Unraveling the electronic origin of high activity and selectivity of single-atom catalysts for NO electroreduction

Abstract

The electrochemical reduction of nitric oxide (NO) to ammonia (NH₃) is an emerging technology with dual benefits for environmental remediation and resource conversion. However, this process still faces significant challenges, including low catalytic activity, poor selectivity, and severe competition from side reactions. In this study, we systematically investigated the catalytic behavior of transition metal single-atom catalysts (TM@g-C₄N₃) anchored on a novel two-dimensional carbon nitride material (g-C₄N₃) for the NO reduction reaction (NORR) using first-principles density functional theory (DFT) calculations. Six candidate catalysts were identified as stable under both thermodynamic and electrochemical conditions. Their electronic structures, NO adsorption and activation abilities, and reaction pathways were thoroughly analyzed. The results reveal that the Ag single-atom catalyst exhibits the best catalytic performance, with the lowest limiting potential and excellent selectivity toward NH₃. Further analysis shows that the d-band center of the Ag atom is farthest from the Fermi level, leading to an optimal adsorption strength for NO and thereby the highest catalytic activity. This study not only proposes an effective screening strategy for high-performance NORR catalysts but also provides theoretical guidance for the rational design of novel electrocatalytic materials.

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1. Introduction

Nitric oxide (NO) is a major environmental pollutant generated primarily by fossil fuel combustion, industrial emissions and vehicle exhaust.^1–5 It severely degrades environmental resources and threatens human health, causing respiratory, cardiovascular and neurological disorders. Consequently, controlling and reducing NO emissions is a critical challenge. Ammonia (NH₃), a key chemical feedstock, finds extensive use in agriculture, industry and medicine.^6–10 In agriculture, it serves as the primary precursor for nitrogen fertilizers, playing a vital role in boosting crop yields and ensuring food security. Industrially, NH₃ is employed to produce nitric acid, nylon, plastics and explosives, and is also used as a refrigerant and water-treatment agent. Traditionally, NH₃ synthesis relies on the Haber–Bosch process, which operates at high temperature and pressure, resulting in high energy consumption, elevated costs and significant environmental impact.^11–13 In recent years, the ambient-condition electrochemical nitrogen reduction reaction (NRR) has emerged as a promising alternative.^14–16 However, the NRR faces formidable barriers: the N≡N triple bond in N₂ exhibits a bond energy of 941 kJ mol⁻¹, hindering adsorption and activation on catalyst surfaces, while the low solubility of N₂ in aqueous electrolyte limits reactant concentration and mass-transport kinetics, leading to poor efficiency. By contrast, electrochemical conversion of nitrogenous pollutants such as NO offers the combined benefits of pollution remediation and NH₃ synthesis.^17,18 Owing to its higher intrinsic reactivity and lower N–O bond dissociation energy compared to N≡N, NO can be more readily activated and reduced under mild conditions. Therefore, the development of stable, efficient catalysts composed of earth-abundant elements—capable of promoting the NO reduction reaction (NORR) while suppressing the competing hydrogen evolution reaction (HER)—is of paramount scientific and practical significance.^19–24

Over the past decade, single-atom catalysts (SACs) have demonstrated immense potential in electrocatalysis by maximizing metal atom utilization and delivering outstanding activity and selectivity,^25–29 particularly in the hydrogen evolution reaction (HER),^30–32 CO₂ reduction,^33–35 nitrogen reduction reaction (NRR),^36–38 and nitrogen oxide electroreduction (NORR).^39,40 However, practical deployment of SACs requires excellent stability and resistance to aggregation. Consequently, the choice of support is critical: strong interactions between the support and single atoms not only enhance structural stability but also modulate the electronic properties of active sites, thereby improving catalytic performance. Two-dimensional carbon–nitrogen (2D C–N) materials—especially porous variants—are ideal supports due to their large surface area, high conductivity, and chemical robustness.^41–43 The unsaturated lone-pair electrons on the pore-edge nitrogen atoms form strong chemical bonds with metal atoms; for example, Cu single atoms anchored on g-C₃N₄ and Zr single atoms anchored on porous C₂N exhibit exceptional stability, aggregation resistance, and NORR activity.^44,45

Inspired by the exceptional single-atom anchoring capabilities of various C–N materials, we propose using the recently synthesized g-C₄N₃ monolayer as a support for a series of transition-metal single atoms in the electrocatalytic reduction of NO. The g-C₄N₃ material, formed by substituting a C atom for a N atom in nonmagnetic g-C₃N₄, exhibits a ferromagnetic ground state and half-metallic character. This electronic structure transition thereby confers superior single-atom anchoring capability and excellent catalytic activities. Systematic density functional theory calculations reveal that anchoring a series of metals on g-C₄N₃ confers outstanding thermodynamic, kinetic, and electrochemical stability. Further analysis shows that these catalysts exhibit varying NO activation behaviors. In particular, Ag single atoms—owing to their unique electronic structures, including charge distribution and d-band center position—achieve an optimal degree of NO activation, with limiting potentials of −0.30 V, respectively, resulting in superior NO electroreduction activity. Moreover, the catalyst strongly suppresses the competing hydrogen evolution reaction, ensuring excellent selectivity. This study not only identifies highly efficient NO electroreduction catalysts but also extends the application potential of 2D C–N materials in electrochemical systems.

2. Computational methods and models

The spin-polarized density functional theory (DFT) implemented in the Vienna Ab Initio Simulation Package (VASP)^46,47 was employed for all calculations to optimize the structures involved and compute their corresponding electronic properties. To treat the exchange–correlation interactions between electrons, the Perdew–Burke–Ernzerhof (PBE)⁴⁸ functional within the Generalized Gradient Approximation (GGA) was adopted. The interaction between ions and electrons was described using the projector augmented wave (PAW)^49,50 potentials, and a plane-wave cutoff energy of 450 eV was used for the basis set. During the structural optimization, the convergence thresholds for energy and force were set to 10⁻⁴ eV and 0.05 eV Å⁻¹, respectively. To account for possible van der Waals (vdW) interactions, the DFT-D3 method⁵¹ within the Grimme scheme was applied for correction. Additionally, a vacuum layer of 15 Å along the z-direction was introduced to avoid interactions between periodic images. For geometry optimization and density of states (DOS) calculations, a Monkhorst–Pack k-point mesh of 5 × 5 × 1 centered at Γ was used. Bader charge analysis was performed to obtain information on the charge distribution and charge transfer. The thermal stability of the selected catalysts was investigated using ab initio molecular dynamics (AIMD) simulations⁵² at 500 K with a time step of 10 ps.

Based on the computational hydrogen electrode (CHE) model,^53,54 the Gibbs free energy change (ΔG) for each elementary step can be expressed as: ΔG = ΔE + ΔE_zpe − TΔS + ΔG_U, where ΔE is the electronic energy change between the product and reactant, ΔE_zpe is the zero-point energy difference, TΔS is the entropy change, and T is the temperature (298.15 K in this case). ΔE_zpe and TΔS can be obtained through vibrational frequency calculations. ΔG_U represents the effect of the electrode potential (U), calculated as: ΔG_U = −eU. The potential-determining step (PDS) is defined as the elementary reaction step with the largest free energy change (ΔG_max) during the proton–electron pair transfer process, with the onset potential (U_onset) given by U_onset = −ΔG_max/e. The binding energy (E_b) is calculated as: E_b = E_TM@g-C4N3 − E_TM − E_g-C4N3, where E_TM, E_TM@g-C4N3, and E_g-C4N3 represent the energy of isolated transition metal atoms, the energy of g-C₄N₃ monolayers anchored with transition metal atoms, and the energy of g-C₄N₃ monolayers without transition metal atoms, respectively. Additionally, the electrochemical stability of TM@g-C₄N₃ is evaluated through the dissolution potential U_diss, defined as: U_diss = U⁰_diss (metal, bulk) −E_f/ne, where E_f = E_TM/g-C4N3 − E_g-C4N3 − E_M (metal, bulk). Here, U⁰_diss (metal, bulk) is the bulk metal dissolution potential, n is the number of electrons involved, E_f is the energy difference at the electrode, and E_M (metal, bulk) is the energy of the bulk metal.

3. Results and discussion

3.1. Structure, stability, and electronic properties of TM@g-C₄N₃

To construct the TM@g-C₄N₃ catalytic materials, the 2 × 2 supercell of g-C₄N₃ was chosen as the substrate, containing 28 atoms all lying within the same plane. According to DFT optimization calculations, the lattice constants of g-C₄N₃ were found to be a = 9.67, b = 8.37 Å. Subsequently, transition metal atoms from the 3d (Ti, V, Cr, Mn, Fe, Co, Ni, Cu), 4d (Zr, Nb, Mo, Ru, Pd, Ag), and 5d (Hf, Ta, W, Os, Ir, Pt, Au) series were embedded into the g-C₄N₃ substrate to obtain 21 TM@g-C₄N₃ catalysts (shown in Fig. 1a). These TM@g-C₄N₃ catalysts were then subjected to systematic geometric optimization. The optimized structures revealed that the anchored metal atoms protrude upward and form TM–N chemical bonds with three nitrogen atoms in the substrate, with bond lengths ranging from 1.78 to 2.29 Å.

Fig. 1 (a) The structure of TM@g-C₄N₃ and the selected TM atoms. (b) The difference between binding energy and cohesive energy (E_bind − E_coh) and dissolution potential (U_diss) of the TM@g-C₄N₃ catalysts. (c) Charge density difference of Ag@g-C₄N₃, where yellow and cyan regions represent electron donation and electron accumulation. (d) The band and DOS of Ag@g-C₄N₃.

The stable anchoring of metal atoms on g-C₄N₃ is a prerequisite for its practical applications. To quantitatively assess the stability of 21 TM@g-C₄N₃ candidate compounds, we calculated the binding energy (E_bind), with the results listed in Table S1. According to the definition, a more negative E_bind value indicates stronger binding between the TM atom and g-C₄N₃. Table S1 shows that all TM@g-C₄N₃ systems have negative E_bind values, ranging from −10.70 to −2.06 eV, indicating that these systems are stable. However, due to the relatively high cohesive energy (E_coh) of TM@g-C₄N₃, the experimental feasibility of atomically dispersed TM@g-C₄N₃ still needs further evaluation. To study the possibility of TM atom aggregation on the g-C₄N₃ substrate, we calculated the difference between E_bind and E_coh (E_bind − E_coh). For thermodynamically stable TM@g-C₄N₃ candidates, the condition E_bind − E_coh < 0 should be met. The results indicate that, except for W, Pt, Os, and Au, all anchored single metal atoms exhibit E_bind − E_coh values less than zero, suggesting excellent thermodynamic stability, which are thus ruled out as promising NORR catalysts. We then calculated the dissolution potential (U_diss) to evaluate the electrochemical stability of the remaining SACs. Materials with U_diss > 0 eV are considered electrochemically stable. The results, shown in Fig. 1b, indicate that only 6 candidate compounds (i.e., Ti, Cr, Ni, Cu, Ag, and Ir@g-C₄N₃) are stable under both thermodynamic and electrochemical conditions (Fig. 1b). We also evaluated the stabilities of Ti, Cr, Ni, Cu, Ag, and Ir@g-C₃N₄. As shown in Table S2, the computed E_b − E_coh values are positive and the U_diss values are negative, indicating the instability under thermodynamic and electrochemical conditions for TM anchored s-triazine-based g-C₃N₄ (except Cu@g-C₃N₄).

In addition, Ag@g-C₄N₃ was selected as a representative catalyst (referred to as the surface-optimal catalyst hereafter) to investigate its dynamic stability through first-principles molecular dynamics (AIMD) simulations under the NVT ensemble at 500 K (Fig. S2). The results show that, throughout the 10 ps simulation, the total energy of both systems fluctuates around the equilibrium value, and the geometric structure remains intact without noticeable structural degradation or atomic displacement, further demonstrating the excellent dynamic stability of the Ag@g-C₄N₃ catalyst.

Based on the above calculations, we explored the electronic properties of the six stable catalysts. Due to the strong interaction between the single metal atoms and the g-C₄N₃ substrate, a significant number of electrons (0.51–1.97 e⁻, Fig. 1c and Table S1) transfer from the anchored metal atoms to the substrate, resulting in positively charged metal atoms, which makes them highly likely to capture NO molecules and serve as active centers. Furthermore, some of these catalysts, namely Cu and Ni, are magnetic materials, with the magnetic moment mainly arising from the anchored metals, which also facilitates the adsorption of NO reactants. In addition, the electronic conductivity of the catalyst is an important indicator for evaluating its catalytic performance. Generally, excellent electronic conductivity promotes electron transfer, greatly enhancing the electrocatalytic activity of the catalyst. To this end, we calculated the band structure and density of states (DOS) for these six catalysts and compared them with the results for pure g-C₄N₃. The band structure and DOS of pure g-C₄N₃ were also computed in Fig. S1d. The results show that pure g-C₄N₃ is a semiconductor with a bandgap of 1.64 eV, indicating weak conductivity. However, once metal atoms are anchored, some impurity energy levels are introduced into g-C₄N₃ near the Fermi level, significantly reducing its bandgap. For example, after anchoring Ag single atoms, the Fermi level crosses part of both the valence band and conduction band, indicating that these two materials exhibit metallic properties, thus greatly enhancing their conductivity. Furthermore, the DOS results show sharp peaks near the Fermi level, further confirming their excellent conductivity. Additionally, the local density of states analysis reveals significant orbital hybridization between the metal d-orbitals and the N-2p orbitals in the substrate, further corroborating the strong interaction between the two.

3.2. Adsorption and activation of the NO reactant on TM@g-C₄N₃

In the NORR process, the adsorption and activation of NO is the first and most critical step, as the effectiveness of NO activation determines whether the subsequent reduction reaction can proceed smoothly. On the other hand, the adsorption mode and activation degree of NO directly influence its reduction reaction pathway and catalytic activity. To comprehensively assess the feasibility of NO activation by these six catalysts, we calculated the adsorption of NO on these catalysts. Given the positive charge on the anchored metal atoms, we considered three possible adsorption modes for the NO reactant on these metal sites via “donor–acceptor” interactions: the N or O atom of NO adsorbing to the metal site in an end-on configuration, or the N and O atoms of NO simultaneously adsorbing to the metal active site in a side-on configuration (Fig. 2a). After careful geometric optimization, we found that for all six candidate catalysts, the NO molecule preferentially adsorbs through the N atom to the metal site, forming a TM–N chemical bond with bond lengths ranging from 1.60 to 2.00 Å. Furthermore, due to the transfer of significant electron density from the metal d-orbitals to the NO 2π* orbitals, the N–O bond length is elongated from 1.15 Å in the gas-phase NO molecule to 1.17–1.20 Å, indicating that the adsorbed NO molecule is effectively activated. The energy analysis further confirms the strong activation of NO on these catalysts: the adsorption energies of NO on these six catalysts range from −2.93 to −1.19 eV, which is more negative than the typical adsorption energy for chemisorption (−0.80 eV), indicating that NO molecules can be chemically adsorbed on these catalysts. Clearly, catalysts Ir and Ni exhibit the strongest NO adsorption capabilities, while catalysts Cu and Ag exhibit moderate NO adsorption, which may directly influence the catalytic performance differences in NORR, a topic that will be discussed in detail later. After considering corrections for zero-point energy and entropy, the free energy changes for NO adsorption on these catalysts remain negative, indicating that the NO reactant can thermodynamically adsorb effectively on these catalysts, leading to its full activation.

Fig. 2 (a) The adsorption energy of NO (ΔG_*NO) on TM@g-C₃N₄via N-end, O-end, and NO-side patterns. (b) Charge density difference of NO adsorbed on Ag@g-C₄N₃, where yellow and cyan regions represent electron accumulation and depletion. Projected crystal orbital Hamilton population (pCOHP) and partial density of states (PDOS) of NO adsorbed on Ag@g-C₄N₃ (c) and Ir@g-C₄N₃ (d).

To further investigate the activation of NO reactants on these catalysts, we calculated the electronic differential charge of NO adsorption on the catalysts. Taking Ag@g-C₄N₃ as an example, during the adsorption of the NO molecule, its π orbitals interact with the Ag-4d orbitals, forming partially occupied d-π orbitals. Additionally, due to the hybridization of the Ag-4d orbitals with the NO-σ orbitals at the Fermi level (E_F), occupied d-σ orbitals are also observed. Thus, the interaction mechanism between Ag and NO can be summarized as an “electron donation/feedback” process (Fig. 2b). Specifically, the empty Ag-4d orbitals can accept electrons from the NO-σ orbitals, while the occupied Ag-4d orbitals donate electrons back to the empty π* orbitals of the NO molecule. This “donation/feedback” mechanism is also applicable to several other catalysts. More importantly, these catalysts donate electrons to the adsorbed NO, resulting in a significant accumulation of negative charge around the adsorbed NO species. This favors the electrostatic attraction of positively charged H⁺ species, thereby facilitating the further reduction of NO. For comparison with N-end configuration, we also analyzed the partial density of states (PDOS) and charge density difference for the O-end pattern of NO adsorption on Ag@g-C₄N₃ as an example (Fig. S3). The p states of NO in the N-end adsorption configuration exhibit a stronger interaction with the orbitals of the Ag atom than the O-end pattern. Furthermore, a greater electron transfer from the Ag@g-C₄N₃ substrate to NO is observed in the N-end configuration. The enhanced orbital interaction and greater electron donation synergistically stabilize the N-end configuration, making it the more favorable adsorption mode.

To further evaluate the activation of the N–O bond upon NO adsorption on these catalysts, we calculated the integrated crystal orbital Hamilton population (ICOHP) of NO before and after adsorption. A more negative ICOHP value indicates a stronger N–O bonding interaction and thus a lower degree of activation. As shown in Fig. 2c and Fig. S4, after NO adsorption, the bonding states shift to higher energies, while the antibonding states move significantly closer to the Fermi level (E_F). Notably, the ICOHP value of NO increases from −19.25 in the gas phase (Fig. S5) to −18.23 upon adsorption on the Ag@g-C₄N₃ catalyst (Fig. 2c), clearly indicating effective adsorption and activation of NO on this surface. Ir@g-C₄N₃ exhibits weaker NO activation than Ag@g-C₄N₃, as evidenced by its less negative ICOHP value of −17.36 (Fig. 2d). The computed ICOHP may provide insights into the differences in NORR activity across various catalysts.

3.3. Catalytic performance and reaction mechanism of the NORR

After confirming the excellent stability, high electrical conductivity, and remarkable NO activation capabilities of the six catalysts, we investigated their catalytic performance for the NO reduction reaction (NORR). According to previous studies,⁴⁴ the NORR can proceed through various reaction pathways (Fig. 3a) depending on the NO adsorption configuration, including O-distal, O-alternative, N-distal, N-alternative, NO-distal, NO-alternative, and mixed mechanisms. However, in this study, NO molecules preferentially adsorb onto the single-atom active sites via the nitrogen end (N-end). Therefore, the N-distal pathway was considered. To identify the most favorable reaction pathway and assess the catalytic activity of each system, we optimized all plausible intermediates along the N-end pathway and calculated the Gibbs free energy changes for each elementary step. Based on these data, we constructed the NORR Gibbs free energy profiles for the selected catalysts, providing insights into their reaction feasibility and rate-determining steps.

Fig. 3 (a) The detailed reaction pathway for the NORR on TM@g-C₄N₃, as well as the NO-dimer pathway to N₂. (b) The free energy diagram and corresponding intermediate configurations of the NORR on Ag@g-C₄N₃. (c) The limiting potentials for the most favorable pathway of the NORR reaction on Ti/Cr/Ni/Cu/Ag/Ir@g-C₄N₃.

To facilitate discussion, we take the Ag@g-C₄N₃ catalyst as a representative example to illustrate the NORR reaction pathway in detail. As shown in Fig. 3b, the NO molecule is initially chemisorbed on the Ag site of Ag@g-C₄N₃, with a Gibbs free energy change of −0.47 eV. Subsequently, the activated NO species, containing both nitrogen and oxygen reactive sites, can be hydrogenated to form either *NHO or *NOH intermediates—two competing species that remain under debate in the NORR mechanism. Our DFT calculations reveal that the hydrogenation of adsorbed NO to *NHO requires only 0.30 eV, significantly lower than the 1.64 eV needed to form *NOH. This suggests that, thermodynamically, *NHO is the more favorable intermediate on the Ag surface. Once *NO is hydrogenated to *NHO, the subsequent reaction pathway proceeds smoothly. Specifically, *NHO is further hydrogenated to *NH₂O and then to *NH₂OH, eventually releasing NH₃ as the final product. Notably, all three elementary steps are exergonic, as indicated by their negative Gibbs free energy changes (ΔG = −0.26, −0.57 and −1.15 eV), confirming their thermodynamic spontaneity. After the release of the H₂O product, the remaining *NH₂ intermediate on the Ag surface (with an Ag–N bond length of 2.01 Å) undergoes further hydrogenation to form *NH₃. This step remains exergonic, with a ΔG of 1.48 eV. Since NH₃ interacts weakly with the Ag surface through physisorption, with an adsorption energy of only 0.22 eV, it can be readily desorbed, thereby completing the NORR catalytic cycle. Based on these results, the hydrogenation of *NO to form *NHO exhibits the highest Gibbs free energy change among all elementary steps, making it the potential-determining step (PDS) in the NORR process. The corresponding limiting potential is calculated to be −0.30 V.

In addition to the Ag catalyst, we also evaluated the NORR catalytic activity of the remaining five catalysts (Fig. 3c and Fig. S7). Based on the constructed Gibbs free energy diagrams, we found that different catalysts facilitate the conversion of activated NO to NH₃via distinct reaction pathways. Specifically, on the Cu catalysts, NORR preferentially proceeds through the deamination mechanism, with the potential-determining step identified as the second elementary reaction. The corresponding limiting potentials are −0.57 V. In contrast, for the Ti, Cr, Ni and Ir catalysts, the dehydration pathway is found to be the most favorable, with the final and second ones acting as the PDS and limiting potentials ranging from −1.09 V to −0.42 V (Fig. S6). Taken together, the Ag catalyst exhibits the highest NORR activity among all evaluated systems, owing to its lowest limiting potential. Notably, its limiting potential of −0.42 V is comparable or even lower than that of several previously reported theoretical catalysts such as Zr–C₂N (−0.33 V),⁴⁴ Si–N₄Gr (−0.56 V),⁵⁵ and hBN-graphene hetero structures (−0.22 V),⁵⁶ and some SACs proposed by previous reports (Table S3), further confirming its superior catalytic performance for the NORR process. We also computed the detailed NORR reaction pathway for O-end adsorption configuration of NO on Ag@g-C₄N₃. As shown in Fig. S7, the PDS is the initial adsorption of NO, which requires a higher energy input than the N-end pattern, corresponding to a U_L of −0.46 V.

In catalytic reactions, a competing pathway that could lower NH₃ selectivity is the hydrogen evolution reaction (HER), where H⁺ ions in solution are reduced to H₂. To evaluate this, we examined the HER activity of the Ag catalyst. Interestingly, due to the electrostatic repulsion between the positively charged Ag active sites and H⁺ ions, the key *H intermediate binds very weakly, with a large Gibbs free energy change of 1.01 eV (Fig. S8), suggesting that the HER is highly suppressed on the Ag catalyst. The negligible HER activity ensures excellent NH₃ selectivity during the NORR process.

3.4. Origin of the superior NORR catalytic activity on Ag@C₄N₃

After identifying Ag@C₄N₃ as the most active catalyst among the evaluated candidates, a natural question arises: what is the origin of its superior catalytic performance in the NORR? To answer this, we revisited the adsorption strength of NO on all the studied catalysts. In heterogeneous catalysis, an ideal catalyst should exhibit moderate adsorption strength—not too strong to hinder the desorption of products, and not too weak to fail in activating the reactants. Optimal catalytic activity is typically achieved when reactants and key intermediates bind with intermediate strength to the catalyst surface. Excitingly, our results show that all the investigated catalysts are capable of effectively adsorbing and activating NO. However, certain catalysts such as Ir bind NO too strongly, making the desorption of intermediates or products energetically unfavorable and thereby reducing overall catalytic efficiency. In contrast, the Ag@C₄N₃ catalyst exhibits the weakest NO adsorption strength among the candidates, as indicated by the least negative Gibbs free energy change, while still maintaining stable chemisorption. This near-optimal adsorption behavior is believed to be a key factor underlying its exceptional catalytic performance in the NO reduction reaction.

Building on this, a new question arises: why does the Ag catalyst exhibit the weakest adsorption strength toward NO molecules? Clearly, the chemical reactivity of a material is fundamentally governed by its electronic structure. To further understand the origin of the adsorption behavior, we calculated the projected density of states (PDOS) of active sites in each catalyst and extracted their d-band center (ε_d), aiming to explore the intrinsic correlation between electronic properties and NO adsorption strength. Notably, ε_d serves as a simple yet physically meaningful quantitative descriptor that provides a powerful tool for revealing and predicting electrocatalyst adsorption performance from the perspective of electronic structure.⁴⁴ In general, a higher ε_d (i.e., closer to the Fermi level) implies better density-of-states availability and energy-level alignment between the metal surface and adsorbates, facilitating σ-donation and π-back donation processes. This leads to stronger adsorption bonds and enhanced chemisorption capacity. Our calculations reveal that among the six stable TM@C₄N₃ catalysts, the ε_d values range from −2.58 to −0.32 eV (Fig. S9). Specifically, the Ag active site exhibits the lowest ε_d, farthest from the Fermi level, resulting in the weakest interaction with NO molecules. In contrast, Ir and Ni catalysts show even positive ε_d values, which rationalizes their strongest NO adsorption capacities. Interestingly, a strong linear relationship is observed between ε_d and the NO adsorption strength, with a correlation coefficient (R²) as high as 0.92 (Fig. 4a). Therefore, the weak interaction between Ag and NO, due to its ε_d being far from the Fermi level, explains its superior NORR catalytic activity.

Fig. 4 (a) The linear relationship between the d band center (ε_d) and ΔG_NO. (b) Charge variation during the process of NORR on Ag@g-C₄N₃. Moiety-1, moiety-2 and moiety-3 represent adsorbed molecules, Ag atom and C₄N₃ substrate, respectively.

Additionally, we also explored the charge variation characteristics of each fundamental step along the most favorable reaction pathway for the NORR on the Ag@g-C₄N₃ catalyst. As displayed in the Fig. 4b, step 1 refers to the adsorption configuration of NO on candidates, while steps 2–6 correspond to the protonated intermediates generated in the subsequent stages, which are made up of three moieties: the multiple adsorbed species (moiety 1), Ag atom (moiety 2), and C₄N₃ (moiety 3). For moiety 1 and moiety 3, their charge variation curves show entirely opposite trends. Meanwhile, moiety 2 maintains an almost constant electron loss during the NORR process and the corresponding curve demonstrates minimal fluctuations. Moiety 3 functions as an electron buffer and regulates the electron transfer between moiety 1 and moiety 2. When the electron demand of moiety 1 increases, the electron transferred from the Ag atom to moiety 3 is reduced, whereas a decreased demand enhances the electron transfer to moiety 3. Functioning as an electron transmitter, the Ag atom accelerates electron transfer and thus facilitates the progression of the reduction reaction.

4. Conclusions

In summary, we designed 21 transition-metal single-atom catalysts (TM@g-C₄N₃) based on a g-C₄N₃ 2D carbon–nitrogen substrate and systematically screened six candidates with excellent thermodynamic, electrochemical, and kinetic stability using first-principles calculations. Among them, the Ag catalyst exhibited superior NORR catalytic activity, characterized by low limiting potentials and high NH₃ selectivity. Reaction free energy diagrams confirmed that the hydrogenation of NO to *NHO is the potential-determining step, directly correlated with NO adsorption strength. Particularly, the Ag@g-C₄N₃ catalyst achieves optimal performance due to its weak yet sufficient NO chemisorption, facilitating product desorption and intermediate turnover. Electronic structure analysis reveals that the d-band center (ε_d) plays a pivotal role in modulating NO adsorption, with a clear positive correlation with catalytic activity. This work establishes a fundamental structure–activity relationship for the NORR on single-atom catalysts and provides theoretical insights for designing next-generation electrocatalysts through electronic-structure engineering.

Conflicts of interest

The authors declare no competing financial interest.

Data availability

All data supporting this study are included in the article and its supplementary material (SI). Supplementary material is available. See DOI: https://doi.org/10.1039/d5nj03455h.

Acknowledgements

This work was financially supported by the Heilongjiang Provincial Natural Science Foundation Joint Fund Cultivation Project (No. PL2024B007).

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