Introduction

Single-atom catalysts (SACs) have drawn increasingly intense attention in electrocatalysis, as they have great potential to provide unmatched high activity and selectivity for multiple chemical reactions1,2,3. The catalytic activity of SAC active centers is strongly correlated to their coordination environment4,5,6,7. In recent years, much progress has been made, and various SACs have been developed both theoretically8,9,10,11 and experimentally12,13,14,15. The catalytic properties of some theoretically predicted SACs have been verified experimentally16,17,18. Nonetheless, these investigations mostly focus on nonmetal or transition-metal atoms as SAC active centers19. While the catalytic activity of the nonmetal SACs is caused by hybridized s-p orbitals, transition-metal SACs benefit from the localized character of d orbitals20,21,22,23. The introduction of elements besides nonmetal and transition-metal atoms as SAC active centers remains to be explored.

In contrast to transition metals, main-group metal elements such as Mg, Al, and Ga, generally exhibit a delocalized s/p-band, which is prone to broaden the adsorbate states22,24,25. Such interaction is thought to yield either too strong or too weak adsorption for adsorbates. This would poison active centers or fail to activate adsorbates, which thus seemingly excludes any possibility to achieve high-performing SACs based on main-group metal elements25. Nevertheless, recently main-group metal elements have been employed as co-electrocatalysts in dual atomic catalysis, where they act as promising separators and facilitate the electroactivity of the connected transition-metal atoms19. Moreover, Mg ion that is contained in enzymes has been proven to show a suitable affinity for oxygenated species26,27,28,29. These observations suggest that, despite the unbefitting delocalized s/p-band, main-group metal elements might still offer the potential to be active centers in SACs.

Among various electrocatalysis reactions, the direct electrochemical NO reduction reaction (NORR) toward NH3 receives special attention as it combines both NO removal and NH3 synthesis30,31,32,33. For NO removal, the conventional technology is based on selective catalytic reduction, which consumes valuable NH3 or H234,35. The alternative, electrochemical NH3 synthesis from N2, suffers from low reaction rate and Faradaic efficiency36,37,38,39. Undoubtedly, a successful realization of NORR, converting NO into NH3 directly, will be a breakthrough20,30,40. Though highly valuable, the direct NO-to-NH3 conversion is essentially unexplored, and only a few NORR electrocatalysts have been reported to date30,31,32,33,40,41. Exploring suitable NORR catalysts thus is of great economic interest and scientific importance, but a formidable task.

In this work, we systematically investigate the possibility of introducing main group metal elements (i.e., Mg, Al, and Ga) to form graphene-based SACs and investigate their suitability to drive the NORR. In strong contrast to expectations, i.e., that suitable active centers are either nonmetal or transition-metal atoms, we demonstrate that indeed main-group metal elements can serve as promising active centers for SACs toward NORR. Through high-throughput screening based on first-principles calculations, six SAC systems out of 51 candidates have been selected as they exhibit superior catalytic activity and selectivity for NORR toward NH3. Importantly, the NORR process can occur spontaneously in these systems. The excellent performances of these systems are closely related to the modulation of s/p-band filling of the main-group metal centers derived from regulating the coordination environment. A rational and generally applicable four-step screening principle is mapped out. Furthermore, we discover that the adsorption free energy of NO is an efficient catalytic descriptor for such SACs. Our findings provide an effective guidance for understanding the potential introduction of main-group metal elements in SACs, and shed light on the further development of NORR catalysts.

Results and discussion

Constructing of main group metal single-atom electrocatalysts

To support the dispersed Mg/Al/Ga atoms, we have chosen N-doped graphene as a substrate in light of the following reasons. First, N-doped graphene is well defined and has been demonstrated to act as an excellent substrate for different SACs both theoretically and experimentally. It merits structural flexibility and thermostability, so it can be used in harsh chemical environments4,5,42,43,44,45,46. Second, it has different coordination modes and thus offers various coordination environments for active centers. Third, N-doped graphene exhibits excellent conductivity, facilitating fast electron transfer during electrocatalysis. Figure 1a–c illustrates the schematic configurations of single Mg/Al/Ga atom supported on graphene with the coordination of N atoms. By regulating the N-coordination, 17 configurations are constructed for each case, including four SV-N3−nCn, seven DV-N4−nCn and six PP-N4−nCn (Fig. 1a–c), which results in a total of 51 SAC candidates. By comparing the adsorption energy and the cohesive energy of the Mg/Al/Ga, our results indicate that for all the candidates, the main group metal atoms can stably anchor on the substrate (Supplementary Table 2), and the corresponding optimized crystal structures are shown in Supplementary Figs. 1–3. The previous work43 has synthesized the configurations of Mg atom coordinated with N atom on graphene, and they also point out that all similar systems including Al and Ga can be prepared following the same method as well. The Bader charge analysis indicates that the supported main group atom donates electrons to the substrate for all these systems, as listed in Supplementary Table 3. The resultant positively charged metal atoms act as Lewis acids and hence become active sites for catalytic reactions47,48,49.

Fig. 1: Schematic illustrations of single Mg/Al/Ga atom supported on N-doped graphene with different coordination environments and a screening strategy flowchart for NORR toward NH3.
figure 1

a Single vacancy site coordinated with three C/N atoms (SV-N3−nCn, n = 0–3). b Double vacancy site coordinated with four C/N atoms (DV-N4−nCn, n = 0–4). c Porphyrin site coordinated with four C/N atoms (PP-N4−nCn, n = 0–4). The unit cells are marked in dotted lines, and the solid rectangles highlight the local configurations with different numbers of N atoms. Atoms marked with dotted circles in (a–c indicate the replaceable C atoms. d Flowchart of the screening scheme to identify the promising SACs with main group metal active centers for NORR toward NH3. e Color code map corresponding to the flowchart of the screening scheme shown in (d). The red, blue, orange and gray color codes indicate the eliminated systems from the first, second, third, and fourth screening steps, respectively, and the green color code indicates the final candidates.

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Screening of superior main group metal SACs for NORR

The electrochemical NORR for NH3 synthesis is a complex process involving five hydrogenation steps, i.e., NO + 5H+ + 5e− = NH3 + H2O. To identify suitable NORR SACs, we design a four-step screening strategy, as schematically illustrated in Fig. 1d. First of all, the NO molecule should be chemisorbed and activated on the SAC center (ΔG*NO < 0, where ΔG*NO is the Gibbs free energy of activated *NO adsorption), which is required to facilitate the subsequent hydrogenation process. Second, the competitive proton adsorption should be suppressed to protect the electrocatalyst from being poisoned (∆G*NO < ∆G*H, where ΔG*H is the Gibbs free energy change for H adsorption). Third, the criterion of ∆Gmax-NH3 < 0 (∆Gmax-NH3 is the maximum Gibbs free energy change of hydrogenation steps for NH3 synthesis via the most favorable reaction mechanism) guarantees the reaction could proceed spontaneously. Finally, ∆Gmax-NH3 < ∆Gmax-N2O, ∆Gmax-NH3 < ∆Gmax-N2 and ∆Gmax-NH3 < ∆Gmax-H2 (∆Gmax-N2O/N2/H2 is the maximum Gibbs free energy change of hydrogenation steps for N2O/N2/H2 synthesis via the corresponding most favorable reaction mechanism) are adopted to select systems of high NH3 selectivity. Following this four-step screening strategy, the highly efficient NORR SACs with main-group metal elements as active centers for NH3 synthesis can be identified.

For NORR process, the first reaction step is adsorption (and activation) of NO, which plays a critical role for the subsequent reactions. Given the non-equivalence between N and O atoms, three possible adsorption patterns of NO are considered, i.e., N-end, O-end and NO-side patterns (Fig. 2a). This gives rise to 153 adsorption configurations in total. The corresponding ΔG*NO for all these configurations are shown in Fig. 2b and Supplementary Tables 4–6. Intriguingly, the N-end pattern is most preferred in energy for almost all SAC candidates, except for Mg-SV-C3 (O-end) and for Mg-PP-C4/-NC3, Al-PP-C4 and Ga-DV-C4 (NO-side), see Supplementary Figs. 4–6. This behavior is expected due to the smaller electronegativity of N atom compared to O atom, making N atom more attractive to coordinate with the SAC Lewis acid site. Note that to guarantee sufficient activation of the adsorbed NO, spontaneous chemisorption of NO (ΔG*NO < 0) is regarded as a necessary prerequisite for NORR process. Thus, following the first screening stage, the systems shown in red color in Fig. 1e are discarded (ΔG*NO > 0). The other SAC candidates show negative adsorption free energies between −0.08 and −3.21 eV.

Fig. 2: Adsorption performance of NO molecule and selectivity between the adsorptions of NO and H on SAC candidates.
figure 2

a The possible adsorption patterns of H and NO (i.e., N-end, O-end and NO-side patterns). b Gibbs free energy changes for NO adsorption with N-end, O-end and NO-side patterns. c Comparison of the adsorption free energies of H proton and NO molecule with the corresponding most favorable adsorption pattern.

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To ensure an effective chemisorption of NO, the competitive adsorption of proton should be excluded as well, which we consider by calculating the selectivity between the adsorptions of both species on the remaining SAC candidates. The Gibbs free energy changes for proton adsorption are summarized in Supplementary Table 7, and the comparison of adsorption free energies between NO and H is presented in Fig. 2c. We rule out all systems where protons are preferentially or similarly strongly adsorbed, as they would refer to proton-poisoned SAC (blue colored in Fig. 1e).

Then, we investigate the subsequent hydrogenation steps of NORR process toward NH3 synthesis for the remaining 35 SAC candidates. Depending on adsorption patterns of NO, the reaction pathways of NORR toward NH3 can follow the A/B-distal, A/B/C-alternating, A/B-enzymatic and C-O/N distal mechanisms (Fig. 3a). Remember that the NO adsorption patterns are O-end for Mg-SV-C3 and NO-side for Mg-PP-C4/NC3, Al-PP-C4 and Ga-DV-C4, the B-distal/alternating/enzymatic and C-O distal/alternating/N-distal mechanisms are considered for them, respectively. While for the other systems, as the adsorption pattern is N-end, the A-distal/alternating/enzymatic mechanisms are explored. Also, the corresponding mixed mechanisms shown in Fig. 3a are investigated for all these systems. To determine the most favorable reaction mechanism for the NORR process, we comprehensively calculate the Gibbs free energies of all the possible reaction intermediates. And we plot the ∆Gmax-NH3 in Fig. 3c. Here, we set ∆Gmax-NH3 < 0 as strict screening criterion, so the reaction can proceed spontaneously. As shown in Fig. 3c, the systems depicted in orange in Fig. 1e are eliminated. We wish to emphasize that although Mg-DV-NC3, Mg-PP-NC3, Al-DV-C4/-N2C2a/-N2C2c/-DV-N3C/-N4, Al-PP-N2C2a/-N3C/N4, and Ga-DV-C4 are excluded here, they exhibit low limiting-potentials with 0.0 < ∆Gmax-NH3 < 0.5 eV. For the remaining 12 SAC candidates (shown in gray and green colors in Fig. 1e), the NORR process occurs spontaneously. It should be noted that these candidates with high activity are all based on DV-N4−nCn or PP-N4-nCn cases, while SV-N3−nCn is completely excluded.

Fig. 3: Reaction mechanism and electrocatalytic activity of NORR on SAC candidates.
figure 3

a Schematic depiction of possible NORR pathways toward NH3 synthesis. b Schematic depiction of possible NORR pathways toward N2O and N2 synthesis. c ΔGmax-NH3 on the remaining 35 SAC candidates via the corresponding most favorable reaction pathways. Type 1 to 6 in (c) is defined in Supplementary Figs. 1–6.

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To inspect the selectivity of NORR toward NH3 synthesis for the remaining 12 SAC candidates, we further investigate the possible formation of byproducts N2O and N2 during the NORR process. The reaction mechanisms of NORR toward N2O and N2 are illustrated in Fig. 3b. For both byproducts, the precondition is the stable adsorption of NO-dimer on the active centers20,50. We therefore first study the adsorption free energy of NO-dimer by considering different adsorption configurations. As shown in Supplementary Fig. 7a, the configuration with both NO featuring N-end pattern is found to be most stable for all the systems. For Ga-DV-N2C2a and Ga-PP-C4, the positive adsorption free energy of NO-dimer prevents the formation of byproducts and suggest their high selectivity for NORR toward NH3. Except these two cases, other ten systems exhibit a negative adsorption free energy of NO-dimer, and we thus further study the subsequent hydrogenation steps of NORR toward N2O and N2 for the remaining ten SAC candidates following the reaction pathways shown Fig. 3b. Supplementary Fig. 7b, c lists the ΔGmax of hydrogenation steps for NORR toward N2O and N2 via the corresponding most favorable reaction mechanisms. To show the selectivity of NORR directly, ΔGmax-NH3 vs. ΔGmax-N2O and ΔGmax-NH3 vs. ΔGmax-N2 for the ten SAC candidates are plotted in Fig. 4a, b. It can be seen that the systems shown in gray color in Fig. 1e display ΔGmax-NH3 > ΔGmax-N2O/ΔGmax-N2, rendering their poor selectivity of NORR toward NH3 synthesis and thus their elimination. On the other hand, the systems shown in green color in Fig. 1e exhibit ΔGmax-NH3 < ΔGmax-N2O/ΔGmax-N2 presenting high selectivity for NORR toward NH3 synthesis. In addition to byproducts N2O and N2 during NORR process, H2 resulted from hydrogen evolution reaction (HER) is another byproduct that should be suppressed for improving the Faraday efficiency20,30. We therefore estimate the competition between NORR toward NH3 and HER for these six candidates. Supplementary Fig. 8a shows the calculated ΔG*H under the limiting potential of NORR toward NH3 (UL-NH3 = −ΔGmax-NH3), and ΔGmax-NH3 vs ΔG*H is summarized in Supplementary Fig. 8b. HER process is significantly suppressed for all these six candidates, ensuring the excellent selectivity of NORR for NH3. This combined with their high NORR activity makes these six systems (Figs. 1c, 4c) very promising SACs for NORR toward NH3. Their corresponding free energy diagrams and the optimized intermediates of these screened SACs during the NORR toward NH3 are shown in Supplementary Fig. 9 and Supplementary Fig. 10 shows the electronic properties of these six SACs. While Al-DV-NC3 is a semiconductor with indirect band gap of 0.70 eV, the other five systems are metallic with states of both spin polarizations crossing the Fermi level. Therefore, all these six SACs harbor high conductivity, facilitating fast electron transfer during the reaction process.

Fig. 4: Electrocatalytic selectivity and summary of the screening strategy for NORR toward NH3.
figure 4

a ΔGmax-NH3 vs ΔGmax-N2O. b ΔGmax-NH3 vs ΔGmax-N2. c Illustration of the screening strategy applied to identify high-efficient electrocatalysts for NORR. Insets in (c) show the corresponding selected high-efficient SAC catalysts.

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While the thermodynamic analyses indicate Al-DV-NC3, Al-DV-N2C2b, Al-PP-N2C2b, Ga-DV-N2C2a, Ga-DV-N2C2c, and Ga-PP-N4 are promising NORR electrocatalyst candidates, it is also important to investigate the kinetic barriers of the most thermodynamically favored pathway for NORR to guarantee the excellent kinetic properties for these electrocatalysts. Therefore, we further calculate the kinetic barriers for each reaction step of the most thermodynamically favored pathway for Al-DV-NC3, Al-DV-N2C2b, Al-PP-N2C2b, Ga-DV-N2C2a, Ga-DV-N2C2c, and Ga-PP-N4. The corresponding transition states and kinetic barriers are presented in Fig. 5 and Supplementary Table 8. We can see that the hydrogenation of *NH2 to NH3(g) (TS6) is the rate-limiting step of Al-DV-NC3 for the NORR, and the maximum kinetic barrier is 0.859 eV. The rate-limiting step is the hydrogenation of *NHOH to *NH + H2O(l) (TS4) for both Al-DV-N2C2b and Al-PP-N2C2b, and the maximum kinetic barriers are 1.076 eV and 0.775 eV, respectively. While for Ga-DV-N2C2a, Ga-DV-N2C2c, and Ga-PP-N4, the rate-limiting step is the hydrogenation of *NH2OH to *OH + NH3(g), and the corresponding maximum kinetic barriers are 0.347 eV, 1.041 eV, and 0.401 eV, respectively. For Ga-DV-N2C2a and Ga-PP-N4, the small activation barriers can be conquered at room temperature, so their NORR possess a high kinetic reaction rate. For the other four systems, although the activation barriers are relatively large, they can be easily conquered under the applied electrode potential51,52,53.

Fig. 5: Kinetic barriers.
figure 5

Corresponding kinetic barriers of the six screened SACs during the NORR toward NH3 synthesis along the most thermodynamic favored reaction pathway. The insets are the structures of the transition states.

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To further understand the electrocatalytic performance of these six screened SACs for NORR, we simulate their electrochemical polarization curve using the microkinetic modeling analysis under the quasi-equilibrium approximation (the computational details are shown in “Methods”). The corresponding kinetic equations for all reaction steps of Al-DV-NC3, Al-DV-N2C2b, Al-PP-N2C2b, Ga-DV-N2C2a, Ga-DV-N2C2c, and Ga-PP-N4 are summarized in Supplementary Table 8. The calculated polarization curves of the screened six SACs during the NORR toward NH3 are given in Supplementary Fig. 11. We can see that the polarization curve of Al-DV-NC3, Al-DV-N2C2b, Al-PP-N2C2b, Ga-DV-N2C2a, Ga-DV-N2C2c, and Ga-PP-N4 display an onset potential of −0.75 V, −1.30 V, −2.20 V, −1.15 V, −1.30 V, and −2.30 V, respectively. Therefore, Al-DV-NC3 has the highest activity for NORR toward NH3 synthesis.

In fact, recent works show that Li-atom-doped MgO exhibits high catalytic activity for oxidative coupling of methane reaction54 and Pb single-atom catalyst exhibits good activity for combustion of energy materials55. Yet concerning SACs for NORR, the nonmetal and transition-metal atoms are exclusively active centers. Our work suggests that main group metal elements indeed can serve as compelling active centers of SACs for NORR, which has important guiding significance for NORR and SAC research. Furthermore, in contrast to previously reported metal bulk and TM-based electrocatalysts31,32,33,34,35, these candidate structures display a potential-free NORR process. Moreover, they can avoid catalyst poisoning as they show a sizable ΔG*NO (0~−1 eV vs. −2~−7 eV in competing systems31,32,35,41). We also calculate the turnover frequencies of these six screened SACs by using microkinetic modeling. The calculated turnover frequencies of these electrocatalysts for NORR toward NH3 synthesis are much larger than the previously reported NRR toward NH3 synthesis and the traditionally Harbor Bosch method toward NH3 synthesis (Supplementary Table 9)56,57. Therefore, the six screened SACs exhibit superior thermodynamic and kinetic catalytic performance.

Reaction mechanism of the main group metal SACs for NORR

Moreover, we investigate the reaction mechanism of the main group metal SACs for NORR. The relationship between the ΔG*NO and NORR activity are summarized in Fig. 6a (for the candidates before the third screening step). It can be seen that there is a strong negative correlation between ∆Gmax-NH3 and ΔG*NO, suggesting ΔG*NO as an excellent descriptor for NORR catalytic activity. By examining the partial density of states (PDOS) of the s/p-band for main-group metals shown in Supplementary Figs. 12–14, we find that ΔG*NO is closely related to the s/p-band center (εs/p) of the main-group metal elements. The scaling relationships between εs/p and ΔG*NO for these 51 SAC candidates are illustrated in Supplementary Fig. 15. For the analysis of the valence electrons contributions, we distinguish between the outer s for Mg and p electrons for Al/Ga atoms, with their respective orbital energies εs and εp. Intriguingly, for Al/Ga-related systems, there is a strong linear relation between ΔG*NO and εp (Fig. 6c). While for Mg-related systems, the relationship is a little complicated. In detail, ΔG*NO is strongly correlated with εs for Mg-SV-N3−nCn and Mg-PP-N4−nCn (Fig. 6b), while it is rather poor for Mg-DV-N4−nCn (Supplementary Fig. 15b). The same is true for a correlation between ΔG*NO and εp for the same systems (Supplementary Figs. 15f, 16).

Fig. 6: Descriptor and physical mechanism of catalytic activity.
figure 6

a ∆Gmax-NH3 as a function of ΔG*NO. b ∆G*NO as a function of s-band centers of Mg on SV/PP-related SAC candidates. c ∆G*NO as a function of p-band centers of Al/Ga on SV/DV/PP-related SAC candidates. d, e Schematic illustrations of the interactions between NO molecular orbitals and s/p-band of main-group metals. The color code of (a–c) is consistent with Fig. 1d.

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The interaction between NO and the SAC’s main-group metals reveals deeper insight into their catalytic activity. According to orbital analysis, the bonding state of NO adsorption on main-group metal center originates from the hybridization between the σ molecular orbital of NO and s/p-band of Mg/Al/Ga. Shapes and relative positions of NO molecular orbitals are slightly affected by the adsorption for most of the systems, and the σ orbital of NO mainly locates around −5 to −10 eV (Supplementary Figs. 17–20). While the s/p-band contribution of main-group metals is almost negligible as it lies within the range of −5 to −10 eV, the electrons of s/p-band of main-group metals, concentrated within 0 to −5 eV, are responsible to the binding strength of NO, as illustrated in Supplementary Figs. 12–14. Interestingly, we find that although the s/p-band of main group metals is generally delocalized58, the s/p-band of metals within the energy range of 0 to −5 eV is relatively localized for Mg-SV-N3−nCn/-PP-N4−nCn and Al/Ga-related systems. In this regard, as depicted in Fig. 6d, by varying the s/p-band center (εs/p), the hybridization between the σ molecular orbital and s/p-band upon adsorption will be changed, thus affecting the interaction as well as the activation strength. In detail, with a high(low)-lying εs/p modulated by less (more) band filling, the coupling strength is weakened (enhanced), yielding a low (high) activity for NORR toward NH3. Therefore, the high NORR activity can be readily achieved through tuning the εs/p in these systems. We wish to emphasize that the position of εs/p can be effectively modulated in such systems through engineering of the N-coordination environment. On the other hand, εs/p is an intrinsic physical parameter that is relevant to the NORR activity. Because s/p-band center can be directly measured in experiment, it should arise the attention for designing main-group metal elements as active centers for NORR.

In contrast to the other systems, for Mg-DV-N4−nCn, the delocalized character of the Mg s-bands is well preserved (Supplementary Fig. 12), and thus the coupling between NO electrons and s-band of Mg cannot be regulated by εs. Such feature generally is prone to broaden the adsorbate states22,24,25,59, yielding either too strong or too weak adsorption for adsorbates depending on the hybridization. But fortunately, the density of s-band is relatively low within the energy range of 0 to −5 eV (Supplementary Fig. 12), thus the interaction between the Mg and adsorbed NO is moderate with ΔG*NO between 0 and −1 eV. With this result in hand, we understand why the εs cannot define ΔG*NO for Mg-DV-N4−nCn.

In summary, we comprehensively studied main-group metal elements as graphene-based active single-atom catalyst centers for direct NO-to-NH3 conversion. By means of first-principles calculations, out of 51 candidates we identified six SAC systems with excellent catalytic activity and selectivity for NORR. For these SACs, the NORR process proceeds spontaneously without any limiting potential, and with moderate ΔG*NO of 0 to −1 eV, which effectively avoids catalyst poisoning. Therefore, counter-intuitively, main-group metal elements indeed can serve as promising active centers for NORR SACs. We rationalize the excellent performance of these systems to the modulation of s/p-band filling of the main-group metal centers by regulating coordination environment. Our rational four-step screening principle is generally applicable for exploring the possibility of introducing other main-group metals beyond Mg/Al/Ga to form SACs. We further discovered that the adsorption free energy of NO is an efficient catalytic descriptor for such SACs. The underlying physical mechanisms are revealed in detail. This work provides effective guidance for extending NORR SACs to main-group metal elements as well as for designing high-efficient NORR catalysts.

Methods

Spin-polarized first-principles calculations are performed using the Vienna ab initio simulation package (VASP)60. The projector augmented wave (PAW) method is used to describe the ion-electron interactions61,62. The exchange-correlation interactions are treated by the generalized gradient approximation (GGA) in form of Perdew-Burke-Ernzerhof (PBE) functional63. The plane-wave cutoff energy of 500 eV is adopted. To construct single (SV-N3−nCn, n = 0~3) and double (DV-N4−nCn, n = 0–4) vacancy systems, we substitute single and double carton atoms in the 4 × 4 × 1 graphene supercells by single main group metal atom (Ma/Al/Ga), respectively. Brillouin zone is sampled using a Monkhorst-Pack grid of 3 × 3 × 1. All structures are optimized with the convergence criteria of 10−5 eV and 0.01 eV A−1 for energy and force, respectively. A vacuum space larger than 20 Å is employed to prevent adjacent interactions. Grimme’s DFT-D3 correction is adopted to describe the van der Waals (vdW) interaction64. The corresponding optimized lattice parameters of the 51 SAC candidates are shown in Supplementary Table 1. The transition states and kinetic barriers are identified by the climbing image nudged elastic band (CI-NEB) method65. VASPKIT is adopted to obtain free energy correction66. Details on the Gibbs free energy calculations can be found in the Supplementary Method.

Microkinetic modeling is performed to simulate the electrochemical polarization curve. Under the quasi-equilibrium approximation67,68, the reaction steps are all in equilibrium states except for the rate limiting step. θi and P represent the coverage and pressure of reactants, respectively. The sum of coverage of all the reactants defines as Ʃθi = 1.

For NO adsorption step, the equilibrium constant (Ki), forward (ki) and backward (k-i) reaction rates are calculated by

$$K_i = {{{\mathrm{e}}}}^{\frac{{ - G_i}}{{k_bT}}}$$
(1)
$$k_i = \frac{{{{{{k}}}}_{\rm{b}}T}}{h}{{{\mathrm{e}}}}^{\frac{{ - \Delta G_{{{{\mathrm{TS}}}}}}}{{k_{\rm{b}}T}}}$$
(2)
$$k_{ - i} = \frac{{k_i}}{{K_i}}$$
(3)

where Gi, GTs, kb, T, and h are the free energy change, kinetic barrier, Boltzmann constant, room temperature, and Planck constant, respectively.

For electrochemical reaction steps, the equilibrium constant (Ki), forward (ki) and backward (k−i) reaction rates are calculated by

$$K_i = {{{\mathrm{e}}}}^{\frac{{ - {{{\mathrm{e}}}}(U - G_i)}}{{k_bT}}}$$
(4)
$${{{{k}}}}_i = \frac{{{{{{k}}}}_{\rm{b}}T}}{h}{{{\mathrm{e}}}}^{\frac{{ - \Delta G_{{{{\mathrm{TS}}}}}}}{{k_{\rm{b}}T}}}{{{\mathrm{e}}}}^{\frac{{ - {{{\mathrm{e}}}}\beta (U - G_i)}}{{k_{\rm{b}}T}}}$$
(5)
$$k_{ - i} = \frac{{k_i}}{{K_i}}$$
(6)

where Ui = −ΔGi/e, β = 1/2, and U is the applied electrode potential.

The turnover frequency (TOF) is calculated by solving the kinetic equations, and the current density (j) is obtained by j = eρTOF, where e = 1.6 × 106 C, and ρ is the surface density of active sites.

The s/p-band center of MGMs is defined as

$$\varepsilon _{{\rm{s}}/{\rm{p}}} = \frac{{{\int}_{ - \infty }^{ + \infty } {E \times {{{\mathrm{\rho }}}}_{{{{\mathrm{s}}}}/{{{\mathrm{p}}}}}{\rm{d}}E} }}{{{\int}_{ - \infty }^{ + \infty } {{{{\mathrm{\rho }}}}_{{{{\mathrm{s}}}}/{{{\mathrm{p}}}}}{\rm{d}}E} }}$$
(7)

where ρs/p is the density of s/p-band of main-group metals.