Edge-doped substituents as an emerging atomic-level strategy for enhancing M–N₄–C single-atom catalysts in electrocatalysis of the ORR, OER, and HER

Abstract

M–N₄–C single-atom catalysts (MN₄) have gained attention for their efficient use at the atomic level and adjustable properties in electrocatalytic reactions like the ORR, OER, and HER. Yet, understanding MN₄'s activity origin and enhancing its performance remains challenging. Edge-doped substituents profoundly affect MN₄'s activity, explored in this study by investigating their interaction with MN₄ metal centers in ORR/OER/HER catalysis (Sub@MN₄, Sub = B, N, O, S, CH₃, NO₂, NH₂, OCH₃, SO₄; M = Fe, Co, Ni, Cu). The results show overpotential variations (0 V to 1.82 V) based on Sub and metal centers. S and SO₄ groups optimize FeN₄ for peak ORR activity (overpotential at 0.48 V) and reduce OER overpotentials for NiN₄ (0.48 V and 0.44 V). N significantly reduces FeN₄'s HER overpotential (0.09 V). Correlation analysis highlights the metal center's key role, with ΔG_*H and ΔG_*OOH showing mutual predictability (R² = 0.92). E_g proves a reliable predictor for Sub@CoN₄ (ΔG_*OOH/ΔG_*H, R² = 0.96 and 0.72). Machine learning with the KNN model aids catalyst performance prediction (R² = 0.955 and 0.943 for ΔG_*OOH/ΔG_*H), emphasizing M–O/M–H and the d band center as crucial factors. This study elucidates edge-doped substituents' pivotal role in MN₄ activity modulation, offering insights for electrocatalyst design and optimization.

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New concepts

Our study introduces a novel concept in the realm of M–N₄–C single-atom catalysts by systematically examining the influence of edge-doped substituents on the electrocatalytic performance of MN₄ in the ORR, OER, and HER. The innovation here lies in our comprehensive exploration of the interactions between various substituents (B, N, O, S, CH₃, NO₂, NH₂, OCH₃, and SO₄) and diverse metal centers (Fe, Co, Ni, and Cu). We demonstrate that strategic edge modification can drastically enhance catalytic activity, revealing unprecedented tunability in MN₄ catalysts. This represents a significant deviation from the traditional focus on metal centers alone, highlighting the critical role of substituents. Our work provides new insights into nanoscience and nanotechnology by correlating the substituent electronic properties, metal center characteristics, and catalytic activity. We identify key determinants such as M–O/M–H bond characteristics and the d band center for efficiency. Furthermore, our application of machine learning algorithms, particularly the KNN model, to predict catalyst performance based on these factors marks a conceptual leap in catalyst design, surpassing conventional trial-and-error methods. This study not only underscores the importance of edge-doped substituents but also establishes a predictive framework for designing high-efficiency electrocatalysts, advancing the field towards more sustainable energy technologies.

1. Introduction

The growing demand for clean and cost-effective energy conversion and storage has led to a search for efficient devices such as fuel cells, metal–air batteries, and water electrolysis systems.^1–4 Key reactions in these processes include oxygen reduction (ORR), oxygen evolution (OER), and hydrogen evolution (HER). To enable widespread application of these technologies, it is crucial to develop low-cost, high-performance catalysts^5,6 that can significantly lower the kinetic barriers of these reactions. However, many current catalysts still rely heavily on precious metals. Among various catalysts explored so far, such as precious metal alloys (e.g., Pt–Hg),^7–10 inexpensive metals (iron, cobalt, nickel, etc.),^11,12 and heteroatom-doped carbon materials,^13–15 carbon-based catalysts with isolated transition metals fixed by nitrogen groups (MN₄) have garnered increasing attention for their atomic-level utilization efficiency and adjustable properties.^16–19

Understanding the origin of true activity in MN₄ catalysts and fine-tuning their performance present challenges for the practical application of MN₄ catalysts.^20,21 It is now recognized that the active sites in MN₄ materials extend beyond the M–N₄ structure (metal center and first coordination shell).²² Factors such as axial coordination,^23–25 the second coordination shell,^26,27 and edge/defect sites^28,29 can also influence catalytic activity to varying degrees. Notably, during the synthesis of MN₄ materials, heteroatoms from the carbon precursor exist not only in coordination with metal ions but also at the edges. These edge heteroatoms significantly impact the electronic structure of MN₄ catalysts and, thus, their activity.^30–33 For instance, S located at the edge of FeN₄ greatly enhances the ORR activity. Mun et al. demonstrated that using SO₂ to extract electrons from the Fe center could optimize intermediates' adsorption capacity, thus improving FeN₄ performance.³⁴ Subsequent research on S-doped FeN₄ materials showed high ORR activity and increased stability.³⁰ Moreover, the presence of O at the edge of CoN₄ leads to the electrocatalytic synthesis of H₂O₂ instead of H₂O. Oxygen-rich CoN₄ catalysts showed enhanced reaction activity from the metal Co center and improved selectivity for H₂O₂ formation from oxygen.³⁵ Recently, edge-enriched CoN₄ materials with oxygen at the edge were found to enhance H₂O₂ synthesis.³³ Additionally, N or O coordination at the edge of FeN₄ contributes to improved ORR performance.^31,36 Understanding the role of edge heteroatoms in MN₄ catalysts and conducting extensive research with various metal centers, substituents, and catalyzed reactions (e.g., the ORR, OER and HER) are essential for practical applications of MN₄ catalysts in different scenarios.

Most understanding of the impact of edge-doped substituents on MN₄ centers currently relies on experimental “point-to-point” studies. However, achieving directed synthesis through theoretical guidance can lead to the cost-effective discovery of efficient catalysts.^37,38 One widely accepted design criterion is the electron-withdrawing/donating strategy proposed by Mun et al. to regulate FeN₄ catalysts.³⁴ They use charge transfer numbers as descriptors to qualitatively assess the performance of Sub@FeN₄, which has been widely adopted. Nevertheless, this approach only provides qualitative insights into Sub's influence on FeN₄ performance, making it challenging to quantitatively compare Subs with similar properties. Additionally, the applicability of this strategy to other transition metals (e.g., Co, Ni, Cu) requires further confirmation. Recently, predictive approaches based on machine learning (ML) algorithms have gained attention. By training ML models with multiple descriptors, including charge, it becomes possible to predict the catalytic activity of catalysts, offering the potential for high-performance, cost-effective screening of Sub@MN₄ systems.^39–41

In this study, we extensively investigated the Sub@MN₄ system (Sub = B, N, O, S, CH₃, NO₂, NH₂, OCH₃, SO₄; M = Fe, Co, Ni, Cu) using density functional theory (DFT). The findings demonstrate that changing the edge-doped substituents and the type of metal centers significantly impact the ORR/OER/HER activity. Correlation analysis of substituent/metal electronegativity, M–N/M–O/M–H bond length, metal d-band center/d-orbital electron numbers, Fundamental Gap (E_g), and *OOH/*H adsorption free energies (ΔG_*OOH/ΔG_*H) reveals the dominant role of the metal center, with a strong mutual predictability between ΔG_*H and ΔG_*OOH (R² = 0.92). For Sub@CoN₄, E_g can predict ΔG_*OOH/ΔG_*H effectively (with R² values of 0.96 and 0.72, respectively). Machine learning (ML) analysis shows that the KNN model effectively predicts catalyst performance (with R² values of 0.955 and 0.943 for ΔG_*OOH/ΔG_*H), where M–O/M–H and d band center descriptors are primary factors characterizing ΔG_*OOH/ΔG_*H. Overall, this work provides insight into the complex regulatory mechanisms of edge-doped substituents on MN₄ activity, offering guidance for understanding the true origin of MN₄ catalyst activity and optimizing and designing efficient MN₄ electrocatalysts.

2. Model construction and calculation method

All calculations were conducted using density functional theory (DFT) in the Gaussian 09 code.⁴² Geometry relaxation and frequency analysis were performed at the wb97xd/def2svp level.^43,44 For the influence of the aqueous solution, the SMD implicit solvent model was applied.⁴⁵ The formula for calculating the free energy (G) of the system is: G = G_vac + ΔG_sol, where G_vac is the free energy under vacuum condition, and ΔG_sol represents the influence of solvent environment on the free energy. Although the effect of hydrogen bonds on water molecules in explicit solvation has been found, here we focus more on the properties of Sub@MN₄ systems in implicit solvation, which is sufficient for description. In addition, the focus of this work is on the influence of Sub on the electronic structure of MN₄ and its adsorption performance. As for the solvation effect caused by the presence of Sub, it is more complicated and is not within the focus of this work.

Fig. 1 depicts the schematic diagrams of edge-doped MN₄ structures constructed in this study, surrounded by a graphene carbon framework containing 36 carbon atoms with edges saturated by hydrogen atoms.^19,46,47 In the study we are preparing for submission (Fig. S39, ESI†), we found that the size of the carbon material affects the properties of the single atoms, but the size selection for different MN₄ catalysts remains a mystery. Therefore, we comprehensively consider the computing power and the main concern of this work (the influence of edge substituents), and choose 36C@MN₄ as the model for this paper, which is used in many studies.^19,46,47 The model maintains 1500 fs through AIMD at 298.15 K, and still has good structure-preserving properties (Fig. S1, ESI†). The investigated metal centers include transition metals Fe, Co, Ni, and Cu, while the edge-doped substituents comprise B, N, O, S, CH₃, NO₂, NH₂, OCH₃, and SO₄. Detailed optimized structures are presented in Fig. S2–S6 (ESI†).

Fig. 1 Schematic representation of the Sub@MN₄ structures (Sub = B, N, O, S, CH₃, NO₂, NH₂, OCH₃, SO₄; M = Fe, Co, Ni, Cu).

2.1 Calculation of Gibbs free energy for the ORR/OER process

The ORR and OER are two reversible reactions, as shown in the following equations. Under acidic conditions, the reaction from left to right represents the ORR, which produces H₂O, while the reaction from right to left represents the OER, which generates O₂. Here, we do not consider new mechanisms, such as those occupied by *OH,⁴⁸ but rather focus on the intrinsic properties of Sub@MN₄ under traditional mechanisms.

4H⁺ + O₂ + 4e⁻ ↔ 2H₂O (1)

The entire ORR process consists of four steps, each of which involves proton-coupled electron transfer reactions, as previously reported:^49,50

* + O₂ + H⁺ + e⁻ → *OOH (2)

*OOH + H⁺ + e⁻ → *O + H₂O (3)

*O + H⁺ + e⁻ → *OH (4)

*OH + H⁺ + e⁻ → * + H₂O (5)

Here, * represents the active site of the catalyst, and *OOH, *O, and *OH are the corresponding adsorbed intermediates. In fact, due to the varying affinities of different substituents for water molecules, the electronic structure of the more hydrophilic Sub@MN₄ configuration is influenced under solvent conditions, which in turn affects the adsorption of intermediates such as *OOH/*H. Regarding the influence of pH and voltage, we have simplified and incorporated their effects into the thermodynamic calculations of free energy through the adoption of the CHE model (as shown in the following equation).⁵¹ Certainly, such simplification is bound to overlook some practical impacts, for instance, the intermediates formed at different pH levels may vary, and the charged state of the catalyst surface at different voltages may differ, which could even lead to complex interactions with molecules in the interfacial double layer. However, for the purposes of this paper, we focus on calculations based on the CHE model, a method that has been widely applied since its proposal. To calculate the Gibbs free energy change for each individual step, the experimentally measured reaction energy of 2H₂O → O₂ + 2H₂ (4.92 eV) is used to calculate the free energy of O₂ gas. The CHE model is employed to equate the chemical potential of gaseous hydrogen under standard conditions to the chemical potential of the proton–electron pair.⁵¹ The influence of electrode potential U on the electron e is expressed through −eU, and the effect of pH is calculated using k_bT ln 10 × pH. The calculation of the Gibbs free energy change for each step is as follows:

ΔG₃ = ΔG_*OOH − 4.92 eV + eU + k_bT ln 10 × pH (6)

ΔG₄ = ΔG_*O − ΔG_*OOH + eU + k_bT ln 10 × pH (7)

ΔG₅ = ΔG_*OH − ΔG_*O + eU + k_bT ln 10 × pH (8)

ΔG₆ = −ΔG_*OH + eU + k_bT ln 10 × pH (9)

The values of ΔG_*OOH, ΔG_*O, and ΔG_*OH are calculated through the following reactions (2H₂O + * → *OOH + 3/2H₂, H₂O + * → *O + H₂, H₂O + * → *OH + 1/2H₂):

ΔG_*OOH = G_*OOH − G_* − (2G_H2O − 3/2G_H2) (10)

ΔG_*O = G_*O − G_* − (G_H2O − G_H2) (11)

ΔG_*OH = G_*OH − G_* − (G_H2O − 1/2G_H2) (12)

Among these four steps, the rate-determining step is defined as the one with the largest Gibbs free energy change. Therefore, the overpotential of the ORR can be calculated using the following equation:

η_ORR = max{ΔG₃, ΔG₄, ΔG₅, ΔG₆}/e + 1.23 (13)

As the OER is the reversible reaction of the ORR, the overpotential can be calculated using the following equation:

η_OER = −min{ΔG₃, ΔG₄, ΔG₅, ΔG₆}/e − 1.23 (14)

It is worth noting that the HER, OER, and ORR are reactions that occur at different electrode potentials, and thus, they do not compete selectively with each other. Specifically, in the water splitting system, when a positive potential exceeding 1.23 V is applied, the OER reaction takes place at the anode, whereas when a negative potential below 0 V is applied, the HER reaction occurs at the cathode. In the case of metal–air batteries, the ORR will occur when the applied positive potential is between 0 to 1.23 V, while the OER will occur when the applied positive potential exceeds 1.23 V.

2.2 Calculation of Gibbs free energy for the HER process

The HER reaction energy can be described by the following equation⁵² (here, we are not focusing on some recent new mechanisms for the HER, such as *H occupying,⁵³ but rather on the performance of MN₄ on traditional mechanisms):

2H⁺ + 2e⁻ → H₂ (15)

This process is divided into the following two steps:

*+ H⁺ + e⁻ → *H (16)

*H + H⁺ + e⁻ → *+ H₂ (17)

In the equations provided, * represents the active site of the catalyst, and *H is the adsorbed intermediate of the HER process. The CHE model is used to equate the chemical potential of gaseous hydrogen under standard conditions to the chemical potential of the proton–electron pair.⁵¹ The influence of electrode potential U on the electron e is expressed through −eU, and the effect of pH is calculated using k_bT ln 10 × pH. The calculation of the Gibbs free energy change for each step is as follows:⁵¹

ΔG₁₆ = ΔG_*H + eU +k_bT ln 10 × pH (18)

ΔG₁₇ = −ΔG_*H+ eU +k_bT ln 10 × pH (19)

where ΔG_*H = G_*H − G_* − 1/2G_H2.

The overpotential of the entire reaction is:

H_HER = max{ΔG₁₆, ΔG₁₇}/e (20)

2.3 Calculation of electronic structure

The analysis of charge and d-band center was conducted using Multiwfn.⁵⁴ The charge was calculated using the atomic dipole moment correction Hirshfeld (ADCH) method,⁵⁵ and the numerical value of the d-band center of the metal M in the MN₄ catalyst was obtained through the following formula:^56,57 d band center = E_c,M – E_F. Here, E_c,M refers to the energy of the d-band position center of the metal M, which is calculated using this formula: E_F refers to the Fermi energy level, and for the isolated system model constructed in this study, we adopt the value of the highest occupied molecular orbital (HOMO) energy level.

The fundamental gap (E_g) was proposed to describe the electron supply capacity of the Sub@MN₄ system.^58,59 It is obtained by subtracting the vertical electron affinity (VEA) from the vertical ionization potential (VIP): E_g = VIP – VEA = (E(N − 1) − E(N)) + (E(N + 1) − E(N)) = E(N − 1) + E(N + 1) − 2*E(N). Here, E(N − 1), E(N + 1), and E(N) represent the electronic energies of the Sub@MN₄ model with N − 1 electrons, N + 1 electrons, and N electrons, respectively.

In order to investigate the effect of Sub on MN₄, we consider the Sub as a whole and calculate their average electronegativity (χ_Sub). The formula for calculating by harmonic average method is as follows:

where N_Sub represents the total number of atoms in Sub N_C, N_H and N_O respectively represent the number of atoms C, H and O in Sub, and χ_C, χ_H, χ_O, χ_S and χ_N respectively represent the Pauli electronegativity of C, H, O, S and N.

3. Results and analysis

3.1 Influence of edge-doping on the ORR/OER/HER performance of the MN₄ structure

This study investigated the regulatory effect of edge-doping coordination on the MN₄ structure by constructing 36 configurations. Four common transition metals (Fe, Co, Ni, Cu) were selected to form the MN₄ configurations, and nine types of edge-doping groups, including four heteroatoms (B, N, O, S) and five substituents (CH₃, NO₂, NH₂, OCH₃, SO₄), were doped at the same edge position to create different Sub@MN₄ models.

First, we evaluated the impact of different Sub on the ORR/OER performance of MN₄. Both the ORR and OER involve three intermediate species (*OOH, *O, *OH) and four elementary steps.⁴⁹ A strong linear correlation between ΔG_*OOH and ΔG_*OH (Fig. 2a) resulted in a minimum overpotential of 0.63 V at the top of the volcano plot (Fig. S8, ESI†). For the ORR, the free energy evolution of various transition metal systems is shown in Fig. 2b and Fig. S7 (ESI†). FeN₄ exhibits a strong adsorption ability, with most Sub@FeN₄ models limited by the last step (*OH desorption) and located on the left side of the volcano plot (Fig. S8e, ESI†). Three groups (O, S, SO₄) further weaken FeN₄'s *OH adsorption, reducing overpotentials to 0.53 V, 0.56 V, and 0.56 V, respectively, thereby decreasing the overpotential of FeN₄ (1.71 V) by 1.15 V (Fig. 2c). The presence of the S/O group (O, S, SO₄) shifts FeN₄ to the top of the volcano plot, consistent with the results of Mun et al. and Maouchue et al. regarding S regulation^30,34 and Ni et al.'s understanding of O regulation.^36,60 In comparison to Sub@FeN₄, the Sub@CoN₄ system exhibits weaker *OH adsorption (Fig. S8, ESI†), and the B, CH₃, N and NH₂ groups further regulate CoN₄'s intermediate adsorption, reducing overpotentials to 0.48 V, 0.63 V, 0.66 V and 0.58 V, respectively. Additionally, the NO₂ group enhances CoN₄'s *OH adsorption, lowering the overpotential to 1.43 V (Fig. 2c). Compared to Sub@FeN₄ and Sub@CoN₄, the Sub@NiN₄ system demonstrates weaker oxygen binding ability, making the first step (*OOH adsorption) the rate-determining step, located on the right side of the volcano plot (Fig. S8, ESI†). Among these groups, NH₂ exhibits a better regulation ability, reducing NiN₄'s overpotential from 1.56 V to 0.91 V. As for the Sub@CuN₄ system, the differentiation in group regulation is more evident. The O group significantly decreases the CuN₄'s overpotential to 0.63 V, while other groups (such as SO₄) raise the overpotential of CuN₄ to 1.44 V. Regarding the Sub@MN₄ catalyzing the OER, certain similarities to the ORR exist, and the overpotentials are summarized in Fig. 2c and compared with the ORR.

Fig. 2 Influence of edge-doping on the ORR/OER/HER performance of the MN₄ structure. (a) Linear correlation between the adsorption free energies of reaction intermediates *OOH and *OH on Sub@FeN₄ catalysts, (b) free energy profiles and (c) overpotentials for OER/ORR pathways on Sub@MN₄, (d) Activity volcano plot, (e) free energy profiles, and (f) overpotentials for HER pathways on Sub@MN₄.

The impact of different Sub on the HER performance of MN₄ is depicted in Fig. 2d–f. Both Sub@CoN₄ and Sub@CuN₄ systems show promising HER potentials, with overpotentials ranging from 0.10 V to 0.73 V and from 0.01 V to 1.79 V, respectively. However, the Sub@NiN₄ system exhibits an overpotential of at least 0.68 V. For FeN₄, NO₂ weakens ΔG_*H from −0.41 eV to 0.01 eV, while N enhances ΔG_*H to −0.67 eV (Fig. 2d and e). It is worth noting that S/O functional groups (O, S, SO₄) also weaken ΔG_*H but cross the top of the volcano plot to the right side (Fig. S9e, ESI†), resulting in no significant increase in overpotential (0.98–1.05 V). In the Sub@CoN₄ system, different N functional groups have varying effects on CoN₄: N and NH₂ have little influence on ΔG_*H, only changing it from 0.66 eV to 0.61 eV and 0.59 eV, while NO₂ enhances CoN₄'s ΔG_*H to −0.73 eV (Fig. S9b and f, ESI†). These differences indicate that even with similar elements in the substituents, the introduction of other elements can lead to significant variations. In the Sub@NiN₄ system, most substituents primarily weaken its ΔG_*H (similar to the weakening of oxygen adsorption energy). O, S, and SO₄ weaken its ΔG_*H to above 1.93 eV (Fig. S9c and g, ESI†). In contrast, in the Sub@CuN₄ system, the substituents primarily enhance ΔG_*H, with B and CH₃ showing the most significant enhancement, crossing the reducing ΔG_*H to 0.01 eV and −0.07 eV, respectively (Fig. S9d and h, ESI†). The summarized overpotentials for the HER are presented in Fig. 2f.

The analysis of the impact of edge substituent on the ORR/OER/HER performance of MN₄ structures reveals diverse and sometimes contrasting effects on different metals. Additionally, the same edge substituent may yield varying outcomes on different metals, indicating the potential for edge substituent regulation varies. These observations imply complex interactions between edge substituents and metal centers. Understanding the underlying regulatory mechanisms and providing quantitative descriptions will aid in the design and optimization of Sub@MN₄-based catalysts.

3.2 Effects of edge substituent coordination on MN₄ structure

The varying degrees of influence of edge substituent on the catalytic performance of the metal center are closely related to the structural variations in MN₄. The metal center charge and metal–nitrogen (M–N) bond lengths serve as direct indicators of the edge substituent effects on the MN₄ structure.⁶¹ To address this, we measured the bond lengths of the four M–N bonds in Sub@MN₄ and analyzed their average as an indicator. Additionally, the metal center ADCH charges were examined to understand the charge transfer between the edge substituent groups and the metal center.⁵⁵ In the following sections, we will delve into how these physical structures vary with different edge substituent groups.

The influence of the edge substituent on the average M–N bond length in the MN₄ structure is illustrated in Fig. 3a and b. The type of metal center M significantly impacts the M–N bond length. In Sub@FeN₄, the Fe–N bond length ranges from 1.88 to 1.93 Å, in Sub@CoN₄, the Co–N bond length ranges from 1.86 to 1.90 Å, in Sub@NiN₄, the Ni–N bond length ranges from 1.86 to 1.89 Å, and in Sub@CuN₄, the Cu–N bond length ranges from 1.92 to 2.00 Å. Generally, the order of M–N bond length from largest to smallest in Sub@MN₄ is: Sub@CuN₄ > Sub@FeN₄ > Sub@CoN₄ > Sub@NiN₄. However, there are two edge substituents with some differences: for O-doping, the order is Sub@CuN₄ > Sub@FeN₄ > Sub@NiN₄ > Sub@CoN₄; for NH₂-doping, the order is Sub@CuN₄ > Sub@CoN₄ > Sub@FeN₄ > Sub@NiN₄. This indicates that these two edge substituents have specific characteristics concerning the metal center. In Sub@FeN₄, B elongates the Fe–N bond, while CH₃ and NO₂ have minimal effects, and other groups shorten the bond length. In Sub@CoN₄, except for N and O which shorten the Co–N bond, other groups elongate it. In Sub@NiN₄, except for B, S, and SO₄ which elongate the Ni–N bond, other groups have little influence. In the Sub@CuN₄ system, all other Sub groups, except for the N group, elongate the Cu–N bond, especially S, which can increase the Cu–N bond length from 1.93 Å to 1.99 Å.

Fig. 3 Effects of edge substituent coordination on the MN₄ structure. (a) Schematic representation of M–N bonds in Sub@MN₄. (b) Average M–N bond lengths in Sub@MN₄. (c) Schematic representation of the influence of substituent groups on the charge of the metal center in Sub@MN₄. (d) Charge of the metal center in Sub@MN₄.

The influence of edge substituent on the charge of the metal center M in the MN₄ structure is demonstrated in Fig. 3c and d. Sub effectively regulates the charge of the metal center M in FeN₄ and CoN₄ over a wide range, within −0.06 to 1.20 a.u. and −0.16 to 0.62 a.u., respectively. In the Sub@FeN₄ system, N, CH₃, and NO₂ have a weak effect on the Fe center, with only a slight change from 1.2 a.u. to 1.11 a.u., while other groups can significantly lower the charge by at least 1.02 a.u. On the other hand, in the Sub@CoN₄ system, except for OCH₃, which reduces the Co charge from 0.62 a.u. to a higher 0.30 a.u., other groups can transfer the Co charge to negative values. In contrast, the ranges of the metal center M charge in Sub@NiN₄ and Sub@CuN₄ are concentrated in 0.01–0.10 a.u. and 0.31–0.45 a.u., respectively, and the changes in charge due to the substituent are within ±0.08 a.u. These indicate different potentials for charge regulation in different metal centers. To measure the changes in electronic transfer during the adsorption of H/OOH in Sub@MN₄, we also calculated and compared the charges before and after H/OOH adsorption, as shown in Fig. S8–S20 (ESI†). Notably, for the Sub@FeN₄ and Sub@CoN₄ systems, the metal center M after H/OOH adsorption remains within a relatively small range, contrasting with the larger range of charges before adsorption. For Sub@FeN₄, except for S/SO₄@FeN₄ with charges of 0.04 and 0.19 a.u. after adsorbing *H, the remaining Sub@FeN₄ have Fe charges within the range of 0.32–0.43 a.u. after *H adsorption. In Sub@CoN₄, the charges of Co after *H adsorption for S/SO₄@CoN₄ are 0.11 and 0.20 a.u., while the others are between 0.23 and 0.26 a.u. A similar trend is observed for *OOH adsorption. In Sub@NiN₄, the charges before and after adsorption follow the trend Sub@NiN₄ < Sub@NiN₄–H < Sub@NiN₄–OOH, with relatively larger fluctuations in charge compared to the previous cases. For Sub@CuN₄, in the unadsorbed configurations, the charge of the metal center is at least above 0.3 a.u., while after *H adsorption, the Cu charge remains around 0.2 a.u. (except for O/S@CuN₄, which is around 0.3 a.u.), and after *OOH adsorption, the Cu charge remains around 0.3 a.u. (except for O/S@CuN₄, which is above 0.4 a.u.).

The analysis above reveals that even when the Subs are positioned at least 4.68 Å away from the metal center M in the MN₄ structure, they exert a substantial influence on the coordination of the metal M with surrounding nitrogen atoms and the charge of the metal center M. Consequently, this results in interactions between the metal M and the reaction intermediates (*OOH, *H) in the ORR/OER/HER, including charge transfer, leading to varying degrees of catalytic performance. These qualitative insights provide a clear understanding of the underlying mechanisms. However, for the development of MN₄ catalysts, it is crucial to quantitatively evaluate and guide the prediction of the performance and synthesis of Sub@MN₄ catalysts, which has significant importance.

3.3 Exploring the origin of activity in Sub@MN₄

3.3.1 Challenges in the quantitative description of the Sub@MN₄ structures. The previous analysis demonstrated the significant impact of edge substituents on MN₄ structures. However, quantifying these effects poses a cutting-edge challenge, as it requires a deeper understanding of edge substituent doping in a more realistic context.⁶² Previous research on quantification (e.g., using descriptors) has mostly focused on simple MN₄ structures and metal alloys, showing some predictive capabilities for properties such as d-band centers (Fig. S26–S29, ESI†), charges, M–O/M–H bond strengths, etc.^34,52,61,63 In our study, we correlated the ΔG_{*OOH_vac}/ΔG_{*H_vac} of pristine MN₄ structures with commonly used descriptors (including d-band centers), revealing a good correlation (R² between 0.67 and 0.86, as shown in Fig. 4a–c and Fig. S23, ESI†), consistent with some previous research trends^63–66 (please note that we used the adsorption free energy under vacuum conditions rather than the solvation free energy, in order to focus more on the influence of the electronic structure of the catalyst itself on the adsorption free energy). In addition, the focus of this work is on the influence of Sub on the electronic structure of MN₄ and its adsorption performance. As for the solvation effect caused by the presence of Sub, it is more complicated and is not within the focus of this work.). However, when edge substituents were introduced to the MN₄ structures, the relationship between ΔG_*OOH/ΔG_*H and descriptors exhibited scattered distributions (Fig. 4d–f and Fig. S24 (ESI†). Also for the free energy in the solvent shown in Fig. S25, ESI†). Moreover, it is worth noting that different descriptors show different trends with adsorption energies, indicating that they describe different inherent properties. This complex and irregular relationship makes it challenging to identify a unified descriptor that can effectively describe the Sub@MN₄ systems.

Fig. 4 Correlations of ΔG_{*OOH_vac} with (a) metal center charge, (b) d-band center, and (c) M–O bond length in pristine MN₄ structures; correlations of ΔG_{*OOH_vac} with (d) metal center charge, (e) d-band center, and (f) M–O bond length in Sub@MN₄ structures; correlations of ΔG_{*OOH_vac} with (g) metal center charge, (h) d-band center, and (i) M–O bond length in Sub@FeN₄ structures.

We further categorized the data according to different metals and extracted the information (Fig. 4g–i). The structure–performance relationship of Sub@FeN₄ is presented in Fig. 4g–i. When attempting to fit the data points of Sub@FeN₄ with straight lines, it was found that the correlation was not ideal (R² ranging from 0.21 to 0.55). This implies that there is some correlation between them, but it is difficult to quantitatively describe it with a simple formula. Therefore, we are exploring the possibility of predicting and guiding the performance of this system based on a comprehensive understanding of the catalytic origin of Sub@MN₄, thereby facilitating the synthesis of potentially efficient catalysts.

3.3.2 Correlation analysis of Sub@MN₄ structures. To gain a more comprehensive and in-depth understanding of the catalytic activity origins in Sub@MN₄ structures, we performed an analysis from the following perspectives (Fig. 5a): 1. Metal center M: described using metal electronegativity, d-orbital electron count, d-band center,^62,67,68 and charge distribution.^34,68 2. Metal–N coordination: described through M–N bond lengths. 3. Metal-intermediate bonding: described by M–O/M–H bond lengths.⁶¹ 4. Substituents: described based on their electronegativity (calculation method described in Section 2.3). 5. Overall electronic characteristics of the catalyst: characterized by the fundamental gap (E_g).⁴⁶

Fig. 5 (a) Schematic representation of the descriptors analyzed in Sub@MN₄. Correlation analysis of descriptors among (b) Sub@MN₄, (c) Sub@FeN₄, (d) Sub@CoN₄, (e) Sub@NiN₄, and (f) Sub@CuN₄ structures, as well as their correlation with the adsorption free energies of intermediates under vacuum conditions.

In order to further understand these influencing factors, the correlations among various indicators in Sub@MN₄, as shown in Fig. 5a, are presented in the heatmap of Fig. 5b. It is noticeable that there is an almost linear relationship between the ΔG_*OOH and ΔG_*H (correlation coefficient R² = 0.9), indicating that they can be mutually predicted. Another significant correlation is observed between the d-band center and the number of d electrons (correlation coefficient R² = 0.77), which is consistent with our general understanding. The M–O/M–H bond lengths also show certain correlations with the catalytic performance (R² = 0.31, 0.61).⁶¹ It is worth noting that in Sub@MN₄, the contribution of the edge-doping group to the ΔG_*OOH/ΔG_*H seems negligible compared to the contribution of the metal center (R² = 0.001, 0.001), which is contrary to our subconscious perception. Therefore, we further analyzed the correlations between various factors within different metals (Sub@FeN₄, Sub@CoN₄, Sub@NiN₄, Sub@CuN₄) as shown in Fig. 5c–f. In these more detailed heatmaps, we discovered strong correlations that were not evident in Fig. 5b, which may be attributed to the specific characteristics of different metals. In the Sub@FeN₄ system, there are strong correlations between the d-band center, fundamental gap, M–O bond lengths and the ΔG_*OOH/ΔG_*H (R² = 0.53/0.61, 0.57/0.47, 0.55/0.48).^62,67 Particularly in the Sub@CoN₄ system, the E_g can be used to predict the ΔG_*OOH/ΔG_*H effectively (R² = 0.54, 0.51).⁴⁶ For the Sub@CuN₄ system, there are strong correlations between the d-band center, fundamental gap, M–N/M–H bond lengths and the ΔG_*OOH/ΔG_*H (R² = 0.88/0.88, 0.81/0.87, 0.76/0.82, 0.81/0.83).

3.3.3 Predicting the activity of Sub@MN₄ structures using machine learning models. In principle, the machine learning (ML) algorithm can serve as universal approximators, capable of modeling any complex relationships within a system. The general steps involved in constructing ML models are as follows (Fig. 6a): data collection (including feature parameters and target parameters), algorithm selection, model construction, model evaluation, and feature analysis. In this study, the selected feature parameters include the structural parameters shown in Fig. 5a (substituent/metal electronegativity, M–N/M–O/M–H bond lengths, metal d-band center/d-electron count, E_g, ΔG_{*OOH_vac}/ΔG_{*H_vac}). The chosen ML models for training and prediction encompass RFR, KNN, SVR, NN, XGBR, LINER, GBR, GPR, and LASSO, drawing reference from previous studies.^40,41 The data for training and prediction are divided at a ratio of 8 : 1, and the effectiveness of the models is evaluated using R² and RMSE metrics. Among all the tested models (Fig. S30–S37, ESI†), the KNN model (Fig. 6b and c) demonstrates excellent predictive performance.⁴¹ For ΔG_*OOH prediction, the R² is 0.955, and RMSE is 0.102; for ΔG_*H prediction, the R² is 0.943, and RMSE is 0.177. The GBR model closely follows, with an R² of 0.723 and RMSE of 0.267 for ΔG_*OOH prediction, and an R² of 0.995 and RMSE of 0.066 for ΔG_*H prediction. Other models show less satisfactory predictive abilities.

Fig. 6 (a) A schematic representation of the machine learning (ML) process, divided into three parts: data generation, ML model type selection, and feature importance analysis. (b) Comparison of ΔG_*OOH and (c) ΔG_*H calculated from the KNN model with DFT calculations. (d) Importance analysis of various features for ΔG_*OOH and (e) ΔG_*H.

During the feature importance analysis based on the GBR model, we find that, for ΔG_*OOH prediction, the M–O bond length, d band center, N_d and E_g are the primary contributing factors, accounting for 39.9%, 30.9%, 12.9% and 13.0%, respectively. On the other hand, for ΔG_*H prediction, the d band center is the dominant factor, accounting for 59.8% of importance. Charge, M–H bond length, metal center M electronegativity and E_g follow with importance values of 10.4%, 10.1%, 9.8% and 9.4%, respectively. It is worth noting that even if the M–O/M–H bond length is removed as a feature parameter, KNN and GBR still have good predictability, and the d band center still plays the most important role among all feature parameters (Fig. S38, ESI†), which also means that the ML models of these two have good predictive performance.

In conclusion, we have selected the K-Nearest Neighbors (KNN) model as the ML model for predicting the Sub@MN₄ system. The feature importance analysis highlights the d band center and the significance of local M–O/M–H bond lengths. Additionally, in comparison to substituents, the metal center M plays a more crucial role in determining the ORR/OER/HER performance of the material. These analyses can serve as a reference for further investigations into more realistic and complex MN₄ catalysts. Furthermore, they can offer a more efficient, rapid, and cost-effective approach for predicting and guiding the performance and synthesis of Sub@MN₄ catalysts.

For practical applications, the ultimate goal of improving MN₄ catalysts is to enable sustained operation at high current densities.^69–71 Although this paper focuses on the theoretical understanding of atomically regulated MN₄ catalysts, the proposed Sub@MN₄ as a potential catalyst exhibits an overpotential as low as 0.09 V for the HER. This also suggests that combining our findings on the interactions between substituents and the M–N₄ framework could lead to the development of M–N₄ catalysts capable of high current density electrocatalysis. To this end, we believe that experimental verification of computational predictions under high current density conditions should be pursued, as well as the exploration of new materials and designs that can further enhance catalytic performance.

For the synthesis during the experimental process, approaches such as “modification of substituents based on the MN₄ structure” or “selection of carbon precursors with substituents during the synthesis process” can be employed. The identification of specific structures is facilitated by the combination of characterization techniques such as X-ray photoelectron spectroscopy (XPS) and nuclear magnetic resonance (NMR).

4. Conclusion

In this study, we systematically investigated the effects of edge substituent and its interaction with the MN₄ metal center on the catalytic performance of ORR/OER/HER reactions (Sub@MN₄, Sub = B, N, O, S, CH₃, NO₂, NH₂, OCH₃, SO₄; M = Fe, Co, Ni, Cu). The results demonstrated that edge coordination can influence the metal center charge, metal–nitrogen (M–N) bond lengths, and other geometric/electronic structures, thereby regulating their ORR/OER/HER activities. Notably, certain substituents, such as S, O, and SO₄, can significantly reduce the overpotential of FeN₄ by more than 1.15 V, while others like NO₂ can increase the overpotential of CuN₄ by more than 0.73 V. Additionally, for the OER, B, N, CH₃, NO₂, OCH₃ and NH₂ can reduce the overpotential of NiN₄ by more than 1.0 V, while SO₄ can increase the overpotential of NiN₄ by 0.32 V. Furthermore, for the HER, O, S, and SO₄ can increase the overpotential of NiN₄ to at least 1.93 V.

To understand the regulatory mechanisms, we conducted correlation analysis among edge substituents/metal electronegativity, M–N/M–O/M–H bond lengths, metal d-band center/d-orbital electrons, fundamental gap (E_g), and ΔG_*OOH/ΔG_*H. The results indicated that edge substituents remotely influence the electronic structure of the single-atom metal center and also affect the overall electronic structure of Sub@MN₄, thereby impacting its adsorption capacity for key intermediates like *OOH/*H.

Moreover, to further describe and predict Sub@MN₄, we employed machine learning analysis and found that the K-Nearest Neighbors (KNN) model can effectively guide the prediction of catalyst performance (with R² values of 0.955 and 0.943 for predicting ΔG_{*OOH_vac}/ΔG_{*H_vac}, respectively). The d band center and M–O/M–H bond length descriptors were identified as the main factors characterizing the adsorption energies.

In conclusion, our research reveals the regulatory role of edge substituent on the MN₄ catalyst's activity, providing guidance for the design and further optimization of efficient electrocatalysts. These findings contribute to a comprehensive understanding of the catalytic origin of Sub@MN₄ systems, offering valuable insights for the development of high-performance electrocatalysts.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was financially supported by the Natural Science Foundation of Heilongjiang Province (No. YQ2022E027), the Natural Science Foundation of China (No. 52106237) and the Fundamental Research Funds for the Central Universities (No. FRFCU5710051422).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4nh00424h

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