published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User

No abstract

Heterogeneous single-atom catalysts involve isolated metal atoms anchored to a support, displaying high catalytic performance and stability in many important chemical reactions. We present a general theoretical framework to establish the thermodynamic stability of metal single atoms and metal nanoparticles on a support in the presence of adsorbates. As a case study, we establish for Pt−CeO 2 the CO partial pressure and temperature range within which Pt single atoms are more stable than Pt nanoparticles. Density functional theory and kinetic Monte Carlo simulations demonstrate that Pt atoms doped into the CeO 2 surface exhibit a very high CO oxidation activity and thermodynamic stability in comparison to models involving Pt single atoms on terraces and steps of CeO 2 . An intermediate CO adsorption strength is important to explain a high activity. Our work provides a systematic strategy to evaluate the stability and reactivity of single atoms on a support.

Heterogeneous single-atom catalysts (SACs) hold the promise of combining high catalytic performance with maximum utilization of often precious metals. We extend the current thermodynamic view of SAC stability in terms of the binding energy (Ebind) of single-metal atoms on a support to a kinetic (transport) one by considering the activation barrier for metal atom diffusion. A rapid computational screening approach allows predicting diffusion barriers for metal–support pairs based on Ebind of a metal atom to the support and the cohesive energy of the bulk metal (Ec). Metal–support combinations relevant to contemporary catalysis are explored by density functional theory. Assisted by machine-learning methods, we find that the diffusion activation barrier correlates with (Ebind)2/Ec in the physical descriptor space. This diffusion scaling-law provides a simple model for screening thermodynamics to kinetics of metal adatom on a support.

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low-energy structures of Pd n (n = 1−21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pd n clusters of any structure. Low-energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters, and large cluster isomers share similarities in both shape and energy. The findings elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure−energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.