The importance of grand-canonical quantum mechanical methods to describe the effect of electrode potential on the stability of intermediates involved in both electrochemical CO₂ reduction and hydrogen evolution

The rational design of electrocatalysts to convert CO₂ to fuel requires predicting the effect of the electrode potential (U) on the binding and structures of the intermediates involved in CO₂ electrochemical reduction (CO₂ER). In this study, we used grand-canonical quantum mechanics (GC-QM) to keep the potential constant during the reactions (rather than keeping the charge constant as in standard QM) to investigate the effect of U on adsorption free energies (DGs) of 14 CO₂ER intermediates on Cu(111) as well as the intermediates involved in the competitive hydrogen evolution reaction (HER). In contrast to most previous theoretical studies where DGs were calculated under constant charge (= 0, neutral), we calculated DGs under constant potential (U = 0.0, -0.5, -1.0, and -1.5 V_SHE). By comparing the DGs calculated under constant U (= 0.0 V_SHE) to those calculated under constant charge, we found differences up to 0.22 eV which would change the rates at 298 K by a factor of about 5300. In particular we found that the adsorption of species with a CQO functional group (i.e., *COOH, *CO, and *CHO) strengthened by up to 0.16 eV as U became more negative by 1 V, whereas the adsorption of -O- species (i.e., *OH, *OCH₃, *COH, and *CHOH) weakened by up to 0.20 eV. For the (111) index surfaces of Cu, Au, Ag, Ir, Ni, Pd, Pt and Rh, we investigated the effect of U on the reaction free energy (DG) at pH = 0 for the crucial elementary steps for CO₂ER (*CO + (H⁺/e-) - *CHO, DG = (DG_*CHO - DG_*CO) + eU) and HER (* + (H⁺/e-) - *H, DG = DG_*H + eU. Our results indicated that the influence of U on (DG_*CHO - DG_*CO) was metal dependent. In contrast, the energy for converting a proton in solution to H* on the surface, DG_*H, was barely affected by U (for the studied metals). Overall we found substantial differences (MAD 4 0.18 eV) between the DGs calculated under U = -1.0 V_SHE (relevant to experiments) and those calculated under constant charge (= 0, neutral) common to most theoretical investigations. Therefore, we strongly recommend application GC-QM to obtain accurate energetics for CO₂ER.