Nitrogen embedding enhances stability and activity of single-atom motifs of MXenes under anodic polarization

Abstract

MXenes undergo water-mediated surface reconstruction under anodic polarization and spontaneously form single-atom centers, reminiscent of single-atom catalysts (SAC), which exhibit great potential for the oxygen evolution reaction (OER). Yet, the as-formed SAC-type MXene motifs still suffer from the conventional activity-stability trade-off under OER conditions. Here, we propose a nitrogen embedding strategy to modulate the local coordination environment of the single-atom centers, thereby enhancing both their stability under anodic polarization and OER activity. Based on density functional theory calculations, we systematically evaluate 53 N-doped SAC-type MXene motifs, covering M₂X₁O, M₃X₂O, and M₄X₃O MXenes, using a three-step screening approach, which identifies promising candidates that (i) allow nitrogen doping under anodic polarization, (ii) are thermodynamically stable under OER conditions, and (iii) exhibit high OER activity. We demonstrate that N-doped Ta₂C₁O and Ta₂N₁O SAC-like MXenes break the traditional activity-stability trade-off in OER and provide theoretical guidance for designing efficient and durable SAC-like MXene electrocatalysts.

Introduction

Single-atom catalysts (SAC) have attracted much attention and made significant advances in the field of catalysis due to their atomically dispersed active sites, almost 100% utilization of metal atoms, and tunable electronic structures¹. Notably, SAC exhibit excellent activity and selectivity in various electrocatalytic reactions, including the oxygen reduction reaction (ORR)², oxygen evolution reaction (OER)³, and hydrogen evolution reaction (HER)⁴, to name a few. To further improve their performance, various support two-dimensional (2D) materials—such as graphene⁵, carbon nanotubes⁶, and graphitic carbon nitride (g-C₃N₄)⁷—have been developed to stabilize and tailor the single-atom sites.

In the recent years, the rapid development of two-dimensional (2D) materials⁸ has substantially broadened the design space for SACs. Among these materials, MXenes—a family of 2D transition metal carbides, nitrides, and carbonitrides, with the general formula of M_n+1X_nT_x, where M is a transition metal, X denotes carbon and/or nitrogen, n typically ranges from 1 to 4, and T_x represents surface adsorbates such as *O, *H, *OH, or *F, which can be tuned by synthesis conditions—have been extensively studied since the first synthesis of Ti₃C₂T_x by Gogotsi and coworkers⁹. MXenes have attracted significant attention due to their unique physicochemical properties, including high electrical conductivity, hydrophilicity, large specific surface area, and excellent electrochemical performance^10,11,12. Therefore, MXene-based SACs have also recently attracted much attention, exhibiting promising performances in various electrocatalytic reactions such as for nitrogen reduction (NRR) or hydrogen evolution (HER)^13,14. While conventional SACs rely on anchoring a foreign metal atom on the MXene basal plane, by means of ab initio molecular dynamics (AIMD) simulations, Wan et al.¹⁵ found that Ti₂CO₂ MXene undergoes spontaneous water-mediated surface reconstruction under anodic polarization, leading to the formation of single-atom motifs, which are reminiscent of an archetypal SAC active site¹⁶. This theoretically predicted phenomenon corresponds well with Gogotsi’s report on the influence of applied potential on interfacial behavior of MXene in water environment¹⁷.

The main difference between archetypal single-atom catalysts (SACs) and the MXene-SAC motif lies in their formation mechanisms. Conventional SACs are typically synthesized under non-electrochemical conditions, where foreign metal atoms are introduced and anchored ex situ onto a substrate, thereby forming well-defined active sites. In contrast, the MXene-SAC motif does not require any foreign metal atom during its synthesis, since the single-atom center on the MXene basal plane is formed in situ during anodic polarization, with their formation governed by the electrochemical environment. Since these SAC motifs are formed directly under reaction conditions, they may exhibit adaptive behavior and enable in situ regeneration when pulsing the applied electrode potential back and forth¹⁸. This appears to be an advantage over conventional SACs, where in situ regeneration is difficult to achieve. Despite this, the electrochemically formed SAC motifs also exhibit limitations. Their formation is sensitive to the applied electrode potential and their applicability is hitherto restricted to specific two-dimensional materials including MXenes. This differs from conventional SACs, which can be synthesized for a plethora of different support materials.

In a recent communication, Razzaq et al.¹⁶ have demonstrated using density functional theory (DFT) calculations that the SAC-like motif of MXenes exhibits promising activity for OER, while Faridi et al. showed that these SAC-like sites are selective toward the chlorine evolution reaction in brine¹⁹. Notably, the SAC-like motif of on Mo₂C₁O and Mo₂N₁O was predicted to selectively catalyze nitrogen reduction upon pulsing of the electrochemical potential¹⁸. These previous studies provide detailed mechanistic insights into various energy conversion processes catalyzed by a novel class of electrochemically formed SAC-like MXenes.

Although the MXene-SAC motif is capable of catalyzing OER with moderate overpotentials, as estimated from DFT calculations¹⁶, the stability of single atoms anchored to a support under anodic polarization remains a challenge to date. As pointed out by Di Liberto and coworkers²⁰, the single atom site structure can be influenced by the solvent, pH, and applied electrode potential. This can cause deactivation of active sites and structural instability, such as metal diffusion and aggregation, or the formation of new chemical species through reactions with solvent components induced by demetallization. Meng et al.²¹ screened the stability of the MXene-SAC motif in the homologous series of M₂C₁O and M₂N₁O by the construction of Pourbaix diagrams and demonstrated that particularly Mo₂C₁O-, Mo₂N₁O-, Ta₂C₁O-, and Ta₂N₁O-based systems are stable in the potential regime of about 1.50 V vs. RHE (reversible hydrogen electrode) relevant for OER. However, based on thermodynamic considerations, it was predicted that the other SAC-like MXene of the M₂X₁O₂ series would dissolve under OER conditions, suggesting that stabilization strategies are needed to enhance the stability of the MXene-SAC motif under anodic polarization to achieve efficient and durable OER catalytic performance.

Various studies have shown that the SAC performance is governed by the local coordination environment^22,23, particularly the chemical identity of adjacent dopants and their coordination number²⁴. A modulation of charge distribution and electronic structure can ultimately enhance stability and catalytic activity of SACs. Notably, nitrogen doping has emerged as a predominant strategy for archetypal SACs²⁵. For example, Ha et al.²⁶ demonstrated that N-doped graphene-based SACs exhibit superior catalytic performance in both the HER and OER, compared to their undoped C₄-coordinated counterparts. In addition, Liu et al.²⁷ found that introducing nitrogen dopants into graphene-based Ir SACs can significantly enhance its stability, and the bond strength between Ir single atom and graphene can also be improved by increasing the nitrogen content.

Given that a nitrogen coordination environment is also commonly employed in archetypal SACs, we present in this work a strategy to embed nitrogen into the MXene-SAC motifs to modulate the electronic structure and local chemical environment of the single-atom site. It is hypothesized that the nitrogen-doped MXene-SAC motif (cf. Fig. 1b) can suppress unfavorable structure dissolution under high anodic potentials and thus further improve the stability of the electrochemically formed single-atom centers. Nitrogen doping of the MXene-SAC motif also influences OER activity, thus potentially offering a way to solve the activity-stability conundrum in oxygen evolution electrocatalysis^28,29.

Fig. 1: Reconstructed MXene (0001) surfaces under anodic polarization.

Side (left images) and top (right images) views of a reconstructed p(3 × 3) unit cell of the MXene (0001) surface with M₁₈X₉O_9-nN_n composition under anodic polarization (n = 3 for N-doped situations), in which a metal atom is displaced from the basal plane to form a single-atom motif: a Undoped 3O*-M_SAC-*O, with three neighboring *O groups; b nitrogen-doped 3N*-M_SAC-*O, obtained by substituting the three surrounding *O groups with three nitrogen atoms. Surface N and O atoms are represented by light blue and red spheres, respectively, while transition metal M and C atoms are shown as dark blue and brown spheres, respectively.

To date, early transition metal MXenes from groups 4 to 6—including Sc, Ti, V, Y, Zr, Nb, Hf, Ta, and W—have been successfully synthesized³⁰. Moreover, Fe species can also be highly dispersed and stably incorporated into MXenes by tuning the synthesis conditions³¹. In the present work, we systematically investigate the stability of the MXene-SAC motif, and we differentiate between undoped and nitrogen doped cases. Considering realistic electrochemical environments, MXenes in contact with aqueous electrolytes typically form a mixed *OH/*O-terminated surface³². The corresponding Pourbaix diagram analysis further indicates that the *O groups on the SAC site surface are thermodynamically more favorable than *OH groups under OER conditions^32,33. Thus, this study focuses only on the O-terminated SAC-like MXene configuration, in which the undoped MXene-SAC motif is referred to as 3O*-M_SAC-*O (cf. Fig. 1a), where a single metal atom is coordinated to the basal plane by three surface *O adsorbates, while the latter *O corresponds to the intermediate bound to the SAC site above. Similarly, the N-doped MXene-SAC motif is referred to as 3N*-M_SAC-*O (cf. Fig. 1b), where the three surface *O groups are replaced by *N. By building on the existing theoretical support for the formation of the 3*O–M_SAC–*O motif of the M₂X₁O systems, we extend here the investigation to M₃X₂O and M₄X₃O MXenes³⁴, where M = Cr, Fe, Hf, Mo, Nb, Ta, Ti, V, W, or Zr, and X = C or N, as usual. Note that during the structural optimization of the 3*O–M_SAC–*O motif, some MXenes (such as Cr₃C₂O, Cr₄C₃O, Fe₂N₁O, Fe₃X₂O, and Fe₄X₃O) exhibited instabilities; thus, these systems were not further considered. As a result, a total of 53 N-doped MXene-SAC systems were selected as initial candidates for further investigation.

Results

To systematically screen nitrogen-doped SAC-like MXenes as catalysts for the OER, we employ a stepwise funneling strategy based on thermodynamic and activity-related criteria, as shown in Fig. 2. This procedure allows us to progressively narrow down a large number of MXene-SAC motifs systems to a few highly promising candidates. The screening process consists of three fundamental steps: (i) evaluating the thermodynamic feasibility of the nitrogen-doped SAC-like sites in MXenes under anodic polarization (Stage 1 in Fig. 2); (ii) assessing the thermodynamic stability of the nitrogen-doped MXene-SAC motif under OER conditions and comparison with undoped counterparts (Stage 2 in Fig. 2); (iii) analyzing OER activity under anodic polarization and selecting the most promising candidate materials (Stage 3 in Fig. 2). In each stage, increasingly stringent screening criteria are applied to ensure that the final catalysts selected have structural and chemical feasibility, thermodynamic stability, and high electrocatalytic activity under OER conditions.

Fig. 2

Proposed three-step strategy to accelerate the discovery of N-doped SAC-like sites in MXenes for OER: (i) thermodynamic feasibility of nitrogen doping, (ii) thermodynamic stability of the N-doped MXene-SAC motif under OER conditions, and (iii) catalytic activity in the OER.

Thermodynamic feasibility of nitrogen-doped MXene-SAC motifs

The 3O*-M_SAC-*O structure (cf. Fig. 1a), as observed in ab initio molecular dynamics (AIMD) simulations^35,36, serves as the starting point for the nitrogen substitution process. The three oxygen atoms attached to the SAC metal atom are replaced by three nitrogen atoms in an ammonia-saturated aqueous environment, with in situ formed NH₃ serving as the nitrogen source³⁷. To assess the feasibility of forming 3N*-M_SAC-*O (cf. Fig. 1b), we analyze the thermochemistry of Eq. (1):

$$3{\rm{O}}*\mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{O}}+{3{\rm{NH}}}_{3}\to 3{\rm{N}}* -{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{O}}+{3{\rm{H}}}_{2}{\rm{O}}+{3{\rm{H}}}^{+}+{3{\rm{e}}}^{-}$$

(1)

It is worth noting that there is a competition between NH₃ and H₂O adsorption on the SAC site, although we consider that there is no ammonia-saturated environment when OER takes place. Therefore, even if NH₃ has adsorbed on the SAC site, it will be replaced by H₂O under OER conditions. In addition, at pH values below 9.25, where NH₃ and NH₄⁺ are in equilibrium, NH₃ mainly exists as NH₄⁺, whose positive charge limits its propensity to adsorb on the SAC site, thus largely ruling out competitive adsorption.

Structurally, the geometry of 3N*-M_SAC-*O preserves the initial planar coordination environment, and the three coordinated oxygen atoms are directly substituted by nitrogen atoms. Given that Eq. (1) is an oxidation process accompanied by proton-coupled electron transfer (PCET), we apply the computational hydrogen electrode (CHE) model³⁸ to evaluate the applied electrode potential, at which the nitrogen doping process is in electrochemical equilibrium (U_eq). Considering that this study focuses on the OER over the MXene-SAC motif, nitrogen doping via ammonia treatment is thermodynamically feasible only when the equilibrium potential of the doping process is lower than the standard equilibrium potential of OER, which amounts to 1.23 V vs. RHE. Therefore, our first-stage screening criterion is referred to as U_eq < 1.23 V vs. RHE, which was applied to a total of 53 N-doped MXene–SAC motifs (cf. Fig. 3).

Fig. 3: Schematic representation of the thermodynamic feasibility analysis for all 53 N-doped MXene-SAC motifs in the first stage of screening based on the criterion of U_eq < 1.23 V vs. RHE.

A total of 32 motifs were identified as promising candidates.

The U_eq values for the SAC-like motifs of M₂X₁O, M₃X₂O, and M₄X₃O (M = Cr, Fe, Hf, Mo, Nb, Ta, Ti, V, W, or Zr, X = C or N) are summarized in Tables S1–S3 of section S1 in the supporting information (SI). For M₂C₁O-SAC MXene (cf. Table S1), the results indicate that the feasibility of nitrogen doping is sensitive to the chemical nature of transition metal. Specifically, the equilibrium potentials of W-, Mo-, Ta-, Cr-, and Fe-based M₂C₁O-SAC are below the threshold of 1.23 V vs. RHE, thus indicating that the nitrogen-doped structure is available below the OER equilibrium potential. In contrast, the equilibrium potentials of Hf-, Zr-, Nb-, Ti-, and V-based M₂C₁O-SAC exceed 1.23 V, indicating that the doping process is thermodynamically unfavorable below the OER equilibrium potential.

The thermodynamic feasibility of nitrogen substitution in the SAC-like sites of M₂N₁O MXene exhibits a trend comparable to that observed for the carbides (cf. Table S1). In addition to W-, Mo-, Ta-, and Cr-based M₂N₁O-SAC, also V₂N₁O-SAC enables nitrogen substitution at applied electrode potentials below 1.23 V vs. RHE.

We extend the analysis to the SAC-like sites to M₃X₂O MXenes, as summarized in Table S2 of the SI. For the carbide systems, nitrogen doping is thermodynamically favorable for W-, Nb-, V-, Mo-, and Ta-based SAC sites, with U_eq below 1.23 V vs. RHE. Conversely, Hf-, Zr-, and Ti-based SAC-like motifs of M₃C₂O exceed the potential threshold, thus ruling out the possibility of nitrogen doping. We note that these results are consistent with the carbides of the SAC-like motifs of the M₂C₁O MXene. However, Hf- and Zr-based SAC-like sites in M₃N₂O MXene enable nitrogen substitution according to the screening criterion, in contrast to their carbide counterparts M₃C₂O-SAC and the general trend observed above.

In the following, the exploration is further extended to SAC-like sites in M₄X₃O MXenes, as shown in Table S3. Similar to the above carbides systems, W-, Nb-, Mo- and Ta-based SAC-like of M₄C₃O remain thermodynamically feasible at N doping below 1.23 V vs. RHE. In contrast, Hf-, Zr-, V-, and Ti-based systems only become thermodynamically favorable for N substitution at electrode potentials above 1.23 V. For the nitride MXene-SAC motifs, the trend is largely consistent with that of M₄C₃O, except for V-based M₄N₃O, which shows thermodynamic feasibility upon N doping.

Finally, approximately 60% of the initial 53 N-doped MXene–SAC motifs—a total of 32 candidates—meet the thermodynamic feasibility criterion of U_eq < 1.23 V vs. RHE and were selected for further thermodynamic stability screening (Fig. 3). Specially: (i) 10 candidates for M₂X₁O-SAC—W, Mo, Ta, Cr and Fe for M₂C₁O-SAC; W, Mo, Ta, Cr and V for SAC-like M₂N₁O MXenes; (ii) 12 for M₃X₂O-SAC—W, Mo, Ta, Nb and V for M₃C₂O-SAC; W, Mo, Cr, Nb, V, Hf and Zr for M₃N₂O-SAC; (iii) 10 for M₄X₃O-SAC—W, Mo, Ta and Nb for M₄C₃O-SAC; W, Mo, Ta, Cr, Nb and V for M₄N₃O-SAC. These 32 N-doped candidates were selected for further stability analysis and compared with the undoped 3O*-M_SAC-*O motifs of SAC-like M_n+1X_nO to assess their potential as robust single-atom centers for OER.

Thermodynamic stability of nitrogen-doped MXene-SAC motifs

The thermodynamic stability analysis in this section focuses on single-atom metal deactivation and vacancy (*vac) formation in undoped 3O*-M_SAC-*O for the sake of comparison and N-doped 3N*-M_SAC-*O of SAC-like MXenes under applied anodic potentials, as illustrated in Fig. 4. In total, 64 structures—including the 32 N-doped MXene–SAC motifs (3N*-M_SAC-*O) identified in the first stage of screening and their 32 corresponding undoped 3O*-M_SAC-*O counterparts—were investigated. The *vac structures formed after demetallization were fully optimized using DFT calculations.

Fig. 4: Dissolution process of SAC-like MXenes.

Top views of the p(3 × 3) SAC-like MXene (0001) surface under anodic polarization: a undoped 3O*-M_SAC-*O and b doped 3N*-M_SAC-*O. In both cases, the single metal atom is displaced from the basal plane, forming a metal–oxygen (M–O) bond. Upon the dissolution process, the M–O bond is removed through demetallation, resulting in the formation of a surface vacancy (*vac).

To quantitatively assess the dissolution behavior of metal active sites in SAC-like MXenes, a thermodynamic Born–Haber cycle approach was adopted, as originally proposed by Di Liberto et al.²⁰ to evaluate the stability of SAC structures under OER conditions using first-principles calculations. We further go beyond this approach by extending the analysis to both pre-OER and OER scenarios, as discussed by Meng et al.²¹ recently (Figs. S1 and S2). In both cases, the single metal atom at the SAC sites is dissolved into an ionic species (Mⁿ⁺) with various oxidation states (see Table S4). Note that the pre-OER and OER scenarios exhibit a Gibbs free-energy difference of 4.92 eV ), corresponding to the overall OER Gibbs free-energy change at U = 0 V vs. RHE. Therefore, here, for simplicity, we assume that the dissolution potential U_diss (cf. Eq. 10 in “Methods” section) refers only to the pre-OER scenario. Accordingly, 3N*-M_SAC-*O and 3O*-M_SAC-*O systems with U_diss exceeding 1.60 V vs. RHE are considered thermodynamically stable under OER conditions (Fig. 5). The threshold criterion for catalyst stability was chosen to be 1.60 V vs. RHE as this value is slightly above typical OER conditions of 1.53 V vs. RHE, corresponding to an applied overpotential of 0.30 V. An overpotential on this order of magnitude is commonly required for active OER catalysts to achieve a current density of about 10 mA/cm², which is relevant for solar cell applications^39,40,41.

Fig. 5: Schematic representation of the thermodynamic stability analysis for all 32 N-doped MXene-SAC motifs in the second stage of screening based on the criterion of U_diss > 1.60 V vs. RHE.

A total of 11 motifs were identified as promising candidates.

We start with the stability analysis of the 3N*-M_SAC-*O systems together with their 3O*-M_SAC-*O precursors of M₂C₁O-SAC MXenes (M = Cr, Fe, Mo, Ta, W) as a reference in the pre-OER scenario. Note that both U_diss values of the pre-OER and OER scenarios for 3N*-M_SAC-*O and 3O*-M_SAC-*O are summarized in Table S5, S6 and Tables S7, S8 of the SI, respectively. Compared to the 3O*-M_SAC-*O systems (Table S6), nitrogen doping enhances the stability of the SAC sites of W-, Mo-, and Ta-based M₂C₁O-SAC motifs (Table S5). In particular, Mo- and Ta-based 3N*-M_SAC-*O remains stable up to an electrode potential exceeding 4.0 V, while for 3N*-W_SAC-*O a significant stabilization is witnessed compared to its highly unstable 3O*-W_SAC-*O counterpart. However, nitrogen doping leads to decreased stability for Cr- and Fe-based systems, especially for Fe, which tends to dissolve and forms Fe³⁺ at electrode potential below 0 V vs. RHE. Despite this, nitrogen doping contributes positively to the stability of most metal sites in M₂C₁O-SAC MXenes.

Similar to the above analysis, we also constructed Pourbaix diagrams to evaluate the stability behavior of 3N*-M_SAC-*O in the pre-OER scenario, using 3O*-M_SAC-*O as a reference, as shown in Figs. 6, 7, respectively. The analysis is based on the M₂C₁O-SAC motifs under various pH conditions, with a focus on the potential range of 0.8–2.0 V vs. SHE to represent the oxidative environment relevant to the OER. In the pre-OER scenario, the dissolution of the metal atom involves proton consumption, and thus the boundary lines between M₂C₁O-SAC and Mⁿ⁺ exhibits a positive slope on the SHE scale, indicating that the SAC sites are becoming thermodynamically more stable at higher pH values, as shown in Fig. S1 of the SI and Eq. 11 in the “Methods” section.

Fig. 6: Pourbaix diagrams of N-doped SAC-like MXenes.

Pourbaix diagrams assessing the thermodynamic stability of SAC-like sites on the MXene basal plane, 3N*-M_SAC-*O, of a W₂C₁O, b Mo₂C₁O, c Ta₂C₁O, d Cr₂C₁O, and e Fe₂C₁O MXenes in the context of the pre-OER scenario (cf. Fig. S1). The stability of M_SAC is referenced to different oxidative ion states resulting from the dissolution of the corresponding metals (cf. Table S4 in the SI). Regions where 3N*-M_SAC-*O is thermodynamically stable are colored blue, while a yellow background indicates that metal cations are energetically favored. The black, dashed line indicates the OER equilibrium potential on the SHE scale.

Fig. 7: Pourbaix diagrams of SAC-like MXenes.

Pourbaix diagrams assessing the thermodynamic stability of SAC-like sites on the MXene basal plane, 3O*-M_SAC-*O, of a W₂C₁O, b Mo₂C₁O, c Ta₂C₁O, d Cr₂C₁O, and e Fe₂C₁O MXenes in the context of the pre-OER scenario (cf. Fig. S1). The stability of M_SAC is referenced to different oxidative ion states resulting from the dissolution of the corresponding metals (cf. Table S4 in the SI). Regions where 3O*-M_SAC-*O is thermodynamically stable are colored blue, while a yellow background indicates that metal cations are energetically favored. The black, dashed line indicates the OER equilibrium potential on the SHE scale. Panels (a–e) are reproduced with permission from ref. ²¹.

Taking 3N*-Cr_SAC-*O in Fig. 6 as an example, its stability critically depends on the applied electrode potential and the pH value. Under acidic conditions of pH < 5, 3N*-Cr_SAC-*O exhibits poor thermodynamic stability within the anodic potential range of 0.8 to 2 V vs. SHE, and tends to decompose into Cr³⁺ species. As the pH increases, its stability improves significantly, and at pH > 11, 3N*-Cr_SAC-*O becomes thermodynamically stable at an electrode potential of 1.60 V vs. SHE. In contrast, 3N*-Fe_SAC-*O is unstable under any U and pH values, dissolving to form Fe³⁺ species, which is consistent with its low U_diss of −1.44 V listed in Table S5. The Pourbaix diagrams under OER conditions are shown in Figs. S3–S4, following the same analysis method as used for the pre-OER scenario in Figs. 6 and 7.

A detailed comparison of the stability of the M₂N₁O-SAC motifs in the pre-OER and OER scenarios between the N-doped 3N*-M_SAC-*O and undoped 3O*-M_SAC-*O configurations is presented in Tables S9, S10 and Tables S11, S12 of the SI, respectively. The corresponding Pourbaix diagrams are shown in Figs. S5–S8 of the SI. Similar with M₂C₁O-SAC, the results of M₂N₁O-SAC also indicate that nitrogen doping (cf. Table S9 of the SI) significantly reduces the dissolution tendency of metal sites, thereby enhancing their structural stability under pre-OER scenario—especially for Mo- and Ta-based systems with the highest dissolution potential around 4.0 V vs. RHE—thereby broadening the electrochemical window for structural stability during OER. However, Cr-based systems show a deterioration in stability upon nitrogen doping, with an even higher dissolution tendency than that in the undoped state.

We next examine the stability evolution of M₃C₂O-SAC MXenes, and the relevant results for the pre-OER and OER scenarios of 3N*-M_SAC-*O and 3O*-M_SAC-*O are summarized in Tables S13, S14 and Tables S15, S16 of the SI, respectively. The corresponding Pourbaix diagrams are shown in Figs. S9–S12 of the SI. Under pre-OER scenario, nitrogen doping significantly enhances the stability for all metal centers, i.e., W-, Mo-, Ta-, Nb-, and V-based systems (see Table S13 of the SI). Among all systems, 3N*-Mo_SAC-*O and 3N*-Ta_SAC-*O still indicate the highest resistance to dissolution, with 3N*-Mo_SAC-*O in particular showing a dissolution potential of approximately 4.55 V vs. RHE.

Furthermore, we explored the stability of M₃N₂O-SAC MXenes for 3N*-M_SAC-*O and 3O*-M_SAC-*O under pre-OER and OER conditions, and the results are summarized in Tables S17, S18 and Tables S19, S20 of the SI. The corresponding Pourbaix diagrams are shown in Figs. S13–S16. In the pre-OER scenario, it can be observed that nitrogen doping significantly improves the stability of metal sites in W-, Nb-, and V-based systems, which were highly unstable in the undoped state (cf. Fig. S13 of the SI). However, nitrogen doping still fails to improve the inherent instability of Hf- and Zr-based systems, which readily dissolve as HfO₂⁺_(aq) and Zr⁴⁺_(aq), respectively, even under different pH conditions. Notably, 3N*-Mo_SAC-*O still exhibits the highest stability under the pre-OER scenario, with a dissolution potential of 4.78 V vs. RHE (see Table S17).

Finally, the data for SAC-like M₄C₃O (Tables S21–S24 and Figs. S17–S20) and M₄N₃O (Tables S25–S28 and Figs. S21–S24) are summarized accordingly in the SI. The overall conclusion aligns with the above findings, i.e., nitrogen doping can significantly enhance the stability of metal sites, except for Cr-based system (Tables S21 and S25). In addition, Mo- and Ta-based systems, which are already relatively stable before nitrogen doping (Tables S22 and S26), exhibit the greatest thermodynamic stability upon nitrogen doping, as evidenced by their significantly extended potential window (Figs. S17 and S21).

During the second stage of the thermodynamic stability screening from the initial set of 32 candidates, 11 representative MXenes-SAC motifs were selected for the subsequent activity evaluation in the OER. Specifically, the selected candidates include: (i) Mo- and Ta-based 3N*-M_SAC-*O for M₂X₁O-SAC MXenes; (ii) Mo- and Ta-based systems for M₃C₂O-SAC MXenes; 3N*-Mo_SAC-*O for M₃N₂O-SAC MXenes; (iii) Mo- and Ta-based systems for M₄X₃O-SAC MXenes (cf. Fig. 5).

Catalytic activity of nitrogen-doped MXene-SAC motifs for OER

To evaluate the OER catalytic activity of the above candidates, we performed DFT calculations within the CHE framework to describe the proton-electron transfer steps in the mononuclear-Walden mechanism⁴² for OER and applied the thermodynamic descriptor G_max(U)^43,44 to assess the electrocatalytic activity (cf. “Methods” section). We use an applied electrode potential of U = 1.53 V vs. RHE in the analysis, as an applied overpotential of 300 mV typically corresponds to the experimental condition for achieving a current density of approximately 10 mA/cm³⁹. Thus, a threshold¹⁶ of G_max < 0.60 eV @U = 1.53 V vs. RHE is used to evaluate the 11 N-doped candidates identified above. We note that the threshold of 0.60 eV^16,43 to distinguish between active and inactive catalysts is related to previous work¹⁶ on the topic.

The corresponding limiting Gibbs free-energy spans for the N-doped SAC-like MXene are shown in Fig. S25, and the values of the reaction activity descriptor G_max(U) are summarized in Table 1. The related optimized intermediate structures, 3N*-M_SAC-*O, 3N*-M_SAC-*O OH, 3N*-M_SAC-*OO and 3N*-M_SAC-*OH, within the mononuclear-Walden framework are presented in Fig. S26. Among all 11 candidate materials, we observed that at the potential of U = 1.53 V vs. RHE, the limiting step in the approximation of the G_max(U) descriptor consistently corresponds to the formation of the *OOH intermediate (3N*-M_SAC-*O + H₂O → 3N*-M_SAC-*OOH + H⁺ + e^‒), suggesting that this step might be reconciled with the rate-determining step (RDS). However, when the potential is reduced to 1.23 V vs. RHE, the limiting step for N-doped SAC-like Ta₂C and Ta₂N MXenes shifts to 3N*-M_SAC-*OH → 3N*-M_SAC-*OOH, whereas no such transition is observed in the other 9 N-doped SAC-like MXenes. This observation aligns with the findings of Razzaq et al.¹⁶, who reported that MXene-SAC motifs with high electrocatalytic activity exhibit a shift in the RDS under varying applied potentials during OER, which corresponds to a change in the limiting span of G_max(U). Such behavior reflects a favorable reaction kinetics due to a change in the Tafel slope with increasing overpotential^43,44.

Table 1 G_max(U) values and corresponding limiting free-energy spans for the N-doped SAC-like MXene based on the mononuclear-Walden mechanism (cf. Eqs. 3–6) at U₁ = 1.23 and U₂ = 1.53 V vs. RHE

Notably, N-doped Ta₂C₁O- and Ta₂N₁O-SAC exhibit higher catalytic activity compared to the other candidates—particularly Ta₂N₁O-SAC, which has a remarkably low G_max(U = 1.53 V) value of 0.39 eV. Furthermore, Mo-based MXene-SACs, such as Mo₂C₁O, Mo₃C₂O, and Mo₄C₃O, which combine high nitrogen doping feasibility with robust structural stability, exhibit 0.60 eV < G_max(U = 1.53 V) < 1.00 eV (Table 1), and thus are not sufficiently active for OER.

While a previous study⁴⁵ suggested that a Walden-type step (cf. Eq. 15 in “Methods” section) serves as the RDS for the oxygen reduction reaction (ORR) over archetypal SAC catalysts, we conclude based on the evaluation of the G_max(U) descriptor that the desorption-adsorption Walden step is not related to the RDS. This finding suggests that the contribution of desorption-adsorption Walden steps to the electrocatalytic activity is not universal for different catalysts, although for deeper insight the identification of transition states is necessary, which is beyond the scope of the present manuscript.

In summary, during the third stage of screening 11 nitrogen-doped MXene-SAC motifs related to their OER activity, Ta₂C₁O- and Ta₂N₁O-SAC exhibit the most promising performance, with G_max values of 0.56 eV and 0.39 eV at 1.53 V vs. RHE, respectively. These values fall within the proposed activity threshold of G_max (U = 1.53 V) < 0.60 eV. Combined with their thermodynamic feasibility for nitrogen doping, structural stability under both (i) pre-OER and (ii) OER scenarios, and their remarkable catalytic activity, Ta₂C₁O- and Ta₂N₁O-SAC emerge as the most promising candidates for OER (Fig. 8).

Fig. 8: Schematic representation of the activity analysis in the OER for all 11 N-doped MXene-SAC motifs in the third stage of screening based on the criterion of G_max < 0.60 eV @U = 1.53 V vs. RHE.

A total of 2 motifs were identified as promising candidates.

Finally, to gain further insight into how nitrogen doping affects the structural stability and activity of MXene-SAC motifs, a Bader charge analysis was performed, as illustrated in Figs. S27 to S32. Here, we focus on the average charge transfer of the nitrogen or oxygen atoms coordinated to the metal center in 3N*-M_SAC-*O and 3O*-M_SAC-*O, respectively. The result indicates that, in most systems, the 3N* environment exhibits significantly stronger electron accumulation compared to their O*-coordinated counterparts. This can be seen as the primary reason for the enhanced structural stability and catalytic performance of the nitrogen-doped structures. In contrast, Fe- and Cr-based systems deviate from this trend—nitrogen doping leads to reduced electron accumulation (Fig. S27), which in turn decreases the structural stability. We highlight that particularly Ta-based systems show the most prominent effect related to electron accumulation (Figs. S27–S29, S31–S32), indicating their particular ability in stabilizing MXene-SAC configurations.

Discussion

This study systematically investigated the feasibility of nitrogen doping for fully O-terminated MXene-SAC motifs and provides an in-depth analysis of its role in enhancing the stability and activity of a single metal site under anodic polarization conditions, as well its potential application in OER. Thermodynamic analysis based on DFT calculations combined with the CHE model reveals that nitrogen doping can significantly regulate the coordination environment of metal sites, effectively improving their resistance to dissolution under harsh electrochemical conditions while enhancing catalytic activity, thereby breaking the conventional activity-stability trade-off⁴⁶.

Our results indicate that the thermodynamic feasibility of nitrogen substitution in MXene-SAC motifs strongly depends on the chemical nature of the transition metal. More precisely, W-, Mo-, Ta-, Cr-, Nb- and V-based systems generally exhibit a favorable nitrogen doping process across different MXene types, with equilibrium potentials (U_eq) lower than 1.23 V vs. RHE. In contrast, Ti-, Hf- and Zr-based MXene-SAC motifs are unfavorable for nitrogen incorporation regardless of their structural composites.

Nitrogen doping in the MXene-SAC motif also depends on structure and composition, but this effect is limited. Nb favors thicker MXenes (M₃X₂O, M₄X₃O), while V prefers nitrides composition over carbides. For Hf and Zr, nitrogen doping can only occur in M₃N₂O-SAC. In addition, nitrides MXene-SAC motifs are generally more favorable for N doping than carbides. Among all MXene structures considered in this work, M₃N₂O shows the widest adaptability and allows nitrogen doping even in challenging systems.

The second stage of our stability analysis reveals that nitrogen doping generally enhances the stability of metal sites by increasing their dissolution potential under anodic conditions, thereby expanding the electrochemical operating window. In particular, Mo- and Ta-based systems exhibit excellent intrinsic stability due to nitrogen incorporation. Notably, Mo-based system can achieve a dissolution potential of about 4.50 V vs. RHE, significantly extending their stability range. These observations are also consistent with previous studies^47,48 highlighting the stabilizing role of nitrogen doping in catalysts. However, the stabilizing effect of nitrogen incorporation is not universal across all metal species, as Cr- and Fe-based systems exhibit decreased stability upon nitrogen doping. Similarly, the effect of nitrogen doping on the thermodynamic stability of metal sites mainly depends on the intrinsic properties of the transition metal rather than the specific configuration of MXene-SAC motifs. The impact of MXene structure and composition on metal site dissolution is minimal.

In the third stage of our screening protocol, Ta₂N₁O-SAC is identified as the most active catalyst among all thermodynamically stable candidates, exhibiting the lowest G_max(U) value of 0.39 eV at U = 1.53 V vs. RHE, followed by Ta₂C₁O-SAC, which also shows promising OER activity with a G_max(U) value of 0.56 eV at the same potential. The limiting span of the G_max(U) descriptor is related to 3N*-M_SAC-*OH → 3N*-M_SAC-*OOH, which changes to 3N*-M_SAC-*O → 3N*-M_SAC-*OOH at higher overpotentials. This indicates that both Ta₂C₁O- and Ta₂N₁O-SAC show a change in the rate-determining step upon increasing overpotential, which is accompanied with a favorable reaction kinetics.

Overall, this study reveals that nitrogen doping is an effective strategy to improve both the stability and activity of MXene-SAC motifs in OER. N-doped Ta₂C₁O-SAC and N-doped Ta₂N₁O-SAC, as representative systems, break the conventional activity-stability trade-off in the OER⁴⁶, and this finding is consistent with the work by Shim et al.⁴⁹, who revealed that single-atom Ta doping enhances both the activity and stability of RuO₂ under acidic OER conditions. It is worth noting that N-doped Ta₂C₁O-SAC and Ta₂N₁O-SAC remain unaffected as promising candidates when the OER scenario is adopted for the stability analysis (cf. section “Thermodynamic stability of nitrogen-doped MXene-SAC motifs”). This finding could motivate future experimental studies to validate the stability and catalytic performance of N-doped SAC-like MXenes. In particular, the synthesis process—especially the NH₃ treatment—must be optimized to achieve precise nitrogen incorporation while avoiding over- or incomplete doping. The present work may stimulate experimental investigations in this direction by using the reported design principles to develop stable and durable OER electrocatalysts based on N-doped MXene-SAC motifs.

Methods

All calculations were performed using electronic structure theory in the density functional theory (DFT) framework within the Vienna ab initio simulation package (VASP)^50,51. To accurately describe the electronic structure properties of the studied MXene systems, the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional⁵² was employed, which has also been widely used for 2D materials^53,54. In addition, Grimme’s D3 dispersion approach⁵⁵ was applied to consider intermolecular interactions, as the PBE functional is underestimating the adsorption energies unless dispersive interactions are duly accounted⁵⁶. To accurately describe the influence of core electrons on the valence electron density, the projector-augmented wave (PAW) method was employed^57,58. Based on this approach, the valence electron density was expanded using a plane-wave basis set with a kinetic energy cutoff of 440 eV. During optimization, the electronic self-consistent field convergence criterion was set to 10^‒6 eV, and the degrees of freedom of atoms were relaxed until the force on each atom was below 0.01 eV·Å⁻¹. Although hybrid functionals (e.g., HSE06) may provide more accurate descriptions of electronic structures⁵⁹—particularly band gaps and charge transfer—they were not considered in this work, as they offer no significant improvement over PBE in predicting equilibrium potentials or evaluating energetics⁶⁰, and their high computational cost makes them unsuitable for large-scale screening⁶¹. Moreover, a recent study has noted that gas-phase errors in hybrid functionals may propagate through free energy profiles and affect activity predictions⁶². Note that solvation effects were not considered in this study, as our previous work²¹ demonstrated that the inclusion of solvation does not significantly alter the overall trends of the investigated MXene-SAC motifs. All calculations were performed using periodic models, effectively infinite in the basal plane directions. To eliminate interactions between periodic MXene layers, a vacuum spacing of at least 19 Å was introduced along the out-of-plane direction. Integration in the Brillouin zone was carried out using a Γ-centered Monkhorst-Pack k-point mesh of 5 × 5 × 1. Furthermore, all studied SAC-like MXenes—including 3N*-M_SAC-*O and 3O*-M_SAC-*O types in M₂X₁O, M₃X₂O, and M₄X₃O MXenes (where M = Cr, Fe, Hf, Mo, Nb, Ta, Ti, V, W, or Zr, and X = C or N)—were treated with spin polarization. Gas-phase calculations of isolated atoms and molecules were performed in a symmetry-broken cell of 9 × 10 × 11 Å to ensure accurate orbital occupation and energetics.

Besides the above calculation of electronic energy (E_DFT), harmonic vibrational frequencies of the studied systems were obtained by constructing and diagonalizing the relevant block of the Hessian matrix via finite difference of the analytical gradients with a step size of 0.015 Å. Based on the resulting vibrational frequencies, the zero-point energy (${E}_{{ZPE}}$) and entropy (TS) were further estimated (vide infra). In the frequency calculations, only the displacements of the termination adsorbates—9*O in 3O*-M_SAC-*O and 6*O + 3*N in 3N*-M_SAC-*O, together with the M_SAC and *O atoms of M_SAC-*O center, as well the first M layer of the M_n+1X_nO were considered, while the remaining M and X atoms of M_n+1X_nO were fixed at their optimized positions.

Furthermore, the CHE model³⁸ proposed by Nørskov et al. was employed to simulate the effect of the applied electrode potential on the reaction free energy. Under standard equilibrium conditions—${p}_{{\text{H}}_{2}}\,$= 1 bar, T = 298.15 K, U = 0 V vs. SHE, and pH = 0—the electrochemical equilibrium between a proton-electron pair and gaseous hydrogen reads:

$${{\rm{H}}}_{({\rm{aq}})}^{+}+{{\rm{e}}}^{-}\rightleftharpoons 1/2\,{{\rm{H}}}_{2}^{({\rm{g}})}$$

(2)

Note that the present study primarily focuses on a thermodynamic screening protocol based on the CHE model without explicitly including kinetic barriers or solvent dynamics during the reaction. Future work based on AIMD simulations could provide deeper insights into the stability of the MXene-SAC site under constant potential conditions by extending previous work on the topic¹⁵.

Accordingly, the Gibbs free energies (G) of the systems were determined as follows:

$${G}={E}_{DFT}+{E}_{\rm{ZPE}}-{T}\cdot{S}$$

(3)

Regardless of the underlying reaction equation, the change in Gibbs free energy (ΔG) was calculated using the following Eq. (4), which is derived from the individual Gibbs free energies defined in Eq. 3, where ΔG(0, 0) represents the free-energy change at an electrode potential of 0 V vs. SHE and pH = 0.

$$\Delta G(0,0)=\Delta G=\Delta {E}_{{\rm{DFT}}}+\Delta {E}_{{\rm{ZPE}}}-T{{\cdot}}\Delta S$$

(4)

where, ΔE_DFT refers to the change in electronic energy (E_DFT), ΔE_ZPE represents the change in zero-point energy (${E}_{{ZPE}}$), and ΔS is the entropy change.

To evaluate the thermodynamics of reaction processes in the framework of Eq. 4, we set up explicit reaction equations involving relevant intermediates, with Eq. 1 presented above serving as an example that illustrates the thermodynamic feasibility of the N-doping process,

$$3{\rm{O}}* \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{O}}+3{{\rm{NH}}}_{3}\to 3{\rm{N}}* \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{O}}+{3{\rm{H}}}_{2}{\rm{O}}+{3{\rm{H}}}^{+}+{3{\rm{e}}}^{-}$$

(1)

Here, the E_DFT obtained from the structure optimization process can be directly used to calculate the ΔE_DFT term,

$${\Delta E}_{{\rm{DFT}}}={E}_{3{\rm{N}}\ast\mbox{-}{{\rm{M}}}_{{\rm{SAC}}}\mbox{-}\ast {\rm{O}}}+3\ast {E}_{{{\rm{H}}}_{2}{\rm{O}}}+1.5\ast {E}_{{{\rm{H}}}_{2}}-{E}_{3{\rm{O}}\ast \mbox{-}{{\rm{M}}}_{{\rm{SAC}}}\mbox{-}\ast {\rm{O}}}-3\ast {E}_{{{NH}}_{3}}$$

(5)

where, ${E}_{3{\rm{N}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}$ and ${E}_{3{\rm{O}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}$ represent the electronic energies of the 3N*-M_SAC-*O and 3O*-M_SAC-*O systems, respectively. ${E}_{{{\rm{H}}}_{2}{\rm{O}}}$, ${E}_{{{\rm{H}}}_{2}}$, and ${E}_{{{\rm{NH}}}_{3}}$ are the energies of isolated H₂O, H₂, and NH₃ molecules in vacuum. Similarly, the change in the zero-point energy contribution (∆E_ZPE) is obtained as:

$${\Delta E}_{{\rm{ZPE}}}={E}_{3{\rm{N}}\ast -{{\rm{M}}}_{{\rm{SAC}}}-\ast {\rm{O}}}^{{ZPE}}+3\ast {E}_{{{\rm{H}}}_{2}{\rm{O}}}^{{ZPE}}+1.5\ast {E}_{{{\rm{H}}}_{2}}^{{ZPE}}-{E}_{3{\rm{O}}\ast -{{\rm{M}}}_{{\rm{SAC}}}-\ast {\rm{O}}}^{{ZPE}}-3\ast {E}_{{{\rm{NH}}}_{3}}^{{ZPE}}$$

(6)

where, ${E}_{3{\rm{N}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}^{{ZPE}}$ and ${E}_{3{\rm{O}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}^{{ZPE}}$ represent the zero-point energies (ZPE) of the 3N*-M_SAC-*O and 3O*-M_SAC-*O systems, respectively. ${E}_{{{\rm{H}}}_{2}{\rm{O}}}^{{ZPE}}$, ${E}_{{{\rm{H}}}_{2}}^{{ZPE}}$, and ${E}_{{{\rm{NH}}}_{3}}^{{ZPE}}$ are the ZPE of H₂O, H₂, and NH₃ molecules in vacuum. The zero-point energy term, E_ZPE, is calculated from the vibrational frequencies obtained through DFT calculations as follows:

$${E}_{{ZPE}}=\frac{1}{2}\mathop{\sum}\limits_{i}h{v}_{i}$$

(7)

where h is the Planck constants, v_i is the vibrational frequency of the ith mode. For a system with N atoms, the normal vibrational modes (NVMs) are determined from its molecular geometry. For gas-phase linear molecules such as H₂, the NVM are 3N‒5; for nonlinear molecules like H₂O and NH₃, it is 3N−6. For the studied extended systems, such as 3N*-M_SAC-*O and 3O*-M_SAC-*O, all 3N degrees of freedom are treated as vibrational modes, since translational and rotational modes become frustrated, turning into vibrational modes. Similar to the calculation of ∆E_ZPE, the entropy contribution ∆S is evaluated as follows:

$$\Delta S={S}_{3{\rm{N}}\ast -{{\rm{M}}}_{{\rm{SAC}}}-\ast {\rm{O}}}+3\ast {S}_{{{\rm{H}}}_{2}{\rm{O}}}+1.5\ast {S}_{{{\rm{H}}}_{2}}-{S}_{3{\rm{O}}\ast -{{\rm{M}}}_{{\rm{SAC}}}-\ast {\rm{O}}}-3\ast {S}_{{{NH}}_{3}}$$

(8)

where, ${S}_{3{\rm{N}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}$ and ${S}_{3{\rm{O}}* -{{\rm{M}}}_{{\rm{SAC}}}-* {\rm{O}}}$ represent the entropies of the 3N*-M_SAC-*O and 3O*-M_SAC-*O systems, respectively, while ${S}_{{{\rm{H}}}_{2}{\rm{O}}}$, ${S}_{{{\rm{H}}}_{2}}$, and ${S}_{{{NH}}_{3}}$ denote the entropies of gas-phase H₂O, H₂, and NH₃ molecules in vacuum. The entropy contributions of these gas-phase molecules were taken from standard thermodynamic data sources⁶³. For the studied systems such as 3N*-M_SAC-*O and 3O*-M_SAC-*O, due to the frustrated translational and rotational modes, only the vibrational entropy (S_vib) was considered,

$${\rm{T}}S={k}_{B}T\mathop{\sum}\limits_{i}^{n}\left[\frac{\frac{h{v}_{i}}{{k}_{B}T}}{{e}^{\frac{h{v}_{i}}{{k}_{B}T}}-1}-{{ln}}\left(1-{e}^{\frac{-h{v}_{i}}{{k}_{B}T}}\right)\right]$$

(9)

where v_i is the vibrational frequency of the ith mode, n denotes the total number of vibrational modes, T represent the temperature in Kelvin, and k_B, h are the Boltzmann and Planck constants, respectively.

Furthermore, as mentioned in the section “Thermodynamic stability of nitrogen-doped MXene-SAC motifs”, the Born–Haber thermodynamic cycle was originally proposed by Di Liberto et al.²⁰ to estimate the stability of SAC structures under OER electrochemical conditions; however, the simultaneous O₂ evolution was not considered in the original model. Thus, to provide a more comprehensive analysis, we considered two distinct dissolution pathways in this study following our previous work²¹: (a) pre-OER scenario (U < 1.23 V vs. RHE), with no O₂ generation during demetallization of the single atom center of MXene (cf. Fig. S1); (b) OER scenario (U > 1.23 V vs. RHE), with O₂ evolution during demetallization of the single atom center of MXene (cf. Fig. S2).

In both scenarios, the single metal atom may dissolve into ionic species (Mⁿ⁺) with various oxidation states (see Table S4 of the SI). The overall dissolution process, illustrated in Figs. S5 and S6 of the SI includes three steps: (i) removing metal atom from the M_SAC site to the gas phase (ΔG₁); (ii) cohesive energy to convert the gas-phase atom into the solid phase (ΔG₂); (iii) oxidizing the solid metal atom into an ionic species (ΔG₃). Among them, only ΔG₁ of (i) step is calculated via DFT using the CHE model, while ΔG₂ and ΔG₃ are derived from data in the thermodynamic tables^64,65 and standard electrode potential (ΔE°)^66,67, respectively. The total Gibbs free energy change, referred to as ΔG_1-3, is used to estimate the dissolution potential, U_diss:

$${U}_{{diss}}=\frac{{\varDelta G}_{1-3}}{n}\,=\frac{\Delta {G}_{1}\,+\,\Delta {G}_{2}+\,\Delta {G}_{3}}{n}$$

(10)

where n is the number of electrons transferred in the overall reaction.

The free energy change ΔG(pH, U) as a function of pH and U can be derived as follows:

$$\Delta G({pH},U\,)=\Delta G\,(0,0\,)-\upsilon ({{\rm{H}}}^{+})\,{k}_{B}T{{\cdot}}{\mathrm{ln}}10{{\cdot}}{pH\;-\;\upsilon }({e}^-){eU}$$

(11)

where ν(H⁺) and ν(e⁻) denote the stoichiometric coefficients of protons and electrons involved in the reaction equation for the elementary step. Based on this approach, pH- and U-dependent Pourbaix diagrams can be constructed by determining the equilibrium lines between various dissolved species, which are derived from the above-calculated ΔG(pH, U) to illustrate the thermodynamically stable regions of the system³².

Similarly, as described in the section “Thermodynamic feasibility of nitrogen-doped MXene-SAC motifs”, the thermodynamic feasibility of the N-doping process was evaluated based on Eq. 1:

$$3{\rm{O}}\ast \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}\ast {\rm{O}}+3{{\rm{NH}}}_{3}\to 3{\rm{N}}\ast \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}\ast {\rm{O}}+{3{\rm{H}}}_{2}{\rm{O}}+{3{\rm{H}}}^{+}+{3{\rm{e}}}^{-}$$

The corresponding Gibbs free energy change (ΔG) can be obtained based on the above reaction equation and invoking the CHE model³⁸. The ΔG value is used to estimate the equilibrium potential (U_eq) according to the following equation:

$${U}_{{eq}}=\frac{\Delta G}{3}$$

(12)

where 3 corresponds to the number of electrons transferred in Eq. 1. Values of U_eq below 1.23 V vs. RHE indicate that the N-doping process is thermodynamically favorable before OER can proceed. Conversely, when U_eq exceeds 1.23 V vs. RHE, the incorporation of nitrogen atoms is thermodynamically unfavorable below the OER equilibrium potential.

As mentioned in the section “Catalytic activity of nitrogen-doped MXene-SAC motifs for OER”, the OER reaction mechanism employed here deviates from the conventional mononuclear pathway^68,69, as reported for MXenes in our previous work¹⁶. Specifically, the adsorption of the reactant H₂O and the release of the product O₂ proceeds in a concerted manner, while the formation of reaction intermediates does not follow the conventional sequence of a mononuclear mechanism^68,69. Notably, previous studies^45,70 indicate that highly active OER catalysts tend to follow such a pathway, deviating from the traditional mononuclear route. The elementary steps of the mononuclear-Walden OER mechanism are shown in Eqs. 13–16,

$$3{\rm{N}}*{\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}*{\rm{O}}+{{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{l}})}\to 3{\rm{N}}* {\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OOH}}+({{\rm{H}}}^{+}+{{\rm{e}}}^{-}),{\Delta G}_{1}$$

(13)

$$3{\rm{N}}* \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OOH}}\to 3{\rm{N}}* {\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OO}}+({{\rm{H}}}^{+}+{{\rm{e}}}^{-}),{\Delta G}_{2}$$

(14)

$$3{\rm{N}}*{\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OO}}+{{\rm{H}}}_{2}{{\rm{O}}}_{({\rm{l}})}\to 3{\rm{N}}* {\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OH}}+{{\rm{O}}}_{2({\rm{g}})}+({{\rm{H}}}^{+}+{{\rm{e}}}^{-}),{\Delta G}_{3}$$

(15)

$$3{\rm{N}}*{\mbox{-}{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{OH}}\to 3{\rm{N}}* \mbox{-}{{\rm{M}}}_{{\rm{SAC}}\mbox{-}}* {\rm{O}}+({{\rm{H}}}^{+}+{{\rm{e}}}^{-}),{\Delta G}_{4}$$

(16)

The values of ∆G₁, ∆G₂, ∆G₃, and ∆G₄ were determined using density functional calculations an invoking the CHE model. These corresponding ∆G values and the related intermediate structures within the mononuclear-Walden framework are presented in Figs. S25 and S26. In addition, we included gas-phase error corrections for H₂O_(l) and O₂^(g) involved in Eq. 15. Specifically, the chemical potential of gaseous H₂O was corrected under the conditions of T = 298.15 K and p = 0.035 bar⁷¹, at which liquid and gaseous H₂O are in thermodynamic equilibrium. To address the well-known deviation associated with the GGA functional evaluating the free energy of O₂ molecules⁷², a correction^62,73 was also applied based on the experimental enthalpy (${\Delta}_{f}{H}^{\circ }$) of –2.51 eV⁷⁴ for the water formation reaction, as shown in Eqs. 17 and 18:

$$\frac{1}{2}{O}_{2(g)}+{H}_{2\left(g\right)}\rightleftharpoons {H}_{2}{O}_{(g)}$$

(17)

$${\Delta}_{f}{{H}^{\circ }}_{{H}_{2}{O}_{(g)}}-{\Delta}_{f}{{H}^{\circ }}_{{{H}_{2}}_{\left(g\right)}}-{\frac{1}{2}{\Delta}_{f}}{{H}^{\circ}}_{{{O}_{2}}_{(g)}}=-2.51\,{{\rm{eV}}}$$

(18)

where ${\Delta}_{f}{H}^{\circ }$ is expressed as ${\Delta}_{f}{E}_{D{FT}}$ + ${\Delta}_{f}{E}_{Z{PE}}$, thus, the gaseous O₂ can be corrected as Eq. 19;

$${E}_{c{orr},{O}_{2(g)}}=2({E}_{D{FT},{H}_{2}{O}_{(g)}}-{E}_{D{FT},{{H}_{2}}_{(g)}}+{E}_{Z{PE},{H}_{2}{O}_{(g)}}-{E}_{Z{PE},{{H}_{2}}_{(g)}}+2.51\,{{\rm{eV}}})$$

(19)

After the correction of the gaseous O₂ Gibbs free energy, the Gibbs free energy of the H₂O_(aq) → O_2(g) + H_2(g) reaction agrees with the experimental value when referring to the standard equilibrium potential of OER”.

In addition, to quantify the electrocatalytic activity of the N-doped MXene-SAC motifs for OER, we employed the activity descriptor G_max(U)^43,44, which refers to a free-energy span model that identifies the largest energy difference between the OER intermediate states at a given electrode potential. This energy span exhibits a Brønsted–Evans–Polanyi (BEP) relationship with the highest transition state in the catalytic cycle and can therefore be associated with the rate-determining step (RDS). Ten different free-energy spans between the relevant intermediate states of Eqs. 20–29 are possible:

$${G}_{{\rm{span\#}}1}(U)={G}_{{\rm{M}}-* {\rm{OH}}+{{\rm{O}}}_{2}}(U)-{G}_{{\rm{M}}-* {\rm{OO}}}(U)$$

(20)

$${G}_{{\rm{span\#}}2}(U)={G}_{{\rm{M}}-* {\rm{OH}}+{{\rm{O}}}_{2}}(U)-{G}_{{\rm{M}}-* {\rm{OOH}}}(U)$$

(21)

$${G}_{{\rm{span\#}}3}(U)={G}_{{\rm{M}}-* {\rm{OH}}+{{\rm{O}}}_{2}}(U)-{G}_{{\rm{M}}-* {\rm{O}}}(U)$$

(22)

$${G}_{{\rm{span\#}}4}(U)={G}_{{\rm{M}}-* {\rm{OH}}+{{\rm{O}}}_{2}}(U)-{G}_{{\rm{M}}-* {\rm{OH}}}(U)$$

(23)

$${G}_{{\rm{span\#}}5}(U)={G}_{{\rm{M}}-* {\rm{OO}}}(U)-{G}_{{\rm{M}}-* {\rm{OOH}}}(U)$$

(24)

$${G}_{{\rm{span\#}}6}(U)={G}_{{\rm{M}}-* {\rm{OO}}}(U)-{G}_{{\rm{M}}-* {\rm{O}}}(U)$$

(25)

$${G}_{{\rm{span\#}}7}(U)={G}_{{\rm{M}}-* {\rm{OO}}}(U)-{G}_{{\rm{M}}-* {\rm{OH}}}(U)$$

(26)

$${G}_{{\rm{span\#}}8}(U)={G}_{{\rm{M}}-* {\rm{OOH}}}(U)-{G}_{{\rm{M}}-* {\rm{O}}}(U)$$

(27)

$${G}_{{\rm{span\#}}9}(U)={G}_{{\rm{M}}-* {\rm{OOH}}}(U)-{G}_{{\rm{M}}-* {\rm{OH}}}(U)$$

(28)

$${G}_{{\rm{span\#}}10}(U)={G}_{{\rm{M}}-* {\rm{O}}}(U)-{G}_{{\rm{M}}-* {\rm{OH}}}(U)$$

(29)

Based on the free-energy spans of Eqs. 20–29, the descriptor G_max(U) is defined as follows:

$${G}_{\max }(U)=\max [{G}_{{\rm{span\; \#}}k}(U),\,k=1,\ldots ,n]$$

(30)

where n denotes the above ten free-energy spans, and G_max(U) representing the largest span, that is, the span between the reaction intermediate with the lowest and highest free energy in the free energy landscape, in dependence of the applied electrode potential. Albeit the definition of the G_max(U) descriptor is reminiscent of the free-energy span model of Kozuch and Shaik⁷⁵ related to homogeneous catalysis, the notion of G_max(U) relies on the thermodynamic information and does not capture any kinetic parameters, such as the transition state with the highest free energy, in its framework. The reason for this choice is that the calculation of transition states in an electrochemical environment is still in its infancy^53,76,77, considering that most theoretical works only determine selected transition states of chemical steps, whereas the calculation of barriers for charge-transfer steps at constant electrode potential is accompanied with additional challenges⁷⁸. In the framework of the original free-energy span model of Kozuch and Shaik⁷⁵, the G_max(U) descriptor estimates electrocatalytic activity based on the turnover-determining intermediate (TDI), which appears to be a valid approximation for electrocatalytic processes on surfaces, as discussed elsewhere⁴³. Compared with the conventional approach that relies solely on the thermodynamic overpotential η_TD, G_max(U) offers a more comprehensive assessment of the electrocatalytic activity by enabling potential-dependent activity analysis. Further details on the G_max(U) descriptor can be found in previous publications^79,80.