Theoretical insights of nickel-based dual-metal atoms supported on C₂N sheets for urea electrooxidation

Abstract

The electrocatalytic urea oxidation reaction (UOR) enables energy-saving hydrogen production and waste degradation but requires efficient catalysts due to its complex, sluggish 6-electron transfer mechanism. In this study, we designed a series of stable 3d transition metal heterometal atom pairs (TMNi, TM refers to Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, or Zn) supported on the C₂N substrate as UOR catalysts, systematically investigating their potential to enhance the activity of Ni₂/C₂N. Among these, CrNi/C₂N displayed a superior capability to lower the limiting potential of the UOR compared to CuNi/C₂N and Ni/C₂N. The enhanced catalytic CrNi/C₂N system primarily stems from the stronger TM–Ni interactions, notable differences in charge distribution, more localized electronic states, and a higher d-band center associated with CrNi/C₂N relative to CuNi/C₂N and Ni₂/C₂N. These attributes not only ensure the stability of the well-dispersed CrNi pairs on C₂N but also amplify the ability of the active center to adsorb and activate reaction intermediates. Moreover, CrNi/C₂N demonstrates good selectivity for the UOR by exhibiting reduced susceptibility to forming NO₂ by-products and undergoing the competing oxygen evolution reaction. This theoretically driven work identifies CrNi/C₂N as the top-performing UOR dual-metal-atom catalysts, combining 0.99 V limiting potential with selective N₂ generation through electronic structure modulation, offering guidance for advanced catalyst design through the strategic use of transition metal heterometal atom pairs.

Keywords: Urea oxidation reaction; C₂N; Dual-atom catalyst; Nickel-based compounds; DFT calculations.

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1 Introduction

Urea, a nitrogen-rich compound, is prevalently found in domestic sewage, industrial wastewater and agriculture wastes. The degradation of urea in these wastewaters is one of the useful methods that prevent urea from transferring into harmful nitrogen oxides that pollute the environment.^1–3 In recent years, the coupling of the urea oxidation reaction (UOR) with the hydrogen evolution reaction in an electrolytic cell has garnered significant interest.^4,5 This method offers a relatively low theoretical potential of 0.37 V vs. RHE, which is 0.86 lower than that of the anodic oxygen evolution reaction (OER) in water electrolysis (1.23 V). UOR not only facilitates the degradation of urea-containing waste with minimal energy consumption but also generates high-value hydrogen, thereby contributing to both green energy production and environmental protection. Nevertheless, the UOR involves a sluggish 6-electron transfer step and the formation of multiple reaction intermediates, resulting in a rather complex reaction mechanism. Hence, the development of highly efficient catalysts is crucial for facilitating the efficient progress of the UOR. Currently, the research on UOR catalysts mainly focuses on Ni-based materials, such as nickel-based alloys, nickel-based metal compounds (such as Ni-based oxides, phosphides, sulfides, etc.).^6–10 Despite the advantages of certain UOR activity, good conductivity, low cost, and easy accessibility of these materials, the UOR activity on these materials is still restricted by unclear active sites, ambiguous catalytic mechanism, and insufficient material stability.^11,12 Developing Ni-based materials with high activity, stability, and clear active sites and elucidating the catalytic mechanism remain the main tasks in the current research on UOR catalysts.

In the past decade, the emergence of single-atom catalysts (SACs) has aroused great interest due to their high atomic utilization efficiency and excellent catalytic activity. Researchers have combined different metal single atoms and various types of support materials to form SACs for catalyzing various electrocatalytic reactions.^13–15 Despite promising prospects, SACs usually have simple structures and lack coordinated active sites, which prevent them from breaking the linear relationship between the adsorption energy of reaction intermediates, activating the complex intermediates, and surpassing the inherent electrocatalytic performance limitations, such as activity, stability and high selectivity.^16,17 To address this issue, a more promising strategy is to introduce a second metal atom on the support substrate to form dual-metal-atom catalysts (DACs). DACs can combine the advantages of two metal atoms and introduce atomic-level synergistic interactions, which are expected to break the theoretical limits of SACs.^18,19 For DACs, the substrate interacts with metal atoms through chemical bonds, stabilizing the metal atoms and altering their electronic structure.^20,21 Therefore, in addition to the type and inherent properties of the metal atom, the substrate for DACs is equally important.

Different from the commonly utilized graphene-based materials, C₂N monolayers, as a prominent two-dimensional material, feature a uniform nitrogenated pore structure. The edges of these pores, rich in sp²-bonded nitrogen atoms, can effectively anchor metal atoms or clusters and hinder their diffusion or aggregation.²² As a result, C₂N has proven to be an excellent substrate for accommodating dual atoms. Various metal atoms have been anchored onto the C₂N substrate to form catalysts with atomically-doped pairs, such as Sc₂/C₂N, Ti₂/C₂N, and Cu₂/C₂N, which have been developed for catalyzing various electrocatalytic reactions, including hydrogen evolution, nitrogen reduction, oxygen reduction, and hydrazine oxidation.^23–26

Although there has been limited research on the use of C₂N-supported metal atoms for the UOR, our previous studies have confirmed that Ni single atoms loaded on C₂N to form Ni/C₂N exhibit certain UOR activity.²⁷ Building upon this, by introducing a second Ni atom into the pores of C₂N to design the dual-atom catalyst Ni₂/C₂N, it can provide dual anchoring sites for N-containing intermediates, thus facilitating the adsorption and transformation of nitrogen-containing intermediates and ultimately enhancing UOR activity.²⁷ However, compared to some Ni-based catalysts, Ni₂/C₂N still shows certain activity deficiencies. One approach to enhancing the activity of dual-atom catalysts is to achieve atom pair heterogenization by introducing a second metal atom, thereby forming catalysts that effectively improve the catalytic activity. For instance, Li et al. synthesized CuCo DACs which exhibit strong synergistic interactions between asymmetrically deployed CuC₄ and CoN₄ sites, resulting in a significantly polarized charge distribution.²⁸ This leads to enhanced capabilities of the catalyst in substrate adsorption and O₂ activation, demonstrating better performance for the oxidative esterification of aromatic aldehydes than the single active component. Ren et al. synthesized a Ni/Fe–N–C catalyst with Ni–Fe pairs, where the synergy between Ni and Fe reduced the energy barriers for *COOH formation and *CO desorption, facilitating CO₂ reduction.²⁹ For the purpose of breaking through the stubborn restriction of scaling relations on SAC catalysts, Wang et al. designed CuCr/C₂N and CuMn/C₂N that show low limiting potentials of −0.37 V and −0.32 V, respectively, for CO₂ reduction to CH₄.³⁰ Thereby, a similar strategy can be applied to enhance the UOR activity of Ni₂/C₂N and further clearly understand the microscopic reaction mechanisms and fundamental factors that determine the catalytic activity, but still remains unexplored.

Based on the above discussion, this study aims to introduce 3d transition metal atoms into the Ni₂/C₂N system to form TM–Ni/C₂N catalysts containing TM–Ni hetero-atom pairs. The potential of TM atoms to enhance the UOR activity of Ni₂/C₂N is investigated using density functional theory calculations along with the selection of heteroatomic pairs with optimal activity. Furthermore, by analyzing the catalytic mechanism, identifying key intermediates, and examining the electronic structures of metal atom pairs within TM–Ni/C₂N along with the interactions of these active sites with key intermediates, the fundamental reasons behind the promotion of UOR activity facilitated by the optimal TM–Ni/C₂N catalysts are explored. Finally, the selectivity and stability of the optimal catalysts are evaluated by excluding the possibility of catalytic side reactions and assessing the kinetic stability of the catalysts.

2 Results and discussion

2.1 The structure and stability analysis of TMNi/C₂N

Based on Ni/C₂N and Ni₂/C₂N structures constructed in previous work,²⁷ we incorporated another TM atom into Ni/C₂N or substituted a Ni atom in Ni₂/C₂N with another TM atom, where TM refers to 3d transition metal atoms such as Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn, as illustrated in Fig. 1a. This resulted in the formation of TMNi dual atoms anchored within the hole of C₂N. Both TM and Ni atoms tend to bond with three surrounding N atoms, forming three TM–N bonds, while TM–Ni bonds are established between TM and Ni through the overlap of their valence orbitals. To assess the thermodynamic stability of the TMNi/C₂N system, we calculated two types of binding energies with consideration of two scenarios during the synthesis process: the sequential anchoring of TM following Ni on C₂N and the simultaneous anchoring of TMNi onto the C₂N substrate. The former one is the binding energy of TM on Ni/C₂N, denoted as E_b(TM), according to the following equation:

E_b(TM) = E_TMNi/C2N − E_Ni/C2N − E_TM (1)

Fig. 1 (a) The structure of TMNi/C₂N. (b) The binding energies of TMNi (E_b(TMNi)) on C₂N and TM (E_b(TM)) on Ni/C₂N.

The latter one is the binding energy of TMNi adding on the hollow of C₂N (E_b(TMNi)) which was defined as:

E_b(TMNi) = E_TMNi/C2N − E_C2N − E_TMNi (2)

Here, E_TMNi/C2N, E_Ni/C2N, E_TM, E_TMNi and E_C2N are the energies of TMNi/C₂N, Ni/C₂N, single TM atom, TMNi atom pair and C₂N, respectively. The results of these binding energies are shown in Fig. 1b. Notably, all calculated values of E_b(TMNi) and E_b(TM) are negative, suggesting that either the TMNi pair or TM can be stably anchored in the not fully occupied hole of C₂N. Besides, E_b(TMNi) is significantly more negative than E_b(TM). This observation indicates that the abundance of N atoms on the edge of the hole of C₂N facilitates the anchoring of the TMNi pair.

2.2 Screen of the promising TMNi/C₂N for UOR

To identify the TMNi/C₂N systems with optimal UOR activity, we need to determine the catalytic pathways first. Based on prior research and the literature,^7,27 we identified two pathways as depicted in Fig. 2a: one pathway, referred to as the O_ter pathway, primarily involves the adsorption of intermediates mainly via O–TM interactions, while the other, referred to as the N_ter pathway, focuses on the adsorption of intermediates via N–TM interactions. In the two pathways, the adsorbed species dehydrogenate gradually, then experience C–N bond breakdown and N₂ formation, and finally CO oxidation to produce CO₂. Due to the presence of bimetallic sites, in the O_ter pathway, nitrogen-containing intermediates form metal–adsorbate bonds with both metal atoms mainly through O and N atoms. In contrast, the N_ter pathway involves the formation of chemical bonds with both metal atoms primarily through two N atoms.

Fig. 2 (a) The schematic diagram of the O_ter pathway and N_ter pathway. (b) The urea adsorption free energy (ΔG_ads) on TMNi/C₂N and the insets are the adsorption model of urea with O_ter (green) and N_ter (blue) structures, respectively. (c) The free energy change of potential determining steps (ΔG_PDS) of the two pathways on TMNi/C₂N. (d and e) The free energy diagrams of the O_ter and N_ter pathway on Ni₂/C₂N, CrNi/C₂N and CuNi/C₂N, respectively.

Following this, we examined the adsorption ability of the TMNi site for urea molecules in both pathways by calculating the adsorption Gibbs free energy (ΔG_ads), and a positive value of ΔG_ads indicates that urea molecules can be spontaneously or easily adsorbed on active sites, while a negative value suggests the opposite. In Fig. 2b, urea tends to be adsorbed on a single metal atom via either an O–TM (O_ter adsorption structure) or a N–TM bond (N_ter adsorption structure) due to the saturated coordination of N in urea molecules. For one TMNi/C₂N, the O_ter adsorption structure exhibits a more negative ΔG_ads value than the N_ter structure, indicating better stability for the O_ter adsorption structure. Notably, the ΔG_ads values of urea adsorption on Ni₂/C₂N are positive for both adsorption configurations, whereas all other TMNi/C₂N systems yield more negative ΔG_ads values for urea adsorption. Except for Cu, all other TM variants result in negative ΔG_ads, indicating that urea can be spontaneously adsorbed on the corresponding TMNi/C₂N. Furthermore, the ΔG_ads value decreases as the TM employed occurs earlier in the periodic table, suggesting that introducing heterogeneous TM into the Ni/C₂N system can enhance urea adsorption.

Subsequently, we calculated the free energy changes (ΔG) for each step in both pathways and plotted the free energy profiles of each system (Fig. S1). We summarized the ΔG of the potential determining step (PDS) of all TMNi/C₂N systems, represented as ΔG_PDS, which corresponds to the maximum ΔG (ΔG_max) of each pathway. In Fig. 2c, except for TiNi/C₂N and MnNi/C₂N, all other TMNi/C₂N systems exhibit a lower ΔG_PDS for the N_ter pathway compared to the O_ter pathway, indicating a higher tendency for the N_ter pathway to occur. Taking Ni₂/C₂N as a reference, the ΔG_PDS values for the O_ter and N_ter pathways are 1.62 eV and 1.22 eV, respectively. In the case of the O_ter pathway, except for ZnNi/C₂N, all other TMNi/C₂N systems exhibit ΔG_PDS values lower than that of Ni₂/C₂N. Notably, the introduction of Ti, Cr, and Cu (with ΔG_PDS values of 1.18, 1.09, and 1.18 eV, respectively) significantly reduces the ΔG_PDS for the O_ter pathway on TMNi/C₂N, suggesting that these transition metals can effectively facilitate the UOR through the O_ter pathway. Regarding the N_ter pathway, only certain TM atoms, like V, Cr, Fe, and Cu, successfully lower the ΔG_PDS compared to Ni₂/C₂N, where V, Cr, and Cu especially contribute ΔG_PDS of TMNi/C₂N of 1.11 eV, 0.99 eV, and 1.08 eV, respectively. This indicates that the introduction of V, Cr or Cu can promote the N_ter pathway more effectively. Considering the ΔG_PDS of both pathways, Cr and Cu demonstrate a capacity to decrease the ΔG_PDS for Ni₂/C₂N in both pathways, establishing them as effective alternatives among the chosen 3d transition metals to replace one Ni in the Ni₂/C₂N or to add in the hole of Ni/C₂N and thereby promote the UOR.

Next, the UOR free energy diagrams for CrNi/C₂N and CuNi/C₂N are compared with that for Ni₂/C₂N to explore the differences in the UOR mechanism and activity among these systems. The activation and deprotonation of urea, or the oxidation of the *CO intermediate, are often regarded as key steps for the UOR.^31,32 As shown in Fig. 2d and e, for the O_ter pathway, urea adsorption, activation, and all deprotonation steps on the active sites of Ni₂/C₂N and CuNi/C₂N are endothermic processes, while on CrNi/C₂N, the urea adsorption and first proton desorption steps are exothermic, suggesting that CrNi/C₂N is more favorable for initiating urea oxidation. Additionally, during the *CO oxidation stage (i.e., *CO → *COOH), CrNi/C₂N requires less energy than Ni₂/C₂N and CuNi/C₂N, making it more favorable for *CO oxidation. For the PDS of these three systems, the third proton desorption step (*CONH₂N → *CONHN) prevails, and based on their ΔG_PDS values, the activity follows the sequence CrNi/C₂N > CuNi/C₂N > Ni₂/C₂N. Furthermore, compared to Ni₂/C₂N, the limiting potential U_limiting (calculated as U_limiting = ΔG_PDS/e) for CrNi/C₂N and CuNi/C₂N is reduced by 0.53 V and 0.44 V, respectively, indicating the higher activity of CrNi/C₂N and CuNi/C₂N. Similarly, for the N_ter pathway, the CrNi/C₂N exhibits catalytic characteristics analogous to those seen in the O_ter pathway, favoring urea adsorption, activation, and *CO oxidation. The PDS for the Ni₂/C₂N and CuNi/C₂N corresponds to the second proton desorption step (i.e. *CONH₂NH → *CONH₂N), whereas CrNi/C₂N features the fourth proton desorption step (i.e. *CONHN → *CONN). The activity order remains CrNi/C₂N > CuNi/C₂N > Ni₂/C₂N, with CrNi/C₂N and CuNi/C₂N showing reduction in U_limiting of 0.23 V and 0.14 V, respectively, compared to Ni₂/C₂N. Across both pathways, the subsequent deprotonation steps of nitrogen-containing intermediates in the TMNi/C₂N systems remain critical to the overall reaction. Compared with Ni₂/C₂N, the presence of heterogeneous TM in CrNi/C₂N or CuNi/C₂N enhances the adsorption of nitrogen-containing intermediates, thereby reducing the energy change for key steps and ultimately improving catalytic activity. Besides, the UOR on CrNi/C₂N or CuNi/C₂N is more likely to experience the N_ter pathway than the O_ter pathway due to the lower U_limiting of the N_ter pathway.

Given the critical role of the solvent in electrocatalytic reactions, it is essential to analyze whether the activity trends derived from vacuum calculations are held in a more realistic environment. To this end, we employed an implicit solvation model (VASPsol), which is widely used in theoretical studies of electrocatalysts,^33–36 to recalculate the free energy profiles of the N_ter pathway for three representative catalysts: CrNi/C₂N, CuNi/C₂N, and Ni₂/C₂N. In Fig. S2, the free energy diagram of the N_ter pathway with implicit solvation effect exhibits ΔG_PDS of 0.95, 1.03, and 1.28 eV for CrNi/C₂N, CuNi/C₂N, and Ni₂/C₂N, respectively. This clearly preserves the activity trend CrNi/C₂N > CuNi/C₂N > Ni₂/C₂N, which is identical to that concluded from our initial vacuum-phase screening. Although the absolute adsorption free energies of intermediates experience a shift of 0 to 0.5 eV compared to the vacuum case, the identity of the PDS and the relative activity trend remain unchanged. Therefore, the activity trend based on results of vacuum calculations is effective and reliable for identifying the most promising TM/C₂N candidate for efficient UOR.

To investigate the differences in catalytic activity between the selected optimal heterogeneous bimetallic atom catalysts and their corresponding homogeneous counterparts, we constructed models of Cr₂/C₂N and Cu₂/C₂N. Because CrNi/C₂N and CuNi/C₂N are more prone to converting urea into N₂ and CO₂via the N_ter pathway, we mainly calculated the free energy changes of the UOR catalyzed by Cr₂/C₂N and Cu₂/C₂N along the N_ter pathway. As shown in Fig. S3, the PDS for Cr₂/C₂N corresponds to the step from *CONHN to *CONN, and for Cu₂/C₂N is *CONHNH to *CONHN, with ΔG_PDS values of 1.30 eV and 1.53 eV, respectively. These values are 0.31 eV and 0.45 eV higher than the corresponding ΔG_PDS for CrNi/C₂N and CuNi/C₂N, respectively, verifying that CrNi/C₂N and CuNi/C₂N exhibit superior UOR activity compared to their homogeneous bimetallic counterparts. Thus, we focus on CrNi/C₂N and CuNi/C₂N and the origin of their activity in the next section.

2.3 Electronic structure analysis of promising TMNi/C₂N

The electronic structure of catalysts is crucial for the adsorption of intermediates and overall reaction. In this part, we explore the electronic structure starting from the intrinsic structural properties of the catalysts. We computed the charge density difference, Bader charge, and spin density of the bimetallic pair on C₂N, followed by calculating the density of states (DOS) and the crystal orbital Hamilton population (COHP) of the TMNi pair. The charge density difference diagrams in Fig. 3a and S4 show the difference of charge transfer between the three TMs (Ni, Cr and Cu) and Ni. It is clear that charge transfer occurs between Ni and these TM atoms, and compared with Ni₂/C₂N, the charge transfer between Cr and Ni is more significant, while the charge transfer between Cu and Ni is relatively weak. This indicates stronger interaction between the Cr–Ni pair among the three atomic pairs.

Fig. 3 (a) The charge density difference between Ni and TM/C₂N (i.e. the charge density of TMNi/C₂N minus that of Ni and TM/C₂N); the isosurface level is set as 0.01 e Å⁻³, and yellow/blue represents charge accumulation/depletion. (b) The spin density of TMNi/C₂N with an isosurface level of 0.01 e Å⁻³. (c) PDOS patterns of TM-3d orbitals for each TMNi/C₂N. (d) The crystal orbital Hamilton population (COHP) of the TMNi pair for each TMNi/C₂N.

Further calculations of the surface Bader charge (Table 1, where positive values represent the loss of electrons, negative values represent the gain of electrons) reveal that the Cr (1.05 e) of CrNi/C₂N and Cu (0.60 e) of CuNi/C₂N possess more positive charges than their paired Ni atoms and the Ni (0.59 e) of Ni₂/C₂N. This suggests that Cr and Cu are more prone to transferring electrons to the system. Additionally, the introduction of Cr or Cu instead of Ni to the bimetallic atomic system leads to a partial transfer of electrons to its paired Ni atom, reducing its positive charge. Notably, Ni of CrNi/C₂N exhibits the lowest Bader charge value (0.40 e) among the three systems, indicating that Ni accumulates more electrons from its TM in CrNi/C₂N than the other two TMNi/C₂N, which is consistent with the results observed in the charge density difference (Fig. 3a). The clearly differentiated charge distribution between the Cr and Ni atoms in the CrNi/C₂N system is advantageous for the adsorption and activation of intermediates.³⁷

Table 1 The Bader charge, spin moments and band center of Ni and TM in three TMNi/C₂N (TM = Ni, Cr and cu) systems

Systems	Bader charge (e)		Spin moments (μB)		Band center (eV)
	Ni	TM	Ni	TM	Ni-3d	TM-3d	TM-3p
Ni2/C2N	0.59	0.59	0.00	0.00	−1.41	−1.41	−1.03
CrNi/C2N	0.40	1.05	−0.21	3.28	−1.22	−0.40	−0.78
CuNi/C2N	0.57	0.60	−0.27	0.57	−1.27	−2.52	−0.47

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Moreover, the spin density in Fig. 3b shows almost negligible spin electron distribution on Ni₂/C₂N, indicating that the Ni₂ center is nonmagnetic. In contrast, the TMNi pairs in CrNi/C₂N and CuNi/C₂N exhibit significant spin electron distribution, with a more pronounced distribution around Cr. Calculations of the spin moments (Table 1) further confirm that Cr has significantly higher spin moments of 3.28 μ_B than Cu (0.57 μ_B). This also indicates that the spin electrons in CrNi/C₂N are more localized. The distinctly localized spin moments on the Cr site of CrNi/C₂N will facilitate the adsorption of intermediates.^24,38

To investigate the electronic state distribution of the central metal atoms in the three systems, we calculated the projected density of states (PDOS) of the metal 3d orbitals (Fig. 3c). The central metal pair in Ni₂/C₂N exhibits a relatively symmetrical PDOS distribution with electronic states below the Fermi level primarily localized in the range of −2.5 to 1 eV, confirming its non-magnetic characteristics. In the CrNi/C₂N system, the spin-up and spin-down electronic states of Cr 3d and Ni 3d show a distinctly asymmetric distribution. The filled electronic states of Cr 3d are mainly localized in the spin-up portion with a narrow range of −2.2 to 0 eV, which confirms a more localized distribution of spin electrons on Cr. Furthermore, in CrNi/C₂N, there is significant PDOS resonance between Cr 3d and Ni 3d in the range of −2 to 0 eV, suggesting strong interactions between Cr and Ni. For CuNi/C₂N, the spin-up and spin-down electronic states of Cu 3d and Ni 3d also display an asymmetric distribution, with a more delocalized filling of electronic states (Cu 3d and Ni 3d are primarily distributed in the ranges of −3.5 to 1 eV and −3.5 to 0 eV, respectively). The resonance of Cu 3d and Ni 3d PDOS is confined to the energy regions around −3, −1.7, and 0 eV, indicating weaker interactions between Cu and Ni. Based on the PDOS, we computed the d-band center, shown in Table 1. Generally, the closer the d-band center is to the Fermi level (and the more positive it is), the more favorable it is for the adsorption of intermediates. When Cr or Cu replaces one Ni of Ni₂/C₂N, the d-band center of Ni shifts positively and thus can enhance the adsorption ability of the Ni site. Notably, Cr of CrNi/C₂N exhibits the highest positive d-band center (0.40 eV) among the three TM atoms, thus most favorably facilitating the adsorption of intermediates. Although Cu of CuNi/C₂N has the most negative d-band center among the three TM atoms, its 3d orbitals are more saturated with electrons, and its 3p orbital can also be considered to participate in bonding with intermediates. Therefore, we computed the Cu 3p band center, which yields a value of −0.47 eV, more positive than Ni 3p in Ni₂/C₂N (−1.03 eV), thereby also promoting the adsorption of intermediates. However, compared to CuNi/C₂N, CrNi/C₂N has a superior d-band center that can facilitate the adsorption of intermediates more efficiently.

We then computed the COHP for TM–Ni pairs in all three systems and plotted the –COHP shown in Fig. 3d, with the purpose of exploring the bonding characteristics between TM and Ni. The positive part of –COHP represents bonding contributions, while the negative part denotes antibonding contributions. It is evident that the antibonding contributions of the three TM–Ni pairs below the Fermi level are quite similar, but the bonding contributions for Cr–Ni are significantly greater than those for Ni–Ni and Cu–Ni, with Cu–Ni exhibiting the least bonding contribution. By integrating the –COHP, we obtained the –ICOHP values, where a more positive –ICOHP indicates a greater bonding contribution, thus stronger bonding. The order of –ICOHP for the TM–Ni interactions is Cr–Ni (2.14) > Ni–Ni (1.55) > Cu–Ni (1.38), confirming that Cr–Ni has the strongest interaction, followed by Ni–Ni, with Cu–Ni showing the weakest interaction.

Therefore, the analysis of the electronic structure confirms that compared to CuNi/C₂N and Ni₂/C₂N, CrNi/C₂N exhibits a stronger TM–Ni interaction, more noticeable difference in charge distribution, more localized electronic states and higher d-band center. All these merits contribute to the catalyst's stability and the ability of the active center to adsorb and activate UOR intermediates. The distinct electronic structure characteristics of the active center in CrNi/C₂N compared to the other two systems may arise from the pronounced differences in the physicochemical properties between Cr and Ni atoms. On the one hand, the difference in electronegativity between Cr and Ni (1.66 vs. 1.91) is more significant than that between Cu and Ni (1.90 vs. 1.91), making charge transfer easier. On the other hand, Cr has more unpaired electrons, allowing its spin electrons to localize more easily around Cr after interacting with Ni. Moreover, the 3d electrons of Cr are filled at higher energy levels compared to that of Cu,³⁹ which allows Cr to enhance its orbital energy level and consequently increase its d-band center through orbital coupling when interacting strongly with Ni.

2.4 Key intermediates of UOR analysis on promising TMNi/C₂N

For complex catalytic reactions, it is needed to clarify how active sites influence the adsorption of intermediates from the aspect of the interaction between the active site and key intermediates to understand the effect of active sites on catalytic activity and hence identify the reasons for enhanced activity. The free energy diagrams in Fig. 2e imply that the key steps of the UOR on these three systems involve the deprotonation of the second and fourth protons, with the key species being *CONH₂NH, *CONH₂N, *CONHN and *CONN. To find a representative species, we employed linear regression analysis to investigate the correlations of adsorption free energies among these species. In Fig. 4a and b and Fig. S5, the adsorption free energies of all *CONHN exhibit strong correlations with *CONH₂NH, *CONH₂N, and *CONN (the average R² value for their linear relationships is 0.91). The average R² value between *CONH₂NH and the other three intermediates is 0.87; between *CONH₂N and the others, it is 0.91; and for *CONN, it is 0.87. Based on these results, *CONHN was selected as the key species for subsequent studies of the interactions between adsorbates and adsorption sites.

Fig. 4 The linear relationship between the adsorption free energy of *CONHN and *CONH₂NH (a) and between that of *CONHN and *CONN (b) on all TMNi sites of TMNi/C₂N. (c) The charge density difference between *CONHN and TM/C₂N (TM = Ni, Cr and Cu) and corresponding Bader charge. (d–f) The –COHP of main metal–intermediate bonds on Ni₂/C₂N, CrNi/C₂N and CuNi/C₂N, respectively.

Next, we examined the adsorption structure of *CONHN and calculated the charge density difference and charge transfer between *CONHN and the three catalysts. As depicted in Fig. 4c, in the Ni₂/C₂N system, due to the homogeneity and symmetry of the metal atom pair, *CONHN tends to have its two N atoms positioned atop the two Ni, forming two Ni–N bonds. In contrast, the heterogeneity of the metal atom pairs in CrNi/C₂N and CuNi/C₂N leads to the N atom (denoted as N1) in *CONHN that does not connect with H adsorbing at the TM–Ni bridge site, while the N atom (denoted as N2), which connects with H, adsorbing at the top site of TM, thus forming two TM–N bonds (i.e. TM–N1 and TM–N2) and one Ni–N2 bond. This leads to stronger bonding between *CONHN and the CrNi and CuNi centers compared to that between *CONHN and Ni₂. The charge density difference in Fig. 4c reveals significant charge transfer between *CONHN and the metal centers through TM–N bonds. Notably, for Ni₂/C₂N, due to the higher electronegativity of N compared to Ni, charge accumulation occurs around N, while charge depletion is observed around Ni, indicating that Ni transfers electrons to N. Furthermore, the charge transfer from Ni to N1 is more pronounced than from Ni to N2, suggesting that N1 acquires more electrons from Ni, resulting in a stronger Ni–N1 interaction compared to the Ni–N2 interaction. Similar behavior is observed in the CrNi/C₂N and CuNi/C₂N systems, where electrons are transferred from the bimetallic centers to *CONHN, with N2 in *CONHN receiving more electrons than N1 from the bimetallic centers. In CrNi/C₂N, electrons are primarily transferred from Cr to both N1 and N2, while in CuNi/C₂N, Cu donates electrons to N1, and both Cu and Ni transfer electrons to N2. Comparing the charge density difference of the three systems, there is more significant charge transfer between the CrNi or CuNi center and *CONHN compared to the transfer between Ni₂ and *CONHN. The calculated Bader charge indicates that the amount of charge transferred to *CONHN from the three systems (CrNi/C₂N, CuNi/C₂N, and Ni₂/C₂N) is 0.99, 0.94, and 0.54 e, respectively. This confirms that CrNi/C₂N and CuNi/C₂N transfer more electrons to *CONHN, suggesting a stronger interaction between CrNi/C₂N, CuNi/C₂N, and *CONHN than that between Ni₂/C₂N and *CONHN.

To further validate the results and investigate which of the CrNi/C₂N or CuNi/C₂N exhibits a stronger interaction with *CONHN, we calculated the –COHP of N1 and N2 with the bimetallic centers of the three systems. From these calculations, we derived the –ICOHP values, which provide a quantitative assessment of bond strength (Fig. 4d–f). For the Ni₂/C₂N system, the bonding contribution of Ni1–N1 is greater than that of Ni2–N2, while its antibonding contribution is smaller than that of Ni2–N2. This strengthens the conclusion that the Ni1–N1 interaction is more robust, and the –ICOHP values reinforce that Ni1–N1 has a stronger bonding effect than Ni2–N2. This finding aligns with the previous charge transfer analysis. For the CrNi/C₂N system, a similar phenomenon is observed, where the bonding contribution between Cr–N1 and Ni–N1 is significantly larger than that between Cr–N2. The –ICOHP value for Cr–N1 reaches 4.78, which is substantially higher than those for Ni–N1 (3.05) and Cr–N2 (2.56). This indicates that the strong interaction between CrNi/C₂N and *CONHN primarily originates from the Cr–N1 bond. In the CuNi/C₂N system, the bonding contributions for both Ni–N1 and Cu–N1 are notably higher than for Cu–N2, and the order of –ICOHP values is as follows: Ni–N1 (3.85) > Cu–N1 (2.24) > Cu–N2 (1.33). It suggests that the strong interaction between CuNi/C₂N and *CONHN arises from the contributions of both metals interacting with N1, which is also consistent with the charge transfer analysis.

Furthermore, comparing the –ICOHP values across the three systems reveals that the metal–N bonds in the CrNi/C₂N system are stronger than those in the CuNi/C₂N system, while the metal–N bonds in the Ni₂/C₂N system are the weakest. These data confirm that the interaction between CrNi/C₂N and *CONHN is the strongest, followed by CuNi/C₂N, and the last is Ni₂/C₂N. The analysis of the interaction between the metal centers and *CONHN indicates that the inclusion of Cr or Cu enhances the adsorption of key UOR intermediates on the bimetallic centers of TMNi/C₂N. Notably, Cr is most effective at strengthening the interaction between the metal center and N-containing intermediates, thereby facilitating the adsorption of key intermediates and promoting their conversion. This finding aligns with the free energy analysis of the UOR (Fig. 2).

Combining these results with the electronic structure analysis, we can understand why CrNi/C₂N favors intermediates adsorption. Firstly, the relatively low electronegativity of Cr and the presence of more unpaired electrons in the Cr–Ni active center allow for easier electron donation, facilitating the capture of N-containing intermediates which have higher electronegativity. Moreover, the significant differences in spin moments between the Cr–Ni active centers enhance their ability to adsorb and activate intermediates, leading to a noticeable spin moment change in key species after adsorption (Fig. S6). Lastly, the higher d-band center of the Cr–Ni active center also favors the adsorption of intermediates. Therefore, these results and analyses demonstrate that the unique electronic structure of the CrNi/C₂N system is beneficial for the adsorption and conversion of reaction intermediates, resulting in higher UOR activity.

2.5 The selectivity of promising TMNi/C₂N

The selectivity of catalysts is one of the key indicators of catalytic performance, and a good catalyst should exhibit high selectivity. In most case, the OER is one of the competing reactions for the UOR. To explore the likelihood that CrNi/C₂N and CuNi/C₂N preferentially undergo the UOR over the OER, we calculated the free energy changes of the OER (Fig. S7) on the bimetallic centers of the CrNi/C₂N and CuNi/C₂N and obtained their limiting potentials. In Fig. 5a, the PDS for the OER on both CrNi/C₂N and CuNi/C₂N is the third step, that is, the conversion of *O to *OOH, with ΔG_PDS of 2.87 eV and 2.15 eV, respectively. Accordingly, their corresponding limiting potentials are 2.87 V and 2.15 V vs. RHE, respectively. Based on our discussion in section 2.2, when limiting potentials of 0.99 V and 1.08 V are applied for CrNi/C₂N and CuNi/C₂N systems, respectively, electrochemical UOR on CrNi/C₂N and CuNi/C₂N becomes spontaneous. The differences in the limiting potentials of the OER and UOR for CrNi/C₂N and CuNi/C₂N systems are 1.88 V and 1.07 V, respectively, so it is difficult for both CrNi/C₂N and CuNi/C₂N to experience the competing OER, and that CrNi/C₂N is less likely to undergo the OER than CuNi/C₂N.

Fig. 5 (a) The free energy diagrams of the OER on CrNi/C₂N and CuNi/C₂N. (b) The main process of urea oxidation to produce 2NO₂ sequentially and simultaneously on CrNi/C₂N. (c) The free energy diagrams of urea oxidation to produce 2NO₂ sequentially and simultaneously on CrNi/C₂N.

In addition to the OER, UOR catalysts at high potentials may also produce undesirable NOx species and their acid ions, particularly NO₂, NO₂⁻ or NO₃⁻ through over-oxidation.^40–42 To investigate the potential formation of NO₂, we calculated the free energy change for NO₂ production during the UOR on CrNi/C₂N. Based on the adsorption modes of urea analyzed before (O_ter and N_ter), we considered two pathways for NO₂ formation: one pathway starts from urea adsorbed in the O_ter mode and sequentially generates NO₂, while the other starts from urea in the N_ter mode and produces NO₂ simultaneously. The sketch of reaction pathways is shown in Fig. 5b, with the calculated free energy change (Fig. 5c). For the pathway that forms NO₂ sequentially, the PDS corresponds to the third hydroxylation step of nitrogen, i.e., the transition from *CON to *CONOH, with ΔG_PDS of 2.74 eV. In contrast, for the simultaneous generation of the NO₂ pathway, the PDS is also the third hydroxylation step of nitrogen, i.e., from *CO(NO)₂ to *CONONOOH, with ΔG_PDS of 2.29 eV. Both pathways have ΔG_PDS that are significantly higher than that for the UOR pathway generating N₂ (>1.20 eV).

Besides, the urea oxidation to formation of NO₂⁻ and NO₃⁻ can also compete with the N₂ formation. Then, we computed the free energy profiles for competing pathways leading to NO₂⁻ and NO₃⁻ on CrNi/C₂N, following the mechanism proposed by Chen et al.⁴² The free energy profiles are shown in Fig. S8. The PDS is *NO oxidation to *NOOH for the NO₂⁻ formation pathway with ΔG_PDS of 2.00 eV, and is *NOO oxidation to *NOOOH for the NO₃⁻ formation with ΔG_PDS of 2.08 eV. These two competing pathways need more energy (at least 1 eV) to overcome the N₂ generation pathway, indicating the priority of the N₂ formation pathway.

These indicate that in the CrNi/C₂N system, the hydroxylation of N-containing intermediates of the UOR is difficult, and the overoxidation to produce NO₂, NO₂⁻ or NO₃⁻ is also challenging. Consequently, the production of UOR by-products is minimized, contributing to higher selectivity for the N₂ product on CrNi/C₂N. Based on the above analysis, we concluded that CrNi/C₂N, which exhibits the highest UOR activity among all constructed TMNi/C₂N, demonstrates a high selectivity for N₂ production during the UOR and is less susceptible to competing with the OER.

2.6 Guidelines for the experimental feasibility of promising TMNi/C₂N

Many strategies have been developed to synthesize well-defined bimetallic single-atom catalysts.^43,44 Based on these strategies, several catalysts with structures similar to TMNi/C₂N, such as dual metal atoms on polymeric carbon nitride (M1M2/PCN, M1 = Zn/Co/Ni/Bi, M2 = Ru/Cu),⁴⁵ FeNi atom pairs embedded in nitrogen-doped carbon (FeNiNC),⁴⁶ FeCu pairs on carbon substrate,⁴⁴ PtNi on C₃N₄ (ref. 47) have been synthesized. Therefore, the applicability of these strategies can provide valuable guidance for achieving the experimental feasibility of the predicted CrNi/C₂N catalyst. Additionally, the thermal stability of the CrNi/C₂N catalyst was evaluated using AIMD simulations at 500 K. In Fig. 6, the structure remained very stable during the dynamical simulations, with no significant structural deformation observed at 500 K. This clearly indicates the high thermal stability of the CrNi/C₂N catalyst. Therefore, it is anticipated that the successful synthesis of the CrNi/C₂N catalyst can be achieved in the future.

Fig. 6 The total energy of CrNi/C₂N during AIMD simulation at 500 K for 10 ps and the corresponding structure before and after the simulation.

3 Conclusions

In this work, we designed a series of stable 3d transition metal heterometal atom pairs (TMNi) supported on C₂N through DFT calculations, systematically investigating their potential to enhance the activity of Ni₂/C₂N. Our results demonstrate that all examined TM atoms can improve urea adsorption at the metallic pair active centers of TMNi/C₂N. Notably, CrNi/C₂N and CuNi/C₂N emerged as promising electrocatalysts for the UOR, exhibiting superior catalytic activity in both the O_ter and the N_ter pathways, significantly surpassing their homonuclear counterparts. Among these, both CuNi/C₂N and CrNi/C₂N prefer the N_ter pathway, with CrNi/C₂N displaying a superior capability to lower the limiting potential of the UOR compared to CuNi/C₂N. In these systems, either the second or the fourth proton desorption step represents the rate-determining step, and we identify *CONHN as the key intermediate by correlating the ΔG_ads of relevant intermediates. Further analysis of charge transfer, spin density, and bonding/antibonding orbital populations indicates that the CrNi center significantly enhances UOR activity by improving the adsorption of key intermediates compared to the CuNi center. The enhanced catalytic performance of Cr in the TMNi/C₂N system primarily stems from the stronger TM–Ni interactions, notable differences in charge distribution, more localized electronic states, and a higher d-band center associated with CrNi/C₂N relative to CuNi/C₂N and Ni₂/C₂N. These attributes not only ensure the stability of the well-dispersed CrNi pairs on C₂N but also amplify the ability of the active center to adsorb and activate UOR intermediates. Moreover, CrNi/C₂N demonstrates good selectivity for N₂ production during the UOR by exhibiting reduced susceptibility to forming NO₂, NO₂⁻ and NO₃⁻ by-product and undergoing the competing OER. Thus CrNi/C₂N is identified as a highly effective catalyst for the UOR, which has the possibility to be produced and verified by experiment. This study provides a comprehensive understanding of the catalytic activity of TMNi/C₂N and highlights the exceptional potential of CrNi/C₂N as a highly efficient electrocatalyst for the UOR, offering guidance for advanced catalyst design through the strategic use of transition metal heterometal atom pairs.

4 Theoretical details

Density functional theory (DFT) calculations with spin polarization correction were conducted using the Vienna Ab initio Simulation Package (VASP). The projected augmented wave (PAW) method was utilized, and the generalized gradient approximation (GGA) implemented by the Perdew–Burke–Ernzerhof (PBE) functional was adopted to incorporate the exchange–correlation functional.^48–51 A 5 × 5 × 1 Monkhorst–Pack K-point mesh was sampled in the Brillouin zone, with a cutoff energy set to 450 eV for geometric optimization. The convergence criteria were 10⁻⁵ eV in energy between two electronic steps and 0.01 eV Å⁻¹ for the forces acting on each atom.⁵² van der Waals effect was included using Grimme's DFT-D3 correction method during optimization.⁵³ To evaluate the stability of the catalysts, ab initio molecular dynamics (AIMD) simulations were carried out in an NVT ensemble for 10 ps with a time step of 1.0 fs, with temperature controlled by the Nosé–Hoover method.⁵⁴

One unit cell of C₂N contains 12 carbon atoms and 6 nitrogen atoms with a lattice parameter of 8.33 Å.⁵⁵ The C₂N slab model was created by adding a vacuum layer of 18 Å thickness in the vertical direction of the C₂N layer to prevent spurious interactions. The TMNi/C₂N was constructed by adding the TM–Ni pair in the hole of the C₂N layer. The adsorption energy (ΔE_ads) of each intermediate of the UOR and the Gibbs free energy change (ΔG) of each step of the UOR were calculated according to our previous method (or see the SI).²⁷

Conflicts of interest

The authors declare no competing financial interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI).

Supplementary information: the UOR free energy diagrams of all systems, relative figures of charge density difference and spin density, adsorption structure of OER intermediates and free energy diagram of by-prouducts formation have been included as part of the SI. See DOI: https://doi.org/10.1039/d5im00252d.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (No. 52200076), the Special Research Fellowship of the Chinese Academy of Science (No. E3296201), the Research Foundation of Chongqing University of Science and Technology (No. ckrc2022015), and the Natural Science Foundation of Chongqing (No. CSTB2025NSCQ-GPX0920). In addition, DFT calculations in this work have been performed at the Hefei Advanced Computing Center, China.

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