Noble Metal Single-Atom Coordinated to Nitrogen, Oxygen, and Carbon as Electrocatalysts for Oxygen Evolution

Abstract

Tuning the coordination environment centering metal atoms has been regarded as a promising strategy to promote the activities of noble metal single-atom catalysts (SACs). In the present work, first-principle calculations are employed to explore the oxygen evolution reaction (OER) performance of Ir and Ru SACs with chemical coordination being nitrogen (M-N₄-C), oxygen (M-O₄-C), and carbon (M-C₄-C) in graphene, respectively. A “three-step” strategy was implemented by progressively investigating these metrics (stability, catalytic activity, structure–activity relationship). A volcano plot of reactivity is established by using the adsorption-free energy of O* (∆G_O*) as a theoretical descriptor. The intrinsic OER activity is IrN₄-C > IrO₄-C > RuO₄-C > RuN₄-C > IrC₄-C > RuC₄-C. The in-depth tuning mechanism of ∆G_O* can be indicated and interpreted by the d-band centers of the active sites and the crystal orbital Hamilton population analysis of metal-oxygen bonds, respectively.

1. Introduction

Electrochemical water splitting is a promising approach for producing highly purified hydrogen using renewable electricity, encompassing both the hydrogen evolution reaction (HER) and the oxygen evolution reaction (OER) [1,2,3,4,5]. Nevertheless, the large-scale application of electrolytic water splitting is hindered by the absence of highly active and cost-effective electrocatalysts to overcome the slow kinetics of the OER. While the prevalent RuO₂ and IrO₂ electrocatalysts are active in driving OER, their large-scale utilization in water-splitting devices is limited by the scarcity [6,7,8]. As a result, atomically dispersed Ir and Ru atoms fixed on various supporting matrices have attracted extensive attention due to their advantages in minimizing the usage of noble metals and promoting reaction kinetics in OER [9,10]. However, it is noteworthy that carbonaceous supports, renowned for their exceptional conductivity and plentiful defects, provide distinct advantages in supporting single-atom electrocatalysts. These heteroatoms (e.g., N, O, S, P) can be intentionally incorporated and controlled using experimental techniques to achieve the desirable OER performance. Additionally, these heteroatoms can establish stable coordination with the single metal atom, to a certain extent, impeding their aggregation during both the reaction and preparation processes [11]. Interestingly, in this field, the local environments of metal atoms play a crucial role in not only anchoring metal atoms, but also tuning the electronic properties of active sites [12,13,14,15]. In recent years, tuning the coordination shell of single-atom catalysts (SACs) using hetero atoms has been widely reported [16,17,18,19,20,21,22]. For instance, Wang et al. demonstrated that Co-N₂C₂ exhibited higher selectivity and activity than those of Co-N₃C₁ and Co-N₄ on electroreduction of CO₂ to CO [23]. Zhao et al. revealed that Mo-S₂O₂-C outperformed Mo-N₄-C, Mo-O₄-C, and Mo-S₄-C sites in oxygen reduction reaction (ORR), with a low theoretical onset potential being 0.87 V [19]. Yuan et al. reported Fe-N₃P as an outstanding ORR catalyst. The limiting potential (1.22 eV) was less than that of Fe-N₄ (1.36 eV) [24]. Jiang et al. revealed that the Ag-N₂C₂ site exhibited much better H₂ evolution activity than the Ag-N₄ site on carbon nitride [25]. Cheng et al. indicated that the hydrogen evolution reaction (HER) activity increases in the order of Mo-O₂N₂, Mo-O₂N₁C₁, and Mo-O₂C₂, with overpotentials being 98 mV, 71 mV, and 61 mV at 10 mA cm⁻² [26]. In addition, SACs have been the subject of extensive research in the field of the OER [27,28,29]. Niu et al. investigated the OER activity of a single transition metal supported on defective g-C₃N₄ with N vacancy (TM/V_N-CN) using DFT calculations. Their findings revealed that Ru/V_N-CN exhibited exceptional performance with an overpotential being 0.32 V [27]. Wang et al. reported the OER performance of FeXY_iN_3−i (X, Y = B, C, O, P, and S; i = 0, 1) moiety in Fe–porphyrin with first-principle calculations, and they indicated that FeC₂N₂-II showed superior catalytic activity with the overpotential being 0.17 V [28]. Su et al. synthesized the Pt₁–C₂N₂ SAC catalyst, which sustained a current density of 120 mA/cm² at an overpotential of 405 mV and exhibited a high mass activity of 3350 Ag⁻¹ at 232 mV [29]. Given these premises, it is imperative to explore the catalytic performance of Ir and Ru coordinated to N, O, and C as electrocatalysts for OER.

In the present work, OER catalytic activities of three distinct coordination environments of graphene-supported Ir SACs and Ru SACs were comprehensively investigated with density functional theory (DFT) calculations. The catalytic performance of these sites was compared in terms of stability, binding strength of intermediate states, and limiting potentials. A volcano plot of activity was established by using the binding free energy of the oxygen atom (ΔG_O*) as a theoretical descriptor. The ΔG_O* is sensitive to the micro-environments of metal atoms. The in-depth binding characteristics of the key intermediate state O* can be revealed by crystal orbital Hamilton population analysis. The quantitative trend of ΔG_O* of different active sites can be indicated by the d-band center of the active sites. This work not only reports IrN₄-C as an outstanding OER catalyst, but also reveals the fundamental structure–activity relationship of single Ir and Ru atoms in different coordination environments.

2. Results and Discussion

2.1. Structures and Stability of Ir, Ru Embedded N₄-C/O₄-C/C₄-C

Figure 1 shows optimized structures of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru). In MN₄-C and MO₄-C, all atoms are nearly in the same plane, which is consistent with previous studies [30,31,32]. In MC₄-C, by contrast, the C atoms in the coordination shell and the M atom protrude out of the graphene substrate. Such structural characteristics can be interpreted by the orbital geometry of sp² (O, N) and sp³ (C) hybridizations. The lattice parameters of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) are a = 12.27 Å~12.30 Å, b = 12.52 Å, and c = 19.82 Å~19.87 Å, which align with a previous study [33]. Experimentally, SACs are often prone to aggregation during synthesis and catalysis, emphasizing the significance of evaluating the thermal stability of SACs in calculations. Currently, comparing the binding energy and cohesive energy of single metal atoms is an effective approach for estimating the thermodynamic stability of SACs [27,34,35]. In this work, the binding energies (E_bind) of metal atoms were calculated as shown in Figure 2. The theoretical cohesive energies of bulk Ir and Ru are 5.15 eV and 5.17 eV, respectively [36]. Thus, MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) exhibit satisfied stabilities considering that their binding energies are less than −5.00 eV. As seen in Figure 2, the Ir atoms in IrO₄-C and the Ru atoms in RuO₄-C (E_bind = −2.19 eV and −2.73 eV, respectively) could potentially undergo aggregation during catalysis. However, the electronic structures and catalytic performance of IrO₄-C and RuO₄-C are still studied in this work in order to obtain the structure–activity relationship.

2.2. OER Catalytic Activity

The free energy profiles of OER on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) were explored by DFT calculations. In the traditional adsorbate evolution mechanism (AEM) mechanism, OER involves four proton-coupled electron transfer (PCET) steps, as shown in Scheme 1. The elementary reactions are [37,38]:

OH⁻ + * → OH* + e⁻

OH* + OH⁻ → O* + H₂O + e⁻

O* + OH⁻ → OOH* + e⁻

OOH* + OH⁻ → * + O₂ (g) + H₂O + e⁻

where * represents the active site of catalysts, and OH*, O*, and OOH* represent three different catalytic intermediates adsorbed on the active site. The first PCET step is the addition of one hydroxyl group to the M (M = Ir, Ru) atom, forming OH* accompanied by the transfer of one electron. Then, OH* further reacts with the second hydroxyl group to attain O*. Subsequently, the third hydroxyl group is absorbed on the surface of O* to give OOH* intermediate. Finally, OOH* combines with the fourth hydroxyl group by PCET, resulting in the release of O₂ and the regeneration of the free active site.

The corresponding Gibbs free energy profiles of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) catalysts are shown in Figure 3. Optimized structures of the different catalytic intermediates for OER can be depicted in Figures S1–S6. Gibbs free energy change (∆G) for each OER reaction step on MN₄-C, MO₄-C, and MC₄-C can be seen in Table S1. In these calculations, the Gibbs free energy of the initial state of OER is defined as 0.00 eV. The cumulative free energy change of the entire OER process is 4.92 eV. By identifying ΔG_max [37,39,40], the initial potential and corresponding potential determination step (PDS) can be extracted from the free energy diagrams of the OER processes. As shown in Figure 3a, the second PCET step (OH* + OH⁻ → O* + H₂O + e⁻), which forms the O* intermediate, is the PDS of OER on IrN₄-C. The free energy of all electrochemical reaction steps becomes downhill if the applied potentials are higher than 1.53 eV for IrN₄-C. The ${\mathsf{\eta }}^{\mathrm{OER}}$ value of IrN₄-C is 0.30 V, indicating that IrN₄-C exhibits outstanding catalytic activity towards OER. The PDSs of OER on IrO₄-C, IrC₄-C, RuN₄-C, RuO₄-C, and RuC₄-C are all the third PCET (O* + OH⁻ → OOH* + e⁻) step with the ${\mathsf{\eta }}^{\mathrm{OER}}$ values being 0.51 V, 1.43 V, 0.99 V, 0.62 V, and 1.73 V, respectively (Figure 3b–f). In addition, the first PCET step (OH⁻ + * → OH* + e⁻) of OER is exothermic for IrC₄-C, RuN₄-C, and RuC₄-C, whereas other PCETs are endothermic, suggesting that stronger OH* binding leads to poorer activity of IrC₄-C, RuN₄-C, and RuC₄-C. Note that the ${\mathsf{\eta }}^{\mathrm{OER}}$ value of IrN₄-C is at least 0.21 V lower than that of IrO₄-C and IrC₄-C, indicating that the OER catalytic activity of IrN₄-C is significantly better than that of IrO₄-C and IrC₄-C. Similarly, the OER catalytic performance of RuO₄-C is superior to that of RuN₄-C and RuC₄-C (0.62 V vs. 0.99 V and 1.73 V). These reveal that OER activities are closely related to the coordination environment of SACs [41,42]. Moreover, the chemical identity of noble metal atoms also plays a crucial role in tuning the catalytic performance [27]. For instance, the ${\mathsf{\eta }}^{\mathrm{OER}}$ value of IrN₄-C (0.30 V) is smaller than that of RuN₄-C (0.99 V). Thus, the OER activity order of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) is: IrN₄-C > IrO₄-C > RuO₄-C > RuN₄-C > IrC₄-C > RuC₄-C.

2.3. Origin of the OER Activity

According to the Sabatier principle [43], too strong or too weak binding interactions of intermediates on catalysts will show a negative impact on energy conversion efficiency. Therefore, the catalytic activities can often be evaluated or predicted by the adsorption energies of intermediates (ΔG_OH*, ΔG_O*, ΔG_OOH*).

Table 1. The adsorption-free energy of OH*, O*, and OOH* for MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru).

Systems	IrN4-C	IrO4-C	IrC4-C	RuN4-C	RuO4-C	RuC4-C
ΔGOH* (eV)	0.96	1.72	−0.42	−0.01	0.40	−0.26
ΔGO* (eV)	2.49	2.94	0.01	0.67	1.52	−0.08
ΔGOOH* (eV)	3.97	4.68	2.66	2.89	3.37	2.88

shows that adsorption-free energies of intermediates vary with the metal atoms and their coordination environments. Interestingly, the variation of adsorption-free energies of OOH* and OH* on the catalysts are smaller than 1.38 eV. Nevertheless, the variation of ΔG_O* on different catalysts is much more profound (about 2.48 eV). Thus, the adsorption of O atoms is more sensitive to the microenvironment of active sites than other intermediate states. The OER activity of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) can probably be evaluated by the binding energy of O* (ΔG_O*).

Figure 4a shows that the relationship between ΔG_OH* and ΔG_OOH* can be expressed as ΔG_OOH* = 0.95ΔG_OH* + 3.03 with a high coefficient of determination (R² = 0.990). This suggests that ΔG_OOH* rises with increasing ΔG_OH*. Therefore, ΔG_OOH* and ΔG_OH* exhibit almost the same weight when they are used as theoretical descriptors. As shown in Figure S7, however, ΔG_OOH* and ΔG_OH* do not exhibit strong correlations with the catalytic activities. We then plot the d-band center with respect to the ΔG_O*. Interestingly, as seen in Figure S8, the linear relationship can only be seen in the planar active sites (M-N₄-C and M-O₄-C). The MC₄-C sites deviated from the scaling relationship due to geometrical distortions. In addition, the formation of O* from OOH* is the PDS of most catalysts. The exception is IrN₄-C, in which the PDS step is the conversion of OH* to O*. These findings indicate that the ${\mathsf{\eta }}^{\mathrm{OER}}$ can be simultaneously related to the ΔG_O*. The volcano plot is therefore established when ΔG_O* is selected as a descriptor for OER activity (Figure 4b). It is apparent that IrN₄-C stands on the top of the OER volcano plot with the ΔG_O* value being 2.49 eV. IrO₄-C exhibits unsatisfied catalytic efficiency owing to weak O* binding (${\mathsf{\eta }}^{\mathrm{OER}}$ = 0.51 V). While the IrC₄-C, RuN₄-C, RuO₄-C, and RuC₄-C exhibit small formation energies of O*, also lead to low OER activity (${\mathsf{\eta }}^{\mathrm{OER}}$ = 1.43 V, 0.99 V, 0.62 V, and 1.73 V, respectively).

Subsequently, crystal orbital Hamilton populations (COHP) and integrated COHP (ICOHP) are employed to describe the adsorption trend of intermediated states [44,45,46]. COHP is a prevalent method to analyze the bonding characteristics between atoms in chemical species and can often provide important information in the study of structure–activity relationships. For instance, Yan et al. demonstrated that there is a strong linear relationship between the ΔG_OH* and ICOHP with an R² of 0.91, explaining the OH* adsorption trend. Thus, the Co-N-C/GDY achieved superior OER performance due to its moderate binding strength with OH* species [45]. Wang et al. revealed that the bonding strength between the 3d metal atom and O* intermediate generally decreases with the atomic number increases for different MBene substrates by employing ICOHP calculations [46]. The binding strength of the M-O bond in MN₄-C-O*, MO₄-C-O*, and MC₄-C-O* (M = Ir, Ru) can be further examined by COHP analysis. As depicted in Figure 5, the bonding (–COHP > 0) and antibonding (–COHP < 0) contributions in each M-O bond are shown on the right and left panels, respectively. The ICOHP values of the M-O bond in IrO₄-C-O* (−4.14 eV) are more than that in IrN₄-C-O* (−5.24 eV). The ICOHP values of the M-O bond in IrC₄-C-O*, RuN₄-C-O*, RuO₄-C-O*, and RuC₄-C-O* are −6.88 eV, −6.62 eV, −5.57 eV, and −8.45 eV, respectively, which is more negative compared to IrN₄-C-O*. These findings reveal that the binding strength of the oxygen atom in IrO₄-C is weaker than that in IrN₄-C, while the strong binding of the oxygen atom is observed in IrC₄-C, RuN₄-C, RuO₄-C, and RuC₄-C compared to IrN₄-C. Thus, IrN₄-C exhibits excellent catalytic OER performance in these catalysts due to the moderate adsorption energy of O*. The OER performance of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) could be evaluated by the binding energy of O* (ΔG_O*), which is consistent with the above discussions about the volcano plot in Figure 4b.

As it has been demonstrated that ΔG_O* is a theoretical descriptor to evaluate the OER activity, it is important to study the structure–property relationship between the binding energy of O* and the microstructure of the active sites. The charge density difference (CDD) of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) was examined with iso-surfaces set at 0.015 e/ų. As shown in Figure 6, electrons transfer (0.54 e~0.82 e) from M atoms to the N₄-C/O₄-C/C₄-C substrate (Tables S3 and S4). Such charge redistributions are consistent with CDD analysis, showing the accumulation of significant positive charges (pink area) around the anchored M atoms (Figure 6). It is worth noting that formal charges carried by metal atoms are strongly dependent on coordination shells. For instance, the Bader charge of Ir atoms are +0.56|e| and +0.72|e| on the C₄-C and N₄-C substrates, respectively. Notably, the d-band center (ε_d) has been extensively employed as an effective descriptor to establish the relation between the intrinsic electronic properties of catalysts and their adsorption behaviors [27,47]. For instance, Niu et al. established a linear correlation between the ε_d and the adsorption energy of OER intermediates, providing a quantitative description of adsorption energies and revealing the origin of activity based on electronic structures. Consequently, Ru embedded in defective g-C₃N₄ exhibits exceptional performance, with an overpotential as low as 0.32 V [27]. Yang et al. demonstrated that the overpotential of CoNi in nitrogen-doped graphene shows a volcano-shaped relationship with the ε_d of the catalytic site Co. This suggests that the ε_d of the catalytic site is a critical parameter influencing the OER activity [47]. The partial density of states (PDOS) of d orbitals for M atoms on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) are shown in Figure 7. As can be seen, replacing carbon with oxygen or nitrogen for coordination with M metal shifts the ε_d of the M atom toward the Fermi level (E_f). For example, the ε_d values for Ir atoms on IrN₄-C, IrO₄-C, and IrC₄-C exhibit the following trend: IrN₄-C (−1.86 eV) > IrO₄-C (−2.20 eV) > IrC₄-C (−2.60 eV). In addition, the ε_d values for Ru atoms on the C₄-C, O₄-C, and N₄-C substrates are −1.81 eV, −1.10 eV, and −1.07 eV (Figure 7b), respectively. The closer the ε_d of the active site is to the Fermi level, the stronger its ability to participate in capturing reaction intermediates and forming bonds, resulting in higher catalytic activity. Specifically speaking, a more negative ε_d is related to weaker adsorption [48,49]. However, in Ru SACs, the activity of RuO₄-C surpasses that of RuC₄-C and Ru-N₄-C. It is explicable that the association between the ε_d and catalytic performance is merely a qualitative description and not a quantitative trend. Thus, the moderate ε_d value of Ir atoms on IrN₄-C can lead to a neither too strong nor too weak binding strength of oxygen atom (ΔG_O*). As a result, IrN₄-C shows excellent OER performance with the lower overpotential being 0.30 V.

2.4. Solvent Effects

Given that OER takes place in aqueous electrolytes, the impact of solvent effects in the reaction pathways of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) has also been investigated using an implicit solvent model. The Gibbs free energy profiles of OER on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) catalysts in a vacuum (black lines) and implicit solvent model (red lines) are shown in Figure S9. Gibbs free energy changes (∆G) for each OER reaction step on MN₄-C, MO₄-C, and MC₄-C can be seen in Table S5. The third PCET (O* + OH⁻ → OOH* + e⁻) is the PDS of OER on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) in the implicit solvent model, which is quite consistent with those in the vacuum. As can be seen in Figure S8, the ${\mathsf{\eta }}^{\mathrm{OER}}$ value of IrN₄-C is 0.33 V in the implicit solvent model, which is only slightly increased by 0.03 V (${\mathsf{\eta }}^{\mathrm{OER}}$ = 0.30 V in a vacuum). The ${\mathsf{\eta }}^{\mathrm{OER}}$ values of IrO₄-C and RuO₄-C are 0.71 V and 0.67 V in the implicit solvent model, which are 0.20 V and 0.05 V higher than that in a vacuum, respectively. The ${\mathsf{\eta }}^{\mathrm{OER}}$ values of IrC₄-C and RuC₄-C are 1.34 V and 1.58 V in the implicit solvent model, which is 0.09 V and 0.15 V less than that in a vacuum. These results are from the diverse influence of the implicit solvent model on ΔG_O*. In addition, the adsorption-free energy of *OH on IrC₄-C, RuN₄-C, and RuC₄-C is decreased compared with that in a vacuum, indicating stronger interactions between the O atom and the M (M = Ir, Ru) atom. While the overpotential of MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) increases by −0.15 V~0.20 V, the qualitative trends of the influence of coordination shells are not affected by the solvation. This finding aligns well with recent research reports [50,51,52]. Zhang et al. reported that in the implicit solvent model, the onset potential of Pt (111) increases by 0.11 V compared to that in a vacuum, and the ORR performance trend of metal surfaces is consistent with that in a vacuum [51]. Peng et al. showed that including solvent effects increases the overpotential of the Fe- or Ni-doped Co₃O₄(001) by around 0.20 V~0.40 V. However, the general OER activity trends of Fe- or Ni-doped Co₃O₄(001) remain unchanged [52]. Therefore, our results demonstrate that the implicit solvent model can enhance O* adsorption by finely tuning the OER activity. Additionally, the implicit solvent model has a minor impact on the Gibbs free energy profile. The trend of catalytic performance in the implicit solvent model closely mirrors that observed in vacuum. IrN₄-C exhibits excellent OER catalytic performance compared to IrO₄-C, IrC₄-C, RuN₄-C, RuO₄-C, and RuC₄-C.

2.5. Structural Distortions and OER Activity

The impact of structural distortions at the evaluated coordination sites on catalytic activity was thoroughly investigated. Among the various SACs studied, IrC₄-C and Ru-C₄-C exhibit the most pronounced structural distortions. Notably, these structural deformations lead to a situation where the single metal atom protrudes from the C₄-C substrate, resulting in excessively strong binding with O* intermediates. Consequently, IrC₄-C and Ru-C₄-C show poor catalytic performance in OER. In addition, RuN₄-C displays minor structural distortions in comparison to IrN₄-C, IrO₄-C, and RuO₄-C, which shows small formation energies of O*, and also leads to low OER activity. These findings indicated that structural distortions induce a strong interaction between the metal atom and reaction intermediates, consequently impeding the efficiency of the oxygen evolution reaction. This discovery provides invaluable insights for the ongoing efforts to optimize catalyst design and achieve enhanced catalytic performance.

3. Computational Methods

All DFT calculations were carried out using a plane-wave basis set within the Vienna Ab Initio Simulation Package (VASP 5.4.4) [53,54,55]. The exchange–correlation function was described by the Perdew–Burke–Ernzerhof (PBE) parameterization of the generalized gradient approximation (GGA) [56,57,58,59]. The projector-augmented wave (PAW) approximation was adopted to describe the ion–electron interactions [60]. The plane-waves expansion of the Kohn–Sham orbitals was expanded to a kinetic energy cutoff of 400 eV. Then, 10⁻⁴ eV was set as the convergence criteria for the energy, and −0.02 eV/Å was set as the convergence criteria for the forces on each atom. The DFT-D3 method with Becke–Jonson damping was adopted to accurately describe the long-range van der Waals (vdW) interactions [61]. The solvation effect was evaluated under an implicit solvent model VASPsol [62].

MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) catalysts were constructed by embedding an M atom in N₄-C, O₄-C, and C₄-C cavities, respectively. A vacuum thickness of more than 15 Å in the vertical direction was utilized to avoid interactions between periodic images. The Brillouin zone was sampled using a 2 × 2 × 1 gamma-centered k-point mesh for structural optimizations, while a denser k-point mesh of 4 × 4 × 1 was employed for electronic property computations. The binding energy (E_bind) was calculated using the equation:

$${\mathrm{E}}_{\mathrm{bind}}={\mathrm{E}}_{\mathrm{total}}-{\mathrm{E}}_{\mathrm{substrate}}-{\mathrm{E}}_{\mathrm{M}}$$

(1)

where ${\mathrm{E}}_{\mathrm{total}}$, ${\mathrm{E}}_{\mathrm{substrate}},$ and ${\mathrm{E}}_{\mathrm{M}}$ are energies of the catalysts, doped graphene substrates, and an isolated M atom in a vacuum, respectively. The adsorption energy of three different catalytic intermediates can be described as follows:

$$∆{\mathrm{E}}_{\mathrm{OH}*}={\mathrm{E}}_{\mathrm{OH}*}+1/2{\mathrm{E}}_{{\mathrm{H}}_2}-{\mathrm{E}}_{*}-{\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$$

(2)

$$∆{\mathrm{E}}_{\mathrm{O}*}={\mathrm{E}}_{\mathrm{O}*}+{ \mathrm{E}}_{{\mathrm{H}}_2}-{\mathrm{E}}_{*}-{\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$$

(3)

$$∆{\mathrm{E}}_{\mathrm{OOH}*}={\mathrm{E}}_{\mathrm{OOH}*}+3/2{\mathrm{E}}_{{\mathrm{H}}_2}-{\mathrm{E}}_{*}-{2\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$$

(4)

where E_*, E_OH*, E_O*, and E_OOH* are energies of the clean catalyst substrate, and surfaces adsorbed by OH*, O*, and OOH* species, respectively. ${\mathrm{E}}_{{\mathrm{H}}_2\mathrm{O}}$ and ${\mathrm{E}}_{{\mathrm{H}}_2}$ are energies of H₂O and H₂ molecules in gas phases, as shown in Table S6. The adsorption-free energies can be obtained in the equation:

$${∆\mathrm{G}}_{\mathrm{ads}}={∆\mathrm{E}}_{\mathrm{ads}}+{ ∆\mathrm{E}}_{\mathrm{ZPE}}-\mathrm{T}∆\mathrm{S}$$

(5)

where ${\mathrm{E}}_{\mathrm{ads}}$ and ${\mathrm{E}}_{\mathrm{ZPE}}$ are the adsorption energy and zero-point energy, respectively. T is fixed at 298.15 K in this study and S is the entropy. For all OER steps on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) catalysts, the Gibbs free energy change (ΔG) can be calculated by the following expression [63]:

$$∆\mathrm{G}=∆\mathrm{E}+{ ∆\mathrm{E}}_{\mathrm{ZPE}}-\mathrm{T}∆\mathrm{S}+∆{\mathrm{G}}_{\mathrm{pH}}$$

(6)

where E is the energy of the reactant and product obtained from DFT computations directly. $∆{\mathrm{G}}_{\mathrm{pH}}={\mathrm{k}}_{\mathrm{B}}\mathrm{Tln}10\times \mathrm{pH}$ represents the free energy contribution due to the variations in the H concentration, where k_B is the Boltzmann constant. In this work, the pH value was set to 14. The theoretical OER overpotential (${\mathsf{\eta }}^{\mathrm{OER}}$) for a given electrocatalyst can be defined as [64]:

$${\mathsf{\eta }}^{\mathrm{OER}}=\max \left\{{\mathsf{\Delta }\mathrm{G}}_1,{ \mathsf{\Delta }\mathrm{G}}_2,{ \mathsf{\Delta }\mathrm{G}}_3, {\mathsf{\Delta }\mathrm{G}}_4\right\}/\mathrm{e}-1.23 \mathrm{V}$$

(7)

where ${\mathsf{\Delta }\mathrm{G}}_{\mathrm{i}}$ (i = 1, 2, 3, 4) represents the Gibbs free energy change for each step of OER, and the value of 1.23 eV is the equilibrium overpotential of OER. The charge density difference was obtained by the following equation:

$$∆\mathsf{\rho }={ \mathsf{\rho }}_{\mathrm{AB}}-{\mathsf{\rho }}_{\mathrm{A}}-{\mathsf{\rho }}_{\mathrm{B}}$$

(8)

where ${ \mathsf{\rho }}_{\mathrm{AB}}$, ${\mathsf{\rho }}_{\mathrm{A}}$, and ${\mathsf{\rho }}_{\mathrm{B}}$ are electron densities of complexes, substrates, and adsorbates, respectively.

4. Conclusions

In summary, by means of first-principle calculations, the theoretical increase in OER activity on MN₄-C, MO₄-C, and MC₄-C (M = Ir, Ru) was IrN₄-C > IrO₄-C > RuO₄-C > RuN₄-C > IrC₄-C > RuC₄-C in the alkaline media. In particular, IrN₄-C exhibits outstanding OER performance with a low overpotential of 0.30 V. Our calculations indicate that the weak binding of O* to IrO₄-C results in poor catalyst activity, and the strong binding of O* is responsible for the lower OER activity observed in IrC₄-C, RuN₄-C, RuO₄-C, and RuC₄-C. Furthermore, the analysis of COHP and PDOS highlights the enhancement of electrocatalytic activity with the tuning of the coordination shells of M atoms, which effectively adjusts the electronic structure of M atoms to balance the binding strength of O*. Our study challenges traditional thinking and inspires more theoretical and experimental investigations into exploring the catalytic properties of SACs by considering different coordination environments with other metals.