Abstract
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 Pdn 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·atom−1, while a geometry breakdown allows only for a qualitative stability screening.
Highlights
Over the last few decades, nanomaterials have become ubiquitous in various industrial and/or technological applications, including, e.g., energy storage [1], antimicrobial agents [2], selective release of drugs [3], heterogeneous catalysts [4], etc
We move forward to exploit high-performance parallel supercomputing facilities combined with a highly parallelised computational code using numeric atom-centred orbitals (NAOs) to push the limit of metal NPs description, allowing for a full shape analysis as a matter of size and permitting breakdown of the NPs energies either in terms of atomic contributions related to their coordination number (CN) or as NP geometric factors; both analyses allow predicting the energy of any NP independently of its size or shape
Exceeding the just mentioned basic adjustment, the mean test errors of the gained equation show an excellent agreement to the created model, with a regression coefficient of R2 = 0.995, and, an excellent associated mean absolute error (MAE) of solely 0.011 eV/atom
Summary
Over the last few decades, nanomaterials have become ubiquitous in various industrial and/or technological applications, including, e.g., energy storage [1], antimicrobial agents [2], selective release of drugs [3], heterogeneous catalysts [4], etc. We move forward to exploit high-performance parallel supercomputing facilities combined with a highly parallelised computational code using numeric atom-centred orbitals (NAOs) to push the limit of metal NPs description, allowing for a full shape analysis as a matter of size and permitting breakdown of the NPs energies either in terms of atomic contributions related to their coordination number (CN) or as NP geometric factors; both analyses allow predicting the energy of any NP independently of its size or shape To this end, Pd NPs, a common playground of previous analyses [30,31] are inspected, and a nanomaterial of catalytic interest, e.g., nanoengineered Pd NPs, are used in nitrite reduction [36], or as catalysts for Suzuki cross-coupling reactions [37]
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