Construction of Single-Atom Catalysts for N, O Synergistic Coordination and Application to Electrocatalytic O₂ Reduction

Abstract

Replacing expensive platinum oxygen reduction reaction (ORR) catalysts with atomically dispersed single-atom catalysts is an effective way to improve the energy conversion efficiency of fuel cells. Herein, a series of single-atom catalysts, TM-N₂O₂C_x (TM=Sc-Zn) with TM-N₂O₂ active units, were designed, and their catalytic performance for electrocatalytic O₂ reduction was investigated based on density functional theory. The results show that TM-N₂O₂C_x exhibits excellent catalytic activity and stability in acidic media. The eight catalysts (TM=Sc, Ti, V, Cr, Mn, Fe, Co, and Ni) are all 4e⁻ reaction paths, among which Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x follow dissociative mechanisms and the rest are consistent with associative mechanisms. In particular, Co-N₂O₂C_x and Ni-N₂O₂C_x enable a smooth reduction in O₂ at small overpotentials (0.44 V and 0.49 V, respectively). Furthermore, a linear relationship between the adsorption free energies of the ORR oxygen-containing intermediates was evident, leading to the development of a volcano plot for the purpose of screening exceptional catalysts for ORR. This research will offer a novel strategy for the design and fabrication of exceptionally efficient non-precious metal catalysts on an atomic scale.

1. Introduction

Fuel cells (FCs) have garnered much attention as a technology for converting chemical energy into electrical energy because of their high energy conversion efficiency, high energy density, and non-polluting characteristics [1,2]. Compared with the anode reaction, the oxygen reduction reaction (ORR) at the cathode is kinetically slow, and in-depth research on the ORR process is of great significance for improving the overall performance of FCs [3,4,5]. Superior catalysts can be effective in solving the bottleneck problem of ORR. Among the many developed catalysts, Pt and its alloys are considered the best ORR catalysts for their high current density and low initial voltage. However, the scarcity of Pt resources, expensive price, poor durability, and easy deactivation limit its large-scale commercial application. Therefore, developing ORR electrocatalysts with a high catalytic activity, cheap availability, and low overpotential has recently been a hot research topic [6,7,8].

Single-atom catalysts (SACs) can achieve a high dispersion of metal atoms, which not only maximizes the utilization of metal atoms but also significantly improves the catalytic activity of the catalyst [9,10,11,12]. Since Pt₁/FeO_x single-atom catalysts were first reported by Zhang et al., a series of SACs have been notified and widely used electrocatalysis [13]. Guo et al. investigated the catalytic performance of a transition metal-anchored N-doped graphene single-atom catalyst (TMN_x-GR) for electrocatalytic CO₂ reduction based on density functional theory [14]. The results showed that TMN_x-GR exhibited good catalytic activity, with NiN₄-GR showing the best selectivity for the product CO. Chen’s group successfully constructed single-atom Cu-containing catalysts on N-doped carbon nanosheets and applied them to overall water splitting [15]. The results indicate that the oxygen evolution reaction at 200 mV and the hydrogen evolution reaction at 216 mV was achieved at a current density of 10 mA·cm⁻², providing a new strategy for constructing non-precious metal catalysts. Wang et al. investigated the potential of transition metal-embedded g-C₄N₃ (TM@g-C₄N₃) single-atom catalysts for nitrogen reduction reactions (NRR) by a high-throughput screening system. Among the 30 candidate materials [4], V@g-C₄N₃ was identified as the most active NRR catalyst, with a limiting potential of −0.37 V. This work leads the way for the construction of efficient NRR single-atom catalysts using g-C₄N₃ as a novel carrier. Yi and co-workers prepared atomically dispersed Fe-N_x species (Fe loading up to 8.3 wt %) on porous porphyrin triazine-based frameworks (FeSAs/PTF) using a simple isothermal method [16]. FeSAs/PTF-600 has a high density of single-atom Fe-N₄ active sites and a high layered porosity, and good electrical conductivity, resulting efficient activity, methanol resistance, and ORR superstability under alkaline and acidic conditions. Hunter et al. theoretically investigated the catalytic performance of N-doped graphene single-atom catalysts (M₁M₂@N₆V₄ and M₁M₂@N₈V₄, M = Co, Pt, Fe, Ni) for ORRs [17]. It was found that CoPt@N₈V₄ exhibited the most desirable ORR catalytic activity (ƞ = 0.30 V), and a basis for the screening of highly active ORR catalysts was proposed by volcano mapping.

Most of the reported ORR SACs are of metal–N₄ coordination [18,19]. However, recent studies have found that single-atom catalysts with N and O co-coordination with metal atoms exhibit excellent catalytic activity, even better than metal–N₄ coordination catalysts. Ge et al. investigated the catalytic performance of the oxygen reduction reaction (ORR) of M-N_4-xO_x (M=Fe, Co, and Ni; x = 1–4) in detail based on density functional theory [20]. The results show that Co-N₃O₁ and Ni-N₂O₂ exhibit the best catalytic activity, with overpotentials of 0.27 and 0.32 V, respectively, which is significantly better than the Pt catalysts. Electronic structure and density of states analyses revealed that one of the reasons for the higher activity of Co-N₃O₁ and Ni-N₂O₂ is their small energy gap. O doping can improve the electronic structure of the original catalyst, which can adjust the adsorption capacity of ORR intermediates. Dong et al. successfully synthesized a low-Mn-content single-atom catalyst (Mn-NO/CNs) with Mn-N₂O₂ sites, which exhibited good activity in the catalysis of CO₂ [21]. The results show that the addition of oxygen atoms changed the coordination environment surrounding the Mn atoms, modifying the electronic structure of the catalyst and improving the catalytic efficiency of Mn-NO/CNs for CO₂ reduction. Wei et al. designed seven two-dimensional (2D) metal–organic framework (MOF) materials with TMN₂O₂ ligand units and conducted theoretical investigations into their catalytic activities towards oxygen reduction and evolution reaction (ORR and OER). The findings demonstrate that CoN₂O₂ manifests superior catalytic performance, displaying low overpotential values of 0.33 V and 0.30 V for ORRs and OERs, respectively [22]. The above reports open up new avenues for the development of ORR catalysts.

Although TM-N₂O₂ active units have been reported as catalytic materials for ORR applications, it has not been explicitly addressed whether the catalytic activity of TM-N₂O₂ active units would be significantly influenced by ligand variations. Based on this, we devised a series of TM-N₂O₂ (TM=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) coordination-type single-atom catalysts (TM-N₂O₂C_x) by employing 4-hydroxy benzonitrile as the ligand and investigated their catalytic activities and reaction mechanisms for electrocatalytic O₂ reduction in an acidic environment. The comprehensive analysis and discussion of the stability, reaction pathway, overpotentials, and electronic structure of TM-N₂O₂C_x elucidate that a majority of the catalysts exhibit remarkable catalytic activity. Furthermore, a comparative analysis of the work conducted by Wei et al [22]. revealed that changing the ligand does indeed exert an effect on the catalytic activity of the TM-N₂O₂ site, but without altering the trend of the volcano curve. These findings will serve as a stimulus for further experimental and theoretical explorations in ORRs.

2. Results and Discussion

2.1. The Structural Features of TM-N₂O₂C_x Single-Atom Catalysts

Figure 1 is the top (1a) and side views (1b-d) of the unit cell structure model of the TM-N₂O₂C_x single-atom catalyst. It can be seen from Figure 1a that the unit cell of the TM-N₂O₂C_x single-atom catalyst contains one transition metal atom, two nitrogen atoms, two oxygen atoms, fourteen carbon atoms, and eight hydrogen atoms, and each transition metal atom coordinates with two nitrogen atoms and two oxygen atoms simultaneously. Due to the different orientations of ligands in the bonding process, the TM-N₂O₂C_x single-atom catalyst has three initial configurations, as shown in Figure 1b–d, respectively. The structural optimization of ten SACs of the first transition metal series (Table S1) offering the stable configurations of Sc-N₂O₂C_x and Cu-N₂O₂C_x are demonstrated in Figure 1b,d, respectively. Structural optimization of ten single-atom catalysts (SACs) from the first transition metal series (refer to Table S1) reveals that stable configurations of Sc-N₂O₂C_x and Cu-N₂O₂C_x are illustrated in Figure 1b and 1d, respectively. In comparison, the regular structures of the remaining eight catalysts are shown in Figure 1c.

A Hirshfeld charges analysis shows that the metal atoms in the ten SACs all have partial positive charges [23], while the N and O atoms coordinated with them all have partial negative charges (Table S1), which indicates that there is charge transfer between the metal atoms and their neighboring atoms in the process of binding with the ligand so that the metal atoms can effectively bind with the ligand. Figure S1 is the projected partial density of states of the TM-N₂O₂C_x SACs. The green line is the 3d orbit of the metal atoms, while the blue and red lines are the 2p orbitals of the N and O atoms, respectively. The orbit’s degree of overlap can reflect the interatomic interaction’s strength. The better the overlap, the stronger the interaction; on the contrary, the weaker it is. Figure S1 shows that the 3d orbitals of the metal atoms and the N and O atoms in the ten poor catalysts overlap very well, proving that metal atoms have a strong coordination ability with N and O atoms in ligands. In addition, except for the metal atoms in Sc-N₂O₂C_x, Ni-N₂O₂C_x, and Zn-N₂O₂C_x, the metal atoms in the other SACs have magnetism and the Mn atom possesses the highest magnetic moment of 4.504 μB, which may also affect the catalytic activity of the catalysts.

2.2. The Structural Stability of TM-N₂O₂C_x

As the structural stability of the catalyst plays an essential role in maintaining the catalytic activity of the motivation, the thermodynamic and electrochemical stability of TM-N₂O₂C_x were studied according to the formation energy (E_f) and dissolution potential (U_diss) [24], respectively. E_f and U_diss can be obtained from the formulas E_f = E_TM-N2O2Cx − E_TM − E_N2O2Cx (1) and U_diss = U°_diss − E_f/ne (2) (detailed data are shown in Table S2), where E_TM-N2O2Cx, E_TM, and E_N2O2Cx are the total energies of TM-N₂O₂C_x, TM, and N₂O₂C_x, respectively. U°_diss and n are the standard dissolution potential and the number of electrons involved in the dissolution of transition metals, respectively. The negative value of formation energy indicates that it is an exothermic reaction in the process of a metal atom combining with a ligand to form a single-atom catalyst; so, the more negative the value of formation energy is, the stronger the thermodynamic stability of the catalyst is and vice versa. Figure 2 shows that the formation energies of ten kinds of SACs are negative, indicating that TM-N₂O₂C_x SACs offer good thermodynamic stability.

During the process of electrocatalysis, if the dissolution potential of metal atoms in the single-atom catalyst is relatively low, it becomes easier for these metal atoms to undergo oxidation and subsequently dissolve into the solvent. This phenomenon ultimately leads to a substantial decrease in the overall catalytic activity exhibited by the catalyst. Consequently, in order to enhance the stability of the catalyst, it is essential for the metal atoms within it to possess a higher dissolution potential. The dissolution potentials of metal atoms for all ten catalysts investigated in Figure 2 were found to be greater than 0 V. Notably, these values surpass the standard dissolution potentials of the respective metals (refer to Table S2), thereby indicating the exceptional electrochemical stability displayed by the ten TM-N₂O₂C_x single-atom catalysts that were examined in this study.

2.3. O₂ Adsorption

Since the electrocatalytic oxygen reduction reaction occurs in an aqueous solution, the O₂ molecule must be effectively adsorbed by the catalyst for the response to happen smoothly. To investigate the adsorption capacity of the TM-N₂O₂C_x single-atom catalyst for O₂, the adsorption energy (taking O₂ adsorption as an example) was obtained by the formula: E_ads = E_TM-N2O2Cx-O2 − E_TM-N2O2Cx − E_O2 (3). E_TM-N2O2Cx-O2 is the total energy of the adsorbed O₂ and TM-N₂O₂C_x, while E_TM-N2O2Cx and E_O2 are the total energy of TM-N₂O₂C_x and the single O₂ molecule. If the adsorption energy is negative, indicating that O₂ can be effectively adsorbed, and the more negative the value, the stronger the adsorption is. There are two forms of O₂ adsorption on the catalyst, namely end-on configuration and side-on configuration (Figure 3). The most stable adsorption states and adsorption energies of O₂ on ten single-atom catalysts of the first transition metal series are listed in Table S3, which shows that the stable adsorption states of O₂ on Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x are side-on configuration (Figure 3a). At the same time, the remaining seven are end-on configuration (Figure 3b). Additionally, the adsorption energies of the ten stable states are in the range of −4.22 ~ −0.39 eV, which indicates that O₂ can be effectively adsorbed on the catalyst to facilitate the reduction reaction.

2.4. ORR Catalytic Performance

2.4.1. Selectivity of Reaction (2e⁻ or 4e⁻)

According to the different reduction products, the ORR can be divided into a 2e⁻ pathway to produce H₂O₂ and a 4e⁻ pathway in which the product is H₂O. The 4e⁻ pathway can be divided into a dissociative mechanism and association mechanism (Figure 4). Compared with the 2e⁻ pathway, the 4e^−- pathway has better energy conversion efficiency, so suitable ORR catalysts must have good 4e⁻ selectivity. The intermediate O*OH (* + O₂ + H⁺ + e⁻ → O*OH) is obtained by one-step protonation of O₂. O*OH can be reduced to H₂O₂ through the path O*OH + H⁺ + e⁻ → * + H₂O₂ or O*OH + H⁺ + e⁻ →O* + H₂O to obtain O*; so, it is necessary to determine whether the catalyst is thermodynamically inclined to the 4e⁻ pathway or the 2e⁻ pathway. Therefore, this paper is determined by comparing the formation barrier of H₂O₂ and the barrier to obtain O* and H₂O.

Guo et al. systematically studied the selectivity of ORRs and found that the Gibbs free energy (∆G_O*) of O* for the 4e⁻ pathway should be less than 3.52 eV (∆G_H2O2 − ∆G_H2O) [25]. On the contrary, the Gibbs free energy for the 2e⁻ pathway should be greater than 3.52 eV. The Gibbs free energy of the reaction was determined using the computational hydrogen electrode model (CHE) proposed by Nørskov and co-workers [26], and the details are described in our previous reports [27]. This paper focuses on reactions under strongly acidic conditions (pH = 0). Figure 5 shows that except for Cu-N₂O₂C_x and Zn-N₂O₂C_x, the Gibbs free energy of ∆G_*O for the other eight catalysts is all less than 3.52 eV, indicating that the ORR mechanism of Cu-N₂O₂C_x and Zn-N₂O₂C_x is the 2e⁻ pathway (Figure S2), and the rest of the SACs are more inclined to the 4e⁻ pathway. Next, we focus on exploring the 4e⁻ pathway mechanism of the above eight catalysts.

2.4.2. 4e⁻ Pathway

As previously mentioned, the 4e⁻ pathway encompasses both associative and dissociative mechanisms, with the specific reaction mechanism employed in the 4e⁻ process being dependent on the stable adsorption configuration of O₂ on the catalyst. Figure 6 demonstrates that when the stable adsorption configuration of O₂ is side-on, the 4e⁻ reaction tends to proceed via the dissociative mechanism, whereas when the stable adsorption configuration of O₂ is end-on, the 4e⁻ reaction follows the associative mechanism. Due to the fact that the stabilization of the adsorption configuration on Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x is side-on, the electrocatalytic O₂ reduction on these catalysts adopts the 4e⁻ dissociative mechanism. In contrast, the five catalysts from Cr- N₂O₂C_x to Ni- N₂O₂C_x exhibit associative mechanisms for the 4e⁻ pathway.

Figure 7 and Figure S3 show the free energy diagrams of the 4e⁻ pathway of electrocatalytic O₂ reduction for the eight TM-N₂O₂C_x single-atom catalysts at three different applied potentials. The black and blue lines represent the applied potentials of 0 V and 1.23 V, respectively, while the red line represents the limiting potential. Figure 7 shows that each step of the protonation process of O₂ reduction by Mn-N₂O₂C_x, Fe-N₂O₂C_x, Co-N₂O₂C_x, and Ni-N₂O₂C_x without applied potential is exothermic; however, the final step of protonation (O*H + H⁺ + e⁻ → * + H₂O) in the 4e⁻ reaction catalyzed by Sc-N₂O₂C_x, Ti-N₂O₂C_x, V-N₂O₂C_x, and Cr-N₂O₂C_x is an endothermic reaction (Figure S3).

The rate-determining step was determined by comparing the maximum increase in the protonation-free energy in the 4e⁻ reaction. It was found that except for Ni-N₂O₂C_x, of which the rate-determining step was * + O₂ + H⁺ + e⁻ → O*OH (Figure 7d), the remaining seven catalysts were all O*H + H⁺ + e⁻ → * + H₂O (

Table 1. The calculated rate-determining steps, limiting potentials (U_L/V), and over-potential (ƞ/V) for the ORR of the TM-N₂O₂C_x SACs are listed.

TM-N2O2Cx	PDS	UL	ƞ
Sc-N2O2Cx	*OH → * + H2O	−1.68	2.91
Ti-N2O2Cx	*OH → * + H2O	−1.44	2.67
V-N2O2Cx	*OH → * + H2O	−0.80	2.03
Cr-N2O2Cx	*OH → * + H2O	−0.02	1.25
Mn-N2O2Cx	*OH → * + H2O	0.23	1.00
Fe-N2O2Cx	*OH → * + H2O	0.35	0.88
Co-N2O2Cx	*OH → * + H2O	0.79	0.44
Ni-N2O2Cx	* + O2 → O*OH	0.74	0.49
Cu-N2O2Cx	* + O2 → O*OH	0.70	0.53
Zn-N2O2Cx	O*OH→ *+H2O2	0.30	0.93

). The limiting potential (U_L) of the ORR can be determined according to the formula U_L = −ΔG_max/ne (4), where ΔG_max and n are the increase in the free energy in the rate-determining step and the number of electrons transferred in the reaction, respectively. Finally, the overpotential (ƞ) of the ORR was determined by the difference between U_L and 1.23 V (ƞ = U_L − 1.23 V), and the detailed data statistics are listed in Table 1.

Among the eight SACs investigated, the limiting potentials of Mn-N₂O₂C_x, Fe-N₂O₂C_x, Co-N₂O₂C_x, and Ni-N₂O₂C_x are all greater than 0 V. At the same time, Sc-N₂O₂C_x, Ti-N₂O₂C_x, V-N₂O₂C_x, and Cr-N₂O₂C_x display limiting potentials lower than 0 V; especially, Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x are all lower than −0.80 V, which results in their overpotentials all being greater than 2 V, meaning that more external potentials need to be applied for the occurrence of the ORR. In comparison, the limiting potential values of the other five catalysts are relatively positive, lowering the corresponding overpotential. With the exception of Cr-N₂O₂C_x, whose overpotential exceeds 1 V, the overpotentials of the other catalysts are all lower than 1 V. Notably, Co-N₂O₂C_x and Ni-N₂O₂C_x possess limiting potentials of 0.79 V and 0.74 V, respectively, leading to overpotentials below 0.50 V, which means that the ORR catalytic performance of Co-N₂O₂C_x and Ni-N₂O₂C_x is comparable to that of Pt catalysts with a working potential of 0.78 V [26] and is better than that of FeN₄-doped graphene (0.35 V) [28], The above results show that Co-N₂O₂C_x and Ni-N₂O₂C_x are expected to be promising ORR catalysts.

2.5. Scaling Relationship between Oxygen-Containing Intermediates

The catalytic performance of the catalyst is determined by its electronic structure. According to Sabatier’s principle, an excellent catalyst has appropriate adsorption capacity for reaction intermediates, which is neither strong nor weak. If the catalyst’s adsorption capacity is too high, it prevents intermediate detachment, causing the catalytic active site to become passivated and, finally, leads to a considerable loss in catalytic performance [29]. Conversely, if the adsorption capacity is too weak, the adsorption of intermediates on the catalyst surface is not favorable, making the reaction unable to proceed. Therefore, if there is a relationship between the adsorption energies of the ORR intermediates, we can effectively discover and design the most suitable ORR catalysts by the descriptor-based method.

Figure 8a–c shows the Gibbs adsorption free energy relationships between different reaction intermediates (such as O*OH, O*H, O*) for the electrocatalytic O₂ reduction by TM-N₂O₂C_x single-atom catalysts. The Gibbs adsorption free energy relative to H₂O and H₂ were calculated based on the following equations: ΔG_{O*H =} G_O*H + 0.5G_H2 − G* − G_H2O (6); ΔG_{O* =} G_O* + G_H2 − G* − G_H2O (7); ΔG_{O*OH =} G_O*OH + 1.5G_H2 − G* − 2G_H2O (8). G* is the free energy of TM-N₂O₂C_x, while G_H2 and G_H2O represent the gas phase free energy of H₂ and H₂O molecules, respectively. The results indicate that no matter the active metal atom, there is a universal scaling relation between O*OH, O*H, and O*. ΔG_O*H can be represented by ΔG_O*OH through the function ΔG_O*H = 1.036ΔG_O*OH − 3.214 eV (Figure 8a) or by ΔG_O* through the function ΔG_O*H = 0.502ΔG_O* − 0.435 eV (Figure 8b). The coefficients of determination (R²) are 0.988 and 0.969, respectively, indicating a very strong linear relationship between ΔG_O*H and ΔG_O*OH or ΔG_O*. In addition, Δ G_O*OH can be created by Δ G_O* through the function Δ G_O*OH = 0.479 Δ G_O* −2.689 eV (Figure 8c), and the same strong linear relationship exists between ΔG_O*OH and ΔG_O* (R² = 0.957). These results are in agreement with previous studies [30,31]. Thus, the catalytic activity of TM-N₂O₂C_x single-atom catalysts for electrocatalytic O₂ reduction can be described by the descriptors ΔG_O*H, ΔG_O*OH, or ΔG_O*.

Figure 8d shows that the adsorption strength of TM-N₂O₂C_x to O*OH (ΔG_O*OH) significantly affects the limiting potential of ORR. With the increasing value of ΔG_O*OH, the limiting potential (U_L) shows a trend of increasing and then decreasing, and there is a significant volcanic relationship between ΔG_O*OH and U_L. Among the ten TM-N₂O₂C_x single-atom catalysts studied in this paper, the limiting potentials of Co-N₂O₂C_x and Ni-N₂O₂C_x are very close to the top of the volcano diagram, making their limiting potential values closest to the potential equilibrium value of the ORR (1.23 V) and allowing a small overpotential of 0.44 V and 0.49 V, respectively (Table 1), which is consistent with the overpotential of commercial Pt (0.45 V). In contrast, the limiting potentials of Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x are far from the top of the volcano plot, leading to an ORR with higher overpotentials (>2 V). Therefore, the volcano curve can effectively help us to screen for superior ORR catalysts.

3. Computational Methods

This study is carried out based on the density functional theory of spin polarization with the help of the Dmol³ module [32]. The structure optimization, total energy, and electronic properties of the TM-N₂O₂C_x models are treated using the Perdew–Burke–Ernzerhof (PBE) exchange-related energy generalization in the generalized gradient approximation (GGA) [33], the basis group is used as a double numerical plus polarization basis group, and the core electrons are treated in an all-electron way. To obtain a high accuracy, the energy convergence criterion is 10⁻⁶ Ha, the Monkhorst–Pack grid uses 5 × 5 × 1 K points for structure optimization and 10 × 10 × 1 for performance calculation, and the vacuum layer is set to 15 Å to eliminate the interaction between TM-N₂O₂C_x layers. In addition, Van der Waals dispersion was introduced to better describe the adsorption of O₂ and reaction intermediates on the TM-N₂O₂C_x surface. Since the ORR occurs in solution, a conductor approximation shielding model (COSMO) is usually used for electrocatalytic reactions to better simulate the real reaction environment, and the dielectric constant of the solvent is set to 78.54 in this paper [34].

4. Conclusions

We designed a single-atom catalyst (TM-N₂O₂C_x) with a TM-N₂O₂ coordination unit and investigated its catalytic performance for electrocatalytic O₂ reduction based on density functional theory. The obtained results demonstrate the outstanding thermodynamic and electrochemical stability of TM-N₂O₂C_x. Notably, most catalysts examined in this study follow the 4e⁻ pathway for O₂ reduction, with the exception of Cu-N₂O₂C_x and Zn-N₂O₂C_x which exhibit a 2e⁻ ORR pathway. Sc-N₂O₂C_x, Ti-N₂O₂C_x, and V-N₂O₂C_x conform to the dissociative mechanism, while the rest follow the associative mechanism. Among the ten catalysts studied in this paper, Co-N₂O₂C_x and Ni-N₂O₂C_x display the lowest overpotential (less than 0.5 V), which is equivalent to the overpotential of the benchmark catalyst Pt, making Co-N₂O₂C_x and Ni-N₂O₂C_x possible as alternative candidates to Pt. It is found that there is a scaling relationship between the adsorption-free energy of oxygen-containing intermediates (O*OH, O*H, O*) and a volcano curve between the adsorption-free energy of O*OH and the limiting potential, providing a foundation for the selection of exceptional ORR catalysts.