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High-Performance of Electrocatalytic CO2 Reduction on Defective Graphene-Supported Cu4S2 Cluster

Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi’an 710127, China
Authors to whom correspondence should be addressed.
Catalysts 2022, 12(5), 454;
Submission received: 16 March 2022 / Revised: 10 April 2022 / Accepted: 14 April 2022 / Published: 19 April 2022
(This article belongs to the Special Issue Heterogeneous Electrocatalysis: Fundamentals and Applications)


Electrochemical CO2 reduction reaction (CO2RR) to high-value chemicals is one of the most splendid approaches to mitigating environmental threats and energy shortage. In this study, the catalytic performance of CO2RR on defective graphene-supported Cu4S2 clusters as well as isolated Cu4Xn (X = O, S, Se; n = 2, 4) was systematically investigated based on density functional theory (DFT) computations. Calculation results revealed that the most thermodynamically feasible product is CH3OH among the C1 products on Cu4X2 clusters, in which the Cu4S2 cluster has the best activity concerning CH3OH synthesis with a limiting potential of −0.48 V. When the Cu4S2 cluster was further supported on defective graphene, the strong interaction between cluster and substrate could greatly improve the performance via tuning the electronic structure and improving the stability of the Cu4S2 cluster. The calculated free energy diagram indicated that it is also more energetically preferable for CH3OH production with a low limiting potential of −0.35 V. Besides, the defective graphene support has a significant ability to suppress the competing reactions, such as the hydrogen evolution reaction (HER) and CO and HCOOH production. Geometric structures, limiting potentials, and reduction pathways were also discussed to gain insight into the reaction mechanism and to find the minimum-energy pathway for C1 products. We hope this work will provide theoretical reference for designing and developing advanced supported Cu-based electrocatalysts for CO2 reduction.

Graphical Abstract

1. Introduction

Global warming and energy shortage have become two major issues in the 21st century. The excessive CO2 emission caused by rapid consumption of fossil resources calls for the instant requirement of clean and renewable energy [1]. CO2 itself is an inert molecule Δ G f 0 = 394.4 KJ / mol [2], so it is urgent to explore a robust catalyst for its reduction and conversion. In recent years, electrochemical CO2 reduction reaction (CO2RR) has attracted widespread attention as one of the most excellent methods to alleviate energy shortage and reduce the global carbon footprint [3,4]. In CO2RR, various metal electrodes play a dual role, not only as an electron conducting medium but also as catalytically active sites. Among them, Cu-based material has excellent activity and selectivity to reduce CO2 into hydrocarbons such as methanol, methane, formic acid, ethylene, etc. [5,6]. In these products, methanol is a desired hydrocarbon because it can be used as feedstock for direct methanol fuel cells [7]. More importantly, the metallic Cu has been verified as an active catalyst for methanol synthesis with a turnover frequency even comparable with that of industrial catalysts [8].
With the development from single-crystal metal electrodes to supported metal nanoparticle electrodes [9,10,11], the supported sub-nanometric Cu clusters [12,13] have received considerable attention in the past few years. The superior catalytic performance comes from three factors: The unique electronic structure of the nano-size cluster; the high specific surface area; and the significant effect of the substrate support. In the catalytic experiments, the support has an important role in immobilizing clusters and preventing them from aggregation. For instance, defect engineering of graphene [14,15] has been used to immobilize the cluster against sinter by providing strong anchoring sites which could effectively regulate the electronic properties and catalytic performance in CO2 reduction. In particular, theoretical results have confirmed that the defective graphene supported Cu (Cu55 [16] and Cu4 [17]) nanocluster can improve the CO2RR selectivity for hydrocarbon fuels at low overpotential. Additionally, Ma et al. reported that the experimental realization of the Cu@CuxO nanoparticles decorated on defective graphene achieved a high CO2 reduction Faradaic efficiency of 60.6% [18]. By analyzing experiments and DFT calculations, Hu et al. demonstrated that the defective graphene-supported Cu13 cluster exhibits excellent performance for CO2RR with a maximum Faradaic efficiency towards methane of 81.7% and an outstanding stability of 40 h [19].
It is noteworthy that the activity and selectivity of CO2RR are highly sensitive to the structure of the supported Cu-based cluster [20]. To date, the size-selected Cu4 cluster is found to present good catalytic activity for producing hydrocarbons at near atmospheric pressure by comparing with other larger-size catalysts [21,22]. In the experiment, the subnanometer-sized Cu nanoclusters have been successfully prepared. For example, the size-controlled naked Cu cluster [23,24,25] can be synthesized by the electrochemical oxidation-reduction method and the one-pot procedure based on wet chemical reduction, or combination of gas-phase cluster ion sources, mass spectrometry, and soft-landing techniques. However, the impurity-doping effects could further enhance the durability, selectivity, and chemical activity of clusters. The modified Cu nanoclusters [26,27] in the experiment and the theoretical have attracted extensive attention with the development of experimental synthetic techniques. For example, Uzunova et al. found that the Cu32O16 and Cu14O7 nanoclusters can improve the catalytic performance of CO2RR to hydrocarbons because of their strong interaction with CO2 [28]. Similarly, Zhao et al. reported that the CuS nanosheet arrays supported on nickel foam are a robust catalyst for CO2RR toward methane, which has high Faradaic efficiency of 73 ± 5% and a low Tafel slope of 57 mV dec 1 [29]. Lu et al. have synthesized Cu3-X clusters (Cu3-CI, Cu3-Br, Cu3-NO3) which have high selectivity for the electrocatalytic reduction of CO2 to C2H4 with a maximum Faradaic efficiency of 55.01% [30].
It can be seen that control type, location, and content of the dopant atoms are important in terms of affecting the catalytic performance for the modified cluster [31,32]. The electronic structure of the nanocluster can be easily regulated by per-oxidization or heteroatom modulation, providing remarkable possibilities to tune the catalytic performance in CO2RR. What is the effect of doped clusters on the catalytic activity and selectivity of CO2 reduction with different valence states Cu as electrocatalyst? How does the defective graphene support affect their performance? To answer these questions, high-precision computational methods are first used to give an in-depth understanding of the CO2 reduction mechanism of the isolated Cu4Xn clusters, to identify the promising candidate with optimal catalytic performance. On this basis, the CO2RR mechanism of the Cu4S2 cluster adsorbed on defective graphene is considered as a representative model to boost its stability and application. The catalytic activity and product selectivity are evaluated via analyzing the limiting potential of CO2RR towards different C1 products. The geometric structure, charge distribution, and all possible reaction pathways were also discussed to help further understand the reaction mechanism and catalytic properties. We also hope that this work can give theoretical guidance for experimental research and provide reference for the design of high-performance supported Cu-based catalysts in the future.

2. Results and Discussion

2.1. Mechanism of CO2RR on the Cu4X2 Cluster

2.1.1. Cu4X2 Cluster and Electrochemical Adsorption of CO2

Potential energy surfaces (PESs) of the Cu4X2 clusters were probed via global optimization algorithms to locate the global minima (GM) structure and low-lying energy isomers (details in Figure S1). The GM of the Cu4O2, Cu4S2, Cu4Se2 cluster exhibit a similar configuration (in Table 1), in which four Cu atoms and one doped atom form a double trigonal pyramidal structure, and the other doped atom binds with two Cu atoms on the side edge of Cu4. With the decrease of electronegativity of the doped atom, the Cu4X2 configuration exhibits small stretch in the xy plane; as for the vertical direction, the lower half (triangular pyramid of Cu4 structure) presents a slight compression, while the upper half presents a small stretch. It is noteworthy that the structure of the Cu4S2 cluster predicted in this paper is partly consistent with the lowest energy structure of the CunS (n = 4) cluster proposed by Li et al. [33], verifying the solidity of our results. The natural bond orbital (NBO) analysis presented in Table S2 shows that the higher electronegativity dopant atoms can form the positively charged Cu sites, which tends to attract the electronegative oxygen in CO2, thus facilitating the initial step of CO2RR.
It is easy to understand that the ability of capturing CO2 molecules is essential as the introductory step in CO2RR. The electrochemical adsorption of CO2 molecules can be typically represented as
CO 2 + H + + e + * COOH * ,
CO 2 + H + + e + * OCHO * .
The electrochemical adsorption of CO2 involves one (H+ + e) pair transfer to the CO2 species, where CO2 is first hydrogenated to generate hydroxyl or carboxyl groups; it is usually controlled via an applied potential. After testing the possible electrochemical adsorption sites of CO2, the calculated reaction free energy of COOH* formation is 0.41 eV, 1.02 eV, and 0.73 eV lower than that of OCHO* formation on the Cu4O2, Cu4S2, Cu4Se2 clusters, respectively. This means that the intermediate COOH* is more preferable in this case, and the lowest-energy configuration is located and presented in Table 1. As seen in Table 1, all reaction free energies are negative, indicating that the electrochemical absorption of CO2 can occur spontaneously. In these three clusters, E r e a c t of COOH* on Cu4S2 and Cu4Se2 are close, but still larger than that of Cu4O2, suggesting the former two clusters are more active for CO2 activation. In the adsorbate COOH, both C and O are binding with the Cu atoms. The binding distances d ( C u C ) and d ( C u O ) enlarge slightly with the decrease of electronegativity of the chalcogen; that is in line with the trend of charge transfer between cluster and adsorbed species. The charge redistributions before and after electrochemical CO2 adsorption are listed in Table S3. The NBO analysis revealed that the adsorption process is accompanied with partial charge transfer of about −0.5 from the Cu4X2 cluster (electron donor) to the COOH adsorbate (electron acceptor). Meanwhile, the transferred charge decreases from Cu4O2 to Cu4S2 (or Cu4Se2), resulting in the weakness of Cu-O and Cu-C bonding between COOH* and Cu4S2 (or Cu4Se2). In addition, the structures of COOH* on three different clusters are similar, in which O C O bends significantly compared with the linear CO2 molecule. Besides, both C-O bonds are elongated to ensure that COOH* retains sufficient activity to continue the subsequent hydrogenation reactions. Notice that the adsorption of COOH* does not change the main structure of doped clusters, which is important to maintain the stability of the Cu4X2 cluster in the CO2RR process.

2.1.2. Reaction Pathway of CO2RR on the Cu4X2 Cluster

In order to obtain a better understanding of the reaction mechanism of electrocatalytic CO2 reduction, the reaction networks for each elementary step were analyzed to identify the most thermodynamically favorable pathway and major side reactions of each doped cluster. The reaction schemes of all possible pathways for the reduction of CO2 to methanol or methane, as well as their competing reactions, are given in the Supplementary Materials. The lowest energy pathway of CO2RR to CH3OH and CH4 is shown in Figure 1, which helps us to explore the catalytic performance explicitly.
As shown in Figure 1, the free energy diagram of CO2RR pathways on the Cu4X2 clusters starts from the intermediate COOH*. The lowest energy pathway for CH3OH formation is identified (pathway 1, in blue), and the other pathway (pathway 2, in red) represents CO2RR towards CH4 formation. The electrochemical adsorption of CO2 on the Cu4O2, Cu4S2, and Cu4Se2 clusters are accompanied with a spontaneous exothermic process with Δ G of −0.24 eV, −0.65 eV, and −0.57 eV, respectively, which means the initial step can effectively adsorb COOH* (state 1). Subsequently, the hydroxyl group is hydrogenated on C to from HCOOH* accompanied by a Cu-C bond cleavage or a Cu-O bond cleavage caused by hydrogenation on O; these are both endothermic reactions, while the Δ G of the former is 0.58 eV, 0.50 eV, and 0.12 eV lower than the latter on the Cu4O2, Cu4S2, and Cu4Se2 clusters, respectively. Then, the intermediate HCOOH* (state 2) undergoes three degrees of hydrogenation to generate CHO* (state 3), CH2O* (state 4), and CH3O* (state 5). Finally, the adsorbate CH3O is hydrogenated at the oxygen atom to produce CH3OH. The rate-determining steps of pathway 1 on the Cu4O2 and Cu4S2 cluster are both the hydrogenation of COOH* to form HCOOH* (from 1→ 2), which is endergonic, and require potentials of −0.56 V and −0.48 V, respectively. However, the rate-determining step for the Cu4Se2 cluster is created concerning CHO* (from 2→ 3) via a (H+ + e) pair transfer from a solution with a larger potential of −0.82 V. It is obvious that the Cu4S2 cluster has the minimum rate limiting reaction energy in methanol formation among these clusters, indicating that it can be considered as a promising electrocatalyst for CH3OH formation during the CO2 reduction process.
In pathway 2 for methane formation, the COOH* undergoes a series of hydrogenations and takes the form of COOH*→HCOOH*→CHO*→CH2O*→CH3O*→CH4+O*→OH*→H2O. At this point, desorption of CH4 is the most difficult step in pathway 2 with limiting potentials of −0.56 V, −0.79 V, and −1.27 V for the Cu4O2, Cu4S2, and Cu4Se2 clusters, respectively. A free energy profile shows that there are partially overlapping intermediates between pathways 1 and 2, while the sixth step is the product-determining step for producing methanol or methane. The kinetic barrier diagram of the sixth step on the Cu4O2 cluster, the Cu4S2 cluster, and the Cu4Se2 cluster is shown in Figure S5. The corresponding results show that the energy barrier for CH3OH formation is 1.73 eV, 0.99 eV, and 1.49 eV lower than that of CH4 formation, respectively. Combined with the free energy diagram, the methanol production step is a spontaneous exothermic process, while the release of methane is endothermic, suggesting the methanol product is both thermodynamically and kinetically favored on the Cu4X2 clusters.

2.1.3. The Catalytic Performance on Cu4X2 Cluster

The activity of the CO2-to-CH3OH reaction is governed by the limiting potentials, which are −0.56 V, −0.48 V, and −0.82 V for the Cu4O2, Cu4S2, and Cu4Se2 clusters, respectively. The results indicated that both the Cu4O2 and Cu4S2 clusters exhibit excellent electrocatalytic activity for methanol synthesis. The presence of two heteroatoms can tune the electronic structure of the adjacent Cu atom, leading to partial charge transfer from Cu to chalcogen. Therefore, the oxidized C u + site can effectively promote CO2 activation, which is an important intermediate for triggering an electroreduction reaction. For the selectivity of the Cu4X2 cluster, the CH3OH formation step is a spontaneous exothermic process, while the branch of CH4 production requires an endothermic process to proceed, in which the intermediate CH3O* is considered as a bifurcation for these two pathways. Therefore, the Cu4X2 cluster exhibits high CO2 selectivity for CH3OH synthesis, instead of producing CH4 via CHO*→CH2O*→CH3O*→ CH4 on the Cu4X cluster [34]. In order to analyze the variation of product selectivity with dopant content, we then examine the bond length, bond energy, and adsorption energy of the adsorbate CH3O on Cu4X2 and Cu4X clusters. As shown in Table 2, the CH3O* binds to the cluster via an oxygen atom; product selectivity at this point depends on how easily the Cu-O or C-O bond can be cleaved. With the dopant content increasing, the bond energy of Cu-O becomes smaller and that of C-O becomes larger, which is consistent with the changes in bond length. The adsorption energy of CH3O* on the Cu4X2 cluster is smaller than that on the Cu4X cluster, which implies the subsequent reaction prefers the desorption of methanol on the Cu4X2 cluster. These calculations further confirmed that the production of CH3OH is more favorable than that of CH4 on the Cu4X2 cluster. In addition, the doping of four O, S, and Se atoms on the Cu4 cluster has also been tested as an electrocatalyst in CO2RR for comparison. The activity of the Cu4X4 cluster will not be explained in detail as it is not improved, and the discussion can be found in the Supplementary Material.

2.2. CO2RR Pathway on the Defective Graphene Supported Cu4S2 Cluster

2.2.1. Geometric Structure and Stability of the Catalyst Model

In view of above discussions, the Cu4S2 cluster is found to be an excellent catalyst due to its being more favorable for CH3OH production and having low limiting potential in CO2RR. Based on the clear understanding of the reduction mechanism of doped clusters, we are committed to investigating the defective graphene supported Cu4S2 cluster as a promising electrode material for CO2RR, so as to broaden its practical applications. The geometric structure and stability of the Cu4S2 cluster which is adsorbed on defective graphene in different orientations are first tested in the case of the fully relaxed system. Figure 2 shows the optimized structure and the charge distributions with the lowest-energy binding configuration (denoted as Cu4S2/SV). The removal of one carbon atom from the graphene sheet leads to the undercoordination of three C atoms around the vacancy, which exerts strong attraction for the Cu atom and allows the Cu4S2 cluster to be stably anchored to the defective graphene. From Figure 2a, the Cu atom at the bottom forms three covalent bonds with the adjacent C atoms on the defective graphene, and the average height of the cluster from the defective surface is 1.61 A ˚ . The electrons of the Cu4S2 cluster prefer to transfer to the substrate, resulting in the positive charges on the cluster with the value of 3.89 e. The density of states (in Figure S7) reveals the metallic behavior that makes the structure unique and have good conductivity, and the C and Cu form a new bond corresponding to the overlap of the C p and Cu d orbitals. Moreover, the binding energy of anchoring the Cu4S2 cluster at the single vacancy site of graphene (VC) is to be defined as:
E b = E V C + E cluster E total ,
where the Etotal, E V C , and Ecluster represent the total energy of the Cu4S2/SV system, the graphene with a single vacancy, and the Cu4S2 cluster, respectively. From the calculation result, the binding energy of the Cu4S2/SV system is +5.07 eV, indicating that the supported Cu4S2 cluster can be stably located on the defective graphene and continue the follow-up reactions.

2.2.2. Reaction Pathway of CO2RR on Cu4S2/SV

As the initial step of Cu4S2/SV in CO2RR, the first hydrogenation reaction involves a (H+ + e) pair transfer to CO2. There are two possible adsorbed species, COOH* or OCHO*, in competition with the H* for HER, as illustrated by Equations (1), (2), and (4), respectively.
H + + e + * H * .
In both cases of CO2 activation, the linear structure of the CO2 molecule transfers into a bent structure for further CO2RR. The calculated reaction free energy of the CO2 hydrogenation occurs on the O site to form intermediate COOH* (0.24 eV) and is found lower than that on C to form OCHO* (0.40 eV). To examine the selectivity of HER on CO2RR, as shown in Figure 3a, the reaction free energy for H* formation is 0.58 eV larger than that of COOH* formation. This means that the Cu4S2/SV catalyst displays higher CO2RR activity as well as lower HER activity. Thus, the CO2 reduction occurs predominantly before the HER process.
In this part, the reaction mechanism for electroreduction of CO2 to CH3OH, CH4, HCOOH, and CO was investigated, beginning with the intermediate COOH*. Among these, the formations of CO and HCOOH are accompanied by the two transfer steps of (H+ + e) pairs, and the reaction pathways are presented in Figure 3b and Figure 3c, respectively. For the Cu4S2/SV catalyst, the optimum pathway of CO production goes through the pathway CO2→COOH*→CO*→ CO. The rate-determining step is the hydrogenation of the hydroxyl group to generate the CO*, whose limiting potential is calculated to be −1.43 V. In the process of HCOOH generation, the last step of HCOOH desorption is the rate-determining step with a high free energy change of 1.15 eV. This is due to the stable adsorption of HCOOH* that hinders its desorption from the catalyst surface. The results clearly showed that these high limiting potentials exhibit poor selectivity for producing CO and HCOOH. In addition, the basic steps of all possible intermediates of CO2 hydrogenation to C1 products on the Cu4S2/SV catalyst and their corresponding reaction free energies are shown in Figure 3d. There are several thermodynamically feasible pathways for the reduction of CO2 to CH3OH and CH4, in which the lowest free energy diagrams are listed in Figure 4.
The blue line in Figure 4 shows the lowest energy reaction pathway for producing CH3OH accompanied by six (H+ + e) pair transfer processes. The first hydrogenation favors the formation of COOH* (state 1); the next step is to generate an adsorbed HCOOH* (2) through transfer of another (H+ + e) pair. Subsequently, HCOOH* is successively hydrogenated to produce CHO* (3) and CH2O* (4). Notably, the fifth step of the proton and electron transfer leads to generation of CH2OH* (5), where the free energy of the evolution of CH2OH* is 0.66 eV lower than the formation of CH3O*. Finally, the CH2OH* can be hydrogenated to form CH3OH (6). In the pathway of CH3OH formation, the rate-determining step is CHO*→CH2O* with a low limiting potential of −0.35 V. The great activity is caused by the strong interaction between Cu4S2 and defective graphene, which could further tune the electronic structure and stability of the supported cluster. The charge transfer from the cluster to the substrate indicates the Cu d orbitals become more vacant and available to be adsorbates. Another red line represents the pathway which takes eight (H+ + e) pairs of transfer steps to produce methane. In Figure 4, the pathway to generate methanol and methane diverges in the sixth step: one is a pair proton–electron transfer to the C end of CH2OH* and eventually produces methanol; the other is to form the H2O molecule first, and then the remaining CH2* undergoes continuous hydrogenations to produce methane at last. Obviously, the step of CH3OH formation is thermodynamically downhill, rather than the branch of CH4 formation requiring the endothermic sort for the next hydrogenation reaction. Hence, the Cu4S2/SV electrode material is more energetically preferable for CH3OH production compared with other C1 products in CO2 reduction. For the pathway of CH4 formation, the calculation shows that removing the OH* from the catalyst is the most endothermic step during the whole reaction process. In this case, the step of releasing H2O becomes the rate-determining step, of which the limiting potential is −0.51 V. Due to the limiting potential of CH3OH formation being lower than that of CH4 formation, the former may be preferred from a thermodynamic point of view.
Based on the above discussions, the calculation results indicate that the Cu4S2/SV catalyst is not only more favorable for generating CH3OH but also can effectively suppress the competing reactions, such as HER, CO, and HCOOH production. In addition, recent experiments [35,36,37] have shown that the supported Cu-based electrode as a electrocatalyst for CO2RR has higher CH3OH selectivity, suggesting that the free energy changes for generating CH3OH are smaller than those of other products. This is consistent with our calculation.

3. Computational Details

Density functional theory (DFT) [38] calculations were used to investigate the reaction mechanism of isolated Cu4Xn clusters in CO2 reduction. The first section in this study is to search for local or even global minima of molecular clusters using ABCluster software [39] which adopts an artificial bee colony algorithm to conduct the global optimization and conformation search. Full details about the global minima nanocluster searching process are available in the Supplementary Material. After that, the subsequent geometry optimizations and vibration frequencies were implemented at the level of B3LYP/6–31g(d, p) [40,41] by the Gaussian16 program [42]. Next, the various active sites for electrochemical CO2 adsorption and hydrogenation reactions on the doped clusters were tested. Following that, the electronic energies were refined with the single-point energy calculation employing the high-level DLPNO-CCSD(T) method [43], along with the cc-pVTZ basis set [44] using the ORCA software [45]. The Gibbs free energies were then obtained through electronic energies at the DLPNO-CCSD(T)/cc-pVTZ level of theory corrected with the zero-point energies (ZPEs) computed by the B3LYP/6–31g(d, p) method. Besides, the conductor-like polarizable continuum model (CPCM) [46] with toluene as the solvent was used in this study. Finally, the reasonable intermediates were sieved using the calculation mentioned above, after that we could obtain the most feasible pathway for CO2 reduction for different products on the doped clusters.
The calculations about the defective graphene supported doped cluster were conducted using the Vienna ab initio simulation package (VASP, version 5.3.2) [47], which is based on the DFT with the projector-augmented wave method (PAW) [48]. The PBE exchange-correlation functional [49] and van der Waals (vdW) interactions described via a pair-wise force field by the DFT-D2 method of Grimme [50] were adopted for all the defective graphene-supported system calculations. In this work, the model structure comprises 5 × 5 single-layer graphene unit cells with a single vacancy as the substrate, and the doped cluster was placed above the vacancy site. The vacuum region was set as 15 A ˚ for preventing the mirror images effect. The MonKhorst–Pack mesh k-points 4 × 4 × 1 was used for calculation, and a plane-wave energy cutoff is used of 520 eV after convergence test (see Figure S8). All the atoms were allowed to relax during the model optimization process. The total energy converged to 10-7 eV and the maximum ionic force was less than 0·01 eV/ A ˚ . In addition, VASPsol [51] was used to describe the effect of electrostatics, cavitation, and dispersion on interactions between solutes and solvents. The VASPsol model considering the solvent molecule as the continuum solvent, and the dielectric constant were used to represent the solvent effect. Here, the dielectric constant of toluene ϵ  = 2.37 was used to simulate the implicit solvent environment.
The computational hydrogen electrode (CHE) model was described by Nørskov et al. in 2004 [52], and is combined with energetic from DFT simulations to calculate the free energy changes Δ G for various basic steps of CO 2 reduction. In the CHE model, the chemical potential of a proton–electron pair is defined as half of the gaseous H 2 at equilibrium, under any pH values and temperatures, the reaction
H + + e 1 / 2 H 2 ,
is equilibrated at 0 V, 1325 Pa reversible hydrogen electrode (RHE). The free energy for a basic electrochemical reduction step is defined as
A * + H + + e A H * ,
Here, “*” denotes an active site on the catalyst. Then the potential-dependent free energy change is thus defined as
Δ G = μ ( A H * ) μ ( A * ) 1 / 2 μ ( H 2 ) e U .
in which μ is the chemical potential, e is the elementary positive charge and U is the electrode potential versus RHE. The chemical potential is shifted by e U when an external potential U is applied. While at zero applied potential, becomes −U L /e, in which U L means the limiting potential in the CO 2 RR process.

4. Conclusions

To sum up, the reaction mechanism of CO2 electroreduction to C1 products on a defective graphene-supported Cu4S2 cluster and isolated Cu4Xn clusters was investigated. DFT calculations indicated the CH3OH is the most feasible product among the C1 products on Cu4X2 clusters, and the limiting potentials for producing CH3OH are in the order of Cu4S2 < Cu4O2 < Cu4Se2. The Cu4S2 cluster has excellent selectivity and the best catalytic activity (−0.48 V) during the conversion of CO2 to CH3OH among these isolated clusters. For the Cu4S2/SV catalyst, defect-engineered graphene could induce a strong interaction between cluster and substrate, which facilitates the improved catalytic performance through adjusting the electronic structure and stability of the Cu4S2 cluster. The Cu4S2/SV catalyst not only shows superior activity to produce CH3OH with a low potential of −0.35 V, but can also significantly suppress other competing reactions, such as HER, CO and HCOOH production. We hope the combination of modification effect and defective support engineering can provide a valuable strategy for the Cu-based catalyst design with highly electrocatalytic performance in CO2 reduction.
References [53,54,55,56,57] are cited in the Supplementary Materials.

Supplementary Materials

The following supporting information can be downloaded at:, Figure S1: The ground minimal structures and low-lying energy isomers of the gas-phase Cu4X2 clusters. Figure S2: Global minimum geometry composition and some selected bond lengths of Cu4X2 clusters and Cu4X4 clusters; Figure S3: Mechanistic free energies diagram of electrochemical CO2 reduction on Cu4O2 cluster, Cu4S2 cluster, and Cu4Se2 cluster with no applied potential; Figure S4: Free energies diagram for producing H2, CO, and HCOOH with no applied potential; Figure S5: Kinetic barrier diagram of product-determining step on Cu4O2 cluster, Cu4S2 cluster, and Cu4Se2 cluster; Figure S6: Mechanistic free energies diagram of electrochemical CO2 reduction on the Cu4O4 cluster, Cu4S4 cluster, and Cu4Se4 cluster with no applied potential; Figure S7: Total density of states (DOS) of Cu4S2/SV catalyst, Projected density of states (PDOS) of p orbitals of C, and PDOS of d orbitals of Cu; Figure S8: Variation the reaction free energy of COOH* on Cu4S2/SV catalyst as a function of the cutoff energy value in the plane-wave calculations; Table S1: Geometric parameters , the maximum, and minimum harmonic vibrational frequencies of the GM structure of gas-phase Cu4X2 clusters; Table S2: The charge distribution of elements in the neutral Cu4X, Cu4X2, and Cu4X4 clusters by the natural bond orbital charge analysis; Table S3: The charge distribution of elements in the neutral Cu4X, Cu4X2, and Cu4X4 clusters with electrochemical CO2 adsorption by the natural bond orbital charge analysis.

Author Contributions

Data curation, Q.Z.; Investigation, Q.Z., Y.L. and H.Z.; Writing—original draft, Q.Z.; Writing—review and editing, Q.Z., H.Z. and B.S. All authors have read and agreed to the published version of the manuscript.


This research was funded by the National Natural Science Foundation of China (21803041, 51572219, and 21873077), the Natural Science Foundation of Shaanxi Province of China (No.2018JM1010 and 2019JM-592), the Graduate’s Innovation Fund of the Northwest University of China (No. YJG15007) and the Double First-class University Construction project of Northwest University.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study and not reported in the Supplementary Materials are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. The lowest free energy diagram of CO2RR to CH3OH and CH4 with no applied potential on Cu4O2 (a), Cu4S2 (b), and Cu4Se2 (c) clusters. (The blue line represents the methanol formation pathway, with the intermediate products shown in the upper part of the figure. The red line represents the methane formation pathway, with the intermediate products shown in the lower part of the figure).
Figure 1. The lowest free energy diagram of CO2RR to CH3OH and CH4 with no applied potential on Cu4O2 (a), Cu4S2 (b), and Cu4Se2 (c) clusters. (The blue line represents the methanol formation pathway, with the intermediate products shown in the upper part of the figure. The red line represents the methane formation pathway, with the intermediate products shown in the lower part of the figure).
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Figure 2. The optimized structure (a) and charge density difference plot (b) for the Cu4S2/SV catalyst. The yellow and blue color regions mean the charge accumulation and depletion, respectively.
Figure 2. The optimized structure (a) and charge density difference plot (b) for the Cu4S2/SV catalyst. The yellow and blue color regions mean the charge accumulation and depletion, respectively.
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Figure 3. Reaction pathways to produce H2 (a), CO (b), and HCOOH (c) on the Cu4S2/SV catalyst with no applied potential. The potential required to carry out over the most endergonic step is listed in the legend. The mechanistic free energy diagram of CO2RR on the Cu4S2/SV catalyst with no applied potential (d). The colorful solid lines label thermodynamically feasible reaction pathways, in which each step involves a (H+ + e) pair transfer. The step of CO or HCOOH desorption (in dashed line) is a thermochemical process that does not involve (H+ + e) pair transfer.
Figure 3. Reaction pathways to produce H2 (a), CO (b), and HCOOH (c) on the Cu4S2/SV catalyst with no applied potential. The potential required to carry out over the most endergonic step is listed in the legend. The mechanistic free energy diagram of CO2RR on the Cu4S2/SV catalyst with no applied potential (d). The colorful solid lines label thermodynamically feasible reaction pathways, in which each step involves a (H+ + e) pair transfer. The step of CO or HCOOH desorption (in dashed line) is a thermochemical process that does not involve (H+ + e) pair transfer.
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Figure 4. Reaction pathways for producing CH3OH and CH4 on the Cu4S2/SV catalyst with no applied potential. (The blue line represents the methanol formation pathway which the intermediate products show in the upper part of the figure. The red line represents the methane formation pathway which the intermediate products show in the lower part of the figure).
Figure 4. Reaction pathways for producing CH3OH and CH4 on the Cu4S2/SV catalyst with no applied potential. (The blue line represents the methanol formation pathway which the intermediate products show in the upper part of the figure. The red line represents the methane formation pathway which the intermediate products show in the lower part of the figure).
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Table 1. The GM of the Cu4X2 cluster and structural details of electrochemical CO2 adsorption on the Cu4X2 cluster.
Table 1. The GM of the Cu4X2 cluster and structural details of electrochemical CO2 adsorption on the Cu4X2 cluster.
Cluster Electrochemical Adsorption of CO2
COOH* E r e a c t δ+Geometric
Cu 4 O 2 Catalysts 12 00454 i001 Catalysts 12 00454 i002−0.240.55 d ( Cu 3 C ) d ( Cu 4 O )
d ( C O 1 ) d ( C O 2 )
d ( O 1 H ) O C O
Cu 4 S 2 Catalysts 12 00454 i003 Catalysts 12 00454 i004−0.650.52 d ( Cu 3 C ) d ( Cu 4 O )
d ( C O 1 ) d ( C O 2 )
d ( O 1 H ) O C O
Cu 4 Se 2 Catalysts 12 00454 i005 Catalysts 12 00454 i006−0.570.52 d ( Cu 3 C ) d ( Cu 4 O )
d ( C O 1 ) d ( C O 2 )
d ( O 1 H ) O C O
The red, yellow, blue, orange, gray, and white spheres denote O, S, Se, Cu, C, and H atoms, respectively. The unit for E r e a c t is eV, d is A ˚ , and O C O is .
Table 2. The structural details and adsorption energy of intermediate CH3O* on Cu4X and Cu4X2 (X=O, S, Se) cluster.
Table 2. The structural details and adsorption energy of intermediate CH3O* on Cu4X and Cu4X2 (X=O, S, Se) cluster.
ClusterCH3O*Bond LengthBond EnergyAdsorption
d ( Cu O ) d ( C O ) E ( Cu O ) E ( C O )
Cu 4 O Catalysts 12 00454 i0071.831.3853.9395.46−1.59
Cu 4 O 2 Catalysts 12 00454 i0081.851.3748.04101.90−0.57
Cu 4 S Catalysts 12 00454 i0091.891.4155.3578.30−1.53
Cu 4 S 2 Catalysts 12 00454 i0101.841.3741.7196.76−0.33
Cu 4 Se Catalysts 12 00454 i0111.891.4153.9877.23−2.01
Cu 4 Se 2 Catalysts 12 00454 i0121.871.4149.4498.31−0.65
The red, yellow, blue, orange, gray, and white spheres denote O, S, Se, Cu, C, and H atoms, respectively. The unit for bond length, bond energy, and adsorption energy is A ˚ , KJ/mol, and eV, respectively.
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Zhang, Q.; Li, Y.; Zhu, H.; Suo, B. High-Performance of Electrocatalytic CO2 Reduction on Defective Graphene-Supported Cu4S2 Cluster. Catalysts 2022, 12, 454.

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Zhang Q, Li Y, Zhu H, Suo B. High-Performance of Electrocatalytic CO2 Reduction on Defective Graphene-Supported Cu4S2 Cluster. Catalysts. 2022; 12(5):454.

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Zhang, Qiyan, Yawei Li, Haiyan Zhu, and Bingbing Suo. 2022. "High-Performance of Electrocatalytic CO2 Reduction on Defective Graphene-Supported Cu4S2 Cluster" Catalysts 12, no. 5: 454.

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