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Article

Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction

by
Kewei Yu
,
Xinyu Liu
,
Meiyan Wang
* and
Jingyao Liu
Institute of Theoretical Chemistry, College of Chemistry, Jilin University, Changchun 130023, China
*
Author to whom correspondence should be addressed.
Catalysts 2025, 15(9), 837; https://doi.org/10.3390/catal15090837 (registering DOI)
Submission received: 30 July 2025 / Revised: 15 August 2025 / Accepted: 20 August 2025 / Published: 1 September 2025
(This article belongs to the Special Issue Catalysis Accelerating Energy and Environmental Sustainability)
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Abstract

Single-atom catalysts supported by two-dimensional materials have been widely used in the electrochemical CO2 reduction reaction (CO2RR). Defects are inevitably generated during the preparation of two-dimensional materials. In this study, six Fe–N4-doped graphene catalysts (CAT1–CAT6) containing single carbon vacancy defects were designed and calculated using density functional theory (DFT) calculations. The stability, catalytic activity and product selectivity of these catalysts for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 were discussed and compared with the defect-free Fe−N4-doped graphene catalyst (CAT0). The results show that CAT1–CAT6 all exhibit excellent thermodynamic and electrochemical stabilities. The possible reaction pathways for CO2 reduction to different C1 products were systematically investigated. The CAT2, CAT3 and CAT6 exhibit high selectivity for HCOOH, whereas the products of CAT1, CAT4 and CAT5 are HCOOH, CH3OH and CH4, the same as those of CAT0. Moreover, these six catalysts more effectively suppress the competing hydrogen evolution reaction (HER) compared to CAT0, indicating that the defect improves the catalytic selectivity of CO2RR. Among all of the catalysts, CAT2 demonstrates the most prominent catalytic activity and selectivity toward the CO2 reduction reaction (CO2RR). The large distortion of Fe−N4 in *HCOO with CAT2 contributes to the lower limiting potential UL. We hope that the finding that the large distortion of Fe−N4 could lower the limiting potential will provide theoretical insights for the design of more efficient CO2RR electrocatalysts.

1. Introduction

Electrocatalytic CO2 reduction reaction (CO2RR) is a green and economical conversion strategy that can transform CO2 into various high value-added chemical products such as CO, HCOOH, CH3OH and CH4 by utilizing renewable electrical energy [1,2,3]. Despite a considerable amount of experimental and theoretical reports, there are still some critical challenges to the industrial application of CO2RR technology [4,5,6,7,8,9,10,11,12,13,14]. The complex proton-coupled electron transfer (PCET) pathways in the process of CO2RR lead to product diversity, reducing the selectivity of a specific product. Additionally, the competition with the hydrogen evolution reaction (HER) further reduces the Faradaic efficiency and poor product selectivity. Therefore, developing novel CO2RR catalysts with high catalytic performance has become pivotal for realizing the practical application of electrocatalytic CO2 reduction technology.
In recent years, single-atom catalysts (SACs) have been widely used in CO2RR as a kind of cost-effective catalyst with well-defined active sites. Two-dimensional (2D) materials, characterized by a high specific surface area and large number of active sites, have been widely adopted as supports for SACs [15,16,17,18,19,20,21,22,23,24]. Among various 2D materials, graphene stands out due to its high carrier mobility, excellent electrical conductivity and structural tunability [23,24]. Notably, graphene-supported transition metal SACs represented by TM−N4 have been proven to be efficient CO2RR catalysts [25,26,27,28,29,30,31,32,33].
Defects are inevitably formed during graphene preparation, and defect engineering has been developed as a critical strategy for modulating the surface chemistry properties of electrocatalysts to enhance the catalytic performance [34,35,36,37,38,39]. Vacancy defects have been widely reported to improve CO2RR performance [36,37,38]. For instance, in Fe−N4-doped graphene, it is reported that the active-site environment, affected by vacancy defects and nitrogen doping, plays pivotal roles in enhancing the catalytic performance of electrochemical CO2 reduction to CO [36]. It has also been demonstrated that intrinsic carbon defects can be significantly modulated by coupling single-atom Fe−N4 moieties. The density functional theory (DFT) calculations reveal that these defects reduce the energy barriers for CO2RR-to-CO pathways while suppressing HER [37]. Furthermore, the effect of the second-shell carbon environment around the metal–nitrogen moiety in Fe−N4-doped graphene has been calculated and it has been found that the defects in this region are significantly influential for the CO2RR generating CO [38]. The single carbon vacancy defects have been confirmed to weaken the adsorption free energy of *OOH in Co−N4 sites, thereby further promoting the ORR process [39]. Although prior studies have explored the role of single carbon vacancies in enhancing oxygen reduction reaction (ORR) activity [39], the effects of such vacancies on CO2RR, specifically for the C1 products CO, HCOOH, CH3OH and CH4, remain underexplored.
Inspired by the promotional effect of single carbon vacancies on ORR, we aim to systematically investigate their influence on CO2RR generating the C1 products CO, HCOOH, CH3OH and CH4. Herein, we design and construct six types of Fe−N4-doped graphene catalysts with a single carbon vacancy defect at distinct sites adjacent to N, which may exert significant impacts. These six catalysts are comprehensively evaluated in terms of their stability, catalytic activity and product selectivity. Our results demonstrate that introducing vacancies markedly enhances both the catalytic activity and selectivity of the CO2RR process relative to the defect-free Fe–N4-doped graphene catalyst. Notably, significant distortion of the Fe–N4 during the formation of the *HCOO intermediate is identified as a critical factor reducing the limiting potential UL, thereby enabling high selectivity toward HCOOH. Although previous studies have reported the effect of vacancy defects on CO2RR generating CO [36,37,38], this work systematically elucidates how small single carbon vacancies modulate CO2RR performance. This study investigates the effect of small vacancy defects on the CO2RR catalytic performance to provide theoretical insights for designing more efficient CO2RR electrocatalysts.

2. Results and Discussion

2.1. Structures and Stability

To investigate the influence of vacancy defects on the CO2RR catalytic performance, based on the structural symmetry of Fe−N4-doped graphene, we designed six types of catalysts with a single carbon vacancy defect at six distinct sites adjacent to N atoms. The optimized structures of the defect-free Fe−N4-doped graphene catalyst (CAT0) and six defective catalysts (CAT1−CAT6) with different single carbon vacancy defects are shown in Figure 1.
To evaluate the stability of these structures, we calculated the binding energies (Eb) of a single Fe atom on the defective N4-doped monolayer graphene substrate. The more negative the binding energy Eb value, the stronger the binding between the single Fe atom and N4-doped graphene substrate. The binding energy Eb of a single Fe atom to the substrate is defined as Equation (1):
Eb = EFe–N4–C − EN4–C − EFe-single
where EFe–N4–C, EN4–C and EFe-single represent the total energy of the Fe−N4-doped graphene catalyst, the N4-doped graphene substrate and the isolated Fe atom, respectively. As shown in Table 1, the binding energies for the catalysts range from −8.58 eV to −6.91 eV, indicating that the Fe atom forms strong bonds with these substrates. The strong interaction between the Fe atom and the substrate can also be observed from the hybridization between the Fe-3d orbital and the N-2p orbital from the projected density of states (PDOS) calculations (see Figures S1 and S2 in the Supporting Information).
Moreover, to evaluate the thermodynamic stability of these catalysts, the formation energy Ef was calculated using Equation (2):
Ef= EFe–N4–C − EN4–C − EFe-bulk
where EFe-bulk is the energy of a single Fe atom in the stable bulk phase. When Ef is less than 0 eV, the catalyst has good thermodynamic stability. As shown in Table 1, CAT0−CAT6 all have negative Ef values, indicating that the Fe atoms do not tend to diffuse or aggregate on these substrates and have high thermodynamic stability.
To evaluate the electrochemical stability of the catalysts, we calculated the dissolution potential Udiss, and the corresponding formula is as shown in Equation (3):
Udiss = U0diss(Fe) − Ef/ne
where U0diss(Fe) is the standard dissolution potential of bulk Fe, and n is the number of electrons involved in the dissolution process. All of the Udiss values listed in Table 1 are positive, indicating that CAT0−CAT6 all have good electrochemical stability.

2.2. Electrocatalytic CO2 Reduction

The electrochemical CO2RR involves multiple PCET steps. As illustrated in Figure 2, the proton–electron pairs interact with CO2 to form two distinct initial configurations (*COOH and *HCOO), resulting in different pathways for CO2RR. For the *COOH intermediate, the PCET is accompanied by the release of a H2O molecule, generating the *CO intermediate, which subsequently desorbs to form the C1 product CO. Both *COOH and *HCOO can undergo hydrogenation to form the shared *HCOOH intermediate, which then desorbs to yield the C1 product HCOOH. Furthermore, sequential PCET steps initiated from *HCOOH and *CO intermediates lead to the formation of the C1 products CH3OH and CH4. The corresponding Gibbs free energy changes for these CO2RR processes on the defect-free Fe−N4-doped graphene catalyst CAT0 are presented in Figure 3.
As depicted in Figure 3, with CAT0, the initial PCET step of CO2 reduction generates two distinct intermediates, namely, *COOH (0.32 eV) and *HCOO (0.40 eV). Subsequently, both *COOH and *HCOO undergo hydrogenation to form the shared *HCOOH intermediate. Notably, the *COOH intermediate can also release a H2O molecule to generate *CO, a process that is thermodynamically spontaneous. Under the electrochemical reaction conditions, *HCOOH can spontaneously desorb from the Fe−N4-doped graphene surface, whereas the desorption of *CO requires substantial free energy (ΔG = 1.10 eV), significantly hindering its effective desorption from the catalyst. The *CO intermediate may be further converted into *CHO, which is endothermic by 0.76 eV, making this transformation energetically unfavorable. In contrast, *HCOOH undergoes exothermic hydrogenation (ΔG = −0.33 eV) to form *CHO. The *CHO intermediate then proceeds to hydrogenate into two possible intermediates, *CHOH or *CH2O (ΔG = 0.24 or 0.36 eV), with the formation of *CHOH being energetically more favorable. Subsequently, the *CHOH intermediate undergoes hydrogenation to generate either *CH (ΔG = 1.09 eV) or *CH2OH (ΔG = −0.08 eV). The latter pathway is both energetically preferred and exothermic, ultimately leading to the formation of the product CH3OH. The *CH3OH can either spontaneously desorb or undergo two consecutive protonation–reduction reactions to be further converted into CH4. Meanwhile, *CH undergoes three consecutive energy-decreasing protonation–reduction processes to ultimately generate CH4. Additionally, *H2COOH is further hydrogenated, giving the intermediate *CH2O, with which multiple protonation–reduction processes proceed to ultimately generate CH3OH or CH4. The potential-determining step (PDS) for CO2 reduction to CO, HCOOH, CH3OH and CH4 with CAT0 is the same (* + CO2 → *COOH), with a limiting potential UL of −0.32 V. However, due to the high desorption energy (1.10 eV) of CO with CAT0, CO is difficult to desorb effectively, so the generation of CO is difficult to achieve on this catalyst surface. While the products HCOOH, CH3OH and CH4 are easy to desorb, they are all likely to be generated on the CAT0 catalyst.
To facilitate a clearer discussion, according to the possibility of C1 products, we categorize the six catalysts CAT1−CAT6 containing different carbon vacancy defects into two groups: (1) catalysts with HCOOH as the primary product, including CAT2, CAT3 and CAT6 (Figure 4); (2) catalysts with HCOOH, CH3OH and CH4 as the primary products, including CAT1, CAT4 and CAT5 (Figure 5). The corresponding calculated structures and relative free energies of all intermediates are provided in Figures S3–S8 and Table S1 of the Supporting Information.

2.2.1. Reduction of CO2 to HCOOH

Figure 4 presents the Gibbs free energy changes for all intermediates along the CO2RR pathways with the CAT2, CAT3 and CAT6 catalysts. For these catalysts, the possible pathways for CO2 reduction to various C1 products (CO, HCOOH, CH3OH and CH4) are similar to those for CAT0. For HCOOH formation, the optimal reaction pathway is * + CO2 →*HCOO →*HCOOH → HCOOH with CAT2 and CAT3, while it is * + CO2 →*COOH →*HCOOH → HCOOH with CAT6. This indicates that CAT2 and CAT3 tend to form HCOOH via *HCOO, while CAT6 tends to form HCOOH through *COOH. The corresponding limiting potential UL for HCOOH formation is −0.07, −0.17 and −0.21 V, respectively. For the generation of CO, similar to CAT0, the desorption of CO requires a high energy of 0.90, 0.96 and 0.89 eV, respectively, so desorbing from the catalyst surface as a product is difficult under normal temperature conditions. For CH3OH and CH4 formation, the optimal pathways are *HCOOH → *CHO → *CH2O/*CHOH →*CH3O/*CH2OH → *CH3OH → CH3OH and *CH3OH → *CH3 → *CH4 → CH4, respectively. Specifically, with CAT2 and CAT3, the PDS for CH3OH and CH4 formation is *CHO → *CH2O while it is *CHO → *CHOH for CAT6. The corresponding limiting potential UL is −0.20, −0.24 and −0.36 V for CAT2, CAT3 and CAT6, respectively. Notably, the limiting potential UL for generating HCOOH (−0.07, −0.17 and −0.21 V) is lower than that for CH3OH and CH4 generation (−0.20, −0.24 and −0.36 V); therefore, the main product with CAT2, CAT3 and CAT6 is HCOOH.

2.2.2. Reduction of CO2 to HCOOH, CH3OH and CH4

The Gibbs free energy changes of CO2RR with CAT1, CAT4 and CAT5 are shown in Figure 5. For these three catalysts, CO desorption from the catalyst surface is difficult due to the relatively large desorption energy of 0.69, 1.02 and 0.97 eV, respectively. The optimal pathways for the reduction of CO2 to CH3OH and CH4 with CAT1 and CAT4 are ∗ + CO2 → *COOH/*HCOO→ *HCOOH → *CHO →*CH2O/*CHOH → *CH3O/*CH2OH → *CH3OH → CH3OH and *CH3OH → *CH3 →*CH4 → CH4, respectively. With CAT5, the optimal pathway for the reduction of CO2 to CH3OH is ∗ + CO2 → *COOH→ *HCOOH → *H2COOH →*CH2O → *CH3O → *CH3OH → CH3OH, in contrast to other catalysts. For all three catalysts, the PDS for the formation of HCOOH, CH3OH and CH4 is the initial PECT step involving intermediate *COOH or *HCOO, with the corresponding limiting potential UL of −0.29, −0.29 and −0.23 V, respectively. Consequently, HCOOH, CH3OH and CH4 emerge as the primary reduction products with CAT1, CAT4, and CAT5.
Table 2 compiles the limiting potential UL values for all of the catalysts. For the defect-free CAT0, three competing products, HCOOH, CH3OH and CH4, are accessible, with a UL of −0.32 V. Among the six defective catalysts CAT1−CAT6, CAT1, CAT4 and CAT5 maintain the same product distribution as CAT0 but with a reduced UL of −0.29, −0.29 and −0.23 V, respectively. In contrast, CAT2, CAT3 and CAT6 display enhanced selectivity toward HCOOH with a corresponding UL of −0.07, −0.17 and −0.21 V, respectively. These findings demonstrate that the introduced single carbon vacancies in CAT2, CAT3 and CAT6 significantly improve both the selectivity and catalytic activity for HCOOH. Among them, CAT2 exhibits the lowest UL for HCOOH (−0.07 V), positioning it as a highly promising candidate for efficient CO2RR applications.
As shown in Table 2, the free energy changes ΔGHCOO of the process * + CO2 → *HCOO is reduced for all defective catalysts except CAT6 compared to the defect-free catalyst CAT0, indicating that the introduced vacancies facilitate *HCOO formation. To evaluate the influence of different vacancy defects on the catalytic performance, we performed a Bader charge analysis and found that the Fe atoms in CAT1 and CAT2 exhibit the largest electron loss (1.18|e| and 1.15|e|, respectively). As CAT2 exhibits the lowest UL among these catalysts, the structures of CAT2 and *HCOO on CAT2 are further analyzed (Figure 6a–c). The analysis reveals that the structure of Fe−N4 in *HCOO becomes distorted, leading to one N atom deviating from the graphene plane. Upon HCOO adsorption, the dihedral angle (∠1−34−2) of the four N atoms increases from 0.35° to 12.51°. The five-membered ring’s smaller internal angle makes its N atom more prone to out-of-plane distortion. Figure 6d shows that the limiting potential UL of the catalysts presents a moderate linear relationship with the dihedral angle θ, suggesting that the larger the dihedral angle, the closer the limiting potential is to zero. To elucidate how Fe−N4 distortion in the *HCOO intermediate enhances the catalytic performance, we compared the PDOS of *HCOO on CAT2 and CAT0 (Figure 6e,f). Compared to CAT0, CAT2 shows stronger hybridization between the Fe-3d orbital and the orbitals of HCOO, suggesting a stronger interaction between the Fe atom and HCOO. This is corroborated by the shorter Fe–OCHO bond length in CAT2 (1.940 Å) versus CAT0 (2.102 Å). Briefly, the distortion of Fe−N4 enhances the interaction of Fe with HCOO, stabilizing the *HCOO intermediate and thereby reducing the limiting potential UL on CAT2.

2.3. Comparison of CO2RR with HER

The HER process (H+ + e− → 1/2 H2) consumes proton–electron pairs in the solution, reducing the selectivity of CO2RR products and leading to a decrease in the Faraday efficiency. Therefore, HER stands as the primary competitive reaction against CO2RR. Figure 7a presents the free energy change of HER with these catalysts. The difference between UL(CO2RR) and UL(HER) is commonly used to evaluate the selectivity of catalysts. The more positive the difference, the higher the selectivity of the catalyst for CO2RR. As illustrated in Figure 7b, all of the UL(CO2RR) − UL(HER) values are positive, and notably larger than that for CAT0. This indicates that the introduction of single carbon vacancy defects significantly enhances the CO2RR selectivity of these catalysts.
To evaluate the thermal stability of these catalysts, we took CAT2 as a representative example and conducted ab initio molecular dynamics (AIMD) simulations at 400 K for 5 ps with a time step of 1 fs. As illustrated in Figure 8, no significant structural disruption or Fe atom diffusion was observed during the simulation, indicating that these catalysts can serve as stable CO2RR electrocatalysts under electrochemical reaction conditions.

3. Computational Methods

Spin-polarized density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP 5.4.4) [40,41]. The projector- augmented wave (PAW) method and Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) were adopted in all calculations [42,43]. A cutoff energy for the electron plane wave expansion was chosen as 400 eV. In structure relaxation and density of states calculations, the k-point grid settings were 3 × 3 × 1 and 9 × 9 × 1, respectively. Convergence thresholds of 10−5 eV for energy and 0.03 eV/Å for force were adopted. A vacuum layer of 20 Å was set along the c direction to eliminate interactions between periodic images. DFT-D3 empirical dispersion correction was applied to describe the long-range van der Waals interactions [44]. The implicit solvation model introduced in VASPsol (5.4.1) was used to consider solvation effects [45]. Ab initio molecular dynamics (AIMD) simulations at 400 K were conducted to assess the thermal stability of the catalyst, with a time step of 1 fs over a total simulation time of 5ps [46].
The Gibbs free energy change (ΔG) of each elementary step was calculated referring to the computational hydrogen electrode (CHE) model [47], as shown in Equation (4):
ΔG = ΔEDFT + ΔEZPE − TΔS + neU + ΔGpH
where ΔEDFT, ΔEZPE and ΔS are changes in the DFT energy, zero-point energy and entropy, respectively. T is set to room temperature (298.15 K), and U is the applied electrode potential. ΔGpH was denoted as kBT × pH × ln 10, where kB is the Boltzmann constant and pH is set as zero here. Additionally, data postprocessing was assisted by the Qvasp [48] and VASPKIT packages [49]. The limiting potential of CO2RR is defined as UL= –ΔGPDS/e, where ΔGPDS is the maximum free energy change along the reaction pathway.

4. Conclusions

In this work, we designed six types of Fe−N4-doped graphene catalysts with distinct single carbon vacancy defects and comprehensively evaluated their electrocatalytic performance for CO2 reduction to C1 products (CO, HCOOH, CH3OH and CH4) via DFT calculations. The binding energy, formation energy and dissolution potential analyses confirm that Fe atoms can be stably anchored on N4-doped graphene, with all catalysts exhibiting excellent thermodynamic and electrochemical stabilities. All possible reaction pathways for the formation of C1 products on catalysts CAT0–CAT6 were located, and the most favorable CO2 reduction products generated with the lowest limiting potential were determined. Our results show that CAT2, CAT3 and CAT6 demonstrate high selectivity toward HCOOH, with CAT2 achieving the highest catalytic activity. In contrast, CAT1, CAT4 and CAT5 display product distributions identical to CAT0, yielding HCOOH, CH3OH and CH4 with no obvious selectivity. Notably, all defective catalysts (CAT1–CAT6) show enhanced preference for CO2RR over the competing hydrogen evolution reaction (HER) compared to the defect-free CAT0, indicating that vacancy defects improve CO2RR selectivity. Furthermore, the AIMD simulations confirm the thermal stability of the catalysts. Among all these catalysts, CAT2 stands out with optimal performance, attributed to the significant distortion of one N atom out of the graphene plane, which stabilizes the *HCOO intermediate and lowers the limiting potential. This study elucidates the influence of single carbon vacancy defects on the CO2RR catalytic performance, revealing that substantial Fe–N4 distortion can reduce the limiting potential. We hope these findings contribute to the design of novel catalysts for electrocatalytic CO2 reduction.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/catal15090837/s1, Figure S1: Projected density of states (PDOS) of CAT0; Figure S2: Projected density of states (PDOS) of (a) CAT1; (b) CAT2; (c) CAT3; (d) CAT4; (e) CAT5; (f) CAT6; Figure S3: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT1; Figure S4: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT2; Figure S5: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT3; Figure S6: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT4; Figure S7: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT5; Figure S8: The calculated structure of the intermediates for CO2RR to C1 products CO, HCOOH, CH3OH and CH4 with CAT6; Table S1: The relative free energies of intermediates on the catalysts CAT0–CAT6.

Author Contributions

Investigation, writing—original draft, K.Y.; investigation, X.L.; writing—review and editing, M.W.; supervision, J.L. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Key Research and Development Program of China, grant number 2021YFA1500403.

Data Availability Statement

Most data acquired for this manuscript are summarized in the manuscript. All other data can be obtained at the request of the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Catalysts 15 00837 g001
Figure 1. The optimized structures of (a) CAT0; (b) CAT1; (c) CAT2; (d) CAT3; (e) CAT4; (f) CAT5; (g) CAT6.
Figure 1. The optimized structures of (a) CAT0; (b) CAT1; (c) CAT2; (d) CAT3; (e) CAT4; (f) CAT5; (g) CAT6.
Catalysts 15 00837 g001
Catalysts 15 00837 g002
Figure 2. The possible reaction pathways for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 with CAT0.
Figure 2. The possible reaction pathways for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 with CAT0.
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Catalysts 15 00837 g003
Figure 3. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 with CAT0.
Figure 3. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 with CAT0.
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Catalysts 15 00837 g004
Figure 4. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 on (a) CAT2, (b) CAT3 and (c) CAT6.
Figure 4. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 on (a) CAT2, (b) CAT3 and (c) CAT6.
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Catalysts 15 00837 g005
Figure 5. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 on (a) CAT1, (b) CAT4 and (c) CAT5.
Figure 5. Free energy diagrams for CO2RR generating C1 products CO, HCOOH, CH3OH and CH4 on (a) CAT1, (b) CAT4 and (c) CAT5.
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Catalysts 15 00837 g006
Figure 6. (a) Charge density difference (CDD) map of Fe–N4 on CAT2, (b) top view of the structure of *HCOO on CAT2, (c) side view of the structure of *HCOO on CAT2, (d) linear relationship between UL and the dihedral angle θ, (e) projected density of states of *HCOO on CAT2, (f) projected density of states of *HCOO on CAT0.
Figure 6. (a) Charge density difference (CDD) map of Fe–N4 on CAT2, (b) top view of the structure of *HCOO on CAT2, (c) side view of the structure of *HCOO on CAT2, (d) linear relationship between UL and the dihedral angle θ, (e) projected density of states of *HCOO on CAT2, (f) projected density of states of *HCOO on CAT0.
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Catalysts 15 00837 g007
Figure 7. (a) Free energy diagram of HER on CAT0−CAT6 catalysts, and (b) difference between CO2RR limiting potential (UL(CO2RR)) and HER limiting potential (UL(HER)) (UL(CO2RR) − UL(HER)).
Figure 7. (a) Free energy diagram of HER on CAT0−CAT6 catalysts, and (b) difference between CO2RR limiting potential (UL(CO2RR)) and HER limiting potential (UL(HER)) (UL(CO2RR) − UL(HER)).
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Catalysts 15 00837 g008
Figure 8. Energy curve versus timesteps and local structures before and after AIMD for CAT2.
Figure 8. Energy curve versus timesteps and local structures before and after AIMD for CAT2.
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Table 1. The binding energy Eb (eV), formation energy Ef (eV) and dissolution potential Udiss (eV) of catalysts CAT0−CAT6.
Table 1. The binding energy Eb (eV), formation energy Ef (eV) and dissolution potential Udiss (eV) of catalysts CAT0−CAT6.
CatalystsEbEfUdiss
CAT0−7.94−2.590.85
CAT1−8.58−3.231.17
CAT2−8.50−3.151.12
CAT3−6.91−1.560.33
CAT4−7.07−1.720.41
CAT5−8.39−3.041.07
CAT6−7.03−1.680.39
Table 2. Limiting potential UL(V), free energy changes ΔGCOOH and ΔGHCOO (eV) for the formation of *COOH and *HCOO, Bader charge QFe (|e|) of Fe atom in catalyst and dihedral angle θ (°) of ∠1−34−2 formed by the four N atoms in*COOH or *HCOO.
Table 2. Limiting potential UL(V), free energy changes ΔGCOOH and ΔGHCOO (eV) for the formation of *COOH and *HCOO, Bader charge QFe (|e|) of Fe atom in catalyst and dihedral angle θ (°) of ∠1−34−2 formed by the four N atoms in*COOH or *HCOO.
CatalystsULΔGCOOHΔGHCOOQFeθ
CAT0−0.320.320.401.100.21
CAT1−0.290.290.301.181.65
CAT2−0.070.210.071.1512.51
CAT3−0.170.360.171.080.24
CAT4−0.290.360.291.090.47
CAT5−0.230.380.231.100.34
CAT6−0.210.210.421.051.80
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Yu, K.; Liu, X.; Wang, M.; Liu, J. Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction. Catalysts 2025, 15, 837. https://doi.org/10.3390/catal15090837

AMA Style

Yu K, Liu X, Wang M, Liu J. Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction. Catalysts. 2025; 15(9):837. https://doi.org/10.3390/catal15090837

Chicago/Turabian Style

Yu, Kewei, Xinyu Liu, Meiyan Wang, and Jingyao Liu. 2025. "Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction" Catalysts 15, no. 9: 837. https://doi.org/10.3390/catal15090837

APA Style

Yu, K., Liu, X., Wang, M., & Liu, J. (2025). Computational Evaluation of Defects in Fe–N4-Doped Graphene for Electrochemical CO2 Reduction. Catalysts, 15(9), 837. https://doi.org/10.3390/catal15090837

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