Theoretical insights into the effect of the overpotential on CO electroreduction mechanisms on Cu(111): regulation and application of electrode potentials from a CO coverage-dependent electrochemical model

A recently proposed CO coverage-dependent electrochemical model combined with the calculation of electronic structure is applied for the first time to study the effect of the overpotential on Cu-catalyzed CO electroreduction mechanisms by changing the coverage of surface adsorbed CO. The results show that the presently defined CH₂O and CHOH pathways may be able to occur parallelly under different overpotentials. However, high overpotentials will facilitate CO electroreduction, thus explaining why a high overpotential is required during CO₂ electroreduction in experiments on Cu electrodes. The potential-limiting step may be further CO electroreduction into CHO, which is considered as the origin of the experimentally observed high overpotentials. The analyses of electronic structure show that an adsorbed CO^δ− species is formed on the Cu electrodes, validating the previous experimental speculations on electron transfer between CO and Cu electrodes. More and more electrons are transferred into the π antibonding orbitals of the adsorbed CO with increasing surface CO coverage, leading to increasing overpotential and weaker and weaker CO bonding with the Cu surface. Thus, the significantly lower barrier of further CO electroreduction at higher overpotential can be correlated with lower CO adsorption energy. Interestingly, it is found that there is greater localization of electrons around the C than the O atom in the adsorbed CO molecule, explaining why the hydrated proton prefers to reach the C atom to form intermediate CHO rather than COH.

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1. Introduction

Electrocatalytic reduction technologies of CO₂ offer a promising pathway to sustainable fuels and chemicals by using renewable electricity and carbon sources.^1,2 Cu with a medium hydrogen overvoltage is the focus of present CO₂ electroreduction investigations and has a unique ability among metals to catalyze CO₂ into hydrocarbons with significant current density and reasonable current efficiency.^3–9 Furthermore, the crystal faces of Cu exhibit high selectivity for the CO₂ electroreduction product, in which the (111) facet of Cu favors CO₂ conversion into CH₄ and more open Cu(100) exhibits greater selectivity toward C₂H₄ production, as reported experimentally by the group of Prof. Hori.^10–15 However, high overpotentials are required on Cu electrodes to achieve significant current efficiency and selectivity to CH₄ and C₂H₄. Also, the formation mechanisms of both of these products remain ambiguous due to the complexities of electrochemical interfaces so far.^3–19 In particular, the mechanism for CH₄ formation on Cu(111) needs more evidence from both theory and experiment.^{3–8,10–16,20–22} Identifying the influence of the overpotential on CO₂ electroreduction mechanisms on Cu electrodes will accelerate the design of efficient Cu-based alloy electrocatalysts that operate at low overpotentials.

In situ infrared spectroscopy has offered some insights into the nature of adsorbed CO₂, CO and formate. Moreover, the observed CH₂ species is able to lead to the formation of hydrocarbons CH₄ and C₂H₄ as shown by in situ X-ray photoelectron spectroscopy and Auger electron spectroscopy on Cu electrodes.^5,23,24 However, experimental understanding of CO₂ electroreduction mechanisms has been challenged and hindered by difficulties in performing spectroscopic characterizations of the various possible intermediates that are crucial to the production of the observed electroreduction products at electrochemical interfaces. Most recently, the feeding technique conducted by Schouten et al. has been used to analyze experimentally CO₂ electroreduction mechanisms on Cu by feeding postulated intermediates into reaction systems and the subsequent product distribution is taken as evidence that the intermediates may indeed play a crucial role in the electrochemical reduction mechanisms.⁷ However, this approach has significant limitations since only stable intermediates can be studied. Thus, only rough and incomplete CO₂ electroreduction pathways can be speculated based on early experiments. In recent decades, theoretical calculations have become a powerful tool for investigating various key electrocatalytic reactions and numerous theoretical studies have contributed to our understanding of CO₂ electroreduction mechanisms on Cu electrodes by using various theoretical models,^{8,15,20–22,25–29} which can provide mechanistic insights that are not accessible from experiments alone and identify favored intermediates. Taking CO₂ electroreduction into the CH₄ product on Cu(111) as an example with the application of various theoretical models, Nørskov et al. reported the first full studies of CO₂ electroreduction into CH₄ on the Cu surface by using the computational hydrogen electrode (CHE) model with a hexagonal H₂O overlayer.⁸ They concluded that CO, CHO, CH₂O and CH₃O are key intermediates during CH₄ formation along which CO electroreduction into CHO is the potential-limiting step. The CHE model could calculate conveniently the reaction free energy changes of the proton-coupled electron transfer (PCET) steps at applied potentials. However, the activation barriers of all PCET steps are neglected by the CHE model and thus accurate kinetics are not available. The kinetic barriers for each PCET step are subsequently considered with incorporation of applied potentials at the electrode/aqueous interfaces. In contrast to the study of the CHE model, Asthagiri et al. reported the complete CO₂ electroreduction pathways by calculating the applied potential-dependent barriers on Cu(111) in the aqueous phase based on Butler–Volmer theory,^15,20,27 in which an adsorbed H atom is used to represent a proton–electron couple under the equilibrium potential and the COH species is predicted to be the kinetically dominant key intermediate, sequentially resulting in CH_x (x = 0–4) species. The difference in electroreduction pathways between both of these models may show the importance of considering kinetic barriers. However, the generality of the assumption that the adsorbed H direct transfer represents the kinetics of a PCET step may be still in question. Moreover, the inclusion of only one or two explicit H₂O molecules or a fixed H₂O bilayer would be insufficient for the modeling of the aqueous-phase environment. By changing the number of H atoms added to the bilayer H₂O structure to tune the electrode potentials, a DFT-based extrapolation scheme was applied to studies of CO₂ electroreduction into CH₄ on Cu(111) by extrapolating the calculated barriers in model systems of increasing cells.^28,29 Skúlason et al. speculated that the COH, CHOH, CH₂OH, CH₂ and CH₃ species are the reduction intermediates after CO formation. The major issue for this scheme is that it is extremely costly computationally due to extrapolation of an increasingly larger size. However, inconsistent conclusions were obtained by Nørskov et al. by using a similar electrochemical model,²¹ in which CHO formation is predicted to be more favorable than COH on Cu(111) thermodynamically and kinetically, subsequently leading to the formation of CHOH and CH_x (x = 2–4), in contradiction to the report from Asthagiri and Skúlason. By using the implicit solvation model, CO₂ electroreduction pathways were studied based on a DFT methodology that predicted onset potentials at constant electrochemical potentials by Goddard et al.²² They proposed that forming COH is more favorable than forming CHO although the difference in the barrier is subtle on Cu(111). The subsequent COH electroreduction results in the formation of CHOH and CH_x (x = 1–4), which is different from the pathways reported by Asthagiri et al. The drawback of this model may be that the implicit solvation model cannot describe hydrogen bonds and interactions between adsorbates and H₂O molecules. Despite numerous theoretical efforts, the mechanism for CH₄ formation on Cu(111) is still under debate, and the difference in the CO₂ electroreduction pathways may lie in the different electrochemical models. Furthermore, most previous theoretical investigations were done at constant charge, resulting in changes of the work function/electrode potential during a PCET step due to the limited cell size, whereas the experimental PCET steps take place at a constant electrode potential. Thus, the modeling of electrode/aqueous interfaces remains a subject of ongoing discussion to obtain sufficiently accurate computational models for describing electrochemical systems and fill in the lacking intermediate in the uncertain reaction mechanisms.^30–32

The previous experimental reports from the groups of Frese, Ito and Hori felt that adsorbed CO was a crucial intermediate during CO₂ electroreduction into CH₄, with further CO electroreduction as the slowest step in the overall reduction pathways, which can dominate most of the Cu electrode surface.^11,33–36 Thus, it can be speculated that the CO₂ electroreduction kinetics is dependent on the coverage of CO. Based on this, an improved CO coverage-dependent electrochemical model can be used to predict CO coverage-dependent equilibrium potentials and elucidate CH₄ production mechanisms during CO₂ electroreduction on Cu(111) by calculating potential-dependent free energy profiles at the predicted equilibrium potentials. The solvent effect is essential in modeling electrode/aqueous interfaces and the previous study from Nørskov et al. validated that even a single H₂O bilayer is sufficient to describe the electrical double layer.³⁷ An explicit solvation model containing two relaxed H₂O bilayers is included in the present model which allows us to better simulate the interactions between H₂O molecules and adsorbates. Furthermore, the interactions between solvent and adsorbents have been elaborated in our most recent work.^38,39 It is aim of this paper to offer in depth insight focused on specifically the influence of the overpotential on the CO₂ reduction mechanisms on Cu(111) by applying the CO coverage-dependent electrochemical model, which may be able to result in better understanding of the possible electroreduction pathways.

2. Determination of CO coverage-dependent equilibrium potentials

Computational details including the surface and solvation model and computational parameters have been elaborated in the ESI.† The method for determining CO coverage-dependent equilibrium potentials has been reported in our most recent study,⁴⁰ which was first employed to model the electroreduction pathways of CO₂ at low overpotentials. For clarity, the corresponding method is again elaborated in this paper. The CO intermediate is formed during CO₂ electroreduction by the following reaction:

CO₂ + * + 2(H⁺ + e⁻) → CO* + H₂O (1)

The Gibbs free energy ΔG(θ) under different CO coverage conditions can be calculated according to eqn (2) based on the approach proposed by Nørskov et al. and Chen et al. for the hydrogen evolution and oxygen reduction reactions,^41–45 where ΔE(θ), ΔS(θ), ΔZPE, and k_BT ln(θ/1 − θ) represent the differential adsorption energy of CO, entropy, zero-point energy, and configurational entropy contributions to ΔG(θ), respectively. Here coverage θ = n/N, in which n is the number of adsorbed CO molecules on the surface and N is the total number of surface Cu atoms. Thereby, the CO coverage-dependent equilibrium potential U (vs. RHE) can be determined when the Gibbs free energy ΔG(θ) is zero.

ΔG(θ) = ΔE(θ) + 2eU − TΔS(θ) + ΔZPE + 2k_BT ln(θ/1 − θ) (2)

The differential adsorption energy of CO, ΔE(θ), can be expressed by eqn (3), in which is the total energy of the surface with different CO coverage.

Considering that the entropies of the adsorbed molecules are small when compared with the entropies of gases and that the zero-point energy of the adsorbed CO molecules on Cu(111) is little based on our present calculations, the contribution from the changes of entropy and ZPE together to ΔG(θ) has been estimated to be −0.42 eV for standard temperature (298 K) according to the available data from Nørskov et al.⁸ Thus, eqn (3) can be converted to the following form of eqn (4).

The values of , E_H2O, E_CO2 and E_H2 are directly available via DFT calculations. By changing the coverage of adsorbed CO on Cu(111), a series of values of can be obtained. The values of ΔE(θ) at various coverages can be obtained according to eqn (3) by differentiating the plots of against θ.

3. Results and discussion

3.1 Relationships between the CO coverage and equilibrium potentials

Various possible surface CO adsorption sites and the relationship between CO coverage and equilibrium potentials have been also given in our most recent study.⁴⁰ As shown in Fig. 1(a), the differential adsorption energy of CO, ΔE(θ), exhibits reasonable linear dependence on θ_CO on Cu(111), implying that CO adsorption on Cu(111) may nearly follow the Termkin adsorption isotherms. Linearly fitting the present ΔE(θ) ∼ θ_CO data to a straight line enables us calculate ΔE(θ) at any θ_CO. Thus, the linear relationships between CO coverage (θ_CO) and the calculated equilibrium potentials (U) can be obtained on Cu(111) based on the above eqn (4), as shown in Fig. 1(b). It can be observed that more CO coverage will lead to a more negative equilibrium potential for CO₂ electroreduction, suggesting that the overpotential may mainly originate from the adsorbed CO on the Cu electrodes. The presently calculated equilibrium potential is ca. 0.27 V (vs. RHE) when θ_CO is close to zero (ca. 0.05), which is comparable with the thermodynamically required equilibrium potential of 0.17 V (vs. RHE) for CO₂ electroreduction and confirms the reasonability of the present theoretical model to some degree. Our present study will focus on the conditions of low and high overpotentials, which correspond to CO adsorption with different coverage on Cu(111). Thus, the effect of the overpotential on the electroreduction pathways of CO₂ can be obtained.

Fig. 1 (a) The relationships between CO coverage (θ_CO) and the differential adsorption energy of CO, ΔE(θ); (b) the relationships between CO coverage (θ_CO) and the calculated equilibrium potentials (U).

3.2 CO coverage-dependent electroreduction mechanisms

The previous experimental studies clearly showed that the Cu electrode surface is dominated by adsorbed CO during CO₂ electroreduction and similar spectra and onset potentials for CO electrochemical reduction in experiments to those observed for that of CO₂ on Cu electrodes have established that CO is a crucial and essential intermediate for producing hydrocarbons. Because of the high implied CO coverage during CO₂ electroreduction, it was felt that the reduction of adsorbed CO was the key rate-determining step for the overall electroreduction of CO₂ into hydrocarbons. Thus, we mainly focus on the CO electroreduction pathways on Cu(111) at the presently simulated equilibrium potentials in this paper, which has the advantage of simplifying the complication found in previous theoretical studies of CO₂ electroreduction with the aim of applying the improved CO coverage-dependent model.

3.2.1 Conditions of low overpotentials. Based on the CO coverage-dependent electrochemical model on Cu(111), the equilibrium potentials are calculated as 0.14 and −0.10 V (vs. RHE) when the coverages of CO are 1/9 and 2/9 ML, respectively, corresponding to the conditions of low overpotentials of ca. 0.13 and 0.37 V compared with the thermodynamically required equilibrium potential of 0.27 V (vs. RHE) when θ_CO is close to zero. Although CO₂ electroreduction pathways at the low overpotential of 0.13 V have been given in our most recent work,⁴⁰ they are still elucidated in this study for comparison. Beginning with the first electroreduction of adsorbed CO, the formation of CHO and COH intermediates is competitive. The presently calculated activation barriers show that CHO formation is more favorable at the presently simulated low overpotentials due to the significantly lower barrier than COH formation on Cu(111), as can be seen in Fig. S1 (ESI†). Simultaneously, it is noted that CHO formation has almost identical barriers of ca. 0.86 eV at the low overpotentials of 0.13 and 0.37 V, suggesting that the barrier of this elementary step will be not changed in the range of low overpotentials. Previously, an activation barrier of ca. 0.90 eV was reported for CHO formation on Cu(111) under conditions of low overpotentials by Goddard et al. through combining with pH effects and implicit solvation,²² which is in excellent agreement with our present value, validating the rationality of our used model to some degree. Further CHO hydrogenation into intermediates CH₂O and CHOH is considered by C–H and O–H bond formation, respectively. Almost identical barriers of ca. 0.45 eV are obtained for CH₂O and CHOH formation at the overpotential of 0.13 V, as can be seen in Fig. S2 (ESI†). Our calculated barriers for CH₂O and CHOH formation are also in excellent agreement with some earlier theoretical studies at low overpotentials. For example, Asthagiri et al. reported a barrier of ca. 0.49 eV for CHO hydrogenation into CH₂O on Cu(111),¹⁵ and a barrier of ca. 0.45 eV was obtained for CHO hydrogenation into CHOH by Goddard et al. at ca. 0 V (vs. RHE).²² The calculated barriers are 0.19 and 0.31 eV for the corresponding pathways at a relatively higher overpotential (0.37 V) on Cu(111) (see Fig. S2, ESI†), respectively, seeming to show that CH₂O formation is more favorable with increasing overpotential. However, we note that both of these barriers are extremely low and surmountable at room temperature. Thus, it is speculated that intermediates CH₂O and CHOH may be able to be formed simultaneously at low overpotentials. Interestingly, it is found that the barriers for the formation of both of these intermediates are decreased at relatively higher overpotential, indicating that increased overpotential will lead to easier formation of CH₂O and CHOH through further CHO electroreduction on Cu(111).

Subsequently, further CH₂O and CHOH electroreduction are considered. Further hydrogenation of intermediate CH₂O may be able to form CH₂OH and CH₃O species on Cu(111). Barriers of 0.32 and 0.23 eV are required for CH₂OH and CH₃O formation at the overpotential of 0.13 V, respectively, being slightly higher than those of the corresponding processes (0.19 and 0.16 eV) at the relatively higher overpotential of 0.37 V, as shown in Fig. S3 (ESI†). Thus, the results show that further CH₂O electroreduction is more favorable at the higher overpotentials. However, both of these intermediates can be easily formed in the range of low overpotentials due to the surmountable barriers at room temperature. Our presently calculated barriers for further CH₂O electroreduction into CH₂OH and CH₃O are significantly lower than those reported by Asthagiri et al. at low overpotentials,²⁰ in which barriers of ca. 0.90 and 0.60 eV need to be overcome at an applied potential of ca. −0.10 V (vs. RHE). The difference in the used solvation models may lead to the inconsistencies, where only a single H₂O molecule or fixed H₂O bilayer structure was employed in previous theoretical studies. Due to the favorable CHOH formation, the CH₂OH species can be also formed by CHOH hydrogenation with almost identical barriers of ca. 0.50 eV at the low overpotentials of 0.13 and 0.37 V (see Fig. S4, ESI†). Simultaneously, we also note that the CH species can be formed by CHOH hydrogenative dissociation along with H₂O formation with extremely low barriers of ca. 0.20 eV in the range of low overpotentials, which are significantly lower than those of CHOH hydrogenation into CH₂OH, thereby suggesting that CH formation is more favorable during further CHOH electroreduction at low overpotentials. Considering the almost identical and extremely low barriers between further CH₂O electroreduction into CH₂OH and CH₃O species and further CHOH electroreduction into CH species, we can speculate that parallel pathways may occur through the CH₂O and CHOH intermediates during CO₂ electroreduction in the range of low overpotentials.

Further electroreduction of intermediate CH₂OH into CH₃OH through direct hydrogenation and into the CH₂ species through hydrogenative dissociation along with H₂O formation are considered on Cu(111). The calculated barriers for further CH₂OH electroreduction into CH₃OH and CH₂ are ca. 0.36 and 0.07 eV at the overpotential of 0.13 V, which is in good agreement with the previously reported values of ca. 0.29 and 0.05 eV from Goddard et al. for the formation of product CH₃OH and intermediate CH₂,⁴⁶ further validating the rationality of our presently employed electrochemical model. However, they are 0.34 and 0.31 eV when the overpotential is increased to 0.37 V, respectively, as shown in Fig. S5 and S6 (ESI†). The results suggest that CH₂ formation is more and more difficult, whereas CH₃OH formation becomes more and more favorable with increasing overpotential. However, it is observed that the CH₃OH and CH₂ species may be able to be formed simultaneously due to the surmountable barriers at room temperature in the range of low overpotentials. Although the CH₃O species can be easily formed, a significantly higher barrier of ca. 0.70 is required for its further hydrogenation into CH₃OH compared to CH₂OH electroreduction at the overpotentials of 0.13 and 0.37 V (see Fig. S5 and S6, ESI†). Thus, we can speculate that the CH₃O species is only a spectator during CO₂ electroreduction at low overpotentials. Additionally, the CH₂ intermediate can be also produced with a low barrier of ca. 0.35 eV at low overpotentials by further hydrogenation of the CH species formed by CHOH hydrogenative dissociation. Subsequently, the final CH₄ product can be formed by CH₂ serial hydrogenation, in which almost identical barriers of ca. 0.32 and 1.30 eV need to be overcome for CH₂ hydrogenation into CH₃ and then CH₄ at the overpotentials of 0.13 and 0.37 V, respectively, as shown in Fig. S7 (ESI†). Almost identical barriers for CH serial hydrogenation into CH₄ are also obtained at low overpotentials based on the electrochemical model proposed by Asthagiri et al.²⁰ Thus, the present results suggest that the barriers for CH serial hydrogenation into CH₄ will be almost not affected in the range of low overpotentials. The corresponding energies of various possible elementary steps during CO₂ electroreduction into CH₄ and CH₃OH on Cu(111) under conditions of low overpotentials are listed in Tables S1 and S2 (ESI†). Based on the energetics, the presently defined CH₂O and CHOH pathways on Cu(111) may be able to be proposed at low overpotentials, as can be seen in Fig. 2 and 3.

Fig. 2 The overall energy diagram of CO electroreduction into CH₄ and CH₃OH on Cu(111) at the low overpotential of 0.13 V: (a) CH₂O pathway; (b) CHOH pathway.

Fig. 3 The overall energy diagram of CO electroreduction into CH₄ and CH₃OH on Cu(111) at the low overpotential of 0.37 V: (a) CH₂O pathway; (b) CHOH pathway.

3.2.2 Conditions of high overpotentials. The calculated equilibrium potential is ca. −0.50 V (vs. RHE) when the coverage of CO is 3/9 ML, which is comparable with the experimental values of ca. −0.70 to −0.35 V (vs. RHE) in the range of pH = 1–7 for CO₂ electroreduction into the CH₄ product²² and corresponds to the conditions of a high overpotential of ca. 0.80 V compared with the thermodynamically required equilibrium potential of 0.27 V (vs. RHE) when θ_CO is close to zero. The various possible elementary steps during CO₂ electroreduction on Cu(111) are considered under conditions of high overpotential. Beginning with adsorbed CO, the calculated activation barriers are 0.51 and 1.29 eV for CHO and COH formation through surface hydrogenation, respectively, as can be seen in Fig. S8 (ESI†). Thus, intermediate CHO is still more facile to form than COH even if under conditions of high overpotentials, which is very much consistent with some previously reported studies on more favorable CHO formation over COH on Cu(111).^8,9,47,48 Previously, barriers for CHO formation were also calculated at relatively higher overpotentials by several other groups. For instance, Asthagiri et al. and Skúlason et al. reported a reaction barrier of ca. 0.61 and 0.57 eV by using the respective electrochemical model at an applied potential of ca. −0.70 V (vs. RHE), respectively.^20,28,29 The excellent agreement for the barriers of CHO formation between our present and previous calculations confirms the rationality of our used theoretical model. However, the opposite conclusion also existed in some other theoretical studies,^15,20,28 namely, COH formation may occur more easily during CO electroreduction at an applied potential of ca. −0.60 V (vs. RHE). The difference in the employed solvation models may lead to the significant inconsistencies; only a single H₂O molecule and fixed H₂O bilayer structure were used in some earlier electrochemical models, being insufficient to describe and capture the solvent effect. CHO can form intermediates CH₂O and CHOH through further electroreduction at its C- and O-center on Cu(111) and the corresponding barriers are 0.17 and 0.09 eV at the high overpotential, respectively, as shown in Fig. S9 (ESI†). Our calculated results suggest that the formation of both of these intermediates may be favorable due to extremely low barriers. Previously, an activation barrier of ca. 0.20 eV was calculated for CH₂O formation at an applied potential of ca. −0.60 V based on the H₂O-solvated model proposed by Asthagiri et al, and a barrier of ca. 0.10 eV was obtained for CHOH formation at an applied potential of ca. −0.90 V.²⁰ Thus, our calculated barriers for CHO hydrogenation into CH₂O and CHOH are also in good agreement with previous theoretical results under conditions of high overpotentials. Compared with conditions of low overpotentials, we note that increased overpotentials can lower significantly the activation barriers for CHO formation and further electroreduction on Cu(111), suggesting that the influence of the overpotential is significant in lowing the reaction barriers. Furthermore, surmountable barriers (≤0.40 eV) at room temperature for formation of CHO can be obtained when an applied potential of ca. −1.15 V (vs. RHE) is used based on the study from Asthagiri et al.,²⁰ thus explaining why a high overpotential is required during CO₂ electroreduction in experiments on Cu electrodes.^3–6

Once CH₂O is formed, the further hydrogenation of CH₂O into CH₃O occurs more easily with a barrier of ca. 0.29 eV compared to that into CH₂OH with a barrier of ca. 0.54 eV on Cu(111) under conditions of high overpotentials (see Fig. S10, ESI†). In fact, based on the electrochemical model previously proposed by Asthagiri et al.,²⁰ activation barriers of ca. 0.25 and 0.60 eV for CH₃O and CH₂OH formation on Cu(111) at an applied potential of ca. −0.80 V (vs. RHE) can be obtained, respectively. Thus, the results calculated by using our present and previous electrochemical models show that CH₃O formation is more favorable during further CH₂O electroreduction on Cu(111) at high overpotentials. However, CH₂OH may be able to be easily formed by further CHOH hydrogenation with a surmountable barrier of ca. 0.24 eV at room temperature at high overpotentials, as shown in Fig. S11 (ESI†). Furthermore, we find that the barrier for further CHOH electroreduction into the CH₂OH species is considerably decreased on Cu(111) compared with that at low overpotentials, again indicating that the effect of the overpotential on the barriers is significant. A barrier of ca. 0.29 eV is required for CHOH hydrogenative dissociation into the CH species along with H₂O formation at high overpotentials, which is almost identical to CHOH hydrogenation into CH₂OH (see Fig. S11, ESI†), suggesting that intermediates CH₂OH and CH may be able to be formed simultaneously through further CHOH electroreduction. Due to more favorable formation of CH₃O and CH₂OH at high overpotentials, CH₃OH may be able to be produced by further CH₃O and CH₂OH hydrogenation with surmountable barriers of ca. 0.01 and 0.40 eV at room temperature, respectively. Moreover, hydrogenative dissociation of CH₂OH into CH₂ and H₂O needs to overcome a higher barrier of ca. 0.56 eV than into CH₃OH, as shown in Fig. S12 (ESI†). Compared with those under conditions of low overpotentials, the barriers of CH₃OH production are considerably reduced, suggesting that CH₃OH formation may be kinetically favorable at high overpotentials. Intermediate CH₂ may be also able to be formed by CH direct hydrogenation. The calculated barrier is 0.36 eV under conditions of high overpotentials, which is lower than that of CH₂ formation through CH₂OH hydrogenative dissociation, showing that the CH₂ species is mainly formed by CH direct hydrogenation. Finally, the product CH₄ can be formed by CH₂ serial hydrogenation, in which barriers of ca. 0.44 and 0.01 eV need to be overcome for CH₂ hydrogenation into CH₃ and then its further hydrogenation into the CH₄ product at high overpotentials (see Fig. S13, ESI†), respectively. We note that the hydrogenation barriers for CH into CH₂ and then CH₃ will be almost not affected with increasing overpotential. However, compared with that under conditions of low overpotentials, the barrier for CH₃ hydrogenation into CH₄ is considerably reduced to barrierless at high overpotentials. In fact, based on the electrochemical model from Asthagiri et al.,²⁰ the hydrogenation barrier of CH₃ to CH₄ on Cu(111) also goes from ca. 0.90 eV at low overpotentials to barrierless at high overpotentials, confirming the rationality of the presently proposed electrode/aqueous interface model. The energies of the various possible elementary steps during CO₂ electroreduction into CH₄ and CH₃OH on Cu(111) under conditions of high overpotentials are listed in Table S3 (ESI†). The corresponding CH₂O and CHOH pathways on Cu(111) are given in Fig. 4.

Fig. 4 The overall energy diagram of CO electroreduction into CH₄ and CH₃OH on Cu(111) at the high overpotential of ca. 0.80 V: (a) CH₂O pathway; (b) CHOH pathway.

3.2.3 Effect of the overpotential on the CO reduction pathways. By scrutinizing the overall energy diagrams, it is observed that the reaction energy for CH₄ formation through CO electroreduction is ca. −2.10 eV under conditions of low overpotentials (see Fig. 3 and 4), which is a strongly exothermic process with a significantly more negative reaction energy than that of CH₃OH formation (ca. −0.80 eV). Furthermore, CH₃OH formation kinetically requires higher barriers than the formation of the CH₂ species that can lead to CH₄ production at low overpotentials. The results suggest that the CH₄ product is more facile to form than CH₃OH on Cu(111) in the range of low overpotentials, confirming the experimental observations of CH₄ formation over CH₃OH on the Cu surface during CO₂ electroreduction.¹¹ The corresponding reaction energies for CH₄ and CH₃OH formation are ca. −3.55 and −2.25 eV under conditions of high overpotentials (see Fig. 4), respectively, seeming to show that CH₄ formation is still more favorable at high overpotentials. However, it is noted that the CH₃OH formation pathway is also strongly exothermic at high overpotentials with a significantly more negative reaction energy than that at low overpotentials. Moreover, further CH₂OH electroreduction into CH₃OH occurs kinetically more and more easily with increasing overpotential and the required barrier is 0.36, 0.34 and 0.01 eV at overpotentials of ca. 0.13, 0.37 and 0.80 V, respectively. In particular, compared with the barrier of ca. 0.70 eV for further CH₃O electroreduction into CH₃OH at low overpotentials, the corresponding barrier is notably reduced to a surmountable value of ca. 0.40 eV at room temperature under conditions of high overpotentials. Simultaneously, it is also observed that further CH₂OH electroreduction into key intermediate CH₂ requires higher and higher barriers with increasing overpotential and the corresponding barrier is 0.07, 0.31 and 0.56 eV at overpotentials of ca. 0.13, 0.37 and 0.80 V, respectively. At the high overpotential of ca. 0.80 V, the CH₂ formation barrier notably exceeds that of CH₃OH formation through further CH₂OH electroreduction. Thus, we can speculate that CH₃OH production may be competitive with CH₄ production on Cu(111) in the range of high overpotentials. In fact, CH₃OH production had been also detected at relatively higher overpotentials in some previous electrochemical experiments during CO₂ electroreduction into hydrocarbons on Cu electrodes.^12,49,50

By comprehensive consideration of the overall energy diagrams during CO₂ electroreduction into the CH₄ product at the overpotentials of ca. 0.13 and 0.37 V (see Fig. 4 and 5), we speculate that the presently defined CH₂O pathway can occur through the CHO, CH₂O, CH₂OH and CH_x (x = 2–4) species in the range of low overpotentials with barriers of ca. 1.10 and 0.88 eV, respectively. Considering that there are two possibilities for further CHOH electroreduction into CH₄, the overall energy diagrams are scrutinized in the CHOH pathways. It is found that the CHOH pathway can parallelly occur through CHOH electroreduction into the CH and CH₂OH species due to almost identical barriers of ca. 1.10 eV at the overpotential of ca. 0.13 V, whereas it may be only able to take place through CHOH electroreduction into the CH species due to the lower required barrier than that of CHOH electroreduction into CH₂OH (1.00 eV vs. 1.22 eV) at the relatively higher overpotential of 0.37 V. In the meantime, we note that the presently defined CH₂O and CHOH pathways may be able to parallelly occur due to the subtle difference in the barriers in the range of low overpotentials. However, higher overpotentials will facilitate CO₂ electroreduction based on the above difference in the barriers. The optimal CO electroreduction pathways on Cu(111) can be proposed under conditions of low overpotential by the above analysis, as can be seen in Fig. 5.

Fig. 5 The optimal CO electroreduction mechanisms on Cu(111) under conditions of low and high overpotentials: (a) CH₂O pathway; (b) CHOH pathway through CHOH electroreduction into CH and CH₂OH; (c) CHOH pathway through CHOH electroreduction into CH.

To further determine the effect of the overpotential on CO₂ electroreduction into the CH₄ product, the overall energy diagrams at the higher overpotential of ca. 0.80 V are scrutinized (see Fig. 5). The CH₂O pathway can occur through the CHO, CH₂O, CH₂OH and CH_x (x = 2–4) species at high overpotentials with barriers of ca. 0.51 eV. In the CHOH pathways, two possibilities via further electroreduction of the CHOH species into CH along with H₂O formation and the CH₂OH species may be able to parallelly occur due to the identical barriers of ca. 0.51 eV. Thus, it is also speculated that the CH₂O and CHOH pathways can parallelly occur and the optimal CO electroreduction pathways on Cu(111) can be proposed at high overpotentials, as shown in Fig. 5. The present results are found to be in excellent agreement with the available experimental data. For example, Dewulf et al. presented that adsorbed CHO and CH₂ species are crucial intermediates for CH₄ formation at Cu electrodes using in situ X-ray photoelectron spectroscopy and Auger electron spectroscopy during electroreduction of CO₂,⁵ and the most recent experiment from Koper et al. studied CO₂ electroreduction into CH₄ on two basal planes, Cu(111) and Cu(100), using online electrochemical mass spectrometry, in which the electrochemical reduction of the various species can be measured online when the electrode potentials are changed by the tip-based sampling technique and the formation and consumption of intermediates during CO₂ reduction can be followed, and showed that CHO is possibly the key intermediate toward the formation of the CH₂ and CH₃ species and CH₄ product through the cleavage of the C–O bond,^7,14 further validating the rationality of the presently employed methodology. However, the presence of high overpotentials notably reduces the barriers of the overall energy pathway. Simultaneously, it is observed that CH₄ formation via further CH₃ electroreduction requires a high barrier of ca. 1.40 eV at low overpotentials, whereas it is an almost barrierless process (ca. 0.01 eV) under conditions of high overpotentials. Thus, the present results can conclude that high overpotentials will be in favor of CO₂ electroreduction into CH₄, again explaining why a high overpotential is required during CO₂ electroreduction into hydrocarbons in experiments on Cu electrodes.^3–6

Additionally, we observed that an extremely low barrier of ca. 0.20 eV is required for the inverse process of further CO electroreduction into CHO, which is lower than that of further CHO electroreduction under conditions of low overpotentials. Thus, it can be speculated that intermediate CHO may be not stable in the range of low overpotentials, and can easily transform back to CO by C–H bond cleavage, leading to not easy formation of key intermediate CHO and preventing CO₂ electroreduction on Cu electrodes. However, the barrier for the inverse process of further CO electroreduction into CHO is increased to ca. 0.39 eV at the high overpotential of ca. 0.80 V, which is notably higher than that of further CHO electroreduction (ca. 0.10 eV). Simultaneously, the barrier for further CO electroreduction into CHO is also significantly lowered at high overpotentials. Thus, we can speculate that the potential-limiting step may be further CO electroreduction into CHO during CO₂ electroreduction into the CH₄ product, which is considered as the origin of the observed experimentally high overpotentials. In fact, the previous experiments from Hori et al. and Frese et al. also showed that adsorbed CO electroreduction is the key rate-determining step for the overall reduction reaction of CO₂ into hydrocarbons.^11,35 Thus, the present finding on the potential-limiting step is also in excellent agreement with the available experimental data.

To further determine the origin of the overpotential, partial density of states (PDOS) analyses of an adsorbed CO molecule that can be further electrochemically reduced into hydrocarbons are performed on Cu(111) with different surface CO coverages in the present study since it can describe the number of electronic states near the Fermi energy level that are available to be occupied, as shown in Fig. 6. A high intensity of the PDOS near the Fermi energy level means high localization of electrons. For comparison, the PDOS of free CO is also included. As can be seen in Fig. 6(a) and (c), almost no obvious peaks exist in the PDOS of s orbitals of C and O atoms of adsorbed CO compared with that of the free CO molecule near the Fermi level, suggesting that maybe no significant electron transfer occurs into the s state of adsorbed CO. However, obvious peaks are observed in the p orbitals of C and O atoms near the Fermi level (ca. 0–3 eV), as shown in Fig. 6(b) and (d), indicating that electrons from the surface and electrochemical interfaces are transferred into π antibonding orbitals of the adsorbed CO molecule. Thus, an adsorbed CO^δ− species is formed on Cu(111), validating the previous experimental speculations on electron transfer between CO and Cu electrodes.^5,11 To ascertain the effect of the CO coverage on electron transfer, the PDOS of p orbitals near the Fermi level in Fig. 6 is amplified, as can be seen in Fig. 7. The calculated value of the Fermi level is ca. 3.45, 3.49, 3.72 and 3.79 eV in the present research range of CO coverage, respectively, which gradually increases with increasing CO coverage. Furthermore, it is clearly observed that the intensity of the peaks becomes larger and larger with increasing CO coverage, indicating more and more electron transfer into π antibonding orbitals of the adsorbed CO molecule and higher and higher localization of electrons around C and O atoms. The higher peak intensities of π antibonding orbitals near the Fermi level (ca. 0–3 eV) indicate weaker CO bonding with the Cu surface, as can be confirmed by the calculated less and less negative CO adsorption energies of −2.86, −1.15, −0.76 and −0.59 eV with increasing surface CO coverage at the presently simulated electrochemical interfaces, suggesting that higher overpotentials will reduce the CO adsorption strength. Thus, the abovementioned significantly lower activation barrier of further CO electroreduction into CHO on Cu(111) at higher overpotential can be correlated with lower CO adsorption energy. Simultaneously, higher peak intensities in the PDOS of p orbitals of C atoms are observed compared to those of O atoms (see Fig. 7), suggesting greater localization of electrons around C atoms, which will be further confirmed by the following Löwdin population analysis.

Fig. 6 Local density of states of free and adsorbed CO on the Cu(111) surface with different CO coverages: (a) s orbital of C; (b) p orbital of C; (c) s orbital of O; (d) p orbital of O. The Fermi level is zero.

Fig. 7 The amplified local density of states of an adsorbed CO molecule that can be further electrochemically reduced into hydrocarbons on Cu(111) with different surface CO coverages: (a) p orbital of C; (b) p orbital of O. The Fermi level is zero.

The quantative analysis of electronic structures will facilitate the further understanding of the origin of the overpotentials and the effect of surface CO coverage on electron transfer during CO₂ electroreduction. The Löwdin charge of an adsorbed CO molecule that can be further electrochemically reduced into hydrocarbons on Cu(111) with different surface CO coverages can be obtained from Löwdin population analysis based on the projected electron densities of states. As shown in Table 1, the net electron gains of the p orbitals of the C and O atoms in the adsorbed CO molecule that can be further electrochemically reduced into hydrocarbons gradually increased with increasing surface CO coverage, which are filled into π antibonding orbitals based on the above PDOS analysis. Furthermore, the total net electron gain of adsorbed CO also gradually increased, indicating that the net electron gain of the s orbital is negligible and further conforming the results obtained by the above PDOS analysis. Interestingly, it is noted that the C atom obtains more electrons than the O atom in the adsorbed CO molecule, which quantatively confirms the abovementioned greater localization of electrons around C atoms and explains why the hydrated proton tends to reach the C atom to form intermediate CHO rather than COH as indicated in the above MEP analysis. Simultaneously, the greater and greater electron transfer into the π antibonding orbitals of the adsorbed CO molecule with increasing CO coverage may lead to increasing overpotential and easier and easier occurrence of further CO electroreduction.

Table 1 The electron gains (Δq) of the C and O atoms in adsorbed CO that can be further electrochemically reduced on Cu(111) with different surface CO coverages compared with the free CO molecule

	Difference of electron/atom (Δq)^a
	Orbital	1CO	2CO	3CO	4CO
a Positive values of Δq imply an electron gain by the component.
C	s	−0.2467	−0.2363	−0.2356	−0.2308
	p	+0.7740	+0.7809	+0.7833	+0.8039
	Total	+0.5237	+0.5446	+0.5477	+0.5730
O	s	+0.0208	+0.0192	+0.0169	+0.0179
	p	+0.0452	+0.0619	+0.0778	+0.0920
	Total	+0.0660	+0.0811	+0.0947	+0.1099

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4. Conclusions

In this paper, a recently proposed CO coverage-dependent electrochemical model combined with the calculation of electronic structure is used for the first time to study the effect of the overpotential on Cu-catalyzed CO electroreduction mechanisms by changing the coverage of surface adsorbed CO. The results show that the presently defined CH₂O and CHOH pathways may be able to parallelly occur at the presently simulated low and high overpotentials based on the analyses of potential-dependent energetics at electrode/aqueous interfaces. However, high overpotentials will be in favor of CO electroreduction into CH₄ due to the notably reduced kinetic barrier of the overall energy pathway, thus explaining why a high overpotential is required during CO₂ electroreduction into hydrocarbons in experiments on Cu electrodes. The potential-limiting step may be further CO electroreduction into CHO during CO₂ electroreduction by analyzing the potential-dependent energetics for the inverse process of CO electroreduction into CHO and further CHO electroreduction, which is considered as the origin of the experimentally observed high overpotentials. The present studies also suggest that CH₄ may be more facile to form than CH₃OH on Cu(111) in the range of low overpotentials, whereas the CH₃OH product may be able to be formed along with the CH₄ product at high overpotentials. Based on the analysis of electronic structure, an adsorbed CO^δ− species is formed on Cu(111), validating the previous experimental speculations on electron transfer between CO and Cu electrodes. Moreover, more and more electrons are transferred into the π antibonding orbitals of the adsorbed CO molecule with increasing surface CO coverage, leading to increasing overpotential and weaker and weaker CO bonding with the Cu surface. Thus, the significant lower activation barrier of further CO electroreduction into CHO on Cu electrodes at higher overpotential can be correlated with lower CO adsorption energy. Interestingly, it is found that there is greater localization of electrons around the C than the O atom in the adsorbed CO molecule, explaining why the hydrated proton prefers to reach the C atom to form intermediate CHO rather than COH. The excellent consistencies between our predicted pathways and the available experimental and partial theoretical data confirm the reasonability of the presently employed electrode/aqueous interface model.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Natural Science Foundation of Hunan Province (Grant No. 2018JJ2273); the Outstanding Youth Foundation of Education Department of Hunan Province (Grant No. 16B178) and the National Natural Science Foundation of China (Grant No. 21303048).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9cp05043d

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