In-Depth First-Principles Study of High-Performance M₂XO₂ MXene Cathode Catalysts for Sodium-Oxygen Batteries

Abstract

Na−O₂ batteries are plagued by high cathodic oxygen reduction (ORR)/oxygen evolution (OER) overpotentials during discharging/charging. Herein, we constructed six carbide/nitride MXenes (M₂XO₂, M = Ti, Zr, and Hf, X = C, and N) and investigated their performance as cathodes for Na−O₂ batteries by first-principles calculations. M₂CO₂ MXenes have a pseudogap, showing semiconducting properties, while M₂NO₂ MXenes are conductive. The nucleophilic O on the M₂XO₂ surfaces prefers to bind with the Na atoms of Na_xO₂ intermediates to activate the Na−O bonds, improving the sodium deintercalation. For all M₂XO₂ MXenes, the OER overpotential is higher than the ORR overpotential, forming a performance bottleneck of Na−O₂ batteries. The overpotentials originate from the too-strong adsorption of Na_xO₂ on M₂XO₂ MXenes. Lowering the O p-band center of the M₂XO₂ MXenes can weaken the Na_xO₂ adsorption, thereby reducing the overpotential. Consequently, the overpotentials of the M₂CO₂ carbides are lower than those of the M₂NO₂ nitrides and further decrease with a decreasing M atomic number. The Ti₂CO₂ MXene shows extremely low ORR, OER, and total overpotentials (0.23, 0.32, and 0.55 V), suggesting a huge potential as cathodes in Na−O₂ batteries.

1. Introduction

The depletion of fossil fuel resources is exacerbated by increasing energy consumption due to population growth and economic expansion. In the quest for more efficient and eco-friendly energy storage solutions, extensive research has been conducted on rechargeable batteries [1,2,3]. Different from conventional battery systems that are self-containing, in the aprotic alkali metal−O₂ batteries (such as Li−O₂ batteries and Na−O₂ batteries), oxygen from the atmosphere participates in the cathode reaction through a gas electrode, which produces a high energy density, resulting in the high energy density battery systems. The electrochemical power devices consist of a Li/Na anode, where Li or Na−metal is oxidized upon discharge to Li⁺/Na⁺ ions, and an oxygen cathode, where Li⁺/Na⁺ ions recombine with electrons to reduce O₂ gas from the ambient environment. The theoretical energy density of alkali metal−O₂ batteries (3600 Wh kg⁻¹ for Li−O₂ batteries and 1100 Wh kg⁻¹ for Na−O₂ batteries) significantly exceeds that of Li−ion batteries (372 Wh kg⁻¹) [4,5]. Compared to Li−O₂ batteries, Na−O₂ batteries exhibit the following advantages [4,5]: (1) Resource abundance: Sodium exhibits significantly higher crustal abundance (~2.3%) compared to lithium (0.0017%), with correspondingly lower production costs. (2) Efficient discharge product: NaO₂ (overpotential ~75 mV) decomposes more readily than Li₂O₂ (~1.5 V overpotential), enabling >97% energy efficiency. (3) Suppressed dendrites: The lower Young’s modulus of sodium (~1 GPa, one-fifth of lithium’s 4.9 GPa) effectively suppresses metallic dendrite growth, extending the cycle life. (4) Electrolyte stability: Operating at a higher redox potential (−2.71 V vs. −3.04 V for Li), sodium substantially reduces electrolyte decomposition. (5) Temperature adaptability: Na−O₂ batteries maintain stable electrochemical performance across a broad temperature range (−20 °C to 80 °C), whereas Li−O₂ systems suffer from severe capacity decay below −10 °C. Therefore, the Na−O₂ battery is a promising alternative to the Li−O₂ battery. During discharge and charge, the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER) occur at the cathode of Na−O₂ batteries, respectively. In the ORR process, atmospheric O₂ on the cathode combines with the Na⁺ + e⁻ pairs to form Na_xO₂ products (x = 1, 2, or 4), which then break down into the original Na⁺ and oxygen molecules in the OER process [6,7]. However, the sluggish ORR/OER dynamics of Na−O₂ batteries strongly hinder their practical applications [6,7]. Therefore, it is urgent to find suitable cathode electrocatalysts for efficient Na−O₂ batteries.

Currently, noble metals such as Au, Pt, Ru, and Ir are the most effective catalysts for the cathode of Na−O₂ batteries [8,9]. However, these metals are expensive and can only perform one of the two required activities: ORR or OER [10,11,12]. Carbon materials are abundant, inexpensive, and easily shaped, but their low catalytic activity limits their use in the cathode matrix [13,14]. Although transition metal oxides have been reported to have good electrocatalytic activity, their poor conductivity forces them to be organically mixed with conductive substances, making them difficult to produce [15,16]. In recent years, MXenes, a new large family of two-dimensional (2D) materials, have attracted considerable research interest due to their unique electronic and structural properties. MXenes have been applied in capacitors [17,18], metal–ion batteries [19,20], metal−N₂ batteries [21], and metal−O₂ batteries [22,23]. Especially, MXenes are considered promising candidates for addressing critical challenges in Na–O₂ batteries, with key advantages including the following [23,24,25,26,27,28]: (1) MXenes (e.g., Ti₂CO₂) combine metallic conductivity (an efficient charge transfer) and tunable surface chemistry (e.g., –O terminals) to optimize intermediate adsorption/desorption (e.g., NaO₂), lowering the ORR/OER activation barriers. (2) Surface oxygen groups stabilize Na⁺ ions and nucleophilic oxygen species, promoting NaO₂ formation/decomposition. (3) Polar surfaces can anchor NaO₂ nanoparticles, suppressing their dissolution/aggregation. (4) They are corrosion-resistant under high oxidative potentials (e.g., OER), ensuring cycling stability. (5) Hydrophilic surfaces enable rapid Na⁺ diffusion, reducing localized current density and dendrite nucleation. (6) Enhanced electrolyte wettability ensures a uniform Na⁺ distribution and lowers interfacial resistance. (7) Structural stability from −50 °C to 300 °C supports reliable operation across wide thermal ranges. Min et al. reported that MXene/Cu-BHT heterostructures have ultralow OER (0.24 V) and ORR (0.32 V) overpotentials for Na−O₂ batteries [24]. Tang et al. constructed the TMD/MXene heterostructures with 0.55 V/0.20 V for the ORR/OER overpotentials, which show high catalytic activity in Na–O₂ batteries [25]. He et al. reported that the h-Ti₃C₂/CNT composite exhibits a low potential gap of 0.11 V after 70 cycles for Na–O₂ batteries [26]. Huang et al. designed a Co–S–N–C@MXene catalyst, which shows excellent ORR activity with a half-wave potential of 0.881 V [27]. The half-wave potential exhibited a minimal decline of only 14 mV after 10,000 cycles of cyclic voltammetry testing. Tan et al. found that the NiFe-P/Ti₃C₂T_x composite exhibits exceptional activity and stability for OER, achieving a low overpotential of 290 mV and a Tafel slope of 72.3 mV/dec at a current density of 10 mA cm⁻² [28].

The M₂XO₂ monolayers (M = Ti, Zr, and Hf; X = C and N), belonging to the Group 4 Ti-type MXenes, exhibit excellent stability, good machinability, high conductivity, and metallic/semimetallic properties, making them highly suitable as electrocatalysts [29]. Ti₂CO₂ MXenes were found to have superior storage capacity and a low diffusion barrier for Na ions [30]. Furthermore, recent studies have identified Ti₂CO₂ MXenes as efficient ORR catalysts [31], while Ti₂NO₂ MXenes show OER performance [32]. These findings suggest a significant potential for applying Group 4 Ti-type MXenes in Na–O₂ batteries. However, the performance of catalysts is closely related to the types of constituent elements. It is interesting to explore the influence of Ti, Zr, and Hf on the catalytic performance of Group 4 Ti-type MXenes towards ORR and OER. In this work, we constructed six M₂XO₂ MXenes (M = Ti, Zr, and Hf; X = C and N) and explored their ORR/OER performance during discharge/charging for Na−O₂ batteries by first-principles density functional theory (DFT) calculations. The purpose of this work is to give our theoretical suggestion about MXenes with different components as cathodes for Na−O₂ batteries to guide the experiments. This work merely considers the intrinsic properties of the electrocatalysts, and thus, some external factors are not considered, including the morphology of discharge products, the stability of electrolytes, the corrosion of sodium metal, and the polarization of oxygen electrodes. First, the geometrical and electronic structure of M₂XO₂ MXenes was carefully studied. All of the M₂CO₂ MXenes exhibit semiconducting properties, while the M₂NO₂ MXenes show conductivity. Then, we studied the adsorption properties of the Na_xO₂ intermediates on M₂XO₂ MXenes. Finally, the formation/dissociation of Na_xO₂ on six MXenes in the ORR/OER processes was simulated, and the overpotentials were calculated to assess their catalytic activity quantitatively. The Ti₂CO₂ MXene was found to exhibit excellent catalytic activity with ultralow ORR, OER, and total overpotentials (0.23, 0.32, and 0.55 V). This work is of great significance in providing available theoretical references of MXenes as cathode catalysts for Na−O₂ batteries.

2. Results and Discussion

2.1. Structure Properties

The schematic models of M₂X and M₂XO₂ MXenes (M = Ti, Zr, and Hf, X = C, and N) are shown in Figure 1, and the corresponding fully optimized configurations are shown in Figures S1 and S2. The lattice constants of Ti₂C, Ti₂N, Zr₂C, Zr₂N, Hf₂C, and Hf₂N are calculated as 3.042, 2.994, 3.274, 3.239, 3.115, and 3.198 Å, respectively, which are consistent with other published findings (3.039, 2.985, 3.280, 3.246, 3.211, and 3.171 Å) [33,34]. As shown in Figure 1, three possible O adsorption sites (i.e., the top, hcp, and fcc sites) were considered. The formation energy (see Table S1) indicates that all adsorption sites can form stable O-terminated MXenes, where the most stable adsorption site is the fcc site. Therefore, in the following part, M₂X-MXenes with full O-coverage of the fcc sites (M₂XO₂: Ti₂CO₂, Zr₂CO₂, Hf₂CO₂, Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂) were chosen to study further.

To explore the electronic properties of M₂XO₂ MXenes, the projected density of the states (PDOS) was plotted (see Figure 2). For all M₂XO₂ MXenes, the valence band is mainly composed of the p-states of the O and C/N atoms, while the conduction band is dominated by the d-states of the transition metal atoms. In addition, the M₂CO₂ carbides (Ti₂CO₂, Zr₂CO₂, and Hf₂CO₂) exhibit semiconducting properties, as reflected by the Fermi level passing through the pseudogap (Figure 2a–c). The M₂NO₂ nitrides (Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂) are conductive due to the Fermi level crossing the conduction band (Figure 2d–f). With an increasing metal atomic number, the pseudogap of M₂XO₂ MXenes gradually widens, indicating that the system stability is gradually improved by increasing covalent interaction. The p-band center (ɛ_p(O)) of the surface O atoms is calculated to be −2.57, −2.52, −2.50, −2.31, −2.22, and −2.16 eV with respect to the Fermi level for Ti₂CO₂, Zr₂CO₂, Hf₂CO₂, Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂, respectively, suggesting that the ɛ_p(O) of the M₂CO₂ carbides is apparently lower than that of the M₂NO₂ nitrides. This indicates that the M₂CO₂ carbides exhibit weaker adsorption of the Na_xO₂ intermediates than the M₂NO₂ nitrides. Moreover, with the decreasing metal atomic number, the ɛ_p(O) gradually shifts downwards, suggesting that the adsorption ability of the M₂XO₂ surfaces towards Na_xO₂ intermediates becomes weaker progressively.

The Hirshfeld charge population analyses of M₂XO₂ MXenes (see Figure 3) show that surface O groups are negatively charged by −0.23 to −0.28 e, while the metal atoms are positively charged by 0.38 to 0.47 e, suggesting strong electron transfer from the metal centers to the surface O groups. As the atomic number of the metal increases, the positive charge localized on the metal center gradually increases. This trend arises from the lower electronegativity of metals with higher atomic numbers, resulting in the reduced binding strength of valence electrons to the atomic nucleus. Consequently, this enhances the charge transfer from the metal center to oxygen atoms. Furthermore, the surface oxygen groups of M₂CO₂ carbides carry more negative charges than those of M₂NO₂ nitrides, indicating stronger nucleophilicity of the M₂CO₂ surfaces. This situation can be further confirmed by the sliced deformation electron density (SDED) maps (see Figure 4). As shown in Figure 4, the surface O groups exhibit apparent electron aggregation (the red color region) for all M₂XO₂ MXenes. Especially, the red region of the O atoms on the M₂CO₂ carbides is larger than that on the M₂NO₂ nitrides, indicating its stronger electron accumulation.

As illustrated in Figure 2, M₂XO₂ MXenes exhibit enhanced electrical conductivity due to the hybridization of oxygen p-orbitals with transition metal d-orbitals. This interaction increases the density of electronic states near the Fermi level. Additionally, the strong electronegativity of surface oxygen leads to partial oxidation of the Ti atoms, as shown in Figure 3. This partial oxidation creates conductive pathways enriched with delocalized electrons, significantly reducing resistivity by improving charge carrier mobility. Moreover, the –O terminations can electrostatically attract Na⁺ ions and electrons, facilitating interfacial charge transfer and thus minimizing polarization losses at the electrode–electrolyte interface. Overall, these mechanisms demonstrate that surface oxygen terminations play a crucial role in enhancing the electronic conductivity of M₂XO₂ MXenes.

2.2. Na_xO₂ Adsorption

During the charging and discharging processes, the intermediate species involved on the cathode surface of Na−O₂ batteries mainly include NaO₂, Na₂O₂, and Na₄O₂ [2,35,36]. Herein, the adsorption of these species (Na_xO₂, x = 1, 2, and 4) was characterized. The calculated adsorption configurations are shown in Figure 5 and Figures S3–S5, and the corresponding structural parameters are tabulated in Tables S2–S4.

As shown in Figure 5 and Figures S3–S5, the surface nucleophilic O groups of M₂XO₂ MXenes prefer to combine with the electropositive Na atoms of Na_xO₂ (x = 1, 2, and 4) to activate the Na–O bonds. Therefore, compared to free Na_xO₂, the Na–O bonds in Na_xO₂* are elongated efficiently, while the O–O bonds in Na_xO₂* are shortened (see Tables S2–S4), which is conducive to the deintercalation of sodium in the charging process. The charge population analyses in Tables S5–S7 indicate that a strong electron transfer from Na to surface O groups occurs on the Na_xO₂*-adsorbed M₂XO₂ MXenes, which weakens the ionic interaction in the Na–O bonds of Na_xO₂*. Therefore, surface oxygen terminals can effectively enhance the OER process during charging. After the Na_xO₂* (x = 1, 2, and 4) adsorption on M₂XO₂ MXenes, the changes in the O–O and Na–O bonds in (Na₂O)₂* are the smallest (Tables S2–S4), suggesting that (Na₂O)₂* is the most difficult to activate among the Na_xO₂* intermediates, which is in good accordance with the experimental reports [25,37]. Furthermore, for all considered M₂XO₂ MXenes, M₂CO₂ carbides with a lower metal atomic number have a stronger activation effect on the Na_xO₂* intermediates, as reflected by the greater change in the Na–O and O–O bond lengths of Na_xO₂* (see Tables S2–S4).

With the increasing Na content, the adsorption energy of Na_xO₂* on the M₂XO₂ surfaces increases gradually (see Figure 6), indicating that the larger the Na_xO₂ particles, the more difficult they are to remove from the catalyst surfaces. Compared to the M₂NO₂ nitrides, the M₂CO₂ carbides show weaker adsorption energy towards Na_xO₂*. In addition, with the decreasing atomic number of M, the adsorption energy of Na_xO₂* on M₂XO₂ MXenes is further weakened, improving the accumulation of Na_xO₂ particles. Therefore, the Ti₂CO₂ MXene with the lowest Na_xO₂* adsorption energy can best promote the electrode reaction, thus avoiding the stacking of insulating and insoluble discharge products. The chemisorption of catalysts is known to be determined by the underlying electronic structure. In this work, the close correlation between the Na_xO₂* adsorption energy and the p-band center (ε_p(O)) of the surface O atoms of M₂XO₂ MXenes is confirmed by a linear relationship of E_ads(NaO₂) = −2.90ε_p(O) − 9.27, E_ads(Na₂O₂) = −4.98ε_p(O) − 16.92, and E_ads(Na₄O₂) = −8.86ε_p(O) − 30.90 (see Figure 7a–c), where the adsorption energy of Na_xO₂* shows a weakened trend with the decrease of ε_p(O).

2.3. Evaluation of Catalytic Activity

According to the previous studies [2,35,36,38], the ORR and OER occur at the cathodes of Na−O₂ batteries during the discharging and charging processes, respectively, as in the Li−O₂ electrochemical system. The 4e⁻ oxygen transfer pathways are involved in the cycling process: (1) O₂ + Na⁺ + e⁻ $\leftrightarrow$ NaO₂*; (2) NaO₂* + Na⁺ + e⁻ $\leftrightarrow$ Na₂O₂*; (3) Na₂O₂* + 2Na⁺ + 2e⁻ $\leftrightarrow$ (Na₂O)₂*, where * denotes the active sites of the reaction intermediates [2,35,36]. During the discharge process, the ORR on the cathodic M₂XO₂ MXenes proceeds via an initial combination of O₂ with (Na⁺ + e⁻) to form an adsorbed NaO₂*. Secondly, the adsorbed NaO₂* reacts with (Na⁺ + e⁻) to generate Na₂O₂*. After that, Na₂O₂* further reacts with (Na⁺ + e⁻) to form the discharge product (Na₂O)₂*. During charging, the OER occurs by gradually removing sodium from (Na₂O)₂* to produce oxygen.

Figure 8 shows the ORR/OER free energy profiles for the M₂CO₂ carbides (Ti₂CO₂, Zr₂CO₂, and Hf₂CO₂) and M₂NO₂ nitrides (Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂). In Figure 8a–f, the green arrowheads represent the ORR process from left to right when discharging, while the purple arrowheads indicate the OER process from right to left when recharging. The ORR is the process of (Na₂O)₂ nucleation on M₂XO₂ MXenes. At the open-circuit potential U = 0 V, all three steps have a downward free energy trajectory on both the M₂CO₂ and M₂NO₂ surfaces (see the black paths in Figure 8a–f), indicating the spontaneous nucleation (i.e., ORR) and endothermic decomposition (i.e., OER) of (Na₂O)₂. As shown in Figure 8a–f, due to the weakened adsorption of the Na_xO₂ (x = 1, 2, and 4) intermediates, the total free energy changes for O₂ → (Na₂O)₂* (ΔG(O₂ → (Na₂O)₂*)) on M₂XO₂ MXenes decrease with the decreasing metal atomic number, leading to the easier decomposition of (Na₂O)₂* in the OER process. Furthermore, the ΔG(O₂ → (Na₂O)₂*) for the M₂CO₂ carbides is less than that for the M₂NO₂ nitrides, suggesting that the carbides can enhance the (Na₂O)₂ decomposition in the OER process.

At an equilibrium potential (U_e), the ORR and OER processes reach an electrochemical equilibrium state (see the orange paths in Figure 8a–f). In this work, U_e is calculated to be 1.50, 2.53, 2.81, 2.89, 2.76, and 3.46 V for Ti₂CO₂, Zr₂CO₂, Hf₂CO₂, Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂, respectively. When U_e is applied, the formation of NaO₂* and Na₂O₂* along the ORR pathway is still downhill for Ti₂XO₂ and Zr₂XO₂, but the step of (Na₂O)₂* formation is changed to be uphill and endothermic (see Figure 8a,b,d,e). For Hf₂XO₂, both Na₂O₂* and (Na₂O)₂* formation steps are uphill on the ORR free energy profiles, but the last (Na₂O)₂* formation step must overcome a larger energy platform (see Figure 8c,f). Thus, the rate-determining step (RDS) of the ORR is the last formation of (Na₂O)₂* (i.e., Na₂O₂* → (Na₂O)₂*) on all M₂XO₂ MXenes. For the OER pathway, after the downhill (Na₂O)₂* decomposition on Ti₂XO₂ and Zr₂XO₂, both the Na₂O₂* and NaO₂* decomposition steps are uphill, but the NaO₂* decomposition requires more energy than the Na₂O₂* decomposition (see Figure 8a,b,d,e). Moreover, only the last NaO₂* decomposition step in the OER process is uphill on Hf₂XO₂ (see Figure 8c,f). Therefore, the NaO₂* decomposition forms the RDS of the OER on all considered M₂XO₂ MXenes.

The discharging potential (U_Ds) is the highest voltage that drives all ORR steps energetically downhill on free energy profiles (the blue paths from left to right in Figure 8a–f). Meanwhile, the charging potential (U_C) is the lowest potential that drives all OER steps energetically downhill on the free energy profiles (the pink paths from right to left in Figure 8a–f). For various M₂XO₂ MXenes, their U_Dc/U_C values are different, which is caused by the different free energy changes of RDS during the ORR/OER process. To further evaluate the discharge–charge efficiency of Na−O₂ batteries, the ORR (${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$) and OER (${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$) overpotentials were calculated by ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}=U_{\mathrm{e}}-U_{\mathrm{D}\mathrm{c}}$ and ${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}=U_{\mathrm{C}}-U_{\mathrm{e}}$, respectively, while the total overpotential (${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$) was calculated by ${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}={\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}+{\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$, which are tabulated in

Table 1. The ORR (${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$), OER (${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$), and total (${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$) overpotentials (in V) for M₂XO₂ MXenes.

Overpotentials	Ti2CO2	Ti2NO2	Zr2CO2	Zr2NO2	Hf2CO2	Hf2NO2
${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$	0.23	0.87	0.47	0.76	1.03	1.25
${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$	0.32	0.92	0.88	1.05	2.68	2.85
${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$	0.55	1.79	1.35	1.81	3.71	4.10

. The ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$/${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$ overpotentials are calculated to be 0.23/0.32, 0.47/0.88, 0.76/1.05, 1.03/2.68, 0.87/0.92, 0.76/1.05, and 1.25/2.85 V for Ti₂CO₂, Zr₂CO₂, Hf₂CO₂, Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂, respectively. For all considered M₂XO₂ MXenes, the OER overpotentials are higher than the ORR overpotentials, which suggests that the OER kinetics are slower than the ORR kinetics, forming a bottleneck in the performance of Na−O₂ batteries. This situation is in good agreement with the experimental results, where the hard decomposition of the discharge products results in high charging overpotentials, low round trip efficiency, and poor rechargeability [2]. As shown in Table 1, the total overpotential (${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$) is calculated to be 0.55, 1.35, 3.71, 1.79, 1.81, and 4.10 V for Ti₂CO₂, Zr₂CO₂, Hf₂CO₂, Ti₂NO₂, Zr₂NO₂, and Hf₂NO₂, respectively, suggesting the M₂CO₂ carbides exhibit lower overpotential than the M₂NO₂ nitrides. Furthermore, the overpotentials of M₂XO₂ MXenes decrease with the decreasing atomic number of M. Among all considered M₂XO₂ MXenes, Ti₂CO₂ has the lowest overpotentials of ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$ (0.23 V), ${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$ (0.32 V), and ${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$ (0.55 V), indicating the highest catalytic activity. As shown in Figure 9, the ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$, ${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$, and ${\eta }_{\mathrm{T}\mathrm{O}\mathrm{T}}$ overpotentials of Ti₂CO₂ MXenes are much lower than those of Si₂Se₂ (0.62, 0.38, and 1.00 V) [39], MoSSe (0.49, 0.59, and 1.08 V) [3], SiSe₂ (0.46, 0.73, and 1.19 V) [39], and NCF (0.56, 0.83, and 1.49 V) [40], indicating Ti₂CO₂ possesses an outstanding catalytic performance as the cathode for Na−O₂ batteries.

For all catalysts, the RDS of the ORR process is the reduction of Na₂O₂* to (Na₂O)₂*. Therefore, the ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$ overpotential is determined by the adsorption energy of Na₂O₂* on M₂XO₂ MXenes. Meanwhile, the RDS of the OER process is the decomposition of NaO₂*, and thus the NaO₂* adsorption energy plays a dominant role in the ${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$ overpotential. For Hf₂NO₂ MXene, the ultra-strong adsorption (see Figure 6b) makes the NaO₂* and Na₂O₂* intermediates firmly adhere to the MXene surfaces, which is difficult to react further, thus forming the highest overpotentials (see Table 1). When Hf₂CO₂ carbides are used as catalysts, the adsorption energy of Na₂O₂* and NaO₂* is reduced effectively, leading to improved overpotentials. Similarly, after reducing the metal atomic number, Ti₂NO₂ exhibits weaker adsorption energy towards Na₂O₂* and NaO₂* and thus has lower overpotentials than Hf₂NO₂. For Ti₂CO₂, it has the weakest Na₂O₂* and NaO₂* adsorption energy, resulting in the lowest ${\eta }_{\mathrm{O}\mathrm{R}\mathrm{R}}$ and ${\eta }_{\mathrm{O}\mathrm{E}\mathrm{R}}$ potentials.

As shown in Figure 5 and Figures S3–S5, the surface nucleophilic O groups of M₂XO₂ MXenes prefer to combine with the electropositive Na atoms of Na_xO₂ (x = 1, 2, and 4) to activate the Na–O bonds. Therefore, compared to free Na_xO₂, the Na–O bonds in Na_xO₂* are elongated efficiently, while the O–O bonds in Na_xO₂* are shortened (see Tables S2–S4), which is conducive to the deintercalation of sodium in the charging process. The charge population analyses in Tables S5–S7 indicate that a strong electron transfer from Na to surface O groups occurs on the Na_xO₂*-adsorbed M₂XO₂ MXenes, which weakens the ionic interaction in the Na–O bonds of Na_xO₂*. After the Na_xO₂* (x = 1, 2, and 4) adsorption on M₂XO₂ MXenes, the change in the O–O and Na–O bonds in (Na₂O)₂* is the smallest (Tables S2–S4), suggesting that (Na₂O)₂* is the most difficult to activate among Na_xO₂* intermediates, which is in good accordance with the experimental reports [25,37]. Furthermore, for all considered M₂XO₂ MXenes, M₂CO₂ carbides with a lower metal atomic number have a stronger activation effect on Na_xO₂* intermediates, as reflected by the greater change in the Na–O and O–O bond lengths of Na_xO₂* (see Tables S2–S4).

To further explore the effect of metal (M) and nonmetal (X) atoms, the PDOS analyses were carried out for the Na_xO₂* (x = 1 and 2)-adsorbed Ti₂CO₂, Ti₂NO₂, Ti₂CO₂, and Hf₂NO₂ MXenes (see Figure 10). As shown in Figure 10, after adsorption, Na_xO₂* forms strong ionic bonding and anti-bonding states with the MXene substrates. The bonding states located below the Fermi energy level are mainly composed of surface O p-orbitals (the orange color in Figure 10a–h), while the anti-bonding states located above the Fermi energy level are primarily composed of Na-s orbitals (the purple color in Figure 10a–h), indicating the electrons transfer from Na of Na_xO₂* to the surface O groups of M₂XO₂ substrates. The main peaks of the bonding and anti-bonding states are shown as the orange and purple dotted lines in Figure 10, respectively. The difference between the two main peaks represents the energy gap between the bonding and anti-bonding states. The energy gap is calculated to be 7.01, 7.53, 7.82, and 8.22 eV for NaO₂*-adsorbed Ti₂CO₂, Ti₂NO₂, Hf₂CO₂, and Hf₂NO₂, respectively (see Figure 10a–d), while it is 7.28, 7.65, 7.82, and 8.56 eV for Na₂O₂*-adsorbed Ti₂CO₂, Ti₂NO₂, Hf₂CO₂, and Hf₂NO₂, respectively (see Figure 10e–h). The larger the energy gap, the stronger the interaction between the Na-s orbitals and surface O p-orbitals; that is, the stronger the adsorption of Na_xO₂ on the substrates. On the same substrate, the energy gap of Na₂O₂* is larger than that of NaO₂*, suggesting stronger adsorption of Na₂O₂* than NaO₂*. For the same Na_xO₂ adsorbent, the energy gap on the M₂NO₂ nitrides is greater than that on the M₂CO₂ carbides, indicating that the M₂NO₂ nitrides exhibit stronger adsorption towards Na_xO₂ than the M₂CO₂ carbides. Ti₂CO₂ has the smallest energy gap, so the interaction with the Na_xO₂ intermediate is the weakest, resulting in the lowest overpotential in the ORR/OER processes. Furthermore, the weakest interaction between Ti₂CO₂ and Na_xO₂ originates from the lowest p-band center of the surface O for Ti₂CO₂ among all M₂XO₂ MXenes (see Figure 7).

3. Materials and Methods

In this work, the Cambridge Serial Total Energy Package (CASTEP) was adopted for the DFT calculations [41,42]. The spin-polarized method was used to account for different wavefunctions for different spins. The Perdew–Burke–Ernzerhof (PBE) functional was chosen as the DFT exchange-correlation potential [43,44]. PBE may underestimate the band gaps and overestimate adsorption energies due to their self-interaction error and insufficient description of long-range electronic correlations. However, the metallic/semimetallic properties of MXenes make the underestimation of the bandgap have little impact on the catalytic activity (such as ORR/OER). The study of MXene systems demonstrates that computational approaches, including PBE, PBE+U, the meta-GGA SCAN functional, and HSE06, yield highly comparable results in structural, electronic, and magnetic properties [45,46]. Additionally, the error in adsorption energy can be partially corrected using DFT-D3. The PBE functional combined with DFT-D3 dispersion correction is the most widely used and validated approach for MXenes systems, particularly in catalytic studies involving surface adsorption [47,48,49]. The DFT-D3 method has proven effective for both molecules and solids, achieving a CCSD(T) accuracy typically within 10% [50]. Therefore, PBE-D3 was used in this work. The valence electrons were described using a plane wave basis, and the norm-conserving pseudopotential represented the ionic cores [51,52]. After convergence testing (see Figures S6 and S7), the 6 × 6 × 1 k-point Monkhorst–Pack mesh and the 500 eV cutoff energy of the plane wave were chosen for all calculations. The convergence criteria for geometric optimization were as follows: an energy less than 10⁻⁵ eV atom⁻¹, a force less than 0.03 eV Å⁻¹, a stress less than 0.05 Gpa, and a displacement less than 0.001 Å. A 20 Å vacuum layer was added to the surface of M₂XO₂ MXenes to eliminate the influence of mirror structures.

The formation energy (E_f) of M₂XO₂ MXenes was determined by

$$E_{\mathrm{f}}=\left[E_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-n_{\mathrm{M}}{E}_{\mathrm{M}}-n_{\mathrm{X}}{E}_{\mathrm{X}}-n_{\mathrm{O}}{E}_{\mathrm{O}}\right]/n_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$$

(1)

where E_total is the energy of the M₂XO₂ system, E_M is the energy of a single M (Ti, Zr, or Hf) atom in bulk metal, E_X is the energy of a single X (C or N) atom in graphene or N₂, n_total is the total atom number in the M₂XO₂ system, and n_M, n_X, and n_O are the numbers of the M, X, and O atoms in the M₂XO₂ system, respectively.

The adsorption energy (E_ads) was determined by

$$E_{\mathrm{a}\mathrm{d}\mathrm{s}}=E_{\mathrm{t}\mathrm{o}\mathrm{t}}-E_{\mathrm{s}\mathrm{u}\mathrm{b}\mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{e}}-E_{\mathrm{a}\mathrm{d}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{e}}$$

(2)

where E_tot, E_substrate, and E_adsorbate denote the energy of the adsorption system, the substrate, and the adsorbate, respectively.

During the discharging/charging process, the free energy change (ΔG) of the intermediates in each step was described as:

$$∆G=∆E+{∆E}_{\mathrm{Z}\mathrm{P}\mathrm{E}}-T∆S-neU$$

(3)

where ΔE, ΔE_ZPE, and ΔS denote the calculated changes in the energy, zero point energy, and entropy at the temperature of T = 298 K, respectively. n is the number of transferred electrons at the potential of U. The theoretical overpotentials ƞ for the ORR and OER were calculated by ƞ_ORR = U_e − U_Dc and ƞ_OER = U_C − U_e, respectively. In this definition, U_Dc and U_C are the discharge and charge potentials calculated by U_Dc = min (ΔG/ne) and U_C = max (ΔG/ne), respectively. U_e is the equilibrium potential calculated by U_e = −ΔG/ne.

The p-band center (ɛ_p) was defined as

$$[{\epsilon }_{\mathrm{p}}={\displaystyle \frac{{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}E{\rho }_{\mathrm{p}}\left(E\right)dE}{{\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\rho }_{\mathrm{p}}\left(E\right)dE}}]$$

(4)

where ${\rho }_{\mathrm{p}}\left(E\right)$ is the density of the p-state at the level of E.

4. Conclusions

In this work, six carbide/nitride MXene models (M₂XO₂, M = Ti, Zr, and Hf, X = C and N) were constructed to evaluate their catalytic activity as cathodes for Na−O₂ batteries. The first-principles calculations suggest that the M₂CO₂ MXenes show semiconductor-like properties, mirrored by the pseudogaps around the Fermi level, while the M₂NO₂ MXenes are conductors, as reflected by the high intensity of DOSs at the Fermi level. For all M₂XO₂ MXenes, the OER overpotential during charging is greater than the ORR overpotential during discharging, forming a performance bottleneck of Na−O₂ batteries. The surface nucleophilic O groups of M₂XO₂ MXenes tend to bind with the Na atoms of Na_xO₂ intermediates to activate the Na−O bonds, which is conducive to the deintercalation of sodium in the charging process. However, the too-strong adsorption of Na_xO₂ intermediates leads to high overpotentials on M₂XO₂ MXenes. Due to the downward shift of the p-band centers of the surface O groups, the Na_xO₂ adsorption on the M₂CO₂ carbides is weaker than that on the M₂NO₂ nitrides and is further weakened with a decreasing M atomic number. Therefore, the overpotentials decrease in the order of Hf₂NO₂ > Hf₂CO₂ > Zr₂NO₂ > Ti₂NO₂ > Zr₂CO₂ > Ti₂CO₂. Notably, the Ti₂CO₂ MXene shows ultralow ORR, OER, and total overpotentials (0.23, 0.32, and 0.55 V), making it an excellent candidate for cathodes in Na−O₂ batteries.

Building on these findings, future studies could focus on (1) exploring diverse MXene compositions (e.g., M₃X₂, M₄X₃) or transition metals (V, Mo) to tailor electronic/adsorption properties, (2) surface modifications (e.g., heteroatom doping) to fine-tune intermediate binding and reduce overpotentials, and (3) experimental validation of the stability and catalytic performance of Ti₂CO₂ MXenes for practical application. Integrating machine learning with computational screening may expedite MXene discovery, while in situ techniques could unravel dynamic reaction mechanisms. These efforts would bridge theoretical insights with real-world battery performance, fostering the development of efficient and durable Na–O₂ systems.