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Counting Active Sites for Nanocatalysis.

Forrest H Kaatz1, Adhemar Bultheel2, Dmitry Yu Murzin3

  • 1Institutional Research, NMSU-Alamogordo, Alamogordo, NM, USA.

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|March 24, 2026
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Summary

This study introduces a novel method using mathematical formulas to count active sites on nanocatalysts, improving predictions of catalytic activity for reactions like the oxidation-reduction reaction (ORR). The findings offer insights into designing more efficient platinum nanostructures.

Keywords:
core‐shell ternary clustersgeneralized coordinationmagic formulasmass activitynanocagesplatinumruthenium

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Area of Science:

  • Materials Science
  • Chemical Engineering
  • Computational Chemistry

Background:

  • Identifying and quantifying active sites on catalysts is crucial for enhancing chemical behavior.
  • Catalytic activity is linked to active sites through generalized coordination numbers (GCNs).

Purpose of the Study:

  • To present a general method for counting active sites on nanocatalysts using mathematical formulas.
  • To model and predict the mass activity of platinum nanostructures for the oxidation-reduction reaction (ORR).

Main Methods:

  • Utilized "magical formulas" based on mathematical properties of face-centered cubic (fcc) nanostructures to calculate GCNs.
  • Modeled various platinum nanostructures including polyhedral clusters, nanocages, and strained heteroepitaxial clusters.
  • Geometric descriptors quantified morphology, size, and layer number to predict mass activity.

Main Results:

  • Predicted a mass activity of ~3 A/mg_Pt for 20 nm octahedral cages with 3 wall layers, a twofold improvement over 6-layer cages.
  • Modeled ternary clusters with monolayer platinum shells, predicting a maximum mass activity of ~1.8 A/mg_Pt for sub-10 nm tetrahedral core-shell clusters with a copper interlayer.
  • Demonstrated the method's general applicability by suggesting its use for ruthenium catalysts in the nitrogen reduction reaction (NRR).

Conclusions:

  • The developed "magical formulas" provide a scalable and element-agnostic approach to quantify active sites and predict nanocatalyst performance.
  • The study highlights the potential for optimizing nanocatalyst design through precise control of morphology, size, and composition for improved catalytic efficiency.