Unravelling Morphological and Topological Energy Contributions of Metal Nanoparticles

Metal nanoparticles (NPs) are ubiquitous in many fields, from nanotechnology to heterogeneous catalysis, with properties differing from those of single-crystal surfaces and bulks. A key aspect is the size-dependent evolution of NP properties toward the bulk limit, including the adoption of different NP shapes, which may bias the NP stability based on the NP size. Herein, the stability of different Pd-n NPs (n = 10-1504 atoms) considering a myriad of shapes is investigated by first-principles energy optimisation, leading to the determination that icosahedron shapes are the most stable up to a size of ca. 4 nm. In NPs larger than that size, truncated octahedron shapes become more stable, yet a presence of larger {001} facets than the Wulff construction is forecasted due to their increased stability, compared with (001) single-crystal surfaces, and the lower stability of {111} facets, compared with (111) single-crystal surfaces. The NP cohesive energy breakdown in terms of coordination numbers is found to be an excellent quantitative tool of the stability assessment, with mean absolute errors of solely 0.01 eV center dot atom(-1), while a geometry breakdown allows only for a qualitative stability screening.

Automated summary

This study investigates the stability of different Pd-n nanoparticles (NPs) with different sizes and shapes by first-principles energy optimization. The results show that icosahedron shapes are the most stable up to a size of approximately 4 nm. For NPs larger than that size, truncated octahedron shapes become more stable, and there is a presence of larger {001} facets than predicted by the Wulff construction. The breakdown of NP cohesive energy in terms of coordination numbers proves to be an excellent quantitative tool for stability assessment.