Correcting Errors in the Adsorbed Intermediates of CO₂ Electroreduction

Abstract

Density functional theory (DFT) has helped propel the advance of electrocatalysis in the past two decades. In view of its massive use, it is worth asking how reliable DFT is for the prediction of adsorption energies, which are paramount in computational electrocatalysis models. Here, we provide an experimental-computational approach to break down overall adsorption-energy errors into separate gas-phase and adsorbed-phase contributions. The method is evaluated using experimental data and various exchange-correlation functionals and materials for C- and O-containing species. Our main conclusion is that no functional is simultaneously accurate for adsorbates and molecules, as adsorbed-phase errors are visibly different from gas-phase errors. Importantly, total, gas-phase, and adsorbed-phase errors are correlated, revealing intrinsic DFT limitations and enabling the elaboration of swift correction routines. To illustrate the benefits of our approach, we deconvolute and correct all errors in CO₂ electroreduction to CO and find an agreement with experiments close to chemical accuracy for numerous transition-metal electrodes and all scrutinized functionals.

References

[1] R. O. Jones, “Density Functional Theory: Its Origins, Rise to Prominence, and Future,” Reviews of Modern Physics 87, no. 3 (2015): 897–923.

[2] X. Liao, R. Lu, L. Xia, et al., “Density Functional Theory for Electrocatalysis,” Energy and Environmental Materials 5, no. 1 (2022): 157–185.

[3] Z. W. Seh, J. Kibsgaard, C. F. Dickens, I. Chorkendorff, J. K. Nørskov, and T. F. Jaramillo, “Combining Theory and Experiment in Electrocatalysis: Insights Into Materials Design,” Science 355, no. 6321 (2017): eaad4998.

[4] B. W. J. Chen, L. Xu, and M. Mavrikakis, “Computational Methods in Heterogeneous Catalysis,” Chemical Reviews 121, no. 2 (2021): 1007–1048.

[5] K. Honkala, A. Hellman, I. N. Remediakis, et al., “Ammonia Synthesis From First-Principles Calculations,” Science 307, no. 5709 (2005): 555–558.

[6] J. T. Mefford, Z. Zhao, M. Bajdich, and W. C. Chueh, “Interpreting Tafel Behavior of Consecutive Electrochemical Reactions Through Combined Thermodynamic and Steady State Microkinetic Approaches,” Energy and Environmental Science 13, no. 2 (2020): 622–634.

[7] J. Zhang, H. B. Yang, D. Zhou, and B. Liu, “Adsorption Energy in Oxygen Electrocatalysis,” Chemical Reviews 122, no. 23 (2022): 17028–17072.

[8] A. J. Medford, A. Vojvodic, J. S. Hummelshøj, et al., “From the Sabatier Principle to a Predictive Theory of Transition-Metal Heterogeneous Catalysis,” Journal of Catalysis 328 (2015): 36–42.

[9] J. K. Nørskov, J. Rossmeisl, A. Logadottir, et al., “Origin of the Overpotential for Oxygen Reduction at a Fuel-Cell Cathode,” Journal of Physical Chemistry B 108, no. 46 (2004): 17886–17892.

[10] J. K. Nørskov, F. Abild-Pedersen, F. Studt, and T. Bligaard, “Density Functional Theory in Surface Chemistry and Catalysis,” Proceedings of the National Academy of Sciences 108, no. 3 (2011): 937–943.

[11] S. Kurth, J. P. Perdew, and P. Blaha, “Molecular and Solid-State Tests of Density Functional Approximations: LSD, GGAs, and Meta-GGAs,” International Journal of Quantum Chemistry 75, no. 4–5 (1999): 889–909.

[12] P. Janthon, S. Luo, S. M. Kozlov, et al., “Bulk Properties of Transition Metals: A Challenge for the Design of Universal Density Functionals,” Journal of Chemical Theory and Computation 10, no. 9 (2014): 3832–3839.

[13] D. Rappoport, N. R. M. Crawford, F. Furche, and K. Burke, “Approximate Density Functionals: Which Should I Choose?,” in Encyclopedia of Inorganic Chemistry (2009).

[14] P. Janthon, S. M. Kozlov, F. Viñes, J. Limtrakul, and F. Illas, “Establishing the Accuracy of Broadly Used Density Functionals in Describing Bulk Properties of Transition Metals,” Journal of Chemical Theory and Computation 9, no. 3 (2013): 1631–1640.

[15] A. D. Becke, “Density-Functional Thermochemistry. III. The Role of Exact Exchange,” Journal of Chemical Physics 98, no. 7 (1993): 5648–5652.

[16] Y. Zhao and D. G. Truhlar, “Density Functionals With Broad Applicability in Chemistry,” Accounts of Chemical Research 41, no. 2 (2008): 157–167.

[17] A. D. Becke, “A New Mixing of Hartree–Fock and Local Density-Functional Theories,” Journal of Chemical Physics 98, no. 2 (1993): 1372–1377.

[18] E. Sargeant, F. Illas, P. Rodríguez, and F. Calle-Vallejo, “Importance of the Gas-Phase Error Correction for O₂ When Using DFT to Model the Oxygen Reduction and Evolution Reactions,” Journal of Electroanalytical Chemistry 896, no. 896 (2021): 115178.

[19] S. Mallikarjun Sharada, R. K. B. Karlsson, Y. Maimaiti, J. Voss, and T. Bligaard, “Adsorption on Transition Metal Surfaces: Transferability and Accuracy of DFT Using the ADS41 Dataset,” Physical Review B 100, no. 3 (2019): 035439.

[20] J. Wellendorff, T. L. Silbaugh, D. Garcia-Pintos, et al., “A Benchmark Database for Adsorption Bond Energies to Transition Metal Surfaces and Comparison to Selected DFT Functionals,” Surface Science 640, no. 640 (2015): 36–44.

[21] A. Patra, H. Peng, J. Sun, and J. P. Perdew, “Rethinking CO Adsorption on Transition-Metal Surfaces: Effect of Density-Driven Self-Interaction Errors,” Physical Review B 100, no. 3 (2019): 035442.

[22] S. Gautier, S. N. Steinmann, C. Michel, P. Fleurat-Lessard, and P. Sautet, “Molecular Adsorption at Pt(111). How Accurate Are DFT Functionals?,” Physical Chemistry Chemical Physics 17, no. 43 (2015): 28921–28930.

[23] N. Gerrits, E. W. F. Smeets, S. Vuckovic, A. D. Powell, K. Doblhoff-Dier, and G. J. Kroes, “Density Functional Theory for Molecule–Metal Surface Reactions: When Does the Generalized Gradient Approximation Get It Right, and What to Do If It Does Not,” Journal of Physical Chemistry Letters 11, no. 24 (2020): 10552–10560.

[24] A. J. R. Hensley, K. Ghale, C. Rieg, et al., “DFT-Based Method for More Accurate Adsorption Energies: An Adaptive Sum of Energies From RPBE and vdW Density Functionals,” Journal of Physical Chemistry C 121, no. 9 (2017): 4937–4945.

[25] A. A. Peterson, F. Abild-Pedersen, F. Studt, J. Rossmeisl, and J. K. Nørskov, “How Copper Catalyzes the Electroreduction of Carbon Dioxide Into Hydrocarbon Fuels,” Energy and Environmental Science 3, no. 9 (2010): 1311–1315.

[26] L. P. Granda-Marulanda, A. Rendón-Calle, S. Builes, F. Illas, M. T. M. Koper, and F. Calle-Vallejo, “A Semiempirical Method to Detect and Correct DFT-Based Gas-Phase Errors and Its Application in Electrocatalysis,” ACS Catalysis 10, no. 12 (2020): 6900–6907.

[27] R. Urrego-Ortiz, S. Builes, F. Illas, and F. Calle-Vallejo, “Gas-Phase Errors in Computational Electrocatalysis: A Review,” EES Catalysis 2, no. 1 (2024): 157–179.

[28] M. Lee, B. Kim, M. Sim, et al., “Correcting Dispersion Corrections With Density-Corrected DFT,” Journal of Chemical Theory Computation 20, no. 16 (2024): 7155–7167.

[29] S. F. Yuk, I. Sargin, N. Meyer, J. T. Krogel, S. P. Beckman, and V. R. Cooper, “Putting Error Bars on Density Functional Theory,” Scientific Reports 14, no. 1 (2024): 20219.

[30] H. Bhattacharjee, N. Anesiadis, and D. G. Vlachos, “Regularized Machine Learning on Molecular Graph Model Explains Systematic Error in DFT Enthalpies,” Scientific Reports 11, no. 1 (2021): 14372.

[31] S. E. Wheeler, K. N. Houk, P. R. Schleyer, and W. D. Allen, “A Hierarchy of Homodesmotic Reactions for Thermochemistry,” Journal of the American Chemical Society 131, no. 7 (2009): 2547–2560.

[32] R. Christensen, H. A. Hansen, and T. Vegge, “Identifying Systematic DFT Errors in Catalytic Reactions,” Catalysis Science and Technology 5, no. 11 (2015): 4946–4949.

[33] L. G. V. Briquet, M. Sarwar, J. Mugo, G. Jones, and F. Calle-Vallejo, “A New Type of Scaling Relations to Assess the Accuracy of Computational Predictions of Catalytic Activities Applied to the Oxygen Evolution Reaction,” ChemCatChem 9, no. 7 (2017): 1261–1268.

[34] R. Christensen, H. A. Hansen, C. F. Dickens, J. K. Nørskov, and T. Vegge, “Functional Independent Scaling Relation for ORR/OER Catalysts,” Journal of Physical Chemistry C 120, no. 43 (2016): 24910–24916.

[35] G. Kresse and J. Furthmüller, “Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set,” Physical Review B 54, no. 16 (1996): 11169–11186.

[36] G. Kresse and D. Joubert, “From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method,” Physical Review B 59, no. 3 (1999): 1758–1775.

[37] J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized Gradient Approximation Made Simple,” Physical Review Letters 77, no. 18 (1996): 3865–3868.

[38] J. P. Perdew and Y. Wang, “Accurate and Simple Analytic Representation of the Electron-Gas Correlation Energy,” Physical Review B 45, no. 23 (1992): 13244–13249.

[39] B. Hammer, L. B. Hansen, and J. K. Nørskov, “Improved Adsorption Energetics Within Density-Functional Theory Using Revised Perdew-Burke-Ernzerhof Functionals,” Physical Review B 59, no. 11 (1999): 7413–7421.

[40] J. Wellendorff, K. T. Lundgaard, A. Møgelhøj, et al., “Density Functionals for Surface Science: Exchange-Correlation Model Development With Bayesian Error Estimation,” Physical Review B 85, no. 23 (2012): 235149.

[41] S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, “A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu,” Journal of Chemical Physics 132, no. 15 (2010): 154104.

[42] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, “Climbing the Density Functional Ladder: Nonempirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids,” Physical Review Letters 91, no. 14 (2003): 146401.

[43] H. J. Monkhorst and J. D. Pack, “Special Points for Brillouin-Zone Integrations,” Physical Review B 13, no. 12 (1976): 5188–5192.

[44] M. Methfessel and A. T. Paxton, “High-Precision Sampling for Brillouin-Zone Integration in Metals,” Physical Review B 40, no. 6 (1989): 3616–3621.

[45] C. J. Bartel, A. W. Weimer, S. Lany, C. B. Musgrave, and A. M. Holder, “The Role of Decomposition Reactions in Assessing First-Principles Predictions of Solid Stability,” NPJ Computational Materials 5, no. 1 (2019): 4.

[46] G. Hautier, S. P. Ong, A. Jain, C. J. Moore, and G. Ceder, “Accuracy of Density Functional Theory in Predicting Formation Energies of Ternary Oxides From Binary Oxides and Its Implication on Phase Stability,” Physical Review B 85, no. 15 (2012): 155208.

[47] R. Urrego-Ortiz, S. Builes, and F. Calle-Vallejo, “Automated Versus Chemically Intuitive Deconvolution of Density Functional Theory (DFT)-Based Gas-Phase Errors in Nitrogen Compounds,” Industrial & Engineering Chemistry Research 61, no. 36 (2022): 13375–13382.

[48] W. M. Haynes, D. R. Lide, and T. J. Bruno, CRC Handbook of Chemistry and Physics, 97th ed. (CRC Press/Taylor & Francis, 2016).

[49] E. Di Simone, G. Vilé, G. Di Liberto, and G. Pacchioni, “Decoding the Role of Adsorbates Entropy in the Reactivity of Single-Atom Catalysts,” ACS Catalysis 15, no. 1 (2025): 447–456.

[50] A. Rendón-Calle, S. Builes, and F. Calle-Vallejo, “Substantial Improvement of Electrocatalytic Predictions by Systematic Assessment of Solvent Effects on Adsorption Energies,” Applied Catalysis, B: Environmental 276, no. 276 (2020): 119147.

[51] F. Calle-Vallejo, R. F. de Morais, F. Illas, D. Loffreda, and P. Sautet, “Affordable Estimation of Solvation Contributions to the Adsorption Energies of Oxygenates on Metal Nanoparticles,” Journal of Physical Chemistry C 123, no. 9 (2019): 5578–5582.

[52] R. Urrego-Ortiz, S. Builes, and F. Calle-Vallejo, “Fast Correction of Errors in the DFT-Calculated Energies of Gaseous Nitrogen-Containing Species,” ChemCatChem 13, no. 10 (2021): 2508–2516.

[53] M. O. Almeida, M. J. Kolb, M. R. V. Lanza, F. Illas, and F. Calle-Vallejo, “Gas-Phase Errors Affect DFT-Based Electrocatalysis Models of Oxygen Reduction to Hydrogen Peroxide,” ChemElectroChem 9, no. 12 (2022): 1–7, e20220021.

[54] R. Urrego-Ortiz, S. Builes, F. Illas, S. T. Bromley, M. C. Figueiredo, and F. Calle-Vallejo, “Minimum Conditions for Accurate Modeling of Urea Production via Co-Electrolysis,” Communications Chemistry 6, no. 1 (2023): 196.

[55] E. Sargeant, P. Rodriguez, and F. Calle-Vallejo, “Cation Effects on the Adsorbed Intermediates of CO₂ Electroreduction Are Systematic and Predictable,” ACS Catalysis 14, no. 11 (2024): 8814–8822.

[56] W. J. Teh, M. J. Kolb, F. Calle-Vallejo, and B. S. Yeo, “Enhanced Charge Transfer Kinetics for the Electroreduction of Carbon Dioxide on Silver Electrodes Functionalized With Cationic Surfactants,” Advanced Functional Materials 33, no. 7 (2023): 2210617.

[57] M. Ma, B. J. Trześniewski, J. Xie, and W. A. Smith, “Selective and Efficient Reduction of Carbon Dioxide to Carbon Monoxide on Oxide-Derived Nanostructured Silver Electrocatalysts,” Angewandte Chemie International Edition 55, no. 33 (2016): 9748–9752.

[58] A. Goyal, G. Marcandalli, V. A. Mints, and M. T. M. Koper, “Competition Between CO₂ Reduction and Hydrogen Evolution on a Gold Electrode Under Well-Defined Mass Transport Conditions,” Journal of the American Chemical Society 142, no. 9 (2020): 4154–4161.

[59] W. Luo, J. Zhang, M. Li, and A. Züttel, “Boosting CO Production in Electrocatalytic CO₂ Reduction on Highly Porous Zn Catalysts,” ACS Catalysis 9, no. 5 (2019): 3783–3791.

[60] P. J. Feibelman, B. Hammer, J. K. Nørskov, et al., “The CO/Pt(111) Puzzle,” Journal of Physical Chemistry B 105, no. 18 (2001): 4018–4025.

[61] J. Paier, M. Marsman, and G. Kresse, “Why Does the B3LYP Hybrid Functional Fail for Metals?”,” Journal of Chemical Physics 127, no. 2 (2007): 024103.

[62] A. Stroppa, K. Termentzidis, J. Paier, G. Kresse, and J. Hafner, “CO Adsorption on Metal Surfaces: A Hybrid Functional Study With Plane-Wave Basis Set,” Physical Review B 76, no. 19 (2007): 195440.

[63] M. Retuerto, L. Pascual, F. Calle-Vallejo, et al., “Na-Doped Ruthenium Perovskite Electrocatalysts With Improved Oxygen Evolution Activity and Durability in Acidic Media,” Nature Communications 10, no. 1 (2019): 2041.

[64] M. Retuerto, F. Calle-Vallejo, L. Pascual, et al., “La_1.5Sr_0.5NiMn_0.5Ru_0.5O₆ Double Perovskite With Enhanced ORR/OER Bifunctional Catalytic Activity,” ACS Applied Materials and Interfaces 11, no. 24 (2019): 21454–21464.

[65] D. Galyamin, J. Torrero, I. Rodríguez, et al., “Active and Durable R₂MnRuO₇ Pyrochlores With Low Ru Content for Acidic Oxygen Evolution,” Nature Communications 14, no. 1 (2023): 2010.

[66] J. Harl, L. Schimka, and G. Kresse, “Assessing the Quality of the Random Phase Approximation for Lattice Constants and Atomization Energies of Solids,” Physical Review B 81, no. 11 (2010): 115126.

[67] J. Harl and G. Kresse, “Accurate Bulk Properties From Approximate Many-Body Techniques,” Physical Review Letters 103, no. 5 (2009): 056401.

[68] J. Yan, J. S. Hummelshøj, and J. K. Nørskov, “Formation Energies of Group I and II Metal Oxides Using Random Phase Approximation,” Physical Review B 87, no. 7 (2013): 075207.

[69] R. Urrego-Ortiz, S. Builes, and F. Calle-Vallejo, “Impact of Intrinsic Density Functional Theory Errors on the Predictive Power of Nitrogen Cycle Electrocatalysis Models,” ACS Catalysis 12, no. 8 (2022): 4784–4791.

[70] I. Aguado-Ruiz, R. Urrego-Ortiz, and F. Calle-Vallejo, “A Computational View on the Thermochemical and Electrochemical Stability of Ruthenium Oxides,” Journal of Materials Chemistry A 13, no. 17 (2025): 12482–12491.

[71] L. Schimka, J. Harl, A. Stroppa, et al., “Accurate Surface and Adsorption Energies From Many-Body Perturbation Theory,” Nature Materials 9, no. 9 (2010): 741–744.

[72] F. Furche, “Molecular Tests of the Random Phase Approximation to the Exchange-Correlation Energy Functional,” Physical Review B 64, no. 19 (2001): 195120.

[73] H. A. Hansen, J. B. Varley, A. A. Peterson, and J. K. Nørskov, “Understanding Trends in the Electrocatalytic Activity of Metals and Enzymes for CO₂ Reduction to CO,” Journal of Physical Chemistry Letters 4, no. 3 (2013): 388–392.

[74] M. P. L. Kang, M. J. Kolb, F. Calle-Vallejo, and B. S. Yeo, “The Role of Undercoordinated Sites on Zinc Electrodes for CO₂ Reduction to CO,” Advanced Functional Materials 32, no. 23 (2022): 2111597.

[75] N. Todoroki, H. Tei, H. Tsurumaki, T. Miyakawa, T. Inoue, and T. Wadayama, “Surface Atomic Arrangement Dependence of Electrochemical CO₂ Reduction on Gold: Online Electrochemical Mass Spectrometric Study on Low-Index Au(hkl) Surfaces,” ACS Catalysis 9, no. 2 (2019): 1383–1388.

[76] N. Hoshi, M. Kato, and Y. Hori, “Electrochemical Reduction of CO₂ on Single Crystal Electrodes of Silver Ag(111), Ag(100) and Ag(110),” Journal of Electroanalytical Chemistry 440, no. 1–2 (1997): 283–286.

[77] Y. Huang, A. D. Handoko, P. Hirunsit, and B. S. Yeo, “Electrochemical Reduction of CO₂ Using Copper Single-Crystal Surfaces: Effects of CO* Coverage on the Selective Formation of Ethylene,” ACS Catalysis 7, no. 3 (2017): 1749–1756.

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2025 The Author(s). Carbon Energy published by Wenzhou University and John Wiley & Sons Australia, Ltd.