Understanding trends in electrochemical carbon dioxide reduction rates

Electrochemical carbon dioxide reduction to fuels presents one of the great challenges in chemistry. Herein we present an understanding of trends in electrocatalytic activity for carbon dioxide reduction over different metal catalysts that rationalize a number of experimental observations including the selectivity with respect to the competing hydrogen evolution reaction. We also identify two design criteria for more active catalysts. The understanding is based on density functional theory calculations of activation energies for electrochemical carbon monoxide reduction as a basis for an electrochemical kinetic model of the process. We develop scaling relations relating transition state energies to the carbon monoxide adsorption energy and determine the optimal value of this descriptor to be very close to that of copper.


Supplementary Note 3: Scaling relations
The adsorption and transition state energies of reaction intermediates on surfaces often scale with the adsorption energies of a small number of adsorbates (typically one or two), due to trends in the underlying surface electronic structure 8 . In this work, the adsorption energies and transition state energies scale linearly with the adsorption energies of CO* on (211) surfaces according to the following equation: E ads/TS = γ × ∆E CO* + ε where the parameters γ and ε are fitted for each intermediate as a function of the binding energies of CO* with all energies being relative to CO, H 2 and H 2 O in the gas phase. The scaling parameters are depicted in Supplementary Figures 2 and 3.

Supplementary Note 4: Kinetics
We took a mean-field approach to microkinetic modelling, where the net rate of an elementary reaction mA ↔ nB was given by r = k + θ A m -kθ B n , where θ i represents the surface coverage of adsorbate i, k +/-represents the rate constants of the forward and backward reaction respectively 9 . The rate constants were calculated through the equation k = P×e -Ga/(kbT) , where P represents the reaction prefactor, G a represents the activation barrier, k b represents the Boltzmann constant and T represents the reaction temperature. Site coverages were modeled using the pseudo-steady state approximation (i.e. the rate of change of all surface intermediate coverages is 0) 9 . These assumptions were implemented in the CatMAP software package 10 , which was applied to solve the microkinetic model.
Lateral adsorbate-adsorbate interactions were modeled using a first-order expansion in the coverage for the differential adsorption energy: where E i (θ i ) is the differential adsorption energy of species i given a vector of coverages θ i , E i 0 is the differential adsorption energy of species i in the low-coverage limit, ϵ ij is a matrix of interaction parameters for the interaction between species i and j, f corresponds to a piecewiselinear function for the energy as a function of coverage. The H* coverage is excluded when calculating f to account for H* being much smaller than CO and therefore has little effect on determining the strength of the interactions. Further information on the interaction model is provided in the former work 11 . The adsorbate cross-interaction parameters were determined using DFT calculations of the adsorption energies of intermediates at high coverages on Pt(111), and were listed below. Convergence of the kinetic model was achieved by first converging the solution with no interactions and incrementally increasing the interaction strength to the fitted value.
Uncertainties associated with the exchange-correlation energies are provided by the BEEF-vdW ensemble. The uncertainty is propagated through the kinetic model by creating an ensemble of microkinetic models corresponding to the BEEF-vdW error estimation ensemble [12][13][14] . This approach ensures that correlations between energetic errors are properly accounted for. Uncertainties on relative rates were approximated by the standard deviation of relative rates and were converged with an ensemble of 500 microkinetic models.
In this simple model, CH 4 (g) was taken as an example of hydrocarbon/alcohol products, and H 2 (g) was included as the main side product. Accordingly the experimental polarization curves included all products further reduced from CO. Both proton-electron transfer and surface hydrogenation pathways were taken into account. The steps after forming CHO* were assumed to be barrierless as we have shown that all the successive steps have smaller barriers than CO* protonation to CHO* on Cu(211). Including the barriers of these steps did not alter the overall reaction rate. We have also shown that on Cu(211) the protonation barrier to form CHOH* from COH* is about 0.6 eV higher than that of forming CHO* from CO*. To get an upper limit of the performance of the COH pathway, we used the CO* to CHO* barrier to estimate the COH* protonation barrier on (211) surface. COH* protonation barriers on (111) surfaces were explicitly calculated. All the elementary steps are described as follows: where * represents a surface site. All the steps had prefactors of 10 13 based on harmonic transition state theory 9 .

Supplementary Note 5: Relative Rates of CO reduction and H 2 production
In Supplementary Figure 4, the rate relative to that of Cu(211) is shown as a function of CO* binding energy, along with the relative uncertainty determined through BEEF-vdW error estimation ensembles. Cu(211) remains to be close to the volcano peak even when uncertainties are accounted for.

Supplementary Note 6: *CO and *H coverages
Overall, *CO and *H predominated under CO reduction conditions. Supplementary Figure 5 shows the coverages of these species at -0.5 and -1.0 V vs. RHE.

Supplementary Note 7: Projected density of states at the transition state
In general, processes taking place at a metal surface are not limited by electron transfer 15 . This is illustrated in Supplementary Figure 6, which shows the projected density of states for the transition state of proton-electron transfer to CO, obtained using a very small smearing width of 0.01 eV and k-point grid of [20×20×1]. Since the width of the adsorbate-induced states is on the order of eV, the Heisenberg uncertainty principle suggests the rate of electron jumps between the adsorbate and metal surface to be more than 10 15 s -1.

Supplementary Note 8: Transition state configurations for molybdenum sulfide and Ni-
doped molybdenum sulfide From a thermodynamic perspective, MoS 2 type materials break the scaling between *CO and *CHO, since *CO binds to metal edge sites and *CHO the sulfur ones 16