Although the excessive consumption of fossil energy has brought great development of society and technology, it has also led to new environmental problems and energy crisis [1,2]. Especially in the context of carbon peak and carbon neutrality, the use of clean energy sources to replace fossil energy sources is extremely significant [3,4]. Researchers have conducted extensive studies on energy sources, such as superoxide generated amines [5] and catalytic oxidation of sulfides [6]. As one of the important renewable carbon-free energy carrier, ammonia (NH₃) is environmentally friendly, low cost, high safety, and the heat loss ratio of ammonia combustion is much lower than that of gasoline and hydrogen, which makes it have a good potential for ammonia energy development [7,8]. At present, the industrial production of NH₃ mainly relies on the Haber-Bosch process, which not only has high conditions for temperature and pressure, but also produces a large amount of carbon dioxide [9,10]. Therefore, it is of great significance to explore the efficient green way of NH₃ production for achieving carbon peak and carbon neutrality.

In search of an effective alternative solution to ammonia production by the Haber-Bosch process, the electrochemical N₂ reduction reaction (NRR) and nitrate reduction reaction (NO₃RR) have attracted considerable research interest in the past few years due to its lower energy consumption and lower CO₂ emissions [11,12]. However, the high dissociation energy of N≡N bond leads to the problems of poor yield and low selectivity [13]. The dissociation energy of the N═O bond for NO₃⁻ (204 kJ/mol) is much lower than that of the N≡N bond (941 kJ/mol) [14], which lays a solid foundation for improving NH₃ formation kinetics. In addition, electroreduction of NO₃⁻ can also effectively mitigate the problem of NO₃⁻ enrichment in water environment, so that other pollutants can be effectively removed by the addition of synthetic cleaning chemical [15,16]. Therefore, electrochemical catalytic NO₃RR provide new opportunities for large-scale production of NH₃ under environmental conditions [17,18], which is of great significance for achieving carbon peak and carbon neutrality [19,20]. Finding efficient and highly selective NO₃RR electrocatalysts is the key to catalyze NO₃⁻ conversion.

In recent years, two-dimensional carbon-nitride materials (e.g., C₂N, C₃N₄, and C₄N) have been widely studied and proved to be the excellent transition metal doped substrates in the field of electrocatalysis [21-23]. Transition metal doped often forms M − N coordination centers, which have been shown to catalyze oxygen reduction reaction, oxygen evolution reaction, NRR, and NO₃RR [24,25]. Zhu et al. have proved that Hf/g-C₂N are predicted as potential electrocatalysts for the NO₃RR with limiting potential (U_L) values of −0.27 V [26]. Lv et al. have been explored that Ru/g-C₃N₄ is the most promising catalysts because of its lowest energy barrier and extraordinary selectivity [27]. The nuclear number of transition metal active centers can significantly regulate the catalytic activity of the catalyst. That is, different from single-atom catalysts, dual-atom catalysts (DACs) can provide more active sites and active configurational space, and the synergistic effect of dual transition metal atoms can effectively regulate the catalytic activity [28-30]. For example, Lv et al. have used DFT methods to calculate NO₃RR catalytic activity for transition-metal dimer embedded N-doped graphene [16]. The calculated results have shown that under the synergistic action of dual transition metal atoms, Cu₂@NG exhibits the lowest U_L of −0.36 V. Wu et al. have efficiently screened dual-atom Fe₂ DAC anchored by N-doped porous graphene (Fe₂@NG) for producing NH₃, which exhibits a rather low U_L = −0.45 V [31]. In addition, Chen et al. have designed novel homonuclear transition metals supported on N-doped graphene (TM₂/N₆-G). Cr₂/N₆-G, Mn₂/N₆-G, and Cu₂/N₆-G have demonstrated that they possess the excellent NH₃ conversion and the Faradic efficiency are greater than 61.28%, which makes them serve as the promising NO₃RR catalysts [32]. Shen et al. have indicated that double atom doped g-C₃N₄ can find efficient NO₃RR catalysts [33]. Recently, Tan et al. have proposed four novel carbon-nitride materials (C₇N₃, C₁₀N₃, C₁₃N₃, and C₁₉N₃) and demonstrated that they have excellent electrical conductivity, which makes them possess excellent potential in the field of electrocatalysis [34]. Transition metal doped them can form M-N active center, which provides the basic guarantee for catalyzing NO₃RR. However, current studies have shown that they have the potential to catalyze ORR and OER [35]. For example, Cai et al. have demonstrated by DFT that C₇N₃ is a good substrate to load transition metal, forming a catalyst that can effectively catalyze ORR [36]. Moreover, Chen et al. have proven that Rh-C₁₃N₃ possesses the lowest overpotentials and exhibits superior ORR and OER bifunctional catalytic activity [35]. The outstanding performance of these materials in ORR and OER raises high expectations for their potential in NO₃RR. Therefore, based on the above analysis, we speculate that transition metal doped C₇N₃, C₁₀N₃, C₁₃N₃, and C₁₉N₃ may exhibit good catalytic potential for NO₃RR.

In this work, we systematically investigated the possibility of homonuclear dual transition metal atoms doped C₇N₃, C₁₀N₃, C₁₃N₃, and C₁₉N₃ (M₂_C_xN₃) as NO₃RR catalysts by DFT methods. The homonuclear dual-atom is doped into the pore of carbon-nitride material to form the M-N_x active center with the surrounding N atoms. Firstly, the stability of M₂_C_xN₃ was evaluated by calculating formation energy (E_f) and dissolution potential (U_diss). The density of states (DOS) and band structures are calculated to describe the electronic properties of the catalyst. Secondly, the adsorption behaviors of NO₃⁻, U_L(NO₃RR) and the free energy diagrams are calculated to evaluate the NO₃RR catalytic performance. In particular, the solvation effects and dispersion correction on catalytic activity were also considered of M₂_C_xN₃ with excellent NO₃RR catalytic performance. Thirdly, the competitive reaction of hydrogen evolution reaction (HER) on M₂_C_xN₃ was studied. Then, the electronic structure analysis of Os₂_C₁₉N₃ were conducted. Finally, the first-principles molecular dynamics (FPMD) calculation of Os₂_C₁₉N₃ was calculated at 300 and 500 K to further evaluate stability. This work can not only effectively predict and high-throughput screening NO₃RR electrocatalysts with high performance, but also provide effective guidance value for experiments.

The spin-unrestricted DFT framework and implemented with the DMol³ module was used in the Materials Studio software [37,38]. The Perdew-Burke-Ernzerhof (PBE) functional of generalized gradient approximation (GGA) was employed as the exchange and correlation model [39]. The atomic orbitals' basic set was described using a double numerical plus polarization (DNP) method [40]. Convergence criteria were set as follows: energy convergence of 2 × 10⁻⁵ Ha, maximum force convergence of 0.004 Ha/Å, and maximum displacement convergence of 0.005 Å. To avoid artificial interactions, a vacuum layer with a thickness of 30 Å was used. For optimization, a 3 × 3 × 1 k-point grid centered around Γ was used, while electronic structure calculations (DOS, Mulliken charge, and deformation charge density) employed a dense 5 × 5 × 1 k-point grid. The FPMD calculations are performed during a period of 2 ps at the temperatures of 300 and 500 K.

The catalyst's stability was assessed in detail using E_f and U_diss [41,42]. E_f mainly focuses on exploring the change of per dopant atom to the stability of the catalyst. The calculation formulas for these parameters are provided below:

Ef=(Etotal−Esubstrate−2ETM)/2

(1)

Udiss=Uodiss(metal, bulk)−Ef/ne

(2)

where, the E_total, E_substrate, and E_TM correspond to the total energy of the catalyst, the substrate, and the energy of transition metal atoms in their bulk structure, respectively. U_diss^o(metal, bulk) denotes the standard dissolution potential of the bulk metal, while n signifies the number of electrons participating in the dissolution process.

In this study, the reaction processes between NO₃RR and intermediates were understood through the framework of thermodynamics. The equation of the whole reaction pathway from NO₃RR to NH₃ is as follows [43]:

$ \mathrm{NO}_3^{-}+9 \mathrm{H}^{+}+8 \mathrm{e}^{-} \rightarrow \mathrm{NH}_3+3 \mathrm{H}_2 \mathrm{O} $

(3)

The Gibbs free energy change (ΔG) of each elementary step during NO₃RR process was computed by the widely employed computational hydrogen electrode (CHE) model [44,45]:

ΔG=ΔE+ΔZPE−TΔS

(4)

where, E, T, ΔZPE, and ΔS represents the total energy, the temperature of 298.15 K, the change of zero-point energy, and the difference of the entropy, respectively.

The adsorption energy (E_ads) is calculated as follows [46]:

Eads=E*species−E*−Especies

(5)

where, the E_*species, E_*, and E_species are the energies of species adsorbed on catalyst, catalyst, and species, respectively.

For the adsorption free energy of ^*NO₃ (ΔG_^*NO3), the calculation formula is as follows [47]:

ΔG*NO3=G*NO3−G*−GHNO3(g)+1/2GH2(g)

(6)

where, G_^*NO3, G_*, G_{HNO3 (g),} and G_{H2 (g)} are the Gibbs free energy of NO₃^– adsorbed on catalyst, catalyst, HNO₃, and H₂ molecules, respectively.

Since the energy of HNO₃ used in the above formula is gaseous energy, it is necessary to correct the formula. The correction formula is as follows:

ΔG*NO3−correct=G*NO3−G*−GHNO3(g)+1/2GH2(g)+ΔGcorrect

(7)

where, ΔG_correct is the correction of free ion energy, and the value is 0.392 eV according to previous studies [47].

The theoretical limiting potential (U_L) can be defined as [48]:

UL=−ΔGmax/e

(8)

The hydrogen adsorption energy (ΔE_*H) is represented by the equation:

ΔE*H=E*H+E*−1/2EH2

(9)

where, E_*H, E_*, and E_H2 are the total energies the total energies of catalyst adsorpted with H atom, catalyst, and H₂ molecule, respectively.

The ΔG_*H can assess the HER catalytic activity and the formula is as follows [49]:

ΔG*H=ΔE*H+ΔZPE−TΔS

(10)

The main purpose of this work is to search for highly active NO₃RR electrocatalysts through efficient screening methods. Therefore, a strategy with four filtering steps is designed, as shown in Scheme 1. For this screening strategy, structural stability is first evaluated by calculating E_f and U_diss. After screening catalysts with excellent stability, the adsorption behaviors of NO₃⁻ is calculated on all catalysts, which is a prerequisite step for NO₃RR. Then, the electrocatalysts with excellent NO₃RR are found by calculating U_L(NO₃RR). Finally, a good electrocatalyst must be able to withstand the competitive impact of HER. If the candidate satisfies both ΔG_^*NO3 < ΔG_*H and U_L(NO₃RR) > U_L(HER), it has great potential to catalyze NO₃RR.

In this work, the crystal structure can be made by graphene supermonomers by removing the C atom of the six-membered ring and replacing the N atom. All substrates (C₇N₃, C₁₀N₃, C₁₃N₃, and C₁₉N₃) are constructed and presented in Fig. 1a and Figs. S1a-c (Supporting information). All transition metals considered in this work are shown in Fig. S1d (Supporting information). Meanwhile, the dual transition metal atom doped with the surrounding N atoms can form two coordination structures, one for M₂N₄ active center, named M₂_C_xN₃-I, and one for M₂N₆ active center, named M₂_C_xN₃-II, as shown in Figs. 1b and c and Fig. S2 (Supporting information).

In order to evaluate whether the electrocatalyst has excellent thermodynamic and electrochemical stability in the catalytic NO₃RR process, E_f and U_diss are respectively calculated as parameters for evaluating thermodynamic and electrochemical stability [46], and the results are presented in Figs. 1d and e and Fig. S3 (Supporting information). When E_f is less than 0 eV, it indicates that the M₂_C_xN₃-I and M₂_C_xN₃-II have the good thermodynamic stability. When U_diss is greater than 0 V, it indicates that the M₂_C_xN₃-I and M₂_C_xN₃-II have the good electrochemical stability. The greater the absolute value of E_f and U_diss, the more stable the catalyst. For the calculated results, it can be observed that most of the M₂_C_xN₃-I and M₂_C_xN₃-II have good stability. In particular, the E_f values of Zn-C_xN₃ can reach −3 eV or even more negative. In addition, taking Ni doped as an example, it can be observed that all Ni₂C_xN₃ have excellent thermodynamic and electrochemical stability. However, the stability of catalyst is different for different doping configurations. For example, the E_f values of Ni₂_C₇N₃-I and Ni₂_C₇N₃-II are −1.16 and −1.28 eV. The U_diss values of Ni₂_C₇N₃-I and Ni₂_C₇N₃-II are respectively 0.32 and 0.38 V. Obviously, for Ni₂_C₇N₃, the catalyst is more inclined to form Ni₂_C₇N₃-II than Ni₂_C₇N₃-I. A similar situation is found in all catalysts. Thus, in the subsequent studies, only the most stable configuration is used and defined as M₂_C_xN₃.

To have a deeper understanding of the interaction between the doped active metal and the surrounding N atoms, taking Os₂_C_xN₃ as an example, the density of state (DOS) is calculated and shown in Figs. S3a-d. It can be clearly observed that the d orbital of Os atoms overlapped significantly with the p orbital of N atoms at the Fermi level near the energy of 0 eV. In other words, there is a strong orbital hybridization between the d orbital of Os atoms and the p orbital of N atoms, which makes Os and N atoms have a strong interaction, which provides a good basis for the stability of the Os₂_C_xN₃. In addition, M₂_C_xN₃ electrocatalytic NO₃RR requires excellent electrical conductivity. Thus, the band structures of Os₂_C_xN₃ are calculated and plotted in Figs. S3e-h. They all have extremely low band gap (E_{band gap}), which indicates that they all have very good electrical conductivity. In other words, the catalyst with lower E_{band gap} value is advantageous for catalyzing the NO₃RR process.

In this work, the reaction considered is detailed in formula 3, involving the transfer of nine protons and eight electrons. The considered reaction pathways are shown in Fig. 2a. For these pathways, the difference mainly lies in the adsorption behavior of ^*NO on all stable catalyst. If the catalyst is adsorbed with ^*NO-end, it will likely move in the direction of removing the H₂O. If the catalyst is adsorbed with ^*NO-side, there are two adsorption configurations for its next hydrogenation, as shown in Fig. 2a. Firstly, the adsorption of NO₃⁻ is the first step, and its adsorption behavior on the catalyst is crucial for the subsequent reaction. By comparing the adsorption behavior of ^*NO₃ in various catalysts, the relative affinity of each catalyst for ^*NO₃ was predicted, and the catalytic potential of the catalyst for NO₃RR was preliminarily predicted. There are respectively two adsorption configurations for NO₃⁻, that is, 1O- and 2O-manner in Fig. S5 (Supporting information). Therefore, we calculated the optimal adsorption configuration of each catalyst. The optimal adsorption energy (E_^*NO3) and free adsorption energy of ^*NO₃ (ΔG_^*NO3) are calculated and shown in Fig. S6 (Supporting information). The more negative the E_^*NO3 and ΔG_^*NO3, the more inclined the reaction species to adsorb on the catalyst. For Fig. S6a, it can be found that some catalysts (Pd-, Os-, Fe-, Rh-, and Ir-C₇N₃) have weak adsorption strength, which may greatly affect the subsequent catalytic process. A similar condition has been observed with other catalysts (e.g., Pd- and Zn-C₁₀N₃, Rh-, and Zn-C₁₃N₃, Rh-, and Zn-C₁₉N₃). Thus, their subsequent NO₃RR activity is not discussed.

Then, the NO₃RR activity on all screened stable catalysts are evaluated and the limiting potentials (U_L(NO₃RR)) are calculated, as shown in Fig. 2b. The closer the value of U_L(NO₃RR) is to 0 V, the higher the NO₃RR activity of the catalyst. In other words, the darker the red region, the better the catalytic activity of the catalyst. Obviously, for M₂_C₇N₃, the U_L(NO₃RR) value of Zn₂_C₇N₃ (−0.36 V) is closest to 0 V, which indicates that it has the best catalytic activity in this type of catalyst. Moreover, the U_L(NO₃RR) values of Au₂_C₁₀N₃, Fe₂_C₁₃N₃, Fe₂_C₁₉N₃, and Os₂_C₁₉N₃ are between −0.60 V and 0 V, which indicates that they have excellent NO₃RR catalytic activity. Moreover, the formation of ^*NO₃H and ^*NOH in the catalytic process of NO₃RR is often accompanied by the input of external energy. Therefore, ΔG_^*NO3H and ΔG_^*NOH as activity descriptors with U_L are used to construct the volcano plot, as shown in the Fig. 2c. It can be seen that the darker the red region, the better the catalytic activity, that is, the best NO₃RR catalytic activity of Os₂_C₁₉N₃. In particular, by comparing their values with other reported excellent NO₃RR catalysts in Table S1 (Supporting information), such as HOF-Ti1 (U_L(NO₃RR) = −0.15 V) [47], V₂-Pc (U_L(NO₃RR) = −0.25 V [50], Os/GDY (U_L(NO₃RR) = −0.37 V) [13], Os₂_C₁₉N₃ has excellent catalytic activity with the U_L(NO₃RR) of −0.15 V. Thus, it can be used as the most promising NO₃RR catalyst.

Since the screened catalysts proved to have good catalytic activity, their catalytic mechanisms are studied in detail. In order to evaluate the reaction pathway on M₂_C_xN₃, the E_ads values of ^*NO are calculated. The more negative the E_ads values, the stronger the adsorption of ^*NO on M₂_C_xN₃. For Zn₂_C₇N₃ in Fig. 2d, ^*NO is more inclined to take the ^*NO-end route rather than the ^*NO-side route, because the adsorption energy (E_^*NO) on Zn₂_C₇N₃ for ^*NO-end (E_^*NO-end = −0.53 eV) is less than that of ^*NO-side (E_^*NO-side = −0.50 eV). For the whole reaction process, the potential-determining step (PDS) is determined to be the largest ∆G. Obviously, the PDS is * + NO₃⁻ → ^*NO₃ and the corresponding value is 0.36 eV, which requires additional energy. The similar condition has been reported for M − N − C catalyst [51]. The NO₃RR pathway of Zn₂_C₇N₃ is * + NO₃⁻ → ^*NO₃ → ^*NO₃H → NO₂ → ^*NO₂H → ^*NO → ^*NOH → ^*N → ^*NH → ^*NH₂ → ^*NH₃ → * + NH₃. For Au₂_C₁₀N₃, Fe₂_C₁₃N₃, and Fe₂_C₁₉N₃ in Fig. S7 (Supporting information), ^*NO also exists in the form of ^*NO-end. Thus, the reaction pathway of them and Zn₂_C₇N₃ are the same. Their PDS are ^*NO, ^*NO₃, and ^*NO₃ hydrogenation, respectively, and the corresponding values are 0.53, 0.58, and 0.60 eV respectively. Moreover, for Os₂_C₁₉N₃ in Fig. 2e, ^*NO₂ is hydrogenated to form ^*NO₂H as the PDS, and the corresponding value is 0.15 eV. Unlike Zn₂_C₇N₃, ^*NO is more likely to adsorb in the form of ^*NO-side (E_^*NO-side = −1.90 eV) than ^*NO-end (E_^*NO-end = 1.75 eV), which changes the subsequent hydrogenation pathway. The results show that ^*NOH is more likely to be hydrogenated to remove H₂O, rather than hydrogenated to produce ^*NHOH. Thus, the NO₃RR pathway of Os₂_C₁₉N₃ is * + NO₃⁻ → ^*NO₃ → ^*NO₃H → NO₂ → ^*NO₂H → ^*NO → ^*NOH → ^*N →^*NH → ^*NH₂ → ^*NH₃ → * + NH₃. In summary, different catalysts will produce different configurations of adsorption intermediates, which will affect the adsorption strength of catalyst for reaction intermediates. Then the PDS of the catalyst may be changed, changing the reaction pathway of the catalyst, thus affecting the catalytic activity of the catalyst.

HER is a competitive reaction of NO₃RR, which will affect the reaction efficiency of NO₃RR. Therefore, it is very necessary to evaluate the performance of catalyst for HER. In this paper, two methods are used to evaluate the selectivity of the catalyst and ΔG_^*NO3, ΔG_*H, U_L(NO₃RR), and U_L(HER) are calculated. The catalyst with more negative ΔG_^*NO3 value and more positive U_L(NO₃RR) value has better catalytic selectivity. First, ΔG_*H values on all screened catalysts are calculated and the free energy diagrams of HER are plotted in Fig. 3a and Figs. S8a-c (Supporting information). Then, the values of ΔG_*H and ΔG_^*NO3 values are compared for preliminary screening of M₂_C_xN₃ with catalytic potential for NO₃RR. The values of ΔG_^*NO3 should be more negative than that of ΔG_*H, indicating that M₂_C_xN₃ preferentially adsorbs NO₃. That is, M₂_C_xN₃ in the yellow region has excellent NO₃RR catalytic selectivity in Fig. 3b and Figs. S8d-f (Supporting information). Obviously, as the number of x increases, more M₂_C_xN₃ have excellent NO₃RR catalytic selectivity. Moreover, U_L is the dominant factor in the entire electrocatalytic process and is more suitable for evaluating the catalytic selectivity of NO₃RR and HER of M₂_C_xN₃. Therefore, to determine that NO₃RR has an energy advantage over HER, U_L(NO₃RR) and U_L(HER) on M₂_C_xN₃ are compared, as shown in Fig. 3c and Figs. S8g-i (Supporting information). M₂_C_xN₃ in the blue region indicates the lower U_L(NO₃RR) values, which means better NO₃RR selectivity. Overall, Os₂_C₁₉N₃ has superior catalytic potential for NO₃RR, and the values of U_L(NO₃RR) is −0.15 V. It is worth noting that although the remaining M₂_C_xN₃ do not have excellent NO₃RR catalytic selectivity, their HER activity is extremely valuable. Rh₂C₁₀N₃, Os₂_C₁₃N₃, and Pd₂C₁₉N₃ possess excellent HER catalytic activity, the corresponding U_L(HER) values are −0.02, −0.05, and −0.03 V, which is far superior to other reported excellent HER catalysts in Table S2 (Supporting information), such as, Rh-2D-SA (U_L(HER) = −0.13 V) [46], Sc@C₃–CN (U_L(HER) = −0.07 V) [52], Ti@Corrole (U_L(HER) = −0.02 V) [53], and Au@BC₃ (U_L(HER) = −0.04 V) [54]. After a series of screening strategies in Fig. S9 (Supporting information), 52 stable catalysts are selected. On this basis, the adsorption behavior of NO₃, catalytic activity of NO₃RR and competitive reaction HER are investigated. Finally, Os₂_C₁₉N₃ with the best NO₃RR catalytic activity is selected.

According to the above calculation results of U_L(NO₃RR), Os₂_C₁₉N₃ has the best catalytic activity of NO₃RR (U_L(NO₃RR) = −0.15 V). Therefore, the detailed electronic structure analysis of Os₂_C₁₉N₃ is carried out. Firstly, Os₂_C₁₉N₃ and reaction species are divided into two moieties respectively. That is, Os₂_C₁₉N₃ is moiety-1 and the reaction species is moiety-2, as shown in Fig. S10a (Supporting information). Then, the Mulliken charge is calculated and charge variation during the process of NO₃RR on Os₂_C₁₉N₃ is analyzed in Fig. S10b (Supporting information). Obviously, it can be observed that there is a significant charge transfer between Os₂_C₁₉N₃ and reaction species, which indicates a strong interaction between them. In addition, the amount of charge transfer between different reaction species and the catalyst is different, which will affect the interaction between the reaction species and the Os₂_C₁₉N₃. This can change the adsorption strength of Os₂_C₁₉N₃ towards reaction species, thereby altering their catalytic activity. In order to more clearly show the interaction between Os₂_C₁₉N₃ and reaction species, deformation charge density of reaction species on Os₂_C₁₉N₃ are calculated and displayed in Fig. S11 (Supporting information). The blue and yellow represent electron accumulation and depletion, respectively. It can be observed that there is obvious accumulation and depletion between Os₂_C₁₉N₃ and reaction species. This further indicates that there is a strong interaction between Os₂_C₁₉N₃ and reaction species during NO₃RR process, which is consistent with the above studies.

Finally, in order to further investigate the stability of Os₂_C₁₉N₃ at different temperatures (300 and 500 K), FPMD is calculated and exhibited in Fig. S12 (Supporting information). The results of FPMD calculation show that the energy always oscillates at the equilibrium state regardless of 300 or 500 K, which indicates that Os₂_C₁₉N₃ can exist stably at 300 and 500 K. This calculation results further verify the excellent stability of Os₂_C₁₉N₃.

It is well known that solvation effects (DFT-Sol) and dispersion corrections (DFT-D) will enhance the adsorption strength of the reaction intermediates on catalyst to a certain extent. In addition, it is extremely important to evaluate the catalytic activity of Os₂_C₁₉N₃ under the conditions of DFT-Sol, DFT-D, and DFT-D-Sol. Therefore, a detailed study is conducted on the catalytic process of Os₂_C₁₉N₃ towards NO₃RR under the conditions of solvation effects and dispersion corrections. The free energy diagrams are plotted in Fig. 4. First, under the condition of solvation in Fig. 4a, the adsorption strength of ^*NO on of Os₂_C₁₉N₃ is enhanced, which are −1.78 (E_^*NO-end) and −1.94 eV (E_^*NO-side). Then, it is found that when Os₂_C₁₉N₃ adsorbs ^*NOH for further hydrogenation, Os₂_C₁₉N₃ is more inclined to form ^*NHOH than ^*N. It is speculated that the solvation effects on ^*NHOH of Os₂_C₁₉N₃ is greater than that on ^*N. That is, the NO₃RR of Os₂_C₁₉N₃ is carried out in pathway Ⅱ. In particular, when the Os₂_C₁₉N₃ adsorbs ^*NH₂OH, Os₂_C₁₉N₃ can form *OH by hydrogenation to remove NH₃ (pathway Ⅲ), and can also form ^*NH₂ by hydrogenation to remove H₂O (pathway Ⅱ). It can be found that ^*NH₂OH to *OH requires the input of additional energy, which is disadvantageous. Thus, ^*NH₂OH is more inclined to hydrogenate to form ^*NH₂. In summary, under DFT-Sol, the optimal reaction pathway of the catalyst is pathway Ⅱ, that is, * + NO₃⁻ → ^*NO₃ → ^*NO₃H → NO₂ → ^*NO₂H → ^*NO → ^*NOH → ^*NHOH → ^*NH₂OH → ^*NH₂ → ^*NH₃ → * + NH₃. Similarly, under the conditions of DFT-D and DFT-D-Sol, the optimal pathway for Os₂_C₁₉N₃ to catalyze NO₃RR are also pathway Ⅱ, as shown in Figs. 4b and c. It can be found that under the three conditions, Os₂_C₁₉N₃ still possesses excellent catalytic activity, and the U_L(NO₃RR) values are −0.06, −0.15, and −0.06 V, respectively. In summary, solvation effects and dispersion corrections can change the adsorption behavior of reaction intermediates on Os₂_C₁₉N₃, thereby regulating the NO₃RR catalytic activity of Os₂_C₁₉N₃.

In summary, this work is aim to search for highly active NO₃RR electrocatalysts through efficient screening strategy by DFT method. The four-step screening strategy was used to search for high-performance NO₃RR electrocatalysts. Firstly, for this screening strategy, structural stability is evaluated by calculating E_f and U_diss. The results show that different transition metal doped will preferentially generate different catalyst configurations. Then, the results of DOS provide strong evidence for the stability of the catalyst and the band structure, which makes it possible for M₂_C_xN₃ to electrocatalyze NO₃RR. Secondly, the adsorption behaviors of NO₃ as a prerequisite step for NO₃RR, the adsorption configuration is considered. Thirdly, the electrocatalyst with excellent NO₃RR is found by calculating U_L(NO₃RR). Different M₂_C_xN₃ will produce different configurations of adsorption intermediates, which will affect the adsorption strength of M₂_C_xN₃ for the intermediates, and thus affect the catalytic activity of M₂_C_xN₃. Au₂_C₁₀N₃, Fe₂_C₁₃N₃ Fe₂_C₁₉N₃, and Os₂_C₁₉N₃ possess lower U_L(NO₃RR) values with −0.53, −0.58, −0.60, and −0.15 V, respectively. In particular, the free energy diagrams of M₂_C_xN₃ with excellent NO₃RR catalytic performance have been studied. The NO₃RR process of Os₂_C₁₉N₃ is * + NO₃⁻ → ^*NO₃ → ^*NO₃H → NO₂ → ^*NO₂H → ^*NO → ^*NOH → ^*N → ^*NH → ^*NH₂ → ^*NH₃ → * + NH₃. In addition, applying the ΔG_^*NO3 < ΔG_*H as evaluation criteria, the results show that as the number of x increases, more M₂_C_xN₃ have excellent NO₃RR catalytic selectivity. The applying U_L(NO₃RR) < U_L(HER) as evaluation criteria, Os₂_C₁₉N₃ has superior catalytic potential for NO₃RR, and the values of U_L(NO₃RR) is −0.15 V. The volcano plot also proves that Os₂_C₁₉N₃ possesses the best NO₃RR catalytic activity. It is worth noting that Rh₂C₁₀N₃, Os₂_C₁₃N₃, and Pd₂C₁₉N₃ possess excellent HER catalytic activity, the corresponding U_L(HER) values are −0.02, −0.05, and −0.03 V. In particular, it can be found that under the conditions of DFT-Sol, DFT-D, and DFT-D-Sol, Os₂_C₁₉N₃ still possesses excellent catalytic activity, and the U_L(NO₃RR) values are −0.06, −0.15, and −0.06 V, respectively. For electronic structure analysis and stability of Os₂_C₁₉N₃ (the best NO₃RR performance), the Mulliken charge is calculated and charge variation during the process of NO₃RR is analyzed. Different amounts of charge transfer can change the adsorption strength of Os₂_C₁₉N₃ towards reaction species, thereby altering their catalytic activity. This conclusion is further proved by the deformation charge density. Finally, the results of FPMD calculation show that Os₂_C₁₉N₃ can exist stably at 300 and 500 K. Thus, Os₂_C₁₉N₃ shows excellent thermodynamic and electrochemical stability by calculating E_f and U_diss, and also possesses low U_L(NO₃RR) values, which is a NO₃RR catalyst with high catalytic potential. This work can provide a possible reference value for further exploration of novel NO₃RR catalysts and ammonia synthesis.

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

Yahui Li: Investigation, Writing – original draft, Formal analysis. Quanchen Feng: Writing – review & editing. Krisztina László: Writing – review & editing. Ying Wang: Methodology, Software, Writing – review & editing, Conceptualization, Funding acquisition.

Acknowledgments

This work was supported by National Natural Science Foundation of China (NSFC, No. 22276138), Science & Technology Commission of Shanghai Municipality (No. 22230712800), and the Fundamental Research Funds for the Central Universities and the Foundation of State Key Laboratory of Pollution Control and Resource Reuse (Tongji University) (No. 2022-4-ZD-07). We acknowledge the National Supercomputing Center in Shenzhen for providing the computational resources and Materials Studio.

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.cclet.2025.111536.