English

• Ammonia (NH₃) is considered a high-energy fuel that does not release carbon dioxide upon combustion, which makes it an important renewable energy source for the future [1]. On the other hand, nitric oxide (NO) is a significant environmental contaminant that causes acid rain and fog, posing a threat to human health [2]. In light of the energy crisis and increasing environmental pollution, there is growing interest in using nitric oxide to produce ammonia as a way to create clean and renewable fuels [3]. One promising approach is the direct electrochemical NO reduction reaction (NORR) towards NH₃ under ambient conditions using renewable electricity [4]. Nevertheless, this process is significantly inhibited by its slow kinetics and the competitive hydrogen evolution reaction (HER), especially in low NO concentrations under real cases [5–7]. Finding catalysts with high NORR to NH₃ activity and selectivity is of great importance.

  Single-atom alloy catalysts (SAACs) have emerged as a promising class of materials in catalysis [8–11]. They are characterized by having active species dispersed as isolated atoms within an inert and catalytically selective host metal matrix. This allows for the maximization of the active phase, reduction of the metal loading, and manipulation of the local environment to adjust the catalytic activity finely [12–15]. SAACs have demonstrated remarkable efficiency for various industrially essential reactions, such as HER, oxygen evolution reduction (OER), oxygen reduction reactions (ORR), nitrogen fixation, and CO₂ reduction reactions (CO₂RR) [16–22]. Meanwhile, Pd and Pd-based materials are traditional catalysts with high stability and catalytic performance in various reactions [23]. Liu et al. investigated the electrochemical nitrate reduction reaction (NO₃RR) over a CuO-based catalyst with Pd single atoms suspended on its interlayer unsaturated bonds (Pd-CuO). The prepared Pd-CuO exhibits strong hydrophilicity and tunable local electronic/coordination structure, achieving a maximum NH₃ Faraday efficiency (FE) of 90% at −0.5 V versus the reversible hydrogen electrode (RHE), with a yield of 4.2 mol g_cat⁻¹ h⁻¹ [24]. Chen et al. reported a single-atom Bi alloyed Pd metallene (Bi₁Pd) as a highly effective NO₃RR catalyst, showing a near 100% NH₃-FE with the corresponding NH₃ yield of 33.8 mg h⁻¹ cm⁻² at −0.6 V vs. RHE [25]. However, the high cost of precious metals prevents their large-scale applications [26,27]. By atomically doping Pd into transition metals (TMs) to form SAACs, the catalyst cost can be greatly reduced, and the synergistic effect of Pd and TM substrate can tune the catalytic performance. Chen et al. designed single-atom Pd-alloyed Cu (Pd₁Cu) as an efficient and robust NORR catalyst at industrial-level current densities (>0.2 A/cm²), exhibiting an unprecedented NH₃ yield rate of 1341.3 µmol h⁻¹ cm⁻² and NH₃-FE of 85.5%, together with excellent long-term durability for 200 h of electrolysis [28]. Qin et al. synthesized a Pd-doped Pt₃Sn-based single-atom alloy catalyst (Pd-Pt₃Sn) which showed superior acidic OER activity with an overpotential of only 0.27 V to reach the current density of 10 mA/cm² [29]. However, research on NORR to electrosynthesis NH₃ with Pd-doped SAACs has not yet been systematically reported, and the underlying physical or chemical features that correlate with the reaction mechanism and performance are unclear.

  Nørskov et al. introduced the computational hydrogen electrode (CHE) model, in which the thermodynamic overpotential (η_TD) serves as an activity descriptor [30]. This model reveals linear relationships in the adsorption energies of intermediate species on TM surfaces for NORR and provides descriptors of the binding free energy of *NOH (ΔG_*NOH) or *NHO (ΔG_*NHO) [31]. It is worth mentioning that η_TD, as a thermodynamic measure for activity, is not directly aligned with the rate-determining reaction step (RDS) governing the reaction rate but rather with the potential-determining step (PDS) [32]. This discrepancy is significant, as the PDS does not necessarily overlap with the RDS, as discussed by Koper [33]. Based on the free-energy span model, an alternate descriptor, G_max(η), has been recommended as a universal approach to evaluate trends in catalytic activity [34]. In contrast to the CHE model, G_max(η) for multiple-electron processes incorporates information on the kinetics and applied overpotential within its framework despite still being a thermodynamic measure.

  In this study, thirteen Pd-doped SAACs (denoted as Pd/TM, TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ru, Rh, and Pt) and fourteen pure transition metals (Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, and Pt) were taken as the model catalysts. To evaluate the thermal stability, we calculated the formation energies (E_f) of these SAACs and screened out stable SAACs with E_f < 0. The Pourbaix diagrams were plotted to examine the electrochemical stability of all the catalysts. We investigated the NO adsorption and activation on the catalyst surfaces. The onset potentials (U_onset) of NORR over TMs usually fall within the range of 0.0–0.3 V vs. RHE [35–38]. Consequently, the overpotentials for the NORR are at least 0.49 V vs. RHE. G_max(η = 0.49 V) was calculated following the density functional theory (DFT) computed free energy span for Pd atom doped SAACs and pure TMs. After further consider the NH₃ selectivity, Cu and Pd/Cu were screened out as potential NORR to NH₃ catalysts. To correlate the intrinsic characteristics of the catalysts and the NORR-to-NH₃ activity, machine learning (ML) investigations were performed. The extreme gradient boosting regression (XGBR) model exhibits excellent performance on the prediction of G_max(η = 0.49 V) with a determination coefficient (R²) of 0.97 and 0.96 for the training set and test set, respectively. Finally, we used the sure independence screening and sparsifying operator (SISSO) model to construct a concise and interpretable formula to predict the G_max(η = 0.49 V) descriptor.

  All DFT calculations were conducted using the Vienna Ab Initio Simulation Package (VASP) [39,40]. The ion-electron interaction was modeled using the projected augmented wave (PAW) pseudopotential, and the exchange-correlation effects were accounted for using the Perdew-Burke-Ernzerhof (PBE) functional within the framework of the generalized gradient approximation (GGA) [41,42]. Spin-polarization was considered for all the DFT calculations. Grimme's DFT-D3 correction was adopted to describe the long-distance van der Waals (vdW) interaction [43]. The Hubbard U approach (PBE+U) was adopted to better describe the on-site Coulomb and exchange (J) interactions of the localized 3d electrons for transition metals [44]. The implicit solvation effect within the VASPsol model was applied to incorporate the solvent effect [45]. We applied the following convergence criteria for self-consistent field iteration calculations: a cutoff energy of 450 eV and a residual energy threshold of 10⁻⁴ eV Geometry optimization was carried out using the conjugate gradient method until the maximum force on any atom reached <0.05 eV/Å. The crystalline structures of pure metals were categorized into three groups: hexagonal close-packed (HCP) for Sc, Ti, Co, Zn, and Ru; body-centered cubic (BCC) for V, Cr, Mn, and Fe; face-centered cubic (FCC) for Ni, Cu, Rh, Pd, and Pt. The adopted surfaces are the close-packed (0001), (110), and (111) planes for HCP, BCC, and FCC, respectively [46]. Since the atomically dispersed doping of TM single atom has very little impact on the crystal structure of the base metals, the exposed surfaces of the single-atom alloy catalysts should be the same as that of the respective base metals [28,47]. The TM surface was modeled by a 4 × 4 slab with four atomic layers. One of the surface TM atoms was replaced by a Pd atom to simulate the Pd/TM SAACs. A 15 Å vacuum space was inserted along the c direction to eliminate the periodic image interactions. The Brillouin zone was sampled using 4 × 4 × 1 gamma center grids. Electron transfer between the catalyst surface and NO was analyzed by Bader charge calculations [48].

  The following equation calculates the adsorption Gibbs free energy of intermediates:

  ΔGads=Gtotal+Gsurface+Gadsorbate

  (1)

  where G_total and G_surface represent the free energies of catalysts with and without adsorbate, G_adsorbate is the free energy of adsorbate. The more negative the adsorption energy value, the more stable the adsorption.

  The reaction Gibbs free energy for each NORR step is calculated using the following formula:

  ΔG=ΔE+ΔEZPE−TΔS

  (2)

  where ΔE represents the total energy difference between the products and reactants calculated by DFT, ΔE_ZPE and ΔS are the zero-point energy change and entropy difference at 298.15 K, and T is the temperature (298.15 K).

  The limiting potential (U_L) of the entire reaction is derived from the reaction free energy of the PDS with maximum ΔG (ΔG_max). U_L is calculated by the equation:

  UL=−ΔGmax/e

  (3)

  The binding energy (E_b) is used to evaluate the stability of SAACs and is calculated by equation:

  Eb=EPd/TM−EPd_single−EDefective_TM

  (4)

  where E_Pd/TM, E_{Pd_single}, and E_{Defective_TM} represent the total energies of the SAACs, one Pd atom, and the TM surface with an atomic defect.

  The cohesive energy E_c is calculated using equation:

  Ec=EPdbulk/n−EPd_single

  (5)

  where E_{Pd_bulk} and n represent the energy of the bulk crystal unit of Pd and the number of atoms in the unit cell.

  The formation energy of a Pd single atom in SAACs is calculated using the formula:

  Ef=Eb−Ec

  (6)

  The XGBR ML algorithm was utilized as implanted in the Scikit-learn Python library [49]. The root mean squared error (RMSE) and coefficient of R² score were applied to evaluate the model performance, which are determined using:

  R2=1−∑i=1n(Yi−yi)2∑i=1n(Yi−Y¯)2

  (7)

  RMSE=1n∑in(Yi−yi)2

  (8)

  where Y_i represents the predicted value, y_i represents the target value, and Y¯ represents the average of the target value. The R² score ranges from 0 to 1; the closer it is to 1, the better the model's prediction accuracy. The RMSE score ranges from 0 to 1, and the closer it is to 0, the higher the accuracy of the model tends to be.

  The calculation details of the activity descriptor G_max(η) are exhibited in Supporting information.

  We have implemented a screening mechanism, as shown in Fig. 1a, to efficiently evaluate suitable catalysts for NORR to NH₃. The first step involves assessing the catalyst's thermodynamic and electrochemical stability, which directly impacts its durability during the reaction. Determining whether NO can be stably adsorbed on the catalyst surface is also crucial, which is important for initiating the subsequent hydrogenation process in NORR and affects the overall reaction efficiency. Additionally, we evaluated the NORR activity trend by taking G_max(η) as the descriptor. Finally, the NH₃ selectivity is investigated compared to the competing HER reaction.

  Figure 1

  

  Figure 1.  The method for screening NORR catalysts, assessing their stability, and analyzing the adsorption behavior of molecules. (a) A DFT-based four-step screening strategy diagram to obtain the optimal NORR catalysts. (b) E_f of different SAACs. Pourbaix diagrams of (c) pure Cu and (d) Pd/Cu. Black dashed lines indicate the redox levels of H⁺/H₂ and O₂/H₂O couples. (e) The adsorption sites and configurations of NO on TM or Pd/TM SAACs. 1, 2, 3 represent O-end-on, N-end-on, and NO-side-on patterns, respectively. h_1, h_2, h_3 represent the hollow_1, hollow_2, and hollow_3 sites, respectively. (f) The adsorption free energies of NO (ΔG_*NO), H (ΔG_*H), and NH₃ (ΔG_*NH3) over various SAACs and pure TM catalysts.

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  We first quantitatively evaluated the stability and experimental feasibility of the 13 Pd/TM (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ru, Rh, Pt) SAACs. According to the definition of E_b, a more negative E_b means a more stable binding between Pd and TM atoms. All Pd/TM systems exhibit negative E_b values, ranging from −3.42 eV to −6.53 eV, indicating that the Pd single atom can be stably embedded in different TM substrates and form strong metallic bonds with surrounding TM atoms. We also calculated the cohesion energy of Pd (E_c = −3.92 eV) and the formation energy (E_f = E_b - E_c) to evaluate the possibility of aggregation of Pd atoms on TM substrate. As shown in Fig. 1b and Table S1 (Supporting information), only the E_f of Pd/Ni is positive. The remaining 12 SAACs (Pd/Sc, Pd/Ti, Pd/V, Pd/Cr, Pd/Mn, Pd/Fe, Pd/Co, Pd/Cu, Pd/Zn, Pd/Ru, Pd/Rh, and Pd/Pt) have good experimental feasibility thermodynamically. This means that the Pd atom has a strong interaction with the TM substrate, making the Pd atom tend to bind with TM rather than undergo aggregation to form Pd clusters. We used the method developed by Pacchioni and colleagues, which utilizes Pourbaix diagrams and a thermodynamic cycle construction, to further analyze the electrochemical stability of SAACs in the operational pH and applied voltage [50–52]. The Pourbaix diagrams of Cu and Pd/Cu are shown in Figs. 1c and d, along with other catalysts (Figs. S1-S4 in Supporting information). Since the onset potentials of NORR over TMs usually fall within the range of 0.0–0.3 V vs. RHE, we are mainly concerned about the electrochemical stability of catalysts under applied potential U ≤ 0.3 V vs. RHE. We take pure Cu and Pd/Cu as examples to discuss the Pourbaix diagrams in detail. The results illustrate that pure Cu is stable in its clean state (*) within the applied potential between 0.05–0.4 V vs. RHE across the whole pH region. With U < 0.05 V vs. RHE, it becomes covered by H atoms, *H. As shown in Table S2 (Supporting information), NO adsorption free energy is more negative than that of *H on Cu. Thus, the NORR process will not be restricted by proton. Under oxidative conditions (U > 0.4 V vs. RHE), *OH or *O species will occupy the active site. After single-atom Pd doping, the Pd site is stable in the form of * or *H for U < 0.67 V vs. RHE. Under oxidative conditions (U > 0.67 V vs. RHE), *O will occupy the active site. Thus, both Cu and Pd/Cu are electrochemically stable under the applied potential we considered (U ≤ 0.3 V vs. RHE). Other TMs or SAACs (Figs. S1-S4) are stable within the whole or part of the applied voltage and pH region.

  For NORR, the effective adsorption and activation of NO are the initial step that significantly influences the subsequent reaction progress. Herein, we considered three typical NO adsorption configurations (N-end-on, O-end-on, and NO-side-on) and four adsorption sites (top, hollow_1, hollow_2, and hollow_3) on the SAAC surfaces (Fig. 1e). As shown in Fig. S5 (Supporting information), the NO-side-on configuration is more favorable on some catalysts (Sc, Ti, V, Cr, Mn, Pd/Sc, Pd/Ti, Pd/V, Pd/Cr) and N-end-on is preferred on other surfaces. On pure TM surfaces, the binding strength between O of NO and TM surface weakens gradually as the atomic number of TMs within the same period in the periodic table increases. Thus the NO adsorption configuration shifts from NO-side-on (for TMs such as Sc, Ti, V, Cr, and Mn) to N-end-on (for TMs such as Fe, Co, Ni, Cu, Zn, Ru, Rh, Pd, and Pt). After Pd single-atom alloying, the NO adsorption ability of Pd/Mn is weakened, and the configuration of NO adsorption changes from NO-side-on to N-end-on. Other Pd/TM SAACs exhibit the same NO adsorption pattern as their pure TM substrate. For Pd/TM (TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Zn, Ru, Rh) SAACs, the most stable adsorption site is hollow-2, far from the Pd dopant atom. As for Pd/Pt and Pd/Cu, NO adsorbs near the doped Pd atom (hollow-1 site).

  We further investigated the adsorption Gibbs free energy of NO (ΔG_*NO) based on the favorable adsorption configurations and sites. As shown in Fig. 1f, except for Pd/Zn, all the values of ΔG_*NO are negative, indicating the favorable adsorption of NO. Based on the Sabatier principle, the binding energy between the catalyst and the reactant should be neither too strong nor too weak [53]. Too strong leads to the unfavorable desorption of products; too weak results in the low activation ability of NO. The adsorption Gibbs free energy of NH₃ (ΔG_*NH3) shows a similar trend to ΔG_*NO on the surfaces we considered, consistent with the Sabatier principle. Catalysts with ΔG_*NO < −0.5 eV and ΔG_*NH3> −0.5 eV, i.e., Sc, Ti, V, Mn, Co, Ni, Cu, Pd/Sc, Pd/Cr, Pd/Mn, Pd/Fe, and Pd/Cu are selected as potential candidates for the following screening process. We also compared ΔG_*NO and the adsorption free energy of H (ΔG_*H), as shown in Fig. 1f. ΔG_*NO and ΔG_*H have almost the same trend. ΔG_*NO is more negative than ΔG_*H on all the pure TM and Pd/TM surfaces, which indicates that NO molecule could be more stably adsorbed on the catalysts. The N—O bond length and charge transfer between NO and the catalyst surface were further investigated. As shown in Fig. S6 and Table S2 (Supporting information), the N—O bond is elongated (ranging from 1.21 Å to 1.48 Å) compared with the free NO molecule (1.16 Å), implying the sufficient activation of NO on the catalyst surface. Interestingly, based on Bader charge analysis, we found that the amount of electron accumulation of NO has a linear correlation with the N—O bond length (R² = 0.92, RMSE = 0.03 Å) in Fig. S7 (Supporting information), which indicates that both the N—O bond length and the electron accumulation of NO can act as good descriptors for NO activation.

  To reveal the underlying physics of the NO adsorption and activation, we investigated the projected density of states (PDOS), the projected crystal orbital Hamiltonian population (-pCOHP) [54], the differential charge density, and the band structure of the catalysts (Figs. S8-S13 in Supporting information). We take Pd/Cu as an example, after NO adsorption, the NO's π* orbital near the Fermi level (E_F) hybridizes with the orbitals of Pd/Cu, leading to the formation of the partially occupied π* orbital of NO (Fig. 2a). The electron injection from SAAC surface to NO weakens the N—O bond, which is further proved by the increased value of integrated crystal orbital Hamilton populations (ICOHP) after NO adsorption (Fig. 2b).

  Figure 2

  

  Figure 2.  The electronic structural characteristics of Cu, Pd, and Pd/Cu. (a) The PDOS of Pd/Cu-total and NO-2p orbitals before and after NO adsorption on Pd/Cu. (b) -pCOHP for N—O interaction of NO before and after NO adsorption on Pd/Cu. (c) Differential charge density of Pd/Cu catalyst. Cyan and yellow represent the charge depletion and accumulation regions, respectively. The isosurface is set to be 0.005 e/ų. The band structure after NO adsorption on (d) Pd/Cu, (e) Cu, and (f) Pd, respectively. The grey lines show the total contribution of the system. Pink, blue, and purple points represent the contribution of NO's 2p orbitals, TMs’ s orbitals, and d orbitals, respectively. The point size denotes the contribution ratio. The Fermi level (E_F) is set to be 0 eV.

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  As illustrated in Fig. 2c, the differential charge density between NO and the surface shows a “back-donation” effect with 0.57 net electrons transferred from Pd/Cu to NO. Based on the band structure analysis of Pd/Cu after NO adsorption (Fig. 2d), it can be seen that the π* orbital of NO mainly hybridizes with the s orbitals of Cu and Pd, so that the π* orbital is broadened. The stable adsorption of NO is caused by the lower energy level position of the π* orbital, and the partially filled π* orbital plays a crucial role in activating N—O bonds. Pure Cu has almost identical orbital hybridization properties with Pd/Cu due to the ten d-electron nature of both Cu and Pd (Fig. 2e). This results in their similar NO adsorption and activation capabilities.

  It is worth noting that in some cases, surfaces with strong NO adsorption do not necessarily have higher N—O activation ability. As shown in Figs. S14 and S15 (Supporting information), the NO adsorbability (ΔG_*NO) has poor correlations with both the N—O bond length (R² = 0.43, RMSE = 0.07 Å) and the electron accumulation of NO (R² = 0.44, RMSE = 0.39 e⁻). Take Pd and Cu as an example; The free energy of NO adsorption on Pd is significantly more negative (−1.93 eV) compared to Cu (−0.54 eV), while the charge accumulation of NO on Pd (0.35 e⁻) is less than that of Cu (0.60 e⁻). These findings indicate that Pd has stronger adsorption of NO, while Cu is more effective in activating the N—O bond. As for Pd/Cu SAAC, after single Pd atom doping, the synergistic effect of Pd and Cu enables a stronger NO adsorption than pure Cu and a more effective activation of the N—O bond than pure Pd. The band structure analysis of Pd after NO adsorption (Fig. 2f) shows that the π* orbital of NO is split into two regions. The energy level of the partially filled part is significantly lower than the Fermi level, leading to strong NO adsorption ability. The small ratio of the filled π* orbital results in weak activation of the N—O bond.

  We further investigated the reaction mechanism of NO-to-NH₃ conversion over SAACs. As shown in Fig. 3a and Table S3 (Supporting information), the NORR process involves six possible pathways following four mechanisms: O-distal, O-alternating, N-distal, and N-alternating. To determine the optimal pathway, we optimized all intermediate configurations (Figs. S16-S19 in Supporting information) and calculated the ΔG of each elementary reaction step for each path (Figs. S20-S23 in Supporting information). We take pure Cu and Pd/Cu as the model catalysts. As illustrated in Fig. 3b, NO first adsorbs on the Cu surface with a downshift free energy of −0.54 eV. The following five electron-involved steps undergo the N-distal reaction pathway (Path 4), all of which are exothermal, with the formation of *H₂NOH as the potential determining step (U_L = 0.05 V). The last step is the desorption of NH₃ with an uphill free energy of 0.17 eV. After single Pd atom doping (Fig. 3c), the NORR reaction path remains unchanged, while stronger NO adsorption leads to PDS changes from *H₂NOH formation to the first hydrogenation step (*NO → *HNO). The U_L of Pd/Cu decreases to −0.25 V.

  Figure 3

  

  Figure 3.  The NORR pathways toward NH₃ production. (a) Schematic illustration of the possible NORR pathways toward NH₃, including O-distal, O-alternating, N-distal, and N-alternating pathways. Free energy diagrams of NORR over (b) Cu and (c) Pd/Cu surfaces.

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  To assess the activity trend of NORR to NH₃, the energetic span approach was used, which calculates the free energy difference between the highest-lying transition state and the lowest-lying intermediate [31]. To avoid the computational expense of optimizing transition state structures, Exner simplified the energetic range by approximating the energetic peak of the catalytic cycle as the highest energy intermediate. He referred to this approximation as G_max(η), where η is the overpotential [32]. G_max(η) factors the applied overpotential and kinetic effects by a dedicated evacuation scheme of adsorption free energies into an analysis of activity trends. Activity descriptor G_max(η) is estimated at a predefined overpotential. The equilibrium potential (U_eq) for NORR to NH₃ is calculated as 0.79 V vs. RHE in this work. Since the NORR onset potentials of TMs are usually in the range of 0.0- 0.3 V vs. RHE, the corresponding overpotentials for NO reduction are at least 0.49 V vs. RHE. Thus, G_max(η) with η = 0.49 V vs. RHE was calculated (Figs. 4a and b, Figs. S24-S27 in Supporting information). The correct determination of G_max(η) requires renumbering of the electron-transfer steps so that the endergonic part of the free-energy landscape is at the beginning of the reaction coordinate, followed by the exergonic part. Take Cu and Pd/Cu as an example (Figs. 4a and b), the G_max(η = 0.49 V) values for Cu and Pd/Cu are 0.26 and 0.55 eV and their RDS are *H₂NO → *H₂NOH and *NO → *HNO, respectively. Fig. 4c and Table S4 (Supporting information) illustrate all the G_max(η = 0.49 V) values for the catalysts we considered. Pure Cu, Zn, and Pd/Cu, Pd/Zn SAACs have relatively small G_max(η = 0.49 V) values (<0.60 eV), indicating high NORR reactivity. Since the NO adsorbability of Zn and Pd/Zn is too weak (ΔG_*NO > −0.5 eV), they are excluded from the NORR candidates.

  Figure 4

  

  Figure 4.  The catalytic activity and selectivity of catalysts. Free energy diagrams of NORR over (a) Cu and (b) Pd/Cu at η = 0.49 V vs. RHE after renumbering the steps so that the reaction intermediate with the lowest free energy locates at the beginning of the reaction coordinate. (c) The G_max(η = 0.49 V) values of all catalysts. (d) The differences between U_L(NORR) and U_L(HER) of all catalysts.

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  The selectivity is crucial for assessing the catalyst's performance. All the catalysts we considered are not preferable for producing hydroxylamine due to a higher reaction free energy for desorption of H₂NOH than the continuous hydrogenation of *H₂NOH to form *NH₂. Furthermore, effectively suppressing the primary competitive HER is essential for increasing NH₃ yield. The limiting potential difference between NORR and HER (U_L(NORR) - U_L(HER)) is used to evaluate the selectivity of the catalyst. As shown in Fig. 4d and Table S4, the U_L(NORR) - U_L(HER) > 0 for pure Cu indicates the preferable NORR selectivity over HER. Although the U_L(NORR) - U_L(HER) < 0 for Pd/Cu (−0.12 V), the NO binding strength on the active site is much stronger than proton and thus inhibits the hydrogen evolution side reaction (Fig. 1f and Table S2). By comprehensively considering the thermal and electrochemical stability, NO adsorption and activation capability, NORR activity, and NH₃ selectivity, Cu and Pd/Cu were selected as potentially effective NORR to NH₃ catalysts.

  We also performed a linear correlation analysis of ΔG_*NO and ΔG of other intermediates (Fig. S28 in Supporting information), and found that none of them have a good linear relationship. This can be attributed to multisite adsorption during the reaction process. Thus, the free energy-related descriptors are deactivated [55]. To explore the underlying correlation between catalysts’ intrinsic features and catalytic performance, as shown in Fig. 5a, we utilized the database constructed by DFT calculations to develop an ML model to predict the catalytic performance of SAACs [56,57]. The SISSO method was further employed to quantitatively verify the relationships between these features and the activity descriptor G_max(η = 0.49 V). We initiated the model-building process by performing feature engineering [2]. Table S5 (Supporting information) shows the physical meaning of the 17 abbreviated features we selected. We analyzed the feature correlation using the Pearson correlation coefficient (p) and plotted a heat map (Fig. S29 in Supporting information). The heat map demonstrates a strong correlation (|p| > 0.8) between the first ionization energy of the substrate TM atom (IE₂) and the average d-band-center of the active site (Ɛ_d), the length of N—O bond (B_L) and the number of d electrons of substrate TM atom (D₂), the Wigner-Seitz radius of the substrate TM atom (RWIGS₂) and atomic radius of the substrate TM atom (R₂). Therefore, we reasonably abandoned these three features (IE₂, B_L, and RWIGS₂). Considering that the path-related feature has p values of 0 with others, we only drew the correlation of the remaining 13 features with |p| < 0.8 in Fig. 5b.

  Figure 5

  

  Figure 5.  Machine learning investigations. (a) Machine learning workflow with feature engineering. (b) Heat map inferred by Pearson's correlation coefficient. (c) Comparison between DFT-calculated and ML-predicted G_max(η = 0.49 V). (d) The ranking of the important features of XGBR. (e) Comparison between DFT-calculated and SISSO-predicted G_max(η = 0.49 V).

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  In Fig. 5c, the XGBR model performs well in predicting the DFT-derived G_max(η = 0.49 V) values. The R² for the training and test sets are 0.97 and 0.96, respectively, and the RMSE are 0.23 and 0.22 eV, respectively. Through the feature importance analysis of the machine learning model (Fig. 5d), the most crucial feature is the electronegativity of the substrate TM atom (X_O) with an importance score of 51.89%, followed by the number of d electrons of the doped atom (D₁), with an importance score of 31.83%. Other relevant features are the number of electron shells of the doped atom (N₁), Ɛ_d, the atomic radius of the doped atom (R₁) and D₂. The SISSO method was utilized to reveal the relation between the corresponding features and the G_max(η = 0.49 V) of the optimal path. The SISSO approach enables us to extract valuable insights into catalyst-related phenomena with significantly reduced computational costs [58]. The model with a dimensional of 2 and feature complexity of 2 was chosen to avoid overfitting, which has the functional form as follows:

  Gmax(η=0.49V)=0.13*XO(RWIGS1−D2)+0.15*R1(RWIGS1+D2)−1.4

  (9)

  As shown in Fig. 5e, the SISSO method predicts G_max(η) well compared to the DFT-calculated ones with R² of 0.95 and RMSE of 0.33 eV Following this formula, we can accurately predict the G_max(η) of a catalyst by just obtaining these four input feature (X_O, RWIGS₁, D₂, and R₁) values. The XGBR and SISSO machine learning results provide a theoretical understanding of the complex NORR to NH₃ mechanisms and shed light on the rational design of efficient NORR catalysts.

  In summary, by DFT calculations, we have demonstrated a valid strategy for screening efficient SAACs for NO-to-NH₃ conversion. We verified the synergistic effect of the Pd single atom and the TM substrate. Pure Cu and Pd/Cu are selected as possible effective NORR to NH₃ catalysts by considering a four-step screening principle. In addition, the XGBR and SISSO machine learning models are constructed to predict the DFT-derived activity descriptor G_max(η = 0.49 V) by exploring the relationship between the features of the active site and G_max(η = 0.49 V). These findings will undoubtedly expedite experimental and theoretical studies to unlock the full potential of SAACs in NORR.

  Declaration of competing interest

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

  CRediT authorship contribution statement

  Jieyu Liu: Writing – review & editing, Supervision, Validation, Software, Methodology, Formal analysis. Junze Zhang: Data curation, Investigation. Haigang Deng: Data curation, Formal analysis. Shuoao Wang: Investigation. Xingxing Jiang: Validation, Supervision. Li Wang: Validation, Formal analysis. Changhong Wang: Writing – review & editing, Validation, Software, Project administration, Formal analysis, Conceptualization.

  Acknowledgments

  The authors appreciate the support from the HeBei Natural Science Foundation (Nos. B2022205029 and B2022205013).

  Supplementary materials

  Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2024.110656.

  
  
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  Figure 1  The method for screening NORR catalysts, assessing their stability, and analyzing the adsorption behavior of molecules. (a) A DFT-based four-step screening strategy diagram to obtain the optimal NORR catalysts. (b) E_f of different SAACs. Pourbaix diagrams of (c) pure Cu and (d) Pd/Cu. Black dashed lines indicate the redox levels of H⁺/H₂ and O₂/H₂O couples. (e) The adsorption sites and configurations of NO on TM or Pd/TM SAACs. 1, 2, 3 represent O-end-on, N-end-on, and NO-side-on patterns, respectively. h_1, h_2, h_3 represent the hollow_1, hollow_2, and hollow_3 sites, respectively. (f) The adsorption free energies of NO (ΔG_*NO), H (ΔG_*H), and NH₃ (ΔG_*NH3) over various SAACs and pure TM catalysts.

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  Figure 2  The electronic structural characteristics of Cu, Pd, and Pd/Cu. (a) The PDOS of Pd/Cu-total and NO-2p orbitals before and after NO adsorption on Pd/Cu. (b) -pCOHP for N—O interaction of NO before and after NO adsorption on Pd/Cu. (c) Differential charge density of Pd/Cu catalyst. Cyan and yellow represent the charge depletion and accumulation regions, respectively. The isosurface is set to be 0.005 e/ų. The band structure after NO adsorption on (d) Pd/Cu, (e) Cu, and (f) Pd, respectively. The grey lines show the total contribution of the system. Pink, blue, and purple points represent the contribution of NO's 2p orbitals, TMs’ s orbitals, and d orbitals, respectively. The point size denotes the contribution ratio. The Fermi level (E_F) is set to be 0 eV.

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  Figure 3  The NORR pathways toward NH₃ production. (a) Schematic illustration of the possible NORR pathways toward NH₃, including O-distal, O-alternating, N-distal, and N-alternating pathways. Free energy diagrams of NORR over (b) Cu and (c) Pd/Cu surfaces.

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  Figure 4  The catalytic activity and selectivity of catalysts. Free energy diagrams of NORR over (a) Cu and (b) Pd/Cu at η = 0.49 V vs. RHE after renumbering the steps so that the reaction intermediate with the lowest free energy locates at the beginning of the reaction coordinate. (c) The G_max(η = 0.49 V) values of all catalysts. (d) The differences between U_L(NORR) and U_L(HER) of all catalysts.

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  Figure 5  Machine learning investigations. (a) Machine learning workflow with feature engineering. (b) Heat map inferred by Pearson's correlation coefficient. (c) Comparison between DFT-calculated and ML-predicted G_max(η = 0.49 V). (d) The ranking of the important features of XGBR. (e) Comparison between DFT-calculated and SISSO-predicted G_max(η = 0.49 V).

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