On the basis of constraints from reported experimental observations and density functional theory simulations, in this paper we propose a mechanism for the reduction of CO<sub>2</sub> to C<sub>2</sub> products on copper electrodes. To model the effects of an applied potential bias on the reactions, calculations are carried out with a variable, fractional number of electrons on the unit cell, which is optimized so that the Fermi level matches the actual chemical potential of electrons (i.e., the applied bias); an implicit electrolyte model allows for compensation of the surface charge so that neutrality is maintained in the overall simulation cell. Our mechanism explains the presence of the seven C<sub>2</sub> species that have been detected in the reaction, as well as other notable experimental observations. Furthermore, our results shed light on the difference in activities toward C<sub>2</sub> products between the (100) and (111) facets of copper. Finally, we compare our methodologies and findings with those in other recent mechanistic studies of the copper-catalyzed CO<sub>2</sub> reduction reaction.
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