Design and catalytic performance investigation of the Ni–N–C catalyst for CO₂RR: a theoretical study

Abstract

The combustion of fossil fuels is increasingly contributing to global warming. The recycling of CO₂ plays a crucial role, and the creation of a highly efficient electrocatalyst is essential for enhancing the efficiency of the reaction. This work focused on the theoretical design of Ni–N–C catalysts with different coordination environments of Ni through quantum chemical calculations and analyzed the differences between the coordination environments of pyridine N and pyrrole N on the performance of catalytic CO₂ reduction to CO in order to identify the most efficient catalyst configuration. The Ni–N bonding energy of the catalyst with a vacancy was greater than that of the catalyst without a vacancy, and the activation ability of Ni-pyridine N₂C₁–C was the best. Ultimately, examining various catalysts for converting CO₂ into CO revealed that Ni-pyridine N₂C₁–C exhibited the most effective catalytic impact. In contrast to the energy barrier ΔG = 2.9903 eV in the absence of a catalyst, the energy barrier ΔG = −1.4029 eV during the CO₂ to CO catalytic reaction decreased by 4.3932 eV. This decrease was the largest among all the catalysts mentioned above, and the reaction could be spontaneous from a thermodynamic perspective. The research results provide a theoretical reference for the experimental preparation of catalysts for CO₂ to CO conversion and the resource utilization of CO₂.

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1 Introduction

Post industrial revolution, swift advancements in fossil fuel technology have emitted substantial quantities of carbon dioxide (CO₂) for energy, intensifying the urgency of achieving carbon neutrality.^1,2 Consequently, the primary emphasis is on carbon capture and utilization, making the advancement of CO₂ reduction a widespread issue in both academic circles and society at large.

In CO₂RR, the electrocatalyst promotes the conversion of carbon dioxide into various “high-value” products with the help of electricity,³ involving the transfer of six or more electrons during the electrocatalytic reaction. In these CO₂RR processes, C₁ products (such as methane (CH₄) and methanol (CH₃OH)), C₂ products (such as ethylene (C₂H₄), acetic acid (CH₃COOH), and ethanol (C₂H₅OH)), and C₃ products (such as n-propanol (C₃H₈O) and acetone (C₃H₅O)) are formed. The activity and selectivity of the electrocatalyst for reduction products are mainly oriented towards C₁ products, mainly CO and HCOO⁻, rather than the highly reduced C₁ and polycarbon (C₂₊) products. CO is the main component of syngas and gas, the main part of C1 compounds, which can also be used as a reducing agent in the metal smelting industry. Therefore, catalysts that catalyze CO₂RR to produce CO are explored in this paper. Compared to photocatalysis,⁴ electrocatalytic CO₂ reduction avoids the critical problem of catalyst deactivation due to electron–hole complexation. Currently, scientists have explored a variety of catalysts that perform well,⁵ such as pure metal catalysts,^6–10 alloy catalysts,¹¹ porous material catalysts,^12–17 atomically dispersed metal-based catalysts,^18–22 and metal oxide catalysts.²³ However, monometallic catalysts have limited performance.^24–26 The adsorption properties of alloy catalysts are influenced by interactions between neighboring metal atoms, and porous material catalysts can regulate electrolyte diffusion and generate a volume gradient, thus affecting local alkalinity and improving the selectivity of CO₂RR. Still, they suffer from problems, such as low conductivity, poor stability, and lack of mesoporosity. The M–N–C catalysts have a lower cost than precious metal catalysts, and the metal sites generate a charge accumulation effect, which is favorable for CO₂ chemisorption and provides good selectivity for CO generation. Different central metal ions have distinct electronic structures, geometrical configurations and d-orbital energy levels, so selecting suitable central metal elements is crucial for improving the electrocatalytic ability of M–N–C materials by optimizing surface adsorption. Among them, transition metal elements and main group elements exhibit good electrocatalytic ability when acting as center metal ions (Fe, Co, Ni, Cu, Zn, Mn, Sn and Sb). Integrating transition metal nickel into the N–C substance markedly enhances the catalytic efficiency of CO₂RR. Computational models indicate that incorporating single-atom Ni lowers the energy barrier for reactions in CO₂RR. Once the atomically scattered Ni was secured to the carbon substance, the single-atom Ni demonstrated peak atomic usage, augmented the concentration of active sites, and enhanced the catalytic efficiency of CO₂RR. Alterations in the d-orbital energy state of the central metal ion occurred as it was encircled by distinct neighboring ligands, suggesting that modifying the coordination setting of the central metal ion might control the electronic configuration of the M–N–C substance. Changes in the coordination environment can alter the nitrogen atom species by changing the coordination number of the nitrogen atoms. Good catalytic activity for CO₂RR compared to other M–N_x structures, such as M–N₂, M–N₃, and M–N₅,^27,28 most M–N₄ structures, were more selective for CO in CO₂RR.^29–31

Nitrogen atoms can cause positive charge aggregation,³² making C adjacent to N the active site for electrocatalytic CO₂RR. Guo³³ conducted a methodical study on the activation capabilities and specificity of N-doped carbon catalysts in electrocatalytic CO₂RR processes. Numerous M–N–C catalysts are known to be employed in the electrocatalytic process of CO₂RR. Jia et al.³⁴ synthesized a single-atom Ni catalyst SA-NiNG-NV with N vacancies possessing higher CO₂RR selectivity. Cheng et al.³⁵ synthesized a large number of Ni–N–C catalytic materials at the edges of the sites by applying microwave stripping, which exhibited extremely high activity in the electrocatalytic CO₂RR process. Wang et al.³⁶ systematically investigated single-atom catalysts with typical transition metals as active sites, and they found that the selectivity in CO₂–CO conversion was ranked as Ni > Co > Fe, and the reactivity was ranked as Co > Ni > Fe. Ni-doped catalysts had high catalytic efficiency, good stability and low price, so this study was aimed at Ni–N–C catalysts. Altering the electron configuration of the coordination center M consequently impacts its location on the active site and the catalyst's specificity. Zhao's team³⁷ discovered through DFT analysis that pyrrole N predominantly generated HCOOH during CO₂RR catalysis, exhibiting the minimal overpotential of 0.24 V compared to other N-doped graphene types, while Wu³⁸ ascertained that pyridinium N, as the primary catalyst, effectively converted CO₂ into CO, demonstrating superior catalytic efficiency in theoretical terms.

Consequently, this study conducts theoretical analyses of the stability, CO₂ adsorption stability, and catalytic efficiency of each catalyst using the DMol³ module in Materials Studio (MS) software. This was performed to evaluate the impact of various coordination settings, including the quantity and nature of nitrogen atom coordination and adsorption type, on the CO₂ reduction efficiency of the Ni–N–C catalysts, and to identify catalysts with superior performance that could inform the use of Ni–N–C catalysts in CO₂RR. DFT calculations can predict and guide experimental design, thereby conserving human and material resources while more effectively screening for catalysts with superior performance. Additionally, DFT enables a deeper understanding of reaction mechanisms.

2 Models and methods

Quantum chemical calculations can be used to design the required catalysts directly on MS software and calculate and predict their catalytic performance, which can reduce the time and workload required for experiments. Many repetitive tasks can be avoided, research efficiency can be improved, and the experimental cost can be reduced, which can provide references and guidance for experiments.

The 5 × 4 graphene was intercepted for reconfiguration, which retained the structural characteristics and reduced the computation. The establishment of the Ni–N–C catalyst model was completed, and geometry optimization was performed by selecting calculation in the DMol³ module, selecting geometry optimization in the task module in the set up tab, and selecting customized in the quality module. Under the generalized gradient approximation (GGA), the functional chosen was selected as the Perdew–Burke–Ernzerhof (PBE) function, and the basis set with a double-valued atomic orbital plus polarization function (DNP) was chosen to describe the atomic orbitals. The energy convergence criteria, maximum force, and maximum displacement were set during geometry optimization at 2 × 10⁻⁵ Ha, 0.004 Ha Å⁻¹, and 0.005 Å, respectively. To accelerate electron convergence, the smearing was set to 0.005 Ha. The maximum number of iterations was set to 1000 in more, with medium selected for overall accuracy. The max SCF cycle was set to 1000, and the COSMO solution environment was used with water selected as the solvent. The energy calculation was also done using the DMol³ module. The binding energy E_B of the catalyst was calculated according to the following formula to select the catalyst configuration with the best stability.

E_B = E_total − E_carrier+Ni, (1.1)

where E_b is the average bond energy of the Ni–N bond. The average bond energy is calculated as follows:

E_b = E_B ÷ n, (1.2)

where n is the number of Ni–N bonds.

Next, the structure optimization of the Ni–N–C–CO₂ structure was carried out. The structure-optimized CO₂ was attached to the active center, and the parameters were set for structure optimization considering single-site adsorption, double-site adsorption and different atoms connected. The specific equations for calculating adsorption energy are as follows:

E_ads = E_a − E_CO2 − E_total. (1.3)

Ultimately, the Gibbs free energies for the CO₂ reduction to CO reaction intermediates, both catalyzed and uncatalyzed, were determined.

3 Results and discussion

3.1 Ni–N–C catalyst design

3.1.1 Ni-Pyridine N–C catalyst design. Ni-Pyridine N_nV_3−n–C catalysts were Ni–N–C catalysts with three pyridine N atoms anchoring Ni and containing vacancies. Each N atom formed a pyridine structure with a six-membered ring with C atoms, and the Ni atoms were not out of the same plane as the graphene C atoms, as shown in Fig. 1.

Fig. 1 Five configurations of Ni-pyridine N_nV_3−n–C catalysts: (a) Ni-pyridine N₃–C; (b) Ni-pyridine N₂V₁–C; (c) Ni-pyridine N₁V₂–C; (d) Ni-pyridine N₂C₁–C; and (e) Ni-pyridine N₁C₂–C.

Ni-Pyridine N_nV_4−n–C catalysts were Ni–N–C catalysts consisting of four pyridine N atoms anchored to Ni atoms and containing vacancies, and each N atom formed a six-membered ring with graphene C in a pyridine structure. Fig. 2 illustrates that the Ni-pyridine N_nV_4−n–C catalysts can be categorized into seven configurations.

Fig. 2 Seven structures of Ni-pyridine N_nV_4−n–C catalysts: (a) Ni-pyridine N₄–C; (b) Ni-pyridine N₃V₁–C; (c) Ni-pyridine N₂V₂–C; (d) Ni-pyridine N₂V₁–C; (e) Ni-pyridine N₃C₁–C; (f) Ni-pyridine N₂C₂–C; and (g) Ni-pyridine N₁C₃–C.

3.1.2 Ni-Pyrrole N–C catalyst design. Ni-Pyrrole N_nV_4−n–C catalysts were Ni–N–C catalysts consisting of four pyrrole N atoms anchored to Ni atoms and containing vacancies, and each N atom formed a five-membered ring with graphene C in a pyrrole structure. The Ni-pyrrole N_nV_4−n–C catalysts can be categorized into seven configurations, as shown in Fig. 3.

Fig. 3 Seven structures of Ni-pyrrole N_nV_4−n–C catalysts: (a) Ni-pyrrole N₄–C; (b) Ni-pyrrole N₃V₁–C; (c) Ni-pyrrole N₂V₂–C; (d) Ni-pyrrole N₂V₁–C; (e) Ni-pyrrole N₃C₁–C; (f) Ni-pyrrole N₂C₂–C; and (g) Ni-pyrrole N₁C₃–C.

3.2 Stability studies of Ni–N–C catalysts

The Ni-pyridine N_nV_3−n–C catalyst was taken as an example, and the study calculated the average bond energies of the Ni–N and Ni–C bonds for each configuration. The results are presented in Table 1. Among the five structures, the one with the largest bond energy was the Ni-pyridine N₂V₁–C catalyst, which had an average bond energy of −0.0898 eV of the Ni–N bond, indicating that the catalyst had good stability. The largest total bond energy was the d structure, the Ni-pyridine N₂C₁–C catalyst, which was anchored by two N atoms and one C atom, with a total summed energy of E_B = −0.1796 eV, showing good stability. In summary, the stable structures of the Ni-pyridine N_nV_3−n–C catalysts were Ni-pyridine N₂V₁–C and Ni-pyridine N₂C₁–C.

Table 1 Bond energies of Ni-pyridine N_nV_3−n–C catalysts

Isomers	Ecarrier+Ni/eV	Etotal/eV	EB/eV	Eb/eV
a	−3536.73	−3536.87	−0.1481	−0.0494
b	−3481.98	−3482.16	−0.1796	−0.0898
c	−3427.27	−3427.31	−0.0500	−0.0500
d	−3520.02	−3520.20	−0.1798	−0.0599
e	−3503.39	−3503.54	−0.1511	−0.0504

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3.3 Effect of the number of vacancies on the performance of Ni–N–C catalysts

Subsequently, the catalysts underwent examination for the most occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Both HOMO and LUMO symbolize the primary levels of molecular orbital energy. HOMO symbolizes the most filled molecular orbitals, while LUMO denotes the least occupied molecular orbital. For the energy band gap ΔE = E_LUMO − E_HOMO, the rate of electron movement within the catalyst can be ascertained using ΔE. A reduced ΔE indicates a quicker electron transfer rate in the front molecular orbitals and a more catalytic catalyst.

The frontline molecular orbital energy levels and ΔE of the three previously selected Ni–N–C catalysts are illustrated in Fig. 4–6. Compared to the catalysts without vacancies, the catalysts containing vacancies were significantly larger for ΔE. The ΔE of the Ni-pyridine N₃V₁–C catalyst with vacancies was 0.872 eV, which was more than three times larger than that of the Ni-pyridine N₄–C catalyst without vacancies (ΔE = 0.278 eV).

Fig. 4 Frontline molecular orbital energy levels and ΔE for Ni-pyridine N_nV_4−n–C catalysts: (a) Ni-pyridine N₄–C; (b) Ni-pyridine N₃V₁–C; (c) Ni-pyridine N₂V₂–C; (d) Ni-pyridine N₂V₁–C; (e) Ni-pyridine N₃C₁–C; (f) Ni-pyridine N₂C₂–C; and (g) Ni-pyridine N₁C₃–C.

Fig. 5 Frontline molecular orbital energy levels and ΔE for Ni-pyridine N_nV_3−n–C catalysts: (a) Ni-pyridine N₃–C; (b) Ni-pyridine N₂V₁–C; (c) Ni-pyridine N₁V₂–C; (d) Ni-pyridine N₂C₁–C; and (e) Ni-pyridine N₁C₂–C.

Fig. 6 Frontline molecular orbital energy levels and ΔE for Ni-pyrrole N_nV_4−n–C catalysts: (a) Ni-pyrrole N₄–C; (b) Ni-pyrrole N₃V₁–C; (c) Ni-pyrrole N₂V₂–C; (d) Ni-pyrrole N₂V₁–C; (e) Ni-pyrrole N₃C₁–C; (f) Ni-pyrrole N₂C₂–C; and (g) Ni-pyrrole N₁C₃–C.

3.4 Study of CO₂ adsorption capacity of Ni–N–C catalysts

All atoms of the Ni-pyridine N₂V₁–C catalyst, Ni-pyrrole N₂V₂–C catalyst and Ni-pyridine N₁V₃–C catalyst were in the same plane, so there was no need to consider the direction of CO₂ binding to the catalyst during structure optimization. Only single-site and double-site adsorption, as well as Ni–C bonding and Ni–O bonding, must be considered for a total of three cases.

The Ni atoms of the Ni-pyridine N₂C₁–C catalyst and the Ni-pyridine N₁V₃–C catalyst were not in the same plane as the carrier graphene. Therefore, not only single-site and double-site adsorption but also the direction of CO₂ molecule adsorption had to be considered, so there were 6 cases.

3.4.1 Active site analysis of Ni–N–C catalysts. The global activity analysis was carried out in the previous section using the front molecular orbital energy levels. Next, the active sites of the catalysts were determined using Fukui indices.

Table 2 demonstrates the Fukui functions for each Ni–N–C catalyst Ni atom as well as the N and C atoms attached to the Ni atom. From the table, it can be observed that the f(+) and f(−) of the Ni atoms of the six catalysts were the maximum values within the catalyst, indicating that this site could react with both Lewis acids and Lewis bases. Taking catalyst Ni-pyridine N₂C₁–C Catalyst Ni–C N–O as a case study, a periodic cell (Fig. S4†) was constructed, and the Fukui indices of all atoms were summarized in Table S1.† Therefore, it was the most suitable catalyst site.

Table 2 Fukui index for Ni–N–C catalysts

	f(+)			f(−)
	Atom	Mulliken	Hirshfeld	Atom	Mulliken	Hirshfeld
Ni-Pyridine N2V1–C	Ni(26)	0.050	0.030	Ni(26)	0.055	0.030
	N(25)	0.002	0.011	N(25)	0.002	0.010
	N(31)	−0.000	0.008	N(31)	0.000	0.008
Ni-Pyridine N2C1–C	Ni(26)	0.044	0.036	Ni(26)	0.055	0.030
	N(25)	0.005	0.013	N(25)	0.005	0.013
	N(31)	0.000	0.007	N(31)	0.000	0.007
	N(53)	0.011	0.013	N(53)	0.011	0.013
Ni-Pyridine N1V3–C	Ni(39)	0.053	0.030	Ni(39)	0.049	0.030
	N(19)	0.002	0.012	N(19)	0.001	0.012
	C(7)	0.002	0.012	C(7)	0.017	0.012
	C(20)	0.015	0.015	C(20)	0.016	0.015
Ni-Pyrrole N2V2–C	Ni(40)	0.076	0.039	Ni(40)	0.069	0.040
	N(19)	0.001	0.013	N(19)	0.000	0.013
	N(20)	0.002	0.014	N(20)	0.002	0.014
Ni-Pyrrole N1V3–C	Ni(39)	0.067	0.036	Ni(39)	0.065	0.037
	N(19)	0.003	0.014	N(19)	0.003	0.014
	C(7)	0.0018	0.014	C(7)	0.018	0.014
	C(20)	0.015	0.014	C(20)	0.015	0.014

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Table 3 showed the Fukui index of CO₂, from which it could be observed that the C atom of CO₂ had the largest f(+) and a greater positron density, so in single-site adsorption, it could be assumed that the stability of the C atom connected to the Ni atom of the catalyst was greater than that of the O atom connected to the Ni atom. Therefore, the Ni–O connection was not considered for the time being.

Table 3 Fukui index for CO₂ catalysts

	f(+)
	Atom	Mulliken	Hirshfeld
Ni-Pyrrole N1C3–C	C(1)	0.462	0.384
	O(2)	0.269	0.308
	O(3)	0.269	0.308

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3.4.2 Stability study of CO₂ adsorption over Ni–N–C catalysts. Next, six selected Ni–N–C catalysts with good stability were determined for adsorption stability.
(1) Ni-Pyridine N₂V₁–C catalysts. The structure of the Ni–N₂V₁–C–CO₂ intermediate was designated (Fig. S1†). The bond lengths, bond angles and adsorption energies of the Ni–N₂V₁–C–CO₂ structure were shown in Table 4.

Table 4 Adsorption energies and bond lengths of Ni-pyridine N₂V₁–C–CO₂ intermediates

Isomers	Eads/eV	dC–O1/Å	dC–O2/Å
a	−0.0092	1.178	1.179
b	−0.0087	1.178	1.178
c	0.0045	1.178	1.178

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As shown in Table 4, the binding energies of (a) and (b) were negative and (c) was positive. Therefore, (c) CO₂ could not be stabilized for adsorption. The C=O bond lengths of (a) were 1.178 Å and 1.179 Å, respectively, which were not much changed compared to the CO₂ bond length of 1.178 Å. The C=O bond lengths of (c) were both 1.178 Å, and there was no change in the bond lengths, so (a) and (b) had a low activation effect on CO₂.

(2) Ni-Pyridine N₂C₁–C catalysts. The bond lengths, bond angles and adsorption energies of the Ni-pyridine N₂C₁–C–CO₂ structure (Fig. 7) are presented in Table 5.

Fig. 7 Isomers of the Ni-pyridine N₂C₁–C–CO₂ intermediate: (a) Ni-pyridine N₂C₁–C–CO₂ single-site adsorption A; (b) Ni-pyridine N₂C₁–C–CO₂ single-site adsorption B; (c) Ni-pyridine N₂C₁–C–CO₂ Ni–C N–O double-site adsorption A; (d) Ni-pyridine N₂C₁–C–CO₂ Ni–C N–O double-site adsorption B; (e) Ni-pyridine N₂C₁–C–CO₂ Ni–O N–C double-site adsorption A; and (f) Ni-pyridine N₂C₁–C–CO₂ Ni–O N–C double-site adsorption B.

Table 5 Adsorption energies and bond lengths of Ni-pyridine N₂C₁–C–CO₂ intermediates

Isomers	Eads/eV	dC–O1/Å	dC–O2/Å
a	−0.0171	1.166	1.188
b	−0.0088	1.178	1.178
c	−0.0204	1.166	1.186
d	−0.0089	1.177	1.178
e	−0.0198	1.166	1.186
f	−0.0085	1.177	1.178

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As shown in Table 5, the adsorption energies of the six structures were negative, so all were stable. The adsorption energies of the three structures where CO₂ was adsorbed from the side close to the Ni atom were significantly more stable. In terms of bond lengths, the structures in which CO₂ was adsorbed from the side close to the Ni atom had a larger change in d_C–O, which had a good activation effect on CO₂ molecules.

(3) Ni-Pyridine N₁V₃–C catalysts. The structure of the Ni-pyridine N₁V₃–C–CO₂ intermediate is shown in Fig. S2.† The bond lengths, bond angles and adsorption energies of the Ni-pyridine N₁V₃–C–CO₂ intermediate are illustrated in Table 6.

Table 6 Adsorption energies and bond lengths of Ni-pyridine N₁V₃–C–CO₂ intermediates

Isomers	Eads/eV	dC–O1/Å	dC–O2/Å
a	−0.0084	1.178	1.179
b	−0.0008	1.178	1.178
c	−0.0093	1.176	1.180
d	0.0039	1.178	1.178
e	0.0027	1.177	1.179
f	0.0018	1.177	1.178

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In terms of binding energy, the binding energies E_ads of (a), (b) and (c) were lower than the energy required for CO₂ to be adsorbed stably, and the adsorption of CO₂ was more stable from the side close to Ni atoms than that from the side far away from Ni atoms. In terms of bond lengths, the C=O bond lengths of (a) and (b) were almost unchanged compared to CO₂, so the catalytic activity of CO₂RR might be very low. The C=O bond lengths of (c) were 1.176 Å and 1.180 Å, which had a certain activation effect on CO₂ molecules.

(4) Ni-Pyrrole N₂V₂–C catalysts. The structure of Ni-pyrrole N₂V₂–C–CO₂ is shown in Fig. 8 as follows: (a) single-site adsorption, with Ni atoms attached to C atoms; (b) double-site adsorption, with Ni–C and N–O bonded; and (c) double-site adsorption, with N–O and N–C bonded. The binding energies and bond lengths of the Ni-pyrrole N₂V₂–C–CO₂ intermediates are illustrated in Table 7.

Fig. 8 Isomers of the Ni-pyrrole N₂V₂–C–CO₂ intermediate: (a) Ni-pyrrole N₂V₂–C–CO₂ single-site adsorption; (b) Ni-pyrrole N₂V₂–C–CO₂ Ni–C N–O double-site adsorption; and (c) Ni-pyrrole N₂V₂–C–CO₂ Ni–O N–C double-site adsorption.

Table 7 Adsorption energies and bond lengths of Ni-pyrrole N₂V₂–C–CO₂ intermediates

Isomers	Eads/eV	dC–O1/Å	dC–O2/Å
a	−0.0093	1.177	1.179
b	−0.0096	1.177	1.178
c	−0.0094	1.178	1.178

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In terms of binding energy, the binding energies of all three intermediates were negative, so all CO₂ could be stably adsorbed on the catalyst. According to the C=O bond lengths, the three intermediates did not change much compared with CO₂. Therefore, the activation of CO₂ molecules of the Ni-pyrrole N₂V₂–C catalysts was low.

(5) Ni-Pyrrole N₁V₃–C catalysts. Fig. S3† depicts the isomers of the Ni-pyrrole N₁V₃–C–CO₂ intermediate as follows: (a) single-site adsorption, with the Ni atom attached to the C atom; (b) double-site adsorption, with Ni–C and N–O bonded; and (c) double-site adsorption, with N–O–N–C bonded. The binding energies and bond lengths of the Ni-pyrrole N₁V₃–C–CO₂ intermediate are shown in Table 8.

Table 8 Adsorption energies and bond lengths of Ni-pyrrole N₁V₃–C–CO₂ intermediates

Isomers	Eads/eV	dC–O1/Å	dC–O2/Å
a	−0.0090	1.178	1.178
b	−0.0101	1.178	1.178
c	−0.0099	1.178	1.178

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As illustrated in Table 8, the binding energies of all three structures were negative, so CO₂ could be stably adsorbed on the catalysts. However, the C=O bond lengths of (a), (b) and (c) were all 1.178 Å, which was the same as that of CO₂. Therefore, the activation of CO₂ molecules by the three catalysts was low.

3.5 Study of the catalytic activity of catalysts for CO₂RR catalyzation

3.5.1 Analysis of the catalytic activity of CO₂RR by single-site adsorption on catalysts. First, the Ni-pyridine N₂C₁–C catalysts were analyzed for single-site adsorption of CO₂. The adsorption energy data were summarized in Table S2.† The reaction paths of the five catalysts for CO₂ to CO under single-site adsorption were illustrated in Fig. 9. In the same case of single-site adsorption, Ni-pyridine N₁V₃–C catalyst A had the best catalytic effect, with a reaction energy barrier ΔG of 0.2714 eV, which was 2.7189 eV lower than that without catalyst (ΔG = 2.9903 eV). Thus, the catalyst exhibited excellent catalytic performance. The energy barriers of the reaction under Ni-pyridine N₂C₁–C catalyst A decreased by 2.6280 eV and under Ni-pyridine N₂C₁–C catalyst B decreased by 2.5789 eV, both of which had good catalytic performance. The energy barriers of the reaction under Ni-pyridine N₁V₃–C catalyst B, ΔG = 0.7259 eV, compared to that of the reaction without the catalyst, ΔG = 2.9903 eV, decreased by 2.2644 eV, which had some catalytic activity.

Fig. 9 Reaction path diagram for catalysts in the case of single-site adsorption (where A represents adsorption from the proximal side and B represents adsorption from the distal side).

Based on the magnitude of the energy barriers, it could be observed that the decisive step for the uncatalyzed and Ni-pyridine N₁V₃–C catalyst B was the formation of *CO, and the rest of the decisive step was the formation of *COOH in the first step.

3.5.2 Analysis of the catalytic activity of CO₂RR by catalyst two-site adsorption. CO₂ can be categorized as Ni–C, N–O bonded and N–O, N–C bonded for two-site adsorption on catalysts, so the same catalyst had two different structures in the same two-site adsorption case.

The catalytic ability of the Ni-pyridine N₂C₁–C catalyst for two-site adsorption of CO₂ from the proximal side with Ni–C, N–O bonding was first investigated. The adsorption energy data were summarized in Table S2.†

Five cases of catalyst two-site adsorption of CO₂ were illustrated in Fig. 10. As observed from the figure, the Ni-pyridine N₂C₁–C catalyst Ni–C N–O A was the best catalyst with a reaction energy barrier of ΔG = −1.4029 eV, which was a decrease of 4.3932 eV compared to the energy barrier of ΔG = 2.9903 eV in the absence of the catalyst, and the reaction was exothermic and thermodynamically capable of proceeding spontaneously. The energy barrier for the reaction under Ni-pyridine N₂C₁–C catalyst Ni–O N–C B was 0.4084 eV, and the energy barrier of the reaction under Ni-pyridine N₂C₁–C catalyst Ni–C N–O B was 1.9764 eV. There was a substantial decrease in the energy barrier compared to the reaction without the catalyst, so both had good catalytic activity; the rest of the catalysts had limited catalytic performance.

Fig. 10 Reaction path diagram for catalysts in the case of two-site adsorption (where A represents adsorption from the near side and B represents adsorption from the far side).

4 Conclusions

In this study, the stability, activation and catalytic performance of the catalysts were analyzed and screened for better catalysts by performing energy calculations and structure optimization of the constructed structures based on the theoretical basis of quantum chemistry. The following conclusions were obtained.

(1) Vacancies could significantly affect the catalyst properties. The Ni–N–C catalyst with vacancies had a higher Ni–N bond energy and good catalyst stability. However, its ΔE was larger, and the electron conduction rate was slower than that of the catalyst without vacancies. The ΔE of the Ni-pyridine N₃V₁–C catalyst was 0.872 eV, which was more than three times that of the catalyst without the Ni-pyridine N₄–C catalyst with ΔE = 0.278 eV.

(2) The catalysts with excellent activation performance for CO₂ were screened as Ni-pyridine N₂C₁–C catalyst, Ni-pyridine N₁V₃–C catalyst and Ni-pyrrole N₂V₂–C catalyst. Among them, the best CO₂ activation ability was the Ni-pyridine N₂C₁–C catalyst.

(3) In single-site adsorption, the best catalytic effect was achieved by Ni-pyridine N₁V₃–C catalyst A, with reaction ΔG = 0.2714 eV. In two-site adsorption, the best catalytic effect was achieved by Ni-pyridine N₂C₁–C Ni–C N–O A, with reaction ΔG = −1.4029 eV, and the reaction was able to proceed thermodynamically and spontaneously.

(4) Both single-site adsorption and dual-site adsorption reduced the reaction energy barrier compared to no catalyst. Overall, most of the catalytic activities of single-site adsorption were better than those of dual-site adsorption.

Data availability

The data used to support the findings of this paper are included within the article.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Supports of the Hefei Advanced Computing Center for this work are gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4cy01394h

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