CO2 Electrocatalyst Design Using Graph Theory

doi:10.21203/rs.3.rs-66715/v1

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CO₂ Electrocatalyst Design Using Graph Theory

https://doi.org/10.21203/rs.3.rs-66715/v1

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The electrochemical reduction of CO₂ (CO₂RR) to higher-order hydrocarbons or oxygenates using low-carbon electricity offers a promising path to generate renewable fuels and chemicals; however, the low selectivity of present-day CO₂RR catalysts toward more valuable C₃ products limits technoeconomically compelling avenues toward productization. Systematically enumerating possible intermediates and reactions to the set of possible {C₁, C₂, and C₃} CO₂RR products entails 3206 intermediates and 4506 reactions. Here we use graph theory to enumerate these possibilities comprehensively, treating intermediates as graph nodes and pathways as graph edges. C₃ products fall into two groups, group A (1-propanol, allyl alcohol, and propionaldehyde) and group B (acetone and hydroxyacetone); and we find that an early branch reaction, three steps after C₁-C₂ coupling, bifurcates these two groups of C₃ products. We develop a set of C₃ descriptors and screen catalysts for CO2RR to C₃products: specifically, we screen bimetallic (doped Cu) catalysts for their combination of CO binding, C₁-C₁ coupling and C₁-C₂ coupling. Cu and also Au- and Ag-doped Cu fulfill the first two requirements; but the set of promising C₁-C₂ coupling catalysts (Ni-doped Pb and Al-doped Pb) needed to get to C₃ is nonoverlapping with that for CO binding and C₁-C₁ coupling. Our findings agree with the experimental picture that Cu, while among the most productive to propanol, has been limited in F.E. to the 10-20% range; and that, to date, no single catalyst has achieved exceptional C₃ productivity. We discuss tandem catalyst designs where a first catalyst promotes CO binding and C₁-C₁, and where these C₂ and C₁ intermediates can come together for coupling on a second distinct class of integrated catalysts.

Physical Chemistry

Catalysis

electrochemical reduction

productization

propionaldehyde

acetone and hydroxyacetone

The electrochemical reduction of carbon dioxide (CO₂RR) converts CO₂ to fuels and chemical feedstocks using renewable electricity¹. CO₂RR can in principle produce a vast array of possible hydrocarbons and oxygenates: the carbon, oxygen, and hydrogen atoms from carbon dioxide and water are building blocks that constitute an extensive combinatorial space. Experimentally, only a few products have been reported to have high selectivity: these are carbon monoxide², formic acid³, methane⁴, ethylene⁵, and ethanol⁶. Designing catalysts that go beyond these products is an important task in CO₂RR.

Rational catalyst design requires an understanding of reaction pathways to the desired product, and also to the competing products. Jaramillo and co-workers observed 16 different products with numbers of carbon from one to three (C₁-C₃) in CO₂RR on metallic copper catalysts⁷; yet the routes to these diverse products – such as, among C₃ products, hydroxyacetone, acetone, allyl alcohol, propionaldehyde, and 1-propanol – have not been reported.

For C₂ products, different groups report distinct reaction mechanisms: for example, C₁-C₁ coupling mechanisms have been proposed that range from OC-CO^8,9 to OC-COH¹⁰ to OC-CHO^11,12 to OC-CHOH¹² and H₂C-CH₂.¹³ The key intermediate species branching ethylene and ethanol pathways are also under debate: Graza et al.¹¹ proposed that this bifurcation occurs immediately after OC-CHO coupling forming OCCHO* (5e^- transferred from CO₂) on Cu(100). Goddard and co-workers⁹ have suggested that HCCOH* (8e^- transferred) is the key surface species on Cu(100) before the bifurcation of ethylene and ethanol. Calle-Vallejo and Koper¹⁴ have reported that the key intermediate is H₂CCHO (9e^- transferred).

The lack of authoritative mechanisms to C₃ products and debate over C₂ routes limits the rational design of new CO₂RR catalysts toward desired products: only once reaction pathways are known does it become feasible to pursue strategies to decrease the energies of intermediates along the pathways toward the desired product while increasing the energies of the intermediates in the competing pathways. For example, the design of CO₂RR catalysts with high ethylene selectivity requires knowledge of the C₁-C₁ coupling steps and the branch reactions to other C₂ products. This can inform the engineering of active sites that favour C₁-C₁ coupling and that limit branching to other products.

The number of possible reaction steps and intermediates in the CO₂RR up to C₃ species is large (Figure 1a): there are 20 elementary steps in the pathway to 1-propanol, including 18 hydrogenation steps and 2 coupling steps. There are many possible choices for each step: for example, in the simple case from CO to CH₄, there are ten different pathways shown in Figure 1b. A comprehensive analysis of CO₂RR must enumerate systematically the possible intermediates and pathways. Further, a quantitative approach will be required: rather than reject certain pathways as unlikely, we propose a quantitative analysis of the energetics of each possible pathway.

We turned to graph theory¹⁵ to enumerate the possibilities systematically, density functional theory (DFT) to calculate reaction energies, and a steady-state solver to evaluate the most favorable pathways. In a reaction network (Figure 1b), species (reactant, intermediates, and products) are represented as nodes; and reactions (edges) convert one species into another. Here we investigate CO₂RR to products up to and including C₃ on both Cu(111) and Cu(100).

Graph theory framework

We began from CO species since the activation of CO₂ to CO has been systematically investigated before^16,17. We first obtained the possible chemical formulas up to the maximum carbon, oxygen and hydrogen atoms subject to C≤3, H≤8 and O≤3 (Figure 2a) using Catkit¹⁸. For each formula, we enumerated the possible structures and removed structures using the rules: no O-O, C-O-C, O-C-O bonds. As one example, the formula C₂H₂O (Figure 2a) has five different structures with oxygen and hydrogen at different positions. With this approach, we obtained 458 species: the structures, formula, and the number of electrons transferred from CO are listed in Supplementary Sheet 1.

We then calculated the formation energies of these species on Cu(111) and Cu(100). We chose the most unsaturated atom as the binding atom, and calculated the adsorption of the unsaturated species on the possible sites, including atop, bridge, hcp hollow and fcc hollow on Cu(111) and atop, bridge, and four-fold hollow on Cu(100) (Figure 2b), using an adsorption vector algorithm¹⁸. Following optimisation using DFT, we checked the connectivity matrix of the intermediates to ensure that there occurred neither dissociation nor reconstruction, and the dissociated or reconstructed species are removed from the species list. The effects of potential, solvent, and ions on the species formation energies are important, and there are several methods in literature to consider these effects, such as the ab initio molecular dynamics with biased sampling method⁹, the grand canonical quantum mechanics (GCQM) method^8,19, charged water model using global optimization method²⁰, and implicit solvent model²¹. To consider the effects of solvent on the adsorption energies, we used the polarizable continuum model (PCM)²¹ in surface adsorption calculations (Supplementary Sheet 2). The energy comparisions between the PCM and GCQM on Cu(111) and Cu(100) are shown in Figure S1. The most common reaction types are hydrogenation, C-C coupling, and water formation, in that order (Figure 2c). We checked the species pairwise to enumerate the possible reactions. For example, if species X and XH had the same structures except for one extra hydrogen, we added the reaction X* + H⁺« XH* to the reaction list. Using this algorithm, we consider the possible hydrogenation, coupling, and dehydroxylation reactions in CO₂RR up to C₃ products. 1144 hydrogenation reactions, 755 coupling reactions, and 354 dehydroxylation reactions were obtained (Supplementary Sheet 3). The reactions containing unstable species were removed, resulting in 1616 reactions on Cu(100) and 1523 reactions on Cu(111), respectively.

With the formation energies of the possible species and the comprehensive reaction list, we then obtain the reaction energies (Figure 2d). We used the reaction energies in one pathway to describe the favourability of this pathway (more details are found in the Supplymentary Information). The effect of applied potential is considered with the computational hydrogen electrode,²² and pH value is taken into account via the concentration of the reactant (proton source) in the steady-state solver (Figure 2d).

In sum, the reaction pathway search framework (Figure 2) generates structures of the species, calculates the adsorption structures of the intermediates, obtains the reaction energies, and builds the reaction graph using Catkit¹⁸ and an ab initio simulation program (VASP)^23-26.

Reaction graph of CO₂RR

Figure 3a shows the reaction graph for CO₂RR, including the possible intermediates and products up to three carbons and their corresponding elementary steps. The number of C₁ species is 13 (Figure 3a), 55 for C₂ species, 385 for C₃ species, and 5 species without carbon. The species react with protons, forming other species with the same number of carbon atoms (black edges for hydrogenation and green edges for dehydroxylation in Figure 3a), or couple with other species to produce species with a higher number of carbons (red edges in Figure 3a). Except for methane, the products in Figure 3a are linked with more than one edge, suggesting that each product can be produced via several possible routes.

Using the simple path algorithm²⁷, we obtained the number of possible pathways for several products (Table S1): for example, there exist 10 distinct pathways from CO to methane as shown in Figure 1b. Ethylene has 4744 different pathways from CO that are at least one intermediate different, while for CO to 1-propanol the possible pathways are more than 27 million. These make it infeasible to enumerate pathways manually.

In graph theory, the degree of the nodes refers to the number of edges connected to the nodes. This corresponds to the number of possible reactions in which a given species is implicated. The average degree of all nodes is ~13.2, and the maximum degrees are CH₂O and CH₃O, with 84 edges connected, suggesting that these two species are the most important in the reaction network from the point of view of connectivity. The high-degree species are C₁ species, since these species participate in coupling to form C₂ and C₃ species.

Formation energies of intermediates

The energy distributions of the intermediates are shown as a function of the number of electrons transferred in Figure 3b. The formation energy is referenced to the free energies of CO₂, H₂O, and H₂, which are the three reactants of CO₂RR. Thus, the formation energy of each intermediate in Figure 3b indicates the reaction energies for the step from CO₂ and H⁺/H₂O to this intermediate. The number of electrons transferred per carbon atom indicates the degree of hydrogenation. In general, the formation energies increase first, and then decrease with further increase in the number of electrons transferred per carbon atom. Thus, the reaction energies of the first few steps are endothermic at low applied potential, indicating that the rate-determining step of CO₍₂₎RR is in the first few steps. When a negative potential is applied, the formation energies of the intermediates shift by the number of electrons transferred × potential: thus the overall reaction energies of intermediates with an electron transferred become more favourable. These results agree with the high overpotential due to the endothermic steps in the initial stages of CO₂RR. Favouring the first few steps using active site engineering enables the design of CO₂RR catalysts with low overpotential.

Figure 3b also shows that the formation energies of intermediates on Cu(100) are more stable than those on Cu(111), indicating that Cu(100) has a greater driving force for CO₂ reduction and is thus the more likely active site for CO₂RR²⁸. The most energetically favourable pathway is in Figure 3b: it is the pathway from one intermediate to the most stable intermediate with one more electron transferred reachable in the graph. However, if the energies of two intermediates are similar, it is difficult to determine the one most likely in energy space; instead, it is necessary to obtain the most representative pathway(s) in rate space.

The formation energy distribution for intermediates having with 0-3 carbons is provided in Figure 3c. The median and the range of C₂ intermediate formation energy is lower than in the case of C₁ intermediate, and this is true both on Cu(111) and Cu(100). This suggests that C₂ is energetically favoured and is the main product of CO₂RR. Regarding C₂ to C₃, the driving force is much lower on both Cu(111) and Cu(100) (Figure 3c), suggesting that it will be hard to make C₃ as the main product of CO₂RR on pure Cu catalysts. Experiments also show that Cu-based catalysts achieve high C₂ productivities in CO₂RR⁵, and lower C₃ productivities⁷.

C₂Reaction mechanisms

C₁-C₁ coupling is the key step for the selectivity of the C₂ products²⁹. Many different C₁-C₁ coupling reaction mechanisms are proposed including OC-CO^8,9, OC-COH¹⁰, OC-CHO^11,12, OC-CHOH¹², H₂C-CH₂¹³. However, no conclusion has been drawn regarding the dominant elementary step for C₁-C₁ coupling. In our reaction graph, we considered all 55 C₁-C₁ possible coupling reactions on both Cu(111) and Cu(100). With the steady-state solver, we obtained the rates for the elementary steps up to C₂ including the C₁-C₁ coupling steps at different applied potentials from 0 to -1.5 V vs. standard hydrogen electrode (SHE).

Despite the large number of possible coupling reactions, there are only a few dominant C₁-C₁ coupling reactions. Figure 4a and 4b show the main C₁-C₁ coupling reactions and their likelihood among the C₂ formation steps at neutral pH and applied potential from 0 to -1.5 V vs. SHE. The C₁-C₁ coupling mechanisms change with applied potentials and facets due to changes in surface coverage. On Cu(100), OC-CO is the only possible pathway at 0 V, in agreement with the reaction step proposed in prior literature^8,9. With an increase of applied potential, the hydrogenation steps become more favourable: thus, CO* is likely to be further hydrogenated. Therefore, the coverage of HCO* increases and the rate of OC-HCO coupling rises. In the applied potential region higher than -0.5 V, OC-HCO is the main reaction mechanism, a finding that has been reported by Nørskov and Head-Gordon^11,12. The H₂CO-H₂CO and COH-COH coupling steps are also possible at high applied potential; however, these applied potential regions correspond to the formation of methane and hydrogen³⁰. On Cu(111), CO-HCO is the main coupling step at potentials ranging from 0 V to -0.75 V, while CO-COH is also possible with a low likelihood (Figure 4b). HCO-HCO coupling takes the place of CO-HCO at more negative applied potentials.

The findings reported above span coupling mechanism in prior reports; and they conclude that there is not a single unique coupling mechanism. Instead, different coupling steps dominate at different conditions and facets.

We then went on to evaluate the set of paths to C₂ products. We show in Figure 4c the reaction mechanisms on Cu(100) to ethanol and ethylene, two main C₂ products for Cu-based catalysts of particular interest experimentally.^6,31 These are shown at -0.5 V and neutral pH. The reaction starts from CO-HCO coupling, forming OCCHO*, the most likely coupling mechanism at this condition (Figure 4a). The next steps are the hydrogenation of OCCHO* to OHCCHO* and then HOCHCHO*. The hydroxyl group in HOCHCHO* is then removed, giving HCCHO* and water. The removal of the second hydroxyl group happens at the intermediate HCCHOH*, and after the dehydroxylation reaction, HCCH* proceeds to ethylene with two more hydrogenation steps. This reaction pathway explains 49% of the ethylene formed. As an alternative next step following the dehydroxylation step, HCCHOH* can be hydrogenated to H₂CCHOH* (Figure 4c). There are two main hydrogenation steps of H₂CCHOH* to H₂CCH₂OH* and H₃CCHOH*, both leading to the formation of ethanol. Interestingly, we found that the H₂CCH₂OH* can also form ethylene, similar to the mechanism reported by Koper and co-worker¹⁴. Therefore, more than one branch reaction exists between ethylene and ethanol on Cu(100) at U=-0.5 V vs. SHE and pH=7, and the HCCHOH* and H₂CCH₂OH* are the two key intermediates for the selectivity of these two products. The reaction pathways to all eight C₂ products on both Cu(100) and Cu(111) are listed in Table S3-S18.

C₃Reaction mechanisms

As shown in Table S1, there exist 27 million different pathways from CO to 1-propanol. More carbon atoms mean more isomers due to the possible arrangements of carbon, hydrogen, and oxygen. We sought to enumerate the possible reaction pathways to C₃ products and explore the highest-rate paths.

The formation of C₃ species starts with C₁-C₂ coupling^32-34. There are 700 coupling reactions for C₁-C₂ coupling due to the large numbers of possible C₂ species. We considered the coupling steps along with their ensuing reaction pathways to C₃ products. Figure 5a shows the reaction mechanism to five products reported experimentally⁷ – 1-propanol, allyl alcohol, propionaldehyde, acetone, and hydroxyacetone – at U=-0.5 V and neutral pH; the reaction mechanisms to all ten C₃ products are found in Supplementary Information (Cu(100) in Table S19-S28 and Cu(111) in Table S29-S38). The most favourable C₁-C₂ coupling mechanism at -0.5 V and neutral pH is OC-OCCHO coupling on Cu(100) (Figure 5a). Three hydrogenation steps follow the formation of OCC(O)CHO* (IM3_1 in Figure 5a), giving OHCC(O)CHOH* (IM3_3). The main branching steps occurs here, resulting in two groups of products: the hydrogenation of the middle oxygen to OHCC(OH)CHOH* (IM3A_1) leads to the formation of propionaldehyde, allyl alcohol, and 1-propanol (group A); while hydrogenation to HOCHC(O)CHOH* (IM3B_1) produces hydroxyacetone and acetone (group B).

Regarding the group A products, the first hydroxyl group removed in the C₃ species is on the middle carbon (Figure 5a). OHCCCHOH (IM3A_2) is then reduced to OHCCHCH₂OH* (IM3A_4) before the removal of the second hydroxyl group (Figure 5), forming OHCCHCH₂* (IM3A_5). This is followed by two possibilities: hydrogenation of CH₂- to CH₃- forming propionaldehyde, and hydrogenation of ketone group to the hydroxyl group. The branch between allyl alcohol and 1-propanol occurs at HOCHCHCH₂* (IM3A_7); then the 1-propanol is formed with three hydrogenation steps. For group B products, the bifurcation of hydroxyacetone and acetone happens at HOCH₂C(O)CH₂* (IM3B_4) (Figure 5a).

Interestingly, previous experiments⁷ have suggested that partial current densities of these five C₃ products in CO₂RR also fall into two groups at pH=6.8 (Figure 5b): 1-propanol has the highest current density, followed closely by allyl alcohol and then propionaldehyde. The current densities to these three products (group A) are generally one order of magnitude higher than to the other two products, acetone and hydroxyacetone (group B). Furthermore, the branch reactions of 1-propanol and other C₃ products occurs in the following orders in the reaction process: {acetone, hydroxyacetone}, propionaldehyde, and allyl alcohol. The current density ordered from lowest to highest proceeds acetone ≈ hydroxyacetone << propionaldehyde < allyl alcohol < 1-propanol.

In sum, there are two main branch reactions in the C₃ pathways: one at the initial stage after C₁-C₂ coupling, OHCC(O)CHOH* (IM3_3), leading two groups of products; and the other one occurs at the very end of the reaction process, OHCCHCH₂* (IM3A_5) and HOCHCHCH₂* (IM3A_7), and these give different products.

We also obtained information on reaction pathways to other C₃ products, including ones that have not been detected experimentally. Obtaining such results offers inputs into catalyst design beyond traditional products already seen in CO₂RR. For example, 1,2-propylene glycol is used in the production of polymers and food processing, and it has not been reported as a direct product of CO₂RR. Our results (Figure 5a) indicate that the 1,2-propylene glycol branches from the group B pathway at HOCHC(O)CH₂* (IM3B_3). If the intermediate state on one catalyst, HOCHC(O)CH₃ (IM3C_1), is more stable than HOCH₂C(O)CH₂ (IM3B_4), the catalyst may produce 1,2-propylene glycol. For such a design, the branching reaction energy differences to 1,2-propylene glycol vs. the competing products should be used as indicators in computational screening: the more negative the branching reaction, the more selective the catalyst. Other C₃ products pathways can be found in the Supplementary Information: 1,3-propylene glycol (Cu(100) in Table S20 and Cu(111) in Table S30), propane (Table S24 and S34), 2-propanol (Table S25 and S35), glycerol (Table S27 and S37).

Catalyst design for C₃products

The framework presented herein allows systematic screening of possible pathways; we acknowledge that the use of reaction energies along the pathway as a surrogate for the favourability of a pathway is an approximation, and we recognize that, in future works, the graph theoretic enumeration can beneficially be combined with (for example) a high-throughput transition state searching method, kinetic Monte Carlo, high-level quantum chemistry, or machine learning.

With that caveat, we evaluate the implications of Figure 6 – a plot that captures CO binding (a), C₁-C₁ coupling (b), and C₁-C₂ coupling (c).

Optimal CO binding is reached near -0.67 V³⁵. Not surprisingly, Cu (both pure and doped) comes closest to fulfilling this condition (Figure 6a). Au and Al include some doping options such as Pd-doped Au, Pd-doped Al, Ir-doped Al, and Rh-doped Al that come within 0.2 eV of the optimum.

Favourable C₁-C₁ coupling is the next prerequisite along the ultimate pathway towards C₃ products. Here the most strongly negative reaction energy in Figure 6b is the most desirable. Cu doped with Ag and with Au is promising here, and Al is particularly favourable, as Cu-doped Ag and Pb-doped Ag.

To go the rest of the way to C₃ products, a favourable reaction energy of C₁-C₂ coupling is further required. Here again the most strongly negative reaction energy is desired. Ni-doped Pb performs exceptionally well. Pure Cu is a reasonable candidate but not strongly favourable. Ag doped with Al, Au, and Pb, shows promise, but the C₁-C₂ coupling energy is not sufficiently strong as to favour C₃ formation overwhelmingly compared to Ni-doped Pb and Al-doped Pb.

Overall these findings are consistent with the observation that, in prior reports, Cu to propanol has been among the most productive, but its Faradaic efficiency has been limited to the 10-20% range; and that, to date, no single-material nor single-material-doped catalyst has achieved exceptional C₃ productivity.

Intriguingly, the finding that doping one catalyst with a single dopant does not simultaneously enable optimal CO binding; and highly reactive C₁-C₁ coupling; and C₁-C₂ coupling; suggests that a new strategy is needed to achieve productive C₃ generation.

One promising solution is tandem catalysts that combine two or more catalysts: a first catalyst (such as Cu) is in charge of CO* intermediate formation and C₁-C₁ coupling; and a second catalyst is specifically designed for C₁-C₂ coupling (in Figure 6, a candidate is Ni-doped Pb, though doped Au variants also suggest promise).

The enticing possibility of designing such tandem catalysts would require careful analysis of a number of considerations. If the first catalyst was responsible for both CO adsorption and C₁-C₁ coupling, it would then need to bind the C₂ intermediate with proper adsorption energy so that this could diffuse onto the second catalyst decorating the first. The average distance of an island of C₁-C₂ coupling catalyst from a given point on the C₁-C₁ coupling catalyst would need to be less than the in-plane diffusion length of the C₂ intermediate species for the intermediate to reach the C1-C2 region with high probability. The C₂ intermediate would need to “hop” to the C₁-C₂ coupling catalyst efficiently, as would a comparable density of C₁ intermediates. A full analysis of this possibility would require using the micro-kinetic modeling or kinetic Monte Carlo that took account of the different sites and their spatial distribution.

We enumerated herein the intermediates in CO₂RR up to C₃H₈O₃ on both Cu(111) and Cu(100). The most favourable reaction pathways were studied as a function of pH and applied potential. We obtained the intermediates in CO₂RR up to C₃ with the optimized structures. This offers candidates for experiment studies related to intermediates, such as in-situ Raman and infrared spectroscopy. We enumerated possible reaction pathways to 20 products, and 1144 hydrogenation reactions, 755 coupling reactions, and 354 dehydroxylation reactions were found. We found that the C₁-C₁ coupling mechanisms vary at different applied potentials and facets, including OC-CO, OC-HCO, H₂CO-OCH₂, and HOC-COH on Cu(100), and OC-HCO, OC-COH, and HCO-HCO coupling on Cu(111). This accounts for the diversity of C₁-C₁ coupling mechanisms in literature. Furthermore, the results also show there are two bifurcation steps between ethanol and ethylene on Cu(100), and the key intermediate states branching two pathways are HCCHOH and H₂CCH₂OH.

We report systematically, for the first time, the suite of reaction pathways available to C₃ products. We found there exists two groups of products bifurcate at the early stage after C₁-C₂ coupling, namely group A (propionaldehyde, allyl alcohol, 1-propanol) and group B (acetone and hydroxyacetone). Previous experimental results showed that products in the same groups have similar partial current densities, and the partial current densities in the case of group A are an order of magnitude higher than those of group B.

We also obtained the reaction pathways to products not previously reported. These results offer the possibility to tune selectivity toward new chemicals and to design catalysts beyond those whose products are already known. The framework can be extended to more complicated products with higher numbers of carbon in CO₂RR and beyond. Based on these understanding, we offered designs of catalysts toward C₃ products.

Computational methods

Density functional theory calculations. In this work, the density functional theory (DFT) calculations were carried out with a periodic slab model using the Vienna ab initio simulation program^23-26 (VASP) (https://www.vasp.at/). Detailed theoretical methods are found in the Supplementary Information.

Data availability

The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

Acknowledgements

This work was financially supported by TOTAL American Services, the Connaught Fund, the Ontario Research Fund: Research Excellence Program, the Natural Sciences and Engineering Research Council (NSERC) of Canada, and the CIFAR Bio-Inspired Solar Energy program. All DFT computations were performed on the IBM BlueGene/Q supercomputer with support from the Southern Ontario Smart Computing Innovation Platform (SOSCIP). SOSCIP is funded by the Federal Economic Development Agency of Southern Ontario, the Province of Ontario, IBM Canada, Ontario Centres of Excellence, Mitacs and 15 Ontario academic member institutions.

Author contributions

E.H.S supervised the project. Z.W. designed and carried out the DFT calculations. All authors discussed, commented on and revised the manuscript.

Competing financial interests: The authors declare no competing financial interests.

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Supplementaryinformation.docx
Supplementary information
Additional information Supplementary Information is available in the online version of the paper. Reprints and permissions information is available online at www.nature.com/reprints. Correspondence and requests for materials should be addressed to E.H.S.
SupplementarySheet1Species.pdf
Information on all species
SupplementarySheet2Energy.pdf
Formation energies of intermediate species
SupplementarySheet3Reaction.pdf
Reaction energies of reactions
CuCO2RRDatabase.db
ASE database of all calculations

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CO₂ Electrocatalyst Design Using Graph Theory

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