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Theoretical Insights into Potential-Dependent C–C Bond Formation Mechanisms during CO2 Electroreduction into C2 Products on Cu(100) at Simulated Electrochemical Interfaces

An improved CO coverage-dependent electrochemical interface model with an explicit solvent effect on Cu(100) is presented in this paper, by which theoretical insights into the potential-dependent C–C bond formation pathways occurring in CO2 electrochemical reduction to C2 products can be obtained. Our present studies indicate that CHO is a crucial intermediate toward C1 products on Cu(111), and dimer OCCO is found to not be a viable species for the production of C2 products on Cu(100). The reaction pathway of CHO with CO and CHO dimerization into dimers COCHO and CHOCHO may be C–C bond formation mechanisms at low overpotential. However, at medium overpotential, C–C bond coupling takes place preferentially through the reaction of COH with CO species and COH dimerization into dimers COCOH and COHCOH. The formed dimers COCHO, CHOCOH, and CHOCHO via reactions of CHO with CO, COH, and CHO species may lead to C2 products, which are regarded as C–C bond formation mechanisms at high overpotential. The difference of obtained adsorption isotherms of CO on Cu(100) with that of Cu(111) may be able to explain the effect of the crystal face of Cu on product selectivity. The excellent consistencies between our present obtained conclusions and the available experimental reports and partial theoretical studies validate the reasonability of the present employed methodology, which can be also used to systematically study potential-dependent CO2 electroreduction pathways toward C2 products on Cu(100) or other metal catalysts.


Surface and Solvation Model
Considering the complexity of real CO 2 electroreduction systems, the aqueous-phase environment is included in the present study, in which 12 explicit H 2 O molecules with two relaxed bilayer structures chosen to fill up the vacuum region were used to model the solvation effect in order to better simulate the interactions between solvent and adsorbates and decrease the size of the simulated systems as much as possible. In fact, the formation of an ordered H 2 O bilayer structure in a hexagonal arrangement with 2/3 monolayer saturation coverage with respect to the surface normal had been demonstrated by X-ray absorption spectroscopy, thermal desorption spectroscopy, low-energy electron diffraction, X-ray photoelectron spectroscopy and scanning electron microscopy along with DFT calculations in previous experimental and theoretical studies on the meal surface. [1][2][3] Our present solvation model is on the basis of the previous studies on structure and orientation of H 2 O. However, many different H 2 O solvation structures may also exist, which all are approximate in energy. 4 Since all energies of interest in this study are energy differences, which are not sensitive to the accurate model of H 2  used and a reasonable model in a local minimum structure is choose when calculating the energy differences.
Considering the coverage is 2/3 of H 2 O monolayer, thus, a (3x3) Cu(100) slab model with nine metal atoms per layer and theoretical equilibrium lattice constant of 3.66 Ǻ by using four metal layers was created.

Computational Parameters
Using the generalized gradient approximation of the Perdew-Burke-Ernzerhof exchange correlation functional, calculations were performed in the framework of DFT. 5 Ultrasoft pseudopotentials were employed to describe the nuclei and core electrons and the Kohn-Sam equations were self-consistently solved using a plane-wave basis set. 6 A kinetic energy cutoff of 30 Ry and a charge-density cutoff of 300 Ry were used to make the basis set finite. The Fermi surface has been treated by the smearing technique of Methfessel-Paxton with a smearing parameter of 0.02 Ry. 7 The PWSCF codes in Quantum ESPRESSO distribution were employed to perform all calculations. 8 Brillouin-zone integrations were implemented using a (3×3×1) uniformly shifted k-mesh for (3×3) supercell with the special-point technique, which was tested to converge to a subset of the relative energies reported herein. A vacuum layer of 16Å was placed above the top layer of slab, which is sufficiently large to ensure that the interactions are negligible between repeated slabs in a direct normal to the surface. The Cu atoms in the bottom two layers are fixed at the theoretical bulk positions, whereas the top two layers and all adsorbates including solvent are allowed to relax to minimize the total energy of the system. Structural optimization was performed until the Cartesian force components acting on each atom were brought below 10 -3 Ry/Bohr and the total energy was converged to within 10 -5 Ry.
Using the climbing image nudged elastic band (CI-NEB) method, the saddle points and minimum energy paths (MEPs) were located by initially setting initial state and final state. 9, 10 Zero point energy (ZPE) corrections were applied into the calculations of the activation and reaction energies from MEP analysis, in which density functional perturbation theory within the linear response was used to study the vibrational properties. 11 The ZPEs were calculated using the PHONONS code that contained in the Quantum ESPRESSO distribution. 8

CO Coverage-Dependent Electrode/Solution Interface Model
We have reported the methodology for CO coverage-dependent equilibrium potentials on Cu(111) in our recent work, 12 which was used to model reduction pathways of CO 2 into CH 4 products at the low overpotentials. In this paper, the corresponding method is again employed to study the potential-dependent S3 C-C bond formation mechanisms on Cu(100). As abovementioned, CO had been identified as a key intermediate during CO 2 reduction, which can be formed by following reaction (S1): (S1) can be calculated according to equation (S3) by differentiating the plots of against , ( ) Considering that the entropies of the adsorbed molecules are small when compared with the entropies of gaseous and that the zero-point energy of the surface adsorbed CO molecules is little according to our calculations, the contributions from the changes of entropy and ZPE together to has been estimated ( ) G   to be -0.42 eV for standard temperature (298 K) based on the available data from Nørskov et al. 18 Combining equation (S2) with (S3), we can obtain the following form of equation (S4). Accordingly, the CO coverage-dependent equilibrium potential U (vs. RHE) can be determined when is equal to zero. ( )

 CO
The Relationship between E() and  CO
S6 Figure S4. The geometries of CO electroreduction into COH species on Cu(111) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S5. The geometries of CO dimerization into OCCO species on Cu(111) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S6. The geometries of CO electroreduction into CHO species on Cu(111) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state).

Condition of Medium Overpotential (θ CO = 2/9 ML)
S7 Figure S7. The geometries of CO electroreduction into COH species on Cu(111) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S8. The geometries of CO dimerization into OCCO species on Cu(111) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S9. The geometries of CO electroreduction into CHO species on Cu(111) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state).

Condition of High Overpotential (θ CO = 1/3 ML)
S8 Figure S10. The geometries of CO electroreduction into COH species on Cu(111) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S11. The geometries of CO dimerization into OCCO species on Cu(111) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state).

Condition of Low Overpotential (θ CO = 1/9 ML)
Figure S12. The geometries of CO electroreduction into CHO species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state).
S9 Figure S13. The geometries of CO electroreduction into COH species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S14. The geometries of CO dimerization into OCCO species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state).

Condition of Medium Overpotential (θ CO = 2/9 ML)
Figure S15. The geometries of CO electroreduction into CHO species on Cu(100) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). S10 Figure S16. The geometries of CO electroreduction into COH species on Cu(100) at the medium overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S17. The geometries of CO dimerization into OCCO species on Cu(100) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S18. The geometries of CO electroreduction into CHO species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). S11 Figure S19. The geometries of CO electroreduction into COH species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S20. The geometries of CO dimerization into OCCO species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S21. The geometries of CHO electroreduction into CH 2 O species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). S12 Figure S22. The geometries of CHO electroreduction into CHOH species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S23. The geometries of dimerization of CHO with CO into COCHO species at the low overpotential (θ CO = 1/9 ML) on Cu(100) (IS represents initial state, TS represents transition state and FS represents final state). Figure S24. The geometries of CHO dimerization into CHOCHO species on Cu(100) at the low overpotential (θ CO = 1/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). S13 Figure S25. The geometries of COH electroreduction into CHOH species on Cu(100) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S26. The geometries of COH electroreduction into C species along with H 2 O on Cu(100) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S27. The geometries of dimerization of COH with CO into COCOH species at the medium overpotential (θ CO = 2/9 ML) on Cu(100) (IS represents initial state, TS represents transition state and FS represents final state). S14 Figure S28. The geometries of COH dimerization into COHCOH species on Cu(100) at the medium overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S29. The geometries of CHO electroreduction into CH 2 O species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S30. The geometries of CHO electroreduction into CHOH species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). S15 Figure S31. The geometries of dimerization of CHO with CO into COCHO species at the high overpotential (θ CO = 1/3 ML) on Cu(100) (IS represents initial state, TS represents transition state and FS represents final state). Figure S32. The geometries of CHO dimerization into CHOCHO species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S33. The geometries of dimerization of CHO with COH into CHOCOH species at the high overpotential (θ CO = 1/3 ML) on Cu(100) (IS represents initial state, TS represents transition state and FS represents final state). S16 Figure S34. The geometries of COH electroreduction into CHOH species on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S35. The geometries of COH electroreduction into C species along with H 2 O on Cu(100) at the high overpotential (θ CO = 1/3 ML) (IS represents initial state, TS represents transition state and FS represents final state). Figure S36. The geometries of dimerization of COH with CO into COCOH species at the high overpotential (θ CO = 1/3 ML) on Cu(100) (IS represents initial state, TS represents transition state and FS represents final state). S17 Figure S37. The geometries of COH dimerization into COHCOH species on Cu(100) at the high overpotential (θ CO = 2/9 ML) (IS represents initial state, TS represents transition state and FS represents final state).