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Optimization of the facet structure of transition-metal catalysts applied to the oxygen reduction reaction


Predicting the optimal structure for a catalytic material has been a long-standing goal, but typically an arbitrary active site on a uniform surface is modelled. Identification of the most-active facet structure for structure-sensitive chemistries, such as the oxygen reduction reaction, is lacking. Here we develop an approach to predict the optimal structure of a catalytic material by identifying the active site and identifying the density and spatial arrangement of such sites while minimizing the surface energy. We find that the theoretical peak performance predicted by linear scaling relations is unattainable because of the lack of suitable active sites on low-index planes, as well as geometric and stability constraints. A random array of vacancies results in a modest performance enhancement compared to ideal facets, whereas defect sites with a maximum density in disordered structures significantly increase the catalyst performance. We applied this methodology to the oxygen reduction reaction on defected Pt(111), Pt(100), Au(111) and Au(100) surfaces.

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Fig. 1: Volcano map for ORR activities on Pt and Au.
Fig. 2: Current density and surface energy simulation results for numerous defected Pt(111)-based crystals that contain different active sites and/or density of active sites.
Fig. 3: Structures of defected crystals.
Fig. 4: Top-down views of the active sites for each surface.
Fig. 5: Pareto front of current density and surface energy.
Fig. 6: Activity of defected metastable structures compared to ideal crystals.

Data availability

All code and data that went into generating the results in this paper can be found at The GitHub repository includes code for the following: structure generation, MKM, DFT data used in parameterizing the Hamiltonian used in the MKM and optimization algorithms.

Code availability

All code that went into generating the results in this paper can be found at All the code is implemented in Python and requires the atomic simulation environment to represent molecular structures and for file input and output (IO). The directory structure is described in the readme.rst file.


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Material developed by Núñez and Vlachos is based on work supported by the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research and Applied Mathematics programme under award no. DE-SC0010549. Funding for Lansford was provided by the Defense Advanced Research Project Agency under grant W911NF-15-2-0122. We thank F. Calle-Vallejo for providing the original data of his group’s work. We thank S. Giles for useful discussion on electrochemistry.

Author information




M.N. implemented the optimization methodology, performed the calculations and analysed the results. J.L.L. performed the DFT calculations and MKM. D.G.V. conceived the problem and provided supervision. All the authors contributed to writing the paper.

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Correspondence to D. G. Vlachos.

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Supplementary Information

Supplementary Results, Supplementary Analysis, Supplementary Methods, Supplementary Figures 1–23, Supplementary Tables 1–8

Supplementary Dataset 1

Snapshot of GitHub repository that contains all code and data used in this work.

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Núñez, M., Lansford, J.L. & Vlachos, D.G. Optimization of the facet structure of transition-metal catalysts applied to the oxygen reduction reaction. Nat. Chem. 11, 449–456 (2019).

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