The importance of grand-canonical quantum mechanical methods to describe the effect of electrode potential on the stability of intermediates involved in both electrochemical CO_2 reduction and hydrogen evolution

The rational design of electrocatalysts to convert CO_2 to fuel requires predicting the effect of the electrode potential (U) on the binding and structures of the intermediates involved in CO_2 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 Uon adsorption free energies (ΔGs) of 14 CO_2ER 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 ΔGs were calculated under constant charge (= 0, neutral), we calculated ΔGs under constant potential (U = 0.0, −0.5, −1.0, and −1.5 V_(SHE)). By comparing the ΔGs 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 C O 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 (ΔG) at pH = 0 for the crucial elementary steps for CO_2ER (*CO + (H+/e−) → *CHO, ΔG = (ΔG_(*CHO) – ΔG_(*CO)) + eU) and HER (* + (H+/e−) → *H, ΔG = ΔG_(*H) + eU. Our results indicated that the influence of U on (ΔG_(*CHO) – ΔG_(*CO)) was metal dependent. In contrast, the energy for converting a proton in solution to H* on the surface, ΔG_(*H), was barely affected by U(for the studied metals). Overall we found substantial differences (MAD > 0.18 eV) between the ΔGs 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 CO_2ER.