# A few basic concepts in electrochemical carbon dioxide reduction

### Subjects

In this perspective, I discuss a few basic concepts in fundamental mechanistic studies of electrochemical carbon dioxide reduction.

With the looming global environmental crisis, electrochemical CO2 reduction (CO2R) is a hot topic. Excellent perspectives on mechanistic studies1,2,3, practical vapor-fed devices4, and technoeconomic and system-level analyses5,6,7 have come out in the past few years, all with compelling visions for the future. We can also harken back to Hori’s timeless review of his work over several decades8, which seeded many of the impressive advances today. But as the French maxim says: parfois, il faut reculer pour mieux sauter. Here, I showcase a few basic concepts in the fundamental mechanistic studies of CO2R.

## What computational electrocatalysis can and cannot do

In heterogeneous catalysis, periodic density functional theory (DFT) simulations have really enabled us to computationally explore reaction mechanisms. For electrocatalysis, the “computational hydrogen electrode” model is our standard method to determine reaction thermodynamics9. This method trivially translates simulations in vacuum to potential-dependent energetics, without requiring we simulate explicitly the ions or potential.

Our models of the electrolyte and electrochemical reaction barriers, in contrast, are far from convergent. Our field abounds with different approaches towards the electrolyte: implicit continuum models, explicit ab initio ones, or a hybrid of the two (Fig. 1a)10. We also have multiple ways to obtain the potential and the potential dependence of the reaction energetics11. While continuum approximations give us huge reductions in computational cost, we see significant deviations in solvation energies determined with implicit vs. dynamic explicit water models12. Furthermore, different ways to set up the applied potential result in differences in the computed reaction energetics13. All these challenges could contribute to the wide range in the computed energetics and mechanisms towards the various C2 products1.

Despite the difficulties in an ab initio treatment of electrochemical reaction barriers, we do need kinetics for mechanistic understanding. Case in point: our evolving understanding of CO(2)R to CH4 on Cu14. A thermodynamic analysis showed a proton–electron transfer to *CO to form *CHO to be the rate-limiting step. Considering the corresponding barriers across different materials, we suggested the transition state of this process to be the descriptor of activity. But when we simply consider the kinetics of electrochemical reactions with multiple proton–electron transfers, we see that this step cannot be rate limiting on Cu. The corresponding Tafel plots have defining features that depend on the symmetry factor β (0 < β < 1) for the rate-limiting step, as well as the number of proton–electron transfers preceding it, n. Figure 1b shows the Tafel slopes and the effect of pH on the overpotential for alkaline solutions, where H2O as the proton donor. Experiments show CH4 activity to have a Tafel slope of <60 mV/dec, and the positive shift in overpotential with an increased pH is <60 mV/pH unit, both consistent with n > 0. Therefore, the rate-limiting step must occur after the initial proton–electron transfer to *CO to form *CHO (or *COH15) . And Hori, in fact, made these observations decades ago8.

To put some numbers on what we can do today, consider the Arrhenius law,

$${\mathrm{TOF}} = A\exp \left( { - \frac{{E_{\mathrm{a}}}}{{kT}}} \right),$$
(1)

where A is the prefactor, TOF the turnover frequency, and Ea the activation energy. Without even considering the electrochemical environment, a typical DFT error in adsorption energy is 0.15 eV 16. A shift in Ea of this magnitude gives a 300× change in the TOF at room temperature! Depending on the reaction process at play, the corresponding theoretical selectivities can have uncertainties that approach 100%17. With electrochemical barriers, the uncertainties are compounded by the challenges mentioned above.

So DFT-based kinetic models do not presently give us predictions of activity or selectivity to the precision of experiments where mass transport and the surface structure of the catalyst are carefully controlled. With error cancellation, we have much more confidence in the relative: the relative magnitudes of barriers within a given mechanism, as well as the relative activity across catalysts16 and across reaction conditions18. Especially with our present degree of accuracy, we should, wherever possible, couple DFT models to ample feedback from experiment. Such joint efforts have given us valuable insights into reaction mechanisms, activity descriptors, and electrolyte effects1.

## The activity towards CO and C2 products is driven by field–dipole interactions

A special feature of CO(2)R is the importance of steps that do not involve a proton–electron transfer (Fig. 1c). On weak binding catalysts (e.g. Au19 and Fe-N-C20 catalysts), the rate of CO2R to CO is limited by CO2 adsorption. On Cu catalysts, CO–CO coupling limits the rate of CO(2) reduction to high-value C2 products such as ethanol and ethylene3.

Now, the dipoles of *CO2 and *OCCO interact strongly with the interfacial electric field. And since the field depends on the absolute potential, e.g. on an SHE scale, so does the activity of the corresponding reactions. Figure 1d shows the variation of the interfacial field E and the corresponding stabilization of the polar intermediates vs. the potential U vs. SHE. On the other hand, the overpotential η depends on U vs. RHE, which shifts on the SHE scale by a Nernstian factor of 60 mV/pH unit. For reduction reactions, a positive shift in η translates to higher activity. For example, a shift in pH from 7 to 13 translates to a whopping shift in η of +0.36 V! We can therefore think of the dramatic pH effect for these products as simply arising from a shift in the RHE reference potential.

We can use different labels for this phenomenon, such as single electron transfer19 or decoupled proton–electron transfer3, but the dipole-field vocabulary allows us to consider the reaction rate in terms of dipoles of the intermediates, μ, and the interfacial capacitance, Cdl. For example, the rate of CO2 adsorption and the corresponding Tafel slope are as follows21,22:

$$j \propto \exp \left( { - \frac{{\mu \left( {{\mathrm{CO}}_2} \right)_{{\mathrm{TS}}} \cdot E}}{{kT}}} \right),$$
(2)
$${\mathrm{Tafel}}\,{\mathrm{slope}} = \left| {\frac{{\partial U}}{{\partial \log j}}} \right| \propto \frac{1}{{\mu \left( {{\mathrm{CO}}_2} \right)_{{\mathrm{TS}}}C_{{\mathrm{dl}}}}}$$
(3)

and we can write analogous expressions for CO dimerization.

Note that the local [OH], which increases with increasing CO(2)R current, plays no direct role in promoting the rate of these two steps23, since they are driven by the field alone. However, the [OH] can alter the CO2 concentration through the bicarbonate equilibria, suppress CH4 formation14, and promote the activity towards acetate, even at a fixed U vs. SHE24.

These very dipole–field interactions also rationalize the sensitivity of activity to cation identity18 (Fig. 1e). In a classical picture of the interface, the ion concentration is limited by the hydrated ion size25. The smaller the size, the greater the surface charge and interfacial field for a given applied potential, which increases Cdl. The slightly smaller hydrated size of Cs+ vs. Li+ leads to the 1–2 orders of magnitude enhancement for the CO activity on Ag and C2 activity on Cu.

This model of the ion effects is an echo of the decades-old “Frumkin diffuse layer correction” to Butler–Volmer kinetics26. This correction accounts for the impact of the composition of the double layer on the local potential drop, which determines the corresponding reaction rate. Beyond electrostatics, specific chemical interactions between ions with the surface or adsorbate may also play a role, and both cations and anions can act as buffers27,28.

The dependence of CO(2)R on adsorbate–field interactions shows us that, in addition to optimizing the adsorption energies of critical intermediates, we can look to tuning Cdl and μ towards higher activity (Eq. 3). Our models suggest that we can tune the former through the electrolyte, and the latter in single-atom catalysts, where the localization of charge on the active site is affected by the coordinating atoms22.

## We need TOF estimates to evaluate intrinsic activity, and Cu’s still the best (but don’t give up)

What do we know about the activity of existing catalysts? Selectivities are often represented by Faradaic efficiencies: $${\mathrm{FE}}_{\mathrm{i}} = \frac{{j_i}}{{j_{{\mathrm{{tot}}}}}}$$, where ji is the partial current density of product i and jtot the total current density. While selectivities are a critical performance metric, FEi’s can’t be used to evaluate the intrinsic activity towards a given product, especially as they shift with respect to changes in the activities of all other products. The intrinsic activity, as determined by the reaction energetics, can really only be evaluated by TOFs (Eq. 1). In practice, we approximate TOFs by partial current densities normalized to the electrochemically active surface area (ECSA), $$j_{{\mathrm{{ECSA}}}} \propto \rho _{{\mathrm{{site}}}}{\mathrm{TOF}}$$, where ρsite is the density of the active site. Comparisons of intrinsic activity with jECSA are therefore accurate within the variations of ρsite among samples, the uncertainty in the ECSA, and the degree of mass transport limitations.

Surface reaction energetics on different facets typically differ by 0.1–1 eV 29, which translates to variations in the corresponding TOFs by orders of magnitude (Eq. 1). Shifts in jECSA of around an order of magnitude (or less) between catalysts with different surface structures are more likely to arise from a change in ρsite than a change in the predominant active site or facet. Recent reviews have shown that nano-structured Cu and Cu-based bimetallics show similar jECSA to those on Cu foils1,2. To date, I am not aware of a new catalyst with intrinsic activity towards C2 products that unequivocally exceeds that of Cu foil. Ongoing efforts to obtain single crystal measurements with product quantification can rigorously evaluate theoretical predictions of the most active Cu facet(s).

The increased C2 selectivities on various high surface area Cu catalysts actually arise from the suppression of other products, such as CH4 and H21,2. Under alkaline conditions, H2 suppression cannot arise from local changes in pH, since H2O is the proton donor. Perhaps nanostructuring shifts the structure and activity of water, such that products that are limited by proton–electron transfer steps are suppressed.

And why haven’t we found alternatives to Cu that either match or exceed its intrinsic activity towards C2 products? Stability is a possible culprit: leaching or surface restructuring, which can be driven by the presence of elements that strongly bind *CO. But I know no fundamental limitation on the existence of stable and active alternatives, especially if we expand our search to emergent classes of materials beyond binary combinations of transition metals30,31. Furthermore, improvements in catalytic efficiency are still needed5,6. With a rigorous consideration of surface stability, the discovery of new catalysts beyond Cu remains a worthwhile and important pursuit.

## Outlook

Even as we develop practical devices and systems for CO2R, we still face fundamental challenges at the level of reaction mechanisms and intrinsic activity. These challenges range from simulating electrochemical kinetics to the discovery of new catalysts beyond Cu. Tremendous opportunity lies in overcoming them. With the increasing dialogue among us and the diversity of expertise we are bringing together—I envision that our collective efforts will ultimately contribute to establishing a sustainable carbon cycle.

## References

1. 1.

Nitopi, S. et al. Progress and perspectives of electrochemical CO2 reduction on copper in aqueous electrolyte. Chem. Rev. 119, 7610–7672 (2019).

2. 2.

Resasco, J. & Bell, A. T. Electrocatalytic CO2 reduction to fuels: progress and opportunities.Trends Chem. 2(1), 12 (2020).

3. 3.

Kortlever, R., Shen, J., Schouten, K. J. P., Calle-Vallejo, F. & Koper, M. T. M. M. Catalysts and reaction pathways for the electrochemical reduction of carbon dioxide. J. Phys. Chem. Lett. 6, 4073–4082 (2015).

4. 4.

Higgins, D., Hahn, C., Xiang, C., Jaramillo, T. F. & Weber, A. Z. Gas-diffusion electrodes for carbon dioxide reduction: a new paradigm. ACS Energy Lett. 4, 317–324 (2019).

5. 5.

Jouny, M., Luc, W. & Jiao, F. General techno-economic analysis of CO2 electrolysis systems. Ind. Eng. Chem. Res. 57, 2165–2177 (2018).

6. 6.

Verma, S. et al. A gross-margin model for defining technoeconomic benchmarks in the electroreduction of CO2. ChemSusChem 9, 1–9 (2016).

7. 7.

Smith, W. A., Burdyny, T., Vermaas, D. A. & Geerlings, H. Pathways to industrial-scale fuel out of thin air from CO2 electrolysis. Joule 3, 1822–1834 (2019).

8. 8.

Hori, Y. In Modern Aspects of Electrochemistry (eds Vayenas, C. G. et al.) 89–189 (Springer, New York, 2008).

9. 9.

Nørskov, J. K. et al. Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B 108, 17886–17892 (2004).

10. 10.

Schwarz, K. & Sundararaman, R. The electrochemical interface in first-principles calculations. Surf. Sci. Rep. 75, 100492 (2020).

11. 11.

Groß, A. Theory of solid/electrolyte interfaces. Surf. Interface Sci. 8, 471–515 (2020).

12. 12.

Heenen, H. H., Gauthier, J. A., Kristoffersen, H. H., Ludwig, T. & Chan, K. Solvation at metal/water interfaces: an ab initio molecular dynamics benchmark of common computational approaches. J. Chem. Phys. 152, 144703 (2020).

13. 13.

Gauthier, J. A. et al. Unified approach to implicit and explicit solvent simulations of electrochemical reaction energetics. J. Chem. Theory Comput. 15, 6895–6906 (2019).

14. 14.

Liu, X. et al. pH effects on the electrochemical reduction of CO2 towards C2+ products on stepped copper. Nat. Commun. 10, 32 (2019).

15. 15.

Nie, X., Esopi, M. R., Janik, M. J. & Asthagiri, A. Selectivity of CO2 reduction on copper electrodes: the role of the kinetics of elementary steps. Angew. Chem. Int. Ed. 52, 2459–2462 (2013).

16. 16.

Medford, A. J. et al. Assessing the reliability of calculated catalytic ammonia synthesis rates. Science 345, 197–200 (2014).

17. 17.

Yang, N. et al. Intrinsic selectivity and structure sensitivity of rhodium catalysts for C2+ oxygenate production. J. Am. Chem. Soc. 138, 3705–3714 (2016).

18. 18.

Ringe, S. et al. Understanding cation effects in electrochemical CO2 reduction. Energy Environ. Sci. 12, 3001–3014 (2019).

19. 19.

Wuttig, A., Yaguchi, M., Motobayashi, K., Osawa, M. & Surendranath, Y. Inhibited proton transfer enhances Au-catalyzed CO2-to-fuels selectivity. Proc. Natl Acad. Sci. USA 113, E4585–E4593 (2016).

20. 20.

Varela, A. S. et al. pH Effects on the selectivity of the electrocatalytic CO2 reduction on graphene-embedded Fe–N–C motifs: bridging concepts between molecular homogeneous and solid-state heterogeneous catalysts. ACS Energy Lett. 3, 812–817 (2018).

21. 21.

Ringe, S. et al. Double layer charging driven carbon dioxide adsorption limits the rate of electrochemical carbon dioxide reduction on gold. Nat. Commun. 11, 33 (2020).

22. 22.

Vijay, S. et al. Dipole-field interactions determine the CO2 reduction activity of 2D Fe-N-C single atom catalysts. ACS Catal. 10, 7826–7835 (2020).

23. 23.

Li, J. et al. Hydroxide is not a promoter of C2+ product formation in the electrochemical reduction of CO on copper. Angew. Chem. Int. Ed. 59, 4464–4469 (2020).

24. 24.

Luc, W. et al. Two-dimensional copper nanosheets for electrochemical reduction of carbon monoxide to acetate. Nat. Catal. 2, 423–430 (2019).

25. 25.

Borukhov, I., Andelman, D. & Orland, H. Adsorption of large ions from an electrolyte solution: a modified Poisson–Boltzmann equation. Electrochim. Acta 46, 221–229 (2000).

26. 26.

Bard, A. J. & Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd edn (John Wiley & Sons, 2000).

27. 27.

Singh, M. R., Kwon, Y., Lum, Y., Ager, J. W. & Bell, A. T. Hydrolysis of electrolyte cations enhances the electrochemical reduction of CO2 over Ag and Cu. J. Am. Chem. Soc. 138, 13006–13012 (2016).

28. 28.

Zhang, F. & Co, A. C. Direct evidence of local pH change and the role of alkali cation during CO2 electroreduction in aqueous media. Angew. Chemie Int. Ed. 59, 1674–1681 (2020).

29. 29.

Nørskov, J. K., Studt, F., Abild-Pedersen, F. & Bligaard, T. Fundamental Concepts in Heterogeneous Catalysis (John Wiley and Sons, 2014).

30. 30.

Piontek, S. et al. Bio-inspired design: bulk iron-nickel sulfide allows for efficient solvent-dependent CO2 reduction. Chem. Sci. 10, 1075–1081 (2019).

31. 31.

Pedersen, J. K., Batchelor, T. A. A., Bagger, A. & Rossmeisl, J. High-entropy alloys as catalysts for the CO2 and CO reduction reactions. ACS Catal. 10, 2169–2176 (2020).

## Acknowledgements

This work was supported by a research grant (9455) from VILLUM FONDEN. I thank Hugh Simons, Nitish Govindarajan, Sudarshan Vijay, and Brian Seger for their writing feedback.

## Author information

Authors

### Contributions

K.C. conceived and wrote the piece.

### Corresponding author

Correspondence to Karen Chan.

## Ethics declarations

### Competing interests

The author declares no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Chan, K. A few basic concepts in electrochemical carbon dioxide reduction. Nat Commun 11, 5954 (2020). https://doi.org/10.1038/s41467-020-19369-6

• Accepted:

• Published: