corrections can be found in Section S4 of the ESI.† (iv) For aqueous (i.e., HCOOH and CH₃OH) and ionic species (i.e., HCOO⁻), solvation and ion corrections have been applied, respectively.⁵⁵ Note that no changes are observed when using either HCOOH or HCOO⁻ to assess the selectivity for formic acid/formate formation. Therefore, for simplicity, we have considered HCOOH instead of HCOO⁻ in our analysis. For a detailed discussion, the reader is referred to Section S5 of the ESI.† Let us finally point out that, while pH effects can play an important role in modulating catalytic activity,^56,57 in this study we are interested in activity and selectivity trends as a function of terminal groups at the experimental working conditions.²⁸

To assess the activity and selectivity for the CO₂RR and HER, we make use of the descriptor G_max(U).^50,51 This activity descriptor quantifies the largest free-energy span between reaction intermediates of a given mechanism at a given potential (U). The free-energy spans are calculated based on the potential-dependent Gibbs free energy of the different intermediates (G_i(U)), which are derived following eqn (S4) in Section S1.1 of the ESI.† For a detailed description of G_max(U) in the CO₂RR, the reader is referred to Section S6 of the ESI.† When evaluating multiple pathways, the mechanism with the lowest G_max(U) value is considered the most plausible mechanism. Interestingly, G_max(U) can incorporate several elementary steps in the analysis, making it a particularly useful descriptor for reactions with a high number of proton–electron transfer steps such as CO₂RR. Note that the lower the G_max(U), the higher the catalytic activity. In our analysis, we extract the lowest G_max(U) among the different possible mechanism that connect reactants to products (Fig. 2). This evaluation is performed for all products (i.e., H₂, CO, HCOOH, CH₃OH and CH₄) across all different surface models (Fig. 1). Then, based on the G_max(U) values of the different reaction channels, we derive selectivity trends.

The free-energy diagram for CO₂RR, HER and the potential dependency of both reactions for the Ti₃C₂–*4OH–3*F surface model at U = −0.4 V vs. RHE is shown in Fig. 4. Similar diagrams for the other surfaces can be found in Section S7 of the ESI† (Fig. S5–S10).

Fig. 4 Gibbs free energy diagram for the Ti₃C₂–4*OH–3*F surface model at U = −0.4 V vs. RHE for (a) CO₂RR and (b) HER. Purple, red, cyan, brown, and black arrows are used to schematically represent the limiting span for CH_4(g), CO_(g), HCOOH_(aq), CH₃OH_(aq) and H_2(g), respectively. Details on the descriptor G_max and intermediates involved in the limiting span for each reaction are shown in the legend. (c) CO₂RR and HER potential dependency of the Ti₃C₂–4*OH–3*F surface model. Green, red, orange, blue, and purple lines represent the G_max value as a function of the applied cathodic potential (U) for the formation of HCOOH_(aq), CO_(g), CH₃OH_(aq), CH_4(g) and H_2(g), respectively. The different labels represent the species involved in the limiting span for each reaction at each condition. Note that for two reactions comprising the same limiting span, black labels are used. (d) Selectivity and G_max(U = −0.4 V vs. RHE) for the different products on the different surface models.

Among the different C₁ products that can be produced during CO₂RR, CH₄ and CH₃OH are the most selectively produced products as evidenced by their lowest G_max(U) value (Fig. 4a). Regarding CO and HCOOH, the stronger interaction of *HCOOH with the surface compared to that of *CO and *CO₂ hinders its formation, making HCOOH the least selectively produced product. Interestingly, at U = −0.4 V vs. RHE, the HER (Fig. 4b) is suppressed in favor of CO₂RR because its G_max(U) value is larger than that for the formation of CH₃OH and CH₄. Importantly, the formation of CH₃OH and CH₄ comprise many proton–electron transfer steps, and their limiting span in the approximation of G_max(U) consists of several elementary reaction steps. On the other hand, the G_max for HER consists of a single step (i.e., *H → H_2(g)). This implies that G_max(U) for CO₂RR is reduced more efficiently than for HER when switching to more cathodic potentials (Fig. 4c). Nevertheless, HER is still favored at low cathodic potentials (Fig. 4c). This feature for HER is maintained for the MXene surfaces with a *F composition equal to or less than 3*F (see Fig. S5–S10, ESI†). This is because the larger the *F coverage, the weaker the *CO₂ interaction with the surface, while the *H interaction is almost the same for all surfaces (Fig. 3). Since *CO₂ is encountered in the limiting span at low cathodic potentials, the lower the CO₂ adsorption, the lower the G_max(U) and the higher the selectivity toward the CO₂RR.

Let us now analyze the selectivity toward CO₂RR and HER at U = −0.4 vs. RHE for all surfaces. From Fig. 4d three interesting patterns can be observed: (i) the highest *OH content favors HER, while increasing the *F content favors CO₂RR, in agreement with experiments.^27,28 This is because the reaction intermediates of CO₂RR interact differently depending on the surface composition, while the *H interaction is similar for all surfaces. (ii) The highest selectivity is observed for CH₃OH and CH₄ at low to medium *F coverage and switches to CH₄ at larger *F composition. The latter is in contrast to experiments in which CO and CH₃OH are produced, but no CH₄.²⁸ (iii) The lowest selectivity is towards CO and HCOOH. While the latter product is not observed in experiments, the former is the most selectively produced product for MXene surfaces at large *F coverages.²⁸ From these results, it is clear that the traditional model based on the analysis of the thermodynamically most stable intermediate states can only partially predict the experimental observations. In the following sections, we discuss the relevance of including less-stable intermediates states and coadsorbates for a refined mechanistic description to derive selectivity trends that are consistent with the experimental results.

5.1 Effect of including less-stable intermediate states

In this section, we discuss the importance of considering less-stable intermediate states in the activity analysis. There are two main reasons why this is important: (i) the configuration of the two most stable states of two consecutive intermediates may not be well connected. For instance, in Fig. 2a, *HCOOH and *HCO reveal a different orientation on the MXene surface: to connect these intermediate states, not only a proton–electron transfer but also an internal rotation is needed. The tacit assumption that adsorbed species can rotate freely with a small energy penalty may not hold true, especially for systems with high coverage. This situation is particularly evident in MXenes, where multiple terminal groups cover the surface and thus rotations from one intermediate state to another can be difficult (vide infra). Therefore, for a better mechanistic description, it appears important to consider configurations that truly connect two intermediate states, even if these new configurations correspond to energetically less-stable intermediates. This allows a more accurate and better representation of the ‘natural pathway’ (without free internal rotation) of a given mechanism. Note that this can also change the predicted activity to lower activities. (ii) By including less-stable intermediate states in the analysis, the number of possible pathways from the reactants to products increases. This enhances the possibilities of finding new pathways with a lower energy and thus higher catalytic activity. Note that we do not consider different sites, but rather the same site with different configurations for the adsorbate.

Fig. 5a depicts the free-energy diagram for CO₂RR including also less-stable intermediates states (marked in light blue). Similar figures for the other surfaces can be found in Section S8 of the ESI† (Fig. S11–S16). Interestingly, there is a decrease in the G_max(U) and a change of the limiting span for CH₃OH and CH₄ compared to the situation where only the most stable intermediate states are considered (Fig. 4a). Let us focus on the example of CH₃OH and discuss the differences. The limiting span when the most stable states are considered is *HCO → *HCOH, which changes to *CO₂ → *COOH if also less-stable intermediate states are considered. The inclusion of less-stable intermediate states (i.e., *OCH, *HOCH and *HOCH₂) opens up new, energetically favorable pathways through these intermediate states. Interestingly, the formation of *OCH from *CO is still exergonic, and the free energy required to form *HOCH from *OCH is lower than the free energy required for the transition of *HCO to *HCOH. Finally, both the formation of *HOCH₂ and CH₃OH_(aq) are downhill in free energy. This situation changes the limiting span to *CO₂ → *COOH and reduces the G_max(U) while increasing the catalytic activity. Note that, while including less-stable intermediate states can lead to new pathways with improved catalytic activity, also situations with lower catalytic activity can be encountered. In particular, we found this situation for the formation of CH₃OH on the Ti₃C₂–7*OH surface model (see Fig. S11b, ESI†) in the potential range of (−0.55 < U < −0.45 V vs. RHE), which is a result of the rigorous connection of two consecutive intermediates, namely *HCOOH and *OCH (or *HCO). A detailed description can be found in Section S9 of the ESI.†

Fig. 5 (a) Gibbs free energy diagram for CO₂RR of the Ti₃C₂–4*OH–3*F surface at U = −0.4 V vs. RHE considering less-stable intermediates. Purple, red, cyan, and brown arrows are used to schematically represent the limiting span for the CO₂RR to CH_4(g), CO_(g), HCOOH_(aq), and CH₃OH_(aq), respectively. For intermediates in which two different states are considered, lighter bars represent the less-stable intermediate while darker bars represent the most stable intermediate. (b) *OCH and *HCO competitive reactions of the Ti₃C₂–4*OH–3*F surface at U = −0.4 V vs. RHE. (c) Potential dependency of CO₂RR to CH₃OH of the Ti₃C₂–4*OH–3*F with(out) considering less-stable intermediate states in orange and blue, respectively. The different labels represent the species involved in the limiting span for each reaction at each condition. Note that for two reactions comprising the same limiting span, black labels are used. (d) Selectivity trends for the different surface models at U = −0.4 V vs. RHE. (e) Gibbs free energy diagram for CO₂RR to CH₃OH of the Ti₃C₂–3*OH–4*F surface at U = −0.4 V vs. RHE. Blue and brown arrows represent the limiting span when less-stable intermediate states are considered or not, respectively.

While we have shown above that including less-stable intermediate states can lead to new reaction channels with improved catalytic activity, it is still not clear whether the less-stable intermediate sates are truly accessible during catalytic operation. To gain deeper insights into their stability and feasibility as new reaction channels, we have calculated the rotational free-energy barrier between the less and most stable intermediate states, as summarized in Table S3 of Section S10 of the ESI.† The rotational energy barrier is then compared with the energy required for the competing protonation reactions, as shown in Fig. 5b for the *OCH and *HCO intermediates as a representative example. Before analyzing Fig. 5b, let us first discuss the accessibility of the *OCH and *HCO intermediates. On the hand, *OCH and *HCO can be formed after *CO protonation, both being exergonic processes (Fig. 5a). On the other hand, if no free internal rotations are assumed, only *OCH—the less-stable intermediate state—can be formed after *HCOOH protonation, with a small free-energy penalty of 0.14 eV. This suggests that the formation of *OCH is more probable and therefore more accessible than *HCO. Nevertheless, the stability of the less-stable intermediate state is still unclear and questions whether *OCH will transition to *HCO or protonate instead.

As shown in Fig. 5b, the rotation of *OCH to *HCO and the reverse process (green region) have a free-energy barrier of 0.51 and 0.82 eV, respectively, while their protonation to *HOCH (blue region) and *HCOH (salmon region) are endergonic processes with a reaction energy of 0.20 and 0.36 eV, respectively. From Fig. 5b it is evident that the rotation from one state to another requires a higher energy barrier (kinetics) compared to the thermodynamic barrier for their protonation, which points to a high stability of the intermediate and suggests that the intermediate will protonate rather than rotate to the other state. Note that for a better comparison, the knowledge of the free-energy barrier for the protonation step is required. While we have not explicitly calculated the protonation energy barriers, they are known to be small (0.15 eV to 0.25 eV).^58,59 Particularly, the *HCO protonation to *HCOH is a process with a small free-energy barrier of 0.16 eV for the Cu(100) surface.⁶⁰ Therefore, if these values are considered (and added to the reaction energy if necessary), the protonation step is also kinetically more favorable (lower free-energy barrier) than the rotation, which suggests that the intermediate will prefer to protonate rather than rotate. Finally, it is important to consider that protonation steps are potential dependent while rotations are not. Therefore, at large cathodic overpotentials, the protonation step is clearly preferred over rotation to the more stable intermediate. Similarly, a high stability of the less-stable intermediate states is also observed for the other surfaces and less-stable intermediates states (i.e., *HOCH and *HOCH₂), with the only exception of *OCH and *HOCH₂ on the 7*OH and 6*OH–1*F surfaces, as summarized in Section S10 of the ESI.† Overall, these results point to a high stability of the less-stable intermediate states and their feasibility as new reaction channels.

The tacit assumption used in previous works^34–38 that the most thermodynamically stable configurations of two consecutive reaction intermediates are well connected may not be true. For an improved mechanistic description, reaction intermediates must be well connected to each other and must not exhibit internal rotations, especially for those systems with high coverage. This implies that energetically less-stable intermediate states have to be considered in the analysis, which can lead to increased or reduced catalytic activity for a particular reaction channel.

Fig. 5c illustrates the potential dependency of CO₂RR to CH₃OH when the most stable (and also less-stable) intermediate states are considered in the analysis. The effect of incorporating less-stable intermediate states in the analysis is rapidly observed (i.e., at U < −0.15 V vs. RHE) and is maintained under larger cathodic potentials. Initially, the limiting span (i.e., *CO₂ → CH₃OH_(aq)) is limited by the strong *CO₂ adsorption and thus no effects are observed. At medium cathodic potentials (i.e., −0.45 < U < −0.15 V vs. RHE), the limiting span for the most stable intermediates is either governed by the presence of the intermediate states *HCO or *HCOH. In contrast, the consideration of the less-stable intermediate states switches the mechanism to an energetically favorable path, which contains neither *HCO nor *HCOH. Finally, at large cathodic potentials (i.e., U < −0.45 V vs. RHE), the limiting span for the most stable intermediate states is *CO → *COH. While in this case no other less-stable configurations are considered for *CO and *COH, the *CO intermediate can form *OCH, which then evolves to CH₃OH via a less energy-intensive pathway, and the limiting span switches to *CO₂ → *COOH.

Let us now evaluate the effect of including less-stable intermediate states on the CO₂RR selectivity for the different surface models at working conditions (i.e., U = −0.4 V vs. RHE). As visible in Fig. 5d, H₂ is still the most selectively produced product for the Ti₃C₂–7*OH surface as observed in experiments with large *OH coverage.²⁷ With increasing *F coverage, CH₃OH and CH₄ become the more selectively produced products, which is in better agreement with the experiments at high *F content,²⁸ where the most selectively produced products are CO and CH₃OH. Interestingly, only when including also less-stable intermediate states in our analysis, we can predict a high selectivity toward CH₃OH compared to the traditional approach (Fig. 4d). We suggest that this change of selectivity is a result of the different *CH₂OH and *HOCH₂ interactions with the surfaces, as exemplified in Fig. 5e for the CO₂RR to CH₃OH on the Ti₃C₂–*3OH–4*F surface model. If only the most stable intermediate states are considered (dark blue lines) the limiting span is *CH₂OH → CH₃OH_(aq). However, when the less-stable *HOCH₂ intermediate state is incorporated into the analysis, the step *HOCH₂ → CH₃OH_(aq) is not energetically demanding and the limiting span switches to *CO₂ → *COH with a decrease in the G_max(U). A change in the limiting span *CH₂OH → CH₃OH_(aq) is also observed for the other surfaces with high *F coverage as shown in Fig. S14–S16 in Section S8 in the ESI.†

So far, we have addressed the underestimation of the selectivity toward CH₃OH for surfaces with high *F content. From our results, we conclude that for large *F composition, the selectivity trend is in the order of CH₃OH > CH₄ > H₂ > CO > HCOOH, which is still not entirely consistent with the experiments where CO is the major product followed by CH₃OH.²⁸ In the following section, we discuss the importance of coadsorbates in the search for less-stable configurations that direct the selectivity toward CO. However, before we move on to the next section, there is still one thing that deserves further explanation. The reader may wonder why we just claimed that the selectivity toward CH₃OH is larger than toward CH₄ when the G_max(U) of CH₃OH and CH₄ are the same (cf. Fig. 5d). We come to this conclusion because electrocatalytic processes with a smaller number of proton–electron transfer steps result in a larger exchange current density, which translates into higher electrocatalytic activity.⁶¹ While CH₃OH formation requires 6 proton–electron transfer steps, the formation of CH₄ requires 8, and therefore we argue that CH₃OH formation is kinetically preferred over CH₄ formation, in line with experimental observations.²⁸

5.2 Effect of including coadsorbates

In this section we evaluate the CO formation in the presence of coadsorbates and discuss how this situation can modify the catalytic activity. We have shown in the previous section that our predicted selectivity toward CO disagrees with experiments.²⁸ The main limitation for CO formation is the strong interaction of *CO₂ and *CO with the surface, which limits CO production at low and large cathodic potentials, respectively (Fig. 4c). Therefore, we have evaluated how the presence of coadsorbates may affect the CO formation. To do so, we have studied the CO₂RR to CO on the neighboring available site (see Fig. S18 in Section S11 in the ESI†) and evaluated how *CO₂, *COOH and *CO coadsorbates affect the CO production.

Fig. 6a depicts the CO desorption energy without coadsorbates and when *CO₂, *COOH and *CO are present as coadsorbates, respectively. From Fig. 6a, it is evident that the presence of neighboring species reduces the CO desorption energy for all the surface models. Larger changes are observed for *CO₂ and *COOH compared to *CO, which we attribute to increased steric effects for the former intermediates. Interestingly, as shown in Fig. 6b, the presence of a *CO₂ coadsorbate leads to a decrease of the descriptor G_max(U), which we trace to a less-stable configuration compared to the situation where the two intermediates are not direct neighbors. Note that the terminology “surfA” and “surfB” is used to distinguish between directly adjacent sites and non-adjacent sites, respectively. It turns out that the new less-stable configuration (*CO_2,surfA) reduces the *CO desorption energy compared to the situation without the coadsorbate or without direct proximity to CO (*CO_2,surfB). Detailed free-energy diagrams including also *COOH and *CO as coadsorbates for all the surfaces can be found in Section S12 of the ESI.†

Fig. 6 (a) Effect of coadsorbate species (i.e., *, *CO₂, *COOH and *CO) on the CO desorption for the different studied surfaces models, (b) Gibbs free energy diagram for CO₂RR to CO with the presence of a CO₂ coadsorbate (light blue bars) at U = −0.4 V vs. RHE for the Ti₃C₂–4*OH–3*F surface. The terminology “surfA” and “surfB” is used to distinguish between directly adjacent sites and non-adjacent sites, respectively. Red and salmon arrows are used to schematically represent the limiting span for CO_(g), while black and green arrows represent the CO desorption energy when including * and *CO₂ as coadsorbates, respectively. (c) Potential dependence of the CO₂RR to CO with the presence of coadsorbates for the Ti₃C₂–4*OH–*3F surface model.

Finally, we evaluate how the presence of coadsorbates changes the activity descriptor G_max(U) as a function of the applied potential (Fig. 6c). For the potential dependency of the other surfaces, we direct the reader to Section S12 of the ESI.† Note that in Fig. 6c, we have considered four different scenarios for the *CO desorption, namely: (i) no coadsorbate is present or (ii) *CO₂, (iii) *COOH, or (iv) *CO is present as a coadsorbate. As explained above, when no coadsorbate is present, *CO₂ adsorption and *CO desorption are limiting the span at low and large cathodic potentials (i.e., *CO₂ → CO_(g) and *CO → CO_(g)), respectively (blue line). As evident from Fig. 6b, the presence of coadsorbates modifies the energetics in such a way that G_max(U) is reduced with the concomitant increase of the catalytic activity. Particularly the presence of a neighboring *CO₂ substantially reduces the G_max(U) and thus promotes CO formation. Interestingly, at working conditions (i.e., U = −0.4 V vs. RHE), it is no longer the *CO desorption that is limiting the span but rather formation of the *COOH intermediate (*CO₂ → *COOH). As shown by the horizontal lines in Fig. 6c, there is a threshold electrode potential where *CO desorption is the limiting step and switching to higher cathodic potentials does not lead to an increase in catalytic activity. Therefore, weakening the *CO interaction with the surface by producing less-stable configurations due to the presence of coadsorbates is an efficient way to control CO formation. To conclude, we suggest that after CO₂ adsorbs on the neighboring site, *CO will efficiently desorb and the remaining *CO₂ can be converted into another C₁ species (Fig. 6b).

5.3 Selectivity trends

Finally, let us evaluate the selectivity on the different surfaces if less-stable intermediate states and coadsorbates effects are considered in our analysis. Table 1 summarizes the calculated G_max(U) at working conditions (U = −0.4 V vs. RHE) for the different products and the predicted selectivity based on such values. We refer the interested reader to Section S13 of the ESI† for the potential dependency of all surface models when less-stable intermediate states and coadsorbates are included in the analysis.

Table 1 G_max(U) at U = −0.4 V vs. RHE of the different products for the different surface models in the CO₂RR and HER over Ti₃C₂T_x MXene. The last column indicates the selectivity order for each surface predicted using the descriptor G_max(U) when less-stable intermediates and coadsorbates are considered

Surface	Gmax (U = −0.4 V vs. RHE)					Selectivity
	H2(g)	CO(g)	HCOOH(aq)	CH3OH(aq)	CH4(g)
7*OH	0.61	0.70	1.71	0.70	0.68	H2 > CH4 > CO > CH3OH > CO > HCOOH
6*OH–1*F	0.62	0.48	1.73	0.48	0.48	CO =CH3OH =CH4 > H2 > HCOOH
5*OH–2*F	0.64	0.39	1.73	0.39	0.39	CO =CH3OH =CH4 > H2 > HCOOH
4*OH–3*F	0.64	0.28	1.73	0.28	0.28	CO =CH3OH =CH4 > H2 > HCOOH
3*OH–4*F	0.64	0.25	1.68	0.25	0.25	CO =CH3OH =CH4 > H2 > HCOOH
2*OH–5*F	0.63	0.20	1.66	0.20	0.20	CO =CH3OH =CH4 > H2 > HCOOH
1*OH–6*F	0.62	0.14	1.63	0.14	0.14	CO =CH3OH =CH4 > H2 > HCOOH

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From Table 1, different three clear trends can be observed: (i) while HER is favored for the fully hydroxylated surface, the selectivity shifts toward CO₂RR with increasing *F content, which is in line with experiments.^27,28 (ii) The larger the *F coverage, the more active (i.e., lower G_max(U)) is the Ti₃C₂T_x surface for CO₂RR. (iii) HCOOH formation is not feasible for the selected systems. Focusing on the most selectively generated CO₂RR products, the predicted selectivity using the descriptor G_max(U) is the same for CO, CH₃OH, and CH₄. Nevertheless, reactions with a smaller number of proton–electron transfer steps are generally faster (higher exchange current density) than reactions that require more proton–electron transfer steps. As the CO₂RR to CO, CH₃OH, and CH₄ consists of 2, 6, and 8 proton–electron transfer steps, respectively, we suggest that the selectivity for the *F-covered surfaces is in the order: CO > CH₃OH > CH₄ > H₂ > HCOOH, which is consistent with the experiments.²⁸ This qualitative agreement with the experimental data could only be achieved if less-stable intermediate states and coadsorbates are included in our computational analysis.

6 Conclusions

In the present manuscript, we introduce a new way of thinking for the investigation of proton-coupled electron transfer steps with applications in energy conversion and storage from a computational perspective. While the traditional approach used in electronic structure theory to derive activity and selectivity trends is based on the construction of free-energy diagrams using the thermodynamically most stable intermediate structures only, we ponder on the importance of incorporating also less-stable intermediate states and coadsorbates in the analysis of adsorption free energies. We benchmark our new concept using the CO₂RR over Ti₃C₂T_x (T_x = *OH and/or *F) surfaces with different *OH/*F coverage as a model system. We demonstrate that less-stable intermediate states lead to energetically favored reaction channels, and only by including these new pathways, we find good agreement with experimental data. Notably, we also show based on rotational barriers that the less-stable intermediates are stable on the electrode surface, which corroborates their feasibility as new reaction channels. In addition, we demonstrate the key aspect of including coadsorbate species in the analysis, which also give rise to less-stable configurations and are particularly relevant for CO formation. We believe that the introduced concept of considering less-stable intermediate states and coadsorbates when analyzing free-energy diagrams to predict activity and selectivity trends is not a unique feature of the CO₂RR over Ti₃C₂T_x, but rather a universal feature to be considered in future computational research to develop improved materials for energy conversion applications.

Data availability

The data supporting this article have been included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

PLR and KSE thank the Ministry of Culture and Science of the Federal State of North Rhine-Westphalia (NRW Return Grant) for financial support to carry out this study. KSE further acknowledges funding by RESOLV Cluster of Excellence, funded by the Deutsche Forschungsgemeinschaft under Germany's Excellence Strategy – EXC 2033 – 390677874 – RESOLV.

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Footnote

† Electronic supplementary information (ESI) available: Computational details, elementary steps for CO₂RR and HER, calculation of formation Gibbs free energies, gas-phase error corrections, CO₂RR to HCOOH under different pH conditions, activity descriptor G_max(U), free energy diagrams and potential dependency for CO₂RR and HER for the different Ti₃C2T_x surface models for different assumptions, negative effect of including less-stable intermediate states, rotational energy barriers, and schematic representation of CO₂RR to CO on the neighboring site of a preadsorbed CO. Relevant inputs and outputs for the different calculations have been also made available a public GitHub repository: https://github.com/plozanore/CO2RR_selectivity_key_role_of_less-stable_intermediate_states. See DOI: https://doi.org/10.1039/d5mh00168d

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