Oxygen coordination engineering in Fe–N–O–graphene single-atom catalysts for enhanced bifunctional oxygen electrocatalysis

Abstract

Developing efficient, durable, and low-cost bifunctional electrocatalysts is essential for renewable energy conversion. In this study, density functional theory (DFT) calculations are employed to systematically investigate Fe–N–O coordination structures anchored on graphene (Fe–N–O–gra), aiming to elucidate the structure–electronic–activity relationship in Fe-based single-atom catalysts. Among seven representative configurations, FeN₃O exhibits the highest structural stability, optimal orbital hybridization, and the largest charge transfer, thereby effectively facilitating O₂ activation. FeN₃O exhibits a longer Fe–O bond and weaker electronic coupling during *OH adsorption, which moderates intermediate binding in a step-specific way—facilitating *OH desorption in the ORR and stabilizing *OOH formation in the OER. This balance leads to exceptionally low overpotentials of 0.41 V for the ORR and 0.55 V for the OER, outperforming other configurations. Furthermore, a volcano plot constructed based on adsorption energy scaling relations identifies the *OH adsorption free energy as an effective descriptor of bifunctional catalytic activity, with FeN₃O located near the apex of the plot. These findings highlight the critical role of oxygen coordination in tuning the electronic structure and catalytic performance of Fe single-atom catalysts and provide theoretical guidance for the rational design of next-generation non-precious metal electrocatalysts.

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1. Introduction

With the growing demand for sustainable energy systems, the development of efficient, stable, and cost-effective electrocatalysts has emerged as a central scientific challenge in energy conversion technologies.¹ This is particularly critical for metal–air batteries (MABs) and proton exchange membrane fuel cells (PEMFCs), where the sluggish kinetics of the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) significantly hinder overall energy conversion efficiency.^2–6 Although noble metal catalysts such as Pt and RuO₂ exhibit excellent catalytic activity, their high cost, limited availability, and inability to simultaneously deliver high ORR and OER performance severely constrain their large-scale deployment in clean energy technologies.^7–9 Consequently, the exploration of non-precious metal alternatives with high catalytic activity and long-term stability has become a focal point of current research.^10–15

Among various non-precious metal catalysts, single-atom catalysts (SACs) have garnered widespread attention due to their maximum atom utilization, well-defined active sites, and tunable electronic structures.^16–18 In particular, transition metal–nitrogen–carbon (M–N–C) moieties have demonstrated remarkable performance in diverse electrocatalytic reactions.^{12,17,19–21} Iron (Fe), owing to its earth abundance, low cost, and environmental benignity, is widely regarded as an ideal candidate for constructing non-precious metal electrocatalysts.²² Moreover, Fe-based M–N–C structures, especially Fe–N₄ moieties, have shown ORR activity comparable to or even exceeding that of commercial Pt catalysts in alkaline and neutral media.^23–26 The 3d electronic configuration of Fe enables effective orbital hybridization with oxygenated intermediates (e.g., O₂, *OOH, *O, *OH), facilitating electron transfer during catalysis.^27,28 Its electronic states are also highly susceptible to modulation by coordination environments, rendering Fe an ideal platform for exploring the structure–electronic–activity relationship in electrocatalysis.

Recent studies have revealed that tailoring the coordination environment of Fe atoms—especially by incorporating heteroatoms such as O, B, P, and S—can effectively modulate the electronic structure of the Fe center without compromising thermal stability.^29–34 Among these, oxygen atoms, with their strong electronegativity and electron-withdrawing capability, offer significant advantages in inducing charge redistribution and enhancing the binding affinity of oxygenated intermediates. Notably, Fe–N–O SACs with N/O co-coordination have been experimentally synthesized and have exhibited promising bifunctional catalytic activity in both the ORR and OER, thus providing a solid foundation for theoretical investigations.³⁵ However, despite preliminary progress, the fundamental understanding of the structure–activity relationship in Fe–N–O SACs remains limited. In particular, key aspects such as electronic structure modulation, intermediate adsorption behavior, and reaction pathways under different Fe–N–O coordination geometries lack systematic theoretical elucidation. The thermodynamic and electrochemical stability, mechanistic differences in reaction pathways, and variations in rate-determining steps (RDSs) across different coordination configurations remain largely unexplored.

In this context, we perform a comprehensive density functional theory (DFT) study to evaluate the bifunctional ORR/OER catalytic behavior of various Fe–N–O–gra configurations. By constructing representative Fe–N–O–gra coordination models, we first evaluate structural stability using ab initio molecular dynamics and then analyze electronic properties via PDOS, Bader charge, and charge-density difference to elucidate how coordination modulates the Fe center. Furthermore, adsorption energies of key intermediates and the corresponding reaction free energy profiles are analyzed to identify the reaction pathways, rate-determining steps, and theoretical overpotentials of each configuration, thereby allowing for a systematic evaluation of their bifunctional electrocatalytic performance. A volcano plot based on scaling relations is subsequently constructed to uncover the descriptor–activity correlation, revealing the coupling mechanism between coordination geometry and catalytic activity. This study not only deepens our understanding of the catalytic mechanisms in N/O co-coordinated Fe–N–O SACs but also provides valuable theoretical guidance for the rational design and structural optimization of next-generation non-precious metal bifunctional electrocatalysts.

2. Computational details

2.1 Computational methods

Density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP 6.1.0),³⁶ with the projector augmented wave (PAW) method employed to describe the electron–ion interactions.³⁷ The exchange–correlation potential was treated using the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA).³⁸ A plane-wave energy cutoff of 500 eV was applied throughout all calculations. To more accurately describe the localized behavior of the 3d electrons in the Fe–N–O single-atom catalyst, a Hubbard U correction with U_eff = 3.29 eV was applied.³⁹ Structural optimizations were carried out until the energy and force convergence thresholds were less than 10⁻⁵ eV and 0.02 eV Å⁻¹, respectively.⁴⁰ A Monkhorst–Pack 3 × 3 × 1 k-point mesh was used for geometry optimization, while a denser 11 × 11 × 1 k-point grid was applied for electronic structure calculations. van der Waals interactions were accounted for using the Grimme DFT-D3 correction scheme.⁴¹ Solvation effects were considered implicitly by applying the VASPsol continuum solvation model during all calculations, including geometry optimization, with a dielectric constant of 78.4 to simulate aqueous conditions.^42,43

2.2 Structural models

A periodic 4 × 4 × 1 monolayer graphene supercell was constructed, with a vacuum space of 15 Å introduced along the z-direction to eliminate interactions between adjacent periodic images. Defective sites were created by removing two adjacent carbon atoms to form double vacancies, followed by substitution of neighboring carbon atoms with nitrogen or oxygen atoms. An Fe atom was subsequently embedded at the center of the vacancy, yielding seven distinct Fe–N–O coordination structures as illustrated in Fig. 1(a)–(g). Among them, the FeN₂O₂ configuration includes three geometric variants: (1) FeN₂O₂-p, in which the Fe atom and surrounding N/O atoms form a five-membered ring; (2) FeN₂O₂-h, a six-membered ring arrangement involving Fe, N, and O atoms; (3) FeN₂O₂-o, where the two nitrogen atoms occupy opposite positions relative to the Fe atom.

Fig. 1 (a) Optimized geometries of seven Fe–N–O–gra configurations, including FeN₄, FeN₃O, FeN₂O₂-pen (five-membered ring), FeN₂O₂-hex (six-membered ring), FeN₂O₂-oppo (opposite N atoms), FeNO₃, and FeO₄. Brown, red, light blue, and gold spheres represent C, O, N, and Fe atoms, respectively. (b–g) Time-dependent total energy profiles from ab initio molecular dynamics (AIMD) simulations at 500 K for FeN₄, FeN₃O, FeN₂O₂-pen, FeN₂O₂-hex, FeN₂O₂-oppo, and FeNO₃ configurations. Insets show the top and side views of the structures at the 10 ps snapshot for each configuration.

2.3 Computational contents

(1) Adsorption energy (ΔE_ads). The adsorption energy of a reaction intermediate, denoted as ΔE_ads, was determined using the following expression:⁴⁴

ΔE_ads = E_*m − E_{Fe–N–O–Gra} − E_m (1)

where E_*m is the total energy of the Fe–N–O–graphene system with the intermediate m adsorbed, E_m is the energy of the isolated intermediate, and E_{Fe–N–O–Gra} is the energy of the pristine catalyst model. A negative ΔE_ads implies that adsorption is energetically favorable, indicating the catalyst's potential to effectively bind and activate the intermediate species.

(2) Gibbs free energy change(ΔG). The change in Gibbs free energy for each elementary reaction step was evaluated as:^45,46

ΔG = ΔE + ΔZPE − TΔS + ΔG_U + ΔG_PH (2)

Here, ΔE represents the reaction energy obtained from DFT calculations, ΔZPE is the correction from zero-point vibrational energy, and ΔS is the entropy contribution at 298.15 K. The electrochemical term ΔG_U is given by −neU, where n is the number of electrons transferred and U is the applied potential. The pH-dependent correction, ΔG_pH, is calculated as κ_BT ln 10 × pH,⁴⁷ where κ_B is the Boltzmann constant; in this work, the pH value was defined to be 0 for acidic medium.

Under acidic media, the ORR proceeds via a four-electron mechanism as follows:^47,48

O₂ + * + H⁺ + e⁻ → *OOH (3)

*OOH + H⁺ + e⁻ → *O + H₂O (4)

*O + H⁺ + e⁻ → *OH (5)

*OH + H⁺ + e⁻ → * + H₂O (6)

Here, * denotes an active site on the catalyst surface. The overpotential η for both the ORR and OER is derived from the step with the highest Gibbs free energy change, according to:⁴⁹

η^{ORR(+)/OER(−)} = max(ΔG₁, ΔG₂, ΔG₃, ΔG₄)/e ± 1.23 V (7)

(3) Adsorption free energy (ΔG_ads). The Gibbs free energies of adsorption for the key oxygenated intermediates (*OOH, *O, and *OH) were computed using the following relationships:⁵⁰

ΔG_*OOH = G_*OOH − G_{Fe–N–O–gra} − (2G_H2O − 3/2G_H2) (8)

ΔG_*O = G_*O − G_{Fe–N–O–gra} − (G_H2O − G_H2) (9)

ΔG_*OH = G_*OH − G_{Fe–N–O–gra} − (G_H2O − 1/2G_H2) (10)

In these expressions, G_*OOH, G_*O, and G_*OH refer to the Gibbs free energies of the systems with the respective intermediates adsorbed. G_H2 and G_H2O correspond to the free energies of isolated hydrogen and water molecules, respectively. G_{Fe–N–O–gra} is the free energy of the Fe–N–O–graphene substrate with varying coordination environments.

3. Results and discussion

To systematically assess the thermal stability of Fe–N–O–gra coordination structures under practical electrocatalytic conditions, ab initio molecular dynamics (AIMD) simulations were performed on seven representative models: FeN₄, FeN₃O, FeN₂O₂-pen, FeN₂O₂-hex, FeN₂O₂-oppo, FeNO₃, and FeO₄. The simulations were conducted at 500 K using the Nosé–Hoover thermostat within the canonical (NVT) ensemble for a total duration of 10 ps, with a time step of 2 fs, ensuring reliable tracking of structural evolution under thermal perturbation. As shown in Fig. 1(b–g), all configurations except FeO₄ maintained structural integrity throughout the simulation period. No signs of bond breakage, metal atom migration, or framework collapse were observed, and the total energy fluctuations remained within a reasonable range, indicating their favorable thermodynamic and geometric stability under ambient conditions. In contrast, the FeO₄ model exhibited rapid structural degradation characterized by early-stage bond dissociation and collapse of the coordination framework, suggesting insufficient thermal robustness under catalytic conditions. Accordingly, FeO₄ was excluded from subsequent electronic structure and catalytic performance analyses. Detailed AIMD results are provided in Fig. S1 of the SI. Compared with other representative configurations, the FeN₃O structure exhibits slight bending deformation and asymmetric energy fluctuations during molecular dynamics simulations. These fluctuations remain within a reasonable range and do not lead to structural collapse, indicating overall dynamic stability. The observed deformation originates from the asymmetric Fe–N–O coordination, where the introduction of O ligands induces local stress release and structural adjustment, without compromising the catalytic performance.

Having established the thermal stability of the Fe–N–O–gra models, we next investigated their electronic structure and conductivity to evaluate their feasibility as electrocatalyst substrates. Projected density of states (PDOS) for the six thermally stable configurations are displayed in Fig. 2(a)–(f), clearly revealing strong hybridization between Fe 3d orbitals and the 2p orbitals of neighboring N/O atoms near the Fermi level. This orbital overlap not only stabilizes the metal–ligand bonding network but also facilitates efficient electron transfer and activation of reactive intermediates (e.g., O₂, *OOH, *O, *OH) during catalytic processes. Additionally, the PDOS of all six structures exhibit continuous states across the Fermi level, indicative of good electronic conductivity, which is crucial for enhancing charge transport in the ORR and OER. These comprehensive thermodynamic and electronic analyses provide a solid theoretical foundation for subsequent investigations into adsorption behavior, charge redistribution, and catalytic mechanisms.

Fig. 2 Projected density of states (PDOS) of Fe–N–O–gra catalysts with different coordination environments: (a) FeN₄, (b) FeN₃O, (c) FeN₂O₂-p, (d) FeN₂O₂-h, (e) FeN₂O₂-o, and (f) FeNO₃. Contributions from Fe 3d (green), N 2p (red), and O 2p (blue) orbitals are shown. The Fermi level is set to 0 eV (indicated by the dashed line).

In both the oxygen reduction reaction (ORR) and the oxygen evolution reaction (OER), the adsorption strength of key intermediates such as O₂, *OOH, *O, and *OH critically governs the reaction kinetics and overall catalytic performance. To elucidate how the Fe–N–O–gra coordination environment influences the interaction with these intermediates, we systematically calculated the adsorption energies (ΔE) for each species across different configurations, as summarized in Table S1 of the SI. For molecular oxygen, two adsorption modes were considered: the “side-on” configuration, in which both O atoms interact with the metal center, and the “end-on” configuration, where only one O atom coordinates with the Fe site, as summarized in Table S1 of the SI. Upon geometry optimization, FeN₄ and FeN₃O show a slight thermodynamic preference for the end-on mode, whereas FeN₂O₂-o/h/p and FeNO₃ favor the side-on configuration. This suggests that the end-on mode is more stable and likely more conducive to initial O₂ capture and activation. Among all structures, the FeN₄ configuration exhibits the weakest O₂ affinity with an adsorption energy of −0.89 eV. In contrast, configurations with higher O coordination, such as FeN₂O₂ and FeNO₃, show significantly stronger O₂ binding, with adsorption energies of approximately −1.10 eV and −1.26 eV, respectively. A similar trend is observed for other intermediates. For example, FeNO₃ binds *OOH with an energy of −1.75 eV, compared to −1.41 eV for FeN₄. The difference becomes even more pronounced for *O adsorption, where FeNO₃ achieves a ΔE as low as −6.85 eV, surpassing FeN₄ (−5.98 eV), indicating the formation of a stronger Fe–O bond. Likewise, the *OH adsorption energy increases from −2.83 eV in FeN₄ to −4.19 eV in FeNO₃, indicating that oxygen coordination modulates the binding strength of intermediates depending on the coordination environment. These results underscore that increasing the degree of oxygen coordination in Fe–N–O–gra structures enhances the electronic interaction between the active Fe site and reaction intermediates, particularly evident in the strong *O and *OH binding observed in FeNO₃. The variation in adsorption strength across different configurations reveals the profound influence of coordination geometry on the reaction pathway and provides valuable insights into the structure–activity relationship of Fe-based single-atom catalysts (SACs) in bifunctional oxygen electrocatalysis.

O₂ adsorption is the first step of the ORR, and O₂ desorption is the last step of the OER. Therefore, a detailed understanding of the electronic coupling between Fe 3d orbitals and O₂ 2p orbitals is critical for elucidating the underlying catalytic mechanism. Fig. 3 presents the projected density of states (PDOS) and charge density difference plots for six representative Fe–N–O–gra models (FeN₄, FeN₃O, FeN₂O₂-o, FeN₂O₂-h, FeN₂O₂-p, and FeNO₃) in their O₂-adsorbed states, highlighting how coordination structure affects electronic interactions and O₂ activation capability. Across all structures, varying degrees of Fe 3d and O₂ 2p orbital overlap are observed near the Fermi level. Charge density difference plots further confirm significant charge redistribution within the Fe–O bonding region upon O₂ adsorption, indicating electron donation from the Fe center. Bader charge analysis reveals that the amount of charge transferred from Fe to O₂ ranges from 0.60 to 0.76 |e|. Notably, the FeN₃O configuration exhibits the highest degree of orbital hybridization and maximum charge transfer (0.76 |e|), suggesting superior O₂ adsorption and activation potential. The FeN₂O₂ series (Fig. 3c–e) show moderate Fe–O₂ coupling and charge transfer values around 0.67–0.68 |e|, with charge accumulation localized beneath the O₂ molecule, reflecting stable yet tunable adsorption strength. In contrast, the FeNO₃ model (Fig. 3f) displays the weakest orbital overlap and minimal charge transfer (0.60 |e|), indicating limited electronic donation capability. This constraint may hinder O–O bond cleavage during the ORR, while simultaneously weakening the electronic coupling required for *OOH formation from *O and *OH in the OER, thereby rendering the O–O coupling step kinetically unfavorable. From an electronic structure perspective, the coordination environment around the Fe center governs its d-orbital distribution and hybridization capacity, ultimately affecting the adsorption strength and activation efficiency of O₂. The FeN₃O configuration, in particular, demonstrates optimal orbital interaction and charge redistribution, implying lower reaction barriers, faster kinetics, and enhanced catalytic performance in practical ORR/OER applications. These findings provide theoretical support for understanding its outstanding bifunctional electrocatalytic behavior.

Fig. 3 (a–f) Electronic structure analysis of O₂-adsorbed Fe–N–O–gra configurations: (a) FeN₄, (b) FeN₃O, (c) FeN₂O₂-o, (d) FeN₂O₂-h, (e) FeN₂O₂-p, and (f) FeNO₃. For each configuration, the left panel shows the projected density of states (PDOS), highlighting the Fe 3d (purple) and O₂ 2p (red) orbital contributions near the Fermi level (set to 0 eV, dashed line); the right panel displays the corresponding charge density difference map, where yellow and cyan regions represent electron accumulation and depletion, respectively. The numerical values indicate the amount of charge transferred from Fe to O₂, as determined by Bader charge analysis (unit: |e|), reflecting the electron-donating ability of the Fe center.

To comprehensively evaluate the bifunctional catalytic activity of Fe–N–O–gra single-atom catalysts in the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER), we calculated and plotted the full reaction free energy profiles for six representative configurations: FeN₄, FeN₃O, FeN₂O₂-o, FeN₂O₂-h, FeN₂O₂-p, and FeNO₃, as shown in Fig. 4. The black dashed lines represent the free energy changes at U = 0 V, while the black solid lines correspond to the standard electrode potential of U = 1.23 V. Key intermediates (*OOH, *O, and *OH) and their respective free energies are labeled at each reaction step, and the overpotentials (η^ORR and η^OER) are marked with red and blue circles to facilitate comparison among the different configurations. Notably, all six structures exhibit a common rate-determining step (RDS) for the ORR: the reduction of *O to *OH, indicating that the desorption of *O plays a dominant role in controlling the overall ORR kinetics. For the OER, the shared RDS is the oxidation of *O to *OOH, emphasizing that further oxidation of the *O intermediate is the critical step governing OER activity. This trend highlights the central importance of *O adsorption strength in both reactions—excessive binding inhibits its reduction to *OH, while insufficient binding impairs its oxidation to *OOH. Quantitatively, the FeN₃O configuration exhibits the most favorable bifunctional catalytic performance, with the lowest overpotentials of 0.41 V for the ORR and 0.55 V for the OER. FeN₄ shows moderate activity, with η^ORR and η^OER values of 0.63 V and 0.96 V, respectively. In contrast, FeNO₃ suffers from overly strong intermediate adsorption, resulting in significantly higher overpotentials of 1.99 V (ORR) and 1.50 V (OER), which severely limits its catalytic kinetics. In summary, Fig. 4 clearly illustrates the distinct free energy landscapes and reaction barriers associated with each Fe–N–O–gra configuration. Among them, FeN₃O demonstrates the lowest energy barriers and the best-matched η^ORR/η^OER values, attributed to its optimal intermediate adsorption strength. These findings corroborate the earlier electronic structure analyses, reaffirming that rational engineering of the local coordination environment around the Fe center is a powerful strategy to achieve balanced energy profiles and enhanced bifunctional electrocatalytic performance.

Fig. 4 Free energy diagrams for the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER) on (a) FeN₄, (b) FeN₃O, (c) FeN₂O₂-o, (d) FeN₂O₂-h, (e) FeN₂O₂-p, and (f) FeNO₃ configurations. The black dashed lines represent the reaction pathways at U = 0 V, while the black solid lines correspond to the free energy changes at the standard electrode potential U = 1.23 V. Each diagram includes structural insets of key reaction intermediates (*OOH, *O, and *OH).

To further elucidate the adsorption characteristics between metal active sites and reaction intermediates in Fe–N–O–gra catalysts, we systematically analyzed the correlations among the adsorption free energies of three key intermediates (*OH, *O, and *OOH) and constructed volcano plots for both the ORR and OER, as shown in Fig. 5. A strong linear correlation was observed between ΔG_*OH and ΔG_*O (Fig. 5a), with a fitting equation of ΔG_*O = 0.99 + 0.44ΔG_*OH (R² = 0.95). Similarly, ΔG_*OOH exhibits a positive correlation with both ΔG_*O(ΔG_*OOH = 2.99 + 0.46ΔG_*O, R² = 0.91; Fig. 5b) and ΔG_*OH (ΔG_*OOH = 3.45 + 0.20ΔG_*OH, R² = 0.87; Fig. 5c). These results suggest intrinsic scaling relationships among intermediate adsorption energies, reflecting the coupled nature of active site interactions with different intermediates. Fig. 5d presents the volcano-type dependence of η^ORR and η^OER on ΔG_*OH. Both overpotentials exhibit a minimum near moderate *OH adsorption strengths, indicating that catalytic activity is highly sensitive to intermediate binding energies. Notably, the FeN₃O configuration lies near the apex of both volcano plots, with low overpotentials of η^ORR = 0.41 V and η^OER = 0.55 V—comparable to those of benchmark noble-metal catalysts such as Pt (η^ORR ∼0.45 V) and RuO₂ (η^OER ∼0.42 V). Overall, the adsorption energy correlations and volcano trends in Fig. 5 reveal a clear structure–performance relationship, highlighting that moderate *OH binding is a key design principle for achieving low-overpotential, high-efficiency bifunctional electrocatalysis.

Fig. 5 Scaling relationships between adsorption free energies of key intermediates and volcano-type trends of ORR/OER overpotentials for Fe–N–O–gra catalysts. (a–c) Linear correlations between ΔG_*OH, ΔG_*O, and ΔG_*OOH. (d) Volcano plot of η^ORR and η^OERversus ΔG_*OH, highlighting its role as a bifunctional activity descriptor.

Building on the preceding free energy analysis, scaling relationships, and volcano plot trends, the FeN₃O configuration is confirmed to exhibit significantly reduced overpotentials for both the ORR and OER, demonstrating outstanding bifunctional electrocatalytic performance. To further elucidate the underlying mechanism of its enhanced activity, we conducted a detailed comparison of the *OH adsorption states and electronic structures between FeN₄ and FeN₃O. As shown in the charge density difference maps (Fig. 6a and b), both configurations exhibit pronounced charge redistribution upon *OH adsorption, with electron accumulation primarily localized along the Fe–O adsorption bond, indicating stable bonding interactions. Notably, the Fe–O bond length in FeN₃O (1.85 Å) is longer than that in FeN₄ (1.81 Å), suggesting a weaker binding strength. Bader charge analysis further shows that FeN₃O transfers slightly more charge to the *OH intermediate (0.72 |e| vs. 0.68 |e| for FeN₄), despite the longer bond length, indicating that the incorporation of O coordination helps moderate the overly strong interaction, thus facilitating intermediate desorption. This observation is corroborated by the adsorption energy comparison in Fig. 6c, where *OH adsorption on FeN₃O yields an energy of −2.48 eV, significantly weaker than the −2.83 eV observed for FeN₄. The reduced binding strength places FeN₃O closer to the optimal region predicted by the volcano plot, where catalytic activity is maximized. Such moderate adsorption ensures sufficient binding of intermediates without passivating the active site, thereby promoting faster reaction kinetics. The projected density of states (PDOS) analyses in Fig. 6d and e provide further insight into the electronic origins of the observed trends. In FeN₄, strong overlap between Fe 3d and O 2p orbitals near the Fermi level indicates strong orbital hybridization, which can hinder intermediate desorption. In contrast, FeN₃O exhibits weaker orbital overlap and more localized Fe 3d states near the Fermi level, reflecting a more moderate binding affinity. Overall, excessively strong Fe–O bonding leads to over-adsorption of *OH, hindering intermediate desorption and slowing reaction kinetics, whereas too weak bonding fails to stabilize intermediates. The FeN₃O configuration features a moderately elongated Fe–O bond, with the *OH adsorption energy reduced from −2.83 eV in FeN₄ to −2.48 eV, accompanied by enhanced charge transfer (0.72 |e| vs. 0.68 |e|). This coupled effect of the synergistic interaction between moderate adsorption and enhanced charge transfer ensures sufficient stabilization of intermediates while avoiding site passivation from overly strong binding, thereby accelerating *OH desorption in the ORR and *OOH formation in the OER, effectively lowering the reaction barriers. To provide quantitative insight into electronic regulation, we systematically analyzed the correlation between the Fe d-band center (ε_d) after O₂ adsorption and the ORR/OER overpotentials of different Fe–N–O coordination structures. As shown in Fig. S2 (SI), an evident inverse correlation was observed: the closer the ε_d lies to the Fermi level, the lower the overpotential. This result is consistent with the PDOS and charge density analyses, further confirming that N₃O coordination optimizes the electronic structure of the Fe active site, thereby facilitating a balanced adsorption–desorption process and enabling superior bifunctional electrocatalytic activity. In summary, the FeN₃O structure achieves a well-coordinated modulation of adsorption strength, charge transfer, and band alignment through its optimized coordination environment and electronic structure. These features collectively result in the lowest overpotentials and enhanced reaction kinetics among the studied configurations. The results further validate that tailoring coordination heterogeneity is an effective strategy for boosting the activity of single-atom catalysts and provide both theoretical guidance and practical insights for the design of high-performance Fe–N–O SACs.

Fig. 6 Electronic structure comparison of FeN₄ and FeN₃O configurations after *OH adsorption. (a and b) Charge density difference maps (top) and top-view geometries (bottom) of FeN₄ and FeN₃O, showing Fe–O bond lengths and Bader charge transfer values. (c) Comparison of *OH adsorption energies on the two configurations.(d and e) Projected density of states (PDOS) of FeN₄ and FeN₃O with adsorbed *OH, illustrating orbital hybridization between Fe 3d and OH 2p states.

4. Conclusion

In this study, we employed density functional theory (DFT) to systematically investigate a series of Fe–N–O–gra single-atom catalyst configurations for their bifunctional electrocatalytic performance toward the oxygen reduction reaction (ORR) and oxygen evolution reaction (OER). The aim was to clarify how the introduction of heteroatom O modulates the electronic structure and catalytic behavior of the Fe center. Seven representative coordination models, including FeN₄, FeN₃O, the FeN₂O₂ variants (pen, hex, and oppo), FeNO₃, and FeO₄, were constructed and evaluated. Ab initio molecular dynamics (AIMD) and projected density of states (PDOS) analyses confirmed that all structures except FeO₄ exhibit good thermodynamic and dynamic stability. Charge density difference plots and Bader charge analysis revealed that FeN₃O undergoes the most significant electron transfer during O₂ adsorption, accompanied by strong d–p orbital hybridization at the Fe–O interface, indicating excellent O₂ activation capability. Adsorption energy and reaction free energy pathway calculations further demonstrated that different coordination environments significantly impact the binding strengths of *OOH, *O, and *OH, thereby altering the rate-determining steps. Among all models, FeN₃O exhibited the lowest overpotentials, with η^ORR = 0.41 V and η^OER = 0.55 V, outperforming the conventional FeN₄ configuration (η^ORR = 0.63 V, η^OER = 0.96 V). This high activity is attributed to the FeN₃O structure's moderate *OH adsorption free energy, optimized Fe–O bond length distribution, and effective electronic coupling. Moreover, scaling relations and volcano plots of adsorption energies further confirmed that FeN₃O lies near the activity apex in the bifunctional catalytic landscape, showing simultaneously excellent ORR and OER performance. Collectively, this work not only establishes a clear structure–activity relationship for Fe–N–O coordination environments but also provides theoretical guidance and design strategies for developing efficient, stable, and cost-effective bifunctional non-precious metal single-atom catalysts.

Conflicts of interest

The authors declare no conflict of interest.

Data availability

Supplementary information is available. See DOI: https://doi.org/10.1039/D5RE00292C.

All the data relevant to the study have been included in the manuscript and as part of the supplementary information (SI). The raw data will be provided by the corresponding authors upon request.

Acknowledgements

This work was supported by the Scientific Research Fund project of Education Department of Yunnan Province (grant no. 2024J0333), the Yunnan Fundamental Research Projects (grant no. 202401AY070001-059), and the High-level Talent Research Start-up Project of Kunming Medical University (Grant No. K132310559). Thanks to Weifang YuanSuan Technology Co., Ltd. for providing the computational platform (yuansuan.top).

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