Computational Pourbaix Diagrams for MXenes: A Key Ingredient toward Proper Theoretical Electrocatalytic Studies

MXenes, a rather new family of 2D carbides and nitrides, have shown to be promising materials in many technological applications, particularly in electrocatalysis. The as‐synthesized MXenes exhibit a variety of surface terminations involving mixtures of O, OH, H, or F surface groups. These terminations play a crucial role in the electrocatalytic performance of these materials as these may change depending on the reaction conditions. The Pourbaix diagrams have long being used to provide the thermodynamically stable surface under certain conditions of pH and potential, U. However, experimental determination of Pourbaix diagrams may be quite challenging while first‐principles studies, considering the most likely terminations, allow deriving reliable insights. Here, Pourbaix diagrams for a series of representative MXenes are provided; the Ti2C, Ti3C2, V2C, and Mo2C MXenes, with the novelty of considering single and several double mixed terminations. The possible implications of the obtained results are discussed, especially for a proper choice of models in theoretical electrocatalysis studies, including the water splitting related hydrogen evolution reaction (HER), or the oxygen reduction reaction (ORR), but also serving as a guide to any further computational studies and also to electrocatalytic experiments.


Introduction
The challenging transition toward sustainable energy models has become an urgent need.3][4] Electrocatalysis-based synthesis, especially when using power from renewable sources of energy, emerges as a clean alternative to fossil fuels, and, also, to obtain many industrial chemical products with low-carbon fingerprint. [5,6]Highly active and durable catalytic materials are required to facilitate the often sluggish kinetics of the electrochemical processes, thus allowing these promising technologies to move from fundamental research to real-world applications. [6][9] Therefore, significant efforts are directed to reveal the fundamental reaction mechanisms in electrocatalysis, to determine the main drawbacks of the existing materials and to foster the discovery of new ones.During the past decade, a new class of two-dimensional materials, named MXenes, [10] have been a focus of research attention given their growing number of practical applications, [11][12][13] expanding from energy conversion and storage [14,15] to supercapacitors, [16] CO 2 abatement technologies, [17][18][19] heterogenous catalysis, [20][21][22][23] including some examples of single atom catalysts, [24,25] and increasingly in electrocatalysis.For instance, MXenes have been explored as electrocatalysts for the hydrogen evolution reaction (HER), [26][27][28] the CO 2 electroreduction, [29] or even the N 2 electroreduction to NH 3 , [30] among others.MXenes are characterized by the M n+1 C n T x general formula with n = 1-3 and 2n+1 total number of atomic layers, where M stands generally for an early transition metal, X tends to be C or N, and T x designates the surface termination that the as-synthesized materials often exhibit, mostly mixtures of -O, -OH, -H, and -F groups, although, depending on the conditions, a specific surface termination of one of these groups can be imposed. [31,32]Indeed, the manipulation and modification of the MXenes termination have also been recently reported. [33]Clearly the termination may largely influence the performance of a given electrocatalyst. [34]hus, identifying the most stable surface termination under well-defined experimental conditions becomes essential to tune the catalyst and also constitutes an essential ingredient for its proper modeling.
In heterogenous catalysis the surface composition is mostly determined by the temperature and partial pressure of the reactants.There, phase diagrams can be built indicating the equilibrium composition for a given set of conditions.From a theoretical point of view, this is achieved by using the ab initio thermodynamics formalism developed by Reuter and Scheffler, [35,36] providing reliable surface phase diagrams.However, in electrocatalysis, one needs to realize that the involved reactions are usually carried out at standard conditions of temperature, but, at the same time, take place under application of an external potential in a solution of given pH conditions, and, therefore, U and pH need to be considered in the modeling to determine a reliable surface structure under these working conditions.This is accomplished by relying on the wellknown Pourbaix diagrams, [37,38] available for a broad number of systems. [39]The Pourbaix diagrams can also be computationally obtained from first-principles theoretical calculations, although relying on a series of approximations, [40][41][42] as commented in detail in a subsequent section.Nevertheless, their utility is out of doubt, and realistic electrocatalysts surface structures have been obtained from simulated Pourbaix diagrams for the oxygen reduction reaction on metallic electrodes, [40] chlorine evolution reaction on RuO 2 , [41] and lithium-ion batteries, [43] just to mention a few.Note, however, that the theoretically derived diagrams include just the explicitly explored surface compositions, which may constitute a limitation.This can be minimized by considering a large enough number of surface motifs.Pourbaix diagrams have also been reported for the HER on some MXenes, [44] although a more systematic work considering a broader family of MXenes with different terminations is still lacking.
In spite of the considerations above, theoretical studies have been reported where the effect of pH and applied potential on the surface composition is not considered at all [45][46][47] which cast serious doubts on the reliability of the corresponding predictions.As already mentioned, many electrochemical reactions have been theoretically or experimentally studied over MXenes, especially the HER.In most of these studies, the effect of pH and potential on the surface structure is not considered, or just in part, e.g., assuming a given surface termination, vide infra.Some authors limit the study to consider the most stable surface without including pH and U, which can be suitable for heterogeneous catalysis, yet not correct when aiming at studying electrocatalytic process. [48]Many published studies just regarded the fully Oterminated MXene surface without previous considerations or based on a free energy criterion obviating the pH-U influence. [45]or instance, Li et al. [29] reported a complete and accurate analysis of the electrochemical CO 2 capture and conversion over bare M 3 X 2 MXenes, yet completely omitting the role of pH and U on defining the appropriate surface termination.Also, an interesting and simple descriptor such as the number of electrons that the surface O atoms gain was proposed for the HER, but considering fully O-terminated MXenes only. [49]The effect of the metal or carbon vacancies on the same terminated MXenes has also been reported [45] as well as a large screening of the HER limiting potential over 36 carbide and nitride MXenes. [47]However, it has been shown that, at typically HER conditions, the majority of MXenes would be partially covered with -O and -OH moieties, and that this may have a direct impact on the obtained results. [44]Indeed, the fully O-terminated MXene surface chosen in these previous studies would be appropriate if the reaction studied would have been the oxygen reduction reaction (ORR) instead of the HER.
Given the above, the purpose of this work is to provide Pourbaix Diagrams for a series of representative MXenes, including V 2 C, Mo 2 C, Ti 2 C, and Ti 3 C 2 , while pedagogically explaining how to build them, thereby considering several possible single and double terminations.Our study aims to complete previous work exploring additional situations [27,28] as well as to set the results into the context of previous investigations of MXene models for HER.

Computational Details
Appropriate supercell models were used to represent the M 2 C (M = Ti, V, and Mo) and Ti 3 C 2 MXenes (0001) clean surfaces as well as the surfaces with different terminations, described in the next section.For the M 2 C bare MXenes, the surface model consists of three atomic layers with a p(3 × 3) supercell following the ABC stacking, with one layer of carbon in the middle and one transition metal layer above and one below the carbon layer.The Ti 3 C 2 model is equivalent to Ti 2 C but with five atomic layers instead of three, with Ti layers at top, bottom, and middle positions, and C layers in-between them, as illustrated in Figure 1.The atomic layers are periodically repeated so as to represent the (0001) basal plane with a perpendicular vacuum gap of at least 12 Å, which is enough to ensure isolation of the translationally repeated MXene layers in the direction perpendicular to the surface. [18,19][54] The effect of the core electrons on the valence electron density was taken into account by means of the projector augmented wave (PAW) approach, and the valence electron density was expressed using a plane-wave basis set with a kinetic energy cutoff of 415 eV.Despite some authors claim that bare MXenes such as Ti 2 C exhibit a magnetic ground state, [55] the present calculations were performed without spin polarization.In particular, we used the tetrahedron smearing method with a smearing width of 0.2 eV in conjunction with Blöchl corrections.The structure was considered converged when the maximum acting forces on each atom in the supercell were all below 0.01 eV Å −1 .The threshold for convergence of the total energy along the self-consistent-field was set to 10 −6 eV.The numerical integration in the reciprocal space was carried out by sampling the Brillouin zone with a 5 × 5 × 1 -centered grid.This computational setup, used in previous work on similar systems, [18,19,22] achieves numerically converged results within less than 0.04 eV.
To build the Pourbaix diagrams, several possible structures have been considered including terminations with a single moiety, but also mixed cases.In the supercell used to represent the MXenes most stable surfaces, there are nine equivalent adsorption sites, see Figure 2. Consequently, 9O, 9OH, 9F, and 9H correspond to the surfaces fully covered by O, OH, F, and H, respectively.Note also that other possible adsorptions sites exist which may lead to large coverage if multiple site occupancy is allowed.Nevertheless, this will lead to adsorbate at small distances with concomitant high steric repulsion.Consequently, single occupancy has been considered in all cases exploring many intermediate adsorbate coverages ranging from 1/9 to 1 monolayer (ML), as described in the Supporting Information (SI).Likewise, a broad range of mixed adsorbate situations has been considered which, in all cases, represent full coverage since, at the conditions of interest, a lower coverage situation is not favored.For instance, both theory and experiments show that partially O-covered MXenes are only attainable at high temperatures. [56,57]This finding represents a general difference between heterogeneous gas-phase catalysis and electrocatalysis.In heterogenous catalysis, partially covered surfaces can be achieved at working conditions whereas this situation is very unlikely in electrocatalysis.This can be explained by referring to the solid/liquid interface, which causes that each active site is in direct contact with the aqueous electrolyte solution, and thus, each active site is at least covered by a water molecule in the double layer above.
Note also that, for each mixed configuration, several possibilities exist.For instance, there are four ways to distribute 3O and 6H in the supercell, see Figure 2, and the most stable one has been chosen to build the Pourbaix diagrams since, as it becomes clear in the next section, the effect of pH and U on the free energy is independent of the surface ordering.

Step-by-Step Building Pourbaix Diagrams from DFT Based Calculations
The Pourbaix diagrams are similar to the standard pressurevolume phase diagrams but indicate the thermodynamic equilibrium surface structure under different conditions of pH and applied over potential, U, normally at a given temperature-e.g., 25 °C, pressure-e.g., 1 bar for gas phase components, and activity of 1 for all components of the liquid phase at such defined standard conditions.In a typical Pourbaix  The main idea to construct Pourbaix diagrams is as follows: one of the structures among the set of investigated surface models is used as a reference.In our case, we refer to the pristine MXene surface, 9*, as reference structure.The formation of adsorbates on the electrode surface, referenced to the 9* surface, is described by reaction equations.Please note that any adsorption process can be written as ∑ i Δv i A i = 0 where v i and A i indicate stochiometric coefficients and reactants or products, respectively.The change in Gibbs free energy for such an adsorption process can be written in a general form as indicated by Equation ( 1): The right hand side terms (G surf −ads , G surf and G ads ) correspond to the free energy of the surface covered by a given ordered structure containing n adsorbates, that of the clean surface and n times that of the adsorbates.For a gas-solid interface, the reference state of the free adsorbates is given by the gas phase molecule.However, for electrochemical systems at the solid/liquid interface, the adsorbates may not exist in the gas phase or may have a radical nature.Therefore, it is a unified standard to introduce a set of reference structures relating to the adsorbates observed in an electrochemical environment.Let us recall that the common adsorbates of MXenes under HER conditions refer to O, OH, F, and H groups.The reference state for O and OH does not refer to the gaseous oxygen molecule but rather to the water molecule at 298.15 K and 0.035 bar, because under these conditions, water vapor is in equilibrium with liquid water, i.e., their chemical potentials are identical. [58]Note that in DFT calculations, it is much easier to calculate the free energy of a gaseous water molecule rather than of liquid water, which necessitates inclusion of hydrogen-bonding between several water molecules, and this renders water vapor under the above conditions as the ultimate choice.
For H and OH groups, an additional reference state refers to the redox couple H + /H 2 , which is known from experimental electrochemistry as standard hydrogen electrode (SHE), when H 2 gas with a pressure of 1 bar is in equilibrium with a solution of protons of activity 1 at 298.15 K: Nørskov and co-workers proposed an elegant and nowadays frequently applied method of how to relate the gas-phase energetics of gaseous hydrogen to the free energy of a proton and the electrode potential, also referred as the computational hydrogen electrode (CHE) in the literature. [58]nder equilibrium conditions, the process in Equation ( 2) obeys ΔG = 0, and thus we infer: where (H + (aq) ) and (e − ) are the chemical potential of the hydrated proton and electron, respectively.This relation is important to factor pH and U into the analysis of Gibbs free energies, as discussed in the following.
Let us recall that all surface structures are evaluated by reaction equations, referenced to the 9* structure.Rewriting Equation (1) relating to the adsorption process for the formation of any surface phase yields: where the only difference with respect to Equation ( 1) is in the last right hand side term which is the adsorbate free energy relative to the chosen reference.In the derivation of Equation (4) we did not account for neither pH nor U, or, equivalently, we assumed that both are zero, which we indicate as ΔG(0, 0).Assuming that the only contribution to entropy is related to the adsorbates, Equation (4) translates to: For a gas-solid system, ΔE tot is the total energy difference between covered surface, and the sum of the energies of the clean surface and of n adsorbates, whereas in an electrochemical environment the energy of the adsorbates is related to the gas phase molecules using the reaction equations in Table 1.Hence, it follows: where the ΔE ZPE terms correspond to the difference in zero-point energy for the adsorbates at the surface and the free adsorbates in the reference state, within the harmonic approximation, as in Equation ( 7) (7)   and the same applies for the TΔS term, see Equation ( 8), as only adsorbate contributions are accounted for The entropy of the gaseous molecules-S ads for H 2 , F 2 , and H 2 O-at room temperature-298 K-has been obtained from thermodynamic tables [59] whereas for the adsorbed phase only the vibrational entropy of adsorbates has been included and estimated as indicated by Equation ( 9), where the v i are the vibrational frequencies of adsorbate i gained within the harmonic approximation, with k B , N A and h denoting the Boltzmann constant, the Avogadro number, and the Planck constant, respectively.Note that the hv i must have the proper energy units of k B T.
Given the above, the only remaining point now is introducing the potential relative to the SHE and the pH in Equation ( 5), which is achieved by making use of the CHE model.From the reaction equation to form a certain adsorbate structure with respect to the 9* reference, the number of transferred protons, v(H + ), and electrons, v(e − ), can be deduced.This information is key for the construction of a Pourbaix diagram because the effect of U and pH is not explicitly accounted for in the DFT calculations, but rather is addressed in the form of an a posteriori analysis.Applying an electrochemical-thermodynamic approach, [41] we obtain: (10)   where e is the elementary charge of an electron and U is the applied electrode potential with respect to the SHE.The ΔG(0, 0) values for all considered surface models of the investigated MXenes are collected in Tables S1-S4 (Supporting Information).
Finally, we need to introduce a reference for the F groups.This is achieved in a similar fashion to the popular CHE model by referring to a CFE electrode, that is, a computational fluorine electrode.The elementary processes of the reversible F -/F 2 redox pair with a redox potential of 2.87 V versus SHE at T = 298.15K, [60] is given by Equation ( 11): The CFE can be easily implemented into the analysis of Equation (10) by adding an additional term indicating the stoichiometric coefficient of fluoride anions in conjunction with the equilibrium potential of reaction (11).Thus, combining Equations ( 10) and ( 11) leads to Let us point out that all reaction equations for the formation of the possible adsorbate structures are compiled in Table 1.Actually, it is possible to obtain the reaction equations for all mixed coverages from simple linear combinations of the four adsorption reactions for the single adsorbates, -O, -H, -OH, and -F-cf.Table 1.In our study, we systematically explored all four terminations for coverages of 1/9, 1/3, 2/3, and 1 ML with the adsorbates on their more stable binding site.Full mixed coverages-1/3A + 2/3B-of all the possible combinations were also explored, see Figures 1 and 2. All these structures are considered for the construction of the Pourbaix diagrams, as discussed in Section 3.
Before heading to the results section, we would like to illustrate of how to obtain all terms needed to apply Equation (12).We demonstrate this for the case of a mixed coverage of 1/3 of O* and 2/3 of F*, where * implies an active surface site.The reaction equation to form this surface phase is (13)   and the ΔG(pH, U) term of this surface includes ΔE tot , ΔE ZPE , TΔS, v(H + ), v(e − ), and v(F − ), with where E(3O * + 6F * ) is the total energy of the slab surface model with 3O * and 6F * , E slab the total energy of the bare MXene, E(H 2 ), the total energy for gas phase hydrogen molecule, and E(H 2 O + F 2 ) the sum of total energies of gas phase water and fluorine molecules.For the ZPE and the entropic correction, we assume that vibrational contributions of the adsorbates are completely decoupled from the slab and neglect the small, phonon vibrations of the electrode and the configurational entropy effects of it, i.e., ZPE slab = 0, S slab = 0. Using the same notation as in Equation ( 14) with ZPE or S instead of E, we obtain: Finally, to obtain the stoichiometric coefficients, v, of the ions relevant to the CHE and CFE models within the adsorption process, the initial surface formation reaction of Equation ( 13) can be rewritten using Equations ( 2) and ( 11): Thus, the stoichiometric coefficients of v(H + ), v(e − ), and v(F − ) amount to 6, 12, and −6, respectively.
Up to this point, we have gathered all the necessary information to compute the ΔG(pH, U) term, with the implicit approximation that solvation contribution was neglected, which is a common approximation in theoretical electrocatalysis. [44,61]This procedure is carried out for all considered surface terminations, and one can evaluate, for any pH and U conditions, which surface termination has the lowest ΔG(pH, U).Alternatively, when two terminations compete with each other, one can equal the ΔG(pH, U) terms, i.e., when ΔG A (pH, U) = ΔG B (pH, U), vide supra, and isolate the pH versus U conditions that satisfy such thermodynamic equilibrium conditions.The only remaining step is to build a surface Pourbaix diagram is to draw a 3D plot with the computed ΔG(pH, U) values and to project it onto the (pH, U) plane of lowest Gibbs free energy, resulting in a 2D plot with pH and U as descriptors on the x and y axes, respectively.

Results and Discussion
For the considered adsorbates, -H, -OH, -O, and -F, the most stable adsorption site for Ti 2 C, Ti 3 C 2 , V 2 C is the hollow M-see site C in Figure 1-, while for Mo 2 C, the situation is slightly different as -OH, -O, and -F prefer the hollow C site-see site D in Figure 1, but -H still prefers hollow M even if the energy difference for H at these two sites is less than 0.09 eV.Apart from the mentioned sites corresponding to the most stable situation, all MXenes show stables adsorption energies at top sites-see site A in Figure 1-except for Ti 3 C 2 , where the adsorbates move toward more stable sites such as hollow M and X. Adsorption at bridge sites-see site B in Figure 1, is not stable in any MXene and consequently are not shown in Table 2.The presented results obtained are in agreement with previous studies. [27,28,62]nce the most stable adsorption site for each adsorbate is found, one can proceed to consider the most likely situation with either a single type of moiety, or having mixtures of two types, as described above.From the density functional calculations, one gets the total energy and, from the corresponding vibrational frequencies, the ZPE and entropy terms as described in the previous sections.This data in conjunction with the stoichiometric coefficients based on the reaction equations allows deriving the ΔG(pH, U) values, necessary to build the Pourbaix diagrams, which, for the systems explored in the present work, are shown in Figure 3.
The Pourbaix diagrams for all explored MXenes exhibit similar trends in the predicted stable surface coverage at different values of pH and U.This is the case even for Mo 2 C where different adsorption sites are involved.Thus, in aqueous environment, MXenes will not show their bare surface at any pH-U working conditions.As expected, for U SHE values below −0.6 V the surface of all four MXenes is fully hydrogenated (reduced) with all reaction sites occupied by H* as a feedstock.Upon increasing the potential, the MXene surface becomes progressively oxidized with OH* starting to replace H*.It is worth noting that this process might be remarkably potential sensitive as only for Ti 2 C such transition coverages, first 6H* + 3OH* and then 3H* + 6OH*, appear to be thermodynamically preferred.As one move toward positive potentials versus the SHE, the surface oxidation process continues until U SHE reaches 0.55 V, where all MXenes are fully covered by oxygen.
A novelty of the present work is the finding that for Mo 2 C and V 2 C the 6O* + 3OH* phase is the only mixed surface composition that appears as the thermodynamically favored one for certain pH-U conditions.Comparing with the values corresponding to both Ti 2 C and Ti 3 C 2, the adsorption energies of O and OH species on these MXene are relatively low, see Table 2. Also, despite fluorine exhibits the strongest adsorption energy on each MXene, stable F-containing surfaces were only found for Ti 2 C and Ti 3 C 2 at highly acidic conditions.This is a direct consequence of the penalty of 2.87 eV for each F* generated according to the CFE part in Equation ( 12). [38]n interesting feature that arises from this discussion is why F-covered surfaces are not stable for large pH values.Inspection of Table 1 provides the answer because in the adsorption process for the formation of F*, it turns out that v(H 2 ) = v(H + ) = 0, and thus, there is no pH dependency for the formation of F*.This is quite in contrast to the cases of H*, O*, and OH* where Table 1 reveals a clear pH dependency because here v(H 2 ) ≠ 0, and thus, v(H + ) ≠ 0. To summarize, the energetics of H*, O*, and OH* is pH dependent with lower free energy with increasing pH whereas the energetics of F* is not.This is the reason why F* phases are only be observed at small pH values in the Pourbaix diagram because by increasing the pH the free energy of H*, O*, and OH* may excel that of F*.In the present work we also considered the effect of the configurational entropy by considering more than one possible distribution of the surface adsorbates, see Figure 2.For most of the combinations explored the distribution (a) in Figure 2 was found to be the most stable.Only three coverages (6OH* + 3H*, 3H* + 6F*, and 6H* + 3*) consistently preferred a different arrangement for Ti 2 C, Ti 3 C 2 , and V 2 C. For the 6OH* + 3H* coverage, the distribution (d) of Figure 2 was always preferred, yet all the entropic configurations present similar energies, around 0.09 eV.Consequently, we assume that for such mixed surface phases there might not be a specific adsorption pattern energetically preferred.For the F*/H* mixtures the difference in electronegativity between the F and H atoms causes a rearrangement on the order of stability of the different considered configurations.Configuration (a) in Figure 2 is no longer preferred as F* tend to sit at vicinal sites and configurations (b), (c), and (d) are close in energy and around 0.1 eV more stable than (a).The (d) arrangement is the most stable distribution for 3H* + 6F*, and (b) for 6H* + 3F*.Mo 2 C shows a similar trend that the previous MXenes in the sense that the (a) pattern is the most stable situation, but for the 3O* + 6OH* and 3O* + 6F* phases all four existing configurations are equally stable; see Table S2 (Supporting Information).However, the small overall differences make us conclude that the effect of the configurational entropy has a low impact on the resulting surface Pourbaix diagrams, and thus can be safely neglected.Now, depending on the chosen reaction of interest carried out using MXenes as electrocatalysts, the Pourbaix diagrams in Figure 3 provide the equilibrium structure.For ORR, where the typically good catalysts are operating around 0.80 V versus SHE, all four MXenes will be fully covered by oxygen, in agreement with the predictions of Seh et al. [27] Under HER equilibrium conditions, the mixed 2/3O* + 1/3OH* surface termination is thermodynamically preferred for all the studied MXenes, close to the results of Seh et al. [27] .However, for Ti 2 C and Ti 3 C 2 , when a modest cathodic overpotential of -100 mV is applied the preferred surface changes to the 1/3O* + 2/3OH* phase.Since this overpotential might be smaller than the necessary overpotential to reach a sufficient HER current density in the order of several mA cm −2 , one should consider also possible surface compositions of Ti 2 C and Ti 3 C 2 beyond the thermodynamically preferred ones at U = 0 V versus SHE (dotted line in Figure 3), i.e., regarding others within a 0.1 V energy window, and so accounting for similarly stable situations within the DFT accuracy.
It is worth noting that Pourbaix diagrams for the studied MXenes, (V 2 C, Mo 2 C, Ti 2 C, and Ti 3 C 2 ) were already reported by Gao et al. [44] and others, [27,[61][62][63][64] although considering a smaller number of possible surface structures and different cell sizes.Comparing the Pourbaix diagrams of Ti 2 C, Ti 3 C 2 , and V 2 C with those reported by Gao et al. [44] one finds that, even if the overall picture is in agreement, different adsorbates and mixtures were chosen for the analysis.Thus, for Ti 2 C, Ti 3 C 2 and V 2 C, the fully oxygen covered situation appears at similar potential even when different mixed ratio of O*/OH* were considered, which indicates the predictive power of this theoretical approach.Moreover, compared to previous works, we choose a larger p(3 × 3) supercell instead of the p(2 × 2) [61] or p(2 × 1) [44,63] ones used in previous work so that a larger number of adsorbate patterns can be taken into account.While the computed Pourbaix diagrams are qualitatively comparable to the results obtained in smaller cell sizes, it should be noted that an important difference with respect to previous work is the consideration of H* and F* adsorbates.Indeed, the fully H* covered situation is preferred for strongly reducing (negative) overpotentials, which may be important in some electrocatalytic processes involving these MXenes, such as the hydrogen evolution versus electrochemical nitrogen reduction or hydrogen evolution versus electrochemical CO 2 reduction.The presence of mixed coverages containing F* adsorbates present at highly acidic conditions for Ti 2 C and Ti 3 C 2 is also to be highlighted, as they are a factor to be regarded in HER conditions, which could indeed affect the overall surface electrocatalytic activity, but has been largely ignored in previous studies. [64]ote that the presence of F* adsorbates seems to be a singular feature of group IV MXenes, observed for Ti 2 C and Ti 3 C 2 , but not seen for group V MXenes (V 2 C) and group VI MXenes (Mo 2 C).Therefore, the potential presence of F* adsorbates seems to be also important for earlier MXenes, e.g., Zr-and Hf-based MXenes, independently of their width.Aside, the surface models seem to be rather defined for HER and ORR conditions on group IV and VI (V

Conclusions
In summary, we have reported a detailed analysis of all necessary modelling and computational steps that are needed to build Pourbaix diagrams for a series of representative MXenes: Ti 2 C, Ti 3 C 2 , V 2 C, and Mo 2 C. In addition to previous works, we considered the four different most common terminations that can be experimentally encountered under standard MXene synthetic conditions, unless specific cleaning and preparation procedures are involved to remove selected surface terminations.
We have shown here that depending on the pH and U conditions, other terminations rather that the typically assumed fully O* or fully OH* covered surfaces should be considered.In particular, we provide evidence that the fully H* terminated surface is of importance for U < -0.6 V versus SHE.In the case of Ti 2 C and Ti 3 C at strong acidic conditions and slightly negative potentials of -0.6 V < U versus SHE < 0 V, which are of relevance to the HER, mixed surface phases involving -F moieties with -O or -OH groups should not be disregarded, which may also be important to other early transition metal MXenes, such as Zr-and Hf-based ones.In addition, for HER conditions, the explored Tibased MXenes feature 1/3O* + 2/3OH* and 2/3O* + 1/3OH* terminations in a close range of potentials, implying that these surface phases should be studied to evaluate the HER performance for any pH conditions.
For the case of mixed configurations, we show that configurational entropy and pH play a negligible role on determining the equilibrium surface structure.Finally under ORR conditions the fully O-covered phase corresponds to the active surface regardless of the explored MXene, while for HER, 2/3O* + 1/3OH* are, apparently, well suited models for all the considered MXenes, although for Ti-based MXenes, the 1/3O* + 2/3OH* model could be also suited.

Figure 1 .
Figure 1.Top (left image) and side (right images) views of a M 2 C(0001) (upper right image, M = Ti, Mo, V) and Ti 3 C 2 (0001) (lower right image) surface p(3 × 3) supercell.Metal atoms at the top and bottom layers are represented by bright and light blue spheres, respectively, while C atoms are represented by light brown spheres, and H atoms are shown in pink.The main high-symmetry surface sites considered are top (A), bridge (B), hollow M (C), and hollow C (D). (C) and (D) sites have either one M or C atom below.

Figure 2 .
Figure 2. Top view of the four possible 1/3A + 2/3B coverage situation with the adsorbates at their most thermodynamically favored adsorption site, hollow M. The red and pink spheres represent the A and B adsorbates, respectively.Only for Mo 2 C the most thermodynamically stable adsorption site is encountered with hollow C.
diagram, U is represented on the vertical axis and the pH on the horizontal one.The different areas in the diagram correspond to different surface structures, and the lines indicate where two structures are in thermodynamic equilibrium.This implies that the Gibbs free energy of surface structures A and B at a given pH and U are equal, i.e., G A (pH, U) = G B (pH, U), or, employing a given reference state for A and B, when the relation ΔG A (pH, U) = ΔG B (pH, U) is met.Thus, the construction of a theoretical Pourbaix diagram implies deriving G(pH, U) or ΔG(pH, U) values for the possible surface structures for a broad range of pH and U. Clearly, Pourbaix diagrams are required to know the equilibrium structure under reaction conditions, which is a necessary ingredient in the study of any electrocatalytic processes using a given electrode.

Figure 3 .
Figure 3. Pourbaix diagrams for Mo 2 C, V 2 C, Ti 2 C, and Ti 3 C 2 .Note that from negative to positive potentials with respect to the SHE scale the surface becomes progressively oxidized, from full H coverage to full O coverage with intermediate -O/-OH or fully O-covered coverage for HER or ORR conditions, respectively.The HER equilibrium potential (U = 0 V vs SHE) as well as typical ORR conditions (U = 0.8 V vs SHE) are marked by dashed blue and black lines, respectively.
2 C and Mo 2 C) considered MXenes, i.e., they are not close to other mixed situations, even if they belong to different d series, although for group IV cases (Ti 2 C and Ti 3 C 2 ), the surface model is clear for ORR conditions; fully O-covered, although for HER, one should regard 1/3O* + 2/3OH* and 2/3O* + 1/3OH* models, and even F-containing models specially at very low pH conditions; 1/3OH* + 2/3F* for Ti 2 C, and 1/3O* + 2/3F* for Ti 3 C 2 , with the caveat that, even if most stable ΔG surface terminations are shown in the Pourbaix diagrams shown in Figure 3, close terminations could indeed represent the MXene electrocatalyst surface under such working conditions.

Table 1 .
Reference states for both single and mixed surface terminations; n and y represent the number of adsorbed species on the studied surface.

Table 2 .
Adsorption energies, E ads , given in eV, for atomic H, O, and F atoms, and the perpendicularly oriented OH at the obtained local minima on the M n+1 C n (0001) surfaces from calculations using the PBE functional.The results correspond to spin unpolarized calculations.