Multi-atomic loaded C₂N₁ catalysts for CO₂ reduction to CO or formic acid

Abstract

In recent years, the development of highly active and selective electrocatalysts for the electrochemical reduction of CO₂ to produce CO and formic acid has aroused great interest, and can reduce environmental pollution and greenhouse gas emissions. Due to the high utilization of atoms, atom-dispersed catalysts are widely used in CO₂ reduction reactions (CO₂RRs). Compared with single-atom catalysts (SACs), multi-atom catalysts have more flexible active sites, unique electronic structures and synergistic interatomic interactions, which have great potential in improving the catalytic performance. In this study, we established a single-layer nitrogen–graphene-supported transition metal catalyst (TM-C₂N₁) based on density functional theory, facilitating the reduction of CO₂ to CO or HCOOH with single-atom and multi-atomic catalysts. For the first time, the TM-C₂N₁ monolayer was systematically screened for its catalytic activity with ab initio molecular dynamics, density of states, and charge density, confirming the stability of the TM-C₂N₁ catalyst structure. Furthermore, the Gibbs free energy and electronic structure analysis of 3TM-C₂N₁ revealed excellent catalytic performance for CO and HCOOH in the CO₂RR with a lower limiting potential. Importantly, this work highlights the moderate adsorption energy of the intermediate on 3TM-C₂N₁. It is particularly noteworthy that 3Mo-C₂N₁ exhibited the best catalytic performance for CO, with a limiting potential (U_L) of −0.62 V, while 3Ti-C₂N₁ showed the best performance for HCOOH, with a corresponding U_L of −0.18 V. Additionally, 3TM-C₂N₁ significantly inhibited competitive hydrogen evolution reactions. We emphasize the crucial role of the d-band center in determining products, as well as the activity and selectivity of triple-atom catalysts in the CO₂RR. This theoretical research not only advances our understanding of multi-atomic catalysts, but also offers new avenues for promoting sustainable CO₂ conversion.

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1. Introduction

The increase in fossil fuel consumption leads to the accumulation of CO₂ in the atmosphere, causing serious environmental problems such as the greenhouse effect and ocean acidification, forcing people to find effective ways to reduce the concentration of CO₂ in the atmosphere and promote green and low-carbon development.^1–5 In recent years, a variety of efficient CO₂ conversion technologies have been developed, including biocatalysis, photocatalysis, and electrocatalysis.^6–8 Among them, the electrocatalytic CO₂ reduction reaction (CO₂RR) has attracted extensive attention as a promising approach.^3,9 However, the excellent thermodynamic stability and high activation barrier of CO₂ make the reaction more difficult.¹⁰ In addition, the hydrogen evolution reaction (HER) is a competitive side reaction of the CO₂RR because it has a low overpotential.¹¹ Therefore, it is of great significance to design a novel CO₂RR electrocatalyst with a low overpotential and HER inhibition.

In recent years, due to the development of nanotechnology, it is possible to fine-tune the structure of an electrocatalyst at the nanoscale to control the structure of the electrocatalyst, making it have better stability, catalytic activity, and product selectivity. Single-atom catalysts (SACs) with isolated transition metal (TM) atoms stabilized by carbon-based materials have attracted more and more attention due to their special electronic structure and platform utilization¹² and have become promising candidate materials in the nitrogen reduction reaction,¹³ HER,^14–16 oxygen reduction reaction,^15,17 oxygen evolution reaction,^18,19 CO₂RR,^20,21 and other reactions.²² Previous studies have indicated that catalysts such as Mn, Mo, Ru, and Ti offer distinct advantages in the CO₂RR compared to the HER, requiring lower overpotentials for the generation of intermediate products (*COOH or *OCHO).^23–29 Unfortunately, the stability of SACs is not satisfactory,³⁰ because when the bond of individual atoms to the carrier is weak, they tend to aggregate into nanoparticles, which inevitably affects their catalytic activity and further hinders their practical application.

In contrast, single-cluster catalysts (SCCs) supported in single-layer nitrogen–graphene have great potential to advance the design and manufacture of high-performance catalysts due to their tunable electronic structure and adaptable active sites and have shown superiority in terms of stability, and are widely regarded as promising alternatives to SACs.³¹ The C₃N₁ monolayer is a two-dimensional material with periodic uniform cavities, and is a derivative of nitrogen-doped graphene. Its cavity is surrounded by 6 nitrogen atoms and is considered an ideal carrier for transition metal loading. Its high thermal stability facilitates the synthesis of stable transition metal catalysts.^32–34

Among SCCs, dual-atomic catalysts (DACs) have been extensively studied and are considered a new frontier.^35–38 Chen et al.³⁷ reported that DACs have the smallest metal alloy size and the largest atom utilization and exhibit excellent performance in various electrocatalytic reactions. In DACs, the binding strength of several intermediates can be optimized simultaneously to achieve multi-intermediate reactions. Zhang et al.⁹ found that the combination of diatomic metal and non-metal sites disrupted the electron density symmetry of the local coordination environment, and the formed symmetrical break sites improved the adsorption of key intermediates (such as *COOH and *OCHO). Wang et al.³⁹ demonstrated that a unique dual Fe₂–N₆ catalyst showed the electrocatalytic reduction of CO₂ to CO configuration, outstanding intrinsic activity, selectivity, and durability compared to SACs. Additionally, Mn and Mo, serving as DACs, are situated at the center and exhibit a polarized bond interaction with CO₂, underscoring the role of metal-centered catalysts in CO₂ and substrate interactions.^40,41 DACs break the structural relationship constructed in traditional metal catalysts and improve the catalytic activity of the catalyst to form higher-order carbon products.^42–44

Furthermore, triple-atom catalysts (TACs) have attracted much attention as a deeper extension of SACs. First, they exhibit a higher loading capacity for metal atoms and are able to get closer to the active site.⁴⁵ The formation of metal–metal bonds or metal–bridge atomic bonds provides a strategic means to control the electron synergistic adsorption of various reactants and intermediates.^46,47 TACs can provide a wider variety of asymmetric adsorption sites. These sites are particularly suitable for more complex catalytic processes involving multiple reaction steps and intermediates, and the synergy between the three atoms can also modulate the d-band electronic structure, thereby enhancing the catalytic performance.^45,48,49 Jia et al.⁵⁰ reported that TACs, as powerful electrocatalysts for the CO₂RR, provide a large number of active sites, and also have a large electrochemical surface area and rapid charge transfer, which improves the reaction rate. Liu et al.⁵¹ found that TACs have abundant active sites for the CO₂RR. their catalytic performance can be enhanced by the interaction of adjacent active sites. In particular, metals such as Mn, Mo, Ru, etc., as catalysts, demonstrate promising experimental feasibility and stable catalytic performance. They effectively suppress the HER while exhibiting excellent selectivity in the CO₂RR.^45,52,53

As excellent CO₂RR catalysts, both single atoms and single clusters demonstrate outstanding catalytic performance. However, the effect of the number of metal atoms on the structure–activity relationship of the catalyst is still unclear. In addition, previous studies have inconsistently described the catalytic properties of catalysts loaded with Mn, Mo, Ru, and Ti. Therefore, it is necessary to systematically analyze the catalytic performance of CO₂ using the above metal atoms and their numbers and provide theoretical guidance for the rational design of low-cost high-performance catalysts.

In this work, density functional theory (DFT) calculations were employed to reveal the structures of single atoms and single clusters composed of four metal elements (Mn, Mo, Ru, and Ti), which were loaded onto C₂N₁ monolayer materials as catalysts for CO₂ electrochemical reduction. First, the stability and conductivity of TM-C₂N₁ were investigated through the analysis of its electronic structure, density of states (DOS), and ab initio molecular dynamics (AIMD). Second, the adsorption and activation effect of TM-C₂N₁ on CO₂ were explored, focusing on the CO₂ configuration, adsorption energy comparison with H₂O, and the competitive adsorption relationship between the CO₂RR and HER. Finally, to better understand the preferred pathways for CO₂ reduction to CO or HCOOH on TM-C₂N₁, calculations were conducted for Gibbs free energy, limiting potential, overpotential, and Crystal Orbital Hamiltonian Population (COHP). The results show that the 3TM-C₂N₁ catalyst has a stable structure, can effectively adsorb and activate CO₂, and has optimal inhibition performance for the HER. Among them, 3Mo-C₂N₁ and 3Ti-C₂N₁ had the best catalytic activity for CO and HCOOH, in the CO₂RR with limiting potentials of −0.62 V and −0.42 V, respectively. These findings not only provide a theoretical basis for the experimental regulation of C₂N₁-based catalysts, but also have guiding significance for the development of other high-efficiency CO₂RR electrocatalysts.

2. Results and discussion

2.1 Structural stability

In this section, first, in order to clearly understand the electrocatalytic process of CO₂ for materials with different types of atoms and different numbers of atoms, a schematic diagram is shown, as shown in Fig. 1a. It shows the reduction pathways of CO₂ at different catalytic sites. Second, all transition metal single-atom catalysts and single-cluster catalyst structures supported on N-doped graphene were constructed, and the optimized structures are shown in Fig. S1–S4.† Then, in order to evaluate the stability of the TM-C₂N₁ structure, the cohesion energy, charge density, and AIMD were calculated to study the stable structure. Finally, the heights of DOS curves for the TM-C₂N₁ and C₃N₁ monolayers were calculated as the key parameters for the conductivity of the catalyst. The TM-C₂N₁ model uses a 5 × 5 supercell of the C₃N₁ monolayer, and there are a total of 54 C atoms and 18 N atoms in the model, as shown in Fig. S1–S4,† and we set a vacuum layer of 20 Å in the z direction to avoid the influence between adjacent lattices. The transition metal was placed in the N6 cavity to form the TM-C₂N₁ configuration.

Fig. 1 (a) Schematics of C₂N₁ with TM loads facilitates CO₂ conversion. (b) Cohesion energy of the TM-C₂N₁ monolayer. (c) The height of the DOS curve for TM-C₂N₁ at the Fermi level. The order of data points in (b) and (c) is Mn, Mo, Ru, and Ti.

High stability is a prerequisite for catalyst applications, so we evaluated the stability of TM-C₂N₁ catalysts with cohesive energy. The higher the cohesion energy, the more stable the corresponding structure.^54–56 Cohesion energy (E_coh) can be calculated according to the following formula:²

where E_C and E_N denote the energies (eV) of C and N atoms, respectively. n₁, n₂, and n₃ are the number of metals and C and N atoms. As shown in Fig. 1b, based on the calculation results of cohesion energy, it can be found that the cohesion energies of 1TM-C₂N₁, 2TM-C₂N₁, 3TM-C₂N₁, and 4TM-C₂N₁ materials are relatively concentrated. The cohesion energies of Mn-C₂N₁, Mo-C₂N₁, Ru-C₂N₁, Ti-C₂N₁, 2Mn-C₂N₁, and 3Mn-C₂N₁ are slightly smaller than that of the initial C₃N₁ monolayer (7.03 eV per atom) but higher than those of carbon phosphide (4.12–6.45 eV per atom) and silane (3.71 eV per atom).¹¹ The cohesion energies of the remaining 10 metal catalysts were all greater than or equal to that of the initial C₃N₁ monolayer. Hence, these findings demonstrate the remarkable stability of all TM-C₂N₁ configurations.

To better understand the interaction between the TM and the monolayer, we calculated the charge density of TM-C₂N₁, and the charge density diagram in Fig. S5–S8† show that the positive charge accumulates around the metal atom and decreases around the N atom, indicating that the electrons are transferred from the metal atom to the N atom, allowing the N atom to bind the TM atom. In addition, in order to judge the stability of the TM-C₂N₁ structure from the thermodynamic properties, AIMD simulation was carried out. It was calculated that the AIMD runs at 500 K for 10 ps and outputs a structure file every 10 fs. The detailed calculations are shown in Fig. S9–S12.† The results show that these materials are able to maintain good stability.

Finally, in order to explore the conductivity of the catalyst, the height of the DOS curve at the Fermi level for the TM-C₂N₁ monolayer represents the conductivity of the catalyst.^2,57–62 DOSs were calculated as the key parameters of catalyst conductivity. As shown in Fig. 1c, the DOS height for TM-C₂N₁ is higher than that of C₃N₁, demonstrating that the conductivity is improved after the introduction of loaded metals. The detailed calculations are shown in Fig. S5–S8,† and the overall DOS shows that after the introduction of the TM, the curve around the Fermi level increases slightly, indicating that the conductivity of the material has improved. In addition, partial density of states (PDOS) calculations were performed to study the behavior of the doped TM in depth. There were obvious overlapping peaks between the d orbital of the TM and the p orbital of the N of the substrate, indicating that the interaction between the TM and the substrate was stronger. The TM can be firmly attached to the C₃N₁ monolayer. This indicates that there is an interaction between the loaded TM atoms and the substrate, ensuring its structural stability.

2.2 Activation and selectivity

In this section, to understand the catalytic performance of catalysts and the advantages of CO₂RR development, the d-band center and activation degree of CO₂ were studied first, and second, the adsorption energies of CO₂ and H₂O were calculated as important references. In addition, we further compared ΔG(*COOH) and ΔG(*OCHO) with ΔG(*H). Further screening of the good TM-C₂N₁ catalyst ensures the normal CO₂RR.

CO₂ adsorption is the first and crucial step in the CO₂RR. Stable CO₂ adsorption is a prerequisite for the continuation of the CO₂RR. The degree of CO₂ activation reflects the catalytic performance of the catalyst to a certain extent. As shown in Fig. S13† (CO₂ planar three-dimensional structure display), CO₂ can be stably adsorbed on the surface of the catalyst, and the molecular configuration of CO₂ has changed significantly, indicating that CO₂ has been initially activated. In addition, in order to more intuitively observe the degree of activation and conductivity, as well as charge accumulation and consumption during the interaction between CO₂ and TM-C₂N₁, the results of charge density analysis are shown in Fig. S13† and the DOSs are shown in Fig. S14–S17.† The results show that TM-C₂N₁ transfers a large amount of charge during gas adsorption. A distinct red color is observed around the CO₂, which clearly indicates that the CO₂ acquires electrons from TM-C₂N₁, indicating that there is an interaction between CO₂ and TM-C₂N₁. Moreover, the p-orbital anchoring of C in the activated CO₂ and the d-orbital of the transition metal in TM-C₂N₁ have a hybridization effect, indicating that there is an interaction between CO₂ and TM-C₂N₁. For quantitative analysis, information such as the CO₂ adsorption energy and CO₂ bond length angle are listed in Table S1.† The smaller the bond angle, the stronger the degree of activation. The change of C–O bond length from 1.18–1.32 Å and the bending of O–C–O bond angle from 127.19°–163.22° (Fig. 2a) indicate that CO₂ has been effectively activated.

Fig. 2 (a) CO₂ activation angle on TM-C₂N₁. (b) Linear relationship between the d-band center of TM-C₂N₁ and the adsorption energy of CO₂. (c) Comparison of H₂O and CO₂ adsorption energies on the TM-C₂N₁ monolayer. (d) Diffusion of CO₂ on the TM-C₂N₁ monolayer.

In order to explore the potential mechanism of the adsorption reaction of CO₂ on the surface of the catalyst, we calculated the d-band center of TM-C₂N₁ because it can reflect the interaction between the gas molecules and the TM atoms on the surface. Fig. 2b shows that the d-band center of TM-C₂N₁ has a linear relationship with the adsorption energy, and the correlation coefficient is in good agreement with the theoretical model of the d-band center. Thus, the elevation of antibonding orbitals contributes to an increase in the adsorption energy.

It is well known that the kinetically prone HER hinders the progress of the CO₂RR as a side reaction. So a good catalyst to inhibit the HER is necessary. First, we calculated the reaction mechanism of the HER by adsorbing H₂O, because the CO₂RR tends to be performed in neutral or alkaline electrolytes. Fig. 2c shows the stark contrast between the adsorption energies of H₂O and CO₂. Due to |E_ads(H₂O)| < |E_ads(CO₂)|, *CO₂ is more easily adsorbed on the surface of TM-C₂N₁ catalysts than *H, thereby inhibiting the HER. Therefore, CO₂ rather than H₂O first occupies the active sites on the surface of TM-C₂N₁, promoting the CO₂RR as the main reaction on these 13 catalysts. Please refer to Tables S1 and S2† for details on the adsorption energy of H₂O and CO₂.Moreover, during the first protonation process, the hydrogenation of CO₂ produces two intermediates *COOH and *OCHO. As shown in Fig. S18,† by comparing ΔG(*COOH) and ΔG(*OCHO) with ΔG(*H), the 2/3TM-C₂N₁ catalysts all fall in the lower right half region (CO₂RR selective), which tends to produce *COOH or *OCHO. Combining the above two points, it can be concluded that the 2/3TM-C₂N₁ catalyst is selective to the CO₂RR and can well inhibit the occurrence of the HER. Therefore, the CO₂RR has a clear advantage over the HER under electrochemical conditions.

The diffusion performance of CO₂ on the catalyst material surface dictates the reaction rate.^63,64 Therefore, to explore the performance of catalysts in practical applications, molecular dynamics simulations were employed to calculate the diffusion coefficients of CO₂ on different material surfaces, thereby obtaining diffusion performance. Fig. S19–S22† depict snapshots of all catalysts capturing CO₂ at equilibrium. First, the mean-squared displacement (MSD) of TM-C₂N₁ was calculated, as shown in Fig. 2d. The results display that 3TM-C₂N₁ has the smallest diffusion performance based on the slopes. Furthermore, diffusion coefficients can be obtained through the Einstein diffusion equation. The detailed data are shown in Table S3.† The diffusion coefficients of 3Mn-C₂N₁, 3Mo-C₂N₁, 3Ru-C₂N₁ and 3Ti-C₂N₁ were 2.91, 2.19, 3.86 and 2.78, respectively. Among which, 3Mo-C₂N₁ and 3Ti-C₂N₁ had the best diffusion performance. The diffusion coefficient has an effect on the diffusion of CO₂ on the surface, and the smaller the diffusion coefficient, the more stable the CO₂ adsorption and the better the catalytic effect.

2.3 CO₂ reduction to CO or HCOOH

In this section, we first present the intermediate structure of the CO₂ reduction process to CO and HCOOH, followed by the calculation of the free energy for each corresponding structure. Finally, we conducted free energy calculations for the reaction pathway. The path of CO₂ to CO on TM-C₂N₁ is: CO₂ → *CO₂ → *COOH → *CO → CO. For HCOOH generation, the CO₂ to HCOOH generation path on TM-C₂N₁ is CO₂ → *CO₂ → *OCHO → *HCOOH → HCOOH. Fig. 3 shows the adsorption structure and free energy distribution of CO₂ intermediates to generate CO and HCOOH via a 2-electron path on the 3TM-C₂N₁ catalyst.

Fig. 3 Gibbs free energy distribution diagram of the CO₂ reduction pathway toward CO or HCOOH on (a) 3Mn-C₂N₁, (b) 3Mo-C₂N₁, (c) 3Ru-C₂N₁, and (d) 3Ti-C₂N₁.

Regarding the CO product, 3Mn-C₂N₁ has a CO₂ → *COOH speed-limiting step and the Gibbs free energy variation is 0.63 eV. For the 3Mo-C₂N₁ catalyst, the speed-limiting step is CO₂ → *COOH and the maximum Gibbs free energy variation is 0.62 eV. Besides, for the 3Ru-C₂N₁ monolayer, the speed-limiting step is CO₂ → *COOH and the maximum Gibbs free energy variation is 0.92 eV. Finally, 3Ti-C₂N₁ has a CO₂ → *COOH speed-limiting step and the maximum Gibbs free energy variation is 1.15 eV. For the production of HCOOH, first, 3Mn-C₂N₁ has a rate-limiting step of CO₂ → *OCHO and a Gibbs free energy variation maximum of 0.91 eV. Then, 3Mo-C₂N₁ has a CO₂ → *OCHO rate-limiting step and a maximum Gibbs free energy variation of 0.93 eV. 3Ru-C₂N₁ has a CO₂ → *OCHO rate-limiting step and a maximum Gibbs free energy variation of 1.39 eV. Finally, for 3Ti-C₂N₁, the rate-limiting step is *OCHO → *HCOOH and the maximum variation of Gibbs free energy is 0.42 eV. Furthermore, these results have also been validated by the dynamic barrier of elementary steps. Thus, the rate-limiting step was elucidated based on both thermodynamic and kinetic processes.

It is worth noting that 1TM-C₂N₁, 2TM-C₂N₁, and 4TM-C₂N₁ generate CO or HCOOH paths and rate-limiting steps are presented in Fig. S23–S25.† The Gibbs free energy of 1TM-C₂N₁ varies greatly overall, and for the CO product, Mn-C₂N₁ has a CO₂ → *COOH rate-limiting step with a maximum free energy difference of 4.83 eV. For HCOOH products, Ru-C₂N₁ has a CO₂ → *OCHO rate-limiting step with a maximum free energy difference of 3.78 eV. For the CO product, 4Ti-C₂N₁ has a CO₂ → *COOH speed-limiting ladder, and the Gibbs free energy becomes 2.18 eV. With regard to the HCOOH product, 4Mn-C₂N₁ has a CO₂→*OCHO rate-limiting step and a Gibbs free energy change of 1.28 eV. Among them, for CO, 3Mo-C₂N₁ has the smallest free energy difference, making it the best CO catalyst. For HCOOH, 3Ti-C₂N₁ has the smallest free energy difference and is the most effective catalyst for HCOOH generation, so 3Mo-C₂N₁ and 3Ti-C₂N₁ exhibit excellent performance.

2.4 Catalytic performance

For a quantitative analysis and clear comparison of catalytic performance, Fig. S26 and S27† show the limiting potential (U_L) and overpotential (η) of CO₂ reduction to CO or HCOOH on TM-C₂N₁. The results demonstrate that TACs exhibit the best catalytic performance, based on the smallest overpotential, compared to other single-atom and multi-atom catalysts. Among them, the 3Mo/3Ti-C₂N₁ catalyst shows the optimal catalytic performance, as indicated by the minimal η for the formation of CO and HCOOH products. This parameter determines the energy cost in experiments. The impact of product separation on catalytic rates cannot be overlooked, as higher adsorption energy makes desorption more challenging. Therefore, establishing the relationship between the catalytic performance (overpotential) and the product adsorption energy is of significant importance for a deeper understanding of the structure–performance relationship of catalysts.

As shown in Fig. 4a, for CO, 3Mo-C₂N₁ exhibits the best performance with a limiting potential of CO generation at 0.62 V. This indicates good catalytic activity and the lowest energy requirement. The vertices of the volcano plot represent the moderate adsorption energy of the product and therefore have the best catalytic performance. Conversely, as illustrated in Fig. 4b, 3Ti-C₂N₁ demonstrates the best overall performance for HCOOH generation. The limiting potential for the formation of HCOOH on 3Ti-C₂N₁ is 0.42 V; the results show that moderate adsorption can ensure a high yield of HCOOH. When |U_L| > 0.9 V, it suggests that the reaction requires a significant amount of energy absorption, making it less likely to occur. The analysis suggests that the CO₂RR catalyzed by TM-C₂N₁ is feasible, with 3TM-C₂N₁ being the optimal catalyst for achieving efficient CO₂RR performance.

Fig. 4 Relationship between the adsorption energy and the overpotential of products on TM-C₂N₁. (a) CO adsorbed on TM-C₂N₁. (b) HCOOH adsorbed on TM-C₂N₁.

The catalytic performance of 3Mn-C₂N₁ is also very good, and the U_L of CO generation is 0.63 V, which is only 0.01 V higher than the that of 3Mo-C₂N₁. The catalyst with the best performance to generate HCOOH is 3Ti-C₂N₁. The U_L for generating HCOOH on 3Ti-C₂N₁ is 0.42 V, which exhibits good catalytic activity and is the lowest energy required among the four catalysts. The analysis shows that the 3TM-C₂N₁-catalyzed CO₂RR is achievable. Our work explores the excellent performance of TM-C₂N₁ for deep hydrogenation of CO₂ under electrocatalysis at lower electrode potentials. In the formation of CO and HCOOH, 3Mo-C₂N₁ and 3Ti-C₂N₁ have the best performance among the 13 catalysts. This result demonstrates the optimal potential of TAC catalysts supported by the C₂N₁ monolayer for the CO₂RR. Therefore, when CO₂ is reduced to CO and HCOOH, 3Mo-C₂N₁ and 3Ti-C₂N₁ have the best catalytic performance.

2.5 Catalytic mechanism

To gain insight into why the catalyst performance of the 3Mo-C₂N₁ and 3Ti-C₂N₁ monolayers is the best, we analyzed the key intermediates, which interact with the catalytically active site, from a molecular orbital perspective. It is the bonding orbital that plays a key role in the adsorption according to previous studies.^36,65–69 First of all, the interaction should not be too strong, which will lead to a sudden increase in the energy barrier of the next step, forming a restrictive link. Second, the interaction should not be too weak, which will lead to a decrease in the catalytic effect of the catalyst and make the catalyst fail. Hence, maintaining a moderate interaction is essential to obtain high-performance catalysts. To achieve this, we conducted COHP calculations for reducing the intermediates of the TM catalysts exhibiting the best performance.

Fig. S29 and S30† depict the most stable adsorption configuration, charge density distribution, and corresponding DOS of *COOH and *OCHO adsorption on 3Mo-C₂N₁ and 3Ti-C₂N₁, respectively. In Fig. S29,† the interaction between the intermediate products (*COOH and *OCHO) and 3Mo-C₂N₁ demonstrates pronounced charge accumulation or depletion, particularly evident in Fig. S29b,† indicating strong adsorption between the surfaces of OCHO and 3Mo-C₂N₁. Additionally, the DOS reveals numerous overlapping peaks between the p orbital of O and the d orbital of Mo, signifying a strong hybrid effect. Consequently, desorption and reduction to CO are facilitated at 3Mo-C₂N₁. Similarly, in Fig. S30,† the interaction between *COOH and *OCHO and 3Ti-C₂N₁ exhibits notable charge accumulation or depletion, particularly evident in Fig. S30b† with strong adsorption observed between *COOH and the surfaces of 3Ti-C₂N₁. Additionally, the DOS highlights numerous overlapping peaks between the p orbital of C and the d orbital of Ti, indicating a strong hybrid effect. Hence, desorption and reduction to HCOOH are facilitated at 3Ti-C₂N₁. Consequently, 3Mo-C₂N₁ and 3Ti-C₂N₁ demonstrate the best catalytic performance for CO₂ reduction to CO and HCOOH, respectively.

To further elucidate the interactions between atoms, we conducted COHP calculations. As depicted in Fig. 5, the bonding and anti-bonding regions between the 3TM and gas atoms are illustrated at the Fermi level, and the ICOHP values (absolute values) were plotted accordingly. For the CO product, it delineates a bonding region spanning from −2.3 eV to 1.2 eV and an anti-bonding region ranging from −12.5 eV to −16 eV between the metal Mo atom and the gas C atom with an ICOHP value of 0.02 eV. Furthermore, the bonding region between the metal Ti atom and the gas C atom spans from −6.6 eV to 2.4 eV with an anti-bonding region from −14.8 eV to −7.1 eV and an ICOHP value of 0.78 eV. As depicted in Fig. S28,† there is an ICOHP value of 0.01 eV between the metal Mn atom and the gas C atom and an ICOHP value of 0.53 eV between the metal Ru atom and the gas C atom. This indicates that the interaction between *C in the intermediate product *COOH and Mo atoms is moderate, thus ensuring the optimal performance of the 3Mo-C₂N₁ catalyst for CO generation.

Fig. 5 ICOHP values of *COOH and *OCHO on 3TM-C₂N₁.

For the HCOOH product, the bonding region between the metal Mo atom and the gas O atom extends from −13.8 eV to −2.7 eV, while the anti-bonding region ranges from −2.8 eV to −0.12 eV with an ICOHP value of 0.07 eV. Meanwhile, the bonding region between the metal Ti atom and the gas O atom ranges from −0.53 eV to 0 eV with an anti-bonding region from −0.88 eV to −0.67 eV and an ICOHP value of 0.03 eV. As depicted in Fig. S28,† there is an ICOHP value of 0.007 eV between the metal Mn atom and the gas O atom, and an ICOHP value of 0.25 eV between the metal Ru atom and the gas O atom. This indicates that the interaction between *O in the intermediate product *OCHO and the Ti atoms is moderate, thus ensuring the optimal performance of the 3Ti-C₂N₁ catalyst for HCOOH generation.

In addition, based on the relationship between the d-band center and the adsorption energy (as shown in Fig. 2b), the height of the d-band center of the catalyst material can be best regulated after the doping of three atoms. Therefore, TACs have a moderate adsorption energy for the intermediate products (*COOH and *OCHO), thus ensuring their optimal catalytic performance. In summary, these results demonstrate that 3Mo-C₂N₁ and 3Ti-C₂N₁ are the best catalysts for the formation of CO and HCOOH, respectively.

3. Conclusions

In summary, the mechanism of the CO₂RR on the SACs and SCCs of Mn, Mo, Ru and Ti anchored on the C₃N₁ monolayer was studied by DFT calculations. The results show that the TM-C₂N₁ catalysts are stable based on cohesion energy. Besides, AIMD was used to further verify the thermodynamic stability of the catalyst material. As an excellent electrocatalytic material, the conductivity of the TM-C₂N₁ monolayer was significantly improved based on the height of DOS at the Fermi level. Furthermore, the PDOS shows the obvious overlapping peaks between the d orbital of the TM and the p orbital of the N of the C₂N₁ monolayer, indicating that the TM can be stably anchored to the substrate. Importantly, CO₂ is significantly activated on the TM-C₂N₁ monolayer and the change in the bond angle is from 127.19° to 163.22°. At the same time, the catalyst can effectively prevent the side reaction of the HER. The good diffusion of the gas reactants is the initial condition for the CO₂RR, so the diffusion performance of CO₂ on the TM-C₂N₁ catalyst was calculated by molecular dynamics simulations. The results show that the 3Mo-C₂N₁ and 3Ti-C₂N₁ catalysts have the smallest diffusion coefficients of 2.19 and 2.78, respectively, and could stably adsorb CO₂ at active sites. Interestingly, 3Mo-C₂N₁ and 3Ti-C₂N₁ also exhibited the best catalytic activity for CO₂ reduction to CO and HCOOH, respectively. The pathway for the reduction of CO₂ to CO involves steps of CO₂ → *COOH → *CO → CO with a U_L of −0.62 V. The pathway for CO₂ reduction to HCOOH was CO₂ → *OCHO → *HCOOH → HCOOH and U_L is −0.42 V. In order to elucidate why the 3TM-C₂N₁ catalyst has the best catalytic performance, we established a volcano diagram relationship curve between η and E_ads. The results emphasize the importance of moderate adsorption energy. In particular, the COHPs of *COOH and *OCHO for 3Mo-C₂N₁ and 3Ti-C₂N₁ catalysts were investigated in detail to compare the bonding and antibonding contributions. ICOHP shows that for CO, the ICOHP value of 3Mo-C₂N₁-COOH is 0.02 eV, and for HCOOH, the ICOHP value of 3Ti-C₂N₁-OCHO is 0.03 eV. It is proved that the optimum catalytic effect can be guaranteed only when the intermediate products have moderate adsorption energy. Therefore, this work provides theoretical guidance for the rational design of high-performance CO₂RR catalysts and offers new insights into understanding the catalytic mechanism of multi-atomic catalysts.

Author contributions

Yimeng Sun: investigation, data curation, formal analysis, methodology, and writing – original draft. Lin Tao: investigation, data curation, methodology, supervision, funding acquisition, conceptualization, validation, and writing – review and editing. Mingjie Wu: methodology, resources, and writing – review and editing. Davoud Dastan: formal analysis and software. Javed Rehman: methodology and software. Lixiang Li: methodology and formal analysis. Baigang An: supervision, formal analysis, and writing – review and editing.

Conflicts of 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.

Acknowledgements

The funding from the National Natural Science Foundation of China (Grant No. 52304330, 52371224, and 22208331), the University of Science and Technology Liaoning Talent Project Grants (6003000317), the Outstanding Youth Fund of University of Science and Technology Liaoning (2023YQ11), and the Youth Fund of the Education Department of Liaoning Province (LJKQZ20222324) is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4nr01082e

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