DFT Study on the CO2 Reduction to C2 Chemicals Catalyzed by Fe and Co Clusters Supported on N-Doped Carbon

The catalytic conversion of CO2 to C2 products through the CO2 reduction reaction (CO2RR) offers the possibility of preparing carbon-based fuels and valuable chemicals in a sustainable way. Herein, various Fen and Co5 clusters are designed to screen out the good catalysts with reasonable stability, as well as high activity and selectivity for either C2H4 or CH3CH2OH generation through density functional theory (DFT) calculations. The binding energy and cohesive energy calculations show that both Fe5 and Co5 clusters can adsorb stably on the N-doped carbon (NC) with one metal atom anchored at the center of the defected hole via a classical MN4 structure. The proposed reaction pathway demonstrates that the Fe5-NC cluster has better activity than Co5-NC, since the carbon–carbon coupling reaction is the potential determining step (PDS), and the free energy change is 0.22 eV lower in the Fe5-NC cluster than that in Co5-NC. However, Co5-NC shows a better selectivity towards C2H4 since the hydrogenation of CH2CHO to CH3CHO becomes the PDS, and the free energy change is 1.08 eV, which is 0.07 eV higher than that in the C-C coupling step. The larger discrepancy of d band center and density of states (DOS) between the topmost Fe and sub-layer Fe may account for the lower free energy change in the C-C coupling reaction. Our theoretical insights propose an explicit indication for designing new catalysts based on the transition metal (TM) clusters supported on N-doped carbon for multi-hydrocarbon synthesis through systematically analyzing the stability of the metal clusters, the electronic structure of the critical intermediates and the energy profiles during the CO2RR.


Introduction
The electrochemical CO 2 reduction reaction (CO 2 RR), as a useful method to convert CO 2 into value-added chemical products, which not only helps to solve the energy and environmental problems caused by fossil fuel combustion but also achieves sustainable development [1][2][3][4]. The main products of CO 2 RR are generally divided into C 1 products (e.g., CO, CH 4 , CH 3 OH, HCOOH, etc.) [5] and C 2 products (e.g., C 2 H 4 , C 2 H 5 OH, CH 3 COOH, etc.) [6]. Cu and Cu-derived materials have been considered the most common electrocatalysts for the CO 2 RR in the early stages [7,8]. Furthermore, Ag-based [9,10] and Au-based [11][12][13] catalysts can selectively reduce CO 2 to CO at low overpotentials. However, they suffer from low utilization of metal atoms and a low C 2+ selectivity.
Recently, the single-atom catalysts (SACs) of metal loaded on carbon substrates (metal nitrogen-doped carbon-based catalysts) have become a rather hot frontier for the maximized atom utilization efficiency and defined active centers. Rossmeisl et al. [14,15] found that the transition metal nitrogen-doped carbon-based catalysts (M-N-C, M = Mn, Fe, Co, Ni or Cu) performed a high CO selectivity for CO 2 RR. Furthermore, both Mn-N-C and Fe-N-C also possessed CO selectivity as well as trace amounts of CH 4 , which was assigned to the stronger CO binding of the Fe and Mn porphyrine-like structures. Zu et al. [16] successfully synthesized atomically dispersed Sn sites on nitrogen-doped carbon, which performs excellent activity and stability for formate generation at a kilogram scale with a quick freeze-vacuum drying-calcination method. Many Ni-based, Fe-based and Co-based SACs have exhibited high electrocatalytic activity and Faradaic effectivity (FE) for the CO 2 RR with CO as the primary product due to the moderate adsorption energies of *COOH and *CO intermediates, as well as the high activation barrier for the hydrogen evolution reaction (HER) [17,18].
Though the widespread study on the single-atom catalysts enhanced the utilization efficiency of metal atoms, most of the current studies are limited to the reduction of CO 2 to C 1 products. Compared to C 1 products, C 2+ products have a higher economic and chemical utilization value [19][20][21]. Cu-based SACs, up to now, have still performed good electrochemical reduction of CO 2 to C 2+ chemicals [22,23]. However, Karapinar [24] revealed that the atomically dispersed CuN x sites could reversibly convert into Cu clusters during CO 2 RR, which are suggested as the real multiple active sites for CH 3 CH 2 OH production. Considering the fact that a single metal atom can accommodate only a single CO, it is difficult to activate two CO 2 molecules simultaneously to trigger the C-C coupling reaction based on an isolated metal center. Thus C-C coupling proceeding on the single metal atoms is quite difficult. Therefore, the catalysts with multiple active sites need to be considered to achieve the conversion from CO 2 to C 2 products [25].
Transition metal (TM) clusters with precise atomic numbers can offer multiple active sites, tune the size-dependent catalytic activity [26], and allow them to find the highest reactivity for the activation and dissociation of strong chemical bonds from CO 2 . Xu et al. [27] reported a facile underpotential deposition technique to fabricate Cu clusters on carbonaceous substrates via rationally introducing S dopants in graphite foam. The obtained free-standing electrode exhibited high activity and excellent long-term stability toward oxygen reduction reaction. Pei et al. [28] found the trimeric metal clusters anchored on N-doped porous graphitic sheets possess a good selectivity and superiority towards CO 2 RR to multi-carbon products due to the multiple active sites.
Considering the loading of metal clusters with a precise number of atoms on the active substrate can not only avoid the problem of low stability of bare metal cluster catalysts at room temperature but also further enhance their stability and catalytic efficiency. Graphitebased materials are currently widely used as substrates for electrocatalysts. To access C 2 products more efficiently, herein, we employed density functional theory (DFT) calculations to explore the CO 2 RR catalyzed by Fe n (n = 1, 3-5) anchoring on N-doped carbon (Fe n -NC) to C 2 H 4 and C 2 H 5 OH in this work. Furthermore, the Co 5 cluster supported on N-doped carbon (Co 5 -NC) was explored comparatively. We found that Fe 5 loaded on NC exhibit significant activity for promoting the reduction of CO 2 to C 2 products, while the Co 5 cluster has higher priority for the selective synthesis of C 2 H 4 . Our findings provide insights into the design of highly active catalysts for CO 2 RR and create a platform for developing metal cluster-NC electrocatalysts.

Theoretical Method
First principle calculations were performed using DFT with spin polarization utilizing the Vienna Ab initio Simulation Package (VASP). The projected augmented wave (PAW) [29][30][31] was used, and the generalized gradient approximation (GGA) realized by the Perdew-Burke-Ernzerhof function (PBE) was adopted to incorporate the exchangecorrection functional [32]. A 2 × 2 × 1 Monkhorst-Pack K-point was sampled in the Brillouin zone, and a cut-off energy of 500 eV was set for geometric optimization. The convergence criteria are of 10 −5 eV in energy between two electronic iteration steps and Nanomaterials 2022, 12, 2239 3 of 12 0.02 eV/Å in force for every atom [33]. Our calculations of catalytic performance are based on the computational hydrogen electrode (CHE) proposed by Nørskov et al. [34]: The change of the free energy for the step * A + H + + e − → * AH can be equal to the reaction: * A + 1 2 H 2 (g) → * AH at 0 V versus the reversible hydrogen electrode (RHE) at all pH values.
We employ five types of small iron clusters Fe n (n = 1, 3-5) supported on nitrogendoped carbon sheets as the calculation models. The defects of NC provide ideal anchor sites for the iron cluster. To estimate the stability of supported TM clusters, the binding energy (E b ) of TM n cluster on NC is calculated by Equation (2) Here E TM n −NC is the total energy of the optimized TM n cluster supported on NC. The terms E TM n and E NC refer to the energies of isolated TM n cluster and support. We calculated the cohesive energy (E c ) of each TM n cluster to further evaluate the stability of TM n -NC catalysts, with E c defined as: Here the E cluster and E TM represent the energy of the total energy of the TM n cluster and the energy of single TM atom; n is the number of TM atoms in the cluster. The more negative cohesive energy (E c ) indicates a more stable structure.
The adsorption energy (E ads ) of every intermediate species is defined by Equation (4) where E C x H y O z −TM n −NC refers to the total energy of the adsorbed species on the supported TM n cluster, and E TM n −NC is the energy of supported TM n cluster. E C x H y O z refers to the energies of C x H y O z in gas phase, respectively. The more negative adsorption energy indicates a stronger binding between TM cluster and NC support. Gibbs free energy change (∆G) [35,36] is defined as: where ∆E, ∆E ZPE , ∆ C P dT and ∆S are the total energy difference, the zero-point energy difference, the difference in enthalpic correction and the entropy change between the products and reactants obtained from DFT calculations, respectively. The zero-point energies (ZPE) and total entropies of the gas phase were computed from the vibrational frequencies, and the vibrational frequencies of the adsorbed species were also computed to obtain the ZPE contribution to the free energy expression. Only vibrational modes of the adsorbates were computed explicitly, while the catalyst sheet was fixed (assuming that vibration contribution to the free energy from the substrate is negligible) [37,38]. T is the temperature (298.15 K). The influence of applied potential is: ∆G U = −neU, where U is the external potential versus RHE, e is the electron transfer, and n is the number of proton-electron pairs. ∆G pH is the free energy correction due to the concentration of H + .
where k B is the Boltzmann constant, and the value of pH was assumed to be zero for acidic conditions.

The STABILITY Analysis of Fe n -NC
For the Fe n clusters supported on the NC substrate (Fe n -NC), n = 1, 3, 4 and 5 were chosen to be studied here since the Fe 2 cluster is unstable [39]. As shown in Figure 1, for the adsorption of a single Fe atom on the NC substrate (Figure 1a), the mono Fe atom coordinated with the four nitrogen atoms and Fe-NC maintains a perfect monolayer structure, which is in agreement with previous results [40]. For the adsorption of Fe n clusters with n ranging from 3 to 5 (Figure 1b-d), one Fe atom is anchored at the same position with that in a single Fe atom. Two Fe atoms bound to the doped nitrogen atoms with distances of about 2.1~2.3 Å, respectively, while the other Fe atoms bound together through Fe-Fe metal bonds.

The STABILITY Analysis of Fen-NC
For the Fen clusters supported on the NC substrate (Fen-NC), n = 1, 3, 4 and 5 we chosen to be studied here since the Fe2 cluster is unstable [39]. As shown in Figure 1, f the adsorption of a single Fe atom on the NC substrate (Figure 1a), the mono Fe ato coordinated with the four nitrogen atoms and Fe-NC maintains a perfect monolay structure, which is in agreement with previous results [40]. For the adsorption of F clusters with n ranging from 3 to 5 (Figure 1b-d), one Fe atom is anchored at the sam position with that in a single Fe atom. Two Fe atoms bound to the doped nitrogen atom with distances of about 2.1~2.3 Å, respectively, while the other Fe atoms bound togeth through Fe-Fe metal bonds. As listed in Table 1, all the binding energies of Fen clusters on NC supports a thermodynamically favorable (Eb < 0). With the increase in Fe atoms, the binding energ decreases except for the magic Fe5 cluster, which means that the small Fe clusters m tend to aggregate from small clusters to bigger clusters on NC support. The reason for t decreased binding energy of the magic Fe5 cluster lies in that the Fe 5site located at the to site, as shown in Figure 1d. Hence there is no interaction with the NC support. What more, the cohesive energy of various Fen clusters was also explored according to Equatio (3), as shown in Table 1. It can be found that with the increase in Fe atoms in the cluste the cohesive energy becomes thermodynamically favorable.  As listed in Table 1, all the binding energies of Fe n clusters on NC supports are thermodynamically favorable (E b < 0). With the increase in Fe atoms, the binding energy decreases except for the magic Fe 5 cluster, which means that the small Fe clusters may tend to aggregate from small clusters to bigger clusters on NC support. The reason for the decreased binding energy of the magic Fe 5 cluster lies in that the Fe 5site located at the top site, as shown in Figure 1d. Hence there is no interaction with the NC support. What is more, the cohesive energy of various Fe n clusters was also explored according to Equation (3), as shown in Table 1. It can be found that with the increase in Fe atoms in the cluster, the cohesive energy becomes thermodynamically favorable.

Electrocatalytic CO 2 RR
The charge difference between two active transition atoms plays a key role during CO 2 RR, and the mixed oxidation state of the catalytic centers can boost the C-C coupling [41,42]. Thus the Bader charges of various Fe clusters adsorbed on NC were investigated. As listed in Table 1, one can find that the electrons can transfer from the clusters to the support, making the whole Fe cluster positively charged, and each Fe atom in the cluster is positively charged as well. Herein, the Fe n clusters are favorable to the CO 2 RR; thus the electron-accepting properties of the positively charged Fe and Co sites are favorable for stabilizing the CO 2 RR intermediates [43]. The largest charge transfer can be determined for the single Fe atom configuration since the monatomic Fe interacts with four coordinated N atoms. Furthermore, significant discrepancies for each charged Fe atom in the Fe 3 , Fe 4 and Fe 5 clusters can be determined, which is beneficial for the C-C coupling reaction.
The conversion of CO 2 to CO catalyzed by various Fe n clusters was calculated, as shown in Figure 2; the PDS is the *CO to CO for all the Fe n -NC with a maximum Gibbs free energy (∆G 3 = ∆G CO − ∆G * CO ). The ∆G 3 are 0.91, 1.14 and 1.58 eV for the Fe-NC, Fe 3 -NC and Fe 4 -NC, respectively. This value increases to 1.94 and 2.29 eV at two different sites of Fe 5 -NC. Thus it can be deemed that the Fe-NC, Fe 3 -NC and Fe 4 -NC require a lower overpotential to drive the desorption of CO, indicating that these structures favor the conversion of CO 2 to CO. The * CO → CO(g) step with strong *CO binding leads to a positive ∆G of CO desorption. The relatively strong binding of *CO on Fe-N x is fully supported by the experimentally confirmed exclusive ability of the Fe-N x catalyst to produce the hydrocarbon CH 4 [44].
In simple terms, one could say that to produce subsequent reaction products from CO during the CO 2 RR; the CO molecule must be bound strong and long enough to undergo subsequent dissociation and hydrogenation steps to arrive at CH 4 or other small organic molecules. Herein, our work focuses on the reduction of CO 2 to C 2 products, which requires improved selectivity and activity by inhibiting the unwanted, i.e., C 1 hydrocarbon reaction pathway, which favors both the stabilization of *CO on the catalyst surface and the formation of C-C bonds. The strongest interaction for CO on the two Fe 5 -NC sites means that CO does not leave the iron cluster surface easily, which, in turn, favors the subsequent C 2 product conversion. Therefore, the following study focuses on the performance of electrocatalytic CO 2 reduction to C 2 H 4 and CH 3 CH 2 OH over the Fe 5 -NC cluster. In order to further extend this result to other systems, the Co 5 cluster supported on NC was chosen to be studied comparatively ( Figure S1). As shown in Table 2, the E b value between the Co 5 cluster and the NC is −10.00 eV, and the E c value of the Co atom is −1.39 eV, which means the Co 5 cluster can adsorb stably on the NC. Nanomaterials 2022, 12, x FOR PEER REVIEW 5 of 12

Electrocatalytic CO2RR
The charge difference between two active transition atoms plays a key role during CO2RR, and the mixed oxidation state of the catalytic centers can boost the C-C coupling [41,42]. Thus the Bader charges of various Fe clusters adsorbed on NC were investigated. As listed in Table 1, one can find that the electrons can transfer from the clusters to the support, making the whole Fe cluster positively charged, and each Fe atom in the cluster is positively charged as well. Herein, the Fen clusters are favorable to the CO2RR; thus the electron-accepting properties of the positively charged Fe and Co sites are favorable for stabilizing the CO2RR intermediates [43]. The largest charge transfer can be determined for the single Fe atom configuration since the monatomic Fe interacts with four coordinated N atoms. Furthermore, significant discrepancies for each charged Fe atom in the Fe3, Fe4 and Fe5 clusters can be determined, which is beneficial for the C-C coupling reaction.
The conversion of CO2 to CO catalyzed by various Fen clusters was calculated, as shown in Figure 2; the PDS is the *CO to CO for all the Fen-NC with a maximum Gibbs free energy (∆ = ∆ − ∆ * ). The ΔG3 are 0.91, 1.14 and 1.58 eV for the Fe-NC, Fe3-NC and Fe4-NC, respectively. This value increases to 1.94 and 2.29 eV at two different sites of Fe5-NC. Thus it can be deemed that the Fe-NC, Fe3-NC and Fe4-NC require a lower overpotential to drive the desorption of CO, indicating that these structures favor the conversion of CO2 to CO. The * → ( ) step with strong *CO binding leads to a positive ΔG of CO desorption. The relatively strong binding of *CO on Fe-Nx is fully supported by the experimentally confirmed exclusive ability of the Fe-Nx catalyst to produce the hydrocarbon CH4 [44]. In simple terms, one could say that to produce subsequent reaction products CO during the CO2RR; the CO molecule must be bound strong and long enough t dergo subsequent dissociation and hydrogenation steps to arrive at CH4 or other organic molecules. Herein, our work focuses on the reduction of CO2 to C2 prod which requires improved selectivity and activity by inhibiting the unwanted, i.e., C drocarbon reaction pathway, which favors both the stabilization of *CO on the ca surface and the formation of C-C bonds. The strongest interaction for CO on the tw NC sites means that CO does not leave the iron cluster surface easily, which, in tur vors the subsequent C2 product conversion. Therefore, the following study focuses o performance of electrocatalytic CO2 reduction to C2H4 and CH3CH2OH over the Fe cluster. In order to further extend this result to other systems, the Co5 cluster supp on NC was chosen to be studied comparatively ( Figure S1). As shown in Table 2, t value between the Co5 cluster and the NC is −10.00 eV, and the Ec value of the Co at −1.39 eV, which means the Co5 cluster can adsorb stably on the NC.   To further study the mechanisms of CO 2 RR catalyzed by Fe 5 -NC and Co 5 -NC, the optimized structures and the energy profiles along the reaction coordinate for CO 2 RR to both C 2 H 4 and CH 3 CH 2 OH on Fe 5 -NC and Co 5 -NC are calculated as shown in Figures 3 and 4, respectively. It can be found that two strongly adsorbed CO molecules adsorbed on the two adjacent metal atoms through carbon atoms either on the Fe 5 or the Co 5 clusters before the C-C bond formation. The two CO molecules will couple with each other via the top Fe or Co atom in the following steps of CO 2 RR. For the CO 2 RR on Fe 5 -NC, the Gibbs free energy for the hydrogenation of the *CO dimer is uphill with an energy value of 0.79 eV, which is the highest energy during the formation of both C 2 H 4 and CH 3 CH 2 OH. Thus, it can be deemed that the C-C coupling reaction for the CO 2 RR from CO 2 to C 2 chemicals is the PDS. Furthermore, it can be speculated that both C 2 H 4 and CH 3 CH 2 OH products can be achieved with Fe 5 -NC catalyst, and the amount of C 2 H 4 should be much more than the CH 3 CH 2 OH. Because the Gibbs free energy for the hydrogenation of *CH 2 CHO to C 2 H 4 is energy thermodynamically favorable, while the hydrogenation of *CH 2 CHO to *CH 3 CHO is an uphill reaction with a free energy of 0.26 eV.
is the PDS. Furthermore, it can be speculated that both C2H4 and CH3C can be achieved with Fe5-NC catalyst, and the amount of C2H4 should be m the CH3CH2OH. Because the Gibbs free energy for the hydrogenation of *C is energy thermodynamically favorable, while the hydrogenation o *CH3CHO is an uphill reaction with a free energy of 0.26 eV.   For the CO2RR on Co5-NC, the Gibbs free energy for the hydrogenation of t dimer is uphill with an energy of 1.01 eV, which is 0.22 eV higher than that of the F However, the Gibbs free energy for the hydrogenation of *CH2CHO to *CH3CHO eV higher) comparable with that in the C-C coupling reaction, which means that drogenation of *CH2CHO to *CH3CHO becomes the PDS. Thus, most of the final C ucts should be C2H4. In general, the Fe5-NC has good catalytic activity towards chemicals with relatively lower free energy change (0.53 eV), while the selectivit as good as Co5-NC. However, Co5-NC possesses better selectivity while the act lower than Fe5-NC.
The d-band center of the TM and its electronic occupancy can affect the b strength between the intermediate and the catalytic surface. As shown in Figur PDOS of Fe d orbit from the top-and sub-layer structures show much more diff than that of the Co d orbit on Co5-NC. Furthermore, the d band center of the top F in the Fe5 cluster is −3.48 eV, while it becomes −1.59 eV for the sub-layer atoms. Ho the d band center of the top Co atom is −1.34 eV, and it only changes to −1.47 eV sub-layer atoms. A much bigger discrepancy of the d band center between the top F and sub-layer atoms than that in the Co5 cluster may boost the C-C coupling r which could be called the synergy effect between the top-and sub-layer metal atom findings are consistent with the synergy effect between Cu + and Cu 0 , and the surf significantly improve the kinetics and thermodynamics of both CO2 activation a dimerization. Cu metal embedded in an oxidized matrix catalyst can promote CO2 tion and CO dimerization for electrochemical reduction of CO2 [41]. For the CO 2 RR on Co 5 -NC, the Gibbs free energy for the hydrogenation of the *CO dimer is uphill with an energy of 1.01 eV, which is 0.22 eV higher than that of the Fe 5 -NC. However, the Gibbs free energy for the hydrogenation of *CH 2 CHO to *CH 3 CHO is (0.07 eV higher) comparable with that in the C-C coupling reaction, which means that the hydrogenation of *CH 2 CHO to *CH 3 CHO becomes the PDS. Thus, most of the final C 2 products should be C 2 H 4 . In general, the Fe 5 -NC has good catalytic activity towards the C 2 chemicals with relatively lower free energy change (0.53 eV), while the selectivity is not as good as Co 5 -NC. However, Co 5 -NC possesses better selectivity while the activity is lower than Fe 5 -NC.
The d-band center of the TM and its electronic occupancy can affect the bonding strength between the intermediate and the catalytic surface. As shown in Figure 5, the PDOS of Fe d orbit from the top-and sub-layer structures show much more differences than that of the Co d orbit on Co 5 -NC. Furthermore, the d band center of the top Fe atom in the Fe 5 cluster is −3.48 eV, while it becomes −1.59 eV for the sub-layer atoms. However, the d band center of the top Co atom is −1.34 eV, and it only changes to −1.47 eV for the sub-layer atoms. A much bigger discrepancy of the d band center between the top Fe atom and sub-layer atoms than that in the Co 5 cluster may boost the C-C coupling reaction, which could be called the synergy effect between the top-and sub-layer metal atoms. Our findings are consistent with the synergy effect between Cu + and Cu 0 , and the surface can significantly improve the kinetics and thermodynamics of both CO 2 activation and CO dimerization. Cu metal embedded in an oxidized matrix catalyst can promote CO 2 activation and CO dimerization for electrochemical reduction of CO 2 [41].
Our theoretical calculations found that the multiple active sites in both the Fe 5 and Co 5 cluster-based catalysts facilitate the stabilization of *CO on the catalyst surface and the formation of C-C bonds. Both geometrical effects and electronic effects are the key factors leading to the Fe 5 and Co 5 clusters exhibiting better activity and/or selectivity over the single metal component. Furthermore, the tunable synthesis of Fe and Co alloys supported on NC may promote both their activity and selectivity toward CO 2 RR. Therefore, Fe 5 , Co 5 and the related tunable alloy clusters show great potential applications in electrocatalytic CO 2 RR, and our methods provide a concept for designing the improved CO 2 RR electrocatalysts. Our theoretical calculations found that the multiple active sites in both the Fe5 a Co5 cluster-based catalysts facilitate the stabilization of *CO on the catalyst surface a the formation of C-C bonds. Both geometrical effects and electronic effects are the k

Conclusions
The stability of the Fe n (n = 1, 3, 4, and 5) clusters was studied first, and it can be found that the Fe n anchors stably on the nitrogen-doped carbon via a basic Fe-NC structure. With the increasing of Fe atoms in the cluster, both the binding energy and cohesive energy become thermodynamically favorable, which means a small cluster tends to aggregate to be a bigger one. While for the Fe 5 cluster, the binding energy decreases because there is no interaction between the topmost Fe atom with the NC support anymore. In addition, the CO desorption is the most difficult on the Fe 5 cluster, which is beneficial to the subsequent reaction products from CO. Hence, the Fe 5 -NC cluster was chosen to be studied as our C 2 catalyst, and Co 5 -NC was comparatively studied as well. The results show that Fe 5 -NC has better activity towards CO 2 RR, and the products should be the mixed C 2 H 4 and CH 3 CH 2 OH, since the PDS is the C-C coupling reaction with a free energy change of only 0.79 eV. The free energy change is only 0.53 eV for the reduction of CH 2 CHO to CH 3 CHO, and the reduction of CH 2 CHO to C 2 H 4 is a spontaneous step without any free energy change. Considering the fact that C 2 H 4 is a gas, Fe 5 -NC should be a good catalyst for CO 2 RR to liquid ethanol with a relatively lower yield since part of the C 2 H 4 gas will also be produced. Furthermore, Co 5 -NC possesses a relatively good selectivity, but bad activity since the reduction of CH 2 CHO to CH 3 CHO is the PDS, and the free energy change is 1.09 eV. The PDOS and d band center analysis demonstrates that the relative energy favorable C-C coupling reaction on the Fe 5 cluster could be attributed to the larger discrepancy of d electrons of the two CO-adsorbing Fe atoms. This paper predicts a good application prospect of TM clusters supported on nitrogen-doped graphene for CO 2 RR, and the new insight into the relationship between selectivity and activity sheds light on a new route for understanding and designing highly efficient non-precious catalysts for CO 2 RR.