Bridging the size gap between experiment and theory: large-scale DFT calculations on realistic sized Pd particles for...

Metal nanoparticles, often supported on metal oxide promoters, are a cornerstone of heterogeneous catalysis. Experimentally, size effects are well-established and are manifested through changes to catalyst selectivity, activity and durability. Density Functional Theory (DFT) calculations have provided an attractive way to study these effects and rationalise the change in nanoparticle properties. However such computational studies are typically limited to smaller nanoparticles (approximately up to 50 atoms) due to the large computational cost of DFT. How well can such simulations describe the electronic properties of the much larger nanoparticles that are often used in practice? In this study, we use the ONETEP code, which is able to achieve more favourable computational scaling for metallic nanoparticles, to bridge this size gap. We present DFT calculations on entire Pd and Pd carbide nanoparticles of more than 300 atoms (approximately 2.5 nm diameter), and find major differences in the electronic structure of such large nanoparticles, in comparison to the commonly investigated smaller clusters. These differences are also manifested in the calculated chemical properties such as adsorption energies for C₂H₂, C₂H₄ and C₂H₆ on the pristine Pd and PdC nanoparticles which are significantly larger (up to twice in value) for the ∼300 atoms structures. Furthermore, the adsorption of C₂H₂ and C₂H₄ on PdC nanoparticles becomes weaker as more C is introduced in the Pd lattice whilst the impact of C concentration is also observed in the calculated reaction energies towards the hydrogenation of C₂H₂, where the formation of C₂H₆ is hindered. Our simulations show that PdC nanoparticles of about 5% C per atom fraction and diameter of 2.5 nm could be potential candidate catalysts of high activity in hydrogenation reactions. The paradigm presented in this study will enable DFT to be applied on similar sized metal catalyst nanoparticles as in experimental investigations, strengthening the synergy between simulation and experiment in catalysis.