We have carried out a periodic Kohn-Sham density functional theory investigation of the pathways by which carbon-carbon bonds could be formed during the electrochemical reduction of CO2 on Cu(100) using a model that includes the effects of the electrochemical potential, solvent, and electrolyte. The electrochemical potential was set by relating the applied potential to the Fermi energy and then calculating the number of electrons required by the simulation cell for that specific Fermi energy. The solvent was included as a continuum dielectric, and the electrolyte was described using a linearized Poisson-Boltzmann model. The calculated potential of zero charge for a variety of surfaces agrees with experiment to within a mean average error of 0.09 V, thereby validating the assumptions of the model. Analysis of the mechanism for C-C bond formation revealed that at low-applied potential, C-C bond formation occurs through a CO dimer. However, at high applied potentials, a large activation barrier blocks this pathway; therefore, C-C bond formation occurs through reaction of adsorbed CHO and CO. Rate parameters determined from our calculations were used to simulate the kinetics of ethene formation during the electrochemical reduction of CO over a Cu(100) surface. An excellent match was observed between previously reported measurements of the partial current for ethene formation as a function of applied voltage and the variation in the partial current for C-C bond formation predicted by our microkinetic model. The electrochemical model reported here is simple, fairly easy to implement, and involves only a small increase in computational cost over calculations neglecting the effects of the electrolyte and the applied field. Therefore, it can be used to study the effects of applied potential and electrolyte composition on the energetics of surface reactions for a wide variety of electrochemical reactions.

Density functional theory (DFT) provides a formally exact framework for quantum embedding. The appearance of nonadditive kinetic energy contributions in this context poses significant challenges, but using optimized effective potential (OEP) methods, various groups have devised DFT-in-DFT methods that are equivalent to Kohn–Sham (KS) theory on the whole system. This being the case, we note that a very considerable simplification arises from doing KS theory instead. We then describe embedding schemes that enforce Pauli exclusion via a projection technique, completely avoiding numerically demanding OEP calculations. Illustrative applications are presented using DFT-in-DFT, wave-function-in-DFT, and wave-function-in-Hartree–Fock embedding, and using an embedded many-body expansion.

Electrochemical reduction of CO using renewable sources of electrical energy holds promise for converting CO to fuels and chemicals. Since this process is complex and involves a large number of species and physical phenomena, a comprehensive understanding of the factors controlling product distribution is required. While the most plausible reaction pathway is usually identified from quantum-chemical calculation of the lowest free-energy pathway, this approach can be misleading when coverages of adsorbed species determined for alternative mechanism differ significantly, since elementary reaction rates depend on the product of the rate coefficient and the coverage of species involved in the reaction. Moreover, cathode polarization can influence the kinetics of CO reduction. Here, we present a multiscale framework for ab initio simulation of the electrochemical reduction of CO over an Ag(110) surface. A continuum model for species transport is combined with a microkinetic model for the cathode reaction dynamics. Free energies of activation for all elementary reactions are determined from density functional theory calculations. Using this approach, three alternative mechanisms for CO reduction were examined. The rate-limiting step in each mechanism is **COOH formation at higher negative potentials. However, only via the multiscale simulation was it possible to identify the mechanism that leads to a dependence of the rate of CO formation on the partial pressure of CO that is consistent with experiments. Simulations based on this mechanism also describe the dependence of the H and CO current densities on cathode voltage that are in strikingly good agreement with experimental observation.