On the basis of constraints from reported experimental observations and density functional theory simulations, we propose a mechanism for the reduction of CO2 to C2 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 C2 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 C2 products between the (100) and (111) facets of copper. We compare our methodologies and findings with those in other recent mechanistic studies of the copper-catalyzed CO2 reduction reaction.