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465565 Rational Design of Nanostructured Metallic Surfaces Via Mathematical Optimization

Progress in our understanding of metallic surfaces for heterogeneous catalysis has brought us to the point where novel materials can be proposed by design *in silico* [2]. However, due to the combinatorial nature of how atoms can arrange themselves on crystalline lattices, the best structures are unintuitive and likely impossible to identify without a rigorous decision-making approach. Fortunately, this material design problem can be formalized and addressed as a mathematical optimization problem such as those traditionally cast and solved in many process systems engineering contexts. In essence, one seeks to identify a material design (i.e., a specific instantiation of the given class of materials of interest) that maximizes some metric of performance.

The proposed design approach capitalizes on the fact that the rate for the limiting step(s) in the overall conversion process can ultimately be correlated to the microstructure of a surface site, typically in the form of a volcano plot [2,3]. Importantly, the activation energy of a chemical reaction can be predicted from the adsorption energies of transition states [4]. Therefore, we can translate local site characteristics to adsorption energies (e.g., as provided by density functional theory computations [5,6]) and to activation energies. Using these demonstrated relationships, we can predict reaction rates of metal surface sites and, thus, be in position to rigorously design periodic surface patterns that maximize the total reactivity on a per area basis.

In this work, we show how correlations that link performance (e.g., catalytic activity) to site descriptors, such as commonly available volcano plots, can be used to determine the optimal (i.e., of highest performance) periodic surfaces of transition metal crystals via a mathematical optimization model. As an illustration, we will use the average neighbor coordination number, chosen both due to its recent and emerging appearance in the literature [6,7] as well as due to its interest from the mathematical modeling viewpoint. We should, however, emphasize that our model can be readily adapted to handle a variety of other site descriptors as well.

Using our optimization model, we conducted extensive computational studies involving an array of crystallographic lattices and structure-function relationships. More specifically, we considered three face-centered cubic (FCC) lattices oriented such that the design surface is aligned with the {1,0,0}, {1,1,0} and {1,1,1} crystallographic planes, respectively, one body-centered cubic (BCC) lattice aligned with the {1,0,0} plane, and one hexagonal close-packed (HCP) lattice aligned with the {0,0,0,1} plane. These design lattices were combined with a set of volcano plots spanning a range of ideal site descriptors in order to identify optimal surface patterns relating to a gamut of catalytic systems.

Our proposed approach validates certain surface patterns that were previously known to be optimal but also reveals a number of non-intuitive designs. We also demonstrate that the optimal surface patterns vary significantly with the target application, which strengthens the need to keep developing those fabrication capabilities that can yield higher levels of structural control.

[1] Stamenkovic V., Mun B. S., Mayrhofer K. J. J., Ross P. N., Markovic N. M., Rossmeisl J., Greeley J., Nørskov J. K., “Changing the activity of electrocatalysts for oxygen reduction by tuning the surface electronic structure,” *Angewandte Chemie - International Edition*, 45(18):2897–2901, 2006.

[2] Nørskov J. K., Bligaard T., Rossmeisl J., Christensen C. H., “Towards the computational design of solid catalysts,” *Nature Chemistry*, 1(1):37–46, 2009.

[3] Hammer B., Norskov J. K., “Theoretical Surface Science and Catalysis — Calculations and Concepts,” *Advances in Catalysis*, 45:71–129, 2000.

[4] Nørskov J. K., Bligaard T., Logadottir A., Bahn S., Hansen L. B., Bollinger M., Bengaard H., Hammer B., Sljivancanin Z., Mavrikakis M., Xu Y., Dahl S., Jacobsen C. J. H., “Universality in Heterogeneous Catalysis,” *Journal of Catalysis*, 209(2):275–278, 2002.

[5] Taylor M. G., Austin N., Gounaris C. E., Mpourmpakis G., “Catalyst Design Based on Morphology- and Environment-Dependent Adsorption on Metal Nanoparticles,” *ACS Catalysis*, 5(11):6296–6301, 2015.

[6] Calle-Vallejo F., Loffreda D., Koper M. T. M., Sautet P., “Introducing structural sensitivity into adsorption-energy scaling relations by means of coordination numbers,” *Nature Chemistry*, 7(5):403–410, 2015.

[7] Calle-Vallejo F., Martínez J. I., García-Lastra J. M., Sautet P., Loffreda D., “Fast prediction of adsorption properties for platinum nanocatalysts with generalized coordination numbers,” *Angewandte Chemie - International Edition*, 53(32):8316–8319, 2014.

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