*Article* **CO<sup>2</sup> and CH<sup>2</sup> Adsorption on Copper-Decorated Graphene: Predictions from First Principle Calculations**

**Oleg Lisovski , Sergei Piskunov , Dmitry Bocharov \* , Yuri F. Zhukovskii † , Janis Kleperis , Ainars Knoks and Peteris Lesnicenoks**

> Institute of Solid State Physics, University of Latvia, Kengaraga Street 8, LV-1063 Riga, Latvia; Olegs.Lisovskis@cfi.lu.lv (O.L.); piskunov@cfi.lu.lv (S.P.); janis.kleperis@cfi.lu.lv (J.K.); ainars.knoks@cfi.lu.lv (A.K.); Peteris.Lesnicenoks@cfi.lu.lv (P.L.)

**\*** Correspondence: bocharov@cfi.lu.lv

† Deceased.

**Abstract:** Single-layer graphene decorated with monodisperse copper nanoparticles can support the size and mass-dependent catalysis of the selective electrochemical reduction of CO<sup>2</sup> to ethylene (C2H<sup>4</sup> ). In this study, various active adsorption sites of nanostructured Cu-decorated graphene have been calculated by using density functional theory to provide insight into its catalytic activity toward carbon dioxide electroreduction. Based on the results of our calculations, an enhanced adsorption of the CO<sup>2</sup> molecule and CH<sup>2</sup> counterpart placed atop of Cu-decorated graphene compared to adsorption at pristine Cu metal surfaces was predicted. This approach explains experimental observations for carbon-based catalysts that were found to be promising for the two-electron reduction reaction of CO<sup>2</sup> to CO and, further, to ethylene. Active adsorption sites that lead to a better catalytic activity of Cu-decorated graphene, with respect to general copper catalysts, were identified. The atomic configuration of the most selective CO<sup>2</sup> toward the reduction reaction nanostructured catalyst is suggested.

**Keywords:** graphene; nanodecoration; first-principles calculations; adsorption; CO<sup>2</sup> electroreduction

### **1. Introduction**

The electroreduction of CO<sup>2</sup> from exhausts to hydrocarbons can provide a sustainable supply of valuable raw materials for the chemical industry and fuels for transport and energetics [1]. The reduction of captured excessive carbon dioxide from the atmosphere could lead to a decrease in the greenhouse effect. CO<sup>2</sup> can be reduced to hydrocarbons—in particular, ethylene and methane (CH4)—by electrochemical reactions 2CO<sup>2</sup> + 12*e* − + 8H2O → C2H<sup>4</sup> + 12OH<sup>−</sup> and CO<sup>2</sup> + 8*e* <sup>−</sup> + 6H2O → CH<sup>4</sup> + 8OH−, respectively. Ethylene has a wide range of applications in industry, polymer production, and agriculture. One of the most promising catalysts that can electroreduce CO<sup>2</sup> to C2H<sup>4</sup> is copper metal [2,3]. However, along with ethylene (C2H4), many other carbon side-products are formed, including methane (CH4), carbon monoxide (CO), and formate anion (HCOO−) [4–7]. Besides, copper catalysts are very susceptible to poisoning and deactivation, usually, within half an hour after the start of the reduction process of carbon dioxide [8,9]. For the aforementioned reasons, significant efforts have recently been made to develop catalysts that can selectively reduce CO<sup>2</sup> to ethylene over long-lasting time periods. [7,10,11]. Polycrystalline Cu surfaces do not show a significant preference towards ethylene formation, with a C2H4/CH<sup>4</sup> product ratio of around 1:2 [3–5,12,13]. Their insufficient selectivity is considered to be due to the large heterogeneity of the centers of different catalytic activities on the polycrystalline surface. This is confirmed by the study of the influence of different copper planes on the selectivity of the electroreduction of carbon dioxide [7,14]. It was found that the (100) surface of single crystals of Cu favors the formation of ethylene more than Cu (111), as indicated by their ratios C2H4/CH<sup>4</sup> 1.3 and 0.2, respectively [7]. Interestingly, when the high index Cu (711), Cu (911), and Cu (810) planes formed by cleaving Cu (100) were

**Citation:** Lisovski, O.; Bocharov, D.; Piskunov, S.; Zhukovskii, Y.F.; Kleperis, J.; Knoks, A.; Lesnicenoks, P. CO<sup>2</sup> and CH<sup>2</sup> Adsorption on Copper-Decorated Graphene: Predictions from First Principle Calculations. *Crystals* **2022**, *12*, 194. https://doi.org/10.3390/ cryst12020194

Academic Editors: Walid M. Daoush, Fawad Inam, Mostafa Ghasemi Baboli and Maha M. Khayyat

Received: 12 November 2021 Accepted: 25 January 2022 Published: 28 January 2022

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examined, an even higher selectivity was displayed toward C2H4, with the C2H4/CH<sup>4</sup> ratio increasing to 10 for Cu (711). The reason for the catalyst's selectivity toward certain hydrocarbons is the increased number of surface steps in the high index facets or periodic formation of Cu terraces. This means that the system that is modified in such a way may exhibit an increased efficiency.

It was shown that copper nanoparticles with a large surface area have good selectivity for the formation of hydrocarbons, especially of ethylene [6]. It has been suggested that the edges and numerous steps formed on the surface of copper nanoparticles may be of decisive importance for the selective formation of ethylene. In favor of this, quantum chemical modeling has shown that intermediate reaction products, such as ∗CHO, are more stable at the steps of the Cu (211) surface than at the Cu (100) terraces. (Hereafter, an asterisk indicates that a species is adsorbed on a surface). This can lead to an increase in their concentration, and, ultimately dimerization to C2H<sup>4</sup> [15].

Composites and hybrid structures, as well as nanoobjects based on graphene, has attracted huge attention in experimental and theoretical studies during the last decade [16–22] after this material was discovered in 2004 by Novoselov and Geim [23]. The decoration of graphene with metals (e.g., Fe [24], Pt [25,26], Pd [27]), as well as organic (e.g., tetracyanoethylene [28]) and inorganic compounds (e.g., Bi2O<sup>3</sup> [29]), could improve electrocatalytic adsorption and gas sensing properties toward different gases

Different graphene-based catalysts for direct electrochemical CO<sup>2</sup> reduction were reported in the literature, e.g., atomic Fe dispersed on nitrogen-doped graphene [30], Bdoped graphene [31], N-doped graphene [32], defective graphene produced by a nitrogen removal procedure from N-doped graphene [33], Ni-decorated graphene [34], Co3O<sup>4</sup> spinel nanocubes on N-doped graphene [35], etc. The review of graphene-based materials for electrochemical CO<sup>2</sup> reduction was published by Ma et al. recently [36]. Several recent studies show that the modification of the graphene surface by copper nanoparticles or by creating Cu-contained heterostructures is an interesting approach in the development of efficient electrocatalysts [37–51] .

These preceding studies have led us to elaborate on a theoretical model for a stable C2H4-selective electrocatalyst based on copper-nanocluster-decorated graphene and to understand how this selectivity can be increased. Carbon-based materials are potentially interesting catalysts for the CO<sup>2</sup> reduction reaction due to their low cost and especially due to their ability to form a wide range of hybrid nanostructures [52–57]. Carbon-based catalysts are chemically inactive at negative bias potentials and provide high overpotentials for the hydrogen evolution reaction compared to metal surfaces [58]. Pristine graphene does not exhibit any catalytic activity. However, by introducing dopants [59–61] and defects [62] during the synthesis, the electronic structure and catalytic properties of nanostructured carbon materials [62] are tailored. In particular, N-doping has been shown to significantly enhance the CO<sup>2</sup> reduction activity [39,41,61,63–66].

Experimental results obtained recently [67] suggest that the reaction pathways of the CH<sup>4</sup> and C2H<sup>4</sup> formation are separated at an early stage of CO reduction. Results from a recent experimental study of CO electroreduction on single-crystal copper electrodes [68] imply that there are two separate pathways for C2H<sup>4</sup> formation: one (i) that shares an intermediate with the pathway to CH4, and a second one (ii) that occurs mainly on Cu (100) and probably involves the formation of a CO dimer as the key intermediate [69]. Considering the pathway (i), it is obvious that the ∗CH<sup>2</sup> dimerization is a crucial step for the final C2H<sup>4</sup> production (the so-called "carbene" mechanism). ∗CH<sup>2</sup> can be produced by the protonation and deoxygenation of ∗CO [5]. ∗CH<sup>2</sup> can be also obtained from subsequent reductions of <sup>∗</sup>HCO, <sup>∗</sup>C, and <sup>∗</sup>CH. The further reduction of a single <sup>∗</sup>CH<sup>2</sup> gives rise to ∗CH<sup>3</sup> and finally to CH4.

In this study, the adsorption of CO<sup>2</sup> is considered to typically be the rate-determining step in the CO<sup>2</sup> reduction reaction, and thus it is desirable to find/design catalyst sites that bond CO<sup>2</sup> strongly—preferably stronger than H adsorption [70]. To shed light on the trends in the catalytic activity of the Cu-decorated pristine and N-doped graphene system, in this work, systematic density functional theory (DFT) calculations of the adsorption of CO<sup>2</sup> and intermediates on Cu-decorated graphene are performed. The first principle calculations is performed for the monodisperse Cu<sup>7</sup> nanocluster deposited at the 5 × 5 supercell of graphene to predict the electronic properties of the Cu<sup>7</sup> facet in light of its different affinities for ∗CO<sup>2</sup> and ∗CH2, and thus to provide deeper insights into its intrinsic activities for CO<sup>2</sup> electroreduction. The reaction energies for the formation of intermediates on Cu7/graphenenanostructured surfaces have been calculated using the hybrid DFT approach. In general, this work may not only give a deep insight into the reaction mechanisms toward C2H<sup>4</sup> formation on Cu-decorated carbon nanomaterials, but may also provide guidelines for designing Cu-based catalysts to effectively produce multicarbon compounds.

### **2. Computational Details**

Modeling was carried out at the DFT level of theory. This approach is based on the linear combination of atomic orbitals (LCAO) method with atom-centered localized Gaussian-type functions (GTFs) forming the basis sets (BS). Fully relaxed Cu7/graphene nanostructures were calculated using hybrid exchange-correlation functional HSE06 according to the prescription given in Refs. [71,72]. Its particular feature is the use of an error-function-screened Coulomb potential for calculating the exchange energy. This functional was chosen to reproduce the basic atomic and electronic properties of both graphene and the most stable Cu (111) qualitatively close to those experimentally observed. The calculations were executed with CRYSTAL17 computational code [73], which was developed for the atomistic modeling of solid state chemistry. Using such a computation strategy, the geometries have been optimized with various species adsorbed on the graphene and metal Cu catalyst, and the adsorption energies of various species that are considered in this study have been calculated for nitrogen, oxygen, the CO<sup>2</sup> molecule, and the CH<sup>2</sup> radical. Besides the graphene and copper catalyst, basis sets are required for atoms of adsorbed species. For all atoms in the studied materials, full electron valence BSs [73] were used. For Cu, C, O, and H atoms, the triple-zeta BSs were obtained from Ref. [74]; on the other side, for the N atom, the basis set in the form of 6s-31sp-1d was obtained from Ref. [75].

To evaluate the Coulomb and exchange series appearing in the SCF equations for periodic systems, five tolerances were controlled: 10−<sup>8</sup> , 10−<sup>8</sup> , 10−<sup>8</sup> , 10−<sup>8</sup> , 10−<sup>16</sup> (related to estimates of overlap or penetration for integrals of Gaussian functions on different centers, which define cut-off limits for series summation). To provide the correct summation in both direct and reciprocal lattices, the reciprocal space was integrated by sampling the interface Brillouin zone (BZ) with the 8 × 8 × 1 Monkhorst–Pack meshes [76] for slab calculations, which gives, in total, 34 k-points evenly distributed in the BZ. The calculations are considered to be convergent if the total energy differs by 10−<sup>7</sup> a.u. or less in two successive cycles of the self-consistent-field (SCF) procedure [73].

The adsorption energy *Eads* was calculated with the following equation:

$$E\_{\rm ads} = E\_{\rm ads/sub} - E\_{\rm molecule} - E\_{\rm sub} \tag{1}$$

where *Eads*/*sub* and *Esub* are the total energy of the Cu7/graphene nanostructure with the adsorbed CO2, molecule or <sup>∗</sup>CH<sup>2</sup> intermediate, and Cu7/graphene nanostructure slab, respectively, and *Emolecule* is the total energy of the isolated CO<sup>2</sup> molecule or <sup>∗</sup>CH<sup>2</sup> intermediate, analogously to Ref. [77]. The energetically favorable adsorption (chemisorption) takes place if the adsorption energy *Eads* is negative [78].

### **3. Results and Discussion**

### *3.1. Cu/Graphene Cluster*

Within the framework of this study, an efficient and reliable model of the monodisperse Cu<sup>7</sup> cluster deposited on single-layered graphene is constructed. The model consists of a 5 × 5 graphene supercell periodically repeated in the *xy* plane, with seven Cu atoms forming a nanodot deposited in every supercell. Such a model is a balanced solution for the efficient use of computer resources and reliable prediction of the electronic structure and energetics of the nanostructures under study. Figure 1 shows schematic views (aside and atop) for the fully optimized two-dimensional Cu7/graphene nanostructure containing the faceted Cu nanodot. For this cluster, a complete relaxation of the atomic coordinates was carried out and the binding energy of Cu atoms was estimated for this model.

**Figure 1.** Top (**a**) and aside (**b**) views of equilibrium structure of six-faceted Cu nanopyramid deposited on graphene monolayer. Grey balls stand for carbon atoms and orange for copper.

The Cu<sup>7</sup> cluster is quite strongly physisorbed to the graphene layer with the binding energy of −1.54 eV/Cu atom. The negative binding energy means that energy is released after the substrate–adsorbate coupling. Single Cu atoms tend to adsorb at the hollow sites of graphene with the binding energy of −2.65 eV/Cu atom. Thus, Cu atoms deposited at graphene could reproduce the facets of the most stable Cu (111) surface. Nevertheless, a single Cu atom deposited at graphene forms quite weak Cu-C graphene bonds, with a bond population of 80 milli electrons.

The strongest bonding between Cu and graphene takes place at the defective graphene layer containing a carbon vacancy (Figure 2). The binding energy of the Cu-C*vacancy* complex is approximately −6.63 eV/Cu atom. However, the energy of vacancy formation is quite high (17.5 eV) and such a mechanism of Cu cluster adsorption at graphene is energetically unfavorable.

**Figure 2.** Equilibrium structure of C*graphene* atom substituted for Cu with the binding energy of −3.59 eV/Cu atom. Grey balls stand for carbon atoms and orange for copper.

Since the N-doping has been shown to significantly enhance the CO<sup>2</sup> reduction activity of graphene [39,41,61,63–66], the six-faceted Cu nanopyramid deposited atop the N-saturated graphene monolayer (Figure 3) is considered as well. The presence of the nitrogen atoms at the graphene support allows for the strong chemisorption of the Cu atom with the bond population of Cu–N = 303 milli electrons and N–C*graphene* = 344 milli electrons. The presence of a nitrogen monolayer may lead to a stronger adsorption of the Cu nanocluster at graphene; however, the presence of N practically does not influence CO<sup>2</sup> adsorption at Cu7/graphene. Therefore, an N layer atop graphene is not considered in the further modeling of CO<sup>2</sup> reduction.

**Figure 3.** Schematic representation of top (**a**) and aside (**b**) views of six-faceted Cu nanopyramid deposited on N-saturated graphene monolayer. Grey balls stand for carbon atoms, orange for copper, red balls are oxygen atoms, and blue ones are nitrogen atoms.

Due to the relatively large distance between carbon layers in double-layered graphene (∼6.94 Å), the layer-to-layer interaction is negligible and does not influence the Cu nanocluster adhesion to the graphene layer. Therefore, in further modeling, it is assumed that the Cu cluster deposited at single-layered graphene can mimic the Cu cluster deposited at double-layered graphene.

Therefore, the constructed model of the six-faceted Cu nanopyramid deposited on the graphene monolayer (Figure 1) is considered as the most appropriate for large-scale ab initio total energy calculations of CO<sup>2</sup> and CH<sup>2</sup> molecules atop periodic Cu7/graphene nanostructures (an electrically neutral system) using state-of-the-art total energy codes to estimate the energetics of a chain of elemental reactions under the influence of the copper nanocatalyst and graphene support.

### *3.2. CO*<sup>2</sup> *Adsorption*

Taking into account that the adsorption of CO<sup>2</sup> is typically assumed to be the ratedetermining step in CO<sup>2</sup> reduction, we pay major attention to the free energies of CO<sup>2</sup> adsorption at the Cu7/graphene nanostructure, and, for comparative reasons, we have modeled CO<sup>2</sup> adsorption on its constituents, the most stable Cu (111) surface, represented by a three-layer and six-layer slab and pristine graphene (Figure 4). For the slabs, we considered the non-symmetrical one-sided and symmetrical two-sided deposition of absorbed CO<sup>2</sup> molecules. The adsorption energies for the CO<sup>2</sup> molecule and ∗CH<sup>2</sup> intermediate for the Cu7/graphene nanostructure, the Cu (111) surface, represented by the three-layer and six-layer slab and pristine graphene, are given in Table 1.

**Table 1.** Calculated adsorption energies (eV) of CO<sup>2</sup> molecule and ∗CH<sup>2</sup> intermediate on Cu7/graphene nanostructure, Cu (111) surface, represented as three-layer and six-layer slab, and pristine graphene layer with 5 × 5 supercell.


**Figure 4.** Schematic representation of the most energetically favorable adsorption positions of CO<sup>2</sup> molecule on (**a**) Cu7/graphene nanostructure, (**b**) Cu (111) surface, and (**c**) pristine graphene monolayer. Grey balls stand for carbon atoms, orange for copper, and red balls are oxygen.

For all materials under consideration, the most energetically favourable adsorption site for the CO<sup>2</sup> molecule is the bridge position. Only the weak physisorption of CO<sup>2</sup> on pristine graphene is predicted from our calculation, with a relatively small free adsorption energy of −0.43 eV, which is in agreement with trends reported in Ref. [28]. The free adsorption energy calculated for the Cu (111) surface is in the range between −6.69 and −6.99 eV depending on the slab thickness and one-sided or two-sided adsorption of CO<sup>2</sup> molecules, whereas the adsorption energy of −6.04 eV per CO<sup>2</sup> molecule is predicted for the Cu7/graphene nanostructure. A lower number points to a stronger chemical binding. The stronger binding of CO<sup>2</sup> to the Cu<sup>7</sup> nanocluster at graphene (similar to the adsorption at the pristine Cu (111) surface) can be explained by the presence of <111> grain boundaries of the Cu<sup>7</sup> nanocluster, which are known to be chemically more reactive. Figure 5a shows the projected density of states (PDOS) calculated for the CO<sup>2</sup> molecule adsorbed at the Cu (111) surface. The strong adsorption of the CO<sup>2</sup> molecule can be explained by Cu 3*d*–O 2*p* orbitals hybridization seen in Figure 5a by the peaks at approximately −4 eV. The Cu–O bond population calculated by Mulliken population analysis is equal to 434 milli electrons. Both O atoms of the CO<sup>2</sup> molecule are strongly bonded to the Cu atoms of the Cu (111) surface. The only weak physisorption of CO<sup>2</sup> is predicted at graphene (PDOS in Figure 5b), with a Cgraphene–CCO<sup>2</sup> bond population of 0.012 milli electrons Our prediction is in agreement with the recent experimental observations. According to the data available in the literature, to improve the selectivity of CO<sup>2</sup> electrochemical reduction in producing C<sup>2</sup> products, Kanan et al. synthesized Cu nanoparticles containing grain boundaries and observed a substantial enhancement in the Faradaic efficiency of generating multi-carbon hydrocarbons [79]. This enhancement is correlated with the density of the grain boundary areas [80]. Cheng et al. conducted the atomistic modeling for the chemical vapor deposition process of Cu nanoparticles and found that strong CO binding with under-coordinated surface square sites could promote C–C coupling ("carbene" mechanism) [81]. According to our predictions, the boundary between the Cu<sup>7</sup> cluster and graphene can demonstrate the best catalytic ability for the C2H<sup>4</sup> formation. This is due to the adsorption properties of neighboring Cu sites that are significantly perturbed by the presence of the nearest C, and the stronger Cu–O bonding is formed on the catalyst surface, which can also enhance H2C=CH<sup>2</sup> evolution [14].

**Figure 5.** Projected density of states (PDOS) calculated for (**a**) CO<sup>2</sup> adsorbed at Cu (111) surface, (**b**) CO<sup>2</sup> adsorbed at graphene, (**c**) CH<sup>2</sup> adsorbed at Cu (111) surface, and (**d**) CH<sup>2</sup> adsorbed at graphene. PDOS onto all orbitals of H, C, and O atoms are magnified 10 times.

### *3.3. CH*<sup>2</sup> *Adsorption*

Results from a recent experimental study of CO electroreduction on single-crystal copper electrodes [5] further implied that one of the most probable pathways for C2H<sup>4</sup> formation is one that shares an intermediate with the pathway to CH4. Considering that pathway, it is reasonable that the <sup>∗</sup>CH<sup>2</sup> dimerization is a crucial step for the final C2H<sup>4</sup> production ("carbene" mechanism). The further reduction of single <sup>∗</sup>CH<sup>2</sup> gives rise to <sup>∗</sup>CH<sup>3</sup> and finally to CH4. Therefore, in this study, the adsorption energy of <sup>∗</sup>CH<sup>2</sup> on Cu7/graphene, pristine Cu (111), and pristine graphene (Figure 6) is calculated. For both pristine Cu (111) and Cu7/graphene nanostructures, the most energetically favorable adsorption site of ∗CH<sup>2</sup> adsorbate is the hollow position between neighboring copper atoms, whereas the bridge position between neighboring C–C atoms is the most energetically preferable for the <sup>∗</sup>CH<sup>2</sup> adsorption on pristine graphene. Figures 5c,d show the PDOS calculated for the CH<sup>2</sup> component adsorbed on the Cu (111) surface and graphene, respectively. CH<sup>2</sup> relatively strongly adsorbed at Cu (111) with hybrydized Cu 3*d*–C 2*p* orbitals, forming square planar *sp*2*<sup>d</sup>* hybridisation (Figure 5c, peaks at approximately <sup>−</sup>4 eV) and a Cu–C bond population of 390 milli electrons, whereas the Cgraphene–CCH<sup>2</sup> bond population of 0.240 milli electrons is calculated for CH<sup>2</sup> at graphene.

Only a weak physisorption of ∗CH<sup>2</sup> on pristine graphene is predicted from our calculation, with a relatively small adsorption energy of −3.12 eV (PDOS in Figure 5d), which is in qualitative agreement with the observation reported in Ref. [28]. This may consequently lead to the relatively small barrier of CH2–CH<sup>2</sup> dimerization. The adsorption energy calculated for the Cu (111) surface is in the range between −6.38 and −6.53 eV for the different thicknesses of slabs and the symmetrical/non-symmetrical deposition of <sup>∗</sup>CH<sup>2</sup> intermediates, whereas a free adsorption energy of −7.31 eV is predicted for the Cu7/graphene nanostructure (Table 1). From the calculated adsorption energies, we predict that the most energetically preferable CH<sup>2</sup> dimerization can take place on pristine graphene, (a) (b) (c)

whereas only a small difference in CH<sup>2</sup> dimerization can be predicted for the Cu (111) and Cu7/graphene nanocluster.

**Figure 6.** Schematic representation of the most energetically favourable adsorption positions of ∗CH<sup>2</sup> intermediate on the top of (**a**) Cu7/graphene nanostructure, (**b**) Cu (111) surface, and (**c**) pristine graphene monolayer. Grey balls stand for carbon atoms, orange for copper, and white balls are hydrogen.

### **4. Conclusions**

The main goal of this study is to contribute to the description of experimentally achievable results, allowing for the further optimization of the cathode composition and structure. In order to give theoretical predictions, we have constructed an efficient and reliable model that can be considered as the most appropriate for large-scale ab initio total energy calculations of CO<sup>2</sup> and CH<sup>2</sup> elements atop periodic Cu7/graphene nanostructures. In these calculations, in order to examine a chain of elemental reactions under the influence of the copper nanocatalyst and graphene support, the state-of-the-art total energy codes were used. In the modeled nanocluster, Cu atoms reproduce the facets of the most stable Cu (111) surface. Adatoms and/or defects, e.g., vacancies, at the graphene support may make Cu–C graphene bonds stronger, facilitating the growth of the nanocluster. Assuming that the adsorption of CO<sup>2</sup> is typically the rate-determining step in the CO<sup>2</sup> reduction reaction, the energies of CO<sup>2</sup> adsorption at the Cu7/graphene nanostructure have been calculated and compared to the adsorption energies of species placed on the pristine Cu (111) surface and pristine graphene. The strong binding of CO<sup>2</sup> to the Cu<sup>7</sup> nanocluster at graphene is close to binding to the pristine Cu (111) surface. This is explained by the presence of <111> facets at the Cu<sup>7</sup> nanocluster. This prediction is in agreement with the recent experimental observations to improve the selectivity of CO<sup>2</sup> electrochemical reduction in producing the CH2–CH<sup>2</sup> intermediates. Cu nanoparticles containing grain boundaries were synthesized and a substantial enhancement in the Faradaic efficiency of generating multi-carbon hydrocarbons was observed [79]. This enhancement is correlated with the density of the grain boundary areas [80]. According to predictions obtained in this study, the Cu cluster at graphene demonstrates the best catalytic ability for C2H<sup>4</sup> formation. This is due to the fact that the adsorption properties of neighboring Cu sites are significantly perturbed by the presence of the nearest C, and the stronger Cu–O bonding is formed on the catalyst surface, which also can enhance H2C=CH<sup>2</sup> evolution. Based on this, it is predicted that the larger the length of the grain boundaries of the Cu*<sup>n</sup>* nanocluster deposited at graphene, the more selective the catalyst is to the C2H4. According to a recent experimental study of CO<sup>2</sup> electroreduction on copper electrodes [81], it is expected that one of the most probable pathways for C2H<sup>4</sup> formation is one that shares an intermediate with the pathway to CH4. Considering this pathway, it is obvious that \*CH<sup>2</sup> dimerization is a crucial step for the final C2H<sup>4</sup> production ("carbene" mechanism). In this respect, the CH2– CH<sup>2</sup> dimerization reaction is responsible for the C2H<sup>4</sup> evolution. The lowest dimerization

barrier can be predicted for the pristine graphene due to the lowest adsorption energy, meaning that the whole CO<sup>2</sup> reduction reaction taking place at the grain boundary of the Cu*n*/graphene nanocluster may lead to an improved selectivity to ethylene.

**Author Contributions:** O.L.: conceptualization, investigation, methodology, visualization, formal analysis, writing—review and editing; S.P.: conceptualization, investigation, methodology, formal analysis, writing—original draft, writing—review and editing; D.B.: investigation, resources, formal analysis, writing—original draft, writing—review and editing; Y.F.Z.: conceptualization, supervision; J.K.: conceptualization, funding acquisition, project administration, writing—review and editing, supervision; A.K.: conceptualization, investigation, writing—review and editing; P.L.: conceptualization, investigation. All authors have read and agreed to the published version of the manuscript.

**Funding:** The authors would like to express their gratitude for funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 768789 (CO2EXIDE project). In the last stage of investigation and during the preparation of the publication, the authors were assisted by the postdoc D.B. with his own funding from project No. 1.1.1.2/VIAA/l/16/147 (1.1.1.2/16/I/001) under the activity "Post-doctoral research aid" realized at the Institute of Solid State Physics, University of Latvia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in article.

**Acknowledgments:** Calculations were performed using Latvian Super Cluster (LASC), located in Center of Excellence at Institute of Solid State Physics, the University of Latvia, which is supported by European Union Horizon2020 Framework Programme H2020-WIDESPREAD-01-2016- 2017-TeamingPhase2 under Grant Agreement No. 739508, project CAMART2.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

### **References**

